Effects of viscous dissipation on miscible thermo-viscous fingering instability in porous media

The thermo-viscous fingering instability associated with miscible displacement through a porous medium is studied numerically, motivated by applications in upstream oil industries especially enhanced oil recovery (EOR) via wells using hot water flooding and steam flooding. The main innovative aspect of this study is the inclusion of the effects of viscous dissipation on thermal viscous fingering instability. An Arrhenius equation of state is employed for describing the dependency of viscosity on temperature. The normalized conservation equations are solved with the finite element computational fluid dynamics code, COMSOL (Version 5) in which glycerol is considered as the solute and water as the solvent and the two-phase Darcy model employed (which couples the study Darcy flow equation with the time-dependent convection-diffusion equation for the concentration). The progress of finger patterns is studied using concentration and temperature contours, transversely averaged profiles, mixing length and sweep efficiency. The sweep efficiency is a property widely used in industry to characterize how effective is displacement and it can be defined as the ratio of the volume of displaced fluid to the total volume of available fluid in a porous medium in the displacement process. The effects of Lewis number, Brinkman number and thermal lag coefficient on this instability are examined in detail. The results indicate that increasing viscous dissipation generates significant enhancement in the temperature and a marked reduction in viscosity especially in the displaced fluid (high viscous phase). Therefore, the mobility ratio is reduced, and the flow becomes more stable in the presence of viscous dissipation

Linear stability analysis and CFD simulation of thermal viscous fingering instability in anisotropic porous media

The water or steam injection in oil fields is a usual method for enhanced oil recovery in petroleum engineering. The thermo-viscous fingering instability is one of the main problems with complex nature that decreases the efficiency of oil extraction. Actually, the oil wells are the porous medium with a level of anisotropy for permeability and diffusion. In this paper, the thermal viscous fingering instability in anisotropic media has been investigated using both linear stability analysis and CFD simulation. For stability analysis, the growth rate of disturbances is determined by solving quasi-steady state equations via shooting method. The CFD simulation is performed by solving the governing equations of heat and mass transfer using a spectral method. It is shown that the longitudinal direction permeability and the transverse direction dispersion have important effect on the instability. The value of thermal-lag coefficient and the Lewis number have opposite effects on the different types of displacements that are considered. For the case of sweeping the porous media via the cold fluid, increasing the Lewis number intensifies the level of flow instability

Multiphase flow in porous media with phase transitions: from CO₂ sequestration to gas hydrate systems

Ongoing efforts to mitigate climate change include the understanding of natural and engineered processes that can impact the global carbon budget and the fate of greenhouse gases (GHG). Among engineered systems, one promising tool to reduce atmospheric emissions of anthropogenic carbon dioxide (CO₂) is geologic sequestration of CO₂, which entails the injection of CO₂ into deep geologic formations, like saline aquifers, for long-term storage. Among natural contributors, methane hydrates, an ice-like substance commonly found in seafloor sediments and permafrost, hold large amounts of the world's mobile carbon and are subject to an increased risk of dissociation due to rising temperatures. The dissociation of methane hydrates releases methane gas-a more potent GHG than CO₂-and potentially contributes to a positive feedback in terms of climatic change. In this Thesis, we explore fundamental mechanisms controlling the physics of geologic CO₂ sequestration and natural gas hydrate systems, with an emphasis on the interplay between multiphase flow-the simultaneous motion of several fluid phases and phase transitions-the creation or destruction of fluid or solid phases due to thermodynamically driven reactions. We first study the fate of CO₂ in saline aquifers in the presence of CO₂-brine-carbonate geochemical reactions. We use high-resolution simulations to examine the interplay between the density-driven convective mixing and the rock dissolution reactions. We find that dissolution of carbonate rock initiates in regions of locally high mixing, but that the geochemical reaction shuts down significantly earlier than shutdown of convective mixing. This early shutdown reflects the important role that chemical speciation plays in this hydrodynamics-reaction coupled process. We then study hydrodynamic and thermodynamic processes pertaining to a gas hydrate system under changing temperature and pressure conditions. The framework for our analysis is that of phase-field modeling of binary mixtures far from equilibrium, and show that: (1) the interplay between phase separation and hydrodynamic instability can arrest the Ostwald ripening process characteristic of nonflowing mixtures; (2) partial miscibility exerts a powerful control on the degree of viscous fingering in a gas-liquid system, whereby fluid dissolution hinders fingering while fluid exsolution enhances fingering. We employ this theoretical phase-field modeling approach to explain observations of bubble expansion coupled with gas dissolution and hydrate formation in controlled laboratory experiments. Unraveling this coupling informs our understanding of the fate of hydrate-crusted methane bubbles in the ocean water column and the migration of gas pockets in hydrate-bearing sediments

