Fractal Distributions of Reservoir Properties and Their Use in Reservoir Simulation

Abstract

Abstract Geostatistics has become a popular way to distribute reservoir properties between wells. One of the geostatistical methods being used is fractal geostatistics. Most porosity well logs have been found to have a fractal character. An analysis of vertical and horizontal logs, core photos, and outcrop photos has led to a rather simple model to describe porosity and permeability distributions. This representation has been tested in reservoir simulation of a mature waterflood and found to match production history with very little history matching. Fractal distributions were found to require much less history matching than classical layer cake models. Conoco is now actively applying this new technology to a number of its reservoirs. Introduction We would like to have exact answers to where oil is and how it can be produced. Based on our limited core and log information, however, this is not possible. Usually, we have measurements on less than one billionth of a reservoir. With this small a sample set, all distributions are suspect. Still, the economics of oil recovery force us to get the best estimates we can. That means using as much of the data as wisely as possible. The approach here is to use statistical analyses of our data and a rather simple statistical model to leverage these data. This paper illustrates how statistical tests can be used to identify fractal distributions. The results of these tests are fed into the statistical model to generate distributions of reservoir properties between wells. These distributions are then used in reservoir simulations. The statistical model is developed from examining core photographs and is also consistent with many porosity well logs. This similarity is used to generate porosity distributions for reservoir simulations. Porosity-permeability relationships are used to assign permeability. With the resulting distributions, we compare three different reservoir simulation methods on a mature waterflood in southwestern United States. The first reservoir simulation method is a hybrid finite-difference/streamtube method that starts with two-dimensional (2-D) vertical cross sections with relatively fine grids. The second method uses pseudorelative permeabilities based again on 2-D cross sections. The third method uses three-dimensional (3-D) distributions. A mature waterflood in a carbonate reservoir serves as a field test case. The average cumulative oil recovery from 20 realizations is nearly the same for all three methods. P. 619^