Numerical Simulation of Steam Displacement of Oil in Naturally Fractured Reservoirs Using Fully Implicit Compositional Formulation: A Comparative Analysis of the Effects of Capillary and Gravitational Forces in Matrix/Fracture Exchange Term

Abstract

A numerical simulator for steam displacement of oil from naturally fracturedreservoirs is developed and tested.The three-dimensional and three phasefield scale model employs a compositional dual-porosity/dual-permeabilitymathematical formulation.Capillary, gravitational and viscous forces areaccounted for in the mathematical model.Using a fully implicit solutionscheme, the model solves for (2nHC+10) primary variables simultaneously, wherenHC is the number of hydrocarbon components.All reservoir parameters areformulated as functions of all the primary variables.The model islinearized using Newton-Raphson method, and the system of linear equations issolved by a direct and an iterative solver.The model is verified againstthe Fourth and Sixth SPE Comparative Solution Projects.The model ishighly stable for the studied extremely dynamic and stiff problems, accommodating large time steps with two to three Newtonian iterations.Thesimulations are carried out up to ten years to test the features of the modelfor long periods of steam injection in naturally fractured systems. Fluid exchange between the fracture and the matrix blocks due to thegravitational, capillary and viscous forces is investigated for a range ofnaturally fractured reservoirs with different matrix block sizes and capillarypressures.Relative effects and relative magnitutes of these acting forceson the displacement of the matrix oil are analysed in these naturally fracturedsystems undergoing steam injection.This comprehensive and comparativeanalysis is conducted using different realizations of the studied naturallyfractured systems such as the dual-permeability and the dual-porositymodels. The steam injection operations are carried out for long periods oftime.The low initial pressures in the studied fractured systemsfacilitate zooming in on and observing how, in particular, the capillary andgravitational forces work, and testing the model under more strained conditionsin a naturally fractured reservoir undergoing a steam injection operation. Introduction Modeling fluid flow in naturally fractured reservoirs, particularlyaccounting for the matrix/fracture fluid exchange, has been an extremelychallenging problem for the researchers[1–6].Steam injection in naturallyfractured reservoirs provides even a more difficult problem numerically and interms of accounting for the gravitational, capillary and viscous forces in thematrix/fracture fluid exchange.It is important to understand how thecontinuously changing roles of these capillary and gravitational forces and theresulting fluid displacement mechanisms work during an entire steam injectionoperation in a naturally fractured reservoir. The single-phase pressure transient anlysis and isothermal multi-phase fluidflow studies form a major part of research conducted in the area of naturallyfractured reservoirs.In this study, the research is focused on the actingforces in the matrix/fracture flow potential in a field scale study of streaminjection operation in a naturally fractured reservoir.A naturallyfracture reservoir with a relatively lower initial formation pressure isinvestigated in order to better focus on and understand the relative roles ofthe capillary and the gravitational forces on the steam displacement of oilfrom the matrix blocks. In this research, a comparative analysis is employed regarding the effectsof the viscous forces, gravitational forces and the matrix capillary pressureterms in the matrix/fracture potential expression on the steam displacement ofthe matrix oil in a range of naturally fractured reservoirs.Thiscomprehensive investigation should provide us with more understanding on therelative interactions among the acting forces in the matrix/fracture flowpotential, and also their relative effects on the fluid flow mechanisms betweenthe matrix and the fracture systems. A wide range of approaches is present in the literature in order to accountfor the effects of gravitational and the capillary forces[7–13].In thisresearch, unmodified capillary pressure and relative permeability values areused in both of the dual-porosity and the dual-permeability models of thenaturally fractured reservoir.The present investigation should contributeto the determination of level of confidence in designing optimum steaminjection operations in naturally fractured reservoirs.

A Parametric Study of the Effects of Reservoir and Operational Properties on the Performance of Steam Displacement of Heavy Oil in Naturally Fractured Reservoirs

“…The mathematical formulation and the numerical solution is presented in an earlier work in detail 17 . The present model is developed using a dual-porosity/dual-permeability mathematical formulation, and is briefly described here for the sake of completeness.…”

An Eos-Based Numerical Simulation of Thermal Recovery Process Using Unstructured Meshes

“…They used an interface model, where the single-phase steam zone was separated from the two-phase liquid region by a steam condensation front. Cicek (2005) developed and tested the numerical simulation of steam displacement of oil in naturally fractured reservoirs using a fully implicit compositional formulation. He investigated the effects of capillary and gravitational forces in the matrix/fracture exchange term.…”

An EOS-Based Compositional Thermal Reservoir Simulator

“…They used an interface model, where the single phase steam zone was separated from the two-phase liquid region by a steam condensation front. Cicek (2005) developed and tested the numerical simulation of steam displacement of oil in naturally fractured reservoirs using fully implicit compositional formulation. He investigated the effects of capillary and gravitational forces in the matrix/fracture exchange term.…”