We study new constitutive relations employing the fundamental theory of elastoplasticity for two coupled irreversible processes: elastoplastic geomechanics and two-phase flow with capillary hysteresis. The fluid content is additively decomposed into elastic and plastic parts with infinitesimal transformation assumed. Specifically, the plastic fluid content, i.e., the total residual (or irrecoverable) saturation, is also additively decomposed into constituents due to the two irreversible processes: the geomechanical plasticity and the capillary hysteresis. The additive decomposition of the plastic fluid content facilitates combining the existing two individual simulators easily, for example, by using the fixed-stress sequential method. For pore pressure of the fluid in multi-phase which is coupled with the geomechanics, the equivalent pore pressure is employed, which yields the well-posedness of coupled multi-phase flow and geomechanics, regardless of the capillarity. We perform an energy analysis to show the well-posedness of the proposed model. And numerical examples demonstrate stable solutions for cyclic imbibition/drainage and loading/unloading processes. Employing the van Genuchten and the Drucker Prager models for capillary and the plasticity, respectively, we show the robustness of the model for capillary hysteresis in multiphase flow and elastoplastic geomechanics.
{"title":"The Modeling for Coupled Elastoplastic Geomechanics and Two-Phase Flow With Capillary Hysteresis in Porous Media","authors":"H. C. Yoon, J. Kim","doi":"10.2118/203910-ms","DOIUrl":"https://doi.org/10.2118/203910-ms","url":null,"abstract":"\u0000 We study new constitutive relations employing the fundamental theory of elastoplasticity for two coupled irreversible processes: elastoplastic geomechanics and two-phase flow with capillary hysteresis. The fluid content is additively decomposed into elastic and plastic parts with infinitesimal transformation assumed. Specifically, the plastic fluid content, i.e., the total residual (or irrecoverable) saturation, is also additively decomposed into constituents due to the two irreversible processes: the geomechanical plasticity and the capillary hysteresis. The additive decomposition of the plastic fluid content facilitates combining the existing two individual simulators easily, for example, by using the fixed-stress sequential method. For pore pressure of the fluid in multi-phase which is coupled with the geomechanics, the equivalent pore pressure is employed, which yields the well-posedness of coupled multi-phase flow and geomechanics, regardless of the capillarity. We perform an energy analysis to show the well-posedness of the proposed model. And numerical examples demonstrate stable solutions for cyclic imbibition/drainage and loading/unloading processes. Employing the van Genuchten and the Drucker Prager models for capillary and the plasticity, respectively, we show the robustness of the model for capillary hysteresis in multiphase flow and elastoplastic geomechanics.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90834750","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}
Yixuan Wang, F. Alpak, G. Gao, Chaohui Chen, J. Vink, T. Wells, F. Saaf
Although it is possible to apply traditional optimization algorithms to determine the Pareto front of a multi-objective optimization problem, the computational cost is extremely high, when the objective function evaluation requires solving a complex reservoir simulation problem and optimization cannot benefit from adjoint-based gradients. This paper proposes a novel workflow to solve bi-objective optimization problems using the distributed quasi-Newton (DQN) method, which is a well-parallelized and derivative-free optimization (DFO) method. Numerical tests confirm that the DQN method performs efficiently and robustly. The efficiency of the DQN optimizer stems from a distributed computing mechanism which effectively shares the available information discovered in prior iterations. Rather than performing multiple quasi-Newton optimization tasks in isolation, simulation results are shared among distinct DQN optimization tasks or threads. In this paper, the DQN method is applied to the optimization of a weighted average of two objectives, using different weighting factors for different optimization threads. In each iteration, the DQN optimizer generates an ensemble of search points (or simulation cases) in parallel and a set of non-dominated points is updated accordingly. Different DQN optimization threads, which use the same set of simulation results but different weighting factors in their objective functions, converge to different optima of the weighted average objective function. The non-dominated points found in the last iteration form a set of Pareto optimal solutions. Robustness as well as efficiency of the DQN optimizer originates from reliance on a large, shared set of intermediate search points. On the one hand, this set of searching points is (much) smaller than the combined sets needed if all optimizations with different weighting factors would be executed separately; on the other hand, the size of this set produces a high fault tolerance. Even if some simulations fail at a given iteration, DQN’s distributed-parallel information-sharing protocol is designed and implemented such that the optimization process can still proceed to the next iteration. The proposed DQN optimization method is first validated on synthetic examples with analytical objective functions. Then, it is tested on well location optimization problems, by maximizing the oil production and minimizing the water production. Furthermore, the proposed method is benchmarked against a bi-objective implementation of the MADS (Mesh Adaptive Direct Search) method, and the numerical results reinforce the auspicious computational attributes of DQN observed for the test problems. To the best of our knowledge, this is the first time that a well-parallelized and derivative-free DQN optimization method has been developed and tested on bi-objective optimization problems. The methodology proposed can help improve efficiency and robustness in solving complicated bi-objective optimization
