# Investigation of longitudinal and transverse dispersion in porous media

Eskandari, Saeid (2019) Investigation of longitudinal and transverse dispersion in porous media. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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## Abstract

Miscible displacement processes are increasingly feasible methods for the recovery of oil from depleted reservoirs as an enhanced oil recovery (EOR) method. However, a fundamental understanding of the dependency of transport phenomenon to medium properties and their consequent impact on oil recovery efficiency is lacking. Moreover, it is generally believed that miscibility may repeatedly develop and break down in a reservoir due to dispersion arising from velocity and reservoir heterogeneity. Thus, miscible processes are assumed to be dependent on the pore geometry of the reservoir. The current research uses mathematical and unique experimental approaches to investigate miscible displacement in two-dimensional media with focus on pore structure to comprehend the relationship between the transport properties to its pore structure. Transport phenomena significantly influence EOR efficiency and this raises the importance of dispersion and miscibility. The mathematical section of this research uses a statistical oriented mathematical approach to investigate miscible displacement assuming various pore properties to comprehend the relationship between dispersion during miscible displacement and the pore structure. This study focuses on examining the dependence of dispersion in both the longitudinal and transverse directions on heterogeneity and pore geometry using statistical models. The pore element is defined by adjustable distribution functions indicating tortuosity and connectivity of the porous medium. Using random walk theory that assumes the mass transfer occurs as a sequence of discrete physical events as particles move between a series of discrete pore elements, the stochastic functions are used to develop a model to estimate the mechanical dispersion properties of the porous media. The introduced model decouples dispersion in the longitudinal and transverse directions and shows a more specific relationship between dispersion and pore size distribution. An analytical approach is applied to model miscible displacement in a fractured medium to study the effect of velocity on the magnitude of mechanical dispersion. Various displacement scenarios are assumed to find the the effect of pore properties on dispersion. Results illustrate a strong dependence of mechanical dispersion on pore properties of the medium. Both longitudinal and transverse dispersion coefficients increased by increasing the velocity and heterogeneity ratio. In the experimental section, a new experimental approach has been developed to estimate the average longitudinal and transverse dispersion co- efficients in a homogeneous anisotropic porous medium during miscible displacement. A series of miscible flooding tests are conducted and studied. Traditionally, most studies of miscible injection have focused on recovery and mechanism of the method and Peclet number that have been used to find the dispersion and diffusion coefficients from a mathematical correlations. This study utilizes a unique method to estimate the mass transfer properties. A unique image processing tool is developed and used to analyze the developing mixing zone in the process and consequently processed images are used to collaborate with a developed Bayesian estimator tool to fit the dispersion coefficients in analytical solution of Advection-Diffusion Equation (ADE). The de- tails of the approach are explained and obtained images are analyzed and interpreted. The results confirm the strong dependency of the velocity of the displacing fluid and dispersion coefficients in both longitudinal and transverse directions. The effects of anisotropy on miscible mass transport are investigated in this study too.

Item Type: Thesis (Doctoral (PhD)) http://research.library.mun.ca/id/eprint/13693 13693 Includes bibliographical references (pages 144-152). Porous Media, Miscible Displacement, Longitudinal Dispersion, Transverse Dispersion, Image Processing Engineering and Applied Science, Faculty of May 2019 Submission Miscible displacement (Petroleum engineering); Porous materials--Transport properties; Enhanced oil recovery