Finite Difference Simulation of the Stokes-Brinkman Equation for Transient Flow in Naturally Fractured Carbonate Karst Reservoirs

摘要

Carbonate reservoirs, despite their simple chemical composition, are notorious for being highly heterogeneous at all scales. The susceptibility of carbonate minerals to chemical changes, mostly dissolution, creates macroscopic pore features like small vugs and big caves which are also collectively known as karst, and mechanical deformation of the brittle carbonate rocks generates natural fractures which may or may not connect those vugs and caves. Carbonate reservoirs may bear karst and fractures having a size range from millimeters to hundreds of meters. Such reservoirs are called naturally fractured carbonate karst reservoirs and commonly found all over the world. Free flow exists in the karst and fractures at multiple levels and couples with Darcy flow in the porous carbonate rocks, making the mathematical modeling and numerical simulation of flow performance in these reservoirs a very challenging problem.;The Stokes-Brinkman equation has been pursued in recent years as a physical yet unified approach toward the simulation of coupled flow in naturally fractured carbonate karst reservoirs, but its application has been somehow restricted to steady-state flow. For the first time, we have proposed a transient Stokes-Brinkman model and lain the theoretical foundation for it, by discovering the applicability of the Stokes-Brinkman equation to transient flow through a detailed examination of its derivation process, and by incorporating a transient material balance equation which proves to be exact in the entire fractured karst reservoir. The finite difference formulation of the transient Stokes-Brinkman model has been derived, again for the first time, and an inhouse reservoir simulator is developed toactually solve this numerical problem.