Effect of fractal permeability correlations on waterflooding performance in carbonate reservoirs

The objective of this paper is to investigate the response of correlated permeability distributions to field scale immiscible flooding and relate the output to correlation parameter. Synthetic cross-section porosity maps are generated using fractional Brownian motion (fBm) statistics in vertical direction and then the porosities are converted to permeabilities using an exponential correlation as data to black oil simulator. The intermittency coefficient, H, that characterizes the roughness of the distribution is varied between two extremes; 0.4 and 0.95. For each set of porosity distributions with different H value, different random number seed is used. Permeabilities are generated from the fBm porosities distributed between the same minimum and maximum values with uniform variance for all Hs. Then, simulations are carried out to explore the effects of H on the waterflooding performance. It is found that the displacement efficiency increases with increasing H of the distribution. The effect of the roughness of the permeability field is more significant on water–oil ratio and breakthrough time than on the cumulative oil production and oil production rate. At the end, an evaluation of a field case is provided. The performance of a five-spot waterflooding in a carbonate reservoir is evaluated for different distribution types, namely vertical and horizontal fBm distributions.