{"title":"An Efficient Bi-Objective Optimization Workflow Using the Distributed Quasi-Newton Method and Its Application to Field Development Optimization","authors":"Yixuan Wang, F. Alpak, G. Gao, Chaohui Chen, J. Vink, T. Wells, F. Saaf","doi":"10.2118/203971-ms","DOIUrl":"https://doi.org/10.2118/203971-ms","url":null,"abstract":"\u0000 Although it is possible to apply traditional optimization algorithms to determine the Pareto front of a multi-objective optimization problem, the computational cost is extremely high, when the objective function evaluation requires solving a complex reservoir simulation problem and optimization cannot benefit from adjoint-based gradients. This paper proposes a novel workflow to solve bi-objective optimization problems using the distributed quasi-Newton (DQN) method, which is a well-parallelized and derivative-free optimization (DFO) method. Numerical tests confirm that the DQN method performs efficiently and robustly.\u0000 The efficiency of the DQN optimizer stems from a distributed computing mechanism which effectively shares the available information discovered in prior iterations. Rather than performing multiple quasi-Newton optimization tasks in isolation, simulation results are shared among distinct DQN optimization tasks or threads. In this paper, the DQN method is applied to the optimization of a weighted average of two objectives, using different weighting factors for different optimization threads. In each iteration, the DQN optimizer generates an ensemble of search points (or simulation cases) in parallel and a set of non-dominated points is updated accordingly. Different DQN optimization threads, which use the same set of simulation results but different weighting factors in their objective functions, converge to different optima of the weighted average objective function. The non-dominated points found in the last iteration form a set of Pareto optimal solutions. Robustness as well as efficiency of the DQN optimizer originates from reliance on a large, shared set of intermediate search points. On the one hand, this set of searching points is (much) smaller than the combined sets needed if all optimizations with different weighting factors would be executed separately; on the other hand, the size of this set produces a high fault tolerance. Even if some simulations fail at a given iteration, DQN’s distributed-parallel information-sharing protocol is designed and implemented such that the optimization process can still proceed to the next iteration.\u0000 The proposed DQN optimization method is first validated on synthetic examples with analytical objective functions. Then, it is tested on well location optimization problems, by maximizing the oil production and minimizing the water production. Furthermore, the proposed method is benchmarked against a bi-objective implementation of the MADS (Mesh Adaptive Direct Search) method, and the numerical results reinforce the auspicious computational attributes of DQN observed for the test problems.\u0000 To the best of our knowledge, this is the first time that a well-parallelized and derivative-free DQN optimization method has been developed and tested on bi-objective optimization problems. The methodology proposed can help improve efficiency and robustness in solving complicated bi-objective optimization","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82969041","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}
Victor de Souza Rios, A. Skauge, K. Sorbie, G. Wang, D. Schiozer, Luiz Otávio Schmall dos Santos
Compositional reservoir simulation is essential to represent the complex interactions associated with gas flooding processes. Generally, an improved description of such small-scale phenomena requires the use of very detailed reservoir models, which impact the computational cost. We provide a practical and general upscaling procedure to guide a robust selection of the upscaling approaches considering the nature and limitations of each reservoir model, exploring the differences between the upscaling of immiscible and miscible gas injection problems. We highlight the different challenges to achieve improved upscaled models for immiscible and miscible gas displacement conditions with a stepwise workflow. We first identify the need for a special permeability upscaling technique to improve the representation of the main reservoir heterogeneities and sub-grid features, smoothed during the upscaling process. Then, we verify if the use of pseudo-functions is necessary to correct the multiphase flow dynamic behavior. At this stage, different pseudoization approaches are recommended according to the miscibility conditions of the problem. This study evaluates highly heterogeneous reservoir models submitted to immiscible and miscible gas flooding. The fine models represent a small part of a reservoir with a highly refined set of grid-block cells, with 5 × 5 cm2 area. The upscaled coarse models present grid-block cells of 8 × 10 m2 area, which is compatible with a refined geological model in reservoir engineering studies. This process results in a challenging upscaling ratio of 32 000. We show a consistent procedure to achieve reliable results with the coarse-scale model under the different miscibility conditions. For immiscible displacement situations, accurate results can be obtained with the coarse models after a proper permeability upscaling procedure and the use of pseudo-relative permeability curves to improve the dynamic responses. Miscible displacements, however, requires a specific treatment of the fluid modeling process to overcome the limitations arising from the thermodynamic equilibrium assumption. For all the situations, the workflow can lead to a robust choice of techniques to satisfactorily improve the coarse-scale simulation results. Our approach works on two fronts. (1) We apply a dual-porosity/dual-permeability upscaling process, developed by Rios et al. (2020a), to enable the representation of sub-grid heterogeneities in the coarse-scale model, providing consistent improvements on the upscaling results. (2) We generate specific pseudo-functions according to the miscibility conditions of the gas flooding process. We developed a stepwise procedure to deal with the upscaling problems consistently and to enable a better understanding of the coarsening process.
