Thermogravitational Column Research Articles

Separation of a binary fluid mixture in a porous horizontal cavity

Thermogravitational separation has, until now, been used in differentially heated vertical cells, called thermogravitational columns (TGCs). The cell can be either a slit or an annular cavity whose two isothermal faces are maintained at different temperatures T1 and T2. In this study, we show contrary to what has been done until now, that it is possible to carry out the separation of the species of a binary mixture in the classical configuration of Rayleigh-Bénard (horizontal cell heated from below with the separation ratio psi>psi(mono)>0 or from above with psi<0); we obtain a monocellular flow for psi>psi(mono) at the onset of convection. The species separation, in a horizontal cell, is obtained without fear of the remixing observed in vertical thermogravitational cells for fluids with negative Soret coefficients. In this situation, the heaviest component concentrates in the upper part of the cell creating an unstable physical situation. We improve the efficiency of separation for the development of an industrial process of separation. We study the thermogravitational separation of the components of a binary fluid mixture saturating a horizontal porous layer, in the presence of the Soret effect. The horizontal walls of the cavity are impermeable and maintained at constant and different temperatures. The system of equations governing the problem has an equilibrium solution with a vertical stratification of temperature and concentration. This solution loses its stability via a stationary bifurcation for values of the separation ratio psi>psi(0) while, for psi<psi(0), stability is lost via a Hopf bifurcation. For a cavity heated from below, the flow resulting from the stationary bifurcation becomes monocellular beyond a certain value of psi>psi(mono)>0 and leads to a separation of the species between the two ends of the cell. We propose to determine whether the monocellular flow remains stable until the optimum of separation and if we can obtain high separation in the case of a horizontal cavity. We verify that the critical Rayleigh number Ra(c2), associated with the transition between monocellular flow and multicellular flow, is higher than the optimum Rayleigh number leading to maximum separation of species. Thus this study reveals that it is possible to obtain optimal separation before the monocellular flow loses its stability. We show also that the separation inside the horizontal cell in a Rayleigh-Bénard configuration permits us to produce the same degree of separation but with a greater quantity of each species compared to a thermogravitational vertical column.

Transient separation of multicomponent liquid mixtures in thermogravitational columns

Transient separation of the individual components in a multicomponent liquid mixture in a thermogravitational column can be used to determine the thermal and molecular diffusion coefficients. Two models of the transient behavior are developed. First, a classical model where density only depends on temperature. Second, a general model where the compositional effect on density is also taken into account. Diffusion coefficients can be determined by fitting experimental data to either model. The procedure is demonstrated for a ternary liquid mixture. The results reveal that the classical model is very unreliable even though composition variation only contributes to the total buoyancy by one-third. Diffusion coefficients can be obtained reliably from the general model provided the experimental noise does not exceed +/-1% of steady-state separation. This level of accuracy in composition measurements is achievable.

Soret Coefficients in Some Water−Methanol, Water−Ethanol, and Water−Isopropanol Systems

In this article, we re-examine the published experimental values of the Soret coefficients of a few water-alcohol systems at a mean temperature of 37.5 degrees C, because we feel that these published values (including microgravity values) are doubtful. The main technique applied is the use of thermogravitational columns to determine the thermodiffusion coefficient. The obtained values did not agree with the published values; worse, sometimes the sign was different.

Boussinesq approximations, and beyond, in a tall thermo-gravitational column

This article focuses on the main aspects of the non-Boussinesq treatment that is required for analyzing the simplest flow regimes occurring in a tall thermo-gravitational column, when the Soret coefficient S T is considered as depending upon temperature and composition, S T ( T , C ) . As a main result, the horizontal dynamics is mainly governed by the Soret thermal sensitivity, and the species vertical separation by its compositional one. To cite this article: G. Labrosse, C. R. Mecanique 335 (2007).

The Rayleigh–Benard problem in extremely confined geometries with and without the Soret effect

We examine the linear stability of a liquid layer heated from below (the classical Rayleigh–Benard problem) but laterally confined between four vertical rigid and adiabatic boundaries. The main feature of the present study is that the height of the layer is much greater than the two other horizontal dimensions. The Soret effect is also taken into account. The ultimate objective of the study is a better knowledge of the operation of thermogravitational columns, and the search for a possible new way to measure positive Soret coefficients based on the variation of the critical Rayleigh number. To cite this article: J.K. Platten et al., C. R. Mecanique 335 (2007).

