Design of Experiments (DoE) is one of the most commonly employed techniques in the petroleum industry for Assisted History Matching (AHM) and uncertainty analysis of reservoir production forecasts. Although conceptually straightforward, DoE is often misused by practitioners because many of its statistical and modeling principles are not carefully followed. Our earlier paper (Li et al. 2019) detailed the best practices in DoE-based AHM for brownfields. However, to our best knowledge, there is a lack of studies that summarize the common caveats and pitfalls in DoE-based production forecast uncertainty analysis for greenfields and history-matched brownfields. Our objective here is to summarize these caveats and pitfalls to help practitioners apply the correct principles for DoE-based production forecast uncertainty analysis. Over 60 common pitfalls in all stages of a DoE workflow are summarized. Special attention is paid to the following critical project transitions: (1) the transition from static earth modeling to dynamic reservoir simulation; (2) from AHM to production forecast; and (3) from analyzing subsurface uncertainties to analyzing field-development alternatives. Most pitfalls can be avoided by consistently following the statistical and modeling principles. Some pitfalls, however, can trap experienced engineers. For example, mistakes made in handling the three abovementioned transitions can yield strongly unreliable proxy and sensitivity analysis. For the representative examples we study, they can lead to having a proxy R2 of less than 0.2 versus larger than 0.9 if done correctly. Two improved experimental designs are created to resolve this challenge. Besides the technical pitfalls that are avoidable via robust statistical workflows, we also highlight the often more severe non-technical pitfalls that cannot be evaluated by measures like R2. Thoughts are shared on how they can be avoided, especially during project framing and the three critical transition scenarios.
实验设计(DoE)是石油工业中最常用的辅助历史匹配(AHM)和油藏生产预测不确定性分析技术之一。尽管在概念上很简单，但是DoE经常被从业者误用，因为它的许多统计和建模原则没有被仔细遵循。我们之前的论文(Li et al. 2019)详细介绍了棕地基于doe AHM的最佳实践。然而，据我们所知，目前还缺乏总结基于doe的绿地和历史匹配棕地产量预测不确定性分析的常见警告和缺陷的研究。我们在这里的目标是总结这些警告和陷阱，以帮助从业者应用基于doe的生产预测不确定性分析的正确原则。总结了DoE工作流程各个阶段的60多个常见陷阱。特别注意以下几个关键的项目过渡:(1)从静态地球模拟到动态油藏模拟的过渡;(2)从AHM到生产预测;(3)从地下不确定性分析到油田开发方案分析。通过始终遵循统计和建模原则，可以避免大多数陷阱。然而，一些陷阱可能会让经验丰富的工程师陷入困境。例如，在处理上述三种转换时所犯的错误可能会产生非常不可靠的代理和敏感性分析。对于我们研究的代表性示例，如果操作正确，它们可能导致代理R2小于0.2而大于0.9。两个改进的实验设计被创建来解决这个挑战。除了可以通过健壮的统计工作流程避免的技术缺陷之外，我们还强调了通常更严重的非技术缺陷，这些缺陷不能通过像R2这样的度量来评估。我们分享了如何避免它们的想法，特别是在项目框架和三个关键的转换场景期间。
{"title":"Caveats and Pitfalls of Production Forecast Uncertainty Analysis Using Design of Experiments","authors":"Boxiao Li, Hemant Ashok Phale, Yanfen Zhang, T. Tokar, X. Wen","doi":"10.2118/203919-ms","DOIUrl":"https://doi.org/10.2118/203919-ms","url":null,"abstract":"\u0000 Design of Experiments (DoE) is one of the most commonly employed techniques in the petroleum industry for Assisted History Matching (AHM) and uncertainty analysis of reservoir production forecasts. Although conceptually straightforward, DoE is often misused by practitioners because many of its statistical and modeling principles are not carefully followed. Our earlier paper (Li et al. 2019) detailed the best practices in DoE-based AHM for brownfields. However, to our best knowledge, there is a lack of studies that summarize the common caveats and pitfalls in DoE-based production forecast uncertainty analysis for greenfields and history-matched brownfields. Our objective here is to summarize these caveats and pitfalls to help practitioners apply the correct principles for DoE-based production forecast uncertainty analysis.\u0000 Over 60 common pitfalls in all stages of a DoE workflow are summarized. Special attention is paid to the following critical project transitions: (1) the transition from static earth modeling to dynamic reservoir simulation; (2) from AHM to production forecast; and (3) from analyzing subsurface uncertainties to analyzing field-development alternatives. Most pitfalls can be avoided by consistently following the statistical and modeling principles. Some pitfalls, however, can trap experienced engineers. For example, mistakes made in handling the three abovementioned transitions can yield strongly unreliable proxy and sensitivity analysis. For the representative examples we study, they can lead to having a proxy R2 of less than 0.2 versus larger than 0.9 if done correctly. Two improved experimental designs are created to resolve this challenge.\u0000 Besides the technical pitfalls that are avoidable via robust statistical workflows, we also highlight the often more severe non-technical pitfalls that cannot be evaluated by measures like R2. Thoughts are shared on how they can be avoided, especially during project framing and the three critical transition scenarios.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86660290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
X. Guan, Gary Li, Hanming Wang, Shubo Shang, T. Tokar, Kevin McVey, C. Ovalles, Dagang Wu, Ji Chen
