Improvements in Simulation of Naturally Fractured Reservoirs

Abstract

Abstract Simulation of multiphase flow in heterogeneous two-porosity reservoirs such as naturally fractured systems is a difficult problem. In the last several years much progress has been made in this area. This paper focuses on progress has been made in this area. This paper focuses on the practical aspects of that technology. It describes a stable, flexible, fully implicit, finite-difference simulator in heterogeneous, two-porosity reservoirs. Flow rates and wellbore pressures are solved simultaneously along with fracture and matrix fluid saturations and pressures at all grid points. Hydrodynamic pressure gradient is maintained at formation perforations in the wellbore. The simulator is accurate enough to match analytical solutions to single-phase problems. The equations have been extended to include polymer flooding and tracer transport with nine-point connection for determining severe local channeling and directional tendencies. It is shown that the two-porosity model presented in this paper will produce essentially the same answers as the paper will produce essentially the same answers as the common single-porosity model of a highly heterogeneous system but with a substantial reduction of computing time. In addition, this paper describes in detail several two-porosity parameters not fully discussed in previous publications. previous publications. Introduction Naturally fractured reservoir simulators are developed to simulate fluid flow in systems in which fractures are interconnected and provide the main flow path to injection and production wells. The fractures have high permeability and low storage volume, the reservoir rock permeability and low storage volume, the reservoir rock (matrix blocks) has low permeability and high storage volume. The idealization of assuming one porosity as the continuum can apply to many heterogeneous systems where one porosity provides the main path for fluid flow and the other porosity acts as a source. Throughout this paper, the fracture should be thought of as the continuum paper, the fracture should be thought of as the continuum and the matrix perceived as the adjacent sources or sinks. For single-phase flow of a gas or liquid, fluid compression and viscous forces control fluid movement. Gravity and capillary forces are not pertinent. Several single-phase idealizations that produce essentially the same practical engineering answers are discussed in the literature. Fig. 1 shows a model with both vertical and horizontal fractures. Separate nodes are used for fracture and matrix. For this case, 77 nodes are used to model the system. Fig. 2 also shows a model that allows vertical and horizontal fractures. However, this model requires far fewer nodes because areas in which the matrix blocks behave similarly are grouped in a single node. Each gridblock may contain many matrix blocks. The matrix blocks act as sources that feed into the fractures in a gridblock. The fractures can be thought of as a system of connected pipes. This model was proposed by Warren and Root. The boundary conditions used can make a dramatic difference in simulation results. Generally, we assume that only the fractures produce into the wellbore and are the path of fluid flow from one gridblock to the next. For multiphase flow, three forces must be properly accounted for--viscous, gravity, and capillary. In this case, we might require that the matrix blocks be further divided into grid blocks to obtain better definition of saturation distribution (Fig. 3). However, this will lead to additional work and may not be required. Kazemi et al. extended the Warren-Root model to multiphase systems to account for capillary and gravity forces. SPEJ P. 695