Improved Permeability Prediction Relations for Low Permeability Sands

Abstract

Abstract This work addresses the problem of estimating Klinkenberg-corrected permeability from single-point, steady-state measurements on samples from low permeability sands. The "original" problem of predicting the corrected or "liquid equivalent" permeability (i.e., referred to as the Klinkenberg-corrected permeability) has been under investigation since the early 1940s — in particular, using the application of "gas slippage" theory to petrophysics by Klinkenberg.1 In the first part of our work, the applicability of the Jones-Owens 4 and Sampath-Keighin 5 correlations for estimating the Klinkenberg-corrected (absolute) permeability from single-point, steady-state measurements is investigated. We also provide an update to these correlations using modern petro-physical data. In the second part of our work, we propose and validate a new "microflow" model for the evaluation of an equivalent liquid permeability from gas flow measurements. This work is based on a more detailed application of similar concepts employed by Klinkenberg. In fact, we can obtain the Klinkenberg result as an approximate form of our result. Our theoretical "micro-flow" result is given as a rational polynomial in terms of the Knudsen number (the ratio of the mean free path of the gas molecules to the characteristic flow length (typically the radius of the capillary)). The following contributions are derived from this work:Validation and extension of the correlations proposed by Jones-Owens and Sampath-Keighin for low permeability samples.Development and validation of a new "microflow" model which correctly represents gas flow in low permeability core samples. This model is also applied as a correlation for prediction of the equivalent liquid permeability in much the same fashion as the Klinkenberg model, although our new model is substantially more theoretical (and robust) as compared to the Klinkenberg correction model. Introduction The gas slippage phenomenon typically occurs in the laboratory when gas flow experiments are conducted at low pressures. Gas slippage is defined as the condition where the mean free path of the gas molecules is no longer negligible compared to the average effective rock pore throat radius — i.e., the gas molecules tend to "slip" on the surfaces of the porous media. This effect yields an overestimation of the measured gas permeability compared to the true absolute permeability if it were measured using a liquid. For flow in tubes, the gas slippage phenomenon has been investigated since the end of the nineteenth century. The first study of gas slippage in porous media was conducted by Klinkenberg.1 The Klinkenberg model approximates a linear relationship between the measured gas permeability and the reciprocal absolute mean core pressure.2 This model has been a consistent basis for the development of methods computing the absolute liquid permeability of a core sample based on a single data point — i.e., single-point steady-state permeability measurement methods. Subsequent work focused on correlating the parameters of the Klinkenberg model (i.e, the Klinkenberg-corrected permeability or equivalent liquid permeability (k¥) and the Klinkenberg gas slippage factor (bK). Heid et al 3 and Jones and Owens 4 proposed two correlations similar in form between bK and k¥, while Sampath and Keighin 5 proposed a different form of correlation using effective porosity (f) as a third parameter.