Stochastic modeling of porosity distribution in a multi-zonal carbonate reservoir

Petrophysical variables, such as porosity and permeability in reservoir rocks, result from complex geological processes, and are characterized by considerable amounts of heterogeneity in their spatial distribution. The challenging task for geologists and engineers is to represent such heterogeneity in numerical reservoir models for flow simulation, leading to better predictions of reservoir performance. Stochastic simulation techniques have commonly been adopted to construct numerical reservoir models in recent years. These techniques provide a range of equi-probable images or realizations of variable under consideration with a realistic level of heterogeneity. The Sequential Gaussian Simulation (SGS) is one of the popular conditional simulation techniques employed in reservoir characterization. The SGS algorithm provides a simulated value at any location by first determining the probability distribution at that location, and then drawing a number at random from this distribution. The SGS technique was adopted to generate a three-dimensional, high-resolution reservoir model of porosity within the Upper Jurassic multi-zonal Arab-D carbonate reservoir in the Harmaliyah oil field, located in the Eastern Province of Saudi Arabia. The study was based on the well-log derived porosity measurements from 44 vertical wells. The generated models display the general pattern of the porosity distribution within the reservoir and provide the basic input for the flow simulation. As expected, the simulation model appears to have reproduced a realistic level of heterogeneity. Comparison of the histogram and statistical parameters of the input data with those of the simulated values reveals a close match in both the distribution patterns and the parameters.