Solids-liquid mass transfer coefficient

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. 

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

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 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. 

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. 

Figure 12. Correlations for liquid-solid mass transfer coefficient in bubble columns. The dashed curve is from Jadhav and Pangarkar [112] for dp = 100 pm, dc =0.3m, N c = 1000 and v L from eq 60.

The liquid-solid mass-transfer coefficient depends mainly on the agitation speed, the particle size, and the physical properties of the system. While ks oc N°-2 this relationship may depend on the particle size (Sano et al., 1974). In a dimensionless form, Sh oc RemSc0 5 however, the value of m changes at some critical Reynolds number when all particles are suspended. The most generalized relationship is given by Eq. (3.34), and its use is recommended. 

Internal recycle reactors are designed so that the relative velocity between the catalyst and the fluid phase is increased without increasing the overall feed and outlet flow rates. This facilitates the interphase heat and mass transfer rates. A typical internal flow recycle stirred reactor design proposed by Berty (1974, 1979) is shown in Fig. 18. This type of reactor is ideally suited for laboratory kinetic studies. The reactor, however, works better at higher pressure than at lower pressure. The other types of internal recycle reactors that can be effectively used for gas-liquid-solid reactions are those with a fixed bed of catalyst in a basket placed at the wall or at the center. Brown (1969) showed that imperfect mixing and heat and mass transfer effects are absent above a stirrer speed of about 2,000 rpm. Some important features of internal recycle reactors are listed in Table XII. The information on gas-liquid and liquid-solid mass transfer coefficients in these reactors is rather limited, and more work in this area is necessary. 

C. Determination of the Liquid-Solid Mass-Transfer Coefficient... 

In a batch slurry reactor, the liquid-solid mass-transfer coefficient can be measured by dissolving a sparingly soluble solid in liquid. The concentration of dissolved solid in liquid (Bt) can be measured as a function of time, preferably by a continuous analytical device. Systems such as the dissolution of benzoic acid, jS-naphthol, naphthalene, or KMn04 in water can be used. A plot of B( as a function of time and the slope of such plot at time t = 0 can give ks as... 

The liquid-solid mass-transfer coefficient can also be measured by the reverse process, namely adsorption on a solid from solution. Furusawa and Smith (1973) studied adsorption of benzene from aqueous solution on to activated carbon particles. The concentration of benzene in the liquid was monitored by a gas chromotograph. The liquid-solid mass-transfer coefficient from such a dynamic adsorption method can be obtained from the expression (Furusawa and Smith, 1973)... 

For a semi-batch operation, the liquid-solid mass-transfer coefficient can also be obtained by monitoring a reaction between the dissolving solid B and a liquid reactant C. If this reaction is instantaneous, the enhancement factor for the reaction is... 

The physical methods for the measurement of kLaL in batch, semi-batch, and continuous systems described earlier are accurate. The main limitation for the semi-batch and continuous systems is the availability of the analytical technique for the measurement of the gas concentration in the liquid phase. For gas-liquid-solid systems, Eq. (9.41) can be used to measure both kt and kL simultaneously. The liquid-solid mass-transfer coefficient can also be measured using the method of Ruether and Puri (1973) or the physical methods outlined earlier. 

Just as in the case of gas-liquid mass transfer, two important parameters characterizing the liquid-solid mass transfer are the liquid-solid mass-transfer coefficient and the liquid-solid interfacial area. Various correlations for the estimation of these parameters under a variety of system conditions are discussed in Chaps. 6 through 9. The importance of liquid-solid mass transfer on the reactor performance depends, once again, on the nature of the reaction and the flow conditions. 

Satterfield150 considers a special case of the above equation, in which the gas-phase resistance is neglected (i.e., the second term on the right-hand side of the above equation is zero) and the catalyst effectiveness factor is assumed to be unity. In this case, a series of measurements of AG/R for various catalyst loadings permits a plot of AG/R versus 1/m to be established. The intercept yields the gas-liquid mass-transfer coefficient and the slope yields a combination of the intrinsic rate constant and the liquid- solid mass-transfer coefficient. 

The procedure described above will save on experimentation time. The method is, of course, applied only to the first-order reaction and its accuracy depends upon the appropriate estimations of gas-liquid and liquid-solid mass-transfer coefficients. 

Reuther and Puri 45 proposed another method for estimating the liquid-solid mass-transfer coefficient from rate measurements. They considered reactions... 

If a transport parameter rc — CS/CL is defined, where Cs is the concentration of C at the catalyst surface, then Peterson134 showed that for gas-solid reactions t)c < rc, where c is the catalyst effectiveness factor for C. For three-phase slurry reactors, Reuther and Puri145 showed that rc could be less than t)C if the reaction order with respect to C is less than unity, the reaction occurs in the liquid phase, and the catalyst is finely divided. The effective diffusivity in the pores of the catalyst particle is considerably less if the pores are filled with liquid than if they are filled with gas. For finely divided catalyst, the Sherwood number for the liquid-solid mass-transfer coefficient based on catalyst particle diameter is two. 

In a trickle-bed reactor, due to a very thin liquid film, gas-liquid and liquid solid mass-transfer coefficients are sometimes combined as... 

The liquid-solid mass-transfer coefficient under trickle-flow conditions was first measured by Van Krevelen and Krekels102 from the rate of dissolution of benzoic acid with no gas flow. They presented a relation... 

Here, GL is the mass flux of liquid, Ksas is the volumetric liquid solid mass-transfer coefficient, and AL is the concentration of the reactant in the 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... 

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... 

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