AN ANALYTIC REPRESENTATIVE ELEMENT RATE DECLINE MODEL WITH FRACTURE AND MATRIX COUPLING IN NATURALLY FRACTURED RESERVOIR DEPLETION

Abstract

Naturally Fractured Reservoirs (NFRs) host significant global hydrocarbon reserves but pose considerable modeling challenges due to their inherent heterogeneity and complex flow dynamics. While dual-porosity concepts are widely used, many analytical models, particularly those employing representative element volumes (REVs) for rate decline analysis, simplify the problem by decoupling the fracture and matrix pressure systems. This often involves assuming instantaneous fracture pressure depletion, which may be misleading in flow regime timing in reservoirs with substantial matrix storage or moderate fracture-to-matrix permeability contrasts (kf/kx). An improved analytical REV model that explicitly couples the transient drainage of the matrix with the transient depletion of the fracture system is developed and validated in this thesis to overcome this limitation. The core novelty lies in incorporating a time-dependent average fracture pressure, Pf(t), as the dynamic boundary condition governing 1D linear matrix flow, relaxing the assumption of instantaneous fracture pressure drop. The model is formulated for a 2D REV consisting of a matrix block penetrated by two parallel symmetric fractures and explicitly includes parameters for matrix block geometry (aspect ratio a/b) and size variations (scaling factor S). Analytical solutions for average system pressure, instantaneous flow rate, and their Bourdet derivatives were derived and implemented numerically using Python programming language. Model validation confirmed that the new coupled solution converges to previous decoupled results (Hazlett et al., 2024) under limiting conditions of high permeability contrast (kf/kx > 104). However, significant and theoretically expected departures were observed at lower kf/kx ratios (≤104) and low fracture volume fractions (vf < 0.01), demonstrating the importance of coupling in these regimes. Sensitivity analyses quantified the influence of key parameters: kf/kx primarily controls the transition duration between fracture and matrix linear flow regimes; vf influences the intercepts of these regimes and transition zone magnitude; matrix aspect ratio (a/b) affects the separation and timing of depletion signatures; and the scaling factor (S) introduces a predictable time shift related to block size. Empirical correlations relating transient diagnostic features to kf/kx and vf were developed. Analysis of heterogeneous mixtures (varying a/b or S) revealed that the presence of even small fractions of slower-draining blocks disproportionately impacts the overall system response, thus indicating that a simple volume-weighted averaging can be misleading, especially for derivative analysis. According to this study's findings, the coupled analytical model that was created offers a more physically sound framework for examining the pressure and rate decline in NFRs, particularly in situations where the timescales for matrix depletion and fracture are not widely separated. The explicit inclusion of coupling and geometric factors enhances the understanding of transient behavior and highlights the complex impact of heterogeneity on production signatures.