Radio frequency (RF) heating is recognized as a technique having the potential to thermally enhance remediation of hydrocarbon-impacted soil. RF heating delivers electromagnetic (EM) power to a targeted body of soil, resulting in an increased soil temperature that enhances the in-situ remediation processes such as biodegradation. Antennas are placed either on the ground or installed in the soil near the ground surface. The antennas operate in the hundreds of kHz to MHz range. To model the RF heating process, we successfully coupled a reservoir simulator with a 3-dimensional (3D) EM solver to evaluate the ability of RF technology to heat soil in situ. The coupled reservoir/EM simulator solves the EM fields and associated heating for a heterogeneous reservoir or soil volume in the presence of multiple antennas. The coupling was accomplished through a flexible interface in the reservoir simulator that allows the runtime loading of third-party software libraries with additional physics. This coupled workflow had been previously used for studying RF heating for heavy oil recovery (Li 2019). An RF heating simulation case study was performed in support of a soil remediation field test designed to demonstrate the ability to heat soils using EM energy. The study included field test data analysis, simulation model building, and history matching the model to test data. Results indicate, on average, the soil was heated ∼2-3°C above the initial formation temperature after approximately two days (52 hours) of RF heating. We found that the RF heating was local, and our simulation model, after tuning input parameters, was able to predict a temperature profile consistent with the field test observations. With properly designed RF heating field pilots and tuning of EM and reservoir parameters in simulation models, the coupled reservoir/EM simulator is a powerful tool for the calibration, evaluation, and optimization of RF heating operations.
{"title":"Radio Frequency Heating Simulation Using A Reservoir Simulator Coupled with Electromagnetic Solver for Soil Remediation","authors":"X. Guan, Gary Li, Hanming Wang, Shubo Shang, T. Tokar, Kevin McVey, C. Ovalles, Dagang Wu, Ji Chen","doi":"10.2118/204003-ms","DOIUrl":"https://doi.org/10.2118/204003-ms","url":null,"abstract":"\u0000 Radio frequency (RF) heating is recognized as a technique having the potential to thermally enhance remediation of hydrocarbon-impacted soil. RF heating delivers electromagnetic (EM) power to a targeted body of soil, resulting in an increased soil temperature that enhances the in-situ remediation processes such as biodegradation. Antennas are placed either on the ground or installed in the soil near the ground surface. The antennas operate in the hundreds of kHz to MHz range.\u0000 To model the RF heating process, we successfully coupled a reservoir simulator with a 3-dimensional (3D) EM solver to evaluate the ability of RF technology to heat soil in situ. The coupled reservoir/EM simulator solves the EM fields and associated heating for a heterogeneous reservoir or soil volume in the presence of multiple antennas. The coupling was accomplished through a flexible interface in the reservoir simulator that allows the runtime loading of third-party software libraries with additional physics. This coupled workflow had been previously used for studying RF heating for heavy oil recovery (Li 2019).\u0000 An RF heating simulation case study was performed in support of a soil remediation field test designed to demonstrate the ability to heat soils using EM energy. The study included field test data analysis, simulation model building, and history matching the model to test data. Results indicate, on average, the soil was heated ∼2-3°C above the initial formation temperature after approximately two days (52 hours) of RF heating. We found that the RF heating was local, and our simulation model, after tuning input parameters, was able to predict a temperature profile consistent with the field test observations. With properly designed RF heating field pilots and tuning of EM and reservoir parameters in simulation models, the coupled reservoir/EM simulator is a powerful tool for the calibration, evaluation, and optimization of RF heating operations.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88709675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Physics Inspired Machine Learning (PIML) is emerging as a viable numerical method to solve partial differential equations (PDEs). Recently, the method has been successfully tested and validated to find solutions to both linear and non-linear PDEs. To our knowledge, no prior studies have examined the PIML method in terms of their reliability and capability to handle reservoir engineering boundary conditions, fractures, source and sink terms. Here we explored the potential of PIML for modelling 2D single phase, incompressible, and steady state fluid flow in porous media. The main idea of PIML approaches is to encode the underlying physical law (governing equations, boundary, source and sink constraints) into the deep neural network as prior information. The capability of the PIML method in handling reservoir engineering boundary including no-flow, constant pressure, and mixed reservoir boundary conditions is investigated. The results show that the PIML performs well, giving good results comparable to analytical solution. Further, we examined the potential of PIML approach in handling fluxes (sink and source terms). Our results demonstrate that the PIML fail to provide acceptable prediction for no-flow boundary conditions. However, it provides acceptable predictions for constant pressure boundary conditions. We also assessed the capability of the PIML method in handling fractures. The results indicate that the PIML can provide accurate predictions for parallel fractures subjected to no-flow boundary. However, in complex fractures scenario its accuracy is limited to constant pressure boundary conditions. We also found that mixed and adaptive activation functions improve the performance of PIML for modeling complex fractures and fluxes.
