Triple-Porosity Systems for Representing Naturally Fractured Reservoirs

Abstract

Summary This study develops an improved model for analysis of pressure transient tests of naturally fractured reservoirs. The development was prompted by observations of actual well tests that showed anomalous slope prompted by observations of actual well tests that showed anomalous slope changes during the transition period and where the behavior could not be explained by dual-porosity models. Geometrical configurations studied include both the strata model, where horizontal matrix layers are separated by fractures, and the uniformly distributed blocks, which are separated by an orthogonal set of fractures. These systems were assumed to be under gradient flow conditions. In both cases, two separate sets of matrix proper- ties were assumed. The formulation of response was solved semianalytically. The solutions included the early time effects of both the afterflow and skin. Observations made from the theoretical predictions are that the fracture-controlled early times and portions of the transition period will resemble the behavior of a dual-porosity system. The latter part of the transition zone, however, exhibits slope changes; the duration is a function of 1/ 2 (ratio of interporosity flow coefficients for the two matrix types) and 1 / 2 (ratio of fluid capacitance coefficients). A correlation developed on the basis of numerous sensitivity runs allows the estimation of w1 /w2 and 1/ 2 with the times that correspond to the onset of anomalous slope changes. Because an infinite-acting slope may develop before the matrix blocks of the lowest show their existence during the anomalous slope changes, recognition of the various matrix properties emphasized in this study will also safeguard against properties emphasized in this study will also safeguard against extrapolation of incorrect late-time curves. Introduction During the last 20 years, pressure transient behavior in naturally fractured reservoirs has been the subject of many investigations. Dual-porosity models have been widely used to explain the flow behavior in the matrix/fracture network of such reservoirs. A major flaw with dual-porosity models is the assumption of uniform matrix properties throughout the system. properties throughout the system. Double-porosity models have long been used for representation of naturally fractured reservoirs. Pressure transient behaviors in such reservoirs have been analyzed under the assumption that homogeneous matrix properties prevail throughout the system. Fractures provide the properties prevail throughout the system. Fractures provide the highest permeabilities (very high order of magnitude compared with matrix permeability) and are the main conduits of fluid flow into the producing wells. Matrix blocks do not produce the fluid directly into the wellbore but act as a source that feeds the fluid into the high-permeability fractures. Two parameters have been used commonly to describe the properties of the matrix and the interconnecting fracture network. The interporosity flow parameter, indicates the degree of interporosity flow between the matrix blocks and fracture system. The fluid capacitance coefficient, w, represents the ratio of fracture storage capacity to the total storage capacity. The standard semilog plot of the buildup-pressure response vs. shut-in time or the drawdown-pressure response vs. flowing time, neglecting wellbore storage effects, is characterized by parallel straight lines of the early and late times with a transition period in between. The displacement of these straight lines is a function of and . Under a pseudosteady-state condition, I pressure throughout the matrix blocks instantaneously drops as soon as pressure depletion occurs in the fractures. This assumption has a characteristic "S" -shaped intermediate segment with a point of inflection. For relatively large matrix blocks, however, the unsteady-state assumption may no be valid; here, unsteady-state or gradient flow is a more realistic representation. A notable feature of this assumption is that the transition curve of pressure response exhibits more linearity compared with the case of the pseudosteady-state model. Fig. 1 illustrates the expected pseudosteady-state model. Fig. 1 illustrates the expected behavior of both models. Development of the Proposed Model We propose an improved model for the analysis of pressure transient tests in naturally fractured reservoirs. pressure transient tests in naturally fractured reservoirs. SPEFE p. 113