{"title":"Differences in the Upscaling Procedure for Compositional Reservoir Simulations of Immiscible and Miscible Gas Flooding","authors":"Victor de Souza Rios, A. Skauge, K. Sorbie, G. Wang, D. Schiozer, Luiz Otávio Schmall dos Santos","doi":"10.2118/203970-ms","DOIUrl":"https://doi.org/10.2118/203970-ms","url":null,"abstract":"\u0000 Compositional reservoir simulation is essential to represent the complex interactions associated with gas flooding processes. Generally, an improved description of such small-scale phenomena requires the use of very detailed reservoir models, which impact the computational cost. We provide a practical and general upscaling procedure to guide a robust selection of the upscaling approaches considering the nature and limitations of each reservoir model, exploring the differences between the upscaling of immiscible and miscible gas injection problems.\u0000 We highlight the different challenges to achieve improved upscaled models for immiscible and miscible gas displacement conditions with a stepwise workflow. We first identify the need for a special permeability upscaling technique to improve the representation of the main reservoir heterogeneities and sub-grid features, smoothed during the upscaling process. Then, we verify if the use of pseudo-functions is necessary to correct the multiphase flow dynamic behavior. At this stage, different pseudoization approaches are recommended according to the miscibility conditions of the problem.\u0000 This study evaluates highly heterogeneous reservoir models submitted to immiscible and miscible gas flooding. The fine models represent a small part of a reservoir with a highly refined set of grid-block cells, with 5 × 5 cm2 area. The upscaled coarse models present grid-block cells of 8 × 10 m2 area, which is compatible with a refined geological model in reservoir engineering studies. This process results in a challenging upscaling ratio of 32 000. We show a consistent procedure to achieve reliable results with the coarse-scale model under the different miscibility conditions. For immiscible displacement situations, accurate results can be obtained with the coarse models after a proper permeability upscaling procedure and the use of pseudo-relative permeability curves to improve the dynamic responses. Miscible displacements, however, requires a specific treatment of the fluid modeling process to overcome the limitations arising from the thermodynamic equilibrium assumption. For all the situations, the workflow can lead to a robust choice of techniques to satisfactorily improve the coarse-scale simulation results.\u0000 Our approach works on two fronts. (1) We apply a dual-porosity/dual-permeability upscaling process, developed by Rios et al. (2020a), to enable the representation of sub-grid heterogeneities in the coarse-scale model, providing consistent improvements on the upscaling results. (2) We generate specific pseudo-functions according to the miscibility conditions of the gas flooding process. We developed a stepwise procedure to deal with the upscaling problems consistently and to enable a better understanding of the coarsening process.","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":"84464585","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}
Syamil Mohd Razak, Atefeh Jahandideh, U. Djuraev, B. Jafarpour
We present a deep learning architecture for efficient reduced-order implementation of ensemble data assimilation. Specifically, deep learning is used to improve two important aspects of data assimilation workflows: (i) low-rank representation of complex reservoir property distributions for geologically consistent feature-based model updating, and (ii) efficient prediction of the statistical information that are required for model updating. The proposed method uses deep convolutional autoencoders to nonlinearly map the original complex and high-dimensional parameters onto a low-dimensional parameter latent space that compactly represents the original parameters. In addition, a low-dimensional data latent space is constructed to predict the observable response of each model parameter realization, which can be used to compute the statistical information needed for the data assimilation step. The two mappings are developed as a joint deep learning architecture with two autoencoders that are connected and trained together. The training uses an ensemble of model parameters and their corresponding production response predictions as needed in implementing the standard ensemble-based data assimilation frameworks. Simultaneous training of the two mappings leads to a joint data-parameter manifold that captures the most salient information in the two spaces for a more effective data assimilation, where only relevant data and parameter features are included. Moreover, the parameter-to-data mapping provides a fast forecast model that can be used to increase the ensemble size for a more accurate data assimilation, without a major computational overhead. We implement the developed approach to a series of numerical experiments, including a 3D example based on the Volve field in the North Sea. For data assimilation methods that involve iterative schemes, such as ensemble smoothers with multiple data assimilation or iterative forms of ensemble Kalman filter, the proposed approach offers a computationally competitive alternative. Our results show that a fully low-dimensional implementation of ensemble data assimilation using deep learning architectures offers several advantages compared to standard algorithms, including joint data-parameter reduction that respects the salient features in each space, geologically consistent feature-based updates, increased ensemble sizes to improve the accuracy and computational efficiency of the calculated statistics for the update step.
