Sixth SPE Comparative Solution Project: Dual-Porosity Simulators
Authors: Firoozabadi Abbas , Thomas L. Kent 
Published: December 2007

Summary.
Two problems are used to compare fractured reservoir models:a simple single-block example, anda more complicated cross-sectional example developed to simulate depletion, gas-injection, and water-injection cases.
In selection of the problems for this Comparative Solution Project, some aspects of the physics of multiphase flow in fractured porous media were considered. The influence of fracture capillary pressure on reservoir performance has been addressed by cases with zero and nonzero gas/oil performance has been addressed by cases with zero and nonzero gas/oil capillary pressure in the fractures.

Introduction
In recent years, interest in the simulation of naturally fractured petroleum reservoirs has increased. For this SPE Comparative Solution Project, reservoir test problems were designed to illustrate some aspects of the physics of multiphase flow in fractured physics of multiphase flow in fractured reservoirs and modeling techniques to account for capillary and gravity forces. The approach to the solution of the problems has been limited to dual-porosity models. An important element in simulating a fractured reservoir with a dual-porosity technique is the proper calculation of the fluids exchange between the matrix blocks and the fractures. In the conventional approach, the transfer term for a particular phase is directly related to the shape factor, fluid mobility, and potential difference between the matrix and fracture. Shape factors have been developed based on first-order finite-difference approximations and by matching fine-grid multiphase simulations of matrix/fracture flow. In most dual-porosity models, the matrix block heights are assumed to be at the same depth as the corresponding fracture blocks, and therefore, gravity has no explicit effect on the fluid exchange between the matrix and the fracture. Pseudo capillary pressures have been used to account for the effect of gravity. The gravity-segregation concept has also been used to compute the fluid levels in the matrix and fractures to account for the gravity contribution. An alternative approach has been presented in Ref. 6 (see the second option) to account for gravity effects. Dual-porosity models also must account for the saturation distribution in a matrix block. Because the saturation is evaluated at the center of a grid cell, it represents an average value for that cell. The pseudo-capillary-pressure concept has been used pseudo-capillary-pressure concept has been used to account for both gravity effects and nonuniform saturations within a matrix block. The method of subdomain discretization has also been applied to this problem. In that approach, the matrix is problem. In that approach, the matrix is divided into a number of grid cells and pressures and saturations are calculated for each pressures and saturations are calculated for each grid cell. The subdomain approach can also take care of transient effects. These effects, however, may not be important in field-scale problems. problems. Although fracture capillary pressure is assumed to be zero in most dual-porosity models, a recent paper questions the validity of this concept. In selection of the problems for this Comparative Solution problems for this Comparative Solution Project, the influence of fracture capillary Project, the influence of fracture capillary pressure on reservoir performance was pressure on reservoir performance was addressed by including cases with zero and nonzero gas/oil capillary pressure in the fractures. The nonzero fracture capillary pressures are not based on any actual pressures are not based on any actual measurements, but are intended as a parameter for sensitivity studies. The variation of gas/oil interfacial tension (IFT) with pressure has also been incorporated in the pressure has also been incorporated in the problems. Gas/oil capillary pressure is directly problems. Gas/oil capillary pressure is directly related to IFT, and therefore, the gas/oil capillary pressure should be adjusted according to the ratio of IFT at reservoir pressure divided by IFT at the pressure at which capillary pressures are specified.
Problem Statement Problem Statement We selected two problems to compare fractured reservoir models: a single-block example and a more complicated cross-sectional example developed to simulate depletion, gas-injection, and water-injection cases. Basic PVT data for the above cases were taken from Ref. 3. The rock/fluid data, with the exception of the matrix water/oil capillary pressure, were also taken from Ref. 3. Table 1 gives the matrix water/oil capillary pressure data. Matrix-block shape factors pressure data. Matrix-block shape factors have been specified for use in simulators that directly enter this variable (see Table 2).

Single-Block Studies.
The single-block simulation is a study of gas/oil gravity drainage at 4,500 psig [31.0 MPa] for a cubic matrix block with dimensions of 10 × 10 × 10 ft [3.05 × 3.05 × 3.05 m]. One-cell, dual-porosity runs were made for this case. Two runs were reported: the first with a zero fracture capillary pressure and the second with a constant fracture capillary pressure of 0.1 psi [0.69 kPa]. These runs pressure of 0.1 psi [0.69 kPa]. These runs were terminated at 5 years.
JPT
P. 710