A Look at Issues Related to Stochastic Representation of Naturally Fractured Reservoirs
Authors: Fuad Qasem , Ershaghi Iraj 
Published: December 2007

Abstract
In the conditional simulation of NFRs, reliace on correlations developed from geological data alone may be insufficient. Objective functions for simulated annealing method (SAM) need additional constraints representing spatial location of tight and permeable matrix blocks and effective matrix permeability. Based on our studies, for small correlation lengths, the capillary forces dominate the gravity forces in the most permeable matrix sections due to formation of many discontinuities among the layers caused by low permeability sections. For reservoirs with higher correlation lengths in the vertical setting, gravity forces become predominant in permeable blocks which can lead to an efficient recovery process. A heterogeneity index is defined in terms of correlation length (CL). Presence of permeable blocks in the upper section of NFR, under solution gas drive based on the cases studied, will result in high recoveries. This is caused by an efficient gravity drainage where blocks are surrounded by gas at early stages of depletion. In these sections, reservoir pressure and oil relative permeability are high and the capillary pressure is low. A new parameter nhpu, introduced in this paper, measures the fraction of permeable section above certain height in the reservoir. The combined effects of the above parameters may significantly influence the image representation and performance prediction.

Introduction
For prediction of reservoir performance, the practice seems to favor stochastic representation of reservoir geometry and structure. This is to account for the range of possible predictions. Incorporating the uncertainties in reservoir description is an important task in reservoir characterization. The purpose of this study is to show the complications in using stochastic prediction for NFRs if the basis is strictly geological correlation data. We will be demonstrating that because of the role and influence of matrix block permeabilities and their structural position, geologically based correlations alone may be insufficient and certain process controlled adjustments need to be incorporated in the conditional concept of image generation to bring a degree of reality to the conceptualization of the reservoir.

Model Assumptions
In this research the equivalency of a porous medium model1 for the fracture network is assumed valid, which means that there are sufficient amounts of well connected fractures in the reservoir. The cause of heterogeneity is attributed to variations in matrix permeability where the system is densely fractured and is in full hydraulic communication throughout the reservoir. Another assumption is that the matrix absolute permeability is the effective permeability. This assumption is defined as absolute permeability averaged over a Representative Elementary Volume2, REV, within the simulator grid block (homogeneous and isotropic within the grid block). The dual-permeability model is used with matrix-matrix connectivity. Water saturation is constant and immobile during depletion of the reservoir. The production occurs through fractures intersecting the wellbore. Fluid and reservoir properties are given by references 3 and 4.