An existing equation-of-state compositional simulator is extended to include proppant transport. The simulator determines the final location of the proppant after fracture closure, which allows the computation of the permeability along the hydraulic fracture. The simulation then continues until the end of the production. During hydraulic fracturing, proppant is injected in the reservoir along with water and additives like polymers. Hydraulic fracture gets created due to change in stress caused by the high injection pressure. Once the fracture opens, the bulk slurry moves along the hydraulic fracture. Proppant moves at a different speed than the bulk slurry and sinks down by gravity. While the proppant flows along the fracture, some of the slurry leaks off into the matrix. As the fracture closes after injection stops, the proppant becomes immobile. The immobilized proppant prevents the fracture from closing and thus keeps the permeability of the fracture high. All the above phenomena are modelled effectively in this new implementation. Coupled geomechanics simulation is used to model opening and closure of the fracture following geomechanics criteria. Proppant retardation, gravitational settling and fluid leak-off are modeled with the appropriate equations. The propped fracture permeability is a function of the concentration of immobilized proppant. The developed proppant simulation feature is computationally stable and efficient. The time step size during the settling adapts to the settling velocity of the proppants. It is found that the final location of the proppants is highly dependent on its volumetric concentration and slurry viscosity due to retardation and settling effects. As the location and the concentration of the proppants determine the final fracture permeability, the additional feature is expected to correctly identify the stimulated region. In this paper, the theory and the model formulation are presented along with a few key examples. The simulation can be used to design and optimize the amount of proppant and additives, injection timing, pressure, and well parameters required for successful hydraulic fracturing.
{"title":"Numerical Simulation of Proppant Transport in Hydraulically Fractured Reservoirs","authors":"S. E. Gorucu, V. Shrivastava, L. Nghiem","doi":"10.2118/203927-ms","DOIUrl":"https://doi.org/10.2118/203927-ms","url":null,"abstract":"\u0000 An existing equation-of-state compositional simulator is extended to include proppant transport. The simulator determines the final location of the proppant after fracture closure, which allows the computation of the permeability along the hydraulic fracture. The simulation then continues until the end of the production.\u0000 During hydraulic fracturing, proppant is injected in the reservoir along with water and additives like polymers. Hydraulic fracture gets created due to change in stress caused by the high injection pressure. Once the fracture opens, the bulk slurry moves along the hydraulic fracture. Proppant moves at a different speed than the bulk slurry and sinks down by gravity. While the proppant flows along the fracture, some of the slurry leaks off into the matrix. As the fracture closes after injection stops, the proppant becomes immobile. The immobilized proppant prevents the fracture from closing and thus keeps the permeability of the fracture high.\u0000 All the above phenomena are modelled effectively in this new implementation. Coupled geomechanics simulation is used to model opening and closure of the fracture following geomechanics criteria. Proppant retardation, gravitational settling and fluid leak-off are modeled with the appropriate equations. The propped fracture permeability is a function of the concentration of immobilized proppant. The developed proppant simulation feature is computationally stable and efficient. The time step size during the settling adapts to the settling velocity of the proppants. It is found that the final location of the proppants is highly dependent on its volumetric concentration and slurry viscosity due to retardation and settling effects. As the location and the concentration of the proppants determine the final fracture permeability, the additional feature is expected to correctly identify the stimulated region.\u0000 In this paper, the theory and the model formulation are presented along with a few key examples. The simulation can be used to design and optimize the amount of proppant and additives, injection timing, pressure, and well parameters required for successful hydraulic fracturing.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86700132","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}
Xueying Lu, K. E. Jordan, M. Wheeler, Edward O. Pyzer-Knapp, Matthew Benatan
We present a framework of the application of Bayesian Optimization (BO) to well management in geological carbon sequestration. The coupled compositional flow and poroelasticity simulator, IPARS, is utilized to accurately capture the underlying physical processes during CO2 sequestration. IPARS is coupled to IBM Bayesian Optimization (IBO) for parallel optimizations of CO2 injection strategies during field-scale CO2 sequestration. Bayesian optimization builds a probabilistic surrogate for the objective function using a Bayesian machine learning algorithm, Gaussian process regression, and then uses an acquisition function that leverages the uncertainty in the surrogate to decide where to sample. IBO addresses the three weak points of the standard BO in that it supports parallel (batch) executions, scales better for high-dimensional problems, and is more robust to initializations. We demonstrate these algorithmic merits by an application to the optimization of the CO2 injection schedule in the Cranfield site using field data. The performance is benchmarked with genetic algorithm (GA) and covariance matrix adaptation evolution strategy (CMA-ES). Results show that IBO achieves competitive objective function value with over 60% less number of forward model evaluations. Furthermore, the Bayesian framework that BO builds upon allows uncertainty quantification and naturally extends to optimization under uncertainty.