{"title":"Physics Inspired Machine Learning for Solving Fluid Flow in Porous Media: A Novel Computational Algorithm for Reservoir Simulation","authors":"C. Sambo, Yin Feng","doi":"10.2118/203917-ms","DOIUrl":"https://doi.org/10.2118/203917-ms","url":null,"abstract":"\u0000 The Physics Inspired Machine Learning (PIML) is emerging as a viable numerical method to solve partial differential equations (PDEs). Recently, the method has been successfully tested and validated to find solutions to both linear and non-linear PDEs. To our knowledge, no prior studies have examined the PIML method in terms of their reliability and capability to handle reservoir engineering boundary conditions, fractures, source and sink terms. Here we explored the potential of PIML for modelling 2D single phase, incompressible, and steady state fluid flow in porous media.\u0000 The main idea of PIML approaches is to encode the underlying physical law (governing equations, boundary, source and sink constraints) into the deep neural network as prior information.\u0000 The capability of the PIML method in handling reservoir engineering boundary including no-flow, constant pressure, and mixed reservoir boundary conditions is investigated. The results show that the PIML performs well, giving good results comparable to analytical solution. Further, we examined the potential of PIML approach in handling fluxes (sink and source terms). Our results demonstrate that the PIML fail to provide acceptable prediction for no-flow boundary conditions. However, it provides acceptable predictions for constant pressure boundary conditions.\u0000 We also assessed the capability of the PIML method in handling fractures. The results indicate that the PIML can provide accurate predictions for parallel fractures subjected to no-flow boundary. However, in complex fractures scenario its accuracy is limited to constant pressure boundary conditions. We also found that mixed and adaptive activation functions improve the performance of PIML for modeling complex fractures and fluxes.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82784159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. A. B. Reveron, H. Holm, O. Møyner, S. Krogstad, Knut-Andreas Lie
The Ensemble Smoother with Multiple Data Assimilation (ES-MDA) method has been popular for petroleum reservoir history matching. However, the increasing inclusion of automatic differentiation in reservoir models opens the possibility to history-match models using gradient-based optimization. Here, we discuss, study, and compare ES-MDA and a gradient-based optimization for history-matching waterflooding models. We apply these two methods to history match reduced GPSNet-type models. To study the methods, we use an implementation of ES-MDA and a gradient-based optimization in the open-source MATLAB Reservoir Simulation Toolbox (MRST), and compare the methods in terms of history-matching quality and computational efficiency. We show complementary advantages of both ES-MDA and gradient-based optimization. ES-MDA is suitable when an exact gradient is not available and provides a satisfactory forecast of future production that often envelops the reference history data. On the other hand, gradient-based optimization is efficient if the exact gradient is available, as it then requires a low number of model evaluations. If the exact gradient is not available, using an approximate gradient or ES-MDA are good alternatives and give equivalent results in terms of computational cost and quality predictions.
{"title":"Numerical Comparison Between ES-MDA and Gradient-Based Optimization for History Matching of Reduced Reservoir Models","authors":"M. A. B. Reveron, H. Holm, O. Møyner, S. Krogstad, Knut-Andreas Lie","doi":"10.2118/203975-ms","DOIUrl":"https://doi.org/10.2118/203975-ms","url":null,"abstract":"\u0000 The Ensemble Smoother with Multiple Data Assimilation (ES-MDA) method has been popular for petroleum reservoir history matching. However, the increasing inclusion of automatic differentiation in reservoir models opens the possibility to history-match models using gradient-based optimization. Here, we discuss, study, and compare ES-MDA and a gradient-based optimization for history-matching waterflooding models. We apply these two methods to history match reduced GPSNet-type models. To study the methods, we use an implementation of ES-MDA and a gradient-based optimization in the open-source MATLAB Reservoir Simulation Toolbox (MRST), and compare the methods in terms of history-matching quality and computational efficiency. We show complementary advantages of both ES-MDA and gradient-based optimization. ES-MDA is suitable when an exact gradient is not available and provides a satisfactory forecast of future production that often envelops the reference history data. On the other hand, gradient-based optimization is efficient if the exact gradient is available, as it then requires a low number of model evaluations. If the exact gradient is not available, using an approximate gradient or ES-MDA are good alternatives and give equivalent results in terms of computational cost and quality predictions.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84018246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The objectives of this study are to develop (a) the Julia Flow and Transport Simulator (JFTS), a serial and parallel, high performance non-isothermal, multi-phase, multi-component general simulator of flow and transport through porous/fractured media, and (b) an associated module that describes quantitatively the Equation-of-State (EOS) of the complete H2O+CH4 system by covering all combinations of phase coexistence that are possible in geologic media and including all the regions of the phase diagram that involve CH4-hydrates. The resulting simulator (hereafter referred to as the JFTS+H code) can describe all possible scenarios of hydrate occurrence, dissociation and formation/evolution and is to be used for the investigation of problems of (a) gas production from natural CH4-hydrate accumulations in geologic media, as well as for (b) the analysis of any laboratory experiments involving CH4-hydrates. As indicated by the JFTS name, this simulator is written in the Julia programming language and its parallelization is based on the Message Passing Interface (MPI) approach. The JFTS+H simulator is a fully-implicit, Jacobian-based compositional simulator that describes the accumulation, flow and transport of heat, and up to four mass components (H2O, CH4, CH4-hydrate and a water-soluble inhibitor) distributed among four possible phases (aqueous, gas, hydrate, and ice) in complex 3D geologic systems. The dissociation and formation of CH4-hydrates can be described using either an equilibrium or a kinetic model. The automatic derivate capability of Julia greatly simplifies and enhances the Jacobian computations. The MPI Interface (Blaise, 2019) is implemented in all components of the code, and the METIS library (Karypis, 2013) is used for the domain decomposition needed for the effective parallelization of the solution of the Jacobian matrix equation that is accomplished using the LIS library (Nishida, 2010) of parallel Conjugate Gradient solvers for large systems of simultaneous linear equations. The JFTS+H code can model the fluid flow, thermal and geochemical processes associated with the formation and dissociation of CH4-hydrates in geological media, either in laboratory or in natural hydrate accumulations. This code can simulate any combination of the three possible gas hydrate dissociation methods (depressurization, thermal stimulation, and inhibitor effects), and computes all associated parameters describing the system behavior. The JFTS+H results show very good agreement with solutions of standard reference problems, and of large 2D and 3D problems obtained from another well-established and widely used numerical simulator. The code exploits the speed, computational efficiency and low memory requirements of the Julia programming language. The parallel architecture of JFTS+H addresses the persistent problem of very large computational demands in serial hydrate simulations by using multiple processors to reduce the overall execution time and a
