Quantification of Density-Driven Natural Convection for Dissolution Mechanism in CO<Subscript>2</Subscript> Sequestration

Dissolution of CO₂ into brine causes the density of the mixture to increase. The density gradient induces natural convection in the liquid phase, which is a favorable process of practical interest for CO₂ storage. Correct estimation of the dissolution rate is important because the time scale for dissolution corresponds to the time scale over which free phase CO₂ has a chance to leak out. However, for this estimation, the challenging simulation on the basis of convection–diffusion equation must be done. In this study, pseudo-diffusion coefficient is introduced which accounts for the rate of mass transferring by both convection and diffusion mechanisms. Experimental tests in fluid continuum and porous media were performed to measure the real rate of dissolution of CO₂ into water during the time. The pseudo diffusion coefficient of CO₂ into water was evaluated by the theory of pressure decay and this coefficient is used as a key parameter to quantify the natural convection and its effect on mass transfer of CO₂. For each experiment, fraction of ultimate dissolution is calculated from measured pressure data and the results are compared with predicted values from analytical solution. Measured CO₂ mass transfer rate from experiments are in reasonable agreement with values calculated from diffusion equation performed on the basis of pseudo-diffusion coefficient. It is suggested that solving diffusion equation with pseudo diffusion coefficient herein could be used as a simple and rapid tool to calculate the rate of mass transfer of CO₂ in CCS projects.     

Effect of Gas Diffusion Layer Properties on Breakthrough Time and Pressure

The gas diffusion layer (GDL) plays an important role in the removal of product water from the catalyst layer to the flow plate in a fuel cell. Numerous studies have reported water management, especially in the GDL, as the limiting factor hindering convective and diffusive transport of reactants which results in lowering power density. In this paper, an experimental technique is presented to study the GDL water transport properties associated with the breakthrough conditions which are critical to overall water management. Fluorescence microscopy technique is used to measure the pressure and time required for water to penetrate and break through the surface of the GDL. The results obtained for GDLs produced by different manufacturers confirm that the breakthrough time and pressure are larger for PTFE treated hydrophobic GDLs. The results are analyzed in terms of the contact angle, thickness, and SEM images to see the effects of different structural properties. The changes in morphology due to compression are also presented. In addition, the changes in breakthrough conditions when samples are reused are presented. The results provide basic insights into the water transport properties of the GDL, leading to the design of new materials with enhanced water management.     

Natural convective diffusion between two nonconcentric spheres

A study is made of the natural convective diffusion in a nonconcentric spherical layer formed by a ball of radius R₁ in a sphere of radius R₂. The centers of the ball and sphere are separated by a distance d R₁. The spherical layer is filled with a binary electrolyte, and the outer surface of the ball and the inner surface of the sphere serve as the anode and cathode, respectively, of an oxidation—reduction reaction. It is assumed that the reaction proceeds in accordance with diffusion kinetics, i.e., the current in the circuit limits the rate at which the reacting substances reach the electrodes [1]. If a current passes in the system, a concentration gradient develops in the reacting substances, and in a gravitational field a convective motion of the fluid is generated, which changes the rate at which the reacting substances arrive at the electrodes. For a binary eletrolyte in the leading approximation in the small parameter r_D(R₂ – r₁)^–1, where r_D is the Debye radius, the migration current can be eliminated, and one need consider only the diffusion and convective fluxes of the ions [2]. If the centers of the ball and the sphere coincide, the integrated diffusion flux at small Grashof numbers is not changed, and there is merely a local redistribution.[3–5]. At small Grashof numbers, a strong dependence of the integrated diffusion flux on the eccentricity of the spherical layer must be expected. In the present paper, the hydrodynamic velocity field of the fluid, and also the change in the integrated diffusion flux due to the convective transport of the ions are found in the linear approximation in the small parameter = d/R₁.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 151–154, January–February, 1984.     

Linear Stability Analysis of Double-Diffusive Convection in Porous Media,with Application to Geological Storage of CO<Subscript>2</Subscript>

Onset of double-diffusive buoyancy-driven flow resulted from vertical temperature and concentration gradients in a horizontal layer of a saturated and homogenous porous medium is investigated using amplification factor theory. After injection of CO₂ into a deep saline aquifer, the density of the brine saturated with CO₂ increases slightly. This increase in density induces natural convection. The effect of geothermal gradient is also considered in this work as a second incentive for convection and the double-diffusion convection was studied. Linear stability analysis is used to predict the inception of instabilities and initial wavelength of the convective instabilities. The analysis presented is applied to acid gas injection (as an analogue for CO₂ storage) into saline aquifers in the Alberta basin. It is found that the geothermal gradient does not have significant effect on the onset of convection for these aquifers. It is shown that the geothermal effects on the onset of natural convection are negligible as compared to the solutal effects induced by dissolution and diffusion of CO₂ in deep saline aquifers. Therefore, the linear stability analysis and the long-term numerical simulation of CO₂ sequestration into such saline aquifers may be assumed to be isothermal in terms of natural convection occurrence.     