{"title":"Bayesian Optimization for Field Scale Geological Carbon Sequestration","authors":"Xueying Lu, K. E. Jordan, M. Wheeler, Edward O. Pyzer-Knapp, Matthew Benatan","doi":"10.2118/203950-ms","DOIUrl":"https://doi.org/10.2118/203950-ms","url":null,"abstract":"\u0000 We present a framework of the application of Bayesian Optimization (BO) to well management in geological carbon sequestration. The coupled compositional flow and poroelasticity simulator, IPARS, is utilized to accurately capture the underlying physical processes during CO2 sequestration. IPARS is coupled to IBM Bayesian Optimization (IBO) for parallel optimizations of CO2 injection strategies during field-scale CO2 sequestration. Bayesian optimization builds a probabilistic surrogate for the objective function using a Bayesian machine learning algorithm, Gaussian process regression, and then uses an acquisition function that leverages the uncertainty in the surrogate to decide where to sample. IBO addresses the three weak points of the standard BO in that it supports parallel (batch) executions, scales better for high-dimensional problems, and is more robust to initializations. We demonstrate these algorithmic merits by an application to the optimization of the CO2 injection schedule in the Cranfield site using field data. The performance is benchmarked with genetic algorithm (GA) and covariance matrix adaptation evolution strategy (CMA-ES). Results show that IBO achieves competitive objective function value with over 60% less number of forward model evaluations. Furthermore, the Bayesian framework that BO builds upon allows uncertainty quantification and naturally extends to optimization under uncertainty.","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":"79279858","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 research of multiphysical thermal-hydraulic-mechanical (THM) simulation has achieved significant progress in the past decade. Currently, two general approaches for poromechanical simulation co-exist in the reservoir simulation community, namely the stress approach with stress as the primary variable for the mechanical governing equations and the displacement approach with displacement as the primary variable. In this work, we aim to provide a theoretical foundation and a practical semi-analytical solution for the stress approach based on the Navier-Beltrami-Michell Equations. Moreover, we will clarify the relationship (and equivalence) between the two approaches. We have firstly proven the existence and uniqueness of the stress solution of Navier-Beltrami-Michell equation with given pressure and temperature field. Moreover, we have demonstrated the equivalence of the stress formulation to the displacement formulation. Based on Fourier's expansion, we have developed a general semi-analytical solution for thermal-hydraulic-mechanical process. The semi-analytical solution takes the pressure solution from the hydraulic simulation module (or a commercial reservoir simulator) and directly predicts the stress tensor of the multiphysical system. As such, the solution can be programmed fully coupled with the hydraulic simulation module to predict the stress field with varying pressure and temperature of homogeneous poroelastic rocks under given stress boundary conditions. From the work above, we have laid a theoretical foundation for the stress approach. The derived semi-analytical solution of the stress field shows excellent accuracy. The solution has been used to predict the transient stress field of a dual-porosity system during primary depletion. This paper is arguably the first trial to clarify the relationship between the stress approach and the displacement approach. Moreover, the derived semi-analytical solution provides a convenient yet precise way to obtain the stress field without time-consuming numerical simulation.
