Comparisons of Fractal Normalized Relative Permeability Models and Its Application in P Oilfields, China

Power law normalized relative permeability models have been widely used in petroleum industry, high regression accuracy of two-phase relative permeability curves from single core plug can be obtained by using power law functions. However, since no fine correlations between water, oil indexes and other reservoir parameters, e.g., porosity, permeability, initial or residual oil saturation, etc., can be established, the intention of forecasting the shape of relative permeability curves of reservoirs without coring cannot be realized. Based on capillary flow model and fractal geometry theory, four sets of normalized fractal relative permeability models have been derived, and displayed clearer physical meanings and variation ranges on fractal parameters. According to fractal dimension, which characterizes pore structure, those models were divided into two groups and were applied into 26 sets laboratory tested water-oil displacement relative permeability curves of P oilfield. It is confirmed that fractal models are applicable to single core samples, furthermore, the correlation between function parameters and RQI can also be established, thus the relative permeability shape and water cut rising law of reservoir without coring in P oilfields can be preliminarily obtained.