Improved Permeability Prediction Relations for Low-Permeability Sands

摘要

This work addresses the problem of estimating Klinkenbergcorrected 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 Klinkenbergcorrected 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- Owens4 and Sampath-Keighin5 correlations for estimating the Klinkenberg-corrected (absolute) permeability from singlepoint, steady-state measurements is investigated. We also provide an update to these correlations using modern petrophysical 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 "microflow" 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.