Transport properties in mixtures involving carbon dioxide at low and moderate density: test of several intermolecular potential energies and comparison with experiment

It is the purpose of this paper to extract unlike intermolecular potential energies of five carbon dioxide-based binary gas mixtures including CO₂–He, CO₂–Ne, CO₂–Ar, CO₂–Kr, and CO₂–Xe from viscosity data and compare the calculated potentials with other models potential energy reported in literature. Then, dilute transport properties consisting of viscosity, diffusion coefficient, thermal diffusion factor, and thermal conductivity of aforementioned mixtures are calculated from the calculated potential energies and compared with literature data. Rather accurate correlations for the viscosity coefficient of afore-cited mixtures embracing the temperature range 200 K < T < 3273.15 K is reproduced from the present unlike intermolecular potentials energy. Our estimated accuracies for the viscosity are to within ±2%. In addition, the calculated potential energies are used to present smooth correlations for other transport properties. The accuracies of the binary diffusion coefficients are of the order of ±3%. Finally, the unlike interaction energy and the calculated low density viscosity have been employed to calculate high density viscosities using Vesovic–Wakeham method.     

质子交换膜燃料电池扩散层电阻的实验研究

气体扩散层是质子交换膜燃料电池的重要组件,其与极板之间的接触电阻是燃料电池内阻的重要组成部分,也是导致燃料电池功率损失的重要因素。为了得到扩散层与极板间接触电阻以及扩散层本体电阻,首先在扩散层试样表面溅射厚度为50nm的金属铜,再在实验室搭建的燃料电池压力-位移测试平台上用四点法测得试样的总电阻,而后用斜率-截距法分离了气体扩散层本体电阻和其与极板的接触电阻,计算出了相应的电阻率,得到了压力和接触电阻之间的关系。结果表明,接触电阻随着接触面压强的增大而减小,接触电阻率和接触压强关系满足经验公式ρ=43.39P-0.725。     

Comparison of different models for non-equilibrium CO2 flows in a shock layer near a blunt body

The paper presents results of a numerical simulation of a supersonic two-dimensional (2D) viscous flow containing CO₂ molecules near a spacecraft entering the Mars atmosphere. The gas–dynamic equations in the shock layer are coupled to the equations of non-equilibrium vibrational and chemical kinetics in the five-component mixture CO₂/CO/O₂/C/O. Transport and relaxation processes in the flow are studied on the basis of the rigorous kinetic theory methods; the developed transport algorithms are incorporated in the numerical scheme. The influence of the vibrational excitation of CO₂ and chemical reactions on the gas flow parameters and heat transfer is analyzed. The obtained results are compared with those found using two simplified models based on the two-temperature and one-temperature vibrational distributions in CO₂. The accuracy of the simplified models and the limits of their validity within the shock layer are evaluated. The effect of bulk viscosity in a flow near a re-entry body is discussed. The role of different diffusion processes, chemical reactions, and surface catalytic properties in a flow of the considered mixture in the shock layer is estimated.     

Modeling Gas Transport in the Shallow Subsurface During the ZERT CO<Subscript>2</Subscript> Release Test

We used the multiphase and multicomponent TOUGH2/EOS7CA model to carry out predictive simulations of CO₂ injection into the shallow subsurface of an agricultural field in Bozeman, Montana. The purpose of the simulations was to inform the choice of CO₂ injection rate and design of monitoring and detection activities for a CO₂ release experiment. The release experiment configuration consists of a long horizontal well (70 m) installed at a depth of approximately 2.5 m into which CO₂ is injected to mimic leakage from a geologic carbon sequestration site through a linear feature such as a fault. We estimated the permeability of the soil and cobble layers present at the site by manual inversion of measurements of soil CO₂ flux from a vertical-well CO₂ release. Based on these estimated permeability values, predictive simulations for the horizontal well showed that CO₂ injection just below the water table creates an effective gas-flow pathway through the saturated zone up to the unsaturated zone. Once in the unsaturated zone, CO₂ spreads out laterally within the cobble layer, where liquid saturation is relatively low. CO₂ also migrates upward into the soil layer through the capillary barrier and seeps out at the ground surface. The simulations predicted a breakthrough time of approximately two days for the 100kg d⁻¹ injection rate, which also produced a flux within the range desired for testing detection and monitoring approaches. The seepage area produced by the model was approximately five meters wide above the horizontal well, compatible with the detection and monitoring methods tested. For a given flow rate, gas-phase diffusion of CO₂ tends to dominate over advection near the ground surface, where the CO₂ concentration gradient is large, while advection dominates deeper in the system.     

