Search Results (15)

Depleted gas reservoirs with bottom water show significant potential for long-term CO₂ storage. The residual gas influences mass-transfer dynamics, further affecting CO₂ dissolution and convection in porous media. In this study, we conducted a series of numerical simulations to explore how residual-gas mixtures impact CO₂ dissolution trapping. Moreover, we analyzed the CO₂ dissolution rate at various stages and delineated the initiation and decline of convection in relation to gas composition, thereby quantifying the influence of residual-gas mixtures. The findings elucidate that the temporal evolution of the Sherwood number observed in the synthetic model incorporating CTZ closely parallels that of the single-phase model, but the order of magnitude is markedly higher. The introduction of CTZ serves to augment gravity-induced convection and expedites the dissolution of CO₂, whereas the presence of residual-gas mixtures exerts a deleterious impact on mass transfer. The escalation of residual gas content concomitantly diminishes the partial pressure and solubility of CO₂. Consequently, there is an alleviation of the concentration and density differentials between saturated water and fresh water, resulting in the attenuation of the driving force governing CO₂ diffusion and convection. This leads to a substantial reduction in the rate of CO₂ dissolution, primarily governed by gravity-induced fingering, thereby manifesting as a delay in the onset and decay time of convection, accompanied by a pronounced decrement in the maximum Sherwood number. In the field-scale simulation, the injected CO₂ improves the reservoir pressure, further pushing more gas to the producers. However, due to the presence of CH₄ in the post-injection process, the capacity for CO₂ dissolution is reduced. Full article

Double-diffusive convection plays an important role in many physical phenomena of practical importance. However, the numerical simulation of these phenomena is challenging since fine meshes are often required to capture the flow physics. Hence, several different numerical methods have been employed in the past. This work reports the development and application of an adaptive finite element method for the simulation of these phenomena, thereby avoiding the need for the use of very fine meshes over the whole domain. The weak formulation of the conservation equations for mass, momentum, energy and species concentration is used. The Boussinesq approximation relates the density of the fluid to the temperature and/or the species concentration. A second-order backward difference method is used for time discretization and the Galerkin method is employed for spatial discretization. Both adaptive time step and grid refinement techniques are employed, and the code is parallelized using MPI. Three different stabilization methods of the convective-diffusion equations are compared; namely, the streamline upwind Petrov–Galerkin (SUPG) method, and two modified methods aimed at diminishing spurious oscillations that include an artificial diffusion term. This diffusion term may be either isotropic or orthogonal to the streamlines. The addition of artificial isotropic diffusion to the SUPG method provides enhanced stability. The method is applied to double-diffusive finger convection in a sucrose-salt aqueous mixture and a stratified salt solution heated from below. The method accurately reproduces the experimentally observed temporal evolution of the salt fingers in the former case and the location of the interfaces between convective and non-convective zones in the latter. Full article

Alongside classical effects driven by gravity or surface tension in non-isothermal fluids, the present experimental study concentrates on other exotic (poorly known) modes of convection, which are enabled in a fluid layer delimited from below by a hot plate and unbounded from above when its container is inclined to the horizontal direction. By means of a concerted approach based on the application of a thermographic visualization technique, multiple temperature measurements at different points and a posteriori computer-based reconstruction of the spatial distribution of wavelengths, it is shown that this fluid-dynamic system is prone to develop a rich set of patterns. These include (but are not limited to), spatially localized (compact) cells, longitudinal wavy rolls, various defects produced by other instabilities and finger-like structures resulting from an interesting roll pinching mechanism (by which a single longitudinal roll can be split into two neighboring rolls with smaller wavelength). Through parametric variation of the tilt angle, the imposed temperature difference and the volume of liquid employed, it is inferred that the observable dynamics are driven by the ability of gravity-induced shear flow to break the in-plane isotropy of the system, the relative importance of surface-tension-driven and buoyancy effects, and the spatially varying depth of the layer. Some effort is provided to identify universality classes and similarities with other out-of-equilibrium thermal systems, which have attracted significant attention in the literature. Full article

