Interphase mass transfer solid-liquid

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

Chapter 11 treats reactors where mass and component balances are needed for at least two phases and where there is interphase mass transfer. Most examples have two fluid phases, typically gas-liquid. Reaction is usually confined to one phase, although the general formulation allows reaction in any phase. A third phase, when present, is usually solid and usually catalytic. The solid phase may be either mobile or stationary. Some example systems are shown in Table 11.1. 

In connection with solid-liquid systems agitated so as to achieve interphase mass transfer or heterogeneous chemical reaction it may be noted that various workers have begun to consider the combined fluid dynamic, mass-transfer, and chemical kinetic problem in which a fluid moves past a solid with which it reacts chemically. The paper by Acrivos and Chambr6 (Al) is an example of this approach. 

Liquid-solid (catalytic) reactions. Heat transfer is likely to be more important within the pellet than in the surrounding film, and mass transport more important in the film than within the pellet. In other words, intraphase heat transfer and interphase mass transfer would normally be the dominant transport processes. 

Table 1.1 is a list of the commonly used continuous separation operations based on interphase mass transfer. Symbols for the operations that are suitable for process flow diagrams are included in the table. Entering and exit vapor and liquid and/or solid phases are designated by V, L, and S, respectively. Design procedures have become fairly well standardized for the operations marked by the superscript letter a in Table 1.1. These are now described qualitatively, and they are treated in considerable detail in subsequent chapters of this book. Batchwise versions of these operations are considered only briefly.

INTERPHASE MASS TRANSFER AT THE SOLID-LIQUID INTERFACE... 

These results are similar to those for interphase mass transfer across solid-liquid interfaces, given by (11-109) and (11-110). Hence, the penetration theory for... 

Your experimental apparatus consists of a two-phase column in which mobile component A is transported from a stationary solid phase to a moving liquid phase that flows through the column. How should you quantify the average rate of interphase mass transfer, with units of moles per time, from very simple experimental measurements Your analytical device is not sophisticated enough to measure any concentrations within the column, but you do have experimental data that characterize the inlet stream at z = 0 and the outlet stream at z = L. 

I-power dependence of the dimensionless mass transfer coefficient on Re reveals fbat the flow regime is laminar. Turbulent mass transfer across high-shear no-slip interfaces also scales as Shaverage Sc, but the exponent of Re in this correlation is somewhere between 0.8 and 1. AU of these dimensionless scaling laws for interphase mass transfer are summarized in Table 12-1 for solid-liquid and gas-Uquid interfaces. 

Alternative Approach in the Absence of Liquid-Phase Chemical Reaction. The previous scaling law for the dissolution of spherical solid particles in a surrounding quiescent liquid can be addressed by performing an unsteady-state macroscopic mass balance on the liquid solution, with volume Viiquid- The accumulation of species A is balanced by the rate of interphase mass transfer (MT) when no chemical reaction occurs. Hence,... 

Now, it is instructive to re-analyze the unsteady-state macroscopic mass balance on an isolated solid pellet of pure A with no chemical reaction. The rate of output due to interphase mass transfer from the solid particle to the liquid solution is expressed as the product of a liquid-phase mass transfer coefficient c, liquids a Concentration driving force (Ca, — Ca), and the surface area of one spherical pellet, 4nR. The unsteady-state mass balance on the solid yields an ordinary differential equation for the time dependence of the radius of the peUet. For example,... 

Even less is known about the liquid-solid transfer in bubble columns. Ghosh [83] has recently studied the liquid-solid mass transfer by monitoring the rate of dissolution of benzoic acid pellets suspended in a bubble column. He elucidated the effect of gas velocity (air), axial position of pellet and the types of sparger. Figure 8 shows the effect of gas velocity on the interphase mass transfer coefficient (k ) in a 1% aqueous CMC solution when the solute particles are positioned at various heights from the distributor. Within the narrow range of conditions, he found that the type and details of the sparger did not exert any influence on the value of the mass transfer coefficient. He presented his results in terms of Stanton number. 

Introduction to interphase mass transfer. In Chapter 7 we considered mass transfer from a fluid phase to another phase, which was primarily a solid phase. The solute A was usually transferred from the fluid phase by convective mass transfer and through the solid by diffusion. In the present section we shall be concerned with the mass transfer of solute A from one fluid phase by convection and then through a second fluid phase by convection. For example, the solute may diffuse through a gas phase and then diffuse through and be absorbed in an adjacent and immiscible liquid phase. This occurs in the case of absorption of ammonia from air by water. 

For the design of the multiphase chemical reactors, one has to deal with hydrodynamics, mass and heat transfer, and catalyst activity. For heterogeneously catalyzed reactions, the rate of the reaction is often limited by interphase mass transfer instead of the intrinsic kinetics (Figure 5.5). The rate-Umiting step can be the gas-liquid mass transfer, liquid-solid mass transfer, and... 

We shall now apply the methods developed in the previous chapters to model PTC reactions in liquid-liquid and solid-liquid systems, including solid-supported systems. For a more detailed account of these methods, reference may be made to the articles, among others, of Naik and Doraiswamy (1998), and Yadav and collaborators (1995,2004). The rate of the overall PTC cycle is dependent on the relative rates of the different steps in the PTC cycle. Thus, when the basic conservation equations for mass balance are written for a PTC system, the individual steps that comprise the PTC cycle must be accounted for. These steps are the ion-exchange reaction, interphase mass transfer of both inactive and active forms of the phase transfer (PT) catalyst, partitioning of the catalyst between the two phases (in liquid-liquid systems), and the main organic phase reaction. When these are considered, the normal assumption of pseudo-first-order kinetics (Equation 16.1) is no longer valid. 

Interphase Mass Transfer. There are a number of interphase mass transfer steps that must occur in a trickle flow reactor. The mass transfer resistances can be considered as occurring at the more or less stagnant fluid layer interfaces, i.e., on the gas and/or the liquid side of the gas/llquld Interface and on the liquid side of the liquid/solid Interface. The mass transfer correlations (8) indicate that the gas/llquld Interface and the liquid/solid interface mass transfer resistances decrease with higher liquid velocity and smaller particle size. Thus, in the PDU, the use of small inert particles partially offsets the adverse effect of low velocity. These correlations indicate that for this system, external mass transfer limitations are more likely to occur in the PDU than in the commercial reactor because of the lower liquid velocity, but that probably there is no limitation in either. If a mass transfer limitation were present, it would limit conversion in a way similar to that shown for axial dispersion and incomplete catalyst wetting illustrated in Figure 1. Due to the uncertainty in the correlations and in the physical properties of these systems, particularly the molecular diffuslvities, it is of interest to examine if external mass transfer is influencing the PDU results. 

Interphase mass transport also represents a possible input to or output from the system. In Fig. 1.13., transfer of a soluble component takes place across the interface which separates the two phases. Shown here is the transfer from phase G to phase L, where the separate phases may be gas, liquid or solid. 

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. 

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