Fluid—solid extraction mass transfer

Size of solid particles Mass transfer in gas extraction from solid substrates in most cases depends heavily on the transport rate in the solid phase. The length of the transport path determines mass transport in the solid phase. In general the extraction rate increases with decreasing particle size. On the other hand, mass transfer has to be achieved into the fluid phase. If the smaller particles hinder fluid flow in the fixed bed, then mass transfer rate decreases with smaller particles. 

Principles and Characteristics Supercritical fluid extraction uses the principles of traditional LSE. Recently SFE has become a much studied means of analytical sample preparation, particularly for the removal of analytes of interest from solid matrices prior to chromatography. SFE has also been evaluated for its potential for extraction of in-polymer additives. In SFE three interrelated factors, solubility, diffusion and matrix, influence recovery. For successful extraction, the solute must be sufficiently soluble in the SCF. The timescale for diffusion/transport depends on the shape and dimensions of the matrix particles. Mass transfer from the polymer surface to the SCF extractant is very fast because of the high diffusivity in SCFs and the layer of stagnant SCF around the solid particles is very thin. Therefore, the rate-limiting step in SFE is either... 

The interest in mass transfer in high-pressure systems is related to the extraction of a valuable solute with a compressed gas. This is either a volatile liquid or solid deposited within a porous matrix. The compressed fluid is usually a high-pressure gas, often a supercritical fluid, that is, a gas above its critical state. In this condition the gas density approaches a liquid—like value, so the solubility of the solute in the fluid can be substantially enhanced over its value at low pressure. The retention mechanism of the solute in the solid matrix is only physical (that is, unbound, as with the free moisture), or strongly bound to the solid by some kind of link (as with the so-called bound moisture). Crushed vegetable seeds, for example, have a fraction of free, unbound oil that is readily extracted by the gas, while the rest of the oil is strongly bound to cell walls and structures. This bound solute requires a larger effort to be transferred to the solvent phase. 

Mathematical models derived from mass-conservation equations under unsteady-state conditions allow the calculation of the extracted mass at different bed locations, as a function of time. Semi-batch operation for the high-pressure gas is usually employed, so a fixed bed of solids is bathed with a flow of fluid. Mass-transfer models allow one to predict the effects of the following variables fluid velocity, pressure, temperature, gravity, particle size, degree of crushing, and bed-length. Therefore, they are extremely useful in simulation and design. 

The shrinking-core model (SCM) is used in some cases to describe the kinetics of solid and semi-solids-extraction with a supercritical fluid [22,49,53] despite the facts that the seed geometry may be quite irregular, and that internal walls may strongly affect the diffusion. As will be seen with the SCM, the extraction depends on a few parameters. For plug-flow, the transport parameters are the solid-to-fluid mass-transfer coefficient and the intra-particle diffusivity. A third parameter appears when disperse-plug-flow is considered [39,53],... 

Besides fluid mechanics, thermal processes also include mass transfer processes (e.g. absorption or desorption of a gas in a liquid, extraction between two liquid phases, dissolution of solids in liquids) and/or heat transfer processes (energy uptake, cooling, heating, drying). In the case of thermal separation processes, such as distillation, rectification, extraction, and so on, mass transfer between the respective phases is subject to thermodynamic laws (phase equilibria) which are obviously not scale dependent. Therefore, one should not be surprised if there are no scale-up rules for the pure rectification process, unless the hydrodynamics of the mass transfer in plate and packed columns are under consideration. If a separation operation (e.g. drying of hygroscopic materials, electrophoresis, etc.) involves simultaneous mass and heat transfer, both of which are scale-dependent, the scale-up is particularly difficult because these two processes obey different laws. 

Supercritical fluid extraction (SFE) utilizes the properties of supercritical fluids for extraction of analytes from solid samples. A supercritical fluid (SCF) is a substance above its critical temperature and pressure, when it is between the typical gas and liquid state. Low viscosity and near-zero surface tension and heat of vaporization allow SCFs to penetrate into solids more rapidly than liquid solvents, which leads to more favorable mass transfer. The density of an SCF is close to the liquid density. 

The use of supercritical fluids in separation processes has received considerable attention in the past several years and the fundamentals of supercritical fluid (SCF) extraction and potential applications have been described in a recent review article (p. It is generally known that supercritical conditions enhance the dissolution of solid particles. In comparison with liquid solvents, supercritical fluids have a high diffusivity, a low density and a low viscosity, thus allowing rapid extraction and phase separation. Little information is available in the literature however, on mass transfer coefficients between supercritical fluids and solids. 

