Adsorption Controlled Gas Transport In Nanoporous Media

Nanoporous media consist of pores with sizes similar to the size of the fluid molecules, making fluid transport within them substantially different from that in the high permeable porous media and the bulk fluid. This poses challenges for modeling and predicting the transport and storage of fluids in nanoporous media, particularly in the presence of adsorption. Accordingly, the main goal of this dissertation is to develop rigorous yet straightforward approaches for analyzing and understanding the complex transport and sorption behaviors of high-pressure gas in nanoporous media through theoretical analysis and mathematical modeling. The hydraulic (pressure) diffusivity equation is commonly utilized to describe the fluid transport through porous media. However, the diffusivity equation appears as a second-order, nonlinear, partial differential equation due to the pressure-sensitive properties of the fluid and porous media. A unified approach is proposed in Chapter 2 that can be implemented to assess the nonlinearity associated with the transient linear flow of single-phase fluid flow from a pressure-sensitive formation (e.g., oil and gas reservoirs) subject to the constant pressure boundary conditions. The proposed approach provides a reliable avenue to assess the accuracy of the pseudo-time, which is commonly used to linearize the hydraulic diffusivity equation. The approach can also be utilized to identify the cases where pseudo-time may cause significant errors. Instead of using the pseudo-time approach, in Chapter 3, a piecewise constant coefficient approach is presented to linearize the hydraulic diffusivity equation. Using the piecewise approach, a semi-analytical model is developed for transient linear flow subject to constant pressure boundary conditions by considering pressure-dependent rock and fluid properties. The piecewise approach divides the domain under consideration into an arbitrary number of subdomains and assigns them with a constant hydraulic diffusivity coefficient. The results prove that the model can accurately estimate reservoir properties even for highly nonlinear equations. Due to the ultralow permeability (i.e.,