Miscible viscous fingering occurs when a less viscous fluid displaces a more viscous one in porous media or a Hele–Shaw cell. Such flow instabilities are of particular interest in a variety of applications in flows and displacements in subsurface energy and environment systems. In this study, we investigate the miscible viscous fingering dynamics experimentally using water to displace glycerol in a sealed Hele–Shaw cell with two wells located in it instead of at the boundary or corners. We comprehensively examine the spatial and temporal variations of fingering dynamics, different flow regimes, and how they are affected by the water injection rate and control of pressure or rate at the outlet. Alongside the widely recognized diffusion-dominated and convection-dominated flow regimes, we identify three new regimes: a slow expansion regime prior to breakthrough, a rapid shrinkage regime immediately after breakthrough, and a uniform, slow expansion regime without fingering instability. Each regime is characterized by interesting flow dynamics, which has not been reported previously. The duration of each regime depends on the water injection rate and whether constant pressure or a constant production rate is applied at the outlet. The variations of swept area, interfacial length, and count of fingers are also quantitatively examined. This study provides new insights into the fundamental mechanisms for miscible fluid displacements in a variety of applications such as CO₂ sequestration, hydrogen storage, enhanced oil recovery, and groundwater contaminate remediation. Full article

The present analysis has interesting applications in physiology, industry, engineering and medicine. Peristaltic pumps acquire an elliptical cross-section during motion. Peristaltic pumps, roller pumps and finger pumps also have highly useful applications. Transportation through these pumps provides an effective fluid movement and the substance remains separate from the duct walls. Convection and diffusion analyses were executed with accentuated viscous dissipation for the non-Newtonian flow that occurs inside a duct. The viscous effects are reviewed with an integrated convection and diffusion analysis that elucidates in-depth heat flux. Viscous dissipation appears to be the primary cause of increased heat generation. The Cartesian coordinate system is availed to develop this problem under consideration. A dimensionless set of coupled partial differential equations is attained by utilizing the relevant transformations that eventually simplify this complex problem. These coupled equations are solved step by step with a consideration of a polynomial solution method for coupled equations. The unfolded graphical outcomes of velocity, temperature and concentration reveal an axial symmetric flow. A higher rate of convection is observed due to viscous effects. Both the velocity and temperature profiles have an increasing function of $Q$. Full article

A model is developed to explore fire–atmosphere interactions due to the convective sink and vorticity sources in a highly simplified and idealized form, in order to examine their effect on spread and the stability of various fire front geometries. The model is constructed in a cellular automata framework, is linear, and represents a background flow, convective sink, and vortices induced by the fire plume at every burning cell. We use standard techniques to solve the resulting Poisson equations with careful attention to the boundary conditions. A modified Bresenham algorithm is developed to represent convection. The three basic flow types—large-scale background flow, sink flow, and vortex circulation—interact in a complex fashion as the geometry of the fire evolves. Fire-generated vortex–sink interactions produce a range of fire behavior, including unsteady spread rate, lateral spreading, and dynamic fingering. In this simplified framework, pulsation is found associated with evolving fire-line width, a fire-front acceleration in junction fires, and the breakup of longer initial fire lines into multiple head fires. Fuel is very simply represented by a single burn time parameter. The model fuel is uniform yet patchiness occurs due to a dynamic interaction of diffusive and convective effects. The interplay of fire-induced wind and the geometry of the fire front depends also on the fuel burn time. Full article

Sea-tide effects on the fresh-saline water interface (FSI) in a stratified coastal aquifer are examined through laboratory experiments. The physical model, a two-dimensional rectangular flow tank, is filled with layered aquifers and aquitards. The aquifers serve as the main entrances/exits of water to/from the system through significant horizontal flows, creating unstable conditions of heavier saline water above lighter freshwater for short periods of time. Several processes create mixing; this instability results in haline convection, creating downward fingering, stable rising of horizontal saltwater front, and unstable upward fingerings of flushing freshwater. The time lag between the sea tide fluctuations and the emergence of adequate fresh- and saltwater is higher in a stratified system compared to a homogeneous system. Furthermore, longer tide cycles lead to the enlargement of the FSI’s toe horizontal movement range. The combination of tidal forcing with a layering aquifer structure leads to a wider FSI by creating a significant salt- and freshwater mixing inside each layer, vertical flows between the layers, and saltwater bodies at isolated areas. Haline convection within the FSI might be the reason for the wider fresh-saline interfaces that are found in field studies. Full article