On thermal diffusion and convection in multicomponent mixtures with application to the thermogravitational column

The theoretical framework for describing the multicomponent mixtures with the Soret effect is revised and extended. The separation ratio, a fundamental parameter characterizing the influence of thermal diffusion on convective phenomena, is generalized to the multicomponent case. It is shown how to define this parameter for a particular component of the mixture. To characterize multicomponent system as a whole, the net separation ratio Ψ, which does not depend on the choice of solvent, is introduced. Based on these results, the dimensionless equations for convection in multicomponent mixture are derived. The proposed formulation is applied to analyzing the steady state separation in the thermogravitational column (TGC). The approximation neglecting vertical diffusion in the column is employed and conditions for its validity are analyzed. The distributions of velocity, temperature, and composition in a multicomponent system are found. The relevant parameters here are the solutal Rayleigh numbers, which characterize the vertical separation of species, and the net solutal Rayleigh number R, which quantifies the overall effect of this separation on the system behavior. It is shown that the key relation of TGC theory, which relates the vertical compositional gradients to the thermal diffusion coefficients, reduces to the dependence of Ψ on R. A detailed study of this dependence is performed. The evolution of vertical velocity and density profiles with changing the net separation ratio is investigated. It is shown that the solution is unique for Ψ≳−1, nonunique for −5≲Ψ≲−1, and does not exist for Ψ≲−5. A particular ternary mixture is considered and its behavior in the column is analyzed.

Study of Transversal Dimension Influence on Species Separation in Thermogravitational Diffusion Columns

Many studies have been made on species separation in thermogravitational columns. All the analytical modelling resolutions developed so far for parallelepipedic columns take only into account the thickness e and the height h of the cavity when the experimental work concerns obviously three-dimensional cavities. We propose a study of the fluid behaviour and the resulting species separation taking into account the width b . The system of three-dimensional modelling equations is integrated using the usual geometric conditions of thermal diffusion columns ( h ≫ e ). The width influence on velocity profiles is validated by comparison with experimental measurements made with the PIV (particle image velocimetry) technique. The analytical solution proposed gives temperature and velocity profiles and the whole concentration distribution within the cavity. It appears that the use of small width cavities generates higher species separation than those predicted with classical two-dimensional approaches. A simple correlation between this deviation and the transversal aspect ratio e/b is proposed.

Convective Instabilities in Thermogravitational Columns

Convective Instabilities in Thermogravitational Columns

Thermodiffusion Coefficient for Binary Liquid Hydrocarbon Mixtures

In this work, the thermogravitational technique has been used to determine the thermodiffusion coefficient of 18 binary mixtures of normal alkanes formed with the n-octadecane as the densest component and mixed with normal alkanes from n-pentane to n-tridecane in two series of experimental tests (nine binary mixtures with mass fraction c = 0.5 and nine binary mixtures with molar fraction x = 0.5 in each component for each mixture). The measurement of the steady separation of these mixtures in the thermogravitational column, as well as their corresponding thermophysical properties, has been determined at the average temperature of 25°C.

Molecular and Thermal Diffusion Coefficients of Alkane−Alkane and Alkane−Aromatic Binary Mixtures: Effect of Shape and Size of Molecules

New molecular and thermal diffusion coefficients of binary mixtures of normal decane-normal alkanes and methylnaphthalene-normal alkanes are measured at atmospheric pressure and T = 25 degrees C. The normal alkanes used in this work include nC5-nC20. Thermal diffusion coefficients were measured in a thermogravitational column. Molecular diffusion coefficients were measured using an open-ended capillary tube technique. Results show a significant effect of molecular shape and size on thermal and molecular diffusion coefficients. Molecular diffusion coefficients show a monotonic behavior in both aromatic-normal alkane and normal decane-normal alkane mixtures. Thermal diffusion coefficients reveal a nonmonotonic trend with molecular size in the normal decane-normal alkane mixtures. This is the first report of the nonmonotonic behavior in the literature. The data presented in this paper provide an accurate self-molecular diffusion coefficient for nC10 from binary data.