{"title":"Theoretical Analysis and Semi-Analytical Formulation for Efficient Thermal-Hydraulic-Mechanical Reservoir Simulation","authors":"Shihao Wang, Yushu Wu, X. Wen","doi":"10.2118/203923-ms","DOIUrl":"https://doi.org/10.2118/203923-ms","url":null,"abstract":"\u0000 The research of multiphysical thermal-hydraulic-mechanical (THM) simulation has achieved significant progress in the past decade. Currently, two general approaches for poromechanical simulation co-exist in the reservoir simulation community, namely the stress approach with stress as the primary variable for the mechanical governing equations and the displacement approach with displacement as the primary variable. In this work, we aim to provide a theoretical foundation and a practical semi-analytical solution for the stress approach based on the Navier-Beltrami-Michell Equations. Moreover, we will clarify the relationship (and equivalence) between the two approaches.\u0000 We have firstly proven the existence and uniqueness of the stress solution of Navier-Beltrami-Michell equation with given pressure and temperature field. Moreover, we have demonstrated the equivalence of the stress formulation to the displacement formulation. Based on Fourier's expansion, we have developed a general semi-analytical solution for thermal-hydraulic-mechanical process. The semi-analytical solution takes the pressure solution from the hydraulic simulation module (or a commercial reservoir simulator) and directly predicts the stress tensor of the multiphysical system. As such, the solution can be programmed fully coupled with the hydraulic simulation module to predict the stress field with varying pressure and temperature of homogeneous poroelastic rocks under given stress boundary conditions.\u0000 From the work above, we have laid a theoretical foundation for the stress approach. The derived semi-analytical solution of the stress field shows excellent accuracy. The solution has been used to predict the transient stress field of a dual-porosity system during primary depletion.\u0000 This paper is arguably the first trial to clarify the relationship between the stress approach and the displacement approach. Moreover, the derived semi-analytical solution provides a convenient yet precise way to obtain the stress field without time-consuming numerical simulation.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"101 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81291829","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}
It is very challenging to simulate unconventional reservoirs efficiently and accurately. Transient flow can last for a long time and sharp solution (pressure, saturation, compositions) gradients are induced because of the severe permeability contrast between fracture and matrix. Although high-resolution models for well and fracture are required to achieve adequate resolution, they are computationally too demanding for practical field models with many stages of hydraulic fracture. The paper aims to innovate localization strategies that take advantage of locality on timestep and Newton iteration levels. The strategies readily accommodate to complicated flow mechanisms and multiscale fracture networks in unconventional reservoirs. Large simulation speed-up can be obtained if performing localized computations only for the solution regions that will change. We develop an a-priori method to exploit the locality, based on the diffusive character of the Newton updates of pressure. The method makes adequate estimate of the active computational gridblock for the next iterate. The active gridblock set marks the ones need to be solved, and then the solution to local linear system is accordingly computed. Fully Implicit Scheme is used for time discretization. We study several challenging multi-phase and compositional model cases with explicit fractures. The test results demonstrate that significant solution locality of variables exist on timestep and iteration levels. A nonlinear solution update usually has sparsity, and the nonlinear convergence is restricted by a limited fraction of the simulation model. Through aggressive localization, the proposed methods can prevent overly conservative estimate, and thus achieve significant computational speedup. In comparison to a standard Newton method, the novel solver techniques achieve greatly improved solving efficiency. Furthermore, the Newton convergence exhibits no degradation, and there is no impact on the solution accuracy. Previous works in the literature largely relate to the meshing aspect that accommodates to horizontal wells and hydraulic fractures. We instead develop new nonlinear strategies to perform localization. In particular, the adaptive DD method produces proper domain partitions according to the fluid flow and nonlinear updates. This results in an effective strategy that maintains solution accuracy and convergence behavior.
{"title":"Efficient Localized Nonlinear Solution Strategies for Unconventional-Reservoir Simulation with Complex Fractures","authors":"Jiamin Jiang","doi":"10.2118/203987-ms","DOIUrl":"https://doi.org/10.2118/203987-ms","url":null,"abstract":"\u0000 It is very challenging to simulate unconventional reservoirs efficiently and accurately. Transient flow can last for a long time and sharp solution (pressure, saturation, compositions) gradients are induced because of the severe permeability contrast between fracture and matrix. Although high-resolution models for well and fracture are required to achieve adequate resolution, they are computationally too demanding for practical field models with many stages of hydraulic fracture. The paper aims to innovate localization strategies that take advantage of locality on timestep and Newton iteration levels. The strategies readily accommodate to complicated flow mechanisms and multiscale fracture networks in unconventional reservoirs.\u0000 Large simulation speed-up can be obtained if performing localized computations only for the solution regions that will change. We develop an a-priori method to exploit the locality, based on the diffusive character of the Newton updates of pressure. The method makes adequate estimate of the active computational gridblock for the next iterate. The active gridblock set marks the ones need to be solved, and then the solution to local linear system is accordingly computed.