A generalized model for gas flow prediction in shale matrix with deduced coupling coefficients and its macroscopic form based on real shale pore size distribution experiments

Abstract

As an unconventional natural gas resource, shale gas is attracting increasing attention worldwide because of its potential to strengthen global energy security and reduce carbon emissions. The shale gas flow in nanopores is one of the main concerns affecting its development process. However, due to the strong nonlinearity and complexity of gas flow at the nanoscale, there is no satisfactory consensus on a physically sound flow mechanism scheme and its corresponding coupling method. Furthermore, although the integration method using specific functions has been proposed to facilitate the consideration of various pore sizes in shale matrix, the real shale experiments are rarely involved to realize this integration method with definitely determined parameters. In this study, the concept of “wall-associated diffusion” is firstly utilized to clarify the relationship among several flow mechanisms, and thereby a comprehensive flow mechanism scheme differing from common research is proposed, which physically considers both the division of mechanical mechanisms in nanopores and partition of flow space. Besides, the deficiencies in the mathematical models of viscous flow and several diffusion processes for flow description are illustrated. Using the molecular collision frequency expressions, a new coupling coefficient-based flow model in nanopores is derived to eliminate the aforementioned deficiencies by strengthening the correspondence between the flow models and Knudsen number (Kn), which is applicable in the full flow regime scope and avoids segment processing. Furthermore, based on the pore size distribution experiments of the real shale samples from a gas field, the fitting parameters needed for the macroscopic form of the above coupled model are obtained, so as to establish an integration method-based unified model for gas flow prediction in shale matrix. Results show that the prediction accuracy of the new model for the two tested shale samples is at least 2.2 times higher than several typical models and is also 1.9 and 7.5 times more accurate than the model without coupling coefficients, respectively. And the application of the proposed model to the flow experiment on another shale sample at higher pressure levels is in accordance with these observations. Interestingly, as temperature increases, the flow rate decreases with minor amplitudes. Under the conditions studied, the pressure change can cause over 10 times variation of the flow rate, revealing measures should be taken to maintain relatively high reservoir pressures to guarantee appreciable gas production from matrix if the other factors remain unchanged. In addition, the difference between the average flow shape in the whole rock and the gas motion in the pore of mean radius is revealed. Sounder in theoretical bases and better in application effects, the proposed model is expected to be of practical significance for guiding shale gas reservoir development.