CO₂ convective dissolution has been regarded as one of the fundamental mechanisms to accelerate the mass transfer of CO₂ into brine. We present a new spectrophotometric method to characterize the convective instability and measure the dissolved CO₂ mass, which enables the real-time quantitative visualization of CO₂/brine transport mechanisms. Successive images were captured to identify the finger development regimes, and the convection morphologies were analyzed by the fingers length and affected area. CO₂ solubility was experimentally studied, and the results are in agreement with the theoretical calculations. CO₂ mass transfer flux was investigated as the Sherwood number changed. The increase in salinity and temperature has a negative effect on CO₂ dissolution; here, numerical simulation and experimental phenomena are qualitatively consistent. In general, these findings confirm the feasibility of the method and improve the understanding of the physical process of CO₂ convective dissolution, which can help assess the CO₂ solubility trapping mass. Full article

In this study, we visualised CO₂-brine, density-driven convection in a Hele-Shaw cell. Several experiments were conducted to analyse the effects of the salinity and temperature. The salinity and temperature of fluids were selected according to the storage site. By using charge coupled device (CCD) technology, convection finger formation and development were obtained through direct imaging and processing. The process can be divided into three stages: diffusion-dominated, convection-dominated and shutdown stages. Fingers were formed along the boundary at the onset time, reflecting the startup of convection mixing. Fingers formed, moved and aggregated with adjacent fingers during the convection-dominated stage. The relative migration of brine-saturated CO₂ and brine enhanced the mass transfer. The effects of salinity and temperature on finger formation, number, and migration were analysed. Increasing the salinity accelerated finger formation but suppressed finger movement, and the onset time was inversely related to the salinity. However, the effect of temperature on convection is complex. The dissolved CO₂ mass was investigated by calculating the CO₂ mass fraction in brine during convection mixing. The results show that convection mixing greatly enhanced mass transfer. The study has implications for predicting the CO₂ dissolution trapping time and accumulation for the geological storage of CO₂. Full article

Satellite data products and high-resolution in situ observations were combined to investigate the evolution and structure of the Kuroshio Extension Front in Spring 2019. The former reveals the variation of the front is influenced by the northward movement of the Kuroshio Extension through transporting warm and saline water to a cold and brackish water region. The latter indicates steep upward slopes of the isopycnals, tilting northward in the frontal zone, as well as several ~300 m thick blobs of North Pacific Intermediate Water between 26.25 and 26.75 kg/m³, where conspicuous thermohaline intrusions occur. Further analysis indicates these thermohaline intrusions prefer to alternate salt fingering and diffusive convection interfaces, and are affected by strong shears. Full article

Carbon dioxide density-driven dissolution in a water-filled laboratory flume of the dimensions 60 cm length, 40 cm height, 1 cm thickness, was visualized using a pH-sensitive color indicator. We focus on atmospheric pressure conditions, like in caves where CO₂ concentrations are typically higher. Varying concentrations of carbon dioxide were applied as boundary conditions at the top of the experimental setup, leading to the onset of convective fingering at differing times. The data were used to validate a numerical model implemented in the numerical simulator DuMu^x. The model solves the Navier–Stokes equations for density-induced water flow with concentration-dependent fluid density and a transport equation, including advective and diffusive processes for the carbon dioxide dissolved in water. The model was run in 2D, 3D, and pseudo-3D on two different grids. Without any calibration or fitting of parameters, the results of the comparison between experiment and simulation show satisfactory agreement with respect to the onset time of convective fingering, and the number and the dynamics of the fingers. Grid refinement matters, in particular, in the uppermost part where fingers develop. The 2D simulations consistently overestimated the fingering dynamics. This successful validation of the model is the prerequisite for employing it in situations with background flow and for a future study of karstification mechanisms related to CO₂-induced fingering in caves. Full article