{"title":"JFTS+H: A Julia-Based Parallel Simulator for the Description of the Coupled flow, Thermal and Geochemical Processes in Hydrate-Bearing Geologic Media","authors":"Kotaro Anno, G. Moridis, T. Blasingame","doi":"10.2118/203953-ms","DOIUrl":"https://doi.org/10.2118/203953-ms","url":null,"abstract":"\u0000 The objectives of this study are to develop (a) the Julia Flow and Transport Simulator (JFTS), a serial and parallel, high performance non-isothermal, multi-phase, multi-component general simulator of flow and transport through porous/fractured media, and (b) an associated module that describes quantitatively the Equation-of-State (EOS) of the complete H2O+CH4 system by covering all combinations of phase coexistence that are possible in geologic media and including all the regions of the phase diagram that involve CH4-hydrates. The resulting simulator (hereafter referred to as the JFTS+H code) can describe all possible scenarios of hydrate occurrence, dissociation and formation/evolution and is to be used for the investigation of problems of (a) gas production from natural CH4-hydrate accumulations in geologic media, as well as for (b) the analysis of any laboratory experiments involving CH4-hydrates. As indicated by the JFTS name, this simulator is written in the Julia programming language and its parallelization is based on the Message Passing Interface (MPI) approach.\u0000 The JFTS+H simulator is a fully-implicit, Jacobian-based compositional simulator that describes the accumulation, flow and transport of heat, and up to four mass components (H2O, CH4, CH4-hydrate and a water-soluble inhibitor) distributed among four possible phases (aqueous, gas, hydrate, and ice) in complex 3D geologic systems. The dissociation and formation of CH4-hydrates can be described using either an equilibrium or a kinetic model. The automatic derivate capability of Julia greatly simplifies and enhances the Jacobian computations. The MPI Interface (Blaise, 2019) is implemented in all components of the code, and the METIS library (Karypis, 2013) is used for the domain decomposition needed for the effective parallelization of the solution of the Jacobian matrix equation that is accomplished using the LIS library (Nishida, 2010) of parallel Conjugate Gradient solvers for large systems of simultaneous linear equations.\u0000 The JFTS+H code can model the fluid flow, thermal and geochemical processes associated with the formation and dissociation of CH4-hydrates in geological media, either in laboratory or in natural hydrate accumulations. This code can simulate any combination of the three possible gas hydrate dissociation methods (depressurization, thermal stimulation, and inhibitor effects), and computes all associated parameters describing the system behavior. The JFTS+H results show very good agreement with solutions of standard reference problems, and of large 2D and 3D problems obtained from another well-established and widely used numerical simulator.\u0000 The code exploits the speed, computational efficiency and low memory requirements of the Julia programming language. The parallel architecture of JFTS+H addresses the persistent problem of very large computational demands in serial hydrate simulations by using multiple processors to reduce the overall execution time and a","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87553253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Equation-of-state (EOS) compositional simulation is commonly used to model the interplay between phase behavior and fluid flow for various reservoir and surface processes. Because of its computational cost, however, there is a critical need for efficient phase-behavior calculations using an EOS. The objective of this research was to develop a proxy model for fugacity coefficient based on the Peng-Robinson EOS for rapid multiphase flash in compositional flow simulation. The proxy model as implemented in this research is to bypass the calculations of fugacity coefficients when the Peng-Robinson EOS has only one root, which is often the case at reservoir conditions. The proxy fugacity model was trained by artificial neural networks (ANN) with over 30 million fugacity coefficients based on the Peng-Robinson EOS. It accurately predicts the Peng- Robinson fugacity coefficient by using four parameters: Am, Bm, Bi, and ΣxiAij. Since these scalar parameters are general, not specific to particular compositions, pressures, and temperatures, the proxy model is applicable to petroleum engineering applications as equally as the original Peng-Robinson EOS. The proxy model is applied to multiphase flash calculations (phase-split and stability), where the cubic equation solutions and fugacity coefficient calculations are bypassed when the Peng-Robinson EOS has one root. The original fugacity coefficient is analytically calculated when the EOS has more than one root, but this occurs only occasionally at reservoir conditions. A case study shows the proxy fugacity model gave a speed-up factor of 3.4% in comparison to the conventional EOS calculation. Case studies also demonstrate accurate multiphase flash results (stability and phase split) and interchangeable proxy models for different fluid cases with different (numbers of) components. This is possible because it predicts the Peng-Robinson fugacity in the variable space that is not specific to composition, temperature, and pressure. For the same reason, non-zero binary iteration parameters do not impair the applicability, accuracy, robustness, and efficiency of the model. As the proxy models are specific to individual components, a combination of proxy models can be used to model for any mixture of components. Tuning of training hyperparameters and training data sampling method helped reduce the mean absolute percent error to less than 0.1% in the ANN modeling. To the best of our knowledge, this is the first generalized proxy model of the Peng-Robinson fugacity that is applicable to any mixture. The proposed model retains the conventional flash iteration, the convergence robustness, and the option of manual parameter tuning for fluid characterization.