Effects of CO<Subscript>2</Subscript> Compressibility on CO<Subscript>2</Subscript> Storage in Deep Saline Aquifers

The injection of supercritical CO₂ in deep saline aquifers leads to the formation of a CO₂ plume that tends to float above the formation brine. As pressure builds up, CO₂ properties, i.e. density and viscosity, can vary significantly. Current analytical solutions do not account for CO₂ compressibility. In this article, we investigate numerically and analytically the effect of this variability on the position of the interface between the CO₂-rich phase and the formation brine. We introduce a correction to account for CO₂ compressibility (density variations) and viscosity variations in current analytical solutions. We find that the error in the interface position caused by neglecting CO₂ compressibility is relatively small when viscous forces dominate. However, it can become significant when gravity forces dominate, which is likely to occur at late times of injection.     

Laboratory Flow Experiments for Visualizing Carbon Dioxide-Induced,Density-Driven Brine Convection

Injection of carbon dioxide (CO₂) into saline aquifers confined by low- permeability cap rock will result in a layer of CO₂ overlying the brine. Dissolution of CO₂ into the brine increases the brine density, resulting in an unstable situation in which more-dense brine overlies less-dense brine. This gravitational instability could give rise to density-driven convection of the fluid, which is a favorable process of practical interest for CO₂ storage security because it accelerates the transfer of buoyant CO₂ into the aqueous phase, where it is no longer subject to an upward buoyant drive. Laboratory flow visualization tests in transparent Hele-Shaw cells have been performed to elucidate the processes and rates of this CO₂ solute-driven convection (CSC). Upon introduction of CO₂ into the system, a layer of CO₂-laden brine forms at the CO₂-water interface. Subsequently, small convective fingers form, which coalesce, broaden, and penetrate into the test cell. Images and time-series data of finger lengths and wavelengths are presented. Observed CO₂ uptake of the convection system indicates that the CO₂ dissolution rate is approximately constant for each test and is far greater than expected for a diffusion-only scenario. Numerical simulations of our system show good agreement with the experiments for onset time of convection and advancement of convective fingers. There are differences as well, the most prominent being the absence of cell-scale convection in the numerical simulations. This cell-scale convection observed in the experiments may be an artifact of a small temperature gradient induced by the cell illumination.     

Coupled pore network model for the cathode gas diffusion layer in PEM fuel cells

Acta Mechanica Sinica - A pore network model (PNM) is developed for gas diffusion layer (GDL) in the cathode side of polymer electrolyte membrane fuel cells (PEMFCs). The model is coupled to...     

Determination of heat fluxes in the neighborhood of a double curvature stagnation point in a flow of dissociating gas of arbitrary chemical composition

Numerical solutions are obtained for the equations of a uniform compressible boundary layer with variable physical properties in the vicinity of a stagnation point with different principal curvatures in the presence of an injected gas with the same properties as the incident flow. The results of the numerical solutions are approximated for the heat flux in the form of a relation that depends on the variation of the product of viscosity and density across the boundary layer and on the ratio of the principal radii of curvature.Using the concepts of effective diffusion coefficients in a multicomponent boundary layer, previously introduced by the author in [1], and the generalized analogy between heat and mass transfer in the presence of injection, together with the numerical solutions obtained, it is always possible, even without additional solutions of the boundary-layer equations, to derive final formulas for the heat fluxes in a flow of dissociating gas of arbitrary chemical composition, provided that we make the fundamental assumption that all recombination reactions take place at the surface.By way of example, formulas are given for the heat transfer to the surface of a body from dissociating air, regarded as a five-component mixture of the gases O, N, NO, O₂, N₂, and from a dissociating mixture of carbon dioxide and molecular nitrogen of arbitrary composition, regarded as an eleven-component mixture of the gases O, N, C, NO, C₂, O₂, N₂, CO, CN, C₃, CO₂.In the process of obtaining and analyzing these solutions it was found that, in computing the heat flux, a multicomponent mixture can be replaced with an effective binary mixture with a single diffusion coefficient only when the former can be divided into two groups of components with different (but similar) diffusion properties. In this case the concentrations of one group at the surface must be zero, while the diffusion flows of the second group at the surface are expressible, using the laws of mass conservation of the chemical elements, in terms of the diffusion flows of the first. Then the single effective diffusion coefficient is the binary diffusion coefficient D(A,M), where A relates to one group of components and M to the other.In view of the small amount of NO(c(NO) < 0.05), the diffusion transport of energy in dissociated air maybe described with the aid of a single binary diffusion coefficient D(A, M)(A=O, N, M=O₂, N₂, NO). However even in the case of complete dissociation into O and C atoms at the outer edge of the boundary layer, the diffusion transport of energy in dissociated carbon dioxide can not be described accurately enough by means of a model of a binary mixture with a single diffusion coefficient, since the diffusion properties of the O and C atoms are distinctly different.     

