Nonlinear Poroelastic Solutions for the Pore Fluid Flow and Sorption in Deformable Rocks
Restricted (Penn State Only)
- Author:
- Zhang, Wei
- Graduate Program:
- Energy and Mineral Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- February 14, 2022
- Committee Members:
- Luis Ayala H, Major Field Member
Hamid Emami-Meybodi, Major Field Member
Albert Segall, Outside Unit & Field Member
Amin Mehrabian, Chair & Dissertation Advisor
Mort Webster, Professor in Charge/Director of Graduate Studies - Keywords:
- Adsorption
Poroelasticity
Nonlinear solution
Constitutive modeling
Geomechanics - Abstract:
- Fluid transport through porous media can be coupled with deformation of the solid frame and sorption of the pore fluid against the pore surface. The three-way coupling among these physical processes is studied in this dissertation within the framework of the theory of poroelasticity. Presentation of the developed models starts with the coupled problem of fluid flow and rock deformation without consideration of sorption effects. A generic model considering permeability variation arising from the described coupling between solid deformation and pore pressure disturbances in porous rocks is derived in Chapter 2. Radial and linear flows of fluid in porous media with arbitrary forms of pressure-dependent permeability are considered for this purpose. The homotopy perturbation is used to develop analytical solutions to the described problems. Results of these solutions are discussed in terms of productivity index, a commonly used parameter to describe the performance of subsurface rocks to deliver pore fluids toward a producing boundary. Constitutive modeling of surface sorption effects on the coupling between the pore fluid pressure and solid deformation in a multiple-porosity porous medium is studied in Chapter 3. The general case of N overlapping porosities is considered where the pore fluid may exist in the free phase or in the adsorbed phase within any chosen number of the porosity systems. The constitutive relations are obtained from the thermodynamics outlook of the free energy density function for a porous, fluid-saturated, elastic, and sorptive medium. The presented generic constitutive model successfully recovers the previously published works on the subject, as special cases. The dual-porosity case of the constitutive relations developed in Chapter 3 is applied to the problem of natural gas flow toward a producing boundary in fractured shale. The gas flow problem involves a set of entangled nonlinearities arising from the coupled processes of sorption and solid strain, the resulting changes in rock permeability, as well as the gas equation of state. An analytical solution to this strongly nonlinear problem is developed using the homotopy perturbation method. Local dependence of the involved physical parameters on pore fluid pressure is rigorously accounted for in the developed solution. Solution results are demonstrated in terms of the problem dimensionless variable groups. The asymptotic behavior of the solution in the parametric space of these dimensionless groups is discussed in detail. Application of the solution in rock characterization is demonstrated by estimating the in-situ coupling coefficient between sorption and strain, as well as the rock fractures porosity and permeability, via the history-matched field data of gas production rate from Barnett shale. The case of binary gas transport in shale is addressed in Chapter 5. The previously derived constitutive model is utilized in a numerical solution that simulates cyclic injection of CO2 in shale before producing CO2 and CH4 from the same. Likewise, the three-way coupling among rock deformation, pore fluid transport, and surface sorption of the pore fluid components is considered in the solution. Here, molecular diffusion, Knudsen diffusion, and surface diffusion are considered as the dominant mechanisms of pore fluid transport through the organic-rich shale. Results indicate that removing any of the described coupled processes from the solution would underestimate both the CO2 storage capacity and enhanced natural gas recovery factor of the organic-rich shale. Gas sorption, surface diffusion, sorption-induced deformation, as well as strain-induced changes in gas sorption affinities, are all conducive to both outcomes. This dissertation offers improvements to the constitutive models for coupled processes of transport, deformation, and adsorption in porous media. The developed solutions enable a better understanding of the relevance and magnitude of these coupled processes in the expected outcomes of the related practical problems such as hydrocarbon recovery and CO2 geological sequestration.