Slurry reactors mass-transfer coefficient

If the process is continuous and under plug flow, for both the gas and slurry phases, the equations derived for trickle bed reactors are applicable (see Section 3.7.2) (Hopper el al., 2001) by using the appropriate mass transfer coefficients. Note that in trickle beds, the material balances are based on the reactor volume. 

In mass-transfer correlations, the volumetric mass-transfer coefficient is expressed using the gas-liquid interfacial area per unit volume of slurry (or expanded column or reactor, VR) (Koide, 1996 Kantarci el al., 2005 NTIS, 1983) ... 

With a finely divided solid catalyst as typically used In the Flscher-Tropsch synthesis In slurry reactors It Is generally agreed that the major mass-transfer resistance, If It occurs, does so at the gas-liquid Interface. There are considerable disagreements about the magnitude of this resistance that stem from uncertainties about certain physical parameters, notably interfacial area, but also the solubility and mass transfer coefficients for H2 and CO that apply to this system. However when this resistance Is significant, the concentrations of Hg and CO in the liquid in contact with the solid catalyst become less than they would be otherwise, which not only reduces the observed rate of reaction but can also affect the product selectivity and the rate of formation of free carbon. 

The above correlations are recommended for calculations of gas-liquid mass transfer coefficients in conventional stirred slurry reactors. 

In some cases, a slurry reactor with multiple agitation is used. For example, Bern et al. (1976) used the reactor shown in Fig. 15 for the hydrogenation of oils. In this reactor type, horizontal partitions are also introduced at various stages to reduce the extent of backmixing. These authors proposed the following correlation for the gas-liquid mass transfer coefficient, kLaL, in this type of reactor based on pilot-plant data (30 and 500 L capacity) ... 

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... 

For laboratory slurry reactors the following correlation can be used to calculate the mass transfer coefficient [7] ... 

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. 

An interesting study of the gas liquid mass transfer in a three-phase agitated slurry reactor was recently reported by Joosten et al.51 They showed that in the absence of solids, the volumetric mass-transfer coefficient can be well correlated to total power (power dissipated by stirrer + gas) per unit volume, but poorly correlated to the power dissipated by the stirrer only, as done in Fig. 9-14. Their data were well correlated by the correlation of Van Dierendock.23... 

Lemcoff and Jameson71 measured the volumetric gas-liquid mass-transfer coefficient during hydrogenation of acetone in a vibrating slurry reactor. They correlated the data obtained with Raney nickel Nicat 102 catalyst (92 percent nickel) to the temperature (in the range 7 through 21 °C) and the frequency of oscillation /. The correlation is graphically illustrated in Fig. 9-25 and analytically-represented by the equation... 

Any form of convection, of course, increases the value of Ks. In slurry operation with no liquid flow, gas flow induces convection. In an agitated slurry reactor, stirring causes convection. In a pulsating slurry reactor, pulsation of the slurry induces convection and in a three-phase fluidized bed, the movements of both gas and liquid phases cause convection. Any one or more modes of convection will increase the value of the solid-liquid mass-transfer coefficient. In broad terms, the convective liquid-solid mass-transfer coefficient is correlated by-two steady state theories. Here we briefly review and compare them. 

Bubble columns are convenient for catalytic slurry reactions also (67). It is therefore important to know how the hydrodynamic properties of the gas-in-liquid dispersion is influenced by the presence of suspended solid particles. In the slurry reactor absorption enhancement due to chemical reaction cannot be expected. However, if particle sizes are very small, say less than 5 yum, and if, in addition, the catalytic reaction rate is high a small absorption enhancement can occur ( 8). Usually the reaction is in the slow reaction regime of mass transfer theory. Hence, it is sufficient to know the volumetric mass transfer coefficient, kj a, and there is no need to separate k a into the individual values. 

In catalytic slurry reactors the locale of the reaction is the catalyst surface. Hence, in addition to the mass transfer resistance at the gas-liquid interface a further transport resistance may occur at the boundary layer around the catalyst particle. This is characterized by the solid-liquid mass transfer coefficient, kg, which has been the subject of many theoretical and experimental studies. Brief reviews are given by Shah (82). In general, the liquid-solid mass transfer coefficient is correlated by expressions like... 

Fundamentals The basic reaction and transport steps in trickle bed reactors are similar to those in slurry reactors. The main differences are the correlations used to determine the mass transfer coefficients. In addition, if there is more than one component in the gas phase (e.g., liquid has a high vapor pressure or one of the entering gases is inert), there is one additional transport step in the gas phase. Figure 12-17shows the various transport steps in trickle bed reactors. Following our analysis for slurry reactors we develop the equations for the rate of transport of each step. The steps involving reactant A in the gas phase are... 

