Mass transfer solid-liquid

Snider and Perona3 measured Ksas, the volumetric liquid-solid mass-transfer coefficient, for the case of hydrogenation of a-methyl styrene on 3-mm alumina spheres coated with palladium catalyst. The results were obtained in the bubble-flow regime. The measurements of Ks, the liquid-solid mass-transfer coefficient in a nonreacting system, were first reported by Mochizuki and Matsui.20 They 

U is the mean velocity of fluid and D is the molecular difTusivity of the solute in question in liquid. The subscripts L and G refer to liquid and gas phases, and the subscript 0 on the Sherwood number represents its value when RcG = 0. The validity of Eqs. (7-32), (7-33), and (7-34) under the conditions of an actual reactor, where all particles are active, and under the conditions where Sc 1,170 

Most recently. Kirillov and Nasamanyan15 carried out a very interesting unsteady-state analysis of liquid-solid mass transfer for cocurrent upflow in a fixed-bed reactor. The analysis was compared and verified by the steady-state measurements of liquid-solid mass-transfer coefficients in a 10-cm x 10-cm square column with a height of 50 cm. Three types of packings, 30-mm and 8-mm 

Sh is the Sherwood number based on the equivalent radius of the packing material, R is the equivalent radius of the packing material, ReL = l/i.i /vL(l — hG) (where vL is the kinematic viscosity of the liquid), Sc is the Schmidt number, and m is the thickness of the liquid layer on the packing obtained from the relation 

Recommendations Under bubble-flow conditions, the use of Eq. (7-36) for large particles and the correlation shown in Fig. 7-31 for small particles is recommended. Further experimental work in the pulsed-flow regime and with hydrocarbon systems is needed. 

Under certain conditions, for example, in the case of highly soluble gases, fast reactions of highly active catalysts, these reactions become partially or fully controlled by the rate of the Uquid-solid mass transfer. Liquid-solid mass transfer resistance is significant when the following inequality is satisfied [13]  

A significant amount of research has been performed on the measurement of liquid-solid mass transfer [67], Generally, liquid-solid mass transfer in fixed-bed reactors has been studied by five methods dissolution of slightly soluble solids into the liquid [68-73], chemical reaction with significant liquid-solid mass transfer resistance [74], ion exchange followed by an instantaneous irreversible reaction [75], dynamic absorption [76], and electrochemical technique [77-80]. The electrochemical method has certain advantages over the other it facilitates direct and instantaneous measurements of solid-liquid mass transfer and is thus very useful to measure mass transfer fluctuations, especially under pulse flow conditions. 

Reactions carried out in three-phase fixed-bed reactors such as hydrogenation, oxidation, and hydrodesulfurization can be highly exothermic. Such situations require incorporation of an efficient heat removal system in order to avoid hot spots or catalyst deactivation as much as possible [13, 92]. A good knowledge of the packed-bed heat transfer parameters is necessary for the design of the reactor and heat removal system. 

In this heat transport model, the radial heat transfer is represented by a Fourier-like law, using an equivalent radial thermal conductivity of the medium with flowing fluids 4r = A dT/dr. The bed radial effective thermal conductivity was expressed as sum of two terms—conductive contribution and convective contribution A -Aso+ gf In Hashimoto et al. [94] and Mat-suura et al. s [95] approach, the theory of single-phase gas flow 

heat transfer in three-phase fixed-bed reactors has been investigated using a two-dimensional homogeneous model with two parameters [94, 96]—the bed radial effective thermal conductivity and the heat transfer coefficient at the wall  

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Liquid/Solid Mass Transfer The dissolved gas and the solvent react in contact with the surface of the catalyst. For studying the rate of transfer to the surface, an often-used system was benzoic acid or naphthalene in contact with water. A correlation of Dharwadkar and Sylvester (AJChE Journal, 23, 376 [1977]) that agrees well with some others is... 