{"title":"Deep Learning for Latent Space Data Assimilation LSDA in Subsurface Flow Systems","authors":"Syamil Mohd Razak, Atefeh Jahandideh, U. Djuraev, B. Jafarpour","doi":"10.2118/203997-ms","DOIUrl":"https://doi.org/10.2118/203997-ms","url":null,"abstract":"\u0000 We present a deep learning architecture for efficient reduced-order implementation of ensemble data assimilation. Specifically, deep learning is used to improve two important aspects of data assimilation workflows: (i) low-rank representation of complex reservoir property distributions for geologically consistent feature-based model updating, and (ii) efficient prediction of the statistical information that are required for model updating. The proposed method uses deep convolutional autoencoders to nonlinearly map the original complex and high-dimensional parameters onto a low-dimensional parameter latent space that compactly represents the original parameters. In addition, a low-dimensional data latent space is constructed to predict the observable response of each model parameter realization, which can be used to compute the statistical information needed for the data assimilation step. The two mappings are developed as a joint deep learning architecture with two autoencoders that are connected and trained together. The training uses an ensemble of model parameters and their corresponding production response predictions as needed in implementing the standard ensemble-based data assimilation frameworks. Simultaneous training of the two mappings leads to a joint data-parameter manifold that captures the most salient information in the two spaces for a more effective data assimilation, where only relevant data and parameter features are included. Moreover, the parameter-to-data mapping provides a fast forecast model that can be used to increase the ensemble size for a more accurate data assimilation, without a major computational overhead. We implement the developed approach to a series of numerical experiments, including a 3D example based on the Volve field in the North Sea. For data assimilation methods that involve iterative schemes, such as ensemble smoothers with multiple data assimilation or iterative forms of ensemble Kalman filter, the proposed approach offers a computationally competitive alternative. Our results show that a fully low-dimensional implementation of ensemble data assimilation using deep learning architectures offers several advantages compared to standard algorithms, including joint data-parameter reduction that respects the salient features in each space, geologically consistent feature-based updates, increased ensemble sizes to improve the accuracy and computational efficiency of the calculated statistics for the update step.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87951140","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. Heidari, Christopher Istchenko, W. Bailey, T. Stone
The paper examines new horizontal drift-flux correlations for their ability to accurately model phase flow rates and pressure drops in horizontal and undulating wells that are part of a Steam-Assisted Gravity Drainage (SAGD) field operation. Pressure profiles within each well correlate to the overall performance of the pair. SAGD is a low-pressure process that is sensitive to reservoir heterogeneity and other factors, hence accurate simulation of in situ wellbore pressures is critical for both mitigating uneven steam chamber evolution and optimizing wellbore design and operation. Recently published horizontal drift-flux correlations have been implemented in a commercial thermal reservoir simulator with a multi-segment well model. Valid for horizontally drilled wells with undulations, they complement previously reported drift-flux models developed for vertical and inclined wells down to approximately 5 degrees from horizontal. The formulation of these correlations has a high degree of nonlinearity. These models are tested in simulations of SAGD field operations. First, an overview of drift-flux models is discussed. This differentiates those based on vertical flow with gravity segregation to those that model horizontal flow with stratified and slug flow regimes. Second, the most recent and significant drift-flux correlation by Bailey et al. (2018, and hereafter referred to as Bailey-Tang-Stone) was robustly designed to be used in the well model of a reservoir simulator, can handle all inclination angles and was optimized to experimental data from the largest available databases to date. This and earlier drift-flux models are reviewed as to their strengths and weaknesses. Third, governing equations and implementation details are given of the Bailey-Tang-Stone model. Fourth, six case studies are presented that illustrate homogeneous and drift-flux flow model differences for various well scenarios.