During the extraction phase the whole mass transfer may be regarded as a quasi-stationary process. Scale-up rules therefore take account of external mass transfer from the solid surface to the supercritical fluid only. If pilot and production plants are required to display the same mass transfer properties, then... 

Thomas Kilgore Sherwood (1903-1976) completed his PhD under the supervision of Warren K. Lewis, after whom the Lewis number was named, in 1929 at the Massachussetts Institute of Technology (MIT), Boston, USA. The subject of his thesis was The Mechanism of the Drying of Solids . He was a professor at MIT from 1930 until 1969. His fundamental work on mass transfer in fluid flow and his book Absorption and Extraction which appeared in 1937 made him famous worldwide. 

The most common extraction techniques for semivolatile and nonvolatile compounds from solid samples that can be coupled on-line with chromatography are liquid-solid extractions enhanced by microwaves, ultrasound sonication or with elevated temperature and pressures, and extraction with supercritical fluid. Elevated temperatures and the associated high mass-transfer rates are often essential when the goal is quantitative and reproducible extraction. In the case of volatile compounds, the sample pretreatment is typically easier, and solvent-free extraction methods, such as head-space extraction and thermal desorption/extraction cmi be applied. In on-line systems, the extraction can be performed in either static or dynamic mode, as long as the extraction system allows the on-line transfer of the extract to the chromatographic system. Most applications utilize dynamic extraction. However, dynamic extraction is advantageous in many respects, since the analytes are removed as soon as they are transferred from the sample to the extractant (solvent, fluid or gas) and the sample is continuously exposed to fresh solvent favouring further transfer of analytes from the sample matrix to the solvent. 

Experimental extraction curves can be represented by this type of model, by fitting the kinetic coefficients (mass transfer coefficient to the fluid, effective transport coefficient in the solid, effective axial dispersion coefficient representing deviations from plug flow) to the experimental curves obtained fi om laboratory experiments. With optimized parameters, it is possible to model the whole extraction curve with reasonable accuracy. These parameters can be used to model the extraction curve for extractions in larger vessels, such as from a pilot plant. Therefore, the model can be used to determine the kinetic parameters from a laboratory experiment and they can be used for scaling up the extraction. 

Supercritical fluids exhibit gas-like mass transfer rates and yet have liquid-like solvating capability. The high diffusivity and low viscosity of supercritical fluids enable them to penetrate and transport solutes from porous solid matrices. From this point of view, SFE is an ideal method to extract uranium and lanthanides from solid wastes. Carbon dioxide (CO2) is most frequently used in SFE because of its moderate critical pressure (Pc) nd temperature (Jc), inertness, low cost, and availability in pure form. Figure 1 illustrates moderate values of Pc and Tc compared with those of water. 

SFE processes typically involve mass transfer between a supercritical fluid, such as CO2, and a solid or liquid phase matrix under conditions of high pressure and temperature. Slight changes in temperature or pressure of the system can cause large changes in the density of the solvent and consequently the solvent s ability to dissolve heavy, nonvolatile compounds from the sample matrix. Nonvolatile compounds can be extracted by proper manipulation of the system pressure. A reduction in pressure, generally to a pressure below the solvent critical pressure, results in the complete precipitation of the solute. 

Step 1. Reactants enter a packed catalytic tubular reactor, and they must diffuse from the bulk fluid phase to the external surface of the solid catalyst. If external mass transfer limitations provide the dominant resistance in this sequence of diffusion, adsorption, and chemical reaction, then diffusion from the bulk fluid phase to the external surface of the catalyst is the slowest step in the overall process. Since rates of interphase mass transfer are expressed as a product of a mass transfer coefficient and a concentration driving force, the apparent rate at which reactants are converted to products follows a first-order process even though the true kinetics may not be described by a first-order rate expression. Hence, diffusion acts as an intruder and falsifies the true kinetics. The chemical kineticist seeks to minimize external and internal diffusional limitations in catalytic pellets and to extract kinetic information that is not camouflaged by rates of mass transfer. The reactor design engineer must identify the rate-limiting step that governs the reactant product conversion rate. 

According to the previous chapters the reader may come to the conclusion that countercurrent columns are dominant as has been shown for mass transfer equipment used in the areas of rectification, absorption, and extraction. However, this is not true because the continuous transport of solid granular material is much more difficult in comparison to a fluid. Therefore, nearly all adsorbers are fixed beds which are operated batchwise. As a rule, at least two fixed beds are installed in continuously operated industrial processes. The first bed is used for the adsorption step whereas in the second the adsorbates is removed or desorbed at the same time. The duty of the two beds is changed when the adsorption capacity is exhausted. Sometimes several beds are arranged to cany out pressurization and depressurization steps. 

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