Semidry Scrubbers The advantage of semidry scrubbers is in that they remove contaminants by way of a solid waste that is easier to dispose of (less expensive). Initially, the scrubbing medium is wet (such as a lime or soda ash slurry). Then a spray dryer is used to atomize the slurry into the gas which evaporates the water in the droplets. As this takes place, the acid in the gas neutralizes the alkali material and forms a fine white solid. Most of the white solids are removed at the bottom of the scrubber while some are carried into the gas stream and have to be removed by a filter or electrostatic precipitator (discussed later). Although semidry systems cost 5-15% more than wet systems, when combined with a fabric filter, they can achieve 90-95% efficiencies. Dry scrubbers are sometimes used in a very similar fashion, but without the help of gas-liquid-solid mass transfer, these systems use much higher amounts of the solid alkali materials. 

Mass transfer across the liquid-solid interface in mechanically agitated liquids containing suspended solid particles has been the subject of much research, and the data obtained for these systems are probably to some extent applicable to systems containing, in addition, a dispersed gas phase. Liquid-solid mass transfer in such systems has apparently not been studied separately. Recently published studies include papers by Calderbank and Jones (C3), Barker and Treybal (B5), Harriott (H4), and Marangozis and Johnson (M3, M4). Satterfield and Sherwood (S2) have reviewed this subject with specific reference to applications in slurry-reactor analysis and design. 

Johnson et al. (J4) investigated the hydrogenation of a-methylstyrene catalyzed by a palladium-alumina catalyst suspended in a stirred reactor. The experimental data have recently been reinterpreted in a paper by Polejes and Hougen (P4), in which the original treatment is extended to take account of variations in catalyst loading, variations in impeller type, and variations of gas-phase composition. Empirical correlations for liquid-side resistance to gas-liquid and liquid-solid mass transfer are presented. 

Henry Law coefficient (bar m3/kmol) kLa = Gas-liquid volumetric mass transfer coefficient (s-1) ks = Liquid-solid mass transfer coefficient (m/s)... 

The proposed catalyst loading, that is the ratio by volume of catalyst to aniline, is to be 0.03. Under the conditions of agitation to be used, it is estimated that the gas volume fraction in the three-phase system will be 0.15 and that the volumetric gas-liquid mass transfer coefficient (also with respect to unit volume of the whole three-phase system) kLa, 0.20 s-1. The liquid-solid mass transfer coefficient is estimated to be 2.2 x 10-3 m/s and the Henry s law coefficient M = PA/CA for hydrogen in aniline at 403 K (130°C) = 2240 barm3/kmol where PA is the partial pressure in the gas phase and CA is the equilibrium concentration in the liquid. 

The liquid-solid mass transfer coefficient was estimated from the correlation provided by Temkin et al. (14). The method is based on the estimation of Sherwood number (Sh), starting from Reynolds (Re) and Schmidt (Sc) numbers. 

For the semi-batch stirred tank reactor, the model was based on the following assumptions the reactor is well agitated, so no concentration differences appear in the bulk of the liquid gas-liquid and liquid-solid mass transfer resistances can prevail and finally, the liquid phase is in batch, while hydrogen is continuously fed into the reactor. The hydrogen pressure is maintained constant. The liquid and gas volumes inside the reactor vessel can be regarded as constant, since the changes of the fluid properties due to reaction are minor. The total pressure of the gas phase (P) as well as the reactor temperature were continuously monitored and stored on a PC. The partial pressure of hydrogen (pnz) was calculated from the vapour pressure of the solvent (pvp) obtained from Antoine s equation (pvpo) and Raoult s law ... 

Kl = the overall gas-phase mass transfer coefficient as defined in equation (3.59) kf = the liquid-solid mass transfer coefficient... 

Liquid-solid mass transfer in trickle-bed reactors... 

The liquid-solid mass transfer coefficient is given by the Mochizuki-Matsui correlation (Ramachandran and Chaudhari, 1984) for Reh < 5,... 

Mass transfer coefficients The liquid-solid mass transfer coefficient can be evaluated by using the correlation of Sano el al. (eq. (3.211)) kt = 4.22 x 10 4 m/s, whereas the corresponding interfacial area is (eq. (3.218))... 

