TY - JOUR

T1 - Numerical simulation of two-phase flow in deformable porous media: Application to carbon dioxide storage in the subsurface

AU - Kolditz, O.

AU - Bauer, S.

AU - Bottcher, N.

AU - Elsworth, D.

AU - Gorke, U. J.

AU - McDermott, C. I.

AU - Park, C. H.

AU - Singh, A. K.

AU - Taron, J.

AU - Wang, W.

N1 - The Fourth IMACS Conference : Mathematical Modelling and Computational Methods in Applied Sciences and Engineering" Devoted to Owe Axelsson in ocassion of his 75th birthday

PY - 2012/6/1

Y1 - 2012/6/1

N2 - In this paper, conceptual modeling as well as numerical simulation of two-phase flow in deep, deformable geological formations induced by CO2 injection are presented. The conceptual approach is based on balance equations for mass, momentum and energy completed by appropriate constitutive relations for the fluid phases as well as the solid matrix. Within the context of the primary effects under consideration, the fluid motion will be expressed by the extended Darcy's law for two phase flow. Additionally, constraint conditions for the partial saturations and the pressure fractions of carbon dioxide and brine are defined. To characterize the stress state in the solid matrix, the effective stress principle is applied. Furthermore, the interaction of fluid and solid phases is illustrated by constitutive models for capillary pressure, porosity and permeability as functions of saturation. Based on this conceptual model, a coupled system of nonlinear differential equations for two-phase flow in a deformable porous matrix (H2M model) is formulated. As the displacement vector acts as primary variable for the solid matrix, multiphase flow is simulated using both pressure/pressure or pressure/saturation formulations. An object-oriented finite element method is used to solve the multi-field problem numerically. The capabilities of the model and the numerical tools to treat complex processes during CO2 sequestration are demonstrated on three benchmark examples: (1) a 1-D case to investigate the influence of variable fluid properties, (2) 2-D vertical axi-symmetric cross-section to study the interaction between hydraulic and deformation processes, and (3) 3-D to test the stability and computational costs of the H2M model for real applications.

AB - In this paper, conceptual modeling as well as numerical simulation of two-phase flow in deep, deformable geological formations induced by CO2 injection are presented. The conceptual approach is based on balance equations for mass, momentum and energy completed by appropriate constitutive relations for the fluid phases as well as the solid matrix. Within the context of the primary effects under consideration, the fluid motion will be expressed by the extended Darcy's law for two phase flow. Additionally, constraint conditions for the partial saturations and the pressure fractions of carbon dioxide and brine are defined. To characterize the stress state in the solid matrix, the effective stress principle is applied. Furthermore, the interaction of fluid and solid phases is illustrated by constitutive models for capillary pressure, porosity and permeability as functions of saturation. Based on this conceptual model, a coupled system of nonlinear differential equations for two-phase flow in a deformable porous matrix (H2M model) is formulated. As the displacement vector acts as primary variable for the solid matrix, multiphase flow is simulated using both pressure/pressure or pressure/saturation formulations. An object-oriented finite element method is used to solve the multi-field problem numerically. The capabilities of the model and the numerical tools to treat complex processes during CO2 sequestration are demonstrated on three benchmark examples: (1) a 1-D case to investigate the influence of variable fluid properties, (2) 2-D vertical axi-symmetric cross-section to study the interaction between hydraulic and deformation processes, and (3) 3-D to test the stability and computational costs of the H2M model for real applications.

U2 - 10.1016/j.matcom.2012.06.010

DO - 10.1016/j.matcom.2012.06.010

M3 - Article

VL - 82

SP - 1919

EP - 1935

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

IS - 10

ER -