Numerical modelling of multiphase flow in naturally fractured reservoirs is a challenging issue for petroleum reservoir engineers. As a result of high degree heterogeneity in flow characteristics in fractured reservoirs, several mathematical, discretization, and numerical methods are introduced to forecast the hydrodynamic behaviour of naturally fractured reservoirs. This paper demonstrates two different numerical modelling approaches that have been developed using the discrete-fracture matrix model (DFM) for studying the behavior of multiphase flow in fractured porous media. The first model utilizes the viscous loss term as a source term in the momentum equation to capture the value of permeability in both free channel (fracture) and porous matrix. On the other hand, the second model is based on the coupled Navier-Stokes equation in the free channel of fracture and viscous loss term as a mass source term to measure the permeability in the porous matrix. Later, the Corey method is employed to observe saturation, relative permeability, and capillary pressure at the fracture matrix interface. Both models are validated against a Berea Sandstone imbibition core flooding experimental data. Furthermore, the first and second model numerical simulation results match with the Berea Sandstone experimental core flooding data within a 4.2% and 29% error margin, respectively. The simulation results prove that the first model which uses viscous loss term to capture permeability in the fracture and porous matrix is more accurate in comparison to the implementation of the Navier-Stokes equation in the fracture channel in the second model.

1. Introduction

The modelling of multiphase flow in naturally fractured and tight rock reservoirs is a major issue for petroleum reservoir engineers. One of the factors that are responsible for this issue is the challenge related to coupling of multiphase flow at the fracture matrix interface owing to a large contrast of permeability values between fracture and porous matrix. The complexity of reservoir modelling increases when the reservoir characteristics are presented implicitly. A comprehensive understanding of multiphase flow behaviour between fractures and matrix blocks requires the quality of fracture network geometry and multiphase flow properties to be represented explicitly. To model naturally fractured reservoirs (NFRs), various types of approaches have been introduced and developed (Karimi-Fard and Firoozabadi, 2003; Li and Lee, 2008; Warren and Root, 1963). Presently, discrete fracture matrix model approaches (DFM) have achieved substantial interest to model naturally fractured reservoirs explicitly. Furthermore, it is significant to examine distinct mathematical formulations to represent and capture the nature of multiphase flow behaviour in the porous matrix blocks and within the fracture flow channels.

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