{"title":"Use of Horizontal Drift-Flux Models For Simulating Wellbore Flow in SAGD Operations","authors":"M. Heidari, Christopher Istchenko, W. Bailey, T. Stone","doi":"10.2118/203955-ms","DOIUrl":"https://doi.org/10.2118/203955-ms","url":null,"abstract":"\u0000 The paper examines new horizontal drift-flux correlations for their ability to accurately model phase flow rates and pressure drops in horizontal and undulating wells that are part of a Steam-Assisted Gravity Drainage (SAGD) field operation. Pressure profiles within each well correlate to the overall performance of the pair. SAGD is a low-pressure process that is sensitive to reservoir heterogeneity and other factors, hence accurate simulation of in situ wellbore pressures is critical for both mitigating uneven steam chamber evolution and optimizing wellbore design and operation.\u0000 Recently published horizontal drift-flux correlations have been implemented in a commercial thermal reservoir simulator with a multi-segment well model. Valid for horizontally drilled wells with undulations, they complement previously reported drift-flux models developed for vertical and inclined wells down to approximately 5 degrees from horizontal. The formulation of these correlations has a high degree of nonlinearity. These models are tested in simulations of SAGD field operations.\u0000 First, an overview of drift-flux models is discussed. This differentiates those based on vertical flow with gravity segregation to those that model horizontal flow with stratified and slug flow regimes. Second, the most recent and significant drift-flux correlation by Bailey et al. (2018, and hereafter referred to as Bailey-Tang-Stone) was robustly designed to be used in the well model of a reservoir simulator, can handle all inclination angles and was optimized to experimental data from the largest available databases to date. This and earlier drift-flux models are reviewed as to their strengths and weaknesses. Third, governing equations and implementation details are given of the Bailey-Tang-Stone model. Fourth, six case studies are presented that illustrate homogeneous and drift-flux flow model differences for various well scenarios.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89546499","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}
Mechanistic modeling of the non-Newtonian CO2-foam flow in porous media is a challenging task that is computationally expensive due to abrupt gas mobility changes. The objective of this paper is to present a local equilibrium (LE) CO2-foam mechanistic model, which could alleviate some of the computational cost, and its implementation in the Matlab Reservoir Simulation Tool (MRST). Interweaving the LE-foam model into MRST enables users quick prototyping and testing of new ideas and/or mechanistic expressions. We use MRST, the open source tool available from SINTEF, to implement our LE-foam model. The model utilizes MRST automatic differentiation capability to compute the fluxes as well as the saturations of the aqueous and the gaseous phases at each Newton iteration. These computed variables and fluxes are then fed into the LE-foam model that estimates the bubble density (number of bubbles per unit volume of gas) in each grid block. Finally, the estimated bubble density at each grid block is used to readjust the gaseous phase mobility until convergence is achieved. Unlike the full-physics model, the LE-foam model does not add a population balance equation for the flowing bubbles. The developed LE-foam model, therefore, does not add much computational cost to solving a black oil system of equations as it uses the information from each Newton iteration to adjust the gas mobility. Our model is able to match experimental transient foam flooding results from the literature. The chosen flowing foam fraction (Xf) formula dictates to a large extent the behavior of the solution. An appropriate formula for Xf needs to be chosen such that our simulations are more predictive. The work described in this paper could help in prototyping various ideas about generation and coalescence of bubbles as well as any other correlations used in any population balance model. The chosen model can then be used to predict foam flow and estimate economic value of any foam pilot project.
多孔介质中非牛顿co2泡沫流动的力学建模是一项具有挑战性的任务，由于气体迁移率的突然变化，计算成本很高。本文的目的是提出一个局部平衡(LE) co2 -泡沫机理模型，以减轻部分计算成本，并在Matlab油藏模拟工具(MRST)中实现。将LE-foam模型交织到MRST中，用户可以快速制作原型并测试新想法和/或机械表达。我们使用SINTEF提供的开源工具MRST来实现我们的LE-foam模型。该模型利用MRST自动微分能力，在每次牛顿迭代时计算水相和气相的通量和饱和度。这些计算出的变量和通量然后被输入LE-foam模型，该模型估计每个网格块中的气泡密度(单位体积气体中的气泡数)。最后，利用每个网格块上估计的气泡密度来重新调整气相迁移率，直到达到收敛。与全物理模型不同，LE-foam模型没有为流动的气泡添加种群平衡方程。因此，所开发的LE-foam模型不会增加求解黑油方程组的计算成本，因为它使用每次牛顿迭代的信息来调整气体迁移率。我们的模型能够与文献中的实验瞬态泡沫驱结果相匹配。所选择的流动泡沫分数(Xf)公式在很大程度上决定了溶液的行为。需要为Xf选择合适的公式，以便我们的模拟更具预测性。本文中描述的工作可以帮助建立关于气泡产生和合并的各种想法的原型，以及在任何人口平衡模型中使用的任何其他相关性。所选择的模型可以用来预测泡沫流动和估计任何泡沫试点项目的经济价值。
{"title":"Local Equilibrium Mechanistic Simulation of CO2-Foam Flooding","authors":"M. Almajid, Z. Alyousef, Othman Swaie","doi":"10.2118/203922-ms","DOIUrl":"https://doi.org/10.2118/203922-ms","url":null,"abstract":"\u0000 Mechanistic modeling of the non-Newtonian CO2-foam flow in porous media is a challenging task that is computationally expensive due to abrupt gas mobility changes. The objective of this paper is to present a local equilibrium (LE) CO2-foam mechanistic model, which could alleviate some of the computational cost, and its implementation in the Matlab Reservoir Simulation Tool (MRST). Interweaving the LE-foam model into MRST enables users quick prototyping and testing of new ideas and/or mechanistic expressions.