Adsorption-Controlled Gas Transport in Nanoporous Media
Restricted (Penn State Only)
- Author:
- Liu, Zizhong
- Graduate Program:
- Energy and Mineral Engineering (PHD)
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 14, 2022
- Committee Members:
- Xiaofeng Liu, Outside Unit & Field Member
Luis Ayala H, Major Field Member
Hamid Emami-Meybodi, Chair & Dissertation Advisor
Eugene Morgan, Major Field Member
Mort Webster, Professor in Charge/Director of Graduate Studies - Keywords:
- Nanoporous media
Nonlinear governing equation
Piecewise constant coefficients
Apparent diffusion coefficient
Adsorption-controlled diffusion model
Simplified local density method
Modified Peng-Robinson equation of state - Abstract:
- 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., < 200 nD) and the substantial existence of nanopores in nanoporous media such as shales, the notion of advection-dominated mass transport may become irrelevant, and diffusion-based models become more appropriate. Hence, diffusion-based governing equations (e.g., Fickian-like equations) need to be used for mass transport modeling in nanoporous media instead of hydraulic diffusion equations. Chapter 4 presents a diffusion-based model for a single-component gas transport within nanoporous media considering multiple transport and storage mechanisms, including molecular diffusion, Knudsen diffusion for free-phase, and surface diffusion and monolayer-adsorption for sorbed phase. The diffusion-based model honors the physics of fluid transport in nanoporous media, with diffusion coefficients that naturally entrain the influencing variables (i.e., pressure, temperature, and concentration) and are self-consistent. For fluid in the nanoporous media with high adsorption affinity (e.g., shales and coals), monolayer assumptions may become too ideal under certain conditions, and multilayer adsorption should be considered. An apparent diffusion coefficient is proposed in Chapter 5 to account for the multilayer adsorption-controlled diffusion of gases within nanoporous media. The complex effects of the real gas effect, confinement effect, dynamic adsorption layer thickness, and free-phase concentration-dependent fluid properties are considered. The adsorption information is obtained by the pore-scale simplified local density method. The proposed apparent diffusion coefficient represents the overall mass transport subject to the competing effects of free-phase and surface diffusion, sorbed- and free-phase volume fraction, and their concentration dependence. The continuum-scale gas transport with multilayer adsorption is studied in Chapter 6. A continuum-scale diffusion-based model informed by pore-scale adsorption properties for single-component high-pressured gas through nanoporous media is developed. A simplified local density method is utilized to predict pore-scale density distribution and estimate sorbed-phase volume fraction and multilayer adsorption isotherm. The piecewise approach is used to solve the nonlinear diffusion equation for the diffusive flux and temporal concentration distribution within the nanoporous media. In summary, this dissertation investigates the mass transport of high-pressure fluids in nanoporous media by considering the physics of fluid storage and transport and provides a new avenue and theoretical ground for the future investigation of the diffusive transport based on the apparent diffusion coefficient.