Published Papers
Browse foundational peer-reviewed research authored by engineers and technical advisors associated with Gaussian Wellworks. These articles serve as supporting technical references and provide deeper insight into the scientific foundations of our work.
Probabilistic CO2 Storage Capacity Appraisal of the Greensand Project in the Depleted Nini Oil Field, Offshore Denmark
The Greensand Geological Carbon Storage (GCS) project aims to repurpose multiple depleted oil fields in the North Sea Basin for carbon sequestration, storing up to 8 megatonnes (Mt) of CO2 per year by 2030. It is anticipated that 0.45 mtpa will be stored in the Nini West oil field, offshore Denmark, between 2026 and 2040. This study provides an independent probabilistic appraisal of the storage capacity feasibility of Project Greensand, utilizing publicly available data and following the SPE Storage Resources Management System (SRMS) framework. Arps Decline Curve Analysis (DCA) demonstrated an excellent fit to the historical production rates, with a cumulative error of 0.41 %, confirming its effectiveness. History matching using the Gaussian Pressure Transient (GPT) equation, supported by Sequential Quadratic Programming (SQP) optimization and sensitivity analysis of reservoir parameters, resulted in a highly accurate fit with an error of just 0.0068 %. Having thus constrained reservoir parameters, the Estimated Ultimate Storage (EUS) capacity appears to surpass the 10-year storage target of 4.5, with a deterministic EUS of 8.38 (average 2,296 t/day). The EUS, using SRMS terminology, accounts for just ∼4.71 % of the Total Storage Resource (TSR), indicating vast additional potential for future storage. Subsequent probabilistic analysis reveals that the deterministic estimate closely aligns with the P50 estimate of 7.73 Mt, whereas the P90 estimate of 3.25 is slightly lower than the planned target of 4.5 Mt. Flow scaling ratio investigation shows that lateral flow will dominate during the early injection stages and in wellbore proximity, whereas buoyancy will become increasingly prevalent after three years of injection. Given that public funding supports Project Greensand, full transparency in the reporting of storage capacity and sharing of relevant data are advocated here. The Greensand Geological Carbon Storage (GCS) project aims to repurpose multiple depleted oil fields in the North Sea Basin for carbon sequestration, storing up to 8 megatonnes (Mt) of CO2 per year by 2030. It is anticipated that 0.45 mtpa will be stored in the Nini West oil field, offshore Denmark, between 2026 and 2040. This study provides an independent probabilistic appraisal of the storage capacity feasibility of Project Greensand, utilizing publicly available data and following the SPE Storage Resources Management System (SRMS) framework. Arps Decline Curve Analysis (DCA) demonstrated an excellent fit to the historical production rates, with a cumulative error of 0.41 %, confirming its effectiveness. History matching using the Gaussian Pressure Transient (GPT) equation, supported by Sequential Quadratic Programming (SQP) optimization and sensitivity analysis of reservoir parameters, resulted in a highly accurate fit with an error of just 0.0068 %. Having thus constrained reservoir parameters, the Estimated Ultimate Storage (EUS) capacity appears to surpass the 10-year storage target of 4.5, with a deterministic EUS of 8.38 (average 2,296 t/day). The EUS, using SRMS terminology, accounts for just ∼4.71 % of the Total Storage Resource (TSR), indicating vast additional potential for future storage. Subsequent probabilistic analysis reveals that the deterministic estimate closely aligns with the P50 estimate of 7.73 Mt, whereas the P90 estimate of 3.25 is slightly lower than the planned target of 4.5 Mt. Flow scaling ratio investigation shows that lateral flow will dominate during the early injection stages and in wellbore proximity, whereas buoyancy will become increasingly prevalent after three years of injection. Given that public funding supports Project Greensand, full transparency in the reporting of storage capacity and sharing of relevant data are advocated here.
View full paperUltra-fast reservoir characterization and well-performance evaluation enabled by digital permeability twins
Industry practice for forecasting production rates of oil and gas wells is traditionally split between complex, physics-based simulators and empirical decline-curve analysis (DCA). Recently developed digital permeability twins coupled with closed-form Gaussian production models bridge the gap by offering a fast, physics-based alternative that avoids the over-parameterisation of numerical simulators while staying clear of the oversimplifications typical for purely empirical DCA approaches. Onshore and offshore case studies show that robust, production forecasts, well-design optimisation, and SPE compliant reserves classification can be achieved prior to drilling or history-matching limited production data (as little as one month). Applicable across diverse well and reservoir systems, fast decision-making is enabled through probabilistic well-performance forecasting, real-time and pre-drilling, while accurately representing the uncertainty in available data. Gaussian well-performance and resource evaluation thus provides a powerful new option for production analysis and reserves estimation under uncertainty, supporting optimisation efforts and enabling faster field-development decision-making without comprising accuracy. Industry practice for forecasting production rates of oil and gas wells is traditionally split between complex, physics-based simulators and empirical decline-curve analysis (DCA). Recently developed digital permeability twins coupled with closed-form Gaussian production models bridge the gap by offering a fast, physics-based alternative that avoids the over-parameterisation of numerical simulators while staying clear of the oversimplifications typical for purely empirical DCA approaches. Onshore and offshore case studies show that robust, production forecasts, well-design optimisation, and SPE compliant reserves classification can be achieved prior to drilling or history-matching limited production data (as little as one month). Applicable across diverse well and reservoir systems, fast decision-making is enabled through probabilistic well-performance forecasting, real-time and pre-drilling, while accurately representing the uncertainty in available data. Gaussian well-performance and resource evaluation thus provides a powerful new option for production analysis and reserves estimation under uncertainty, supporting optimisation efforts and enabling faster field-development decision-making without comprising accuracy.
View full paperComputation of pressure depletion and productivity of multi-fractured wells with variable fracture spacing using fast and accurate solution method
This study presents a fast method that can model the pressure depletion around hydraulically fractured wells accurately. The Gaussian Pressure-Transient (GPT) method has infinite resolution, because no discrete-grid computations are required − the method solves the pressure field using closed-form solutions. After extensive testing on field cases and calibration against other (independent) solution-methods, it appeared that the pressure interference of multiple fractures represented by pressure transients − in the early phases of pressure advance − behaves according to the traditional superposition-method. However, when pressure interference advances, the traditional superposition method gives increasingly unrealistic and inaccurate results. Therefore, the traditional superposition method typically used for steady-state, needs adjustment when applied to transient systems, modeled here with Gaussian pressure-diffusion probability-density functions. The new solutions are valid for the advance of pressure changes both in the early and late stages of the well-life. A second new insight presented here is that the superposition of multiple fractures using Gaussian solutions (together with pressure-gradient computations and application of Darcy’s) can accurately forecast the future production rate and cumulative production of the well over the economic well-life, accounting for the impact of fracture-spacing changes. The new method is validated by history-matching of our Gaussian forecasts using real well-data to constrain specific reservoir properties (hydraulic diffusivity) and completion parameters (fracture half-lengths), and then was benchmarked against independent simulations with CMG-IMEX. This study presents a fast method that can model the pressure depletion around hydraulically fractured wells accurately. The Gaussian Pressure-Transient (GPT) method has infinite resolution, because no discrete-grid computations are required − the method solves the pressure field using closed-form solutions. After extensive testing on field cases and calibration against other (independent) solution-methods, it appeared that the pressure interference of multiple fractures represented by pressure transients − in the early phases of pressure advance − behaves according to the traditional superposition-method. However, when pressure interference advances, the traditional superposition method gives increasingly unrealistic and inaccurate results. Therefore, the traditional superposition method typically used for steady-state, needs adjustment when applied to transient systems, modeled here with Gaussian pressure-diffusion probability-density functions. The new solutions are valid for the advance of pressure changes both in the early and late stages of the well-life. A second new insight presented here is that the superposition of multiple fractures using Gaussian solutions (together with pressure-gradient computations and application of Darcy’s) can accurately forecast the future production rate and cumulative production of the well over the economic well-life, accounting for the impact of fracture-spacing changes. The new method is validated by history-matching of our Gaussian forecasts using real well-data to constrain specific reservoir properties (hydraulic diffusivity) and completion parameters (fracture half-lengths), and then was benchmarked against independent simulations with CMG-IMEX.
View full paperElastic Stiffening of Reservoir Rocks with Rising Pore Pressures under Constant Biaxial Far-Field Stress: Application to the Porthos Geological Carbon-Dioxide Sequestration Project
This study systematically quantifies elastic stiffening in fluid-saturated porous media, distinguishing the critical influence of biaxial far-field stress from simplified uniaxial conditions. The Linear Superposition Method (LSM) of elastic displacements is used to quantify solutions of the detailed stress state within a pressure-saturated poro-elastic framework, consisting of regularly arranged cylindrical pores under uniaxial and bi-axial loads. The model examines the impact on the effective bulk modulus of changes in internal pressure, while varying the relative magnitude of the horizontal and vertical stresses ( $$sigma_{yy}$$ = $$lambda sigma_{xx}$$ ). A sensitivity analysis reveals that lateral confinement under biaxial loading significantly accelerates the stiffening process. Specifically, the effective bulk modulus reaches a porosity-independent state when the internal pore pressure balances the far-field confining stress, a condition reached at a significantly lower pressure-to-stress ratio than observed under uniaxial loading. To demonstrate practical implications, the model is applied to the Porthos Geological Carbon Sequestration (GCS) project in a depleted offshore gas field (Netherlands). The results indicate that injection-induced pore pressure increases lead to a non-linear increase in the reservoir’s bulk modulus, which in turn increases hydraulic diffusivity. This suggests that depleted gas reservoirs may accommodate slightly higher injection rates than predicted if the faster pressure dissipation associated with elastic stiffening is neglected. This study systematically quantifies elastic stiffening in fluid-saturated porous media, distinguishing the critical influence of biaxial far-field stress from simplified uniaxial conditions. The Linear Superposition Method (LSM) of elastic displacements is used to quantify solutions of the detailed stress state within a pressure-saturated poro-elastic framework, consisting of regularly arranged cylindrical pores under uniaxial and bi-axial loads. The model examines the impact on the effective bulk modulus of changes in internal pressure, while varying the relative magnitude of the horizontal and vertical stresses ( $$sigma_{yy}$$ = $$lambda sigma_{xx}$$ ). A sensitivity analysis reveals that lateral confinement under biaxial loading significantly accelerates the stiffening process. Specifically, the effective bulk modulus reaches a porosity-independent state when the internal pore pressure balances the far-field confining stress, a condition reached at a significantly lower pressure-to-stress ratio than observed under uniaxial loading. To demonstrate practical implications, the model is applied to the Porthos Geological Carbon Sequestration (GCS) project in a depleted offshore gas field (Netherlands). The results indicate that injection-induced pore pressure increases lead to a non-linear increase in the reservoir’s bulk modulus, which in turn increases hydraulic diffusivity. This suggests that depleted gas reservoirs may accommodate slightly higher injection rates than predicted if the faster pressure dissipation associated with elastic stiffening is neglected.
View full paperA probabilistic appraisal of Project Greensand: Economic viability of offshore geological CO₂ storage under uncertainty.
This study presents an economic appraisal of Project Greensand in the Danish North Sea, a leading offshore CO₂ storage initiative that conducted injection pilot tests in 2023 and is slated for further development. Deterministic results indicate that, at concurrent CO₂ prices in the EU Emissions Trading System (ETS) of approximately $75.6/t, Greensand will be unprofitable, with a negative cumulative cash flow of about $6 million over its 10-year injection period. However, when considering certain price guarantees, the effective CO₂ price rises to ∼$113/t, which significantly increases the internal rate of return (IRR) to ∼21.8% , thereby surpassing the 15% hurdle rate for minimum return on investment. A subsequent probabilistic cash flow analysis revealed a pronounced downside risk profile, with a median IRR of 12.9%. Only under favorable assumptions of uncertain input parameters will the IRR exceed 15%. Our findings establish reference conditions for the price boundaries required to make offshore geological carbon storage (GCS) projects like Greensand bankable. Further sensitivity analyses of outcomes to variability in input parameters confirm that well and platform operating expenditure, shipping capital expenditure, and all-in revenue are the dominant value drivers. Likewise, the methodology employed in this study emphasizes the importance of probabilistic appraisal to adequately capture risk and uncertainty when developing and implementing effective policy support mechanisms for the early deployment of offshore GCS projects. This study presents an economic appraisal of Project Greensand in the Danish North Sea, a leading offshore CO₂ storage initiative that conducted injection pilot tests in 2023 and is slated for further development. Deterministic results indicate that, at concurrent CO₂ prices in the EU Emissions Trading System (ETS) of approximately $75.6/t, Greensand will be unprofitable, with a negative cumulative cash flow of about $6 million over its 10-year injection period. However, when considering certain price guarantees, the effective CO₂ price rises to ∼$113/t, which significantly increases the internal rate of return (IRR) to ∼21.8% , thereby surpassing the 15% hurdle rate for minimum return on investment. A subsequent probabilistic cash flow analysis revealed a pronounced downside risk profile, with a median IRR of 12.9%. Only under favorable assumptions of uncertain input parameters will the IRR exceed 15%. Our findings establish reference conditions for the price boundaries required to make offshore geological carbon storage (GCS) projects like Greensand bankable. Further sensitivity analyses of outcomes to variability in input parameters confirm that well and platform operating expenditure, shipping capital expenditure, and all-in revenue are the dominant value drivers. Likewise, the methodology employed in this study emphasizes the importance of probabilistic appraisal to adequately capture risk and uncertainty when developing and implementing effective policy support mechanisms for the early deployment of offshore GCS projects.
View full paperProduction Optimization in Shale Formations: Focus on Proppant Delivery Schedules and Mitigation of Fracture Conductivity Damage
This study presents recent advances in modeling capacity and provides optimization guidelines for key operational parameters controlling well performance, using real well data. A new Gaussian solution method can both accurately forecast well rates prior to drilling and history match actual well performance after completion once early production data become available. Unlike other history-matching tools, excellent matches are achieved with daily production data spanning just a few months. The study also addresses key challenges in achieving precision in hydraulic fracturing and horizontal well design, emphasizing unresolved subsurface heterogeneity, variability in treatment quality, and modeling tool limitations. Advanced analytical methods, such as the Gaussian Production Forecasting (GPT) method, offer improved accuracy and computational efficiency for production predictions. Empirical data from the Eagle Ford and Wolfcamp formations demonstrate significant performance gains over the past decade, driven by optimized fracture spacing, increased lateral lengths, and enhanced proppant usage. However, performance gaps persist due to poor proppant conductivity, closure stress impacts, and proppant transport inefficiencies. This study highlights the critical impact of fracture conductivity damage on shale well performance, as revealed by Gaussian well performance curves derived from historical data. The findings emphasize the need for integrating advanced modeling tools, optimizing proppant delivery strategies, and improving transport simulations to achieve sustained productivity gains in shale reservoirs. This study presents recent advances in modeling capacity and provides optimization guidelines for key operational parameters controlling well performance, using real well data. A new Gaussian solution method can both accurately forecast well rates prior to drilling and history match actual well performance after completion once early production data become available. Unlike other history-matching tools, excellent matches are achieved with daily production data spanning just a few months. The study also addresses key challenges in achieving precision in hydraulic fracturing and horizontal well design, emphasizing unresolved subsurface heterogeneity, variability in treatment quality, and modeling tool limitations. Advanced analytical methods, such as the Gaussian Production Forecasting (GPT) method, offer improved accuracy and computational efficiency for production predictions. Empirical data from the Eagle Ford and Wolfcamp formations demonstrate significant performance gains over the past decade, driven by optimized fracture spacing, increased lateral lengths, and enhanced proppant usage. However, performance gaps persist due to poor proppant conductivity, closure stress impacts, and proppant transport inefficiencies. This study highlights the critical impact of fracture conductivity damage on shale well performance, as revealed by Gaussian well performance curves derived from historical data. The findings emphasize the need for integrating advanced modeling tools, optimizing proppant delivery strategies, and improving transport simulations to achieve sustained productivity gains in shale reservoirs.
View full paperEstimation of Storage Capacity Coefficients: Porthos GCS Project Case Study
Concurrent approaches for estimating storage coefficients (E) of Geological Carbon Sequestration (GCS) target reservoirs are critically reviewed, and a robust procedure for estimation of such coefficients, which are time-dependent, is proposed. Our method is based on close analogy of what historically is done in hydrocarbon production and reserves estimations using recovery factors (F). Typically, F is computed by first estimating the original hydrocarbons in place (OHIP), then the cumulative production to a certain date (of the economic limit) is computed using production forecasting methods. The production forecast provides an estimated ultimate resource (EUR), and then F follows from the ratio EUR/OHIP. We propose to similarly compute the estimated ultimate storage (EUS) or cumulative injection by forward modeling, using Gaussian-based solutions of the pressure diffusivity equation, and after estimating the total storage resource (TSR), the coefficient E follows from the ratio EUS/TSR. The new method is demonstrated in a case study using representative data from the Porthos GCS Project, which repurposes the depleted P18 gas field (offshore, Dutch shelf area) for geological CO2 sequestration (GCS). The storage coefficient for the P18-6 segment of the Porthos GCS field after 20 years of injection reaches 18 %. In addition to the deterministic storage coefficient estimation, probabilistic values after 20 years of injection for E were estimated: P90-16 %, P50-36 % and P10-59 %. Separately, it is shown how a GCS project in a depleted gas field offers significant operational advantages over storage in saline aquifers. The competitive edge of depleted gas fields over saline aquifers has not been articulated before. The new methods for computing TSR, EUS and E, can handle probabilistic storage resource classification in compliance with the SPE SRMS classification framework for storage resource estimation. Concurrent approaches for estimating storage coefficients (E) of Geological Carbon Sequestration (GCS) target reservoirs are critically reviewed, and a robust procedure for estimation of such coefficients, which are time-dependent, is proposed. Our method is based on close analogy of what historically is done in hydrocarbon production and reserves estimations using recovery factors (F). Typically, F is computed by first estimating the original hydrocarbons in place (OHIP), then the cumulative production to a certain date (of the economic limit) is computed using production forecasting methods. The production forecast provides an estimated ultimate resource (EUR), and then F follows from the ratio EUR/OHIP. We propose to similarly compute the estimated ultimate storage (EUS) or cumulative injection by forward modeling, using Gaussian-based solutions of the pressure diffusivity equation, and after estimating the total storage resource (TSR), the coefficient E follows from the ratio EUS/TSR. The new method is demonstrated in a case study using representative data from the Porthos GCS Project, which repurposes the depleted P18 gas field (offshore, Dutch shelf area) for geological CO2 sequestration (GCS). The storage coefficient for the P18-6 segment of the Porthos GCS field after 20 years of injection reaches 18 %. In addition to the deterministic storage coefficient estimation, probabilistic values after 20 years of injection for E were estimated: P90-16 %, P50-36 % and P10-59 %. Separately, it is shown how a GCS project in a depleted gas field offers significant operational advantages over storage in saline aquifers. The competitive edge of depleted gas fields over saline aquifers has not been articulated before. The new methods for computing TSR, EUS and E, can handle probabilistic storage resource classification in compliance with the SPE SRMS classification framework for storage resource estimation.