Two-Phase Multicomponent Diffusion and Convection for Reservoir Initialization

Summary We present formulation and numerical solution of two-phase multicomponent diffusion and natural convection in porous media. Thermal diffusion, pressure diffusion, and molecular diffusion are included in the diffusion expression from thermodynamics of irreversible processes. The formulation and the numerical solution are used to perform initialization in a 2D cross section. We use both homogeneous and layered media without and with anisotropy in our calculations. Numerical examples for a binary mixture of C1/C3 and a multicomponent reservoir fluid are presented. Results show a strong effect of natural convection in species distribution. Results also show that there are at least two main rotating cells at steady state: one in the gas cap, and one in the oil column. Introduction Proper initialization is an important aspect of reliable reservoir simulations. The use of the Gibbs segregation condition generally cannot provide reliable initialization in hydrocarbon reservoirs. This is caused, in part, by the effect of thermal diffusion (caused by the geothermal temperature gradient), which cannot be neglected in some cases; thermal diffusion might be the main phenomenon affecting compositional variation in hydrocarbon reservoirs, especially for near-critical gas/condensate reservoirs (Ghorayeb et al. 2003). Generally, temperature increases with increasing burial depth because heat flows from the Earth's interior toward the surface. The temperature profile, or geothermal gradient, is related to the thermal conductivity of a body of rock and the heat flux. Thermal conductivity is not necessarily uniform because it depends on the mineralogical composition of the rock, the porosity, and the presence of water or gas. Therefore, differences in thermal conductivity between adjacent lithologies can result in a horizontal temperature gradient. Horizontal temperature gradients in some offshore fields can be observed because of a constant water temperature (approximately 4°C) in different depths in the seabed floor. The horizontal temperature gradient causes natural convection that might have a significant effect on species distribution (Firoozabadi 1999). The combined effects of diffusion (pressure, thermal, and molecular) and natural convection on compositional variation in multicomponent mixtures in porous media have been investigated for single-phase systems (Riley and Firoozabadi 1998; Ghorayeb and Firoozabadi 2000a).The results from these references show the importance of natural convection, which, in some cases, overrides diffusion and results in a uniform composition. Natural convection also can result in increased horizontal compositional variation, an effect similar to that in a thermogravitational column (Ghorayeb and Firoozabadi 2001; Nasrabadi et al. 2006). The combined effect of convection and diffusion on species separation has been the subject of many experimental studies. Separation in a thermogravitational column with both effects has been measured widely (Schott 1973; Costeseque 1982; El Mataaoui 1986). The thermogravitational column consists of two isothermal vertical plates with different temperatures separated by a narrow space. The space can be either without a porous medium or filled with a porous medium. The thermal diffusion, in a binary mixture, causes one component to segregate to the hot plate and the other to the cold plate. Because of the density gradient caused by temperature and concentration gradients, convection flow occurs and creates a concentration difference between the top and bottom of the column. Analytical and numerical models have been presented to analyze the experimental results (Lorenz and Emery 1959; Jamet et al. 1992; Nasrabadi et al. 2006). The experimental and theoretical studies show that the composition difference between the top and bottom of the column increases with permeability until an optimum permeability is reached. Then, the composition difference declines as permeability increases. The process in a thermogravitational column shows the significance of the convection from a horizontal temperature gradient.

An analysis of species separation in a thermogravitational column filled with a porous medium

In the past, the analysis of species separation in a thermogravitational column filled with porous media has been based on strong dependency of thermal and molecular diffusion to dispersion. In this work, we suggest an alternative and show that the dispersion effect is negligible for the conditions in a packed hermogravitational column and that compositional dependency of the thermal diffusion should be accounted for.

On the unsteady-state species separation of a binary liquid mixture in a rectangular thermogravitational column

This paper investigates the unsteady-state species segregation of binary liquid mixtures in rectangular thermogravitational columns. The analysis leads to a procedure to obtain both molecular and thermal diffusion coefficients from transient separation measurements. Two models are presented: first, an ideal model where buoyancy only depends on temperature and second, a general model where buoyancy also varies with composition. Steady-state measurements are not required regardless of which model is chosen. As a result, the new procedure is faster than steady-state procedures. When either the molecular or thermal diffusion coefficient is known a priori, the other can be obtained without knowledge of fluid properties such as density, viscosity, thermal expansion, and compositional coefficients.

Measurements of molecular and thermal diffusion coefficients in ternary mixtures

Thermal diffusion coefficients in three ternary mixtures are measured in a thermogravitational column. One of the mixtures consists of one normal alkane and two aromatics (dodecane-isobutylbenzene-tetrahydronaphthalene), and the other two consist of two normal alkanes and one aromatic (octane-decane-1-methylnaphthalene). This is the first report of measured thermal diffusion coefficients (for all species) of a ternary nonelectrolyte mixture in literature. The results in ternary mixtures of octane-decane-1-methylnaphthalene show a sign change of the thermal diffusion coefficient for decane as the composition changes, despite the fact that the two normal alkanes are similar. In addition to thermal diffusion coefficients, molecular diffusion coefficients are also measured for three binaries and one of the ternary mixtures. The open-end capillary-tube method was used in the measurement of molecular diffusion coefficients. The molecular and thermal diffusion coefficients allow the estimation of thermal diffusion factors in binary and ternary mixtures. However, in the ternaries one also has to calculate phenomenological coefficients from the molecular diffusion coefficients. A comparison of the binary and ternary thermal diffusion factors for the mixtures comprised of octane-decane-1-methylnaphthalene reveals a remarkable difference in the thermal diffusion behavior in binary and ternary mixtures.