Concentration-dependent diffusion in a composite slab with and without chemical reactions

Concentration-dependent diffusion of solute in a composite slab is investigated. The complex diffusion problem can be described by a set of nonlinear diffusion equations which is coupled to each other through the nonlinear interfacial boundary conditions. A two-layer diffusion is illustrated and the coupled nonlinear diffusion equations are conveniently solved by the orthogonal collocation method. Numerical simulation of the example reveals many interesting diffusion characteristics which are quite different from those in a single slab diffusion system.Nomenclature a _j expansion coefficient - A _i,j element of collocation matrix - B _i,j element of collocation matrix - C _a , C _b surface concentration - C _i concentration in the ith layer - D _i diffusion coefficient in the ith layer - D _i0 diffusion coefficient at very low concentration - k _i reaction rate in the ith layer - K _i dimensionless reaction rate, k _i l _i ² c _a ^m–1 /D ₁₀ - l _i thickness of the ith layer - m order of chemical reaction - n order of the orthogonal polynomial approximation - P _j–1(x _i ) orthogonal polynomial of order j - t time - x _i coordinate of the ith layer - X _i dimensionless coordinate of the ith layer, x _i/l _i - ratio of diffusion coefficient at low concentration, D ₂₀/D ₁₀ - ratio of thicknesses of layer, l ₁/l ₂ - _i dimensionless parameter in the concentration-dependent function of the ith layer - ratio of surface concentration, C _b /C _a - dimensionless time, tD ₁₀/l ₁ ² - _i dimensionless concentration in the ith layer, C _i /C _a      

Experiments on the instability modes of buoyant diffusion flames and effects of ambient atmosphere on the instabilities

Large scale dynamic behavior of buoyant diffusion flames were studied experimentally. It was found that buoyant diffusion flames originating from circular nozzles exhibit two different modes of flame instabilities. The first mode results in a sinuous meandering of the diffusion flame, characteristic of flames originating from small diameter nozzles. This instability originates at some distance downstream of the nozzle exit in the contraction region of the buoyant flame envelope and develops into a sinuous motion of the flame. The second mode is the varicose mode which develops very close to the nozzle exit as axisymmetric perturbations of a contracting flame surface. In this mode, flame oscillations result in the formation of toroidal vortical structures that convect through the flame and cause periodic burn out at the flame top resulting in the observed flame height fluctuations. The average flame heights are found to be typically shorter for these flames. The oscillation frequencies and their scaling for the two modes are also different with the sinuous mode having higher frequencies than the varicose mode. It was also observed that the instability can switch from one mode to the other and the probability of observing the varicose mode appears to increase with increasing Richardson number. Additionally, the feasibility of altering the behavior of buoyant diffusion flames was explored through variation of the oxidizer medium density. It was found that the flame oscillations can be completely suppressed for flames burning in helium rich helium–oxygen mixtures. At lower helium concentrations, the oscillation frequency can be significantly reduced. In order to enhance the buoyancy effect, CO₂–O₂ mixtures were also studied. However, the density increase and its effects on flame oscillation frequency were found to be small compared to those flames burning in air. These experiments point towards the feasibility of altering buoyant flame behavior under earth gravity and studying the large scale dynamical aspects of buoyant flames without the need of variable gravity environment. Received: 2 March 1999/Accepted: 6 August 1999     

