An enhanced sequential fully implicit scheme for reservoir geomechanics

Un schéma séquentiel entièrement implicite amélioré pour la géomécanique des réservoirs

Omar Duran (1, 2) , Manouchehr Sanei (3) , Philippe R B Devloo (3) , Erick S R Santos (4)

1 ENPC - École des Ponts ParisTech
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 UNICAMP - Universidade Estadual de Campinas = University of Campinas
4 Petrobras [Rio de Janeiro]

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 algorithm SFI 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 the ESFI algorithm to reduce the number of iterations to approximate several porome-chanical 1D, 2D and 3D problems with linear and nonlinear settings. When it was possible the results were verified with analytic solutions and approximated solutions with an explicit Runge-Kutta solver for axisymmetric 2D poro-elastoplastic problems.

Mots clés: Reservoir geomechanics; Nonlinear acceleration; Mixed finite elements; Poro-elastoplasticity; Enhanced fixed-stress split iterative scheme; Poroelastoplasticity

Domaines: Science non linéaire [physics]; Ingénierie de l'environnement

Omar Duran, Manouchehr Sanei, Philippe R B Devloo, Erick S R Santos. An enhanced sequential fully implicit scheme for reservoir geomechanics. Computational Geosciences, 2020, 24 (3), pp.1557-1587. ⟨10.1007/s10596-020-09965-2⟩. ⟨hal-02464446⟩