\u0000 We use MRST, the open source tool available from SINTEF, to implement our LE-foam model. The model utilizes MRST automatic differentiation capability to compute the fluxes as well as the saturations of the aqueous and the gaseous phases at each Newton iteration. These computed variables and fluxes are then fed into the LE-foam model that estimates the bubble density (number of bubbles per unit volume of gas) in each grid block. Finally, the estimated bubble density at each grid block is used to readjust the gaseous phase mobility until convergence is achieved.\u0000 Unlike the full-physics model, the LE-foam model does not add a population balance equation for the flowing bubbles. The developed LE-foam model, therefore, does not add much computational cost to solving a black oil system of equations as it uses the information from each Newton iteration to adjust the gas mobility. Our model is able to match experimental transient foam flooding results from the literature. The chosen flowing foam fraction (Xf) formula dictates to a large extent the behavior of the solution. An appropriate formula for Xf needs to be chosen such that our simulations are more predictive.\u0000 The work described in this paper could help in prototyping various ideas about generation and coalescence of bubbles as well as any other correlations used in any population balance model. The chosen model can then be used to predict foam flow and estimate economic value of any foam pilot project.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73247152","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 sequential fully implicit (SFI) scheme was introduced (Jenny et al. 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and sequentially solve the pressure and transport sub-problems. In standard SFI, the sub-problems are usually fully solved at each outer iteration. This can result in wasted computations that contribute little towards the coupled solution. The issue is known as ‘over-solving’. Our objective is to minimize the cost while maintain or improve the convergence of SFI by preventing ‘over-solving’. We first developed a framework based on the nonlinear acceleration techniques (Jiang and Tchelepi 2019) to ensure robust outer-loop convergence. We then developed inexact-type methods that prevent ‘over-solving’ and minimize the cost of inner solvers for SFI. The motivation is similar to the inexact Newton method, where the inner (linear) iterations are controlled in a way that the outer (Newton) convergence is not degraded, but the overall computational effort is greatly reduced. We proposed an adaptive strategy that provides relative tolerances based on the convergence rates of the coupled problem. The developed inexact SFI method was tested using numerous simulation studies. We compared different strategies such as fixed relaxations on absolute and relative tolerances for the inner solvers. The test cases included synthetic as well as real-field models with complex flow physics and high heterogeneity. The results show that the basic SFI method is quite inefficient. When the coupling is strong, we observed that the outer convergence is mainly restricted by the initial residuals of the sub-problems. It was observed that the feedback from one inner solver can cause the residual of the other to rebound to a much higher level. Away from a coupled solution, additional accuracy achieved in inner solvers is wasted, contributing to little or no reduction of the overall residual. By comparison, the inexact SFI method adaptively provided the relative tolerances adequate for the sub-problems. We show across a wide range of flow conditions that the inexact SFI can effectively resolve the ‘over-solving’ issue, and thus greatly improve the overall performance. The novel information of this paper includes: 1) we found that for SFI, there is no need for one sub-problem to strive for perfection (‘over-solving’), while the coupled residual remains high because of the other sub-problem; 2) a novel inexact SFI method was developed to prevent ‘over-solving’ and minimize the cost of inner solvers; 3) an adaptive strategy was proposed for relative tolerances based on the convergence rates of the coupled problem; and 4) a novel SFI framework was developed based on the nonlinear acceleration techniques to ensure robust outer-loop convergence.
引入了顺序全隐式(SFI)方案(Jenny et al. 2006)来解决耦合流动和运输问题。SFI的每个时间步长由一个外环组成，外环内有牛顿内环，隐式顺序求解压力子问题和输运子问题。在标准的SFI中，子问题通常在每次外部迭代时得到完全解决。这可能导致对耦合解决方案贡献不大的浪费计算。这个问题被称为“过度解决”。我们的目标是通过防止“过度求解”来保持或提高SFI的收敛性，同时最小化成本。我们首先开发了一个基于非线性加速技术的框架(Jiang和Tchelepi 2019)，以确保鲁棒的外环收敛。然后，我们开发了不精确类型的方法，以防止“过度求解”并最小化SFI内部求解器的成本。其动机类似于不精确牛顿方法，其中内部(线性)迭代以一种不降低外部(牛顿)收敛的方式进行控制，但总体计算工作量大大减少。我们提出了一种基于耦合问题收敛速度提供相对容差的自适应策略。开发的不精确SFI方法通过大量模拟研究进行了测试。我们比较了不同的策略，如固定松弛的绝对容限和相对容限。测试用例包括复杂流动物理和高非均质性的合成模型和实际模型。结果表明，基本的SFI方法效率很低。当耦合较强时，外收敛性主要受子问题初始残差的限制。观察到，来自一个内部解算器的反馈可以使另一个内部解算器的残差反弹到更高的水平。远离耦合解决方案，在内部求解器中获得的额外精度被浪费了，有助于很少或没有减少总体残差。通过比较，非精确SFI方法自适应地为子问题提供了足够的相对容差。我们在广泛的流动条件下表明，不精确的SFI可以有效地解决“过度求解”问题，从而大大提高整体性能。本文的新信息包括:1)我们发现对于SFI，不需要一个子问题追求完美(“过度求解”)，而由于另一个子问题的存在，耦合残差仍然很高;2)开发了一种新的非精确SFI方法，以防止“过度求解”并最小化内部求解器的成本;3)基于耦合问题的收敛速度，提出了相对公差的自适应策略;4)提出了一种基于非线性加速技术的SFI框架，以保证鲁棒外环收敛。
