Interfacial instability of reactive and anisotropic dispersive miscible displacements flows

Flow processes that involve the displacement of a viscous fluid by a less viscous one often lead to a hydrodynamic instability known as viscous fingering. The objective of the study is to investigate the effects of anisotropic velocity-dependent dispersion and chemical reaction on this instability. The results of this study are relevant to applications that include improved oil recovery, the spreading of reactive pollutants in groundwater, frontal polymerization, and reactive infiltration in geochemical setting. In order to understand the physics of this flow displacement, the basic equations of conservation of mass, energy and momentum are solved for a homogenous porous media. A numerical code based on a semi-implicit spectral method using Hartley series is developed fot this purpose.;Finally, the effect of hydrodynamic dispersion and chemical reaction on interfacial instability is investigated. A numerical model is developed for reactive miscible displacement, and the effects of the reaction type, order and rate are analyzed for both diffusive and anisotropic dispersive displacements. Physical discussions of how chemical reaction affects the viscous fingering patterns are presented and some new mechanisms of interfacial instability in comparison with non-reactive isotropic miscible displacement are analyzed.;In a first stage, the viscous fingering instability for anisotropic non-reactive dispersive flows is addressed. Stream-function and concentration fields are tracked using an iteration process for two dimensional flows in every time-step. Different types of anisotropic velocity dependent dispersions are considered and their effects on the finger patterns are examined. Physical discussion of how medium dispersivity affects hydrodynamics and results in interesting instability schemes are presented. The role of some parameters that affect the anisotropic dispersion are examined by both linear stability analysis and nonlinear simulations. In particular, the development of the instability is analyzed for different values of the Peclet number, dispersivity coefficient and dispersion strength. The close interplay between the anisotropic dispersion and the hydrodynamics of the flow and their effects on the growth of the interfacial instability is thoroughly analyzed. Based on the conclusions of the present study and those of earlier relevant ones, it is found that the anisotropic nature of the dispersion tensor and its velocity dependence are two important factors that need to be incorporated in any study that attempts to model dispersion in porous media.