Single Medium Simulation of Reservoirs with Conductive Faults and Fractures

Abstract

This paper describes a technique to incorporate conductive faults and -fractures in a reservoir simulation model. The technique is appropriate for reservoirs with significant primary matrix productivity, and a large spacing between fractures (in the order of tens of meters). The single porosity (one grid) formulation is applied. Any fracture geometry can be represented accurately without grid modifications. The key elements of the approach are pseudo relative permeability curves for grid bocks containing fractures. These curves are determined through an analytical procedure, based on the local fracture and matrix properties. The method is applied successfully to a Middle East carbonate reservoir. Introduction Conductive faults and -fractures are common features in reservoirs worldwide. Several methods have been proposed to model fluid flow in fractured reservoirs. Well known is the Warren and Root [1] approach, which applies homogenization of the fracture properties and a dual porosity formulation (separate matrix and fracture grids). The homogenization of the fracture properties is possible when the Representative Elementary Volume (REV) [2] of the fracture network is smaller than the reservoir simulation grid. This paper focuses on fracture patterns that can not be homogenized, because the fracture REV is several times larger that the grid block size. Figure 1 provides an illustration. This figure represents a 10 by 22 kilometer sector of a much larger carbonate reservoir. The displayed fracture pattern is obtained from fracture analysis [3]. It is superimposed on a 250 by 250 meter simulation grid. In this example the conductive fractures are identified as the key contributor to unstable movement of the water injection front. Consequently, the fracture pattern must be incorporated when a simulation model is to be built. Several methods are available in the literature to integrate conductive fractures in a reservoir simulation model. Some of these methods are described below, with their strengths and weaknesses summarized in Table 1. Phelps et al [4] apply local grid refinement (LGR) to model conductive fractures explicitly. This approach is thorough in the handling of the physical elements of the displacement process. However, numerical difficulties may be experienced due to a large flow rate in grid blocks with a small pore volume. This is especially the case when a rapidly advancing water tongues develop due to gravity segregation in the fractures. Henn et al [5] extend the LGR technique by applying vertical lumping of the fractured grid blocks, in combination with an analytical treatment of capillary/gravity equilibrium in the fracture. Their method strongly improves numerical performance of the simulation model. The general disadvantage of these LGR approaches is that they are impractical for complex fracture patterns like the one shown in Figure 1. Cosentino et al [6] apply a dual media (dual permeability dual porosity) formulation to model conductive fractures explicitly. Their approach facilitates the capture of any complex fracture geometry without the need for modifications to the grid geometry. The method is thorough in its treatment of the processes that may take place during water flooding. The numerical challenges, with respect to high flow rates in grid cells with a small pore volume, are comparable to those experienced in the conventional LGR approach. Subsequently, relatively small time steps are required to adhere to stability criteria.

The study of relative phase-permeability functions for anisotropic media

“…We note the qualitative agreement of the obtained curves with the curves proposed for the simulation of fractured systems in [4], where, PERGAMENT, TOMIN however, the question on the tensor relationship between the phase and relative permeabilities is not dis cussed.…”

“…For the symmetry of anisotropic textures and symmetry groups of a hexagonal system (4) where and , and is the basis tensor specifying the symmetry of anisotropic tex tures. Tensor (4) prescribes transverse isotropic properties.…”

“…The single porosity model describing a medium's properties in the context of the united continuum was constructed in [4] in order to take into account subseismic fractures, the characteristic distance between which is rather large (of the order of 10 m) and whose extension is of the order of 10 2 m. Both absolute and relative phase permeabil ities were of a scalar nature in this study, and, for sake of describing the stage of the fast motion of water through fractures, they were of the particular form. This approach appeared to be reasonable, and using this model in computations, the authors managed to catch the peculiarities of the flooding of the pilot sec tor of one of the largest field in the Middle East.…”

Assessment of carbon dioxide plume behaviour within the storage reservoir and the lower caprock around the KB-502 injection well at In Salah

“…During simulations the transmissibility of Fault-12 is explicitly accounted for by employing a technique proposed by van Lingen et al (2001) as implemented in ECLIPSE 300 compositional simulator used at Imperial College. Under this method, the matrix absolute permeability (k m ) of a gridblock containing one or more conductive fractures in the directions parallel to the fracture plane is replaced with a lumped permeability k b taking into account the contribution from the fracture(s)…”

Simulation of Naturally Fractured Reservoirs. State of the Art

“…That situation of quasi-instantaneous matrix-fracture transfers is often encountered during the single-phase depletion phase of many fractured reservoir production histories. Another application example of the single-porosity approach can be found in Van Lingen et al (2001). The single-porosity formulation was successfully applied to a Middle East carbonate reservoir, produced by peripheral water injection and with significant primary matrix productivity, and a large spacing between large-scale disconnected fractures (in the order of one or several hundred meters).…”