{"title":"Inexact Methods for Black-Oil Sequential Fully Implicit SFI Scheme","authors":"Yifan Zhou, Jiamin Jiang, P. Tomin","doi":"10.2118/203900-ms","DOIUrl":"https://doi.org/10.2118/203900-ms","url":null,"abstract":"\u0000 The sequential fully implicit (SFI) scheme was introduced (Jenny et al. 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and sequentially solve the pressure and transport sub-problems. In standard SFI, the sub-problems are usually fully solved at each outer iteration. This can result in wasted computations that contribute little towards the coupled solution. The issue is known as ‘over-solving’. Our objective is to minimize the cost while maintain or improve the convergence of SFI by preventing ‘over-solving’.\u0000 We first developed a framework based on the nonlinear acceleration techniques (Jiang and Tchelepi 2019) to ensure robust outer-loop convergence. We then developed inexact-type methods that prevent ‘over-solving’ and minimize the cost of inner solvers for SFI. The motivation is similar to the inexact Newton method, where the inner (linear) iterations are controlled in a way that the outer (Newton) convergence is not degraded, but the overall computational effort is greatly reduced. We proposed an adaptive strategy that provides relative tolerances based on the convergence rates of the coupled problem.\u0000 The developed inexact SFI method was tested using numerous simulation studies. We compared different strategies such as fixed relaxations on absolute and relative tolerances for the inner solvers. The test cases included synthetic as well as real-field models with complex flow physics and high heterogeneity. The results show that the basic SFI method is quite inefficient. When the coupling is strong, we observed that the outer convergence is mainly restricted by the initial residuals of the sub-problems. It was observed that the feedback from one inner solver can cause the residual of the other to rebound to a much higher level. Away from a coupled solution, additional accuracy achieved in inner solvers is wasted, contributing to little or no reduction of the overall residual. By comparison, the inexact SFI method adaptively provided the relative tolerances adequate for the sub-problems. We show across a wide range of flow conditions that the inexact SFI can effectively resolve the ‘over-solving’ issue, and thus greatly improve the overall performance.\u0000 The novel information of this paper includes: 1) we found that for SFI, there is no need for one sub-problem to strive for perfection (‘over-solving’), while the coupled residual remains high because of the other sub-problem; 2) a novel inexact SFI method was developed to prevent ‘over-solving’ and minimize the cost of inner solvers; 3) an adaptive strategy was proposed for relative tolerances based on the convergence rates of the coupled problem; and 4) a novel SFI framework was developed based on the nonlinear acceleration techniques to ensure robust outer-loop convergence.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"31 Suppl 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":"79958908","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}
Thermal compositional simulators rely heavily on multicomponent, multiphase flash calculations for a variety of reasons, including reservoir and wellbore initialization, phase appearance and disappearance, and property calculation. In a mass variable formulation, an isenthalpic flash is used for phase split computation, phase saturation update, component mole fraction update in different phases, and temperatures. A natural variable formulation utilizes an isothermal flash mainly for phase appearance and disappearance as well as computation of component mole fractions in appearing phases. Multiphase multicomponent isothermal flash calculations cannot be performed in narrow boiling systems which are very common in the simulation of thermal EOR operations such as Steam-Assisted Gravity Drainage (SAGD) or Steam Flooding (SF). In a narrow boiling point system, pressure and temperature are not linearly independent, and an isothermal flash will fail. In addition, flash calculations are computationally expensive, and reservoir simulators use different techniques to perform them as little as possible. A new thermal stability check has been developed that can be used in thermal compositional simulators and replaces an isothermal flash calculation. The new stability check quickly determines the phase state of a fluid sample and can be used as an initial guess for mole fraction of a phase appearing in the next simulation cycle. In this method, primary variables of the simulator are used as input for the stability check immediately after the nonlinear solver update so that computation of global mole fractions is not required. The new stability check can also be used in separator and isenthalpic flash calculations to determine the phase state of a fluid. An algorithm is provided, covering all different transitions of phase states in a thermal compositional simulator. The proposed algorithm is significantly faster than a flash calculation and saves simulation time spent in this calculation, hence the overall speed up is case dependent. The new stability check is simple, computationally inexpensive, and robust. It can be used for multicomponent and single-component systems, and we tested it rigorously against real field and synthetic models. The new thermal stability check always predicts the number of phase states correctly and never fails. In this paper, we demonstrate a thermal compositional simulation that is run without performing a single flash calculation.
