A Three-Parameter Dual Porosity Model for Naturally Fractured Reservoirs

Abstract

AbstractThis study presents a new model to analyze the behavior of naturally fractured reservoirs (NFRs). The model considers the geomechanical behavior of the fractured reservoirs and the corresponding effects on the fracture aperture, which may be an important parameter for stress-sensitive NFRs. It includes the elasticity parameters, such as Poisson's ratio and Young's modulus.Pressure depletion in an NFR, inherent to production, can result in effective stress change that, in turn, may change fracture permeability in NFRs. This may influence the behavior of NFRs, which has been studied thoroughly in the literature; however, not analytically but only numerically. A rigorous mathematical model is developed in this study which couples geomechanical and fluid flow aspects for characterizing a stress-sensitive NFR. In the model, we consider a semi-infinite radial flow with flux boundary conditions at the wellbore (Neumann condition) and constant pressure at infinity (Dirichlet condition). It is also assumed that the external forces acting to the reservoir are constant, that there is interaction between the two regions, i.e. matrix and fracture system, via the change of pore pressure and effective stress.Since the change in effective stress induced by reservoir compaction may affect the pressure buildup curves in NFRs, new equations on buildup interpretation are developed to better understand this effect, and to precisely evaluate the reservoir properties. An iterative algorithm is also developed which enables us not only to interpret the buildup data to compute the fracture parameters, namely fracture porosity, fracture permeability, fracture storage capacity, and the elasticity parameter, but also to evaluate them more accurately. Such a new technique improves NFR characterization through the inclusion of the fourth dimension, time, into buildup interpretation. This new well test interpretation method is a dynamic reservoir characterization, which is usually the mission of time-lapse (4-D) multicomponent seismology.From this study, we found that knowing three parameters is sufficient to both distinguish a reservoir with dual porosity from that of a homogenous one and to characterize a dual porosity reservoir. Two of the parameters represent the fracture storage capacity and matrix-fracture interaction. A third one reflects the effect of both matrix geomechanics and fracture aperture decline on the behavior of NFRs as time progresses. These parameters can be obtained by precisely interpreting drawdown or buildup tests. This solution is applicable to any reservoir containing dual porosity rocks.