Pub Date : 2023-08-22DOI: 10.1007/s10596-023-10245-y
Junpeng Song, H. Rui, Zhijiang Kang
{"title":"A reduced-order model based on C-R mixed finite element and POD technique for coupled Stokes-Darcy system with solute transport","authors":"Junpeng Song, H. Rui, Zhijiang Kang","doi":"10.1007/s10596-023-10245-y","DOIUrl":"https://doi.org/10.1007/s10596-023-10245-y","url":null,"abstract":"","PeriodicalId":10662,"journal":{"name":"Computational Geosciences","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45203590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-31DOI: 10.1007/s10596-023-10229-y
I. Landim, M. Murad, Patricia A. Pereira, E. Abreu
{"title":"A new computational model for karst conduit flow in carbonate reservoirs including dissolution-collapse breccias","authors":"I. Landim, M. Murad, Patricia A. Pereira, E. Abreu","doi":"10.1007/s10596-023-10229-y","DOIUrl":"https://doi.org/10.1007/s10596-023-10229-y","url":null,"abstract":"","PeriodicalId":10662,"journal":{"name":"Computational Geosciences","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52164202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-28DOI: 10.1007/s10596-023-10238-x
Stefano Nardean, Massimiliano Ferronato, Ahmad Abushaikha
Abstract This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase flow models. This preconditioner, denoted as Block CPR (BCPR), is specifically designed for Lagrange multipliers-based flow models, such as those generated by Mixed Hybrid Finite Element (MHFE) approximations. An original MHFE-based formulation of the two-phase flow model is taken as a reference for the development of the BCPR preconditioner, in which the set of system unknowns comprises both element and face pressures, in addition to the cell saturations, resulting in a $$3times 3$$ 3×3 block-structured Jacobian matrix with a $$2times 2$$ 2×2 inner pressure problem. The CPR method is one of the most established techniques for reservoir simulations, but most research focused on solutions for Two-Point Flux Approximation (TPFA)-based discretizations that do not readily extend to our problem formulation. Therefore, we designed a dedicated two-stage strategy, inspired by the CPR algorithm, where a block preconditioner is used for the pressure part with the aim at exploiting the inner $$2times 2$$ 2×2 structure. The proposed preconditioning framework is tested by an extensive experimentation, comprising both synthetic and realistic applications in Cartesian and non-Cartesian domains.
{"title":"Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements","authors":"Stefano Nardean, Massimiliano Ferronato, Ahmad Abushaikha","doi":"10.1007/s10596-023-10238-x","DOIUrl":"https://doi.org/10.1007/s10596-023-10238-x","url":null,"abstract":"Abstract This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase flow models. This preconditioner, denoted as Block CPR (BCPR), is specifically designed for Lagrange multipliers-based flow models, such as those generated by Mixed Hybrid Finite Element (MHFE) approximations. An original MHFE-based formulation of the two-phase flow model is taken as a reference for the development of the BCPR preconditioner, in which the set of system unknowns comprises both element and face pressures, in addition to the cell saturations, resulting in a $$3times 3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>×</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> block-structured Jacobian matrix with a $$2times 2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> inner pressure problem. The CPR method is one of the most established techniques for reservoir simulations, but most research focused on solutions for Two-Point Flux Approximation (TPFA)-based discretizations that do not readily extend to our problem formulation. Therefore, we designed a dedicated two-stage strategy, inspired by the CPR algorithm, where a block preconditioner is used for the pressure part with the aim at exploiting the inner $$2times 2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> structure. The proposed preconditioning framework is tested by an extensive experimentation, comprising both synthetic and realistic applications in Cartesian and non-Cartesian domains.","PeriodicalId":10662,"journal":{"name":"Computational Geosciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135557008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-27DOI: 10.1007/s10596-023-10215-4
Olav Møyner, Atgeirr F. Rasmussen, Øystein Klemetsdal, Halvor M. Nilsen, Arthur Moncorgé, Knut-Andreas Lie
Abstract We discuss a nonlinear domain-decomposition preconditioning method for fully implicit simulations of multicomponent porous media flow based on the additive Schwarz preconditioned exact Newton method (ASPEN). The method efficiently accelerates nonlinear convergence by resolving unbalanced nonlinearities in a local stage and long-range interactions in a global stage. ASPEN can improve robustness and significantly reduce the number of global iterations compared with standard Newton, but extra work introduced in the local steps makes each global iteration more expensive. We discuss implementation aspects for the local and global stages. We show how the global-stage Jacobian can be transformed to the same form as the fully implicit system, so that one can use standard linear preconditioners and solvers. We compare the computational performance of ASPEN to standard Newton on a series of test cases, ranging from conceptual cases with simplified geometry or flow physics to cases representative of real assets. Our overall conclusion is that ASPEN is outperformed by Newton when this method works well and converges in a few iterations. On the other hand, ASPEN avoids time-step cuts and has significantly lower runtimes in time steps where Newton struggles. A good approach to computational speedup is therefore to adaptively switch between Newton and ASPEN throughout a simulation. A few examples of switching strategies are outlined.
