Slurry reactors mass-transfer correlation

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) ... 

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

Since dissolved gas concentrations in the liquid phase are more difficult to measure experimentally than the liquid reactant concentration, Equation 8 evaluated at the reactor exit 5=1 represents the key equation for practical applications involving this model. Nevertheless, the resulting expression still contains a significant number of parameters, most of which cannot be calculated from first principles. This gives the model a complex form and makes it difficult to use with certainty for predictive purposes. Reaction rate parameters can be determined in a slurry and basket-type reactor with completely wetted catalyst particles of the same kind that are used in trickle flow operation so that DaQ, r 9 and A2 can be calculated for trickle-bed operation. This leaves four parameters (riCE> St gj, Biw, Bid) to be determined from the available contacting efficiency and mass transfer correlations. It was shown that the model in this form does not have good predictive ability (29,34). 

SECTION 10-7 MASS-TRANSFER CORRELATIONS (SLURRY REACTORS)... 

An accurate evaluation of kxa is complicated by the heterogeneous nature and poor definition of contaminant/soil systems. Some success has been achieved in modeling mass transfer from a separate contaminant phase. During degradation these nonaqueous phase liquids (NAPLs) often dissolve under conditions where phase equilibrium is not achieved and dissolution is proportional to k a. Experimental determinations and correlations for k-p depend on interfacial area of the NAPL and liquid velocity at the interface (Geller Hunt, 1993). For adsorbed contaminants, kxa varies with soil composition and structure, concentration and age of contamination, and therefore with time. For example, slurry reactor tests indicate that the rate of naphthalene mass transfer decreases with time, with media size, and with aging of the tar prior to testing (Luthy et al., 1994). 

Gas holdup is an important hydrodynamic parameter in stirred reactors, because it determines the gas-liquid interfacial area and hence the mass transfer rate. Several studies on gas holdup in agitated gas-liquid systems have been reported, and a number of correlations have been proposed. These are summarized in Table VIII. For a slurry system, only a few studies have been reported (Kurten and Zehner, 1979 Wiedmann et al, 1980). In general, the gas holdup depends on superficial gas velocity, power consumption, surface tension and viscosity of liquids, and the solid concentration. The dependence of gas holdup on gas velocity, power consumption, and surface tension of the liquid can be described as... 

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) ... 

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. 

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... 

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. 

For the case of FTS and CO methanation in molten wax slurry system the parameters Involved in model equations, i.e. the physicochemical properties, the hydro-dynamic and mass transfer parameters, can be estimated with sufficient accuracy. There exist reliable data for the physicochemical properties obtained from independent measurements and summarized by Hammer (14) and Declcwer and coworkers (15). The hydrodynamic and mass transfer parameters can be calculated from empirical correlations given by Deckwer et al. (15), which were partly established from measurements in Icibscale reactors under synthesis conditions and seem to be applicable for larger scale equipment (17). This data and correlations were successfully used to perform a kinetic study on the experimental data reported in the literature on the FTS (16) and to simulate the results obtained in the Rheinpreussen-Koppers demonstration plant predicting fairly well the optimal gas velocity (17,18). 

Deckwer et al. (33) proposed a model for a laboratory scale slurry reactor which is essentially the same as that proposed by Satterfield and Huff (32) with the only difference that their model accounts for the contraction in the gas volume. The experimental data of various investigators were analyzed and the estimated rate constants were correlated to the iron content in the slurry which is believed to be the intrinsic catalytic component. The authors concluded that the FT synthesis is predominantly controlled by the chemical reaction provided the reactor is operated at the relevant industrial conditions and that mass transfer limitations could be important only at very low gas velocities, high catalytic concentrations and for very active catalysts. 

The physico-chemical properties have been measured independently and are summarized in refs. (56,62,85). As discussed in part 2.1 the hydrodynamic and mass transfer properties can be calculated from correlations which were at least partly established from measurements under synthesis conditions. There is also enough experimental information that these correlations may be applicable for larger scale equipment. In the foregoing section 2.3 it was shown that first order rate constants for syngas conversion could be evaluated which seem to be reasonable and consistent. The kinetic law applied is very simplified indeed and, for instance, cannot account for changes of kjj with variations of the inlet gas composition. Nevertheless it is thought that the available information should be sufficient to develop a more sophisticated reactor model for the FTS in slurry phase which... 

Bubble columns. Tracers are used in bubble columns and gas-sparged slurry reactors mainly to determine the backmixing parameters of the liquid phase and/or gas-liquid or liquid-solid mass transfer parameters. They can be used for evaluation of holdup along the lines reviewed in the previous Section 6.2.1. However, there are simpler means of evaluating holdup in bubble columns, e.g. monitoring the difference in liquid level with gas and without gas flow. Numerous liquid phase tracer studies of backmixing have been conducted (132-149). Steady-state or continuous tracer inputs (132,134,140,142) as well as transient studies with pulse inputs (136,141,142,146) were used. Salts such as KC Jl or NaCil, sulfuric acid and dyes were employed as tracers. Electroconductivity detectors and spectrophotometers were used for tracer detection. The interpretation of results relied on the axial dispersion model. Various correlations for the dispersion... 

Several correlations (Calderbank and Moo-Young 1961 Misic and Smith 1971 Juvekar and Sharma 1973) for the mass transfer coefficient kt, in a slurry reactor are available. One correlation (Calderbank and Moo-Young 1961) that accounts for the energy dissipation due to agitation by the impeller gives ... 

The liquid—solid and gas—liquid mass transfer coefficients can be estimated by the approach discussed in detail in Chapter 10, which is based on the correlation between Sherwood number and Reynolds and Schmidt numbers. The critical issue in the calculation of the Reynolds number is the energy dissipated, which, in many cases, can be much lower than the energy imposed by the stirrer of a slurry reactor. 

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