{"title":"A Proxy Peng-Robinson EOS for Efficient Modeling of Phase Behavior","authors":"M. Zhao, R. Okuno","doi":"10.2118/203914-ms","DOIUrl":"https://doi.org/10.2118/203914-ms","url":null,"abstract":"\u0000 Equation-of-state (EOS) compositional simulation is commonly used to model the interplay between phase behavior and fluid flow for various reservoir and surface processes. Because of its computational cost, however, there is a critical need for efficient phase-behavior calculations using an EOS. The objective of this research was to develop a proxy model for fugacity coefficient based on the Peng-Robinson EOS for rapid multiphase flash in compositional flow simulation. The proxy model as implemented in this research is to bypass the calculations of fugacity coefficients when the Peng-Robinson EOS has only one root, which is often the case at reservoir conditions.\u0000 The proxy fugacity model was trained by artificial neural networks (ANN) with over 30 million fugacity coefficients based on the Peng-Robinson EOS. It accurately predicts the Peng- Robinson fugacity coefficient by using four parameters: Am, Bm, Bi, and ΣxiAij. Since these scalar parameters are general, not specific to particular compositions, pressures, and temperatures, the proxy model is applicable to petroleum engineering applications as equally as the original Peng-Robinson EOS. The proxy model is applied to multiphase flash calculations (phase-split and stability), where the cubic equation solutions and fugacity coefficient calculations are bypassed when the Peng-Robinson EOS has one root. The original fugacity coefficient is analytically calculated when the EOS has more than one root, but this occurs only occasionally at reservoir conditions.\u0000 A case study shows the proxy fugacity model gave a speed-up factor of 3.4% in comparison to the conventional EOS calculation. Case studies also demonstrate accurate multiphase flash results (stability and phase split) and interchangeable proxy models for different fluid cases with different (numbers of) components. This is possible because it predicts the Peng-Robinson fugacity in the variable space that is not specific to composition, temperature, and pressure. For the same reason, non-zero binary iteration parameters do not impair the applicability, accuracy, robustness, and efficiency of the model. As the proxy models are specific to individual components, a combination of proxy models can be used to model for any mixture of components. Tuning of training hyperparameters and training data sampling method helped reduce the mean absolute percent error to less than 0.1% in the ANN modeling.\u0000 To the best of our knowledge, this is the first generalized proxy model of the Peng-Robinson fugacity that is applicable to any mixture. The proposed model retains the conventional flash iteration, the convergence robustness, and the option of manual parameter tuning for fluid characterization.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"123 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85671466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A novel higher resolution spectral volume method coupled with a control-volume distributed multi-Point flux approximation (CVD-MPFA) is presented on unstructured triangular grids for subsurface reservoir simulation. The flow equations involve an essentially hyperbolic convection equation coupled with an elliptic pressure equation resulting from Darcy’s law together with mass conservation. The spectral volume (SV) method is a locally conservative, efficient high-order finite volume method for convective flow. In 2D geometry, the triangular cell is subdivided into sub-cells, and the average state variables in the sub-cells are used to reconstruct a high-order polynomial in the triangular cell. The focus here is on an efficient strategy for reconstruction of both a higher resolution approximation of the convective transport flux and Darcy-flux approximation on sub-cell interfaces, which is also coupled with a discrete fracture model. The strategy involves coupling of the SV method and reconstructed CVD-MPFA fluxes at the faces of the spectral volume, to obtain an efficient finer scale higher resolution finite-volume method which solves for both the saturation and pressure. A limiting procedure based on a Barth-Jespersen type limiter is used to prevent non-physical oscillations on unstructured grids. The fine scale saturation/concentration field is then updated via the reconstructed finite volume approximation over the sub-cell control-volumes. Performance comparisons are presented for two phase flow problems on 2D unstructured meshes including fractures. The results demonstrate that the spectral-volume method achieves further enhanced resolution of flow and fronts in addition to that of achieved by the standard higher resolution method over first order upwind, while improving upon efficiency.