{"title":"Nonlinear domain-decomposition preconditioning for robust and efficient field-scale simulation of subsurface flow","authors":"Olav Møyner, Atgeirr F. Rasmussen, Øystein Klemetsdal, Halvor M. Nilsen, Arthur Moncorgé, Knut-Andreas Lie","doi":"10.1007/s10596-023-10215-4","DOIUrl":"https://doi.org/10.1007/s10596-023-10215-4","url":null,"abstract":"Abstract We discuss a nonlinear domain-decomposition preconditioning method for fully implicit simulations of multicomponent porous media flow based on the additive Schwarz preconditioned exact Newton method (ASPEN). The method efficiently accelerates nonlinear convergence by resolving unbalanced nonlinearities in a local stage and long-range interactions in a global stage. ASPEN can improve robustness and significantly reduce the number of global iterations compared with standard Newton, but extra work introduced in the local steps makes each global iteration more expensive. We discuss implementation aspects for the local and global stages. We show how the global-stage Jacobian can be transformed to the same form as the fully implicit system, so that one can use standard linear preconditioners and solvers. We compare the computational performance of ASPEN to standard Newton on a series of test cases, ranging from conceptual cases with simplified geometry or flow physics to cases representative of real assets. Our overall conclusion is that ASPEN is outperformed by Newton when this method works well and converges in a few iterations. On the other hand, ASPEN avoids time-step cuts and has significantly lower runtimes in time steps where Newton struggles. A good approach to computational speedup is therefore to adaptively switch between Newton and ASPEN throughout a simulation. A few examples of switching strategies are outlined.","PeriodicalId":10662,"journal":{"name":"Computational Geosciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135702361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-27DOI: 10.1007/s10596-023-10225-2
Kevin LARNIER, Jérôme MONNIER
Estimating discharges Q(x, t) from altimetric measurements only, for ungauged rivers (in particular, those with unknown bathymetry b(x)), is an ill-posed inverse problem. We develop here an algorithm to estimate Q(x, t) without prior flow information other than global open datasets. Additionally, the ill-posedness feature of this inverse problem is re-investigated. Inversions based on a Variational Data Assimilation (VDA) approach enable accurate estimation of spatio-temporal variations of the discharge, but with a bias scaling the overall estimate. This key issue, which was already highlighted in our previous studies, is partly solved by considering additional hydrological information (the drainage area, $$A (km^2)$$ ) combined with a Machine Learning (ML) technique. Purely data-driven estimations obtained from an Artificial Neural Network (ANN) provide a reasonably good estimation at a large scale ( $$approx 10^3$$ m). This first estimation is then employed to define the first guess of an iterative VDA algorithm. The latter relies on the Saint-Venant flow model and aims to compute the complete unknowns (discharge Q(x, t), bathymetry b(x), friction coefficient K(x, t)) at a fine scale (approximately $$10^2$$ m). The resulting complete inversion algorithm is called the H2iVDI algorithm for "Hybrid Hierarchical Variational Discharge Inference". Numerical experiments have been analyzed for 29 heterogeneous worldwide river portions. The obtained estimations present an overall bias (less than 30% for rivers with similar characteristics than those used for calibration) smaller than previous results, with accurate spatio-temporal variations of the flow. After a learning period of the observed rivers (e.g. one year), the algorithm provides two complementary estimators: a dynamic flow model enabling estimations at a fine scale and spatio-temporal extrapolations, and a low complexity estimator (based on a dedicated algebraic low Froude flow model). This last estimator provides reasonably accurate estimations (less than 30% for considered rivers) at a large scale from newly acquired WS measurements in real-time, therefore making it a potentially operational algorithm.