View full paperBenchmarking physics-based GPT and empirical Arps DCA for EUR and CO2 storage capacity assessment of depleted gas reservoirs
Accurate well performance forecasting is crucial for optimizing hydrocarbon recovery and also for repurposing depleted reservoirs for CO2 storage. This study compares the physics-based Gaussian Pressure Transient (GPT) method with the empirical Arps Decline Curve Analysis (DCA) method for history matching and predicting production/injection behavior of legacy gas wells in the UK North Sea. Using bootstrapping of historical production-rate data from the Kelvin, Mimas, and Tethys Fields, we evaluate each method’s effectiveness in capturing reservoir performance over the full well-life. Our findings show that both methods can accurately history-match historical production data. However, GPT outperforms the Arps method in predicting production from bootstrapped, short-term production data, demonstrating better resilience to noisy data and more accurate estimation of the ultimate recovery (EUR). Subsequently, CO2 injectivity and storage capacity were evaluated for abandoned wells in lease Blocks 43 and 48. The Kelvin Field well (Block 43) showed the highest injectivity at 10.96 Mscf/day/psi, more than three times that of the Mimas and Tethys wells (2.04–3.00 Mscf/day/psi) in Block 48. The three wells collectively offer a storage capacity of 16.91 Bscf (∼1 Mt) over a certain injection-period duration. Wells in Block 48, have potential for continued CO2 injection, suggesting opportunities for long-term storage optimization. Accurate well performance forecasting is crucial for optimizing hydrocarbon recovery and also for repurposing depleted reservoirs for CO2 storage. This study compares the physics-based Gaussian Pressure Transient (GPT) method with the empirical Arps Decline Curve Analysis (DCA) method for history matching and predicting production/injection behavior of legacy gas wells in the UK North Sea. Using bootstrapping of historical production-rate data from the Kelvin, Mimas, and Tethys Fields, we evaluate each method’s effectiveness in capturing reservoir performance over the full well-life. Our findings show that both methods can accurately history-match historical production data. However, GPT outperforms the Arps method in predicting production from bootstrapped, short-term production data, demonstrating better resilience to noisy data and more accurate estimation of the ultimate recovery (EUR). Subsequently, CO2 injectivity and storage capacity were evaluated for abandoned wells in lease Blocks 43 and 48. The Kelvin Field well (Block 43) showed the highest injectivity at 10.96 Mscf/day/psi, more than three times that of the Mimas and Tethys wells (2.04–3.00 Mscf/day/psi) in Block 48. The three wells collectively offer a storage capacity of 16.91 Bscf (∼1 Mt) over a certain injection-period duration. Wells in Block 48, have potential for continued CO2 injection, suggesting opportunities for long-term storage optimization.
View full paperStiffening of Bulk Modulus in Poroelastic Medium with Rising Pore Pressure: A Comprehensive Sensitivity Study using a Closed-Form Solution Method
This study presents high-resolution stress models of synthetic porous media consisting of regularly arranged cylindrical pores, with and without internal pressure. The stress distribution within the elastic solid matrix surrounding fluid-filled pores under uniaxial compressive stress is analyzed for: (1) drained conditions (negligible pore pressure) and (2) undrained conditions (with various pore pressures). A Linear Superposition Method (LSM) is applied to quantify elastic displacements and solve for the stress tensor field throughout the porous medium. Resolving for the pore-scale stresses in a poroelastic medium is relevant for diverse engineering disciplines. Oversimplified assumptions about the geometry and stress distribution can result in inaccurate predictions of mechanical behavior under different loading conditions. The study systematically investigates the effects of internal pressure, pore size, and porosity on the effective bulk modulus. Results reveal a non-linear, pressure-dependent relationship between bulk modulus and porosity. Notably, we identify a critical pressure state (PCRIT) where the bulk modulus becomes nearly independent of porosity. Beyond this point, a counterintuitive phenomenon of pressure-induced stiffening emerges under high pore pressure. Analysis of stress-strain distributions elucidates the mechanisms underlying this behavior. The new approach in this study for estimating macroscopic properties from microstructural parameters is highly applicable in designing durable engineering structures, optimizing geothermal and petroleum reservoir practices, and enhancing underground storage operations. This study presents high-resolution stress models of synthetic porous media consisting of regularly arranged cylindrical pores, with and without internal pressure. The stress distribution within the elastic solid matrix surrounding fluid-filled pores under uniaxial compressive stress is analyzed for: (1) drained conditions (negligible pore pressure) and (2) undrained conditions (with various pore pressures). A Linear Superposition Method (LSM) is applied to quantify elastic displacements and solve for the stress tensor field throughout the porous medium. Resolving for the pore-scale stresses in a poroelastic medium is relevant for diverse engineering disciplines. Oversimplified assumptions about the geometry and stress distribution can result in inaccurate predictions of mechanical behavior under different loading conditions. The study systematically investigates the effects of internal pressure, pore size, and porosity on the effective bulk modulus. Results reveal a non-linear, pressure-dependent relationship between bulk modulus and porosity. Notably, we identify a critical pressure state (PCRIT) where the bulk modulus becomes nearly independent of porosity. Beyond this point, a counterintuitive phenomenon of pressure-induced stiffening emerges under high pore pressure. Analysis of stress-strain distributions elucidates the mechanisms underlying this behavior. The new approach in this study for estimating macroscopic properties from microstructural parameters is highly applicable in designing durable engineering structures, optimizing geothermal and petroleum reservoir practices, and enhancing underground storage operations.
View full paperEvaluating Poro-Elastic Production Drive Mechanisms: Quantifying the Potential Contribution to Well-Rates and Risk of Core Handling Damage Inflating Pore-Volume Compressibility Measurements
By analyzing core data from an offshore Gulf of Mexico reservoir and developing analytical solutions, it can be demonstrated that laboratory measurements on pore-volume compressibility include artifacts, leading to a misinterpretation of porosity and permeability trends. A systematic evaluation of poro-elastic changes in pore volumes (and quantifying any consequent fluid expulsion during reservoir compaction) suggests that poro-elastic relaxation may enhance fluid production rates from deep reservoirs by up to 25 %. This value may be inadvertently inflated if the core samples used for pore-volume compressibility measurements suffered from handling damage. Nonetheless, poro-elastic fluid expulsion from the pores in producing reservoirs can provide additional lift and thus may enhance the recovery factor. Therefore, the possible contribution to well performance from poro-elastic production drive mechanisms ought to be carefully evaluated in reserves estimation. Reversely, injection wells may encounter poro-elastic suppression of injectivity due to elastic resistance, which would adversely affect the storage coefficient. By integrating geomechanical reservoir response with traditional fluid production models, reservoir model predictions of production under pressure depletion and injection conditions will be more accurate. The new insights reported here are essential for optimizing well performance, improving reservoir management, and extending the economic life of geological reservoirs. However, caution is warranted regarding pore-volume compressibility measurements. To what degree laboratory measurements of pore-volume compressibility measure true values or mainly record handling damage could not be conclusively settled in the present study. By analyzing core data from an offshore Gulf of Mexico reservoir and developing analytical solutions, it can be demonstrated that laboratory measurements on pore-volume compressibility include artifacts, leading to a misinterpretation of porosity and permeability trends. A systematic evaluation of poro-elastic changes in pore volumes (and quantifying any consequent fluid expulsion during reservoir compaction) suggests that poro-elastic relaxation may enhance fluid production rates from deep reservoirs by up to 25 %. This value may be inadvertently inflated if the core samples used for pore-volume compressibility measurements suffered from handling damage. Nonetheless, poro-elastic fluid expulsion from the pores in producing reservoirs can provide additional lift and thus may enhance the recovery factor. Therefore, the possible contribution to well performance from poro-elastic production drive mechanisms ought to be carefully evaluated in reserves estimation. Reversely, injection wells may encounter poro-elastic suppression of injectivity due to elastic resistance, which would adversely affect the storage coefficient. By integrating geomechanical reservoir response with traditional fluid production models, reservoir model predictions of production under pressure depletion and injection conditions will be more accurate. The new insights reported here are essential for optimizing well performance, improving reservoir management, and extending the economic life of geological reservoirs. However, caution is warranted regarding pore-volume compressibility measurements. To what degree laboratory measurements of pore-volume compressibility measure true values or mainly record handling damage could not be conclusively settled in the present study.
View full paperBeyond Biot – Nonlinear stiffening of the bulk modulus in fluid-saturated porous media
This paper comprehensively investigates the elastic behavior of fluid-saturated porous media, considering a far-field stress, a range of pore pressures, and varying pore sizes. A Linear Superposition Method (LSM) was used to quantify the stress distribution and effective bulk moduli within a synthetic micropore model under both drained and undrained conditions. Our a posteriori upscaling approach reveals a significant nonlinear stiffening of the bulk modulus with increasing pore pressure—up to 25 % in high-pressure regimes—driven by pore size, porosity, and localized stress concentrations, a behavior unpredicted by conventional poroelasticity theories reliant on a priori upscaling. Unlike Biot’s framework, which assumes uniform stress and linear softening with porosity, we demonstrate distinct stiffening regimes where elevated pressures enhance stiffness at higher porosity levels, challenging traditional assumptions. This elastic stiffening, quantified through closed-form solutions, emphasizes poroelasticity as a nonlinear, pore-scale process rather than a macroscopic property. A practical method is proposed for a posteriori upscaling of micropore model results into an analytical expression, for direct use in reservoir engineering operations, where huge variations in pore pressure may occur over the project-life of the reservoir, such as geological carbon sequestration. These findings provide a robust, predictive framework for understanding and managing porous media in dynamic subsurface environments. This paper comprehensively investigates the elastic behavior of fluid-saturated porous media, considering a far-field stress, a range of pore pressures, and varying pore sizes. A Linear Superposition Method (LSM) was used to quantify the stress distribution and effective bulk moduli within a synthetic micropore model under both drained and undrained conditions. Our a posteriori upscaling approach reveals a significant nonlinear stiffening of the bulk modulus with increasing pore pressure—up to 25 % in high-pressure regimes—driven by pore size, porosity, and localized stress concentrations, a behavior unpredicted by conventional poroelasticity theories reliant on a priori upscaling. Unlike Biot’s framework, which assumes uniform stress and linear softening with porosity, we demonstrate distinct stiffening regimes where elevated pressures enhance stiffness at higher porosity levels, challenging traditional assumptions. This elastic stiffening, quantified through closed-form solutions, emphasizes poroelasticity as a nonlinear, pore-scale process rather than a macroscopic property. A practical method is proposed for a posteriori upscaling of micropore model results into an analytical expression, for direct use in reservoir engineering operations, where huge variations in pore pressure may occur over the project-life of the reservoir, such as geological carbon sequestration. These findings provide a robust, predictive framework for understanding and managing porous media in dynamic subsurface environments.
View full paperRapid Estimation of Fracture Half-Length and Fracture Propagation-Rate in Individual Hydraulic Fracturing Stages Using Post-Frac-Job Reports: Benchmark Results from Eagle Ford Case Study Well
This study presents a practical method for estimating the propagation-rate and half-length of hydraulic fractures created in the individual fracturing Stages, using operational data recorded in so-called post-frac reports. The fluid volumes and pressures used during the actual pumping of individual fracturing Stages are routinely recorded in post-frac reports. However, these data are rarely analyzed in detail, and mostly serve as work-completion reports, based on which the service company that executed the hydraulic fracturing treatment will invoice the well owner. The new method elaborated here uses the hydraulic pressures and pumped volumes of frac fluid, as detailed in the frac-job reports. The required post-frac report data (from the actual completion job) and historic production rates were kindly availed by the operator, for this comprehensive case study using Eagle Ford well data. Starting from the pressures recorded at the wellhead, all the subsequent pressure gains and losses are computed as fluid moves toward the evolving fractures. The fluid pump-rate at the wellhead is also used in mass-balance calculations, considering fluid losses (if any) due to leak-off. The fracture propagation-rate and associated incremental growth of the fracture half-length and fracture width are quantified for all of the 22 Stages in the study well. The fracture half-lengths vary between 110 and 240 ft; the average fracture half-length is 157 ft. A back-check for accuracy of the new method is applied by comparing the average fracture half-length for the well obtained by averaging the Stage-based solutions (based on frac-report data) with independent solutions (based on history-matching production data), which gave 144 ft fracture-half-length (revealing a limited mismatch of 9.5%). The difference can be largely attributed to fracture closure prior to the production from which data was used to estimate the 144 ft fracture half-length. Other major insights from our in-depth analysis are (1) fluid leak-off over the time of the fracturing in the shale well studied is negligibly small, and (2) pressure-loss occurring in the fracture slots cannot be accurately computed by a Cubic Law equation, for reasons first detailed in the present study. This study presents a practical method for estimating the propagation-rate and half-length of hydraulic fractures created in the individual fracturing Stages, using operational data recorded in so-called post-frac reports. The fluid volumes and pressures used during the actual pumping of individual fracturing Stages are routinely recorded in post-frac reports. However, these data are rarely analyzed in detail, and mostly serve as work-completion reports, based on which the service company that executed the hydraulic fracturing treatment will invoice the well owner. The new method elaborated here uses the hydraulic pressures and pumped volumes of frac fluid, as detailed in the frac-job reports. The required post-frac report data (from the actual completion job) and historic production rates were kindly availed by the operator, for this comprehensive case study using Eagle Ford well data. Starting from the pressures recorded at the wellhead, all the subsequent pressure gains and losses are computed as fluid moves toward the evolving fractures. The fluid pump-rate at the wellhead is also used in mass-balance calculations, considering fluid losses (if any) due to leak-off. The fracture propagation-rate and associated incremental growth of the fracture half-length and fracture width are quantified for all of the 22 Stages in the study well. The fracture half-lengths vary between 110 and 240 ft; the average fracture half-length is 157 ft. A back-check for accuracy of the new method is applied by comparing the average fracture half-length for the well obtained by averaging the Stage-based solutions (based on frac-report data) with independent solutions (based on history-matching production data), which gave 144 ft fracture-half-length (revealing a limited mismatch of 9.5%). The difference can be largely attributed to fracture closure prior to the production from which data was used to estimate the 144 ft fracture half-length. Other major insights from our in-depth analysis are (1) fluid leak-off over the time of the fracturing in the shale well studied is negligibly small, and (2) pressure-loss occurring in the fracture slots cannot be accurately computed by a Cubic Law equation, for reasons first detailed in the present study.
View full paperFast Analysis Method of Diagnostic Fracture Injection Test Data: Examples from Four Different Shale Formations (Bakken, Three Forks, Wolfcamp, and Eagle Ford)
This study introduces a new methodology for analyzing DFIT data by applying Gaussian Pressure Transient (GPT) solutions to model pressure fall-off behavior in hydraulically fractured wells. Diagnostic Fracture Injection Test (DFIT) data from 7 wells were analyzed; the wells were drilled in four different shale formations (Wolfcamp, Eagle Ford, Bakken, and Three Forks). All wells analyzed were hydraulically fractured, and as a first step in the fracturing treatment operation, each of the completion companies involved in the different wells applied a DFIT test to determine the ISIP and the formation leak-off rate to estimate the permeability. The original pressure fall-off excel sheets, availed by different operators, were analyzed in detail. For each test, the relevant part of the leak-off test data was identified and isolated for further in-depth study of the leak-off rate. Instead of relying on traditional DFIT interpretation techniques such as G-function or Carter leak-off assumptions, the method leverages the Gaussian diffusion model to capture the pressure propagation and leak-off characteristics more accurately. The Gaussian pressure transient analysis combines pressure and volume balancing principles directly on the actual field measurements. The results show that the Gaussian method successfully matched the pressure fall-off curves for all 7 wells, with improved accuracy in estimating leak-off rates and hydraulic diffusivity. Moreover, the GPT method requires only a short-term pressure fall-off curve to accurately determine reservoir properties, and this can significantly shorten the typical long fall-of time in low permeability rocks. The Gaussian pressure model provided excellent matches with field data, confirming the method’s reliability for unconventional reservoir analysis. The proposed methodology thus offers significant advancement over conventional techniques, better aligning DFIT analysis with the complex realities of unconventional reservoirs. This study introduces a new methodology for analyzing DFIT data by applying Gaussian Pressure Transient (GPT) solutions to model pressure fall-off behavior in hydraulically fractured wells. Diagnostic Fracture Injection Test (DFIT) data from 7 wells were analyzed; the wells were drilled in four different shale formations (Wolfcamp, Eagle Ford, Bakken, and Three Forks). All wells analyzed were hydraulically fractured, and as a first step in the fracturing treatment operation, each of the completion companies involved in the different wells applied a DFIT test to determine the ISIP and the formation leak-off rate to estimate the permeability. The original pressure fall-off excel sheets, availed by different operators, were analyzed in detail. For each test, the relevant part of the leak-off test data was identified and isolated for further in-depth study of the leak-off rate. Instead of relying on traditional DFIT interpretation techniques such as G-function or Carter leak-off assumptions, the method leverages the Gaussian diffusion model to capture the pressure propagation and leak-off characteristics more accurately. The Gaussian pressure transient analysis combines pressure and volume balancing principles directly on the actual field measurements. The results show that the Gaussian method successfully matched the pressure fall-off curves for all 7 wells, with improved accuracy in estimating leak-off rates and hydraulic diffusivity. Moreover, the GPT method requires only a short-term pressure fall-off curve to accurately determine reservoir properties, and this can significantly shorten the typical long fall-of time in low permeability rocks. The Gaussian pressure model provided excellent matches with field data, confirming the method’s reliability for unconventional reservoir analysis. The proposed methodology thus offers significant advancement over conventional techniques, better aligning DFIT analysis with the complex realities of unconventional reservoirs.
