Algorithms for determining vertical permeability distribution

The presented paper describes an extension of the earlier proposed technique for determining vertical permeability variation in a wellbore (permeability profile) by integrating results of log data interpretation with average reservoir permeability from well testing and the information on reservoir vertical heterogeneity from core samples or oil displacement dynamics. Mathematically, the objective is to find a functional relationship between true and log-derived permeability, represented in a given type of permeability distribution. As a solution of this task, it was proposed to use generalization of a well-known mathematical statistics tool – quantile-quantile transformation. The paper also presents a detail procedure for determining the Dykstra-Parsons coefficient (as a measure of vertical permeability variation) from historical data on oil displacement dynamics.