Reservoir Performance Prediction Methods Based on Fractal Geostatistics

A. S. Emanuel, R. A. Behrens, T. A. Hewett, G. K. Alameda

This paper describes a methodology for blending fractal statistics, detailed geologic data, finite difference simulation, and stream-tube models into a systematic approach for predicting reservoir performance. The objective is to make accurate predictions for large-scale projects by detailed accounting of reservoir heterogeneity without the necessity of history matching and at a lower overall cost.

The approach is based on the following strategy:

1. Establish the porosity-permeability character of the reservoir from well logs and cores and determine their statistical structure from R/S analysis.

2. Project the well data to the inter-well region using a random fractal interpolation scheme. The R/S analysis establishes the fractal character of the particular reservoir.

3. Establish fluid flow parameters from pressure, volume, temperature, relative permeability and, if available, core-flood data.

4. Assemble the geologic and fluid data into a highly detailed finite difference cross-section model representing reservoir flow between a typical injector-producer pair.

5. Run the finite difference model for projected injection strategy and develop a dimensionless characteristic solution that relates fractional flow at the producer to pore volumes injected. This solution represents displacement efficiency and vertical sweep.

6. Develop a stream-tube model of the reservoir to represent areal conformance. The stream tube model is formulated to accommodate arbitrary mobility ratio, permeability distribution, and boundary conditions. Couple the stream-tube model with the characteristics solution to project fieldwide project performance.

Example applications are shown for four field cases.

AAPG Search and Discovery Article #91030©1988 AAPG Annual Convention, Houston, Texas, 20-23 March 1988.