View full paperComprehensive Permeability-Transform Solutions for Shale and Sandstones using Data Sets from around the Globe
This study uses 13 proprietary data sets from sedimentary basins around the globe to constrain the permeability and porosity ranges occupied by clastic rocks (sandstones and shale). The combined data sets represent a total sample size of 21,767 data pairs of measured porosity and permeability. The data are combined in various ways and analyzed in considerable detail, in what is presently assumed the most comprehensive permeability analysis of clastic data sets. First, comprehensive porosity-permeability transforms are plotted with the aim to understand how well the two quantities actually correlate, and what may be the root cause(s) of the huge variation in their correlation. The analysis of the empirical data is embedded in a review of prior work related to permeability transforms. The Kozeny-Carman relationship is revisited and a modified scaling approach is proposed. First, it is shown how hydraulics of pore tubes of various shapes and tortuosity relate to macroscopic permeability. The key scaling factor, called here the permeability-reduction factor, , is the ratio of the coefficient of hydraulically effective pore space, , and the tortuosity, . Whereas it is concluded that the porosity is a very poor predictor of the permeability, there appears to exist a close relationship between the permeability-reduction factor and the permeability, confirming the fundamental physical nature of as an excellent predictor of hydraulic transmissibility in porous media made up of sedimentary mineral aggregates. The inferred relationship provides the basis for a new method to construct permeability transforms, from bootstrapped data sets, using Monte-Carlo simulation. This study uses 13 proprietary data sets from sedimentary basins around the globe to constrain the permeability and porosity ranges occupied by clastic rocks (sandstones and shale). The combined data sets represent a total sample size of 21,767 data pairs of measured porosity and permeability. The data are combined in various ways and analyzed in considerable detail, in what is presently assumed the most comprehensive permeability analysis of clastic data sets. First, comprehensive porosity-permeability transforms are plotted with the aim to understand how well the two quantities actually correlate, and what may be the root cause(s) of the huge variation in their correlation. The analysis of the empirical data is embedded in a review of prior work related to permeability transforms. The Kozeny-Carman relationship is revisited and a modified scaling approach is proposed. First, it is shown how hydraulics of pore tubes of various shapes and tortuosity relate to macroscopic permeability. The key scaling factor, called here the permeability-reduction factor, , is the ratio of the coefficient of hydraulically effective pore space, , and the tortuosity, . Whereas it is concluded that the porosity is a very poor predictor of the permeability, there appears to exist a close relationship between the permeability-reduction factor and the permeability, confirming the fundamental physical nature of as an excellent predictor of hydraulic transmissibility in porous media made up of sedimentary mineral aggregates. The inferred relationship provides the basis for a new method to construct permeability transforms, from bootstrapped data sets, using Monte-Carlo simulation.
View full paperCO2 Storage capacity classification and compliance
The Society of Petroleum Engineers (SPE) has proposed a framework for the classification of CO2 storage resources and storage capacity, known as the Storage Resources Management System (SRMS, 2017). The SRMS framework aims to provide guidelines for the classification and reporting of CO2 assets. It’s similar to SPE’s well-established framework for hydrocarbon resources and reserves classification, known as the Petroleum Resource Management System (PRMS, 2018). Meanwhile, revisions of both the 2018 version of PRMS and 2017 version of SRMS are underway, with public consultations of practitioners completed in 2024 (PRMS, 2024; SRMS, 2024). While the PRMS is actually used industry-wide, this cannot be said for the SRMS. There is a nascent CO2 storage business segment, with mushrooming carbon removal startups. This fledgling new industry is now proposing a carbon removal quality assurance Code of Practice, at the same time as SPE is spending efforts on revising its carbon resources management system. The absence of track record and weak incentives, as well as a lack of case studies on how to apply SRMS in practice, are lurking in the background. Additionally, the groundswell of arguably opportunistic providers of storage capacity has created an unprecedented situation where carbon removal companies offer mostly unclassified storage capacity (in SRMS classification’s sense), as will be detailed below. The lack of validated storage capacity is an important hurdle in startup credibility — investors should be wary. The Society of Petroleum Engineers (SPE) has proposed a framework for the classification of CO2 storage resources and storage capacity, known as the Storage Resources Management System (SRMS, 2017). The SRMS framework aims to provide guidelines for the classification and reporting of CO2 assets. It’s similar to SPE’s well-established framework for hydrocarbon resources and reserves classification, known as the Petroleum Resource Management System (PRMS, 2018). Meanwhile, revisions of both the 2018 version of PRMS and 2017 version of SRMS are underway, with public consultations of practitioners completed in 2024 (PRMS, 2024; SRMS, 2024). While the PRMS is actually used industry-wide, this cannot be said for the SRMS. There is a nascent CO2 storage business segment, with mushrooming carbon removal startups. This fledgling new industry is now proposing a carbon removal quality assurance Code of Practice, at the same time as SPE is spending efforts on revising its carbon resources management system. The absence of track record and weak incentives, as well as a lack of case studies on how to apply SRMS in practice, are lurking in the background. Additionally, the groundswell of arguably opportunistic providers of storage capacity has created an unprecedented situation where carbon removal companies offer mostly unclassified storage capacity (in SRMS classification’s sense), as will be detailed below. The lack of validated storage capacity is an important hurdle in startup credibility — investors should be wary.
View full paperFast Production and Water-Breakthrough Analysis Methods Demonstrated Using Volve Field Data
When producing from conventional fields, the well rates are primarily constrained by the production-system in the early years of the field-life, while later in the field-life the production rates are primarily constrained by the reservoir deliverability. For the post-plateau production period, the reservoir deliverability will no longer potentially exceed the production-system well-rate constraints. Traditionally, analytical equations are used in a nodal analysis method that balances the pressure at the well inflow point from the reservoir (inflow performance relationship; IPR) with the pressure required for the vertical lift performance (VLP; or vertical flow performance; VFP) from the same point upward. A faster and simpler approach is proposed in the present study. Whereas, the classical IPR solutions are based on a constant well-rate solution of the diffusivity equation, use of a constant bottomhole pressure assumption can bypass the need for nodal analysis type pressure matching solutions to obtain the well rate. Instead, the well rate can be directly computed from the pressure decline in the reservoir and any production system capacity constraint can be imposed on the theoretical well rate due to the reservoir quality. The merits of the new approach are explained and illustrated by way of a detailed production analysis case study using open-access data from the Volve Field (Norwegian Continental Shelf). In addition, the case study of the Volve Field wells demonstrates a new water-breakthrough analysis method. When producing from conventional fields, the well rates are primarily constrained by the production-system in the early years of the field-life, while later in the field-life the production rates are primarily constrained by the reservoir deliverability. For the post-plateau production period, the reservoir deliverability will no longer potentially exceed the production-system well-rate constraints. Traditionally, analytical equations are used in a nodal analysis method that balances the pressure at the well inflow point from the reservoir (inflow performance relationship; IPR) with the pressure required for the vertical lift performance (VLP; or vertical flow performance; VFP) from the same point upward. A faster and simpler approach is proposed in the present study. Whereas, the classical IPR solutions are based on a constant well-rate solution of the diffusivity equation, use of a constant bottomhole pressure assumption can bypass the need for nodal analysis type pressure matching solutions to obtain the well rate. Instead, the well rate can be directly computed from the pressure decline in the reservoir and any production system capacity constraint can be imposed on the theoretical well rate due to the reservoir quality. The merits of the new approach are explained and illustrated by way of a detailed production analysis case study using open-access data from the Volve Field (Norwegian Continental Shelf). In addition, the case study of the Volve Field wells demonstrates a new water-breakthrough analysis method.
View full paperPressure-Transient Solutions for Unbounded and Bounded Reservoirs Produced and/or Injected via Vertical Well-Systems with Constant Bottomhole-Pressures
Various analytical solutions for computing production and injection-induced pressure changes in aquifers and oil reservoirs have been derived over the past century. All prior solutions assumed a constant well rate as the boundary condition. However, in many practical situations, the fluid withdrawal from and/or injection into such subsurface reservoirs occurs with the aid of pump devices that maintain a constant bottomhole pressure in the well. Until now, how the well rate will decline over time, based on the pressure difference in the well relative to the initial reservoir pressure, could not be rapidly computed analytically (using the diffusivity as the key governing system parameter), because no concise expression had been derived with the boundary condition of a constant bottomhole pressure. The present study shows how the pressure diffusion equation can be readily solved for wells acting as sinks and sources with a constant bottomhole pressure condition. We consider both fractured and unfractured completions, as well as injection and production modes. The new solutions do not require an elaborate time-stepped pressure-matching procedure as in nodal analysis, the only other physics-based analytical method currently available to compute the well rate decline when a constant bottomhole pressure production system is used, which unlike our new method proposed here is limited to single well systems. Various analytical solutions for computing production and injection-induced pressure changes in aquifers and oil reservoirs have been derived over the past century. All prior solutions assumed a constant well rate as the boundary condition. However, in many practical situations, the fluid withdrawal from and/or injection into such subsurface reservoirs occurs with the aid of pump devices that maintain a constant bottomhole pressure in the well. Until now, how the well rate will decline over time, based on the pressure difference in the well relative to the initial reservoir pressure, could not be rapidly computed analytically (using the diffusivity as the key governing system parameter), because no concise expression had been derived with the boundary condition of a constant bottomhole pressure. The present study shows how the pressure diffusion equation can be readily solved for wells acting as sinks and sources with a constant bottomhole pressure condition. We consider both fractured and unfractured completions, as well as injection and production modes. The new solutions do not require an elaborate time-stepped pressure-matching procedure as in nodal analysis, the only other physics-based analytical method currently available to compute the well rate decline when a constant bottomhole pressure production system is used, which unlike our new method proposed here is limited to single well systems.
View full paperGaussian Pressure-Transients: A Toolkit for Production Forecasts and Optimization of Multi-Fractured Well Systems in Shale Formations
High development cost of shale fields produced with multi-fractured well systems prompts for improved and faster production forecasting tools. This study advances the use of a Gaussian pressure transient-based reservoir model (GRM). In this new simulator, the migration of reservoir fluids is fully controlled by the hydraulic diffusivity; the value of which can be initially estimated for any particular reservoir by history-matching a Gaussian decline curve to early production data. In a next step, the reservoir model based on the Gaussian pressure transient will compute—from the bottomhole pressures in the well system (imposed by the engineering intervention on the initial reservoir pressure)—the spatial and temporal advance of the pressure depletion and fluid flow near the multistage fractured wells. Real-world data from the Hydraulic Fracture Test Site-1, Midland Basin (West Texas), is utilized to validate the Gaussian solutions in comparison with a commercial simulator through history-matching and a comprehensive sensitivity analysis. The validated GPT method allows for fast iteration of well productivity sensitivity to the placement and orientation of the hydraulic fractures, allowing for proper planning to optimize field development plans. High development cost of shale fields produced with multi-fractured well systems prompts for improved and faster production forecasting tools. This study advances the use of a Gaussian pressure transient-based reservoir model (GRM). In this new simulator, the migration of reservoir fluids is fully controlled by the hydraulic diffusivity; the value of which can be initially estimated for any particular reservoir by history-matching a Gaussian decline curve to early production data. In a next step, the reservoir model based on the Gaussian pressure transient will compute—from the bottomhole pressures in the well system (imposed by the engineering intervention on the initial reservoir pressure)—the spatial and temporal advance of the pressure depletion and fluid flow near the multistage fractured wells. Real-world data from the Hydraulic Fracture Test Site-1, Midland Basin (West Texas), is utilized to validate the Gaussian solutions in comparison with a commercial simulator through history-matching and a comprehensive sensitivity analysis. The validated GPT method allows for fast iteration of well productivity sensitivity to the placement and orientation of the hydraulic fractures, allowing for proper planning to optimize field development plans.
View full paperDeferring Flood Damage in Coastal Lowlands: Assessing Surface Uplift by Geo-Engineered CO2-Sequestration with Easy-to-Use Land-Uplift Model
Mitigating flood risk of heavily urbanised coastal regions by geo-engineered surface uplift via CO2-sequestration may help to create commercially viable storage opportunities for greenhouse gases like CO2. Recent projections for increased global flood risk due to sea level rise induced by rising CO2-emissions are briefly reviewed. Next, a practical geo-mechanical model is presented, suitable for quick technical assessments of the key physical parameters that contribute most to achieving a specific surface uplift rate required to outpace the projected relative sea level rise for a certain region at risk. The model allows for probabilistic inputs to (1) capture the uncertainty in the value of key input parameters, and (2) link and rank the sensitivity of the surface uplift, to the individual input parameters (in tornado and spider graphs). Three uplift scenarios are given to demonstrate the feasibility of flood mitigation with CO2-sequestration. Finally, a discussion places the emergence of CO2-injection projects in a historic perspective, and highlights the critical key factors in the future screening of any CO2-injection prospects. These factors include the evaluation of technical challenges, potential risks, stakeholder management, public education and perception management. Mitigating flood risk of heavily urbanised coastal regions by geo-engineered surface uplift via CO2-sequestration may help to create commercially viable storage opportunities for greenhouse gases like CO2. Recent projections for increased global flood risk due to sea level rise induced by rising CO2-emissions are briefly reviewed. Next, a practical geo-mechanical model is presented, suitable for quick technical assessments of the key physical parameters that contribute most to achieving a specific surface uplift rate required to outpace the projected relative sea level rise for a certain region at risk. The model allows for probabilistic inputs to (1) capture the uncertainty in the value of key input parameters, and (2) link and rank the sensitivity of the surface uplift, to the individual input parameters (in tornado and spider graphs). Three uplift scenarios are given to demonstrate the feasibility of flood mitigation with CO2-sequestration. Finally, a discussion places the emergence of CO2-injection projects in a historic perspective, and highlights the critical key factors in the future screening of any CO2-injection prospects. These factors include the evaluation of technical challenges, potential risks, stakeholder management, public education and perception management.
View full paperSensitivity Analysis of CO2-Migration Paths in Geological Carbon-Dioxide Sequestration: Case Study of the Gorgon GCS Project
Tracking the flow path of injected fluid in geological carbon-dioxide sequestration (GCS) studies is important for flow conformance control. A Gaussian Pressure Transient method is applied in a sensitivity study of the world’s largest GCS-project associated with the Gorgon-Io natural gas extraction project, Australia. The Gorgon GCS project aims to inject around 120 million tons (2 Tscf) CO2 produced from the LNG processing plant into a deep saline aquifer (Dupuy Formation) over the 40+ years project life. The CO2 injection started in August 2019, and is currently operating at one-third of planned capacity, due to well-control and pressure-management issues. The recently developed Gaussian simulation method was employed to independently assess and show under which conditions the CO2 migration path will be conformant to safe sequestration in the target zone by the avoidance of pressure escalation. The study outcome demonstrates that if rock wettability shifts from water-wet to weakly water-wet during the course of a GCS project, this could cause a shift in critical CO2 saturation, which impacts both the flow paths and migration rates of the injected CO2. Furthermore, increasing water withdrawal rates from the production wells and strategically adjusting CO2 injection pressure can further reduce the risk of premature CO2 break-through. The modeling approach used in this study, provides valuable insights for optimizing the number and spacing of injectors and producers, as well as for adjustment of water-withdrawal rates, and injection pressures, in response to possible changes in rock wettability during CO2 flooding in aquifers with pressure relief wells, similar to the Gorgon GCS Project. The reservoir pressure, fluid migration rates and flow paths can be quantified with unlimited resolution, because the GPT-solution method is closed-form based. Tracking the flow path of injected fluid in geological carbon-dioxide sequestration (GCS) studies is important for flow conformance control. A Gaussian Pressure Transient method is applied in a sensitivity study of the world’s largest GCS-project associated with the Gorgon-Io natural gas extraction project, Australia. The Gorgon GCS project aims to inject around 120 million tons (2 Tscf) CO2 produced from the LNG processing plant into a deep saline aquifer (Dupuy Formation) over the 40+ years project life. The CO2 injection started in August 2019, and is currently operating at one-third of planned capacity, due to well-control and pressure-management issues. The recently developed Gaussian simulation method was employed to independently assess and show under which conditions the CO2 migration path will be conformant to safe sequestration in the target zone by the avoidance of pressure escalation. The study outcome demonstrates that if rock wettability shifts from water-wet to weakly water-wet during the course of a GCS project, this could cause a shift in critical CO2 saturation, which impacts both the flow paths and migration rates of the injected CO2. Furthermore, increasing water withdrawal rates from the production wells and strategically adjusting CO2 injection pressure can further reduce the risk of premature CO2 break-through. The modeling approach used in this study, provides valuable insights for optimizing the number and spacing of injectors and producers, as well as for adjustment of water-withdrawal rates, and injection pressures, in response to possible changes in rock wettability during CO2 flooding in aquifers with pressure relief wells, similar to the Gorgon GCS Project. The reservoir pressure, fluid migration rates and flow paths can be quantified with unlimited resolution, because the GPT-solution method is closed-form based.