Immiscible thermo-viscous fingering in Hele-Shaw cells

We investigate immiscible radial displacement in a Hele-Shaw cell with a temperature dependent viscosity using two coupled high resolution numerical methods. Thermal gradients created in the domain through the injection of a low viscosity fluid at a different temperature to the resident high viscosity fluid can lead to the formation of unstable thermo-viscous fingers, which we explore in the context of immiscible flows. The transient, multi-zone heat transfer is evaluated using a newly developed auxiliary radial basis function-finite collocation (RBF-FC) method, which locally captures variation in flux and field variable over the moving interface, without the need for ghost node extrapolation. The viscosity couples the transient heat transfer to the Darcy pressure/velocity field, which is solved using a boundary element - RBF-FC method, providing an accurate and robust interface tracking scheme for the full thermo-viscous problem. We explore the thermo-viscous problem space using systematic numerical experiments, revealing that the early stage finger growth is controlled by the pressure gradient induced by the varying temperature and mobility field. In hot injection regimes, negative temperature gradients normal to the interface act to accelerate the interface, promoting finger bifurcation and enhancing the viscous fingering instability. Correspondingly, cold injection regimes stabilise the flow compared to isothermal cases, hindering finger formation. The interfacial mobility distribution controls the late stage bifurcation mode, with non-uniformities induced by the thermal diffusivity creating alternate bifurcation modes. Further numerical experiments reveal the neutral stability of the thermal effects on the fingering evolution, with classical viscous fingering dynamics eventually dominating the evolution. We conclude the paper with a mechanistic summary of the immiscible thermo-viscous fingering regime, providing the first detailed analysis of the thermal problem in immiscible flows

Pore-scale modeling of phase change in porous media

The combination of high-resolution visualization techniques and pore-scale flow modeling is a powerful tool used to understand multiphase flow mechanisms in porous media and their impact on reservoir-scale processes. One of the main open challenges in pore-scale modeling is the direct simulation of flows involving multicomponent mixtures with complex phase behavior. Reservoir fluid mixtures are often described through cubic equations of state, which makes diffuse-interface, or phase-field, theories particularly appealing as a modeling framework. What is still unclear is whether equation-of-state-driven diffuse-interface models can adequately describe processes where surface tension and wetting phenomena play important roles. Here we present a diffuse-interface model of single-component two-phase flow (a van der Waals fluid) in a porous medium under different wetting conditions. We propose a simplified Darcy-Korteweg model that is appropriate to describe flow in a Hele-Shaw cell or a micromodel, with a gap-averaged velocity. We study the ability of the diffuse-interface model to capture capillary pressure and the dynamics of vaporization-condensation fronts and show that the model reproduces pressure fluctuations that emerge from abrupt interface displacements (Haines jumps) and from the breakup of wetting films

Mixed convection instability in a viscosity stratified flow in a vertical channel

The present study examines the linear instability characteristics of double-diffusive mixed convective flow in a vertical channel with viscosity stratification. The viscosity of the fluid is modelled as an exponential function of temperature and concentration, with an activation energy parameter determining its sensitivity to temperature variation. Three scenarios are considered: buoyancy force due to thermal diffusion only, buoyancy force due to temperature and solute acting in the same direction, and buoyancy force due to temperature and solute acting in opposite directions. A generalized eigenvalue problem is derived and solved numerically for linear stability analysis via the Chebyshev spectral collocation method. Results indicate that higher values of the activation energy parameter lead to increased flow stability. Additionally, when both buoyant forces act in opposite directions, the Schmidt number has both stabilizing and destabilizing effects across the range of activation energy parameters, similar to the case of pure thermal diffusion. Furthermore, the solutal-buoyancy-opposed base flow is found to be the most stable, while the solutal-buoyancy-assisted base flow is the least stable. As expected, an increase in Reynolds number is shown to decrease the critical Rayleigh number.Comment: 10 pages, 9 figures, Physics of Fluid

A numerical study on the viscous fingering instability of immiscible displacement in Hele-Shaw cells