The gas-liquid mass transfer for organic solutions and the liquid-solid mass transfer are evaluated using the appropriate correlations (eqs. (3.427) and (3.435), respectively), while the Fogler s overall coefficient (K°A) is (eq. (3.379))... 

In the case of saturated liquid feed, the conversion achieved is almost identical for both reactors. This is why in the respective reactor model, the gas-phase mass transfer is theoretically infinite and the difference in the liquid-solid mass transfer between the reactors is small, only 1.21 times higher than that in the packed bubble bed reactor. 

The effectiveness factor is very low, indicating that intraparticle mass transfer resistance is very significant. The gas-liquid mass transfer resistance is also important, as expected. On the other hand, the liquid-solid mass transfer resistance is negligible. As a result, the rate of reaction in the slurry reactor is about 50 times higher than that in the trickle-bed. Therefore, in cases of such high rates of reaction, the slurry reactor is a better choice, although the gas-liquid mass transfer and the filtration of the catalyst may be a problem. 

Liquid-solid mass transfer has also been studied, on a limited basis. Application to systems with catalytic surfaces or electrodes would benefit from such studies. The theoretical equations have been proposed based on film-flow theory (32) and surface-renewal theory (39). Using an electrochemical cell with rotating screen disks, liquid-solid mass transfer was shown to increase with rotor speed and increased spacing between disks but to decrease with the addition of more disks (39). Water flow over naphthalene pellets provided 4-6 times higher volumetric mass transfer coefficients compared to gravity flow and similar superficial liquid velocities (17). 

Munjal S, Dudukovic MP, Ramachandran P. Mass transfer in rotating packed beds— I. Development of gas-liquid and liquid-solid mass-transfer correlations. Chem Eng... 

Sedahmed GH, Al-Abd MZ, El-Taweel YA, Darwish MA. Liquid-solid mass transfer behavior of rotating screen discs. Chem Eng J 2000 76 247-252. 

Solid particles are in the range of 0.01 to 1.0 mm (0.0020 to 0.039 in), the minimum size limited by filterability. Small diameters are used to provide as large an interface as possible to minimize the liquid-solid mass-transfer resistance and intraparticle diffusion limitations. Solids concentrations up to 30 percent by volume may be handled however, lower concentrations may be used as well. For example, in hydrogenation of oils with Ni catalyst, the solids content is about 0.5 percent. In the manufacture of hydroxylamine phosphate with Pd-C, the solids content is 0.05 percent. 

The hydrodynamic parameters that are required for stirred tank design and analysis include phase holdups (gas, liquid, and solid) volumetric gas-liquid mass-transfer coefficient liquid-solid mass-transfer coefficient liquid, gas, and solid mixing and heat-transfer coefficients. The hydrodynamics are driven primarily by the stirrer power input and the stirrer geometry/type, and not by the gas flow. Hence, additional parameters include the power input of the stirrer and the pumping flow rate of the stirrer. 

Liquid-solid mass transfer is typically not limiting due to the small particle size resulting in large particle surface area/volume of reactor, unless the concentration of the particles is very low, and or larger particles are used. In the latter case, intraparticle mass-transfer limitations would also occur. Ramachandran and Chaudhari (Three-Phase Catalytic Reactors, Gordon and Breach, 1983) present several correlations for liquid-solid mass transfer, typically as a Sherwood number versus particle Reynolds and Schmidt numbers, e.g., the correlation of Levins and Glastonbury [Trans. Inst. Chem. Engrs. 50 132 (1972)] ... 

An appropriate model for trickle-bed reactor performance for the case of a gas-phase, rate limiting reactant is developed. The use of the model for predictive calculations requires the knowledge of liquid-solid contacting efficiency, gas-liquid-solid mass transfer coefficients, rate constants and effectiveness factors of completely wetted catalysts, all of which are obtained by independent experiments. 

Liquid/solids mass transfer rate very high high... 

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