Dynamic effective permeability of a laminated structure with cross flow in the transient flow process and its application to reservoir simulation

Abstract

The effective permeability of a laminated structure is an important parameter related to the practical necessity of coarsening of grid blocks in large scale reservoir simulations. Traditional effective permeability derived under steady state flow conditions can cause great errors in the transient flow process due to the great heterogeneity and anisotropy of laminated formations. To handle this error, the unsteady oil flow in the matrix between hydraulic fractures of a laminated system during an oil depletion process is analyzed in this study. Based on material balance, we present an analytical method for calculating the dynamic effective permeability of the laminated structure considering the cross flow between laminae in the transient flow process. The proposed dynamic effective permeability can be used to conduct coarsening of grid blocks and can be incorporated into numerical models for accurate modeling of transient flow in a laminated structure in the reservoir simulation. It is shown that the simulation results using the proposed effective permeability model match well with those from two-dimensional (2D) simulations. Further, the effects of the horizontal permeability, vertical permeability, thickness of the laminae, and the length of the matrix between fractures are studied.