View full paperProbabilistic Production Forecasting and Reserves Estimation: Benchmarking Gaussian Decline Curve Analysis Against the Traditional Arps Method (Wolfcamp Shale Case Study)
This study provides novel insights into how a relatively new, Gaussian DCA method may be used to forecast well rates and estimate resource volumes produced from unconventional reservoirs. Production data of two wells in the Wolfcamp Shale Formation (Midland Basin, West Texas) were history-matched using both the Arps and Gaussian DCA method. Production forecasts were constructed based on the history-matching of historical production data, and the estimated ultimate recovery (EUR) was determined from the cumulative production at the end of the economic well-life (assumed here to be 40 years). Comparing the results of the conventional Arps and new Gaussian DCA method, we found the Gaussian DCA technique compared favorably to the conventional Arps method, the former being faster and having less error in the history-matching process. The traditional Arps history-matching technique is always initiated with very high initial well rates. In contrast, the very first spike in the actual production rates can be accurately captured by the Gaussian DCA method. The hydraulic diffusivity parameter that was obtained from the history-matching in the Gaussian DCA method was also compared with a calculated diffusivity using primary values obtained from laboratory and well log data. The hydraulic diffusivity parameter obtained from the Gaussian history-match of field data is at the lower side of the probabilistic values calculated based on the laboratory and well log data. A probabilistic regression analysis was applied and the estimated values’ distribution was then adjusted to match the values from the history matches as a basis for the final probabilistic EUR estimations for the study wells. Separately, a bootstrapping method can be used to produce probabilistic EUR estimates based on single well data. This study provides novel insights into how a relatively new, Gaussian DCA method may be used to forecast well rates and estimate resource volumes produced from unconventional reservoirs. Production data of two wells in the Wolfcamp Shale Formation (Midland Basin, West Texas) were history-matched using both the Arps and Gaussian DCA method. Production forecasts were constructed based on the history-matching of historical production data, and the estimated ultimate recovery (EUR) was determined from the cumulative production at the end of the economic well-life (assumed here to be 40 years). Comparing the results of the conventional Arps and new Gaussian DCA method, we found the Gaussian DCA technique compared favorably to the conventional Arps method, the former being faster and having less error in the history-matching process. The traditional Arps history-matching technique is always initiated with very high initial well rates. In contrast, the very first spike in the actual production rates can be accurately captured by the Gaussian DCA method. The hydraulic diffusivity parameter that was obtained from the history-matching in the Gaussian DCA method was also compared with a calculated diffusivity using primary values obtained from laboratory and well log data. The hydraulic diffusivity parameter obtained from the Gaussian history-match of field data is at the lower side of the probabilistic values calculated based on the laboratory and well log data. A probabilistic regression analysis was applied and the estimated values’ distribution was then adjusted to match the values from the history matches as a basis for the final probabilistic EUR estimations for the study wells. Separately, a bootstrapping method can be used to produce probabilistic EUR estimates based on single well data.
View full paperFracture Propagation-Rate and Fracture Half-Length Estimated for an Individual Stage using Dynamic Balancing of Fluid Pressures: Eagle Ford Case Study
This study presents a new analytical model for determining the growth-rate of hydraulic fractures during the pumping of a fracturing stage. Unlike existing commercial and numerical tools for final fracture half-length estimation, the present model is able to accommodate time-dependent parameters used in actual field operations and shows how this controls the stepwise evolution of fracture half-length over the duration of the stage treatment. The model analyzes the pressure gains and losses across the well system during the fracturing treatment operation, which solves for the Sneddon pressure used subsequently to estimate the extent and rate of the hydraulic fracture growth from the perforation clusters outward until the ultimate half-length is established. Using a practical spreadsheet template, the pressure balance model accounts for all the pressure gains and losses occurring during a typical hydraulic fracturing job. The model revealed practical results and reasonable values for the fracture half-length, in close agreement with independent estimations of fracture half-length for the same Eagle Ford well. The average propagation rate of a planar fracture, with an elliptical cross-section (in map view) of 1.8 mm width for the minor axis and fixed height of 100 ft, is 1.54 ft/min (0.026 ft/s), with high and low rates ranging between 2.81 and 0.220 ft/min. The final hydraulic fracture half-length at the end of the fracturing job was 212 ft. However, the effectively propped fracture half-length determined in independent studies using production analysis is somewhat smaller (144 ft), which indicates that the tip-end of the final fracture (212-144 ft= 68 ft) was not effectively propped, and effectively closed after the treatment. This study presents a new analytical model for determining the growth-rate of hydraulic fractures during the pumping of a fracturing stage. Unlike existing commercial and numerical tools for final fracture half-length estimation, the present model is able to accommodate time-dependent parameters used in actual field operations and shows how this controls the stepwise evolution of fracture half-length over the duration of the stage treatment. The model analyzes the pressure gains and losses across the well system during the fracturing treatment operation, which solves for the Sneddon pressure used subsequently to estimate the extent and rate of the hydraulic fracture growth from the perforation clusters outward until the ultimate half-length is established. Using a practical spreadsheet template, the pressure balance model accounts for all the pressure gains and losses occurring during a typical hydraulic fracturing job. The model revealed practical results and reasonable values for the fracture half-length, in close agreement with independent estimations of fracture half-length for the same Eagle Ford well. The average propagation rate of a planar fracture, with an elliptical cross-section (in map view) of 1.8 mm width for the minor axis and fixed height of 100 ft, is 1.54 ft/min (0.026 ft/s), with high and low rates ranging between 2.81 and 0.220 ft/min. The final hydraulic fracture half-length at the end of the fracturing job was 212 ft. However, the effectively propped fracture half-length determined in independent studies using production analysis is somewhat smaller (144 ft), which indicates that the tip-end of the final fracture (212-144 ft= 68 ft) was not effectively propped, and effectively closed after the treatment.
View full paperProduction Forecasting of Unruly Geoenergy Extraction Wells Using Gaussian Decline Curve Analysis
Fast and rigorous well performance evaluation is made possible by new solutions of the pressure diffusion equation. The derived Gaussian pressure transient (GPT) solutions can be practically formulated as a decline curve analysis (DCA) equation for history matching of historic well rates to then forecast the future well performance and estimate the remaining reserves. Application in rate transient analysis (RTA) mode is also possible to estimate fracture half-lengths. Because GPT solutions are physics-based, these can be used for production forecasting as well as in reservoir simulation mode (by computing the spatial and temporal pressure gradients everywhere in the reservoir section drained by either an existing or a planned well). The present paper focuses on the physics-based production forecasting of so-called “unruly” wells, which at first seem to have production behavior noncompliant with any DCA curve. Four shale wells (one from the Utica, Ohio; one from the Eagle Ford Formation, East Texas; and two from the Wolfcamp Formation, West Texas) are analyzed in detail. Physics-based adjustments are made to the Gaussian DCA history matching process, showing how the production rate of these wells is fully compliant with the rate implied by the hydraulic diffusivity of the reservoir sections where these wells drain from. Fast and rigorous well performance evaluation is made possible by new solutions of the pressure diffusion equation. The derived Gaussian pressure transient (GPT) solutions can be practically formulated as a decline curve analysis (DCA) equation for history matching of historic well rates to then forecast the future well performance and estimate the remaining reserves. Application in rate transient analysis (RTA) mode is also possible to estimate fracture half-lengths. Because GPT solutions are physics-based, these can be used for production forecasting as well as in reservoir simulation mode (by computing the spatial and temporal pressure gradients everywhere in the reservoir section drained by either an existing or a planned well). The present paper focuses on the physics-based production forecasting of so-called “unruly” wells, which at first seem to have production behavior noncompliant with any DCA curve. Four shale wells (one from the Utica, Ohio; one from the Eagle Ford Formation, East Texas; and two from the Wolfcamp Formation, West Texas) are analyzed in detail. Physics-based adjustments are made to the Gaussian DCA history matching process, showing how the production rate of these wells is fully compliant with the rate implied by the hydraulic diffusivity of the reservoir sections where these wells drain from.
View full paperEstimation of Fracture Half-Length with Fast Gaussian Pressure Transient and RTA Methods: Wolfcamp Shale Formation Case Study
Accurate estimation of fracture half-lengths in shale gas and oil reservoirs is critical for optimizing stimulation design, evaluating production potential, monitoring reservoir performance, and making informed economic decisions. Assessing the dimensions of hydraulic fractures and the quality of well completions in shale gas and oil reservoirs typically involves techniques such as chemical tracers, microseismic fiber optics, and production logs, which can be time-consuming and costly. This study demonstrates an alternative approach to estimate fracture half-lengths using the Gaussian pressure transient (GPT) Method, which has recently emerged as a novel technique for quantifying pressure depletion around single wells, multiple wells, and hydraulic fractures. The GPT method is compared to the well-established rate transient analysis (RTA) method to evaluate its effectiveness in estimating fracture parameters. The study used production data from 11 wells at the hydraulic fracture test site 1 in the Midland Basin of West Texas from Upper and Middle Wolfcamp (WC) formations. The data included flow rates and pressure readings, and the fracture half-lengths of the 11 wells were individually estimated by matching the production data to historical records. The GPT method can calculate the fracture half-length from daily production data, given a certain formation permeability. Independently, the traditional RTA method was applied to separately estimate the fracture half-length. The results of the two methods (GPT and RTA) are within an acceptable, small error margin for all 5 of the Middle WC wells studied, and for 5 of the 6 Upper WC wells. The slight deviation in the case of the Upper WC well is due to the different production control and a longer time for the well to reach constant bottomhole pressure. The estimated stimulated surface area for the Middle and Upper WC wells was correlated to the injected proppant volume and the total fluid production. Applying RTA and GPT methods to the historic production data improves the fracture diagnostics accuracy by reducing the uncertainty in the estimation of fracture dimensions, for given formation permeability values of the stimulated rock volume. Accurate estimation of fracture half-lengths in shale gas and oil reservoirs is critical for optimizing stimulation design, evaluating production potential, monitoring reservoir performance, and making informed economic decisions. Assessing the dimensions of hydraulic fractures and the quality of well completions in shale gas and oil reservoirs typically involves techniques such as chemical tracers, microseismic fiber optics, and production logs, which can be time-consuming and costly. This study demonstrates an alternative approach to estimate fracture half-lengths using the Gaussian pressure transient (GPT) Method, which has recently emerged as a novel technique for quantifying pressure depletion around single wells, multiple wells, and hydraulic fractures. The GPT method is compared to the well-established rate transient analysis (RTA) method to evaluate its effectiveness in estimating fracture parameters. The study used production data from 11 wells at the hydraulic fracture test site 1 in the Midland Basin of West Texas from Upper and Middle Wolfcamp (WC) formations. The data included flow rates and pressure readings, and the fracture half-lengths of the 11 wells were individually estimated by matching the production data to historical records. The GPT method can calculate the fracture half-length from daily production data, given a certain formation permeability. Independently, the traditional RTA method was applied to separately estimate the fracture half-length. The results of the two methods (GPT and RTA) are within an acceptable, small error margin for all 5 of the Middle WC wells studied, and for 5 of the 6 Upper WC wells. The slight deviation in the case of the Upper WC well is due to the different production control and a longer time for the well to reach constant bottomhole pressure. The estimated stimulated surface area for the Middle and Upper WC wells was correlated to the injected proppant volume and the total fluid production. Applying RTA and GPT methods to the historic production data improves the fracture diagnostics accuracy by reducing the uncertainty in the estimation of fracture dimensions, for given formation permeability values of the stimulated rock volume.
View full paperSurface subsidence and uplift resulting from well interventions modeled with coupled analytical solutions: Application to Groningen gas extraction (Netherlands) and CO2-EOR in the Kelly-Snyder oil field (West Texas)
This study presents a novel analytical model for history-matching the observed subsidence and/or uplift due to, respectively, fluid extraction from – or injection into – the pore space of subsurface reservoirs. Development of the model was prompted by the need to have a fast evaluation tool to support the various exploitation modes of subsurface reservoirs, either in fluid extraction projects (hydrocarbons, aquifers, geothermal fields) or in fluid storage projects (waste water, natural gas, hydrogen, and CO2-sequestration). The model proposed here is a novel analytical solution method obtained by coupling the vertical strain changes in a reservoir due to changes in reservoir pressure with a buckling plate model for the overburden. After a brief review of state-of-the-art (numerical and analytical tools), the coupled reservoir pressure change and overburden buckling model (in brief: pressure change-buckling model) is presented. Subsequently, the coupled pressure change-buckling model is applied in two case studies. The first case study history-matches the subsidence of the Groningen Field (Netherlands) over the period 1963–2020, due to the pressure depletion caused by natural gas extraction. The second case study applies the model to history-match the uplift history above an oil field in Scurry County (West Texas) over the period 2007–2011, due to net fluid injection related to enhanced oil recovery (EOR) activities. Separately, in addition to history-matching applications the coupled pressure change-buckling model can also be applied in forward modeling mode to predict the surface response of future operations involving pressure changes in subsurface reservoirs. This study presents a novel analytical model for history-matching the observed subsidence and/or uplift due to, respectively, fluid extraction from – or injection into – the pore space of subsurface reservoirs. Development of the model was prompted by the need to have a fast evaluation tool to support the various exploitation modes of subsurface reservoirs, either in fluid extraction projects (hydrocarbons, aquifers, geothermal fields) or in fluid storage projects (waste water, natural gas, hydrogen, and CO2-sequestration). The model proposed here is a novel analytical solution method obtained by coupling the vertical strain changes in a reservoir due to changes in reservoir pressure with a buckling plate model for the overburden. After a brief review of state-of-the-art (numerical and analytical tools), the coupled reservoir pressure change and overburden buckling model (in brief: pressure change-buckling model) is presented. Subsequently, the coupled pressure change-buckling model is applied in two case studies. The first case study history-matches the subsidence of the Groningen Field (Netherlands) over the period 1963–2020, due to the pressure depletion caused by natural gas extraction. The second case study applies the model to history-match the uplift history above an oil field in Scurry County (West Texas) over the period 2007–2011, due to net fluid injection related to enhanced oil recovery (EOR) activities. Separately, in addition to history-matching applications the coupled pressure change-buckling model can also be applied in forward modeling mode to predict the surface response of future operations involving pressure changes in subsurface reservoirs.
View full paperProbabilistic Estimation of Hydraulic Fracture Half-Lengths: Validating the Gaussian Pressure-Transient Method with the Traditional RTA-Method (Wolfcamp Case Study)
Despite significant advancements in geomodelling technologies, accurately estimating hydraulic fracture half-length remains a challenging task. This paper introduces a detailed estimation approach using the Gaussian Pressure Transient (GPT) method, which is relatively new. The GPT method is iterative, ensuring fast convergence and providing reliable estimations of hydraulic fracture half-length based on a predetermined hydraulic diffusivity value obtained from Gaussian Decline Curve Analysis (DCA). To validate the GPT results, production data from two case study wells in the Wolfcamp Shale Formation, located in the Midland Basin of West Texas, are utilized alongside the traditional Rate-Transient Analysis (RTA) method. Moreover, the GPT method offers the capability to probabilistically estimate hydraulic fracture half-lengths, presenting two innovative approaches to evaluate the robustness of this newly developed method for both deterministic and probabilistic estimations. The simulation results demonstrate a close correlation between the Gaussian method and micro-seismic fracture half-lengths, with separate confirmation from the classic RTA-method. Through the case studies presented in this paper, the GPT-method showcases its utility in estimating hydraulic fracture half-lengths for two Wolfcamp case study wells, effectively demonstrating the validity and practical applicability of this novel method. Despite significant advancements in geomodelling technologies, accurately estimating hydraulic fracture half-length remains a challenging task. This paper introduces a detailed estimation approach using the Gaussian Pressure Transient (GPT) method, which is relatively new. The GPT method is iterative, ensuring fast convergence and providing reliable estimations of hydraulic fracture half-length based on a predetermined hydraulic diffusivity value obtained from Gaussian Decline Curve Analysis (DCA). To validate the GPT results, production data from two case study wells in the Wolfcamp Shale Formation, located in the Midland Basin of West Texas, are utilized alongside the traditional Rate-Transient Analysis (RTA) method. Moreover, the GPT method offers the capability to probabilistically estimate hydraulic fracture half-lengths, presenting two innovative approaches to evaluate the robustness of this newly developed method for both deterministic and probabilistic estimations. The simulation results demonstrate a close correlation between the Gaussian method and micro-seismic fracture half-lengths, with separate confirmation from the classic RTA-method. Through the case studies presented in this paper, the GPT-method showcases its utility in estimating hydraulic fracture half-lengths for two Wolfcamp case study wells, effectively demonstrating the validity and practical applicability of this novel method.
View full paperAdvances in Stress-Strain Constitutive Models for Rock Failure: Review and New Dynamic Constitutive Failure (DCF) model using Core Data from the Tarim Basin (China)
A wide range of constitutive models exists to quantify how the applied forces will lead to breakdown of rock samples. This paper reviews the mechanical models that have been developed to capture the full stress-strain curve for rocks deforming first elastically and then failing by fracturing after an elastic limit has been reached. Existing models are poorly suited for application to rock samples subjected to extreme physical conditions, such as the mechanical behavior of rocks under high temperature and high stress as encountered in ultra-deep oil and gas wells. First, conventional triaxial rock mechanics experiments were carried out on core collected from a 7000 m deep reservoir in the Tarim Basin (China); the effects of temperature and confining pressure on rock mechanical properties were analyzed. After a review of existing stress-strain curve models, it was concluded that none of the current rock constitutive models can accurately describe the stress-strain curve of rocks under high temperature and high pressure. Therefore, a new constitutive model was developed to (1) describe the characteristics of pre-peak and post-peak failure curves, and (2) predict the full stress-strain curve at different temperatures and confining pressure. The model was calibrated with the experimental data from the Tarim well. A new constitutive model was obtained by assigning variables to the parameters of a dynamic constitutive failure (DCF) model, which can be used in other scenarios, such as compression failure of rock under cyclical loading, plastic deformation, and rock creep. The dynamic constitutive failure model first presented here provides a useful reference for future modeling attempts. A wide range of constitutive models exists to quantify how the applied forces will lead to breakdown of rock samples. This paper reviews the mechanical models that have been developed to capture the full stress-strain curve for rocks deforming first elastically and then failing by fracturing after an elastic limit has been reached. Existing models are poorly suited for application to rock samples subjected to extreme physical conditions, such as the mechanical behavior of rocks under high temperature and high stress as encountered in ultra-deep oil and gas wells. First, conventional triaxial rock mechanics experiments were carried out on core collected from a 7000 m deep reservoir in the Tarim Basin (China); the effects of temperature and confining pressure on rock mechanical properties were analyzed. After a review of existing stress-strain curve models, it was concluded that none of the current rock constitutive models can accurately describe the stress-strain curve of rocks under high temperature and high pressure. Therefore, a new constitutive model was developed to (1) describe the characteristics of pre-peak and post-peak failure curves, and (2) predict the full stress-strain curve at different temperatures and confining pressure. The model was calibrated with the experimental data from the Tarim well. A new constitutive model was obtained by assigning variables to the parameters of a dynamic constitutive failure (DCF) model, which can be used in other scenarios, such as compression failure of rock under cyclical loading, plastic deformation, and rock creep. The dynamic constitutive failure model first presented here provides a useful reference for future modeling attempts.
