Computational study of gas transport in shale at pore-scale and beyond

Student thesis: Doctoral Thesis


Unconventional gas resources like shale are poised to enter a golden age thanks to the worldwide increased exploitation potential. Yet, the future of these resources is far from assured since it is still subject to many uncertainties, mainly with regard to gas recoverability. The macroscopic flow properties that allow the prediction of production are directly linked to the microscopic flow where underlying rarefaction effects play a major role. This is due to the pore size which is as small as a few nanometers and comparable to the mean free path. Thus, an in-depth understanding of gas transport in ultra-tight porous media is crucial for the accurate determination of flow properties in shale rocks. This thesis is a fundamental research aiming to aid and benefit shale gas exploration and development. The objective of this work is to provide useful insights for such non-equilibrium porous media flows, where the conventional fluid mechanics theory fails. Even though there are multiple heuristic permeability models in the literature, I find them unsuitable to provide reliable apparent permeability estimates since they often include simplifications of the flow mechanisms and matrix complexity. Notably, I hereby establish/prove the limitations of the accuracy of the Navier-Stokes equations to the first order of Knudsen number. We also thoroughly analyse Klinkenberg’s slip factor behaviour for a wide range of gas rarefaction, utilising gas kinetic theory, for both simple and complex porous media. Moreover, using controllably random porous media, I systematically quantify the impact of numerous structural characteristics, i.e. porosity, tortuosity, specific surface area, heterogeneity and degree of anisotropy, on both intrinsic and apparent permeability.One of the key contributions of this work is a new semi-analytical permeability formulation derived using the produced simulation results. This expression, suitable for both isotropic and anisotropic two-dimensional porous media, accounts for the aforementioned properties as well as for continuum and slip flow. The main advantage of the proposed formulation is the fact that it does not entail any experimental or numerical data as input, unlike other established models. Shale is intrinsically multiscale, thus the direct simulation of transport in all scales is not feasible. Upscaling from the pore-scale is indispensable in order to eventually obtain the essential macroscopic properties in the field-scale. For this reason, I examine well-known analytical and numerical upscaling techniques, verifying the sensitivity and accuracy of the latter ones. Studying microscale sample images, we need to consider the appearance of microfractures. The difference of the characteristic length scales between the nanopores and the microfractures requires a hybrid upscaling method such as the Brinkman approach.The suitability of this model is extensively validated on fractured porous media of interest, especially on the grounds that the exact form of the effective viscosity is still a matter of discussion. We perform this validation comparing numerous direct simulation results with the corresponding ones from the Brinkman solution. Different values of the effective viscosity are investigated, along with a variable permeability model applied at the vicinity of the fluid-porous interface. Due to lack of an appropriate universal treatment of the transition zone of random porous media, we consider effective viscosity equal to fluid viscosity. The accuracy of the Brinkman approach is further examined using several two and three-dimensional random porous media containing fractures, as well as considering rarefied conditions. Although I find that heterogeneity and anisotropy increase the error of the effective permeability derived from the Brinkman approach, generally, the effective perm
Date of Award24 Jan 2020
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsUniversity of Strathclyde
SupervisorYonghao Zhang (Supervisor) & Sina Haeri (Supervisor)

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