{"title":"Higher Resolution Hybrid-Upwind Spectral Finite-Volume Methods, for Flow in Porous and Fractured Media on Unstructured Grids","authors":"Yawei Xie, M. Edwards","doi":"10.2118/203957-ms","DOIUrl":"https://doi.org/10.2118/203957-ms","url":null,"abstract":"\u0000 A novel higher resolution spectral volume method coupled with a control-volume distributed multi-Point flux approximation (CVD-MPFA) is presented on unstructured triangular grids for subsurface reservoir simulation. The flow equations involve an essentially hyperbolic convection equation coupled with an elliptic pressure equation resulting from Darcy’s law together with mass conservation. The spectral volume (SV) method is a locally conservative, efficient high-order finite volume method for convective flow. In 2D geometry, the triangular cell is subdivided into sub-cells, and the average state variables in the sub-cells are used to reconstruct a high-order polynomial in the triangular cell. The focus here is on an efficient strategy for reconstruction of both a higher resolution approximation of the convective transport flux and Darcy-flux approximation on sub-cell interfaces, which is also coupled with a discrete fracture model. The strategy involves coupling of the SV method and reconstructed CVD-MPFA fluxes at the faces of the spectral volume, to obtain an efficient finer scale higher resolution finite-volume method which solves for both the saturation and pressure. A limiting procedure based on a Barth-Jespersen type limiter is used to prevent non-physical oscillations on unstructured grids. The fine scale saturation/concentration field is then updated via the reconstructed finite volume approximation over the sub-cell control-volumes. Performance comparisons are presented for two phase flow problems on 2D unstructured meshes including fractures. The results demonstrate that the spectral-volume method achieves further enhanced resolution of flow and fronts in addition to that of achieved by the standard higher resolution method over first order upwind, while improving upon efficiency.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76185489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sequential Fully Implicit (SFI) schemes have been proposed as an alternative to the Fully Implicit Method (FIM). A significant advantage of SFI is that one can employ scalable strategies to the flow and transport problems. However, the primary disadvantage of using SFI compared with FIM is the fact that the splitting errors induced by the decoupling operator, which separates the pressure from the saturation(s), can lead to serious convergence difficulties of the overall nonlinear problem. Thus, it is important to quantify the coupling strength in an adaptive manner in both space and time. We present criteria that localize the computational cells where the pressure and saturation solutions are tightly coupled. The approach is using terms in the FIM Jacobian matrix, we quantify the sensitivity of the mass and volume-balance equations to changes in the pressure and the saturations. We identify three criteria that provide a measure of the coupling strength across the equations and variables. The standard CFL stability criteria, which are based entirely on the saturation equations, are a subset of the new criteria. Here, the pressure equation is solved using Algebraic MultiGrid (AMG), or a multiscale solver, such as the Multiscale Restricted-Smooth Basis (MsRSB) approach. The transport equations are then solved using a fixed total-velocity. These ‘coupling strength’ criteria are used to identify the cells where the pressure-saturation coupling is strong. The applicability of the derived coupling-strength criteria is tested using several test cases. The first test is using a gravitational immiscible dead-oil lock-exchange under a unit mobility ratio and large differences in density. For this case, the SFI algorithm fails to converge to the fully coupled solution due to the large splitting errors. Introducing a fully coupled solution stage on the local subdomains as an additional correction step restores nonlinear convergence. Detailed analysis of the ‘coupling strength’ criteria indicates that the criteria related to the sensitivity of the mass balance to changes in the pressure and the sensitivity of the volume balance to changes in the saturations are the most important ones to satisfy. Other test cases include an alternate gas-water-gas injection in a top layer of the SPE 10 test case and an injection-production scenario in a three-dimensional reservoir with layered lognormally distributed permeability. We propose novel criteria to estimate the strength of coupling between pressure and saturation. These CFL-like numbers are used to identify the cells that require fully implicit treatment in the nonlinear solution strategy. These criteria can also be used to improve the nonlinear convergence rates of Adaptive Implicit Methods (AIM).