\u0000 Fully Implicit Scheme is used for time discretization. We study several challenging multi-phase and compositional model cases with explicit fractures. The test results demonstrate that significant solution locality of variables exist on timestep and iteration levels. A nonlinear solution update usually has sparsity, and the nonlinear convergence is restricted by a limited fraction of the simulation model. Through aggressive localization, the proposed methods can prevent overly conservative estimate, and thus achieve significant computational speedup. In comparison to a standard Newton method, the novel solver techniques achieve greatly improved solving efficiency. Furthermore, the Newton convergence exhibits no degradation, and there is no impact on the solution accuracy.\u0000 Previous works in the literature largely relate to the meshing aspect that accommodates to horizontal wells and hydraulic fractures. We instead develop new nonlinear strategies to perform localization. In particular, the adaptive DD method produces proper domain partitions according to the fluid flow and nonlinear updates. This results in an effective strategy that maintains solution accuracy and convergence behavior.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"147 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86111206","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}
Automatic differentiation software libraries augment arithmetic operations with their derivatives, thereby relieving the programmer of deriving, implementing, debugging, and maintaining derivative code. With this encapsulation however, the responsibility of code optimization relies more heavily on the AD system itself (as opposed to the programmer and the compiler). Moreover, given that there are multiple contexts in reservoir simulation software for which derivatives are required (e.g. property package and discrete operator evaluations), the AD infrastructure must also be adaptable. An Operator Overloading AD design is proposed and tested to provide scalability and computational efficiency seemlessly across memory- and compute-bound applications. This is achieved by 1) use of portable and standard programming language constructs (C++17 and OpenMP 4.5 standards), 2) adopting a vectorized programming interface, 3) lazy evaluation via expression templates, and 4) multiple memory alignment and layout policies. Empirical analysis is conducted on various kernels spanning various arithmetic intensity and working set sizes. Cache- aware roofline analysis results show that the performance and scalability attained are reliably ideal. In terms of floapting point operations executed per second, the performance of the AD system matches optimized hand-code. Finally, the implementation is benchmarked using the Automatically Differentiable Expression Templates Library (ADETL).
{"title":"Cache-Aware and Roofline-Ideal Automatic Differentiation","authors":"Yuxuan Jing, R. Younis","doi":"10.2118/203933-ms","DOIUrl":"https://doi.org/10.2118/203933-ms","url":null,"abstract":"\u0000 Automatic differentiation software libraries augment arithmetic operations with their derivatives, thereby relieving the programmer of deriving, implementing, debugging, and maintaining derivative code. With this encapsulation however, the responsibility of code optimization relies more heavily on the AD system itself (as opposed to the programmer and the compiler). Moreover, given that there are multiple contexts in reservoir simulation software for which derivatives are required (e.g. property package and discrete operator evaluations), the AD infrastructure must also be adaptable. An Operator Overloading AD design is proposed and tested to provide scalability and computational efficiency seemlessly across memory- and compute-bound applications. This is achieved by 1) use of portable and standard programming language constructs (C++17 and OpenMP 4.5 standards), 2) adopting a vectorized programming interface, 3) lazy evaluation via expression templates, and 4) multiple memory alignment and layout policies. Empirical analysis is conducted on various kernels spanning various arithmetic intensity and working set sizes. Cache- aware roofline analysis results show that the performance and scalability attained are reliably ideal. In terms of floapting point operations executed per second, the performance of the AD system matches optimized hand-code. Finally, the implementation is benchmarked using the Automatically Differentiable Expression Templates Library (ADETL).","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88107899","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}
G. Isotton, C. Janna, N. Spiezia, Omar Tosatto, M. Bernaschi, A. Cominelli, S. Mantica, S. Monaco, G. Scrofani
Modern engineering applications require the solution of linear systems of millions or even billions of equations. The solution of the linear system takes most of the simulation for large scale simulations, and represent the bottleneck in developing scientific and technical software. Usually, preconditioned iterative solvers are preferred because of their low memory requirements and they can have a high level of parallelism. Approximate inverses have been proven to be robust and effective preconditioners in several contexts. In this communication, we present an adaptive Factorized Sparse Approximate Inverse (FSAI) preconditioner with a very high level of parallelism in both set-up and application. Its inherent parallelism makes FSAI an ideal candidate for a GPU-accelerated implementation, even if taking advantage of this hardware is not a trivial task, especially in the set-up stage. An extensive numerical experimentation has been performed on industrial underground applications. It is shown that the proposed approach outperforms more traditional preconditioners in challenging underground simulation, greatly reducing time-to-solution.
