Modeling Fractured Reservoirs With Stochastic Fractals

Abstract The aim of this paper is to present a method of building a heterogeneous reservoir permeability field for flow simulation using pressure transient data. The permeability field will be derived from effective permeability and fractal dimension obtained from well test analysis and conditional simulation techniques. The paper presents and discusses the different levels of heterogeneity that can be created with different values of the fractal exponent. A mathematical model is presented for estimating effective permeability and fractal dimension from transient data from naturally fractured reservoir. This model is more appropriate than existing models because it considers the irregular and random nature of the fractured system in the reservoir matrix. The model is well suited for computer automated well test analysis. An illustrative example of how to use effective permeability and fractal dimension derived from pressure transient test data with some reservoir data to generate consistent reservoir description is presented. Introduction The need to describe reservoir heterogeneity for flow simulation has been realized for many years. However, this has proved to be an almost impossible task because the required petrophysical properties are sampled at a few locations in the reservoir. Reservoir engineering practitioners often have to use constant or interpolated values for porosity and permeability in the simulations cells. Researchers have recently adopted the use of geostatistical techniques and reported favorable results in history matching field data. They have reported that the use of constant porosity and permeability or interpolated property fields lead to a highly optimistic sweep efficiencies and late breakthrough times of the injected fluid. The reason for this optimistic results in terms of breakthrough time and sweep efficiency is because of the absence of the heterogeneity that actually exist in the field. The appropriate high permeability channels and streaks that affects fluid channelling is absent in these constant or interpolated property models. Improvements in reservoir characterization can yield major improvements in reservoir performance predictions but the sparseness of data makes this difficult. The fact that the measured data density is sparse has made the use of stochastic property fields rather more appealing than deterministic reservoir models. The idea behind the stochastic models is to construct property distributions of the reservoir that honor measured data at sampled locations using the correlation derived from the measured data and some conditional simulation algorithm. The scarcity of data is even more serious for permeability which is the most important input data for the reservoir simulator. Usually, unlike porosity, this cannot be accurately derived from well logs. If cores are available, it may be possible to derive a good porosity versus core permeability transform. Most of the time this is not so, and the only data available may be pressure transient measurement from a few wells. P. 352