Numerical Simulation of Natural Convection in an Inclined Square Cavity (original) (raw)
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Energy Procedia, 2013
Storage capacity of carbon dioxide (CO 2) in deep saline aquifers is a challenging task. However, an assessment must be performed to determine whether there is sufficient capacity in a storage site for any CO 2 sequestration project. We evaluated the CO 2 storage capacity for a simplified reservoir system, which the layered potential storage formations are overlaid by sealing cap rock. In this paper, we aim to investigate numerically the storage of CO 2 at supercritical conditions in deep saline aquifer reservoirs. Numerical simulations were carried out on non-deformable saturated porous material inside a vertical enclosure, assumed to be impermeable and isolated on three sides. The porous medium is considered to be homogeneous and isotropic with constant thermo-physical properties with the exception of the density of the fluid varying according to Boussinesq approximations. A dynamic model assuming that flow is two-dimensional and obeying to Darcy's law for motion has been used. We assume also that the thermal equilibrium assumption is valid. The set of the conservation equations along with the appropriate initial and boundary conditions have been resolved numerically by the classical finite volume method [1]. Spatio-temporal variations of different state variables such as pressure, velocity, temperature and concentration were numerically simulated and plotted versus different controlling parameters particularly, thermal and solutal Rayleigh numbers and Lewis number. Great attention was paid to examine the sensitivity of heat and mass transfer rates according to the reservoir form and the operating conditions.
Numerical Simulation of Natural Convection in a Mold
Defect and Diffusion Forum, 2010
In this paper we investigate the mass transfer of CO 2 injected into a homogenous (sub)-surface porous formation saturated with a liquid. In almost all cases of practical interest CO 2 is present on top of the liquid. Therefore, we perform our analysis to a porous medium that is impermeable from sides and that is exposed to CO 2 at the top. For this configuration density-driven natural convection enhances the mass transfer rate of CO 2 into the initially stagnant liquid. The analysis is done numerically using mass and momentum conservation laws and diffusion of CO 2 into the liquid. The effects of aspect ratio and the Rayleigh number, which is dependent on the characteristics of the porous medium and fluid properties, are studied. This configuration leads to an unstable flow process. Numerical computations do not show natural convection effects for homogeneous initial conditions. Therefore a sinusoidal perturbation is added for the initial top boundary condition. It is found that the mass transfer increases and concentration front moves faster with increasing Rayleigh number. The results of this paper have implications in enhanced oil recovery and CO 2 sequestration in aquifers.
AJAST, 2019
Using linear stability theory, the effects of temperature gradient and first-order chemical reaction on the onset of Rayleigh-Benard convection in CO2 sequestration in the isotropic porous medium within Eastern Niger-Delta region, Nigeria is theoretically investigated. A simplified model is envisaged for the interactive relationship between carbon dioxide and ambient brine in deep underground aquifers; the instability which is a favorable process for CO2 sequestration considering the fact that it accelerates dissolution and mixing of CO2 hence, reducing the time needed to safely store CO2 in the aquifer. Analytical expressions for the critical Rayleigh number and their corresponding wave numbers for the onset of stationary convections are determined using linear stability analysis. The time scale for the onset of convection as indicated by diverse linear stability analyses of the short-term base state may be long (for years) but virtually will without a doubt, be notably shortened by mixing during injection of supercritical CO2. The key purpose of this paper is to explore the role porous media isotropy plays in the onset of convective instability of sequestered CO2 in the underground aquifer. It is shown that for changes in permeability in the isotropic porous medium, the onset of instability in the stationary convection mode is experienced faster in areas of higher permeability than in areas of lower permeability regions were the onset of instability in the stationary convection mode experiences a delay, making areas with low permeability in the isotropic medium not suitable for convective instability of sequestered CO2 probably because the rocks lack fractures and high level of compaction is present. It is also observed that the ratio of thermal diffusivity to mass diffusivity (the Lewis Number), lower values of the Damköhler number and the presence of the Solute Rayleigh number, delays the onset of instability of sequestered CO2 in the system in the isotropic porous medium. However, interestingly, at a high solute reaction rate to diffusion rate (increasing Damköhler number from to ), a change in permeability of the porous medium does have a pronounced effect on instability in the isotropic porous medium were the onset of instability is delayed in low permeability region but on the contrary is enhanced/facilitated in higher permeability region.
