Abstract
Shale gas plays an increasingly important role in the current energy industry. Modeling of gas flow in shale media has become a crucial and useful tool to estimate shale gas production accurately. The second law of thermodynamics provides a theoretical criterion to justify any promising model, but it has been never fully considered in the existing models of shale gas. In this paper, a new mathematical model of gas flow in shale formations is proposed, which uses gas density instead of pressure as the primary variable. A distinctive feature of the model is to employ chemical potential gradient rather than pressure gradient as the primary driving force. This allows to prove that the proposed model obeys an energy dissipation law, and thus, the second law of thermodynamics is satisfied. Moreover, on the basis of energy factorization approach for the Helmholtz free energy density, an efficient, linear, energy stable semi-implicit numerical scheme is proposed for the proposed model. Numerical experiments are also performed to validate the model and numerical method.
Highlights
Shale gas has become a significant energy resource over the last decade
These results indicate that the production density has a great effect on the gas production; the increase of cb can largely reduce the cumulative gas production
Different from the existing models, the proposed model uses gas density instead of pressure as the primary variable, and it employs chemical potential gradient rather than pressure gradient as the primary driving force. This distinctive feature brings up with thermodynamical consistency of the proposed model; that is, the model obeys an energy dissipation law, which implies the satisfaction of the second law of thermodynamics
Summary
Shale gas has become a significant energy resource over the last decade. Shale gas refers to natural gas composed of primarily methane, which is trapped within the pores of fine-grained sedimentary rocks with rich micropores and relatively low permeability. For gas flow in tight porous media, the most remarkable phenomenon is the so-called Klinkenberg effect [20], which results from slip flow of gas molecules through very small pores This effect leads to the apparent permeability that is generally greater than the absolute permeability of a porous medium [14, 15]. In this work, using the EF approach, an efficient, linear, energy stable semiimplicit numerical scheme is constructed for the proposed model of shale gas transport.
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