The more advanced model of Wu and Gidapow 19) is used to explore novel reactor designs optimum catalyst size and reactor configuration. The model included the effect of the mass transfer coefficient between the liquid phase and the gas phase and the water-gas shift reaction. With reaction, diis model was used to predict slurry height, gas hold-up and the rate of methanol production of the Air Products/DOE LaPorte slurry bubble column reactor. 

The kinetic theory model was extended to include the effect of the mass transfer coefficient between the liquid and the gas and the water gas shift reaction in the slurry bubble column reactor. The computed granular temperature was around 30 cm /sec and the computed catalyst viscosity was closed to 1.0 cp. The volumetric mass transfer coefficient estimated by the simulation has a good agreement with experimental values shown in the literature. The optimum particle size was determined for maximum methanol production in a SBCR. The size was about 60 - 70 microns, found for maximum granular temperature. This particle size is similar to FCC particle used in petroleum refining. 

In Chap. 10 rate equations were developed (for the overall transfer of reactant from gas bubble to catalyst surface) in terms of the individual mass-transfer and chemical-reaction steps [Eqs. (10-45) and (10-46)]. The purpose there was to show how the global rate r (per unit volume of bubble-free slurry) was affected by such variables as the gas-bubble-liquid interface ag, the liquid-solid catalyst interface and the various mass-transfer coefficients, and the rate constant for the chemical step. Now the objective is to evaluate the performance of a slurry reactor in terms of the results from Chap. 10 that is, we suppose that the global rate, or overall rate coefficient is known, and the goal is to design the reactor. 

The quantity kg is sort of the odd-man-out in most work on slurry reactors (and even also for fluid-bed and gas-liquid reactors). If the bubble (gas) phase consists of pure reactant only, then a mass-transfer resistance in a film inside the bubble loses its meaning and kg drops out of the problem. Even in the case of mixed gas-phase components, gas phase mass-transfer coefficients are so much larger than their liquid-phase counterparts that the gas-phase transport rate would seldom be of importance in determining the overall rate of chemical reaction. 

Chapters 7 and 8 present models and data for mass transfer and reaction in gas-liquid and gas-liquid-solid systems. Many diagrams are used to illustrate the concentration profiles for gas absorption plus reaction and to explain the controlling steps for different cases. Published correlations for mass transfer in bubble columns and stirred tanks are reviewed, with recommendations for design or interpretation of laboratory results. The data for slurry reactors and trickle-bed reactors are also reviewed and shown to fit relatively simple models. However, scaleup can be a problem because of changes in gas velocity and uncertainty in the mass transfer coefficients. The advantages of a scaledown approach are discussed. 

Three phase slurry reactors are characterized by a gas-liquid (K,a) and liquid-solid (k ) mass transfer coefficient. These coefficients were determined for the rotating disc reactor at the appropriate operation conditions ... 

The performance characteristics of a modified rotating disc reactor has been studied in view of its eventual application for slurry reaction processes in practice It has been found that the backmixing characteristic is favorable 6a8 hold-up and mass transfer coefficients approach values known as characteristic for agitated bubble contactors ... 

Hichri H, Accary A, Puaux JP, Andrieu J. (1992) Gas-liquid mass transfer coefficients in a slurry batch reactor equipped with a self-gas-inducing agitator. Ind. Eng. Chem. Res., 31 1864-1867. 

While the lower order models described in Section 6.3 are useful for the quick prediction of the overall performance of a reactor, these models often rely on simplified flow approximations and often fail to account for change in the local fluid dynamics or transport processes during the presence of internal hardware or changes in flow regimes. Moreover, these models are also based on empirical knowledge (as discussed in Section 6.4) of several parameters such as interfacial area, dispersion coefficients, and mass transfer coefficients. Some of these limitations may be avoided by using CFD models for simulations of gas-liquid-solid flows in three-phase slurry and fluidized bed. 

Three-phase packed bed reactors generally have a lower specific capacity than slurry reactors, for two reasons Much larger catalyst particles are used, so that for rapid reactions, with diffusion or mass transfer limitations, much larger catalyst volumes are required. Also, the maximum specific gas/liquid interfacial area is generally smaller. On the other hand, the volumetric mass transfer coefficients at the gas/liquid and at the liquid/solid interfaces are of comparable magnitude, so they are better adapted to one another. Heat transfer rates to the walls are quite limited. 

When the reaction in the porous catalyst is very rapid, the conversion rate will be determined by gas/liquid or liquid/solid mass transfer. Particularly volumetric gas/liquid mass transfer coefficients (liquid side) are not very much different in slurry-reactors and in three phase packed beds (aU under optimum conditions). 

---