{"title":"A GPU-Accelerated Linear Solver for Massively Parallel Underground Simulations","authors":"G. Isotton, C. Janna, N. Spiezia, Omar Tosatto, M. Bernaschi, A. Cominelli, S. Mantica, S. Monaco, G. Scrofani","doi":"10.2118/204011-ms","DOIUrl":"https://doi.org/10.2118/204011-ms","url":null,"abstract":"\u0000 Modern engineering applications require the solution of linear systems of millions or even billions of equations. The solution of the linear system takes most of the simulation for large scale simulations, and represent the bottleneck in developing scientific and technical software. Usually, preconditioned iterative solvers are preferred because of their low memory requirements and they can have a high level of parallelism. Approximate inverses have been proven to be robust and effective preconditioners in several contexts. In this communication, we present an adaptive Factorized Sparse Approximate Inverse (FSAI) preconditioner with a very high level of parallelism in both set-up and application. Its inherent parallelism makes FSAI an ideal candidate for a GPU-accelerated implementation, even if taking advantage of this hardware is not a trivial task, especially in the set-up stage. An extensive numerical experimentation has been performed on industrial underground applications. It is shown that the proposed approach outperforms more traditional preconditioners in challenging underground simulation, greatly reducing time-to-solution.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"112 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76790097","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 properties of fluids flowing in a petroleum reservoir are quantified by understanding the thermodynamic behavior of each flowing phase in the system. This work describes proper techniques to formulate and execute a thermodynamic model for accurately predicting the equilibrium behavior of oil-gas-brine systems within the practical range of pressure and temperature. The three-phase flash algorithm is validated against published data from the available literature. The multiphase flash procedure is implemented to generate linearized physical properties by using an Operator Based Linearization (OBL) modelling technique allowing for a combination of multiple complex physics in the nonlinear solution of governing equations. This is the first implementation of three-phase flash calculations for hydrocarbons and brines based on fugacity-activity models coupled with an advanced highly efficient linearization scheme. Our approach increases the efficiency and flexibility of the modelling process of physical phenomena such as fluid flow in porous subsurface reservoirs.
{"title":"Coupling of Rigorous Multiphase Flash with Advanced Linearization Schemes for Accurate Compositional Simulation","authors":"A. S. Abd, A. Abushaikha, D. Voskov","doi":"10.2118/203956-ms","DOIUrl":"https://doi.org/10.2118/203956-ms","url":null,"abstract":"\u0000 The properties of fluids flowing in a petroleum reservoir are quantified by understanding the thermodynamic behavior of each flowing phase in the system. This work describes proper techniques to formulate and execute a thermodynamic model for accurately predicting the equilibrium behavior of oil-gas-brine systems within the practical range of pressure and temperature. The three-phase flash algorithm is validated against published data from the available literature. The multiphase flash procedure is implemented to generate linearized physical properties by using an Operator Based Linearization (OBL) modelling technique allowing for a combination of multiple complex physics in the nonlinear solution of governing equations. This is the first implementation of three-phase flash calculations for hydrocarbons and brines based on fugacity-activity models coupled with an advanced highly efficient linearization scheme. Our approach increases the efficiency and flexibility of the modelling process of physical phenomena such as fluid flow in porous subsurface reservoirs.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79299139","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}
Yu Jiang, J. Killough, Linkai Li, Xiaona Cui, Jin Tang
The exploitation of shale gas has attracted extensive attention in industry and academia. Multi-scale gas transportation mechanisms in matrix and fractures have been well studied. However, due to the presence of water originating from both fracking fluids and connate water, shale gas production is also greatly affected by water imbibition and flowback, of which the processes have not been thoroughly analyzed. This paper aims at presenting a comprehensive multi-continuum multi-component model to characterize the complicated shale gas flow behaviors as well as the impact of non-Darcy water flow on shale gas production. A two-phase numerical simulator is built up with multi-continuum settings. Shale matrix is split into organic and inorganic matters while natural and hydraulic fractures are modeled using an embedded discrete fracture model (EDFM). Fracture closure and elongation are modeled using a dynamic gridding approach. Different transportation mechanisms are considered to describe gas flow in shale, including Knudsen diffusion, ab/desorption, and convection. The low-velocity non-Darcy flow of water is used in inorganic pores to analyze the effect of water flow. A pre-stage model based on pumping history is simulated firstly before production starts. This serves as an initialization step to model fracking fluid imbibition and early-stage water flowback. This pre-stage simulation gives out more precise pressure and saturation profiles than the conventional non-equilibrium initialization method, especially in enhanced pore volumes and fractures. Based upon simulation results from the production period, Langmuir isotherm absorption has shown a massive impact on gas flow in shale, and Knudsen diffusion weights highest among transport mechanisms. Water non-Darcy flow better benefits in simulating both early-stage water flowback and production process compared with Darcy flow, which gives us a new explanation on the low flowback efficiency in real shale gas operations. Studies on early-stage water flowback also show that the flowback affects saturation distribution, which has a strong relationship with gas production and shall not be ignored. This work establishes a novel method to simulate and analyze shale gas production. It considers multiple and complex flow mechanisms and gives out better estimates of water flux. It is also used to initialize a model for pumping water imbibition and early-stage flowback, which can be used as technical resources for analyzing and simulating unconventional plays.
