Effect of Fracture Compressibility on Oil Recovery From Stress-Sensitive Naturally Fractured Reservoirs
Authors: Aguilera R. 
Published: March 2010

Abstract
The tank material balance (MB) equation for undersaturated and saturated reservoirs has been written taking into account the effective compressibility of matrix and fractures. The solution is presented in finite difference form to achieve a quick convergence of the iteration process. Historically, compressibility has been neglected when carrying out MB calculations of conventional reservoirs producing below the bubble point. This assumes that the reservoir strata are static. It is shown however, that under some conditions, fracture compressibility can have a significant impact on oil rates and recoveries of naturally fractured reservoirs (NFRs) performing below the bubble point, as the fracture permeability and fracture porosity are stress-dependant. Other stress-sensitive properties discussed in this paper include the partitioning coefficient and the exponent for the shape of relative permeability curves. The use of the MB finite difference equations is illustrated with an example.

Introduction
Forecasting the performance of naturally fractured reservoirs (NFRs) is a major challenge. Various authors have tackled the problem throughout the years using MB calculations. To the best of my knowledge, the effect of fracture compressibility below the bubble point has been usually ignored in MB equations for saturated reservoirs. The work presented in this paper is not meant to replace a detailed reservoir simulation, which is the best way to try to solve the problem provided that reservoir characterization and quality of the pressure and production data is good. The objective is to have a tool that can provide a quick indication with respect to potential oil recoveries from stress-sensitive NFRs.
Pirson(1) pioneered efforts to try to explain the high GOR associated with many NFRs once the bubble point is reached. He considered the reservoir to be made of two porosity and permeability systems in parallel and visualized production as a succession of equilibrium stages. Jones-Parra and Seijas-Reytor(2) studied the effect of gas-oil ratio on the behaviour of fractured limestone reservoirs using a two-porosity model. They assumed that gravity segregation took place freely and resistance to fluid flow was very small in the fracture network. In the matrix or fine porosity system, there was high resistance to flow and no segregation. Aguilera(3, 4) used combined log analyses and MB to try to explain the high gasoil ratios observed in many NFRs. More recently, Penuela et al.(5) presented a MB for calculating oil-in-place in matrix and fractures taking into account the compressibility difference between matrix and fractures.
This paper presents MB equations for predicting oil recovery and rates of undersaturated and saturated reservoirs. The equations are written taking into account the effective compressibility of matrix and fractures. Stress-sensitive properties such as fracture porosity, fracture permeability, partitioning coefficient, and exponent for shape of relative permeabilities are taken into account. The solution is presented in finite difference form to achieve a quick convergence of the iteration process.