Competitive Methane Desorption by Supercritical CO2 Injection in Coal

A large diameter (∼70 mm) dry coal sample was used to study the competitive displacement of CH₄ by injection of supercritical CO₂, and CO₂–CH₄ counter-diffusion in coal matrix. During the test, a staged loading procedure, which allows the calibration of the key reservoir modelling parameters in a sequential and progressive manner, was employed. The core-flooding test was history matched using an Enhanced Coalbed Methane (ECBM) simulator, in which Fick’s Law for mixed gas diffusion and the extended Langmuir equations are implemented. The system pressure rise during the two loading stages and the CO₂ breakthrough time in the final production stage were matched by using the pair of constant sorption times (9 and 3.2 days) for CH₄ and CO₂, respectively. The corresponding diffusion coefficients for CH₄ and CO₂ were estimated to be 1.6 ×  10⁻¹² and 4.6 ×  10⁻¹² m²/s, respectively. Comparison was made with published gas diffusion coefficients for dry ground samples (ranging from < 0.063 to ∼3 mm) of the same coal at relatively low pressures (< 4 MPa). The CO₂/CH₄ gas diffusion coefficient ratio was well within the reported range (2–3), whereas the CH₄ diffusion coefficient obtained from history matching of the core-flooding test is approximately 15 times smaller than that arrived by curve-fitting the measured sorption uptake rate using a unipore diffusion model. The calibrated model prediction of the effluent gas composition was in good agreement with the test data for CO₂ mole fraction of up to 20%.     

Thermal diffusion of dilute polymer solutions

In this paper diffusion of a dilute solution of elastic dumbbell model macromolecules under non-isothermal conditions is studied. Using the center of mass definition for the local polymer concentration, the diffusive flux contains a thermal diffusion dyadic d _T .  To get some idea of thermal diffusion d _T is evaluated for steady state isothermal conditions. Explicit results are presented for some homogeneous flows. It is shown that if the polymeric number density is defined via the beads (of the dumbbell) – termed n _b – then the diffusive flux j contains , where τ ^c is the intramolecular contribution to the bulk stress. Though the form of the diffusion equation for n _b thus differs from the corresponding one for n, it is shown that for essentially unbounded systems differences between n and n _b are small. Since the results involve the translational diffusion coefficient they can readily be taken over for Rouse coils. Received: 23 September 1997 Accepted: 5 June 1998     

The effect of material properties on the performance of a new geometry PEM fuel cell

In this paper a computational dynamics model for duct-shaped geometry proton exchange membrane (PEM) fuel cell was used to investigate the effect of changing gas diffusion layer and membrane properties on the performances, current density and gas concentration. The proposed model is a full cell model, which includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Coupled transport and electrochemical kinetics equations are solved in a single domain; therefore no interfacial boundary condition is required at the internal boundaries between cell components. This computational fluid dynamics code is used as the direct problem solver, which is used to simulate the 2-dimensional mass, momentum and species transport phenomena as well as the electron- and proton-transfer process taking place in a PEMFC that cannot be investigated experimentally. The results show that by increasing the thickness and decreasing the porosity of GDL the performance of the cell enhances that it is different with planner PEM fuel cell. Also the results show that by increasing the thermal conductivity of the GDL and membrane, the overall cell performance increases.     

Parameters analysis of fluid diffusion

The influences of fluid density, diffusivity, viscosity, width of the flow channel, travel distance, and flow velocity on fluid diffusion are analyzed theoretically and numerically. Concentration boundary layer is taken as the quantitative index of fluid diffusion in this work. The results show that diffusion is a function of travel distance, diffusivity, fluid density, and flow velocity. Diffusion is independent of the width of the channel. Viscous effect determines the velocity gradient and does not affect diffusion directly. The usually used Péclet number uL/D cannot govern the full condition of fluid diffusion. For two-fluids co-flowing in a two-dimensional straight channel with relative low viscous effect, diffusion is proportional to the square root of travel distance and diffusivity, and is inversely proportional to the square root of flow velocity.     

Optimization and limiting characteristics of CO2 lasers

It is shown that the limiting characteristics of CO₂ lasers are determined mainly by two parameters: the specific power of the electric discharge, referred to the square of the active medium pressure, and the product of the pumping time and the gas pressure. An investigation is made of the dependence of the efficiency and the radiation pulse shape over a wide range of the parameters. For the first time it is noted that the energy from the lower laser level can be given to the upper vibrational states of the symmetric and deformed modes, which allows high radiation density, ～0.2 J/cm³ · atm, to be achieved, as is shown by calculation. Because of energy redistribution in the asymmetric mode the limiting gain coefficient in C₀₂ lasers is ～0.12 cm^?1.