{"title":"Coupling-Strength Criteria for Sequential Implicit Formulations","authors":"J. Franc, O. Møyner, H. Tchelepi","doi":"10.2118/203909-ms","DOIUrl":"https://doi.org/10.2118/203909-ms","url":null,"abstract":"Sequential Fully Implicit (SFI) schemes have been proposed as an alternative to the Fully Implicit Method (FIM). A significant advantage of SFI is that one can employ scalable strategies to the flow and transport problems. However, the primary disadvantage of using SFI compared with FIM is the fact that the splitting errors induced by the decoupling operator, which separates the pressure from the saturation(s), can lead to serious convergence difficulties of the overall nonlinear problem. Thus, it is important to quantify the coupling strength in an adaptive manner in both space and time. We present criteria that localize the computational cells where the pressure and saturation solutions are tightly coupled. The approach is using terms in the FIM Jacobian matrix, we quantify the sensitivity of the mass and volume-balance equations to changes in the pressure and the saturations. We identify three criteria that provide a measure of the coupling strength across the equations and variables. The standard CFL stability criteria, which are based entirely on the saturation equations, are a subset of the new criteria. Here, the pressure equation is solved using Algebraic MultiGrid (AMG), or a multiscale solver, such as the Multiscale Restricted-Smooth Basis (MsRSB) approach. The transport equations are then solved using a fixed total-velocity. These ‘coupling strength’ criteria are used to identify the cells where the pressure-saturation coupling is strong. The applicability of the derived coupling-strength criteria is tested using several test cases. The first test is using a gravitational immiscible dead-oil lock-exchange under a unit mobility ratio and large differences in density. For this case, the SFI algorithm fails to converge to the fully coupled solution due to the large splitting errors. Introducing a fully coupled solution stage on the local subdomains as an additional correction step restores nonlinear convergence. Detailed analysis of the ‘coupling strength’ criteria indicates that the criteria related to the sensitivity of the mass balance to changes in the pressure and the sensitivity of the volume balance to changes in the saturations are the most important ones to satisfy. Other test cases include an alternate gas-water-gas injection in a top layer of the SPE 10 test case and an injection-production scenario in a three-dimensional reservoir with layered lognormally distributed permeability. We propose novel criteria to estimate the strength of coupling between pressure and saturation. These CFL-like numbers are used to identify the cells that require fully implicit treatment in the nonlinear solution strategy. These criteria can also be used to improve the nonlinear convergence rates of Adaptive Implicit Methods (AIM).","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"143 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74531146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reservoir cooling during waterflooding or waste-water injection can significantly alter the reservoir stress field by thermo-poro-elastic effects. Colloidal particles in the injected water decrease the matrix permeability and buildup the injection pressure. Fractures may initiate and propagate from injectors. These fractures are of great concern for both environmental reasons and strong influence on reservoir sweep and oil recovery. This paper introduces methods to fully couple reservoir simulation with wellbore flow models in fractured injection wells. A method to fully couple reservoir-fracture-wellbore models was developed. Fluid flow, solid mechanics, energy balance, fracture propagation, and particle filtration are modelled in the reservoir, fracture and wellbore domains. Effective stress in the reservoir domain is altered by thermo-poro-elastic effects during cold water injection. Fracture initiation and propagation induced by thermal and filtration effects is modelled in the fracture domain. Particle filtration on the borehole and fracture surfaces is modelled by matrix permeability reduction and filter cake build-up. Leakoff through the borehole and fracture surface is balanced dynamically. The coupled nonlinear system of equations is solved implicitly using Newton-Raphson method. We validate our model with existing analytical solutions for simple cases. We show how the poro-elasticity effect, thermo-elasticity effect, water quality, and wellbore open/cased conditions influence well injectivity, induced fracture propagation and flow distribution. Simulation results show that water quality and thermal effects control fluid leak-off and fracture growth. While it is difficult to predict the exact location of fracture initiation due to reservoir heterogeneity, we proposed a reasonable method to handle fracture initiation without predefined fracture location in the water injection applications. In open-hole completions, this may lead to "thief" fractures propagating deep into the reservoir. Thermal stress changes in the injection zone are shown to be significant because of the combined effect of forced convection, heat conduction and poroelasticity. The accurate predictions of thermal stress in different reservoir layers allow us to study fracture height growth and containment numerically for the first time. We show that controlling the temperature and the injection water quality is also found to be an effective way to ensure fracture containment.
{"title":"Coupling a Geomechanical Reservoir and Fracturing Simulator with a Wellbore Model for Horizontal Injection Wells","authors":"Shuang Zheng, M. Sharma","doi":"10.2118/203977-ms","DOIUrl":"https://doi.org/10.2118/203977-ms","url":null,"abstract":"\u0000 Reservoir cooling during waterflooding or waste-water injection can significantly alter the reservoir stress field by thermo-poro-elastic effects. Colloidal particles in the injected water decrease the matrix permeability and buildup the injection pressure. Fractures may initiate and propagate from injectors. These fractures are of great concern for both environmental reasons and strong influence on reservoir sweep and oil recovery. This paper introduces methods to fully couple reservoir simulation with wellbore flow models in fractured injection wells.\u0000 A method to fully couple reservoir-fracture-wellbore models was developed. Fluid flow, solid mechanics, energy balance, fracture propagation, and particle filtration are modelled in the reservoir, fracture and wellbore domains. Effective stress in the reservoir domain is altered by thermo-poro-elastic effects during cold water injection. Fracture initiation and propagation induced by thermal and filtration effects is modelled in the fracture domain. Particle filtration on the borehole and fracture surfaces is modelled by matrix permeability reduction and filter cake build-up. Leakoff through the borehole and fracture surface is balanced dynamically. The coupled nonlinear system of equations is solved implicitly using Newton-Raphson method.