View full paperStream and Potential Functions for Transient Flow Simulations in Porous Media with Pressure-Controlled Well Systems
Gaussian solutions of the diffusion equation can be applied to visualize the flow paths in subsurface reservoirs due to the spatial advance of the pressure gradient caused by engineering interventions (vertical wells, horizontal wells) in subsurface reservoirs for the extraction of natural resources (e.g., water, oil, gas, and geothermal fluids). Having solved the temporal and spatial changes in the pressure field caused by the lowered pressure of a well’s production system, the Gaussian method is extended and applied to compute and visualize velocity magnitude contours, streamlines, and other relevant flow attributes in the vicinity of well systems that are depleting the pressure in a reservoir. We derive stream function and potential function solutions that allow instantaneous modeling of flow paths and pressure contour solutions for transient flows. Such analytical solutions for transient flows have not been derived before without time-stepping. The new closed-form solutions avoid the computational complexity of time-stepping, required when time-dependent flows are modeled by superposing steady-state solutions using complex analysis methods. Gaussian solutions of the diffusion equation can be applied to visualize the flow paths in subsurface reservoirs due to the spatial advance of the pressure gradient caused by engineering interventions (vertical wells, horizontal wells) in subsurface reservoirs for the extraction of natural resources (e.g., water, oil, gas, and geothermal fluids). Having solved the temporal and spatial changes in the pressure field caused by the lowered pressure of a well’s production system, the Gaussian method is extended and applied to compute and visualize velocity magnitude contours, streamlines, and other relevant flow attributes in the vicinity of well systems that are depleting the pressure in a reservoir. We derive stream function and potential function solutions that allow instantaneous modeling of flow paths and pressure contour solutions for transient flows. Such analytical solutions for transient flows have not been derived before without time-stepping. The new closed-form solutions avoid the computational complexity of time-stepping, required when time-dependent flows are modeled by superposing steady-state solutions using complex analysis methods.
View full paperPotential Production Gains of Multi-Stage Fractured Wells in Shale Plays: Sensitivity of Well Performance to Changes in Design Parameters Assessed with Fast and Accurate Gaussian Solutions
Wells drilled and completed in shale acreage are guided by pre-drilling fracturing and reservoir modelling, but commonly exhibit productivity different (usually lower) from what was predicted by the simulations. Additionally, multiple wells completed in the same acreage with identical fracturing schedules will rarely result in identical well performance. Instead, a considerable spread in flow performance appears to be the norm, with some wells only having half the rate, and others twice the rate, of the average (type) well. Adopting a factory model (or cookie-cutter) approach that assumes engineering outcomes involving no uncertainty will not result in optimum field development. Gaussian Pressure-Transient (GPT) solutions (for vertical wells, horizontal wells, with and without hydraulic fractures) of the pressure diffusivity equation can be used to history-match early well-data after drilling and completion to constrain the hydraulic diffusivity of the stimulated reservoir volume and determine the achieved half-length of the hydraulic fractures. Among the principal explanations for the observed variation in well deliverability of numerous study wells are the failing of perforation clusters to produce hydraulic fractures and limited fracture half-lengths from those perforations that succeed to produce hydraulic fractures. This study analyses the sensitivity of well deliverability to variations in bottomhole pressure (controlled by the artificial lift system and choke settings), fracture half-length, fracture spacing and well spacing. Such sensitivity analyses of the impact of well-design parameters on well deliverability can be instantaneously computed (spreadsheet-based) using GPT-solutions, without the need for constructing numerical reservoir simulation models. The application of GPT-methods allows for quick learning, based on production analysis of early wells in the acreage section under development, to then subsequently guide how the productivity of any new wells – prior to their actual drilling and completion – can be improved. Wells drilled and completed in shale acreage are guided by pre-drilling fracturing and reservoir modelling, but commonly exhibit productivity different (usually lower) from what was predicted by the simulations. Additionally, multiple wells completed in the same acreage with identical fracturing schedules will rarely result in identical well performance. Instead, a considerable spread in flow performance appears to be the norm, with some wells only having half the rate, and others twice the rate, of the average (type) well. Adopting a factory model (or cookie-cutter) approach that assumes engineering outcomes involving no uncertainty will not result in optimum field development. Gaussian Pressure-Transient (GPT) solutions (for vertical wells, horizontal wells, with and without hydraulic fractures) of the pressure diffusivity equation can be used to history-match early well-data after drilling and completion to constrain the hydraulic diffusivity of the stimulated reservoir volume and determine the achieved half-length of the hydraulic fractures. Among the principal explanations for the observed variation in well deliverability of numerous study wells are the failing of perforation clusters to produce hydraulic fractures and limited fracture half-lengths from those perforations that succeed to produce hydraulic fractures. This study analyses the sensitivity of well deliverability to variations in bottomhole pressure (controlled by the artificial lift system and choke settings), fracture half-length, fracture spacing and well spacing. Such sensitivity analyses of the impact of well-design parameters on well deliverability can be instantaneously computed (spreadsheet-based) using GPT-solutions, without the need for constructing numerical reservoir simulation models. The application of GPT-methods allows for quick learning, based on production analysis of early wells in the acreage section under development, to then subsequently guide how the productivity of any new wells – prior to their actual drilling and completion – can be improved.
View full paperMultiscale and multiphysics production forecasts of shale gas reservoirs: New simulation scheme based on Gaussian pressure transients
Common numerical solutions for production rate forecasting of shale reservoirs have a limited capability to describe the dynamics of fluid mass transfer during a pressure depletion cycle due to production with hydraulically fractured well systems. The pressure drawdown imposed by the well system triggers continuous expansion of free gas in the larger pores, while molecular diffusion predominates in the smaller pores. The declining reservoir pressure leads to the closure of larger pores, which gives further significance to molecular diffusion as a component of the mass transport process. To capture these multiphysics mechanisms, pressure-diffusion and molecular-diffusion forms of the diffusivity equation, discretized in space and time, were simultaneously solved to simulate mass transfer dynamics and kinematics in shale formations. This new approach uses a Gaussian probability function to describe the advance rate of both types of diffusion processes, creating a unique scheme for simulating shale gas reservoirs based on physical parameters that could be either measured or characterized. The adopted algorithms successfully provide solutions that can match the typical shale production profiles. Results are sensitive to the essential reservoir parameters of pressure depletion, matrix permeability, organic content, and local heterogeneity. The simultaneous solution of molecular and pressure diffusivity equations reveals their interdependencies. The production peaks early and then rapidly declines with a growing effect of pore compaction. The flux of the sorbed phase contributes to the production rate by some factor that is determined by the sorption capacity of the organic matter. The methodology provided in this study can be utilized to simulate mass transport in shale reservoirs and predict hydrocarbon production rates, which may greatly aid asset management decisions and maximization of the ultimate recovery. Common numerical solutions for production rate forecasting of shale reservoirs have a limited capability to describe the dynamics of fluid mass transfer during a pressure depletion cycle due to production with hydraulically fractured well systems. The pressure drawdown imposed by the well system triggers continuous expansion of free gas in the larger pores, while molecular diffusion predominates in the smaller pores. The declining reservoir pressure leads to the closure of larger pores, which gives further significance to molecular diffusion as a component of the mass transport process. To capture these multiphysics mechanisms, pressure-diffusion and molecular-diffusion forms of the diffusivity equation, discretized in space and time, were simultaneously solved to simulate mass transfer dynamics and kinematics in shale formations. This new approach uses a Gaussian probability function to describe the advance rate of both types of diffusion processes, creating a unique scheme for simulating shale gas reservoirs based on physical parameters that could be either measured or characterized. The adopted algorithms successfully provide solutions that can match the typical shale production profiles. Results are sensitive to the essential reservoir parameters of pressure depletion, matrix permeability, organic content, and local heterogeneity. The simultaneous solution of molecular and pressure diffusivity equations reveals their interdependencies. The production peaks early and then rapidly declines with a growing effect of pore compaction. The flux of the sorbed phase contributes to the production rate by some factor that is determined by the sorption capacity of the organic matter. The methodology provided in this study can be utilized to simulate mass transport in shale reservoirs and predict hydrocarbon production rates, which may greatly aid asset management decisions and maximization of the ultimate recovery.
View full paperProduction-induced pressure-depletion and stress anisotropy changes near hydraulically fractured wells: Implications for intra-well fracture interference and fracture treatment efficacy
This study investigates the changes in the principal stress trajectories during development of hydrocarbon (and/or geothermal) reservoirs with hydraulically fractured wells. Our analysis indicates four phases in the well-life with typical stress states, i.e., Pre-fracturing Phase (Stress State 0): the natural stress state prior to the drilling intervention; Fracturing Phase (Stress State 1): stress state prevailing during fracturing treatment; Flowback Phase (Stress State 2): stress state prevailing during flowback; and Production Phase (Stress State 3): stress state prevailing during production. The various stress changes are computed and visualized using the Linear Superposition Method (LSM). Two episodes of stress trajectory alterations occur, a first one during the Fracturing Phase (transition from Stress State 0 to 1), and a second one during the Flowback Phase (transition from Stress States 1 to 2), with respectively positive and negative fracture net pressures. During the Production Phase (Stress State 3), the spatial advance of the pressure depletion around the fractured well system due to production was modeled using recently developed Gaussian pressure transient equations. Our new results show that the early stress reversals (Stress State 1) near the pressured fractures during fracturing treatment are short-lived. In addition, the residual stress change magnitude during flowback (Stress State 2) depends on the final fracture-width aperture. In any case, the local stress reversals due to engineering interventions are a short-term phenomenon and remain limited to the near-fracture regions. The regions with the reversed stress will increase when more stages are fractured, assuming the elevated fracture pressure is not fully released before the next stage is completed. Subsequently, the stress anisotropy decreases during production as a result of pressure depletion. Our improved analysis of the stress reversal phenomenon is important for optimizing drilling plans for infill wells, and for improving fracturing treatment designs. This study investigates the changes in the principal stress trajectories during development of hydrocarbon (and/or geothermal) reservoirs with hydraulically fractured wells. Our analysis indicates four phases in the well-life with typical stress states, i.e., Pre-fracturing Phase (Stress State 0): the natural stress state prior to the drilling intervention; Fracturing Phase (Stress State 1): stress state prevailing during fracturing treatment; Flowback Phase (Stress State 2): stress state prevailing during flowback; and Production Phase (Stress State 3): stress state prevailing during production. The various stress changes are computed and visualized using the Linear Superposition Method (LSM). Two episodes of stress trajectory alterations occur, a first one during the Fracturing Phase (transition from Stress State 0 to 1), and a second one during the Flowback Phase (transition from Stress States 1 to 2), with respectively positive and negative fracture net pressures. During the Production Phase (Stress State 3), the spatial advance of the pressure depletion around the fractured well system due to production was modeled using recently developed Gaussian pressure transient equations. Our new results show that the early stress reversals (Stress State 1) near the pressured fractures during fracturing treatment are short-lived. In addition, the residual stress change magnitude during flowback (Stress State 2) depends on the final fracture-width aperture. In any case, the local stress reversals due to engineering interventions are a short-term phenomenon and remain limited to the near-fracture regions. The regions with the reversed stress will increase when more stages are fractured, assuming the elevated fracture pressure is not fully released before the next stage is completed. Subsequently, the stress anisotropy decreases during production as a result of pressure depletion. Our improved analysis of the stress reversal phenomenon is important for optimizing drilling plans for infill wells, and for improving fracturing treatment designs.
View full paperQuantifying micro-proppants crushing rate and evaluating propped micro-fractures
Micro-proppants used in reservoir stimulation to enable oil and gas recovery from tight hydrocarbon reservoirs can be delivered deeper with slick water and prop microfracture networks during hydraulic fracturing. The production of a multi-fractured well system depends on fracture permeability, which is ultimately a function of proppant strength and concentration. However, it is challenging to evaluate the performance of micro-proppants due to their tiny particle size. This paper proposed a practical method for assessing micro-proppant strength based on micro-proppant crushing rates and optimizing micro-proppant delivery to achieve effective concentrations in the pad fluid to prop up the micro-fractures more effectively. Micro-proppants undergo two crushing steps when transported in the fluid and when hydraulic fractures close. Under a pressure of 70 MPa, the crushing rate is 12%–25% of the hydraulic loading, and 42%–66% of the solid loading for three types of micro-proppants. The concentration of micro-proppants in the pad fluid should be higher than 0.9 lbm/gal to maintain economic permeability under high closure stress of 50 MPa. The numerical simulation results demonstrate that adding micro-proppants to the pad fluid will increase the effective propped fracture area, and the initial productivity and stable productivity increase by more than 40% and 20%, respectively. This study has a guiding value for selecting micro-proppants and the number of micro-proppants used in hydraulic fracturing. Micro-proppants used in reservoir stimulation to enable oil and gas recovery from tight hydrocarbon reservoirs can be delivered deeper with slick water and prop microfracture networks during hydraulic fracturing. The production of a multi-fractured well system depends on fracture permeability, which is ultimately a function of proppant strength and concentration. However, it is challenging to evaluate the performance of micro-proppants due to their tiny particle size. This paper proposed a practical method for assessing micro-proppant strength based on micro-proppant crushing rates and optimizing micro-proppant delivery to achieve effective concentrations in the pad fluid to prop up the micro-fractures more effectively. Micro-proppants undergo two crushing steps when transported in the fluid and when hydraulic fractures close. Under a pressure of 70 MPa, the crushing rate is 12%–25% of the hydraulic loading, and 42%–66% of the solid loading for three types of micro-proppants. The concentration of micro-proppants in the pad fluid should be higher than 0.9 lbm/gal to maintain economic permeability under high closure stress of 50 MPa. The numerical simulation results demonstrate that adding micro-proppants to the pad fluid will increase the effective propped fracture area, and the initial productivity and stable productivity increase by more than 40% and 20%, respectively. This study has a guiding value for selecting micro-proppants and the number of micro-proppants used in hydraulic fracturing.
View full paperHydraulic Diffusivity Estimations for US Shale Gas Reservoirs with Gaussian Method: Implications for Pore-Scale Diffusion Processes in Underground Repositories
This paper first presents so-called unified Gaussian solutions for the spatial advance of diffusion transients triggered by a sudden change in pressure, molecular mass concentration and/or temperature. The mathematical description with a Gaussian solution for the pressure transient is similar to that for molecular diffusion and quantifies the diffusion of pressure into the reservoir space due to a change in molecular density initiated at the well intervention point. The resulting pressure gradients due to the pressure transient quantify, via Darcy’s Law, the fluid-particle velocity resulting from that gradient everywhere in the reservoir. Also based on the Gaussian pressure transient, a Gaussian decline curve fitting formula is derived, uniquely scaled by the hydraulic diffusivity. The physics-based, Gaussian decline curve equation was utilized to match 30-year production data from 68 counties in four major US shale gas plays to compute their hydraulic diffusivities. The average hydraulic diffusivities of Marcellus, Haynesville-Bossier, Barnett and Utica shale are 7.43 × 10−9 m2 s−1, 7.9 × 10−9 m2 s−1, 12.3 × 10−9 m2 s−1, and 59.0 × 10−9 m2 s−1, respectively. The empirical history-matched estimates of the pressure-gradient-driven diffusion rates in shale are similar or faster than the shale diffusion-rates measured in the laboratory. It can be assumed that the empirical diffusion rate accounts for the integrated effects of Darcy and non-Darcy flow. Computation of the Gaussian Péclet number in gas plays confirms that the advective flux is much faster than the combined Fickean and non-Fickean mass transport rates. The implications for gas recovery from shale formations, and secure disposal of nuclear waste in the subsurface shale repositories (wellbores and cavities) are discussed. In particular, our field estimations being faster than the laboratory diffusion rates calls for caution because mass transport from leaking containers at disposal sites would diffuse several orders of magnitude faster than suggested by the slower laboratory rates. This paper first presents so-called unified Gaussian solutions for the spatial advance of diffusion transients triggered by a sudden change in pressure, molecular mass concentration and/or temperature. The mathematical description with a Gaussian solution for the pressure transient is similar to that for molecular diffusion and quantifies the diffusion of pressure into the reservoir space due to a change in molecular density initiated at the well intervention point. The resulting pressure gradients due to the pressure transient quantify, via Darcy’s Law, the fluid-particle velocity resulting from that gradient everywhere in the reservoir. Also based on the Gaussian pressure transient, a Gaussian decline curve fitting formula is derived, uniquely scaled by the hydraulic diffusivity. The physics-based, Gaussian decline curve equation was utilized to match 30-year production data from 68 counties in four major US shale gas plays to compute their hydraulic diffusivities. The average hydraulic diffusivities of Marcellus, Haynesville-Bossier, Barnett and Utica shale are 7.43 × 10−9 m2 s−1, 7.9 × 10−9 m2 s−1, 12.3 × 10−9 m2 s−1, and 59.0 × 10−9 m2 s−1, respectively. The empirical history-matched estimates of the pressure-gradient-driven diffusion rates in shale are similar or faster than the shale diffusion-rates measured in the laboratory. It can be assumed that the empirical diffusion rate accounts for the integrated effects of Darcy and non-Darcy flow. Computation of the Gaussian Péclet number in gas plays confirms that the advective flux is much faster than the combined Fickean and non-Fickean mass transport rates. The implications for gas recovery from shale formations, and secure disposal of nuclear waste in the subsurface shale repositories (wellbores and cavities) are discussed. In particular, our field estimations being faster than the laboratory diffusion rates calls for caution because mass transport from leaking containers at disposal sites would diffuse several orders of magnitude faster than suggested by the slower laboratory rates.
