Mathematical modeling and numerical simulation of two-phase flow problems at pore scale

• Main Authors: Paula Luna, Arturo Hidalgo
• Format: Article
• Language: English
• Published: Texas State University 2015-11-01
• Series: Electronic Journal of Differential Equations
• Subjects: Reservoir simulation; numerical simulation; saturation profile; finite volume method
• Online Access: http://ejde.math.txstate.edu/conf-proc/22/l2/abstr.html

Mathematical modeling and numerical simulation of two-phase flow through porous media is a very active field of research, because of its relevancy in a wide range of physical and technological applications. Some outstanding applications concern reservoir simulation and oil and gas recovery, fields in which a great effort is being paid in the development of efficient numerical methods. The mathematical model used in this work is written as a system comprising an elliptic equation for pressure and a hyperbolic one for saturation. Our aim is to obtain the numerical solution of this model by combining finite element and finite volume techniques, with a second-order non-oscillatory reconstruction procedure to build the values of the velocities at the cell interfaces of the FV mesh from pointwise values of the pressure at the FE nodes. The numerical results are compared to those obtained using the commercial code ECLIPSE showing an appropriate behavior from a qualitative point of view. The use of this FE-FV procedure is not the usual numerical method in petroleum reservoir simulation, since the techniques most frequently used are based on finite differences, even in standard commercial tools.