scholarly journals Numerical Simulation of Multiphase Multicomponent Flow in Porous Media: Efficiency Analysis of Newton-Based Method

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 355
Author(s):  
Timur Imankulov ◽  
Danil Lebedev ◽  
Bazargul Matkerim ◽  
Beimbet Daribayev ◽  
Nurislam Kassymbek
Keyword(s):  
Porous Media ◽  
Linear Equations ◽  
Computation Time ◽  
Flow In Porous Media ◽  
Multicomponent Flow ◽  
Original Matrix ◽  
Sparsity Pattern ◽  
Speed Up ◽  
Systems Of Linear Equations ◽  
The One

Newton’s method has been widely used in simulation multiphase, multicomponent flow in porous media. In addition, to solve systems of linear equations in such problems, the generalized minimal residual method (GMRES) is often used. This paper analyzed the one-dimensional problem of multicomponent fluid flow in a porous medium and solved the system of the algebraic equation with the Newton-GMRES method. We calculated the linear equations with the GMRES, the GMRES with restarts after every m steps—GMRES (m) and preconditioned with Incomplete Lower-Upper factorization, where the factors L and U have the same sparsity pattern as the original matrix—the ILU(0)-GMRES algorithms, respectively, and compared the computation time and convergence. In the course of the research, the influence of the preconditioner and restarts of the GMRES (m) algorithm on the computation time was revealed; in particular, they were able to speed up the program.

Speed Up of Lattice Gas Automata Simulation of Polymer Flow Using a Cluster System

2012 ◽  
Author(s):  
Muhammad Taufiq Fathaddina ◽  
Mariyamni Awang
Keyword(s):  
Porous Media ◽  
Parallel Programming ◽  
Lattice Gas ◽  
Computation Time ◽  
Cluster System ◽  
Polymer Flooding ◽  
Flow In Porous Media ◽  
Polymer Flow ◽  
Lattice Gas Automata ◽  
Speed Up

Prestasi banjiran polimer boleh dianggar daripada tingkah laku mikroskopik partikel polimer dalam pori–pori media berliang. Kaedah kekisi gas automata adalah suatu kaedah pemodelan yang telah digunakan oleh penyelidik–penyelidik untuk mengkaji kelakuan aliran pada skala pori. Ia juga boleh digunakan untuk menyelaku aliran polimer dalam media berliang untuk mengkaji interaksi antara batuan dengan polimer. Namun, masa penghitungan terlalu panjang, walaupun untuk sampel media yang panjangnya 5 cm. Dalam kajian ini, penghitungan selari menggunakan komputer berdiri sendiri and sistem gugusan disiasati dalam usaha untuk mengurangkan masa penghitungan pemodelan banjiran polimer menggunakan kekisi gas automata. Daripada hasil kajian, speedup yang berasaskan pengolahan selari didapati lebih daripada 3.75 kali ganda, untuk empat pemprosesan atau kurang. Perbezaan dalam anggaran kecekapan penyesaran dan penepuan antara pengaturcaraan berjujukan dengan pengaturcaraan selari adalah kurang daripada tiga peratus. Oleh itu, dapatlah disimpulkan bahawa pengaturcaraan selari telah berjaya digunakan untuk melajukan penghitungan banjiran polimer tanpa menyebabkan variasi yang bererti daripada hasil keputusan. Kata kunci: Pengiraan selari; kekisi gas automata; penyesaran polimer The performance of polymer flooding may be estimated from microscopic behaviour of polymer particles in the pores of porous media. Lattice gas automata method is a modelling method that has been used by researchers to study flow behaviour on a particle scale. It had been also used to simulate polymer flow in porous media for studying microscopic interactions between rock and polymer. However, the computation time was too lengthy for even a 5 cm long porous media sample. On this study, parallel computing using standalone computers and a cluster system was investigated in an effort to decrease the computation time of modelling polymer flooding using lattice gas automata. From the results, speedup due to parallel processing was greater than 3.75 times for four processors and less. Differences in the estimations of displacement efficiency and saturations between sequential and parallel programming were less then three percent. It was concluded that parallel programming was successfully used to speed up computations in polymer flooding without causing significant variations in the results. Key words: Parallel computation; lattice gas automata; polymer displacement

scholarly journals Modelling Unsaturated Flow in Porous Media Using an Improved Picard Iteration Scheme

2021 ◽  
Author(s):  
S.R. Zhu ◽  
L.Z. Wu ◽  
T. Ma ◽  
S.H. Li
Keyword(s):  
Porous Media ◽  
Convergence Rate ◽  
Unsaturated Flow ◽  
Control Volume ◽  
Linear Equations ◽  
Solution Process ◽  
Coefficient Matrix ◽  
Picard Iteration ◽  
Flow In Porous Media ◽  
Richards Equation

Abstract The numerical solution of various systems of linear equations describing fluid infiltration uses the Picard iteration (PI). However, because many such systems are ill-conditioned, the solution process often has a poor convergence rate, making it very time-consuming. In this study, a control volume method based on non-uniform nodes is used to discretize the Richards equation, and adaptive relaxation is combined with a multistep preconditioner to improve the convergence rate of PI. The resulting adaptive relaxed PI with multistep preconditioner (MP(m)-ARPI) is used to simulate unsaturated flow in porous media. Three examples are used to verify the proposed schemes. The results show that MP(m)-ARPI can effectively reduce the condition number of the coefficient matrix for the system of linear equations. Compared with conventional PI, MP(m)-ARPI achieves faster convergence, higher computational efficiency, and enhanced robustness. These results demonstrate that improved scheme is an excellent prospect for simulating unsaturated flow in porous media.

A novel discontinuous Galerkin model for two-phase flow in porous media using an improved IMPES method

2016 ◽  
Vol 26 (1) ◽  
pp. 284-306 ◽  
Author(s):  
Mehdi Jamei ◽  
H Ghafouri
Keyword(s):  
Porous Media ◽  
Discontinuous Galerkin ◽  
Numerical Scheme ◽  
Two Phase Flow ◽  
Weighted Average ◽  
Computation Time ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Content Type

Purpose – The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme. Design/methodology/approach – The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method. Findings – Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media. Research limitations/implications – The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible. Practical implications – The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers. Originality/value – The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.

scholarly journals POD-Galerkin Model for Incompressible Single-Phase Flow in Porous Media

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 588-601 ◽  
Author(s):  
Yi Wang ◽  
Bo Yu ◽  
Shuyu Sun
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Single Phase ◽  
Galerkin Projection ◽  
Flow In Porous Media ◽  
Computational Time ◽  
Speed Up ◽  
Fast Prediction ◽  
Proper Orthogonal ◽  
Phase Fluid

AbstractFast prediction modeling via proper orthogonal decomposition method combined with Galerkin projection is applied to incompressible single-phase fluid flow in porous media. Cases for different configurations of porous media, boundary conditions and problem scales are designed to examine the fidelity and robustness of the model. High precision (relative deviation 1.0 × 10−4% ~ 2.3 × 10−1%) and large acceleration (speed-up 880 ~ 98454 times) of POD model are found in these cases. Moreover, the computational time of POD model is quite insensitive to the complexity of problems. These results indicate POD model is especially suitable for large-scale complex problems in engineering.

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