View full paperGaussian Decline Curve Analysis of Hydraulically Fractured Wells in Shale Plays: Examples from HFTS-1 (Hydraulic Fracture Test Site-1, Midland Basin, West Texas)
The present study shows how new Gaussian solutions of the pressure diffusion equation can be applied to model the pressure depletion of reservoirs produced with hydraulically multi-fractured well systems. Three practical application modes are discussed: (1) Gaussian decline curve analysis (DCA), (2) Gaussian pressure-transient analysis (PTA) and (3) Gaussian reservoir models (GRMs). The Gaussian DCA is a new history matching tool for production forecasting, which uses only one matching parameter and therefore is more practical than hyperbolic DCA methods. The Gaussian DCA was compared with the traditional Arps DCA through production analysis of 11 wells in the Wolfcamp Formation at Hydraulic Fracture Test Site-1 (HFTS-1). The hydraulic diffusivity of the reservoir region drained by the well system can be accurately estimated based on Gaussian DCA matches. Next, Gaussian PTA was used to infer the variation in effective fracture half-length of the hydraulic fractures in the HFTS-1 wells. Also included in this study is a brief example of how the full GRM solution can accurately track the fluid flow-paths in a reservoir and predict the consequent production rates of hydraulically fractured well systems. The GRM can model reservoir depletion and the associated well rates for single parent wells as well as for arrays of multiple parent–parent and parent–child wells. The present study shows how new Gaussian solutions of the pressure diffusion equation can be applied to model the pressure depletion of reservoirs produced with hydraulically multi-fractured well systems. Three practical application modes are discussed: (1) Gaussian decline curve analysis (DCA), (2) Gaussian pressure-transient analysis (PTA) and (3) Gaussian reservoir models (GRMs). The Gaussian DCA is a new history matching tool for production forecasting, which uses only one matching parameter and therefore is more practical than hyperbolic DCA methods. The Gaussian DCA was compared with the traditional Arps DCA through production analysis of 11 wells in the Wolfcamp Formation at Hydraulic Fracture Test Site-1 (HFTS-1). The hydraulic diffusivity of the reservoir region drained by the well system can be accurately estimated based on Gaussian DCA matches. Next, Gaussian PTA was used to infer the variation in effective fracture half-length of the hydraulic fractures in the HFTS-1 wells. Also included in this study is a brief example of how the full GRM solution can accurately track the fluid flow-paths in a reservoir and predict the consequent production rates of hydraulically fractured well systems. The GRM can model reservoir depletion and the associated well rates for single parent wells as well as for arrays of multiple parent–parent and parent–child wells.
View full paperEconomic Appraisal for an Unconventional Condensate Play Prior to Field Development: Jafurah Basin Case Study (Saudi Arabia)
This study uses a stochastic approach to provide a holistic economic evaluation of the Jafurah field development project, the largest unconventional natural gas field in Saudi Arabia, projected to start first production in 2024. The assessment considers deterministic and probabilistic inputs based on data published in the literature, analogy with Eagle Ford reservoir parameters, and engineering-based assumptions. The uncertainty of discounted net cash flow, internal rate of return, and other target metrics for the Jafurah project is quantified (P90, P50, and P10). The results show the most likely (P50) net present value of 47.21 billion US dollars (at 10% discount rate) and a corresponding internal rate of return of 46.8%. Sensitivity analysis highlights the relative importance of the most critical probabilistic inputs (initial production rate, natural gas price, capital and operational expenses). Based on the current economic ranges and uncertainty analysis, it can be concluded that the Jafurah Field can be profitable in the long term. However, frequent reappraisals are recommended to help direct future decisions on capital expenditure programs for the drilling and completion of new wells, especially when new field performance data becomes available after the earlier wells start first production in 2024. Although hundreds of field delineation and production wells have already been drilled and completed over the past decade, major investment and time were needed to construct new regional pipelines (for gathering natural gas and liquids from each well pad), new chemical plants (for processing of the natural gas liquids), and new underground natural gas storage facilities (to buffer seasonal changes in the production supply and demand of natural gas), which is why first production is planned for 2024. This study uses a stochastic approach to provide a holistic economic evaluation of the Jafurah field development project, the largest unconventional natural gas field in Saudi Arabia, projected to start first production in 2024. The assessment considers deterministic and probabilistic inputs based on data published in the literature, analogy with Eagle Ford reservoir parameters, and engineering-based assumptions. The uncertainty of discounted net cash flow, internal rate of return, and other target metrics for the Jafurah project is quantified (P90, P50, and P10). The results show the most likely (P50) net present value of 47.21 billion US dollars (at 10% discount rate) and a corresponding internal rate of return of 46.8%. Sensitivity analysis highlights the relative importance of the most critical probabilistic inputs (initial production rate, natural gas price, capital and operational expenses). Based on the current economic ranges and uncertainty analysis, it can be concluded that the Jafurah Field can be profitable in the long term. However, frequent reappraisals are recommended to help direct future decisions on capital expenditure programs for the drilling and completion of new wells, especially when new field performance data becomes available after the earlier wells start first production in 2024. Although hundreds of field delineation and production wells have already been drilled and completed over the past decade, major investment and time were needed to construct new regional pipelines (for gathering natural gas and liquids from each well pad), new chemical plants (for processing of the natural gas liquids), and new underground natural gas storage facilities (to buffer seasonal changes in the production supply and demand of natural gas), which is why first production is planned for 2024.
View full paperProduction Rate of Multi-Fractured Wells Modeled with Gaussian Pressure Transients
This study presents new pressure transient solutions, illustrated with some examples of the vast practical application potential. Gaussian pressure transients (GPT) are derived here to quantify the temporal and spatial propagation of instantaneous pressure changes in porous media, as initiated from cylindrical sources (vertical wells) and planar sources (hydraulic fractures). After solving the scalar pressure field in the reservoir space, and adequately accounting for the interference of the various pressure fronts by mathematical integration and superposition, the resulting pressure gradients solve for the velocity field in the reservoir space. Unique for GPT solutions is that the well rate, unlike in the traditional well-testing equations, does not appear as an input. Applying Darcy’s Law, the fluid flux from the reservoir into the well and hydraulic fractures can be directly computed from the GPT solutions. The closed-form production-forecasting model can be implemented either in matrix-coded flow-visualizations of pressure depletion and flow paths for reservoir sections or in grid-less spreadsheet solutions to instantaneously generate production profiles for wells in any type of fluid injection/extraction project (water production, geothermal energy extraction, hydrocarbon production, and fluid disposal wells). Additionally, the Gaussian method also is suitable for physics-based decline curve analysis. The practical examples included in this study are for Eagle Ford shale oil and Marcellus dry gas wells. The hydraulic diffusivities are constrained by the field data, and range between 2.36 x10−10 and 3.48 x10−10 m2 s−1 for the Eagle Ford Formation; for the Marcellus the range is 3.64×10−9 to 5.67×10−8 m2 s−1. The breakthrough solution method of Gaussian pressure transients is placed in the context of past and present modeling approaches for shale plays developed with multi-fractured wells. This study presents new pressure transient solutions, illustrated with some examples of the vast practical application potential. Gaussian pressure transients (GPT) are derived here to quantify the temporal and spatial propagation of instantaneous pressure changes in porous media, as initiated from cylindrical sources (vertical wells) and planar sources (hydraulic fractures). After solving the scalar pressure field in the reservoir space, and adequately accounting for the interference of the various pressure fronts by mathematical integration and superposition, the resulting pressure gradients solve for the velocity field in the reservoir space. Unique for GPT solutions is that the well rate, unlike in the traditional well-testing equations, does not appear as an input. Applying Darcy’s Law, the fluid flux from the reservoir into the well and hydraulic fractures can be directly computed from the GPT solutions. The closed-form production-forecasting model can be implemented either in matrix-coded flow-visualizations of pressure depletion and flow paths for reservoir sections or in grid-less spreadsheet solutions to instantaneously generate production profiles for wells in any type of fluid injection/extraction project (water production, geothermal energy extraction, hydrocarbon production, and fluid disposal wells). Additionally, the Gaussian method also is suitable for physics-based decline curve analysis. The practical examples included in this study are for Eagle Ford shale oil and Marcellus dry gas wells. The hydraulic diffusivities are constrained by the field data, and range between 2.36 x10−10 and 3.48 x10−10 m2 s−1 for the Eagle Ford Formation; for the Marcellus the range is 3.64×10−9 to 5.67×10−8 m2 s−1. The breakthrough solution method of Gaussian pressure transients is placed in the context of past and present modeling approaches for shale plays developed with multi-fractured wells.
View full paperLaboratory Tests and Well Rate Models of Crushed Micro-Proppants to Improve Conductivity of Hydraulic Microfractures, 22IPTC-22209-MS
This study proposes an innovative crushing rate evaluation method for micro-proppants by analyzing hydraulic crushing and steel crushing rates. The effectiveness of using micro-proppants to increase the drainage area of the micro-fractures network was also proved. Our results show that for micro-proppants, there occur two types of crushing evolution during the fracturing process. Under a load of 70 MPa, the hydraulic crushing rate is about 20%, while the steel crushing rate is more than 60%. The critical closure stress of micro-proppants is 50 MPa, which can be used to depths up to 4,200 m. Numerical simulation results showed that due to the presence of micro-proppants, the effectively propped area of the fracture network would sharply increase, accompanied by an over 40% increase in the initial hydrocarbon production rate. The later, steady production period will show a sustained increase of more than 20%. This study proposes an innovative crushing rate evaluation method for micro-proppants by analyzing hydraulic crushing and steel crushing rates. The effectiveness of using micro-proppants to increase the drainage area of the micro-fractures network was also proved. Our results show that for micro-proppants, there occur two types of crushing evolution during the fracturing process. Under a load of 70 MPa, the hydraulic crushing rate is about 20%, while the steel crushing rate is more than 60%. The critical closure stress of micro-proppants is 50 MPa, which can be used to depths up to 4,200 m. Numerical simulation results showed that due to the presence of micro-proppants, the effectively propped area of the fracture network would sharply increase, accompanied by an over 40% increase in the initial hydrocarbon production rate. The later, steady production period will show a sustained increase of more than 20%.
View full paperDiffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media
This study revisits the mathematical equations for diffusive mass transport in 1D, 2D and 3D space and highlights a widespread misconception about the meaning of the regular and cumulative probability of random-walk solutions for diffusive mass transport. Next, the regular probability solution for molecular diffusion is applied to pressure diffusion in porous media. The pressure drop (by fluid extraction) or increase (by fluid injection) due to the production system may start with a simple pressure step function. The pressure perturbation imposed by the step function (representing the engineering intervention) will instantaneously diffuse into the reservoir at a rate that is controlled by the hydraulic diffusivity. Traditionally, the advance of the pressure transient in porous media such as geological reservoirs is modeled by two distinct approaches: (1) scalar equations for well performance testing that do not attempt to solve for the spatial change or the position of the pressure transient without reference to a well rate; (2) advanced reservoir models based on numerical solution methods. The Gaussian pressure transient solution method presented in this study can compute the spatial pressure depletion in the reservoir at arbitrary times and is based on analytical expressions that give spatial resolution without gridding-meaning solutions that have infinite resolution. The Gaussian solution is efficient for quantifying the advance of the pressure transient and associated pressure depletion around single wells, multiple wells and hydraulic fractures. This work lays the basis for the development of advanced reservoir simulations based on the superposition of analytical pressure transient solutions. This study revisits the mathematical equations for diffusive mass transport in 1D, 2D and 3D space and highlights a widespread misconception about the meaning of the regular and cumulative probability of random-walk solutions for diffusive mass transport. Next, the regular probability solution for molecular diffusion is applied to pressure diffusion in porous media. The pressure drop (by fluid extraction) or increase (by fluid injection) due to the production system may start with a simple pressure step function. The pressure perturbation imposed by the step function (representing the engineering intervention) will instantaneously diffuse into the reservoir at a rate that is controlled by the hydraulic diffusivity. Traditionally, the advance of the pressure transient in porous media such as geological reservoirs is modeled by two distinct approaches: (1) scalar equations for well performance testing that do not attempt to solve for the spatial change or the position of the pressure transient without reference to a well rate; (2) advanced reservoir models based on numerical solution methods. The Gaussian pressure transient solution method presented in this study can compute the spatial pressure depletion in the reservoir at arbitrary times and is based on analytical expressions that give spatial resolution without gridding-meaning solutions that have infinite resolution. The Gaussian solution is efficient for quantifying the advance of the pressure transient and associated pressure depletion around single wells, multiple wells and hydraulic fractures. This work lays the basis for the development of advanced reservoir simulations based on the superposition of analytical pressure transient solutions.
View full paperImproving Well Productivity – Ways to Reduce the Lag between the Diffusive and Convective Time of Flight in Shale Wells
This short communication explains how the key to improve shale well productivity lies in reducing the gap between the diffusive and convective time of flight. Diffusive time of flight in a hydrocarbon reservoir controls which reservoir regions will be affected by the pressure transient at a certain time after the onset of production. The convective time of flight is a measure of tracer front advance as well as for fluid withdrawal rates due to a well system draining the reservoir. The difference between the advance rate of a diffusive pressure front and a convective tracer front has been long recognized. However, only recently has it become clear that a thorough grasp of the two concepts is crucial for better decisions about fracture and well spacing in low permeability reservoirs. Although the diffusive time of flight is highlighted in the traditional pressure depletion models, the convective time of flight has a more direct impact on well productivity because it controls the advance rate, to the well system, of hydrocarbon fluids to be produced. The two concepts, diffusive and convective time of flight, are briefly highlighted below, with emphasis on their relevance for decision-making in shale field development solutions. This short communication explains how the key to improve shale well productivity lies in reducing the gap between the diffusive and convective time of flight. Diffusive time of flight in a hydrocarbon reservoir controls which reservoir regions will be affected by the pressure transient at a certain time after the onset of production. The convective time of flight is a measure of tracer front advance as well as for fluid withdrawal rates due to a well system draining the reservoir. The difference between the advance rate of a diffusive pressure front and a convective tracer front has been long recognized. However, only recently has it become clear that a thorough grasp of the two concepts is crucial for better decisions about fracture and well spacing in low permeability reservoirs. Although the diffusive time of flight is highlighted in the traditional pressure depletion models, the convective time of flight has a more direct impact on well productivity because it controls the advance rate, to the well system, of hydrocarbon fluids to be produced. The two concepts, diffusive and convective time of flight, are briefly highlighted below, with emphasis on their relevance for decision-making in shale field development solutions.
View full paperVariation in b-sigmoids with flow regime transitions in support of a New 3-Segment DCA Method: Improved Production Forecasting for tight oil and gas wells
This study uses a commercial reservoir simulator to generate production rate data for shale wells with systematic variations in fracture treatment design parameters using a plausible range of reservoir properties. The synthetic well data is then used to generate diagnostic log-rate log-time plots, which allow for a distinction of four types of flow regimes. Such a distinction of flow regimes is of practical relevance, because of the inverse link with reservoir properties and fracture treatment design parameters. Each flow regime has a characteristic slope, which traditionally has been attributed to typical flow conditions in the reservoir. The synthetic production data from the reservoir simulator are used to constrain b-sigmoid patterns for narrow discrete time increments of production (1 month) throughout the various flow regimes occurring during the economic life of each synthetic well model. Nearly a hundred different models were generated as a basis for our analysis. From the analysis of the DCA parameters for time series, using the difference in inverse of decline rates (loss ratio) for two adjacent time steps, it appears possible to recognize systematic shifts in the instantaneous decline rates and temporal b-values. In particular, the generated b-value patterns (b-sigmoids) appear diagnostic for flow regime changes recognized on diagnostic log-rate log-time plots. The results demonstrate that it is possible, based on well design and reservoir parameters, to establish correlation trends between b-sigmoids and flow regime changes using time series of the DCA parameters. The results are subsequently used to improve the accuracy of a modified 3-segment DCA method based on Arps equation. The proposed method is applied to synthetic production data, generated based on an Eagle Ford shale oil well (with known reservoir and fracture properties), to demonstrate the practical value for production forecasting and reserves estimation. This research paper paves the way for wider, future application of the methods described. This study uses a commercial reservoir simulator to generate production rate data for shale wells with systematic variations in fracture treatment design parameters using a plausible range of reservoir properties. The synthetic well data is then used to generate diagnostic log-rate log-time plots, which allow for a distinction of four types of flow regimes. Such a distinction of flow regimes is of practical relevance, because of the inverse link with reservoir properties and fracture treatment design parameters. Each flow regime has a characteristic slope, which traditionally has been attributed to typical flow conditions in the reservoir. The synthetic production data from the reservoir simulator are used to constrain b-sigmoid patterns for narrow discrete time increments of production (1 month) throughout the various flow regimes occurring during the economic life of each synthetic well model. Nearly a hundred different models were generated as a basis for our analysis. From the analysis of the DCA parameters for time series, using the difference in inverse of decline rates (loss ratio) for two adjacent time steps, it appears possible to recognize systematic shifts in the instantaneous decline rates and temporal b-values. In particular, the generated b-value patterns (b-sigmoids) appear diagnostic for flow regime changes recognized on diagnostic log-rate log-time plots. The results demonstrate that it is possible, based on well design and reservoir parameters, to establish correlation trends between b-sigmoids and flow regime changes using time series of the DCA parameters. The results are subsequently used to improve the accuracy of a modified 3-segment DCA method based on Arps equation. The proposed method is applied to synthetic production data, generated based on an Eagle Ford shale oil well (with known reservoir and fracture properties), to demonstrate the practical value for production forecasting and reserves estimation. This research paper paves the way for wider, future application of the methods described.