The Elder problem is one of the well-known examples of an unstable density-driven flow (DDF) and solute transport in porous media. The goal of this research is to investigate the influence of fracture networks on this benchmark problem due to the great importance of the fractured heterogeneity effect on unstable DDF. For this aim, the fractured Elder problem is solved using COMSOL Multiphysics, which is a finite element method simulator. Uniform and orthogonal fracture networks are embedded to analyze free convective flow and development of unstable salt plumes. The results indicate that the mesh sensitivity of the fractured Elder problem is greater than the homogeneous case. Furthermore, it has been shown that in the fractured cases, the onset of instability and free convection occur with lower critical Rayleigh number, which means that fracture networks have a destabilizing effect. Also, we examined the structural properties of fracture networks that control convective flow patterns, and the simulation results show that the strength of convection and instability at the beginning of the intrusion is proportional to the aperture size of the fractures. Moreover, the increase of the fracture’s density leads different modes of transient convective modes, until a specific fracture density after which the transient convective modes become similar to the homogenous case. Full article

We present a comparative study of the onset and propagation dynamics of the fingering phenomenon in uniform porous media with a radial configuration. With the help of the Finite Element Method (FEM)-based 2D simulations and image processing techniques, we investigate finger morphology, growth rate, interfacial length, finger length and the number of fingers which are affected due to inertial forces and convective acceleration in a two-phase porous media flow. We considered a modified Darcy’s law with inertial force coupled with convective acceleration and investigate their impact on interfacial instability with different velocity-viscosity combinations. Interestingly, the consequences of inertial corrections become significant with changes in viscosity at high Reynolds numbers. Due to the intrinsic bifurcation nature of inertial forces in the radial flow geometry, finger morphology is changed mostly at high viscosity ratios. We find that the effects of inertia and convective acceleration are markedly significant at relatively high Reynolds numbers while the interfacial length and the number of fingers—which are important parameters for Enhanced Oil Recovery (EOR)—are most affected by the neglecting of these forces. Moreover, at high Reynolds numbers, the rate of growth of fingering instabilities and the fractal number tend to deviate from that for Darcy’s law. Full article

When a solute A dissolves into a host fluid containing a reactant B, an A + B → C reaction can influence the convection developing because of unstable density gradients in the gravity field. When A increases density and all three chemical species A, B and C diffuse at the same rate, the reactive case can lead to two different types of density profiles, i.e., a monotonically decreasing one from the interface to the bulk and a non-monotonic profile with a minimum. We study numerically here the nonlinear reactive convective dissolution dynamics in the more general case where the three solutes can diffuse at different rates. We show that differential diffusion can add new dynamic effects like the simultaneous presence of two different convection zones in the host phase when a non-monotonic profile with both a minimum and a maximum develops. Double diffusive instabilities can moreover affect the morphology of the convective fingers. Analysis of the mixing zone, the reaction rate, the total amount of stored A and the dissolution flux further shows that varying the diffusion coefficients of the various species has a quantitative effect on convection. Full article

A simple model of nonlinear salt-finger convection in two dimensions is derived and studied. The model is valid in the limit of a small solute to heat diffusivity ratio and a large density ratio, which is relevant to both oceanographic and astrophysical applications. Two limits distinguished by the magnitude of the Schmidt number are found. For order one Schmidt numbers, appropriate for astrophysical applications, a modified Rayleigh–Bénard system with large-scale damping due to a stabilizing temperature is obtained. For large Schmidt numbers, appropriate for the oceanic setting, the model combines a prognostic equation for the solute field and a diagnostic equation for inertia-free momentum dynamics. Two distinct saturation regimes are identified for the second model: the weakly driven regime is characterized by a large-scale flow associated with a balance between advection and linear instability, while the strongly-driven regime produces multiscale structures, resulting in a balance between energy input through linear instability and energy transfer between scales. For both regimes, we analytically predict and numerically confirm the dependence of the kinetic energy and salinity fluxes on the ratio between solutal and thermal Rayleigh numbers. The spectra and probability density functions are also computed. Full article