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An enhanced sequential fully implicit scheme for reservoir geomechanics
Computational Geosciences ( IF 2.5 ) Pub Date : 2020-06-25 , DOI: 10.1007/s10596-020-09965-2
Omar Duran , Manouchehr Sanei , Philippe R. B. Devloo , Erick S. R. Santos

In this paper, it is proposed an enhanced sequential fully implicit (ESFI) algorithm with a fixed stress split to approximate robustly poro-elastoplastic solutions related to reservoir geomechanics. The constitutive model considers the total strain effect on porosity/permeability variation and associative plasticity. The sequential fully implicit (SFI) algorithm is a popular solution to approximate solutions of a coupled system. Generally, the SFI consists of an outer loop to solve the coupled system, in which there are two inner iterative loops for each equation to implicitly solve the equations. The SFI algorithm occasionally suffers from slow convergence or even convergence failure. In order to improve the convergence (robustness) associated with SFI, a new nonlinear acceleration technique is proposed employing Shanks transformations in vector-valued variables to enhance the outer loop convergence, with a quasi-Newton method considering the modified Thomas method for the internal loops. In this ESFI algorithm, the fluid flow formulation is defined by Darcy’s law including nonlinear permeability based on Petunin model. The rock deformation includes a linear part being analyzed based on Biot’s theory and a nonlinear part being established using Mohr-Coulomb associative plasticity for geomechanics. Temporal derivatives are approximated by an implicit Euler method, and spatial discretizations are adopted using finite element in two different formulations. For the spatial discretization, two weak statements are obtained: the first one uses a continuous Galerkin for poro-elastoplastic and Darcy’s flow; the second one uses a continuous Galerkin for poro-elastoplastic and a mixed finite element for Darcy’s flow. Several numerical simulations are presented to evaluate the efficiency of ESFI algorithm in reducing the number of iterations. Distinct poromechanical problems in 1D, 2D, and 3D are approximated with linear and nonlinear settings. Where appropriate, the results were verified with analytic solutions and approximated solutions with an explicit Runge-Kutta solver for 2D axisymmetric poro-elastoplastic problems.

中文翻译:

储层地质力学的一种增强的顺序完全隐式格式

在本文中,提出了一种具有固定应力拆分的增强顺序完全隐式(ESFI)算法,以近似估计与储层地质力学有关的多孔弹塑性解。本构模型考虑了总应变对孔隙度/渗透率变化和相关塑性的影响。顺序完全隐式(SFI)算法是一种流行的解决方案,用于近似耦合系统的解决方案。通常,SFI由一个外部回路组成,用于求解耦合系统,其中,每个方程式都有两个内部迭代回路,以隐式求解方程式。SFI算法有时会出现收敛缓慢甚至收敛失败的情况。为了提高与SFI相关的收敛性(鲁棒性),提出了一种新的非线性加速技术,该方法在向量值变量中采用Shanks变换来增强外环收敛,并采用一种拟牛顿法,并考虑了内部环的改进的Thomas方法。在该ESFI算法中,流体流动公式由达西定律定义,该定律包括基于Petunin模型的非线性渗透率。岩石变形包括根据Biot理论分析的线性部分和利用Mohr-Coulomb关联塑性对地质力学建立的非线性部分。时间导数通过隐式欧拉方法近似,空间离散化在两个不同的公式中使用有限元进行。对于空间离散化,获得了两个弱语句:第一个使用连续Galerkin进行孔隙弹塑性和达西流动。第二个使用连续Galerkin进行孔隙弹塑性,并使用混合有限元进行达西流动。提出了一些数值模拟,以评估ESFI算法在减少迭代次数方面的效率。1D,2D和3D中不同的poromechanical问题可以通过线性和非线性设置来近似。在适当的情况下,使用解析解决方案和近似解决方案(使用明确的Runge-Kutta求解器)解决了二维轴对称多孔弹塑性问题,对结果进行了验证。1D,2D和3D中不同的poromechanical问题可以通过线性和非线性设置来近似。在适当的情况下,使用解析解决方案和近似解决方案(使用明确的Runge-Kutta求解器)解决了二维轴对称多孔弹塑性问题,对结果进行了验证。1D,2D和3D中不同的poromechanical问题可以通过线性和非线性设置来近似。在适当的情况下,使用解析解决方案和近似解决方案(使用明确的Runge-Kutta求解器)解决了二维轴对称多孔弹塑性问题,对结果进行了验证。
更新日期:2020-06-25
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