Numerical Study of Natural Convective Heat and Mass Transfer in an Inclined Porous Media
Engineering, Technology & Applied Science Research, 2018
In this study, two dimensional natural convection heat and mass transfer generated in an inclined rectangular porous cavity filled with Newtonian fluid has been investigated numerically. The cavity is heated and cooled along horizontal walls while the solutal gradient is imposed horizontally. The physical model for the momentum conservation equation makes use of the Darcy model, and the set of coupled equations is solved using a finite volume approach. The successive-under-relaxation (SUR) method is used in the solution of the stream function equation. The results are presented graphically in terms of streamlines, isotherms and iso-concentrations. The heat and mass transfer rate in the cavity is measured in terms of the average Nusselt and Sherwood numbers for various non-dimensional parameters.
2021
Absorption and mass transfer mechanism of CO2 in a uniformly distributed porous media was analyzed using simulation as well as experimental results. The study was performed in a closed PVT cell containing pressurized CO2 gas above a water saturated porous media. Pressure decay curves obtained from the simulation and the experiments were used to calculate early and late time diffusivity in accordance with analytical model. Mixing regime was visualized over time to comprehend the contribution of natural convection in mass transfer process. Early time diffusion coefficients were two orders of magnitude higher than late time diffusion coefficients in both simulation and experimental results. Density-driven natural convection had a significant impact at early stages giving rise to enhanced mass transfer and hence the disparity in diffusivity. The diffusivity at late stages were close to literature value. Pressure decay observed from large duration simulation results showed that equilibri...
International Communications in Heat and Mass Transfer, 2012
Two-dimensional double-diffusive natural convective heat and mass transfer in an inclined rectangular porous medium has been investigated numerically. Two opposing walls of the cavity are maintained at fixed but different temperatures and concentrations; while the other two walls are adiabatic. The generalized model with the Boussinesq approximation is used to solve the governing equations. The flow is driven by a combined buoyancy effect due to both temperature and concentration variations. A finite volume approach has been used to solve the non-dimensional governing equations and the pressure velocity coupling is treated via the SIMPLER algorithm. The results are presented in streamline, isothermal, iso-concentration, Nusselt and Sherwood contours for different values of the non-dimensional governing parameters. A wide range of non-dimensional parameters have been used including, aspect ratio (2 ≤ A ≤ 5), angle of inclination of the cavity (0 ≤ ϕ ≤ 85), Lewis number (0.1 ≤ Le ≤ 10), and the buoyancy ratio (− 5 ≤ N ≤ 5).
Mechanics & Industry, 2016
The present work refers to the study of natural convection into a confined porous medium, driven by cooperating thermal and solutal buoyancy forces. The side walls are maintained at a uniform temperature and concentration, lower than that of a heat and solute source, which located at the center of the bottom wall, the rest of the horizontal walls are kept insulated. The physical model for the momentum conservation equation makes use of the Brinkman extension of the classical Darcy equation, the set of coupled equations is solved using the finite volume method and the SIMPLER algorithm. To account for the effects of the main parameters such the buoyancy ratio, the Lewis and porous thermal Rayleigh numbers, as well as the source length, heat and mass transfer characteristics are widely inspected and then, new powerful correlations are proposed, which predict within ±1% the numerical results. Note that the validity of the used code was ascertained by comparing our results with experimental data and numerical ones already available in the literature.
A solid understanding of the transport mechanisms of gaseous CO 2 near the land surface is necessary for developing reliable monitoring techniques and predictive models for possible CO 2 leakage from deep underground storage. The objective of this work has been to develop an experimental method along with a simulation model for gaseous CO 2 flow and transport in a system including both the porous media and the free air space above it. The experimental system consisted of a two-dimensional bench scale rectangular sandbox containing homogenous sand with an open space of still air above it. Gaseous CO 2 was injected in different modes and the CO 2 breakthrough was measured on specified ports in the system by using CO 2 concentration sensors. A numerical model combining the gas flow in the porous medium and the free flow region was developed and used to model the experimental data. In this quest, the Discontinuous One-Domain approach was selected for modeling transport between the free flow and porous regions. The observed and simulated CO 2 breakthrough curves both in the dried sand and in the free flow matched very well in the case of uniform injection and satisfactorily even in the case of point injection. Consequently, it seems that the model reasonably matches the observed data in the cases where the boundary condition is well defined. In summary, our results show that the developed experimental setup provides capability to study gaseous CO 2 flow and transport in a coupled porous medium – free flow system and that our modeling approach is able to predict the flow and transport in this system with good accuracy.