View full paperProduction Rates and EUR Forecasts for Interfering Parent-Parent Wells and Parent-Child Wells: Fast Analytical Solutions and Validation with Numerical Reservoir Simulators
Analytical expressions are given to forecast the production decline and estimated ultimate reserves (EUR) for pairs of both parent-parent wells and parent-child wells. The forecasts use physics-based flow rate quantification in elementary flow cells between hydraulic fractures sets. The intrinsic rate in the flow cells for a given shale formation can be obtained and scaled by a type curve specific for its completion and reservoir parameters. The model then can predict how changes in fracture treatment design parameters will affect the performance of new wells in the same target zone. The effect of well down-spacing and the onset of pressure interference on the performance of parent-parent wells can be forecasted with reasonable accuracy. Similarly, the equations can also predict the effect of infill drilling of child wells on the performance of both well types. The method is applied to real world examples from Eagle Ford acreage. The fast analytical model forecasts are benchmarked against the results from an independent numerical reservoir simulator, with satisfactory matches. The validated approach aims to provide a practical analytical tool for the production forecasting of multi-wells in shale formations. Analytical expressions are given to forecast the production decline and estimated ultimate reserves (EUR) for pairs of both parent-parent wells and parent-child wells. The forecasts use physics-based flow rate quantification in elementary flow cells between hydraulic fractures sets. The intrinsic rate in the flow cells for a given shale formation can be obtained and scaled by a type curve specific for its completion and reservoir parameters. The model then can predict how changes in fracture treatment design parameters will affect the performance of new wells in the same target zone. The effect of well down-spacing and the onset of pressure interference on the performance of parent-parent wells can be forecasted with reasonable accuracy. Similarly, the equations can also predict the effect of infill drilling of child wells on the performance of both well types. The method is applied to real world examples from Eagle Ford acreage. The fast analytical model forecasts are benchmarked against the results from an independent numerical reservoir simulator, with satisfactory matches. The validated approach aims to provide a practical analytical tool for the production forecasting of multi-wells in shale formations.
View full paperImproved EUR Prediction for Multi-Fractured Hydrocarbon Wells Based on 3-Segment DCA: Implication for Production Forecasting of Parent and Child Wells
A substantial number of methods has been proposed as part of the quest for better production forecasting and hence more accurate reserves estimations, especially for multi-fractured shale wells producing either gas or liquids (or both). However, none of the current methods stand out to be robust and practical enough to give reliable results for all field cases. The current study proposes a novel 3-segment decline curve analysis (DCA) method that uses the unique flow regime sequence of shale wells to delineate the periods for each of the three segments used in the DCA. The production data of 6 Eagle Ford wells (4 parents and 2 infills) was modeled with over 95% history matching quality. The proposed method, validated using hind-casting, proved to be extremely successful in predicting the production of the child wells, when production data is available from either parent wells or first generation child wells. The proposed method is based on the widely-used Arps’ equation and honors the principal flow regimes recognized in recent studies. The improved history matching capability of the proposed method leads to a much reliable production forecast. Hence, the uncertainty in the reserves estimations significantly reduces, which is why this study argues for conclusive categorization of the estimated reserves based on type curves of later generation parent wells as P90 (proved reserves) rather than P50 (proved plus probable reserves). A substantial number of methods has been proposed as part of the quest for better production forecasting and hence more accurate reserves estimations, especially for multi-fractured shale wells producing either gas or liquids (or both). However, none of the current methods stand out to be robust and practical enough to give reliable results for all field cases. The current study proposes a novel 3-segment decline curve analysis (DCA) method that uses the unique flow regime sequence of shale wells to delineate the periods for each of the three segments used in the DCA. The production data of 6 Eagle Ford wells (4 parents and 2 infills) was modeled with over 95% history matching quality. The proposed method, validated using hind-casting, proved to be extremely successful in predicting the production of the child wells, when production data is available from either parent wells or first generation child wells. The proposed method is based on the widely-used Arps’ equation and honors the principal flow regimes recognized in recent studies. The improved history matching capability of the proposed method leads to a much reliable production forecast. Hence, the uncertainty in the reserves estimations significantly reduces, which is why this study argues for conclusive categorization of the estimated reserves based on type curves of later generation parent wells as P90 (proved reserves) rather than P50 (proved plus probable reserves).
View full paperProbabilistic Techno-Economic Appraisal of Prospective Hydrocarbon Resources in Five Turbidites, Offshore Uruguay
This paper presents a probabilistic techno-economic evaluation of several turbidite prospects recognized, through 3D seismic, in deep to ultra-deep water of the Punta del Este and Pelotas sedimentary basins, offshore of Uruguay. The production potential of many prospective turbidite reservoirs on the Atlantic margin has been recognized before, and new turbidite prospects were identified in Uruguay’s maritime zone after analyzing data from the world’s deepest water-depth well (Raya-X1) drilled in 2016. The estimated ultimate recovery of oil and gas was determined, for each prospect, by carrying out probabilistic resource analyses (Monte Carlo simulations) using 3D seismic and key parameters from analog turbidite fields located in sedimentary basins along the Atlantic margin. Black oil fluid was assumed and the production concept involves FPSO vessels. The produced oil would be exported via tankers and the associated gas would be either sent to shore through a gas pipeline, or re-injected into the formation. For the economic evaluation, the latest fiscal terms of the applicable production-sharing contract, for offshore assets in Uruguay, were considered. The outcomes of the probabilistic economic analyses include, for each prospect, several key performance indicators such as: net present value, internal rate of return, maximum negative cash flow, breakeven oil price, government take and entitlement percentage of hydrocarbons. These indicators were determined after running Monte Carlo simulations, which considered probability distribution functions for fixed and variable capital and operational expenditures, along with well productivities and decline rates. Regarding the economics of the project, several scenarios of incremental profit oil for the government and maximum association percentage for ANCAP, the National Oil Company of Uruguay, were evaluated. The cases considered show how key negotiables and variables, featuring in the tender process offered to oil companies interested in Uruguay’s offshore hydrocarbon assets, may affect the economics and development solutions of a typical field development project. Considering a plausible base case of 20% ANCAP association and no incremental profit oil for the state, the results show that, for the biggest prospects, the breakeven oil price is situated near 60 USD/bbl. The analysis also shows that the smaller prospects would need to be developed as satellites of the nearby principal prospects in order to become attractive for development. This study sheds light on the exploration potential of turbidites, offshore of Uruguay, and analyzed resource volumes, production profiles and economic returns of a hypothetic development in the case of a commercial discovery. The analyses provide useful templates for international oil companies, which, under the new and more flexible Uruguay Open Round licensing regime, may be interested in the exploration and imminent development of the Uruguayan offshore sedimentary basins. This paper presents a probabilistic techno-economic evaluation of several turbidite prospects recognized, through 3D seismic, in deep to ultra-deep water of the Punta del Este and Pelotas sedimentary basins, offshore of Uruguay. The production potential of many prospective turbidite reservoirs on the Atlantic margin has been recognized before, and new turbidite prospects were identified in Uruguay’s maritime zone after analyzing data from the world’s deepest water-depth well (Raya-X1) drilled in 2016. The estimated ultimate recovery of oil and gas was determined, for each prospect, by carrying out probabilistic resource analyses (Monte Carlo simulations) using 3D seismic and key parameters from analog turbidite fields located in sedimentary basins along the Atlantic margin. Black oil fluid was assumed and the production concept involves FPSO vessels. The produced oil would be exported via tankers and the associated gas would be either sent to shore through a gas pipeline, or re-injected into the formation. For the economic evaluation, the latest fiscal terms of the applicable production-sharing contract, for offshore assets in Uruguay, were considered. The outcomes of the probabilistic economic analyses include, for each prospect, several key performance indicators such as: net present value, internal rate of return, maximum negative cash flow, breakeven oil price, government take and entitlement percentage of hydrocarbons. These indicators were determined after running Monte Carlo simulations, which considered probability distribution functions for fixed and variable capital and operational expenditures, along with well productivities and decline rates. Regarding the economics of the project, several scenarios of incremental profit oil for the government and maximum association percentage for ANCAP, the National Oil Company of Uruguay, were evaluated. The cases considered show how key negotiables and variables, featuring in the tender process offered to oil companies interested in Uruguay’s offshore hydrocarbon assets, may affect the economics and development solutions of a typical field development project. Considering a plausible base case of 20% ANCAP association and no incremental profit oil for the state, the results show that, for the biggest prospects, the breakeven oil price is situated near 60 USD/bbl. The analysis also shows that the smaller prospects would need to be developed as satellites of the nearby principal prospects in order to become attractive for development. This study sheds light on the exploration potential of turbidites, offshore of Uruguay, and analyzed resource volumes, production profiles and economic returns of a hypothetic development in the case of a commercial discovery. The analyses provide useful templates for international oil companies, which, under the new and more flexible Uruguay Open Round licensing regime, may be interested in the exploration and imminent development of the Uruguayan offshore sedimentary basins.
View full paperEconomic Appraisal and Scoping of Geothermal Extraction Projects using Depleted Hydrocarbon Wells
This study offers a first step in examining a potential solution for what to do with the ever-increasing number of horizontal shale wells in the United States (and lately, Argentina and China), as they come to the end of their economic life. A comprehensive decision-making tool was developed for scoping assessments based on the technical and economic appraisal of abandoned hydrocarbon wells repurposed into enhanced geothermal systems. We specifically target near end-of-life oil and gas wells, re-commissioned to extract geothermal energy as opposed to hydrocarbons, because these potential geothermal resources are prevalent near a handful of major US population and energy demand centers, including Pittsburgh, Houston, Denver, Dallas, Oklahoma City and San Antonio. This study addresses some of the technical challenges associated with such projects. However, the main focus is on (1) the probabilistic evaluation of the economic net present value, and (2) specific solutions for possible commercial deal structures required for negotiation and project implementation. The backdrop for the test case in this study is the new Texas A&M RELLIS Campus being constructed in College Station, Texas. A successful commercial model for the use of abandoned oil and gas wells to extract low and medium temperature geothermal resources could spur further development and a pilot study is proposed for this green source of energy. Our estimations suggest a net present value of $1.2 billion could be unlocked in the US alone, through the repurposing of wells, previously used for hydrocarbon extraction only. This study offers a first step in examining a potential solution for what to do with the ever-increasing number of horizontal shale wells in the United States (and lately, Argentina and China), as they come to the end of their economic life. A comprehensive decision-making tool was developed for scoping assessments based on the technical and economic appraisal of abandoned hydrocarbon wells repurposed into enhanced geothermal systems. We specifically target near end-of-life oil and gas wells, re-commissioned to extract geothermal energy as opposed to hydrocarbons, because these potential geothermal resources are prevalent near a handful of major US population and energy demand centers, including Pittsburgh, Houston, Denver, Dallas, Oklahoma City and San Antonio. This study addresses some of the technical challenges associated with such projects. However, the main focus is on (1) the probabilistic evaluation of the economic net present value, and (2) specific solutions for possible commercial deal structures required for negotiation and project implementation. The backdrop for the test case in this study is the new Texas A&M RELLIS Campus being constructed in College Station, Texas. A successful commercial model for the use of abandoned oil and gas wells to extract low and medium temperature geothermal resources could spur further development and a pilot study is proposed for this green source of energy. Our estimations suggest a net present value of $1.2 billion could be unlocked in the US alone, through the repurposing of wells, previously used for hydrocarbon extraction only.
View full paperBenchmarking EUR Estimates for Hydraulically Fractured Wells With and Without Fracture Hits Using Various DCA Methods
Various decline curve analysis (DCA) methods can be applied to forecast the production performance of hydrocarbon wells, including horizontal wells stimulated with hydraulic fracturing. Yet, which method is more preferable remains in doubt. The objective of this study is to evaluate various DCA methods by history matching and hindcasting both synthetic and field production data in order to assess for each method the reliability of production forecasts and the estimated ultimate recovery (EUR). Five DCA methods have been evaluated because of their computational simplicity and broad application. These methods are the Modified Hyperbolic Decline model (MHD), Duong model, Logistic Growth Analysis Model (LGM), and the Power Law Exponential (PLE, with and ) Decline models. Each method was evaluated using three data sets: synthetic shale oil production rates based on a CMG reservoir model using Eagle Ford reservoir characteristics, data from producing Eagle Ford wells and from Austin Chalk wells. The hindcast method was applied to the Eagle Ford synthetic wells to establish the EUR deviation between the synthetic reservoir model production forecast and the various DCA methods. The weighted residuals of history matched production rates for Eagle Ford indicate that the MHD and Duong models give the lowest matching errors (as low as 1.32%) and the highest EUR estimations (as high as 3,447,609 stb). The PLE model (with ) gives the most conservative EUR estimation, and also the least reliable history matching method (on our Eagle Ford data sets), which therefore is the least preferable DCA method. For the Austin Chalk wells in our study, all methods generate fairly similar EUR predictions with similar matching errors (from 13% to 15%) so that the DCA method preference becomes indifferent. This study also touches upon the relationship between DCA results when well interference occurs due to various hydraulic fracture hits. Shale wells that primarily contain hydraulic fractures and few natural fractures (Eagle Ford) give the most reliable forecasts using the MHD and Duong DCA methods. However, wells in the Austin Chalk, a naturally fractured reservoir, show little difference between the forecast accuracy from the various DCA methods. Various decline curve analysis (DCA) methods can be applied to forecast the production performance of hydrocarbon wells, including horizontal wells stimulated with hydraulic fracturing. Yet, which method is more preferable remains in doubt. The objective of this study is to evaluate various DCA methods by history matching and hindcasting both synthetic and field production data in order to assess for each method the reliability of production forecasts and the estimated ultimate recovery (EUR). Five DCA methods have been evaluated because of their computational simplicity and broad application. These methods are the Modified Hyperbolic Decline model (MHD), Duong model, Logistic Growth Analysis Model (LGM), and the Power Law Exponential (PLE, with and ) Decline models. Each method was evaluated using three data sets: synthetic shale oil production rates based on a CMG reservoir model using Eagle Ford reservoir characteristics, data from producing Eagle Ford wells and from Austin Chalk wells. The hindcast method was applied to the Eagle Ford synthetic wells to establish the EUR deviation between the synthetic reservoir model production forecast and the various DCA methods. The weighted residuals of history matched production rates for Eagle Ford indicate that the MHD and Duong models give the lowest matching errors (as low as 1.32%) and the highest EUR estimations (as high as 3,447,609 stb). The PLE model (with ) gives the most conservative EUR estimation, and also the least reliable history matching method (on our Eagle Ford data sets), which therefore is the least preferable DCA method. For the Austin Chalk wells in our study, all methods generate fairly similar EUR predictions with similar matching errors (from 13% to 15%) so that the DCA method preference becomes indifferent. This study also touches upon the relationship between DCA results when well interference occurs due to various hydraulic fracture hits. Shale wells that primarily contain hydraulic fractures and few natural fractures (Eagle Ford) give the most reliable forecasts using the MHD and Duong DCA methods. However, wells in the Austin Chalk, a naturally fractured reservoir, show little difference between the forecast accuracy from the various DCA methods.
View full paperEconomic Benchmark of Deepwater field development projects in the Perdido fold belt at either side of the U.S.-Mexico Transboundary Zone: Which fiscal regime offers the most competitive return on investment?
Development of Mexican hydrocarbon reservoirs by foreign operators is now made possible by the energy reforms implemented in 2015. This study benchmarks the economic return of deepwater hydrocarbon field development projects located in the Perdido foldbelt at either side of the maritime border between the United States and Mexico to assess the competitiveness of the respective fiscal frameworks. We use a nodal analysis production model to first history match real field performance in the US Perdido project and then forecast production of an analogous, undeveloped field in the Mexican extension of the Perdido foldbelt, Gulf of Mexico. The new Mexican profit sharing contract imposes basic royalties that appear equitable for both the contractor and the government, albeit slightly less attractive than the to the U.S. federal lease terms. The contracts for deepwater assets in Mexico open up commercially viable options, provided the oil price will recover to render such oil projects profitable. Our sensitivity analysis shows that profitable development of 300 MMbbls oil in place becomes possible when oil prices rise above $75/bbl. For larger reservoirs (~900 MMbbls) the profit hurdle rate of 15% is already met for $60/bbl. Any over-royalty offered by a contractor in the bidding process renders the royalties in Mexican operations slightly higher than in the U.S. Development of Mexican hydrocarbon reservoirs by foreign operators is now made possible by the energy reforms implemented in 2015. This study benchmarks the economic return of deepwater hydrocarbon field development projects located in the Perdido foldbelt at either side of the maritime border between the United States and Mexico to assess the competitiveness of the respective fiscal frameworks. We use a nodal analysis production model to first history match real field performance in the US Perdido project and then forecast production of an analogous, undeveloped field in the Mexican extension of the Perdido foldbelt, Gulf of Mexico. The new Mexican profit sharing contract imposes basic royalties that appear equitable for both the contractor and the government, albeit slightly less attractive than the to the U.S. federal lease terms. The contracts for deepwater assets in Mexico open up commercially viable options, provided the oil price will recover to render such oil projects profitable. Our sensitivity analysis shows that profitable development of 300 MMbbls oil in place becomes possible when oil prices rise above $75/bbl. For larger reservoirs (~900 MMbbls) the profit hurdle rate of 15% is already met for $60/bbl. Any over-royalty offered by a contractor in the bidding process renders the royalties in Mexican operations slightly higher than in the U.S.
