Permeability of Idealized Fractured Rock

Abstract The over-all apparent single-phase permeability of fracture-rock systems was studied using two different two-dimensional models. In a strict sense the results are applicable only to these models, yet may give some insight into real reservoir behavior. The regular fracture-matrix model can have any number of regular fracture sets. All fractures within each set have the same orientation, width and spacing. The gross behavior is analytically equivalent to that of an anisotropic permeable medium. In the heterogeneous fracture systems, individual fracture conductivities vary within a two-dimensional network pattern. A computer program calculates the overall permeability after the conductivities are randomly placed in the network. The calculated permeability depends upon the distribution of these conductivities and the particular fracture pattern into which they are placed. Although detailed information on actual reservoir fracture systems is not available, this study shows bow some of the possible variables may affect observed gross reservoir characteristics. INTRODUCTION Characteristics of reservoir rocks are determined by direct (core analysis) or indirect (logging and production tests) examination. Both methods, singly and together, are widely used in reservoir evaluations. For fractured reservoirs a problem exists in relating characteristics of cores to the in situ reservoir properties. Knowing fracture characteristics can be of value in determining production mechanisms. Because of the limitations of observation, the intimate details of a fractured rock system will never be known. One approach in analyzing fractures is to study the behavior of some conceptually simple models. The two models analyzed contain features which may be realistic, yet are mathematically tractable. Flow is considered in two dimensions only, with the plane of interest at right angles with the fractures. This concept represents the horizontal flow in a reservoir system with the fractures oriented vertically. Only single-phase, laminar flow is considered. The regular fracture-rock system permeability is calculable from a simple analytical expression. The heterogeneous system requires a computer program for calculating overall permeability. FLOW IN A SINGLE FRACTURE Fluid flow in a single fracture is assumed equal to laminar flow between two infinite parallel smooth plates. This is expressed as:1Equations 1 and 2 Turbulent flow in fractured reservoirs is quite unlikely. As with flow in circular pipes, a Reynolds number can be defined to characterize the flow regime (2Wv?/µ). Values of this dimensionless group at the- onset of the transition to turbulent flow vary from 1,800 to 4,000, depending on the reference.1-3 Surface roughness on the fracture faces lowers this number.2-4