A Thermal Simulator for Naturally Fractured Reservoirs

Abstract

Because of the relatively heavy oil (8 - 12 deg. API) encountered in many naturally fractured reservoirs, thermal recovery processes could be viable recovery techniques to produce oil from these reservoirs. To facilitate the simulation of these processes, a simulator to model thermal effects in naturally fractured reservoirs has been developed. The model uses the double porosity concept and is three dimensional, three phase, and compositional. It allows the rock matrix block to be subdivided into a two-dimensional (r-z) grid block in order to study effects of gravity, capillary pressure, and mass and energy transfer between fractures and matrix blocks. The simulator is fully implicit and has a coupled wellbore mathmatical formulation, and simultaneously solves the unknowns for fractures and matrix blocks. An efficient solution procedure is implemented so that the cost of modelling naturally fractured reservoirs is not significantly greater than the cost of conventional single porosity thermal simulation. An example, steam injection into a five-spot pattern, is included to illustrate the significant effects of physical properties and model construction. Oil recovery predictions are sensitive to capillary pressure values, the number of cells used to divide the matrix block, and the size of the matrix blocks. Introduction The numerical simulation of fluid flow in naturally fractured reservoirs, which consists of interconnected fractures and discontinuous matrix blocks, has progressed significantly in the pass few years since the dual porosity concept was developed by Barenblatt et al. and introduced to the petroleum industry by Warren and Root. The dual porosity concept assumes that a fracture system and a matrix system occupy the same computational grid block, Field scale fractured reservoir simulator development has progressed in several areas. Specifically there have been improvements in (a) representation of fluids in the reservoir, (b) modelling of fluid flow between fractures and matrix blocks, (c) modelling of fluid flow between matrix blocks in adjacent computational grid blocks, and (d) discretization of the matrix block. The single-phase flow equations derived by Warren and Root were extented by Kazemi et al. to the two-phase flow equations which included capillary and gravity forces. Kazemi's three-dimensional numerical simulator was used to model water drive in a five-spot pattern and a five-well reservoir. That simulator can handle uniformly or nonuniformly distributed fractures and also handle no fractures at all in the reservoir. In 1983, Thomas et al., Gilman and Kazemi, and Saidi developed fully implicit threedimensional, three-phase, fractured reservoir simulators. In order to account for the effects of gravity on the matrix/fracture flow term, various approaches were presented in these papers. Thomas et al. used pseudo-relative permeability and capillary pressure curves for both the matrix and fracture. Gilman and Kazemi proposed to assign different depths for the matrix and fracture within a computation grid. P. 169^

Visualization and simulation of immiscible displacement in fractured systems using micromodels: Steam injection

“…Chen et al [5] tlevelopetl a. dual porosity mo~lel for the simulation of thermal effects in naturally fractured reservoirs. Their si mulator was 3-D, th rec-ph ase, and corn posi tion al.…”

“…Unfortunately, the irnclerstanding of steam injection in fractured systems is currently based mostly on phenomenology and typically consists of applying a double porosity formalism to commercial steam simulators [5], 1111, [13]. Most of these use capillary imbibition as the key mechanism for the exchange of fluids between the ma.trix blocks and the fracture network.…”

Numerical Simulation of Liquid-Solid Coupling in Multi-Angle Fractures in Pressure-Sensitive Reservoirs

“…In 1986, Nakornthap et al [2] built a numerical simulation model capable of simulating heterogeneous isotropic matrices and heterogeneous anisotropy fracture systems, and characterized fracture permeability in tensor form. In 1987, Chen et al [3] coupled the mathematical equations of shafts, and developed a simulator for the numerical simulation of the dual-medium, three-dimensional, three-phase, and multi-component thermal recovery of fractured reservoirs based on the fully implicit solution. In 1988, Sonier et al [4] considered the effect of fractures in numerical simulation, and introduced a saturation function to simulate the dynamic changes of gravity.…”