仅从高程测量中估计流量Q(x, t)，对于未测量的河流(特别是那些具有未知水深b(x)的河流)，是一个不适定逆问题。我们在这里开发了一种算法来估计Q(x, t)，而不需要除全局开放数据集以外的先验流信息。此外，还研究了该逆问题的病态性。基于变分数据同化(VDA)方法的反演能够准确估计流量的时空变化，但总体估计存在偏差。我们之前的研究已经强调了这个关键问题，通过考虑额外的水文信息(流域面积，$$A (km^2)$$)和机器学习(ML)技术，可以部分解决这个问题。从人工神经网络(ANN)获得的纯数据驱动估计在大尺度上提供了相当好的估计($$approx 10^3$$ m)。然后使用该第一次估计来定义迭代VDA算法的第一次猜测。后者依赖于Saint-Venant流动模型，旨在计算精细尺度(近似$$10^2$$ m)下的完全未知数(流量Q(x, t)、水深b(x)、摩擦系数K(x, t))，得到的完全反演算法称为“Hybrid Hierarchical Variational discharge Inference”的H2iVDI算法。对全球29条非均质河段进行了数值试验分析。获得的估计呈现出总体偏差(小于30)% for rivers with similar characteristics than those used for calibration) smaller than previous results, with accurate spatio-temporal variations of the flow. After a learning period of the observed rivers (e.g. one year), the algorithm provides two complementary estimators: a dynamic flow model enabling estimations at a fine scale and spatio-temporal extrapolations, and a low complexity estimator (based on a dedicated algebraic low Froude flow model). This last estimator provides reasonably accurate estimations (less than 30% for considered rivers) at a large scale from newly acquired WS measurements in real-time, therefore making it a potentially operational algorithm.
{"title":"Hybrid Neural Network - Variational Data Assimilation algorithm to infer river discharges from SWOT-like data","authors":"Kevin LARNIER, Jérôme MONNIER","doi":"10.1007/s10596-023-10225-2","DOIUrl":"https://doi.org/10.1007/s10596-023-10225-2","url":null,"abstract":"Estimating discharges Q(x, t) from altimetric measurements only, for ungauged rivers (in particular, those with unknown bathymetry b(x)), is an ill-posed inverse problem. We develop here an algorithm to estimate Q(x, t) without prior flow information other than global open datasets. Additionally, the ill-posedness feature of this inverse problem is re-investigated. Inversions based on a Variational Data Assimilation (VDA) approach enable accurate estimation of spatio-temporal variations of the discharge, but with a bias scaling the overall estimate. This key issue, which was already highlighted in our previous studies, is partly solved by considering additional hydrological information (the drainage area, $$A (km^2)$$ ) combined with a Machine Learning (ML) technique. Purely data-driven estimations obtained from an Artificial Neural Network (ANN) provide a reasonably good estimation at a large scale ( $$approx 10^3$$ m). This first estimation is then employed to define the first guess of an iterative VDA algorithm. The latter relies on the Saint-Venant flow model and aims to compute the complete unknowns (discharge Q(x, t), bathymetry b(x), friction coefficient K(x, t)) at a fine scale (approximately $$10^2$$ m). The resulting complete inversion algorithm is called the H2iVDI algorithm for \"Hybrid Hierarchical Variational Discharge Inference\". Numerical experiments have been analyzed for 29 heterogeneous worldwide river portions. The obtained estimations present an overall bias (less than 30% for rivers with similar characteristics than those used for calibration) smaller than previous results, with accurate spatio-temporal variations of the flow. After a learning period of the observed rivers (e.g. one year), the algorithm provides two complementary estimators: a dynamic flow model enabling estimations at a fine scale and spatio-temporal extrapolations, and a low complexity estimator (based on a dedicated algebraic low Froude flow model). This last estimator provides reasonably accurate estimations (less than 30% for considered rivers) at a large scale from newly acquired WS measurements in real-time, therefore making it a potentially operational algorithm.","PeriodicalId":10662,"journal":{"name":"Computational Geosciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135753937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-26DOI: 10.1007/s10596-023-10240-3