{"title":"Development of a Thermal Stability Method for Phase Appearance and Disappearance Handling in Thermal Compositional Simulators","authors":"M. Heidari, T. Stone","doi":"10.2118/203912-ms","DOIUrl":"https://doi.org/10.2118/203912-ms","url":null,"abstract":"\u0000 Thermal compositional simulators rely heavily on multicomponent, multiphase flash calculations for a variety of reasons, including reservoir and wellbore initialization, phase appearance and disappearance, and property calculation. In a mass variable formulation, an isenthalpic flash is used for phase split computation, phase saturation update, component mole fraction update in different phases, and temperatures. A natural variable formulation utilizes an isothermal flash mainly for phase appearance and disappearance as well as computation of component mole fractions in appearing phases.\u0000 Multiphase multicomponent isothermal flash calculations cannot be performed in narrow boiling systems which are very common in the simulation of thermal EOR operations such as Steam-Assisted Gravity Drainage (SAGD) or Steam Flooding (SF). In a narrow boiling point system, pressure and temperature are not linearly independent, and an isothermal flash will fail. In addition, flash calculations are computationally expensive, and reservoir simulators use different techniques to perform them as little as possible.\u0000 A new thermal stability check has been developed that can be used in thermal compositional simulators and replaces an isothermal flash calculation. The new stability check quickly determines the phase state of a fluid sample and can be used as an initial guess for mole fraction of a phase appearing in the next simulation cycle. In this method, primary variables of the simulator are used as input for the stability check immediately after the nonlinear solver update so that computation of global mole fractions is not required. The new stability check can also be used in separator and isenthalpic flash calculations to determine the phase state of a fluid. An algorithm is provided, covering all different transitions of phase states in a thermal compositional simulator. The proposed algorithm is significantly faster than a flash calculation and saves simulation time spent in this calculation, hence the overall speed up is case dependent.\u0000 The new stability check is simple, computationally inexpensive, and robust. It can be used for multicomponent and single-component systems, and we tested it rigorously against real field and synthetic models. The new thermal stability check always predicts the number of phase states correctly and never fails. In this paper, we demonstrate a thermal compositional simulation that is run without performing a single flash calculation.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80151836","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}
We present an efficient time-continuation scheme for fluid-driven fracture propagation problems in the frame-work of the extended finite element method (XFEM). The fully coupled, fully implicit hydro-mechanical system is solved in conjunction with the linear elastic fracture propagation criterion by the Newton-Raphson method. Therefore, at the end of each time-step solve, the model ensures the energy release rate of weakest fracture tips within the equilibrium propagation regime. Besides, an initialization procedure for newly created fracture space as well as a priori estimate of stress intensity factor (SIF) growth rates are also developed to further improve the solver performance. We validate the model by the analytical solution and extend the problem to the multiple fracture propagation where stress shadow phenomenon occur.
{"title":"A Time-Continuation Solver for Hydraulic Fracture Propagation","authors":"G. Ren, R. Younis","doi":"10.2118/203937-ms","DOIUrl":"https://doi.org/10.2118/203937-ms","url":null,"abstract":"\u0000 We present an efficient time-continuation scheme for fluid-driven fracture propagation problems in the frame-work of the extended finite element method (XFEM). The fully coupled, fully implicit hydro-mechanical system is solved in conjunction with the linear elastic fracture propagation criterion by the Newton-Raphson method. Therefore, at the end of each time-step solve, the model ensures the energy release rate of weakest fracture tips within the equilibrium propagation regime. Besides, an initialization procedure for newly created fracture space as well as a priori estimate of stress intensity factor (SIF) growth rates are also developed to further improve the solver performance. We validate the model by the analytical solution and extend the problem to the multiple fracture propagation where stress shadow phenomenon occur.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76126254","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. Barker, C. S. Lee, F. Forouzanfar, A. Guion, Xiao-hui Wu
We explore the problem of drawing posterior samples from a lognormal permeability field conditioned by noisy measurements at discrete locations. The underlying unconditioned samples are based on a scalable PDE-sampling technique that shows better scalability for large problems than the traditional Karhunen-Loeve sampling, while still allowing for consistent samples to be drawn on a hierarchy of spatial scales. Lognormal random fields produced in this scalable and hierarchical way are then conditioned to measured data by a randomized maximum likelihood approach to draw from a Bayesian posterior distribution. The algorithm to draw from the posterior distribution can be shown to be equivalent to a PDE-constrained optimization problem, which allows for some efficient computational solution techniques. Numerical results demonstrate the efficiency of the proposed methods. In particular, we are able to match statistics for a simple flow problem on the fine grid with high accuracy and at much lower cost on a scale of coarser grids.
{"title":"Scalable Hierarchical Multilevel Sampling of Lognormal Fields Conditioned on Measured Data","authors":"A. Barker, C. S. Lee, F. Forouzanfar, A. Guion, Xiao-hui Wu","doi":"10.2118/203907-ms","DOIUrl":"https://doi.org/10.2118/203907-ms","url":null,"abstract":"\u0000 We explore the problem of drawing posterior samples from a lognormal permeability field conditioned by noisy measurements at discrete locations. The underlying unconditioned samples are based on a scalable PDE-sampling technique that shows better scalability for large problems than the traditional Karhunen-Loeve sampling, while still allowing for consistent samples to be drawn on a hierarchy of spatial scales. Lognormal random fields produced in this scalable and hierarchical way are then conditioned to measured data by a randomized maximum likelihood approach to draw from a Bayesian posterior distribution. The algorithm to draw from the posterior distribution can be shown to be equivalent to a PDE-constrained optimization problem, which allows for some efficient computational solution techniques. Numerical results demonstrate the efficiency of the proposed methods. In particular, we are able to match statistics for a simple flow problem on the fine grid with high accuracy and at much lower cost on a scale of coarser grids.","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":"82501082","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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