In this thesis, the viscous fingering instability of radial immiscible displacement is analysed numerically using novel mesh-reduction and interface tracking techniques. Using a reduced Hele-Shaw model for the depth averaged lateral flow, viscous fingering instabilities are explored in flow regimes typical of subsurface carbon sequestration involving supercritical CO2 - brine displacements, i.e. with high capillary numbers, low mobility ratios and inhomogeneous permeability/temperature fields. A high accuracy boundary element method (BEM) is implemented for the solution of homogeneous, finite mobility ratio immiscible displacements. Through efficient, explicit tracking of the sharp fluid-fluid interface, classical fingering processes such as spreading, shielding and splitting are analysed in the late stages of finger growth at low mobility ratios and high capillary numbers. Under these conditions, large differences are found compared with previous high or infinite mobility ratio models and critical events such as plume break-off and coalescence are analysed in much greater detail than has previously been attempted. For the solution of inhomogeneous mobility problems, a novel meshless radial basis function-finite collocation method is developed that utilises a dynamic quadtree dataset and local enforcement of interface matching conditions. When coupled with the BEM, the numerical scheme allows the analysis of variable permeability effects and the transition in (de)stabilising mechanisms that occurs when the capillary number is increased with a fixed, spatially varying permeability. Finally, thermo-viscous fingering is explored in the context of immiscible flows, with a detailed mechanistic study presented to explain, for the first time, the immiscible thermo-viscous fingering process

A numerical study on the viscous fingering instability of immiscible displacement in Hele-Shaw cells

In this thesis, the viscous fingering instability of radial immiscible displacement is analysed numerically using novel mesh-reduction and interface tracking techniques. Using a reduced Hele-Shaw model for the depth averaged lateral flow, viscous fingering instabilities are explored in flow regimes typical of subsurface carbon sequestration involving supercritical CO2 - brine displacements, i.e. with high capillary numbers, low mobility ratios and inhomogeneous permeability/temperature fields. A high accuracy boundary element method (BEM) is implemented for the solution of homogeneous, finite mobility ratio immiscible displacements. Through efficient, explicit tracking of the sharp fluid-fluid interface, classical fingering processes such as spreading, shielding and splitting are analysed in the late stages of finger growth at low mobility ratios and high capillary numbers. Under these conditions, large differences are found compared with previous high or infinite mobility ratio models and critical events such as plume break-off and coalescence are analysed in much greater detail than has previously been attempted. For the solution of inhomogeneous mobility problems, a novel meshless radial basis function-finite collocation method is developed that utilises a dynamic quadtree dataset and local enforcement of interface matching conditions. When coupled with the BEM, the numerical scheme allows the analysis of variable permeability effects and the transition in (de)stabilising mechanisms that occurs when the capillary number is increased with a fixed, spatially varying permeability. Finally, thermo-viscous fingering is explored in the context of immiscible flows, with a detailed mechanistic study presented to explain, for the first time, the immiscible thermo-viscous fingering process

Coupled Dynamics of Particles and Fluid-Fluid Interfaces

The study of the interaction between particles and fluid-fluid interfaces is essential to a variety of applications. A systematic way to understand those phenomena is to consider them in two different limits: single particle versus multiple particles. One particular example of a single particle problem is the particle’s interaction with an acoustic bubble. Many bubble-based systems use oscillating microbubbles to trap particles, which further leads to applications including live animal trapping and cell manipulation. On the other hand, when multiple particles are involved, the study of the suspension injection and drainage has drawn much attention, which has the implication in biotechnology and food processing. The objective of this research is to study and gain a fundamental understanding of the coupled dynamics between particles and fluid-fluid interfaces via experimental and theoretical approaches. First, we work on a project with a single-particle trapping via acoustic bubble. In this work, we quantify the magnitudes of secondary radiation force exerted by the oscillating bubble inside a microchannel for varying actuation frequencies and voltages. By combining well-developed theories that connect bubble oscillation yielding secondary radiation force to the acoustic actuation, we derive the expression to predict the critical input voltage that leads to particle release into the flow, which agrees with the experimental results. The next phase of the research emphasizes the dynamics of the collection of particles. We experimentally investigate the effect of particle concentration on the viscous fingering behavior when the suspension is withdrawn from a Hele-Shaw cell. In particular, we quantify the fingering growth rate with varying initial particle concentrations. Our results reveal that the fingering growth rate increases with increasing particle concentrations, while the total drainage time also appears to be increasing. This successfully proves that the drainage efficiency is enhanced due to the presence of the particles. In addition, we observe the particles entrained into the thin film on the plate after drainage, which also varies with the particle concentration and the ratio between gap thickness and particle diameter. Using a simplified model, we also find an entrainment criterion in agreement with the experimental results