{"title":"EDFM-based Multi-Continuum Shale Gas Simulation with Low Velocity Non-Darcy Water Flow Effect","authors":"Yu Jiang, J. Killough, Linkai Li, Xiaona Cui, Jin Tang","doi":"10.2118/203988-ms","DOIUrl":"https://doi.org/10.2118/203988-ms","url":null,"abstract":"\u0000 The exploitation of shale gas has attracted extensive attention in industry and academia. Multi-scale gas transportation mechanisms in matrix and fractures have been well studied. However, due to the presence of water originating from both fracking fluids and connate water, shale gas production is also greatly affected by water imbibition and flowback, of which the processes have not been thoroughly analyzed. This paper aims at presenting a comprehensive multi-continuum multi-component model to characterize the complicated shale gas flow behaviors as well as the impact of non-Darcy water flow on shale gas production.\u0000 A two-phase numerical simulator is built up with multi-continuum settings. Shale matrix is split into organic and inorganic matters while natural and hydraulic fractures are modeled using an embedded discrete fracture model (EDFM). Fracture closure and elongation are modeled using a dynamic gridding approach. Different transportation mechanisms are considered to describe gas flow in shale, including Knudsen diffusion, ab/desorption, and convection. The low-velocity non-Darcy flow of water is used in inorganic pores to analyze the effect of water flow.\u0000 A pre-stage model based on pumping history is simulated firstly before production starts. This serves as an initialization step to model fracking fluid imbibition and early-stage water flowback. This pre-stage simulation gives out more precise pressure and saturation profiles than the conventional non-equilibrium initialization method, especially in enhanced pore volumes and fractures. Based upon simulation results from the production period, Langmuir isotherm absorption has shown a massive impact on gas flow in shale, and Knudsen diffusion weights highest among transport mechanisms. Water non-Darcy flow better benefits in simulating both early-stage water flowback and production process compared with Darcy flow, which gives us a new explanation on the low flowback efficiency in real shale gas operations. Studies on early-stage water flowback also show that the flowback affects saturation distribution, which has a strong relationship with gas production and shall not be ignored.\u0000 This work establishes a novel method to simulate and analyze shale gas production. It considers multiple and complex flow mechanisms and gives out better estimates of water flux. It is also used to initialize a model for pumping water imbibition and early-stage flowback, which can be used as technical resources for analyzing and simulating unconventional plays.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76069192","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}
Sanjoy Kumar Khataniar, Daniel de Brito Dias, Rong Xu
A new implementation of a multiscale sequential fully implicit (MS SFI) reservoir simulation method is applied to a set of reservoir engineering problems to understand its utility. An assessment is made to highlight areas where the approach brings substantial advantage in performance as well as address problems not successfully resolved by existing methods. This work makes use of the first ever implementation of the multiscale sequential fully implicit method in a commercial reservoir simulator. The key features of the method and implementation are briefly discussed. The learnings gained during field testing and commercialization on about forty real world models is illustrated through simpler, but representative data sets, available in the public domain. The workhorse robust fully implicit (FI) method is used as a reference for benchmarking. The MS SFI method can faithfully reproduce FI results for black oil problems. We conclude that the MS SFI method has the capability to support reservoir engineering decision making especially in the areas of subsurface uncertainty quantification, representative model selection, model calibration and optimization. The MS SFI method shows immense potential for handling prominent levels of reservoir heterogeneity. The challenge of including fine-scale heterogeneity, which is often overlooked, when scaling up EOR processes from laboratory to field, appears to have found a practical solution with a combination of MS SFI and high-performance computing (HPC).