Metrology of the thermodiffusion coefficients in a ternary system

In a ternary mixture of dodecane, isobutylbenzene, and 1,2,3,4-tetrahydronaphtalene, we succeeded in measuring the two thermodiusion factors using the thermogravitational column technique, and applying the Furry–Jones–Onsager theory. We suggest correlating the thermodiusion factors in the ternary system with those in the three binaries.

Theoretical analysis and comparison with experimentation of the molecular and thermal diffusion coefficients for a ternary hydrocarbon mixture

The thermal diusion phenomena, also known as the Soret eect, is important for the study of compositional variation in hydrocarbon reservoirs. Several theoretical models have been developed over the years to predict the thermodiusion coefficient of an organic mixture. Firoozabadi et al. [1] developed an analytical relationship between the thermal, molecular, and pressure diusion coefficients based on the approach of Dougherty and Drickamer [2]. The distinctive feature of Firoozabadi's model is its ability to be used not only for binary mixtures but also for multicomponent mixtures. The verification of Firoozabadi's model by numerical simulations was limited to binary mixtures only because of a lack of experimental data on thermodiusion coefficients in multicomponent hydrocarbon mixtures. However, Platten et al. [3] were able to measure the thermodiusion coefficients of a ternary hydrocarbon mixture experimentally by utilizing the thermogravitational column technique, hence making it possible to verify the theoretical model. This paper will compare the density, thermodiusion, and molecular diusion coefficients obtained with the Fontainebleau benchmark values for binary mixtures of n-dodecane, isobutylbenzene, and tetrahydronaphtalene. The accuracy of the numerical results from the Firoozabadi's model for ternary hydrocarbon mixtures is investigated. Results reveal a positive agreement between experimental and numerical data. © Copyright 2005 Walter de Gruyter.

On measurement of thermal diffusion coefficients in multicomponent mixtures

We investigate the steady-state separation of the individual components of an incompressible multicomponent liquid mixture in a narrow two-dimensional thermogravitational column. Analytic working equations for measuring thermal diffusion coefficients analogous to the existing equations for a binary mixture are derived. Similar to the binary results, we find that when compositional variation has negligible effect on fluid density and vertical diffusive flux can be ignored, molecular diffusion does not affect steady-state separation. However, when compositional effects on density are taken into account, molecular diffusion does affect the bulk convective flow and the steady-state separation of the components. There may be also two distinct trends in the velocity and separation profiles. With one or more negative thermal diffusion coefficients, there may be more than one convection cell resulting in oscillatory behavior of separation. The working equations presented can be used to measure thermal diffusion coefficients of multicomponent mixtures. Such measurements have not yet been reported in the literature.

Hydrodynamic stability of binary mixtures in Bénard and thermogravitational cells

The Soret coefficient of a binary mixture can be measured indirectly by considering its effect on the hydrodynamics induced by free convection. In this paper, we have analyzed the stability of two configurations commonly used for such measurements, the thermogravitational column and the Bénard cell. We have numerically integrated the three-dimensional partial differential equations that describe these systems in order to provide accurate data of stability boundaries suitable for comparison with experimental measurements.

Enhanced Molecular Separation in Inclined Thermogravitational Columns

We show in this paper that the molecular separation (or the difference in mass fraction) between the top and the bottom in a thermogravitational column can be substantially increased by inclining t...

Free convection of binary liquid with variable Soret coefficient in thermogravitational column: The steady parallel base states

An exhaustive identification is made of the steady parallel base states which might occur in a thermogravitational column, with a constant horizontal thermal gradient, and a Soret coefficient depending both on temperature and composition, ST(T,C). It is shown that the horizontal dynamics is mainly governed by the Soret thermal sensitivity, and the vertical separation by its compositional one. Published ST(T,C) empirical laws are used to define a generic model which allows one to carry out a “normal mode” analysis of these flows. To account for the possible complete species vertical separation, the Boussinesq approximations are updated. To the leading order in the Soret coefficient amplitude, the horizontal dynamics is seen to be controlled by the solutal Péclet number, Pe, and a vertical stratification parameter, both drifting very slowly along the vertical. Stabilizing and potentially unstable vertical stratifications of the species are predicted, and, for each, the steady parallel flows are described for every thermal sensitivity of the Soret coefficient. Then an accurate determination of the vertical stratification profile is given for a constant and linear C-dependence of ST. The determinant peculiarity of the C-dependence is shown to be the number of zeroes that ST possesses in C∈]0,1[. Some suggestions are made regarding the way the Soret coefficient measurement could benefit from this first analysis. It is shown, in particular, that the vertical separation slope may be misleading in real molecular mixtures, such as the 0.5 N NaCl solution about T=12.09 °C, where the Soret term is mainly linear with temperature.