Analytical Study of the Wafer Non-Darcy Flow Experiments

Abstract

Abstract Non-Darcy effect is significant for high velocity gas flow especially when gas approaches the wellbore region. A new semi-theoretical equation was proposed to estimate the non-Darcy coefficient and the equation was verified by comparing differential pressures from simulations with their counterparts from the experiments where nitrogen was injected at various flow rates and in several directions into a wafer-shaped Berea sandstone core sample. In this paper, the geometry of the wafer and flow profiles were simplified and an analytical model was developed to provide a quick method to estimate the directional permeability and non-Darcy coefficient. Data from several directions were processed statistically to find the best correlation for the wafer. The analytical study confirmed that the new semi-theoretical equation was effective to be used to estimate the non-Darcy coefficient. The correlation for the wafer developed from the analytical study was found to lie between the parallel-type model and serial-type model and be closer to the latter one. Combination of correlations from analytical and numerical studies led to a general correlation, which was found to be the best for Berea sandstone samples after performances of the correlations in the literature and from this paper were independently evaluated by using the results of non-Darcy flow experiments in the literature.