View full paperRe-appraisal of the Bakken Shale Play: Accounting for Historic and Future Oil Prices and applying Fiscal Rates in North Dakota, Montana and Saskatchewan
The ascent of the Bakken shale play as a major U.S. oil producer became threatened by the 2014–2016 oil price fall. This benchmark study assesses and compares the economic performance of typical Bakken wells across three different fiscal regimes: North Dakota (ND) and Montana (MT) in the U.S., and the Canadian province of Saskatchewan (SK). Decline curve analysis and discounted cash flow analysis are applied to evaluate and re-appraise both the productivity and economic performance (internal rate of return, IRR) of typical Bakken wells in each region. For wells of similar estimated ultimate recovery (EUR), the fiscal regime of Montana (IRR 27%) is slightly more advantageous than North Dakota’s (IRR 24%). If wells can be identified in SK akin to ND’s reference well of 555 Mbbls EUR, the Canadian province provides the most attractive after tax return (180%). However, type curves for Bakken wells in SK and MT analyzed in our study typically have EURs at only 14% and 37% of the ND reference well (EUR∼555 Mbbls) and IRRs adjusted for EUR in MT and SK are negative in both regions at the historic reference price of $80/bbl. A sensitivity analysis using oil prices ranging between $20–100/bbl accounts for any of the price levels seen in the 2014–2016 price fall, and can be projected forward. The evaluation of single well economics and sensitivity to oil price changes and drilling and completion cost is subsequently expanded with a representative firm approach considering certain asset development options with multiple wells in each of the three Bakken jurisdictions (ND, MT, SK). The ascent of the Bakken shale play as a major U.S. oil producer became threatened by the 2014–2016 oil price fall. This benchmark study assesses and compares the economic performance of typical Bakken wells across three different fiscal regimes: North Dakota (ND) and Montana (MT) in the U.S., and the Canadian province of Saskatchewan (SK). Decline curve analysis and discounted cash flow analysis are applied to evaluate and re-appraise both the productivity and economic performance (internal rate of return, IRR) of typical Bakken wells in each region. For wells of similar estimated ultimate recovery (EUR), the fiscal regime of Montana (IRR 27%) is slightly more advantageous than North Dakota’s (IRR 24%). If wells can be identified in SK akin to ND’s reference well of 555 Mbbls EUR, the Canadian province provides the most attractive after tax return (180%). However, type curves for Bakken wells in SK and MT analyzed in our study typically have EURs at only 14% and 37% of the ND reference well (EUR∼555 Mbbls) and IRRs adjusted for EUR in MT and SK are negative in both regions at the historic reference price of $80/bbl. A sensitivity analysis using oil prices ranging between $20–100/bbl accounts for any of the price levels seen in the 2014–2016 price fall, and can be projected forward. The evaluation of single well economics and sensitivity to oil price changes and drilling and completion cost is subsequently expanded with a representative firm approach considering certain asset development options with multiple wells in each of the three Bakken jurisdictions (ND, MT, SK).
View full paperEagle Ford Shale Play Economics: U.S. versus Mexico
The decline of domestic natural gas supply and rising demand requires Mexico to import 1/3 of its annual gas consumption of 2.5 trillion cubic feet (Tcf). Yet, Mexico’s estimated resource of technically recoverable shale gas (545 Tcf) is the 6th largest such gas resource in the World. Much of Mexico’s shale gas resource is in the Eagle Ford Shale, which is a mature shale gas and oil play in the U.S. To aid in determination of whether development of the Eagle Ford Shale in Mexico could reduce the country’s dependency on natural gas imports, we evaluated the potential of Mexican shale acreage by comparing the after-tax net present value (NPV) and internal rate of return (IRR) of Eagle Ford shale wells on either side of the U.S.-Mexico border. The initial development of Mexican acreage occurs with a much larger well-spacing (leading to higher acreage acquisition cost per well), which would require 25% higher development cost as compared to Texas acreage. Consequentially, Texas wells have better net present value (NPV) and higher internal rate of return (IRR) than Mexican wells, in general. The principal explanation is that the signing bonus will be much higher in Mexico than in Texas, partly effectuated by the lower well spacing for unrisked acreage. Results of our study provide potential operators and investors with a preliminary indication of Eagle Ford Shale well economics in Mexico. Our study includes sensitivity analyses for both non-escalated and escalated gas prices, for drilling and completion (D&C) costs, and for leasehold cost. The economic appraisal accounts for both single- and multiple-well development scenarios with P10, P50 and P90 production forecasts. The decline of domestic natural gas supply and rising demand requires Mexico to import 1/3 of its annual gas consumption of 2.5 trillion cubic feet (Tcf). Yet, Mexico’s estimated resource of technically recoverable shale gas (545 Tcf) is the 6th largest such gas resource in the World. Much of Mexico’s shale gas resource is in the Eagle Ford Shale, which is a mature shale gas and oil play in the U.S. To aid in determination of whether development of the Eagle Ford Shale in Mexico could reduce the country’s dependency on natural gas imports, we evaluated the potential of Mexican shale acreage by comparing the after-tax net present value (NPV) and internal rate of return (IRR) of Eagle Ford shale wells on either side of the U.S.-Mexico border. The initial development of Mexican acreage occurs with a much larger well-spacing (leading to higher acreage acquisition cost per well), which would require 25% higher development cost as compared to Texas acreage. Consequentially, Texas wells have better net present value (NPV) and higher internal rate of return (IRR) than Mexican wells, in general. The principal explanation is that the signing bonus will be much higher in Mexico than in Texas, partly effectuated by the lower well spacing for unrisked acreage. Results of our study provide potential operators and investors with a preliminary indication of Eagle Ford Shale well economics in Mexico. Our study includes sensitivity analyses for both non-escalated and escalated gas prices, for drilling and completion (D&C) costs, and for leasehold cost. The economic appraisal accounts for both single- and multiple-well development scenarios with P10, P50 and P90 production forecasts.
View full paperEconomic appraisal of shale plays in Continental Europe
Development of Mexican hydrocarbon reservoirs by foreign operators has become possible under Mexico’s new Hydrocarbon Law, effective as per January 2015. Our study compares the economic returns of shallow water fields in the Gulf of Mexico applying the royalty and taxes due under the fiscal regimes of the U.S. and Mexico. The net present value (NPV) of the base case scenario is US$1.4 billion, assuming standard development and production cost (opex, capex), 10% discount rate accounting for the cost of capital and revenues computed using a reference oil price of $75/bbl. The impact on NPV of oil price volatility is accounted for in a sensitivity analysis. The split of the NPV of shallow water hydrocarbon assets between the two contractual parties, contractor and government, in Mexico and the U.S. is hugely different. Our base case shows that for similar field assets, Mexico’s production sharing agreement allocates about $1,150 million to the government and $191 million to the contractor, while under U.S. license conditions the government take is about $700 million and contractor take is $553 million. The current production sharing agreement leaves some marginal shallow water fields in Mexico undeveloped for reasons detailed and quantified in our study. Development of Mexican hydrocarbon reservoirs by foreign operators has become possible under Mexico’s new Hydrocarbon Law, effective as per January 2015. Our study compares the economic returns of shallow water fields in the Gulf of Mexico applying the royalty and taxes due under the fiscal regimes of the U.S. and Mexico. The net present value (NPV) of the base case scenario is US$1.4 billion, assuming standard development and production cost (opex, capex), 10% discount rate accounting for the cost of capital and revenues computed using a reference oil price of $75/bbl. The impact on NPV of oil price volatility is accounted for in a sensitivity analysis. The split of the NPV of shallow water hydrocarbon assets between the two contractual parties, contractor and government, in Mexico and the U.S. is hugely different. Our base case shows that for similar field assets, Mexico’s production sharing agreement allocates about $1,150 million to the government and $191 million to the contractor, while under U.S. license conditions the government take is about $700 million and contractor take is $553 million. The current production sharing agreement leaves some marginal shallow water fields in Mexico undeveloped for reasons detailed and quantified in our study.
View full paperCompetitiveness of shallow water hydrocarbon development projects in Mexico after 2015 actualization of fiscal reforms: Economic benchmark of new production sharing agreement versus typical U.S. federal lease terms
Development of Mexican hydrocarbon reservoirs by foreign operators has become possible under Mexico’s new Hydrocarbon Law, effective as per January 2015. Our study compares the economic returns of shallow water fields in the Gulf of Mexico applying the royalty and taxes due under the fiscal regimes of the U.S. and Mexico. The net present value (NPV) of the base case scenario is US$1.4 billion, assuming standard development and production cost (opex, capex), 10% discount rate accounting for the cost of capital and revenues computed using a reference oil price of $75/bbl. The impact on NPV of oil price volatility is accounted for in a sensitivity analysis. The split of the NPV of shallow water hydrocarbon assets between the two contractual parties, contractor and government, in Mexico and the U.S. is hugely different. Our base case shows that for similar field assets, Mexico’s production sharing agreement allocates about $1,150 million to the government and $191 million to the contractor, while under U.S. license conditions the government take is about $700 million and contractor take is $553 million. The current production sharing agreement leaves some marginal shallow water fields in Mexico undeveloped for reasons detailed and quantified in our study. Development of Mexican hydrocarbon reservoirs by foreign operators has become possible under Mexico’s new Hydrocarbon Law, effective as per January 2015. Our study compares the economic returns of shallow water fields in the Gulf of Mexico applying the royalty and taxes due under the fiscal regimes of the U.S. and Mexico. The net present value (NPV) of the base case scenario is US$1.4 billion, assuming standard development and production cost (opex, capex), 10% discount rate accounting for the cost of capital and revenues computed using a reference oil price of $75/bbl. The impact on NPV of oil price volatility is accounted for in a sensitivity analysis. The split of the NPV of shallow water hydrocarbon assets between the two contractual parties, contractor and government, in Mexico and the U.S. is hugely different. Our base case shows that for similar field assets, Mexico’s production sharing agreement allocates about $1,150 million to the government and $191 million to the contractor, while under U.S. license conditions the government take is about $700 million and contractor take is $553 million. The current production sharing agreement leaves some marginal shallow water fields in Mexico undeveloped for reasons detailed and quantified in our study.
View full paperUS shale gas production outlook based on well roll-out rate scenarios
This study models the uncertainty range in the future gas production output from US shale plays up to 2025. The future spread in gas output in our models follows from variations in the number of wells that will be drilled according to three distinct scenarios. Each scenario assumes a well development plan for the six major shale plays over the studied period and then quantifies the cumulative US production output from the combined shale plays. We compare the bottom-up model results with other model projections for future US shale gas output, including the top-down shale gas production forecasts by the US National Energy Modeling System (NEMS). The remarkable growth of North American gas output from unconventional resources has been highlighted in numerous industry reports and government publications, but what has remained relatively underexposed is the deterioration of economic margins due to the failure to predict the gas price decline in the North American market. The past development record of North America’s shale gas resources suggests that security of future gas supplies seems ensured, but here we develop a contrarian view. Our scenario models take into account the effect of recent declines in gas rig counts and decline in gas well completions due to the depressed gas prices. A scenario with declining shale gas output – one of three scenarios considered – cannot be excluded as being unlikely to occur, which means the future security of US gas supply that assumes a steady growth of shale gas supply cannot be ascertained at present. This study models the uncertainty range in the future gas production output from US shale plays up to 2025. The future spread in gas output in our models follows from variations in the number of wells that will be drilled according to three distinct scenarios. Each scenario assumes a well development plan for the six major shale plays over the studied period and then quantifies the cumulative US production output from the combined shale plays. We compare the bottom-up model results with other model projections for future US shale gas output, including the top-down shale gas production forecasts by the US National Energy Modeling System (NEMS). The remarkable growth of North American gas output from unconventional resources has been highlighted in numerous industry reports and government publications, but what has remained relatively underexposed is the deterioration of economic margins due to the failure to predict the gas price decline in the North American market. The past development record of North America’s shale gas resources suggests that security of future gas supplies seems ensured, but here we develop a contrarian view. Our scenario models take into account the effect of recent declines in gas rig counts and decline in gas well completions due to the depressed gas prices. A scenario with declining shale gas output – one of three scenarios considered – cannot be excluded as being unlikely to occur, which means the future security of US gas supply that assumes a steady growth of shale gas supply cannot be ascertained at present.
View full paperAssessing the economic margins of sweet spots in shale gas plays
Ruud Weijermars and Joost van der Linden outline a new reality for shale gas plays where even sweet spots may become sub-economic when gas prices collapse. The North American shale-gas bonanza is reviewed and sweet spot sensitivity to gas price volatility is illustrated for the Haynesville shale play. The second part of this article will follow in the January issue. Ruud Weijermars and Joost van der Linden outline a new reality for shale gas plays where even sweet spots may become sub-economic when gas prices collapse. The North American shale-gas bonanza is reviewed and sweet spot sensitivity to gas price volatility is illustrated for the Haynesville shale play. The second part of this article will follow in the January issue.
View full paperJumps in proved unconventional gas reserves present challenges to reserves auditing
Summary This study analyzes the typical challenges and opportunities related to unconventional-gas-reserves maturation and asset performance. Volatility in natural-gas prices may lead to downgrading of formerly proved reserves when the marginal cost of production cannot be sustained by the wellhead prices realized. New US Security and Exchange Commission (SEC) rules have accelerated the growth of unconventional-gas reserves, which in a way is an additional but unintended source of volatility and hence risk. Concerns about security of investments in unconventional-gas assets are fuelled by the effects of volatile natural-gas prices on production economics and by uncertainty about stability of reported reserves. This concern is exacerbated by an unprecedented rise in proved undeveloped gas reserves (PUDs) reported by unconventional-gas operators, arguably effectuated by favorable interpretations of PUDs when applying the new SEC accounting rules. This study includes a benchmark of proved reserves reported by two peer groups, each comprising four representative companies. The peer group of conventional companies includes Exxon, Chevron, Shell, and BP, and the unconventional peer group is made up of Chesapeake, Petrohawk, Devon, and EOG. Possible sources of undue uncertainty in reported reserves are highlighted, and recommendations are given to improve the reliability of reported reserves, especially from unconventional field assets. Summary This study analyzes the typical challenges and opportunities related to unconventional-gas-reserves maturation and asset performance. Volatility in natural-gas prices may lead to downgrading of formerly proved reserves when the marginal cost of production cannot be sustained by the wellhead prices realized. New US Security and Exchange Commission (SEC) rules have accelerated the growth of unconventional-gas reserves, which in a way is an additional but unintended source of volatility and hence risk. Concerns about security of investments in unconventional-gas assets are fuelled by the effects of volatile natural-gas prices on production economics and by uncertainty about stability of reported reserves. This concern is exacerbated by an unprecedented rise in proved undeveloped gas reserves (PUDs) reported by unconventional-gas operators, arguably effectuated by favorable interpretations of PUDs when applying the new SEC accounting rules. This study includes a benchmark of proved reserves reported by two peer groups, each comprising four representative companies. The peer group of conventional companies includes Exxon, Chevron, Shell, and BP, and the unconventional peer group is made up of Chesapeake, Petrohawk, Devon, and EOG. Possible sources of undue uncertainty in reported reserves are highlighted, and recommendations are given to improve the reliability of reported reserves, especially from unconventional field assets.
View full paperUnconventional Natural Gas Business: TSR Benchmark and Recommendations for Prudent Management of Shareholder Value
Summary Stock-listed independents have played a leading role in the development of unconventional natural-gas resources in the United States and Canada. Shareholders have provided up to 57% of the total capital tied up in a representative panel comprising the 20 leading US and Canadian operators. The accumulated equity-financed capital also provided the collateral for the complementary 43% debt financing. Prudent management of shareholder value in unconventional-gas businesses is therefore essential for ensuring security of gas supply, not only in North America, but also in other countries with emergent unconventional gas plays. This study analyzes and benchmarks the working capital cycles in unconventional-gas companies. The working capital and cashflow cycles are compared with those of diversified oil and gas majors. The ability to accumulate retained earnings is generally much lower for unconventional-gas producers than for integrated majors. Unconventional-gas producers tend to grow their share capital by new issues and not from economic value added by profit from business operations. Although little or no asset value is built from economic profit, shareholder returns may still grow for unconventional-gas companies as long as investor expectations remain positive about future earnings. In contrast, shareholder returns in conventional-gas companies come from genuine economic value added in profitable business operations. The root cause of the weakness or absence of operational profits in unconventional-gas operations is a combination of low gas prices and well flow rates that are too modest to pay for the total cost of the unconventional-gas production. The operating margins for unconventional-gas companies are either close to zero or negative, but not for the integrated oil and gas majors, which have impressive cash margins even at globally suppressed gas prices. The benchmarks provided here help one to understand which parameters impact the financial performance of unconventional-natural-gas companies most significantly. Recommendations are formulated to avoid the destruction of shareholder value, and to instead maximize total shareholder returns (TSRs). Summary Stock-listed independents have played a leading role in the development of unconventional natural-gas resources in the United States and Canada. Shareholders have provided up to 57% of the total capital tied up in a representative panel comprising the 20 leading US and Canadian operators. The accumulated equity-financed capital also provided the collateral for the complementary 43% debt financing. Prudent management of shareholder value in unconventional-gas businesses is therefore essential for ensuring security of gas supply, not only in North America, but also in other countries with emergent unconventional gas plays. This study analyzes and benchmarks the working capital cycles in unconventional-gas companies. The working capital and cashflow cycles are compared with those of diversified oil and gas majors. The ability to accumulate retained earnings is generally much lower for unconventional-gas producers than for integrated majors. Unconventional-gas producers tend to grow their share capital by new issues and not from economic value added by profit from business operations. Although little or no asset value is built from economic profit, shareholder returns may still grow for unconventional-gas companies as long as investor expectations remain positive about future earnings. In contrast, shareholder returns in conventional-gas companies come from genuine economic value added in profitable business operations. The root cause of the weakness or absence of operational profits in unconventional-gas operations is a combination of low gas prices and well flow rates that are too modest to pay for the total cost of the unconventional-gas production. The operating margins for unconventional-gas companies are either close to zero or negative, but not for the integrated oil and gas majors, which have impressive cash margins even at globally suppressed gas prices. The benchmarks provided here help one to understand which parameters impact the financial performance of unconventional-natural-gas companies most significantly. Recommendations are formulated to avoid the destruction of shareholder value, and to instead maximize total shareholder returns (TSRs).
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