Material-Balance Method for Dual-Porosity Reservoirs With Recovery Curves To Model the Matrix/Fracture Transfer

Abstract

Summary This paper presents a material-balance (MB) method applicable to naturally fractured dual-porosity reservoirs by considering the matrix/fracture transfer. The method is based on the recognition that the performance of water and gas displacement from matrix blocks can be depicted in the form of recovery factor vs. time. These recovery curves determine the matrix/fracture oil transfer. The reservoir pressure change depends on the original fluids in place and the strength of the aquifer. Thus, a close relationship between the recovery curves and the observed reservoir state (e.g., pressure, position of the phase contacts, water cut, and gas/oil ratio), the aquifer parameters, and the matrix/fracture oil transfer exists. Concerning the matrix blocks, the surrounding fracture continuum sets the boundary conditions by acting as an injector. The injection rates are predefined by the provided recovery curves, which one can obtain with different methods. They can be calculated by fine-scale single matrix-block models (Pirker et al. 2007), derived from conventional full-field numerical models, measured in a laboratory autoclave (Mattax and Kyte 1962), or determined by theoretical means (Davis and Hill 1982). The recovery curves can be scaled and normalized, making them applicable within a certain rock type to a wide range of rock parameters, namely shape factor, permeability, and porosity (Amiry 2014). While in a full-field model, various rock types can be identified; in MB calculations, however, they must be reduced to a single rock type. MB calculations—irrespective of conventional single-porosity methods or the herein-presented approach for dual-porosity naturally fractured reservoirs—are always conducted on a homogenized reservoir model. Therefore, variations in rock and pressure/volume/temperature properties cannot be taken into account. The recovery process is governed by two parameters—the asymptotic value of the recovery function and the time-scaling factor. These two parameters can be used for matching the observed reservoir performance. The new MB method matches both the reservoir pressure and the positions of the phase contacts. It also provides aquifer and matrix/fracture fluid-transfer models. Applying the parameters of those models in prediction mode and assuming a future production strategy, reservoir-pressure decline and phase-contact movements can be forecasted. The paper presents the calculation schema and the successful application to a field with more than 500 million STB of original oil in place and a 35-year production history. For the first time, it becomes possible to realistically—this means by fully considering the governing recovery mechanisms and thus the matrix/fracture transfer—calculate MB for naturally fractured dual-porosity reservoirs.