I. A. Starkov, D. A. Pavlov, S. B. Tikhomirov, F. L. Bakharev
The paper presents a stochastic analysis of the growth rate of viscous fingers in miscible displacement in a heterogeneous porous medium. The statistical parameters characterizing the permeability distribution of a reservoir vary over a wide range. The formation of fingers is provided by the mixing of different-viscosity fluids — water and polymer solution. The distribution functions of the growth rate of viscous fingers are numerically determined and visualized. Careful data processing reveals the non-monotonic nature of the dependence of the front end of the mixing zone on the correlation length of the permeability of the reservoir formation. It is demonstrated that an increase in correlation length up to a certain value causes an expansion of the distribution shape and a shift of the distribution maximum to the region of higher velocities. In addition, an increase in the standard deviation of permeability leads to a slight change in the shape and characteristics of the density distribution of the growth rates of viscous fingers. The theoretical predictions within the framework of the transverse flow equilibrium approximation and the Koval model are contrasted with the numerically computed velocity distributions.
{"title":"The non-monotonicity of growth rate of viscous fingers in heterogeneous porous media","authors":"I. A. Starkov, D. A. Pavlov, S. B. Tikhomirov, F. L. Bakharev","doi":"10.1007/s10596-023-10240-3","DOIUrl":"https://doi.org/10.1007/s10596-023-10240-3","url":null,"abstract":"<p>The paper presents a stochastic analysis of the growth rate of viscous fingers in miscible displacement in a heterogeneous porous medium. The statistical parameters characterizing the permeability distribution of a reservoir vary over a wide range. The formation of fingers is provided by the mixing of different-viscosity fluids — water and polymer solution. The distribution functions of the growth rate of viscous fingers are numerically determined and visualized. Careful data processing reveals the non-monotonic nature of the dependence of the front end of the mixing zone on the correlation length of the permeability of the reservoir formation. It is demonstrated that an increase in correlation length up to a certain value causes an expansion of the distribution shape and a shift of the distribution maximum to the region of higher velocities. In addition, an increase in the standard deviation of permeability leads to a slight change in the shape and characteristics of the density distribution of the growth rates of viscous fingers. The theoretical predictions within the framework of the transverse flow equilibrium approximation and the Koval model are contrasted with the numerically computed velocity distributions.</p>","PeriodicalId":10662,"journal":{"name":"Computational Geosciences","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-26DOI: 10.1007/s10596-023-10222-5
Harpreet Sethi, F. Hoxha, J. Shragge, I. Tsvankin
{"title":"Modeling 3-D anisotropic elastodynamics using mimetic finite differences and fully staggered grids","authors":"Harpreet Sethi, F. Hoxha, J. Shragge, I. Tsvankin","doi":"10.1007/s10596-023-10222-5","DOIUrl":"https://doi.org/10.1007/s10596-023-10222-5","url":null,"abstract":"","PeriodicalId":10662,"journal":{"name":"Computational Geosciences","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46451071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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