Upscaling of compositional flow simulation based on a non-equilibrium formulation

Advisors

Hamdi Tchelepi, primary advisor
Khalid Aziz, advisor
Denis Voskov, advisor

Abstract

Compositional simulation of oil reservoirs is necessary for accurate representation of the physics associated with processes such as miscible or near-miscible gas injection with the purpose of Enhanced Oil Recovery. Flow simulation of compositional systems with high-resolution models is a computationally intensive effort because of the large number of unknowns and strong nonlinear effects. The need for effective and accurate upscaling techniques for compositional flow problems is the key motivation behind this work. Compared to black-oil models, the interactions between the thermodynamic phase behavior and the subgrid heterogeneities that are associated with compositional displacements pose significant additional challenges to the upscaling procedure. This work entails the development and application of robust upscaling frameworks for multicomponent multiphase flow problems. We introduce a new framework to upscale compositional displacements with special attention to accurate representation of the fine-scale phase behavior on the coarse scale. We employ a mass-conservative formulation and introduce upscaled phase molar mobility functions for coarse-scale modeling of multiphase flow. These upscaled flow functions account for the subgrid absolute and relative permeability variations as well as the effects of compressible flow. They also correct -somewhat- for numerical dispersion effects on the coarse scale. Upscaling of the thermodynamic phase behavior is performed as follows. We assume that instantaneous thermodynamic equilibrium is valid on the fine scale, and we derive coarse-scale equations, in which the thermodynamic phase behavior is not necessarily at chemical equilibrium. Deviation from local equilibrium can be due to different bypassing mechanisms, such as fingering and channeling caused by heterogeneities, adverse mobility ratio, or gravity segregation. A novel framework is proposed to model the non-equilibrium behavior on the coarse scale. Upscaled thermodynamic functions, i.e., the difference of component fugacities between conservative representation of the component mass in the oil and gas phases, are employed to account for non-equilibrium effects. We demonstrate that upscaled thermodynamic functions transform the equilibrium phase space (on the fine scale) to a region of similar shape but with tilted tie-lines (on the coarse scale). The proposed methodology is applied to various challenging gas injection problems with large number of components and highly heterogeneous permeability fields. The non-equilibrium based compositional upscaling provided results in close agreement to the fine-scale solutions for all quantities considered in this work. We also develop a compositional upscaling framework based on transport coefficients (alpha-factors). The results of both upscaling frameworks are compared in terms of accuracy, computational efficiency, complexity and phase behavior on the coarse scale. Both upscaling approaches present comparable accuracy. However, the computational cost of the transport coefficients method is higher. Nonlinear convergence problem on the coarse scale and higher degrees of freedom are the two major drawbacks of alpha-factors approach, which we investigate in detail. Then, we develop a framework to provide thermodynamically consistent transport coefficients based on the non-equilibrium approach. Finally, an upscaling framework for compositional simulations that employs K-values is developed. Based on the orientation of tie-lines in the new non-equilibrium phase space and sign of upscaled thermodynamic functions, K-values are modified for the coarse-scale simulation. We demonstrate that the modified K-values improve the accuracy of coarse-scale solutions to reproduce averaged fine-scale solutions such as component overall compositions and phase saturation distributions.