\u0000 We validate our model with existing analytical solutions for simple cases. We show how the poro-elasticity effect, thermo-elasticity effect, water quality, and wellbore open/cased conditions influence well injectivity, induced fracture propagation and flow distribution. Simulation results show that water quality and thermal effects control fluid leak-off and fracture growth. While it is difficult to predict the exact location of fracture initiation due to reservoir heterogeneity, we proposed a reasonable method to handle fracture initiation without predefined fracture location in the water injection applications. In open-hole completions, this may lead to \"thief\" fractures propagating deep into the reservoir. Thermal stress changes in the injection zone are shown to be significant because of the combined effect of forced convection, heat conduction and poroelasticity. The accurate predictions of thermal stress in different reservoir layers allow us to study fracture height growth and containment numerically for the first time. We show that controlling the temperature and the injection water quality is also found to be an effective way to ensure fracture containment.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82005877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The imbibition process due to capillary force is an important mechanism that controls fluid flow between the two domains, matrix and fracture, in naturally or hydraulically fractured reservoirs. Many simulation studies have been done in the past decades to understand the multi-phase flow in the tight and shale formation. Although significant advances have been made in large-scale modeling for both unconventional and conventional fields, the imbibition processes in the fractured reservoirs remains underestimated in numerical simulation, that limits confidence in long-term field production predictions. In the meanwhile, to simulate the near-fracture imbibition process, traditionally very-fine simulation grids have to be applied so that the physical phenomena of small-length scale could be captured. However, this leads to expensive computation cost to simulate full-field models with a large number of fractures. To improve numerical efficiency in field-scale modeling, we propose a similarity solution for the imbibition process that can be incorporated into the traditional finite difference formulation with coarse grid cells. The semi-analytical similarity solutions are validated by comparing with numerical simulation results with fine-scale grids. The comparison clearly indicates that the proposed algorithm accurately represents the flow behaviors in complex fracture models. Furthermore, we adopt the semi-analytical study to hydraulic fracture models using Embedded Discrete Fracture Model (Lee et al., 2001) in our numerical studies at different scales to represent hydraulic fractures that are interconnected. We demonstrate: 1) the imbibition is critical in determining flow behavior in a capillary force dominant model, 2) conventional EDFM has its limitation in capturing sub-cell flow behaviors near fractures, 3) combining the proposed similarity solution and EDFM, we can accurately represent the multi-phase flow near fractures with coarser grids, and 4) it is straightforward to adapt the similarity solution concept in finite-difference simulations for fractured reservoirs
在天然或水力裂缝性储层中，毛细力的渗吸过程是控制基质与裂缝两个区域之间流体流动的重要机制。在过去的几十年里，人们进行了许多模拟研究，以了解致密和页岩地层中的多相流。尽管在非常规油田和常规油田的大规模建模方面取得了重大进展，但在数值模拟中，裂缝性油藏的渗吸过程仍然被低估，这限制了对长期油田产量预测的信心。同时，为了模拟近裂缝渗吸过程，传统的模拟网格必须采用非常精细的网格，以捕捉小长度尺度的物理现象。然而，这导致模拟具有大量裂缝的全场模型的计算成本昂贵。为了提高现场尺度模拟的数值效率，我们提出了一个吸胀过程的相似解，该解可以纳入传统的粗网格单元有限差分公式。通过与细尺度网格数值模拟结果的比较，验证了半解析相似解的正确性。对比结果表明，该算法能较好地反映复杂裂缝模型中的渗流行为。此外，在不同尺度的数值研究中，我们采用嵌入式离散裂缝模型(Lee et al.， 2001)对水力裂缝模型进行半解析研究，以表示相互连接的水力裂缝。结果表明:1)在毛细管力主导模型中，渗吸是决定流体行为的关键;2)传统EDFM在捕获裂缝附近亚单元流动行为方面存在局限性;3)将相似解与EDFM相结合，我们可以用更粗的网格准确地表示裂缝附近的多相流动;4)相似解概念可以直接应用于裂缝性油藏的有限差分模拟
{"title":"A Similarity Solution for Imbibition Process and its Adaptation in Finite Difference Simulation of Fractured Reservoirs","authors":"S. Du, Seong H. Lee, X. Wen, Y. Efendiev","doi":"10.2118/203959-ms","DOIUrl":"https://doi.org/10.2118/203959-ms","url":null,"abstract":"\u0000 The imbibition process due to capillary force is an important mechanism that controls fluid flow between the two domains, matrix and fracture, in naturally or hydraulically fractured reservoirs. Many simulation studies have been done in the past decades to understand the multi-phase flow in the tight and shale formation. Although significant advances have been made in large-scale modeling for both unconventional and conventional fields, the imbibition processes in the fractured reservoirs remains underestimated in numerical simulation, that limits confidence in long-term field production predictions. In the meanwhile, to simulate the near-fracture imbibition process, traditionally very-fine simulation grids have to be applied so that the physical phenomena of small-length scale could be captured. However, this leads to expensive computation cost to simulate full-field models with a large number of fractures. To improve numerical efficiency in field-scale modeling, we propose a similarity solution for the imbibition process that can be incorporated into the traditional finite difference formulation with coarse grid cells.\u0000 The semi-analytical similarity solutions are validated by comparing with numerical simulation results with fine-scale grids. The comparison clearly indicates that the proposed algorithm accurately represents the flow behaviors in complex fracture models. Furthermore, we adopt the semi-analytical study to hydraulic fracture models using Embedded Discrete Fracture Model (Lee et al., 2001) in our numerical studies at different scales to represent hydraulic fractures that are interconnected. We demonstrate: 1) the imbibition is critical in determining flow behavior in a capillary force dominant model, 2) conventional EDFM has its limitation in capturing sub-cell flow behaviors near fractures, 3) combining the proposed similarity solution and EDFM, we can accurately represent the multi-phase flow near fractures with coarser grids, and 4) it is straightforward to adapt the similarity solution concept in finite-difference simulations for fractured reservoirs","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"55 5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77466204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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