{"title":"Aspects of Multiscale Flow Simulation with Potential to Enhance Reservoir Engineering Practice","authors":"Sanjoy Kumar Khataniar, Daniel de Brito Dias, Rong Xu","doi":"10.2118/203996-ms","DOIUrl":"https://doi.org/10.2118/203996-ms","url":null,"abstract":"\u0000 A new implementation of a multiscale sequential fully implicit (MS SFI) reservoir simulation method is applied to a set of reservoir engineering problems to understand its utility. An assessment is made to highlight areas where the approach brings substantial advantage in performance as well as address problems not successfully resolved by existing methods.\u0000 This work makes use of the first ever implementation of the multiscale sequential fully implicit method in a commercial reservoir simulator. The key features of the method and implementation are briefly discussed. The learnings gained during field testing and commercialization on about forty real world models is illustrated through simpler, but representative data sets, available in the public domain. The workhorse robust fully implicit (FI) method is used as a reference for benchmarking. The MS SFI method can faithfully reproduce FI results for black oil problems.\u0000 We conclude that the MS SFI method has the capability to support reservoir engineering decision making especially in the areas of subsurface uncertainty quantification, representative model selection, model calibration and optimization. The MS SFI method shows immense potential for handling prominent levels of reservoir heterogeneity. The challenge of including fine-scale heterogeneity, which is often overlooked, when scaling up EOR processes from laboratory to field, appears to have found a practical solution with a combination of MS SFI and high-performance computing (HPC).","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"8 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":"80561558","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}
Complex well model has proved to be important for capturing the full physics in wellbore, including pressure losses, multiphase effects, and advanced device modelling. Numerical instability may be observed especially when the well is produced at a low rate from a highly productive multi-phase zone. In this paper, a new multi-level nonlinear solver is presented in a state-of-the-art parallel complex wellbore model for addressing some difficult numerical convergence problems. A sequential two-level nonlinear solver is implemented, where the inner solver is used to address the convergence in the constraint rate equation, and then the entire complex network is solved using an outer solver. Finally, the wellbore model is coupled with the grid solution explicitly, sequentially, or implicitly. This novel formulation is robust enough to greatly improve the numerical stability due to the lagging in the computation of mixture density in wellbore constraint rate equation and the variation in the fluid composition over Newton iterations in network nonlinear solver. The numerical challenge in the complex well model and the improvement of performance with the new nonlinear solver are demonstrated using reservoir simulation. Models with complex wells running into convergence problems are constructed and simulated. With this novel nonlinear solver, simulation gives much more reliable results on well productions without numerical oscillations and computational cost is much less.
{"title":"A Multi-Level Non-Linear Solver for Complex Well Modelling","authors":"Zhen Chen, T. Shaalan, A. Dogru","doi":"10.2118/204009-ms","DOIUrl":"https://doi.org/10.2118/204009-ms","url":null,"abstract":"\u0000 Complex well model has proved to be important for capturing the full physics in wellbore, including pressure losses, multiphase effects, and advanced device modelling. Numerical instability may be observed especially when the well is produced at a low rate from a highly productive multi-phase zone. In this paper, a new multi-level nonlinear solver is presented in a state-of-the-art parallel complex wellbore model for addressing some difficult numerical convergence problems. A sequential two-level nonlinear solver is implemented, where the inner solver is used to address the convergence in the constraint rate equation, and then the entire complex network is solved using an outer solver. Finally, the wellbore model is coupled with the grid solution explicitly, sequentially, or implicitly. This novel formulation is robust enough to greatly improve the numerical stability due to the lagging in the computation of mixture density in wellbore constraint rate equation and the variation in the fluid composition over Newton iterations in network nonlinear solver.\u0000 The numerical challenge in the complex well model and the improvement of performance with the new nonlinear solver are demonstrated using reservoir simulation. Models with complex wells running into convergence problems are constructed and simulated. With this novel nonlinear solver, simulation gives much more reliable results on well productions without numerical oscillations and computational cost is much less.","PeriodicalId":11146,"journal":{"name":"Day 1 Tue, October 26, 2021","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87752881","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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