Solid-liquid mass transfer prediction

Although Eqs. (15) and (16) were obtained for singlesize particles, it is reasonable to assume that they apply to multisized particle dispersions also, in which case dp should be replaced with di,2pe- The effect of agitation on solid-liquid mass transfer can be predicted from these equations. For example, for... 

A solid-liquid mass transfer coefficient of 0.015 cm/s was found by comparing the predictions of [S(IV)] to experimental results obtained under conditions in which the liquid phase kinetics were fast. The model was then applied to slurry oxidation under more general conditions by using liquid phase reaction rate kinetics obtained in clear solutions. The results of the model agree with experimental findings for the total rate of oxidation. 

Gladkii(16) at the State Scientific Research Institute of Industrial and Sanitary Gas Cleaning at Moscow did work on the three-phase calcium sulfite slurry oxidation system, finding that the liquid phase oxidation (pH 3.6-6) is first order with respect to the sulfite species. He pointed out, on the basis of pH versus time data from his semi-batch reaction, that the slurry oxidation had different periods in which either reaction kinetics or solid-liquid mass transfer controlled the oxidation rate. He also presented an omnibus empirical correlation between pH, temperature, and the liquid phase saturation concentration of calcium sulfite solution for predicting the slurry oxidation rate. The catalytic effect of manganese... 

A few reactor models have recently been proposed (30-31) for prediction of integral trickle-bed reactor performance when the gaseous reactant is limiting. Common features or assumptions include i) gas-to-liquid and liquid-to-solid external mass transfer resistances are present, ii) internal particle diffusion resistance is present, iii) catalyst particles are completely externally and internally wetted, iv) gas solubility can be described by Henry s law, v) isothermal operation, vi) the axial-dispersion model can be used to describe deviations from plug-flow, and vii) the intrinsic reaction kinetics exhibit first-order behavior. A few others have used similar assumptions except were developed for nonlinear kinetics (27—28). Only in a couple of instances (7,13, 29) was incomplete external catalyst wetting accounted for. 

Also, data on particle-liquid mass transfer from suspended solids in gas-liquid mechanically agitated vessels are practically nonexistent (R18). However, many studies have been published on mass-transfer experiments in the absence of gas, which give an idea of the magnitude of k. Recent reviews by Nienow (N9) and Blasinski and Pyc (B17, B18) indicate two fundamentally different approaches to the prediction of A s the Kol-mogoroff theory, which implies equal at equal power input per unit volume (B17) and the terminal velocity-slip velocity theory which relates ks to the value that would apply if the solid particle moved at its terminal velocity (H2). As explained by Nienow (N9), the resulting values of A s are approximately the same. Use may be made of the graphical correlation given by Brian et al. (B29). 

Work on the rate of dissolution of regular shaped solids in liquids has been carried out by Linton and Sherwood(1), to which reference is made in Volume 1. Benzoic acid, cinnamic acid, and /3-naphthol were used as solutes, and water as the solvent. For streamline flow, the results were satisfactorily correlated on the assumption that transfer took place as a result of molecular diffusion alone. For turbulent flow through small tubes cast from each of the materials, the rate of mass transfer could be predicted from the pressure drop by using the 1 j-factor for mass transfer. In experiments with benzoic acid, unduly high rates of transfer were obtained because the area of the solids was increased as a result of pitting. 

The observed values of the mass transfer coefficient- in three-phase systems between solid and liquid for the conventional impellers and a typical baffled vessel (e.g. Rushton turbine, propeller) are between the values predicted by Hiraoka (liquid-liquid dispersion, eq. (3.267)) and Levins and Glastonbuty (solid-liquid dispersion, eq. (3.118)) correlations. However, as an approximation, the Levins and Glastonbuty correlation could be used for three-phase systems (Smith, 1981). 

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. 

The above discussion on previous experimental studies in trickle-bed reactors suggests that both liquid-solid contacting and mass transfer limitations play a role in affecting trickle-bed reactor performance. Except for a few isolated cases, the reactor models proposed in the literature for gaseous reactant limiting reactions have not incorporated particle-scale incomplete contacting as paft of their development. For cases where it was used, this parameter served as an adjustable constant to match the observed conversion versus liquid mass velocity data so that the true predictive ability of the model... 

Effects of Total Pressure on kG and kL The influence of total system pressure on the rate of mass transfer from a gas to a liquid or to a solid has been shown to be the same as would be predicted from stagnant-film theory as defined in Eq. (5-298), where... 

Here Sh is the modified Sherwood number defined as Sh = /Csnsdp/fl,D and We is the modified Weber number defined as We = UoLpi.dr/hlci. A graphical illustration of the above correlation is shown in Fig. 6-20. The predictions of Eq. (6-67) also agree fairly well with the data of Lemay el al.so Specchia et al.9i showed that, in a trickle-flow reactor, KLaL and Ksas are essentially of the same order of the magnitudes. They also evaluated the conditions under which the mass-transfer (gas-liquid and liquid-solid) influences significantly the performance of a trickle-bed reactor. 

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