Date of Graduation


Document Type


Degree Type



Statler College of Engineering and Mineral Resources


Chemical and Biomedical Engineering

Committee Chair

Ebrahim Fathi

Committee Co-Chair

Kashy Aminian

Committee Member

Fatemeh Belyadi


Coupled fluid flow, reaction and transport in porous media has been the topic of research in various disciplines for the past few decades. Conventional approach assumes a homogeneous and isotropic porous media, and simplifies the nature of coupling between fluid and rock interactions. However, including the reality of the process, i.e. assuming heterogeneous and anisotropic porous media with fully coupled rock fluid interaction, can lead to more advanced understanding of the fundamental physics behind the problem and developing efficient industrial applications. In the oil and gas industry optimization of different well stimulation techniques such as matrix acidizing in order to enhance oil recovery requires an advanced understanding of fluid flow and also reaction in heterogeneous formations. This thesis is a contribution to development of more general governing equations describing the reactive flow and transport in heterogeneous formations.;The heterogeneity of the porous medium is introduced in the formulation through random permeability field that possess the characteristics of stationary stochastic process. The heterogeneity in permeability field affects the reservoir dynamics over a range of length and time scales by making pressure, concentration, diffusion and reaction coefficients stochastic random fields. Stochastic nature of these parameters helps us to be able to upscale the process while keeping the local information associated with heterogeneous nature of the porous media.;Conventional approaches to deal with this problem are homogenization and smoothing the heterogeneous properties of the formation using averaging based techniques such as up-gridding. However, these techniques do not carry the fundamental physics governing the process and cannot mimic the experimental observations such as acid front movement and instability of the reaction process. The local variations in rock and fluid properties are also ignored in these techniques which might lead to significant impacts in field scale application of acidizing as one of the major stimulation techniques.;In order to upscale the isothermal reaction process in a heterogeneous porous medium, according to the nature of the process, spectral-based small perturbation theory (Gelhar, 1993; Gelhar and Axness, 1983) is used among the various numerical and analytical upscaling techniques. The reaction is a nonlinear dissolution of an injected acid in a homogeneous liquid with constant density in a stationary mineral with constant porosity. In order to follow the acid front a moving coordinate is introduced. The upscaled governing equations are obtained with explicit macro-scale expressions for the coefficients and solved using time adaptive implicit finite difference technique. The results are compared with homogeneous models and sensitivity analysis of the upscaled equations is performed. Finally conclusions and results are discussed showing the importance of applying upscaling techniques to capture the impacts of heterogeneity on fluid dynamics.