Relative Permeability Equation-of-State: The Role of Phase Connectivity, Wettability, and Capillary Number

Open Access
- Author:
- Purswani, Prakash
- Graduate Program:
- Energy and Mineral Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- February 08, 2021
- Committee Members:
- Zuleima T Karpyn, Dissertation Advisor/Co-Advisor
Zuleima T Karpyn, Committee Chair/Co-Chair
Amin Mehrabian, Committee Member
Turgay Ertekin, Special Member
Sharon Xiaolei Huang, Outside Member
Russell Taylor Johns, Dissertation Advisor/Co-Advisor
Mort D Webster, Program Head/Chair - Keywords:
- Relative permeability
Multiphase transport
Two-phase flow
Porous medium
Wettability
Capillary trapping
Equation-of-state
Pore structure
Pore-network modeling
Phase connectivity
Euler characteristic
Capillary number
Capillary pressure
Fluid-fluid interfacial area
Hysteresis - Abstract:
- Relative permeability (kr) is a transport property used for characterizing the flow of multiple phases through a porous medium. Inputs of kr are integral for reservoir simulations. Multiple parameters such as phase saturation, wettability of the medium, fluid properties, flow characteristics, pore topology, fluid phase topology, and fluid/fluid interfacial areas are known to affect relative permeabilities. Current kr models are functions of phase saturation that are matched for specific flow/experimental conditions. The other parameters affecting relative permeabilities are inherently captured through these saturation functions. Representation of relative permeabilities only in the saturation space causes non-uniqueness and path dependency in relative permeabilities which often cause simulations to fail because they lack generality and are not physically based. As a result, hysteresis in relative permeabilities arises, which is a major modeling issue for reservoir simulations. In this dissertation, models for relative permeabilities are presented by considering functional forms that include the effects of the key controlling parameters on relative permeabilities. The purpose of this dissertation is twofold, to (a) understand how different parameters, specifically, phase saturation, phase connectivity, capillary number, and wettability affect relative permeabilities; (b) propose physically-based kr models by including the effects of these parameters. Relative permeabilities are modeled using an equation-of-state (EOS) approach where the exact differential for relative permeability is written in phase connectivity and saturation. A quadratic response-based EOS for relative permeability is modeled in the connectivity-saturation space. Physical limiting conditions on the state parameters are considered to constrain the EOS model. This model is tested for different capillary numbers ranging from one to 10^-6. In addition, we calculated the partial derivatives of relative permeabilities in the state parameters using numerical data sets generated with pore-network modeling. A response for relative permeability is derived in the connectivity-saturation space following the state function approach. The locus bounded by residual nonwetting phase connectivity and residual nonwetting phase saturation is presented for two contact angles in the water-wet regime. Finally, we investigated the role of wettability on phase trapping also using pore-network modeling. An extended Land-based hysteresis trapping model is presented and compared against models from the literature. In addition, models are presented to capture the trends of residual loci for different contact angles. Results show that a simple quadratic response for relative permeability in the connectivity-saturation space captures trends across different capillary numbers. The model tuned for a capillary number in the capillary dominated regime can show predictive capability for other capillary numbers within the same regime. The linear kr-S paths for high capillary numbers (small Corey exponents) and nonlinear kr-S paths for low capillary numbers (high Corey exponents) are found to occur due to fast and slow changes in phase connectivity, respectively. Limiting constraints help in the identification of the physical region in the connectivity-saturation state space. Results also show that the response derived for relative permeability from relative permeability partial derivatives using the state function approach can predict relative permeabilities over the entire numerical data sets, regardless of the direction of flow, thus mitigating hysteresis. Further, the analysis of the effect of wettability shows that both phase trapping as well as the locus of residual saturation and residual phase connectivity are sensitive to contact angle changes. For low receding phase contact angles, the residual locus remains fairly constant, but at higher contact angles, the shape of the residual locus resembles a closed loop. Pore structure constraint at negligible saturation is found to control the shape of the residual locus. Phase trapping was found to reduce significantly for high contact angles owing to pore-scale mechanisms of layer flow of the receding phase and piston-like advance of the invading phase. A newly proposed extended Land-based model is able to capture residual saturation trends for all contact angles. Overall, through this research endeavor, we gain insight into the different intrinsic parameters that affect relative permeability. Through the application of pore-scale measures, these insights are further manifested into practical models that helps describe relative permeabilities physically.