Permeability Prediction Based on Leaky-Capillary-Tubes Using Genetic Algorithm

Abstract

For any reservoir, the cross-plot of permeability vs. porosity data exhibit a non-linear behavior. As a result, there is always an uncertainty associated with the characteristic parameters obtained for any permeability equation using inverse-linear-regression technique. In this paper, unique characteristic parameters of permeability equation based on Civan's leaky-tube-capillary model were determined using genetic algorithm to obtain straight-line plot of the derived permeability vs. normalized porosity data. The statistical inverse-linear-regression techniques are more likely to end up in a local minimum without ever finding the global minimum. Consequently, it results in finding non-unique characteristic parameters of the permeability function. However, heuristic-based optimization technique such as genetic algorithm randomly jump out of the local minima and finds the global minimum of the permeability function. This helps in finding unique value of the characteristic parameters specifically cement exclusion factor, power law exponent, inter-connectivity parameter and other constants resulting in a high correlation coefficient of derived permeability vs. normalized porosity cross-plot. The unique characteristic parameters obtained by global minimization of permeability function can determine a wide range of permeability values with higher accuracy. On the other hand, the non-unique parameters determined from local minimization are suitable for a limited range of porosity-permeability data. The correlation coefficients for the cross-plot of derived permeability vs. normalized porosity using unique characteristic parameters was found to be close to unity for various data sets obtained from literature. The presented method of finding parameters of a permeability function also reduces the experimentation cost and time. The novelty of the heuristic-based optimization techniques such as genetic algorithm is in its capacity to find the global minimum of the permeability function. This helps in obtaining unique characteristic parameters for a particular set of permeability-porosity data.