Mass fluid-solid

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve veiy slow binding steps. In these cases, the mass-transfer parameter k is replaced by a second-order reaction rate constant k. The driving force is written for a constant separation fac tor isotherm (column 4 in Table 16-12). When diffusion steps control the process, it is still possible to describe the system hy its apparent second-order kinetic behavior, since it usually provides a good approximation to a more complex exact form for single transition systems (see Fixed Bed Transitions ). 

FIG. 17-2 Schematic phase diagram in the region of upward gas flow. W = mass flow solids, lh/(h fr) E = fraction voids Pp = particle density, Ih/ft Py= fluid density, Ih/ft Cd = drag coefficient Re = modified Reynolds uum-her. (Zenz and Othmei Fluidization and Fluid Particle Systems, Reinhold, New York, 1960. )... 

Pf = density of fluid within the pores of the solid = pore volume per unit mass of solids... 

Even though the susceptor surface is solid, there is a bulk fluid velocity into the surface that accounts for the mass of solids that are deposited. 

The principal experimental method used to measure the density of a solid is determination of the mass of liquid displaced by a known mass of solid. It is essential that the solid have no appreciable solubility in the liquid, that all occluded air be removed from the solid and that the density of the displacement fluid be less than that of the solid lest the solid float. Densities of crystalline solids also can be determined from the dimensions of the unit cell. Davis and Koch discuss other methods for measuring the density of liquids and solids such as hydrostatic weighing of a buoy and flotation methods. 

When a solid acts as a catalyst for a reaction, reactant molecules are converted into product molecules at the fluid-solid interface. To use the catalyst efficiently, we must ensure that fresh reactant molecules are supplied and product molecules removed continuously. Otherwise, chemical equilibrium would be established in the fluid adjacent to the surface, and the desired reaction would proceed no further. Ordinarily, supply and removal of the species in question depend on two physical rate processes in series. These processes involve mass transfer between the bulk fluid and the external surface of the catalyst and transport from the external surface to the internal surfaces of the solid. The concept of effectiveness factors developed in Section 12.3 permits one to average the reaction rate over the pore structure to obtain an expression for the rate in terms of the reactant concentrations and temperatures prevailing at the exterior surface of the catalyst. In some instances, the external surface concentrations do not differ appreciably from those prevailing in the bulk fluid. In other cases, a significant concentration difference arises as a consequence of physical limitations on the rate at which reactant molecules can be transported from the bulk fluid to the exterior surface of the catalyst particle. Here, we discuss... 

The solids concentration can be expressed in terms of either the solids volume fraction (mass ratio of solids to fluid (R). If volume fraction of solids in the feed stream (flow rate gf) and (pu is the volume fraction of solids in the underflow (flow rate gu), then the solids ratio in the feed, Rf = [(mass of solids)/(mass of fluid)]feed, and in the underflow, Ru = [(mass of solids)/(mass of liquid)]u, are given by... 

Gamson B. W., Heat and Mass Transfer in a Fluid Solid System, Chem. Eng. Progress, 47(1) 19-28 (1951)... 

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve very slow binding steps. In these cases, the mass-transfer parameter k is replaced... 

G, G> Mass flowrate per unit cross sectional area of fluid, solid kg/m2s ML-2 -1... 

In the laboratory experiments of Seyfried et al. (1998), naturally altered sea floor basalt (5 Li = +7.4) was reacted with Li-free alkali-chloride aqueous fluid at 350°C for 890 hours (initial fluid/solid mass ratio 2). Samples of the fluid were taken throughout the experiment, and showed initial rapid influx of isotopically heavy-enriched Li released by early-dissolving alteration minerals. However, with progressive reaction, isotopic composition of the fluid decreased and Li concentration reaehed apparent steady state. Although an equilibrium model applies best to the synthetic results, Rayleigh distillation was considered most likely to apply in hydrothermal reactions occurring in nature. 

The thermochemical conversion of biofuels takes place in the conversion system and belongs to the science of two-phase phenomena (fluid-solid dynamics), that is, heat and mass transport processes take place inside and between a solid phase and a gas phase. This phenomenology is well illustrated by Balakrishnen and Pei [49], see Figure 40. 

The long-term goal in the science of thermochemical conversion of a solid fuel is to develop comprehensive computer codes, herein referred to as a bed model or CFSD (computational fluid-solid dynamics). Firstly, this CFSD code must be able to simulate basic conversion concepts, with respect to the mode, movement, composition and configuration of the fuel bed. The conversion concept has a great effect on the behaviour of the thermochemical conversion process variables, such as the molecular composition and mass flow of conversion gas. Secondly, the bed model must also consider the fuel-bed structure on both micro- and macro-scale. This classification refers to three structures, namely interstitial gas phase, intraparticle gas phase, and intraparticle solid phase. Commonly, a packed bed is referred to as a two-phase system. 

Based on unit mass of solid in fluid-solid systems,... 

In the case of two fluids, two films are developed, one for each fluid, and the corresponding mass-transfer coefficients are determined (Figure 3.2). In a fluid-solid system, there is only one film whereas the resistance within the solid phase is expressed by the solid-phase diffusion coefficient, however, in many cases an effective mass-transfer coefficient is used in the case of solids as well. Consider the irreversible catalytic reaction of the form... 

In fluidized beds, mass transfer involves two different mechanisms. The first one is the ordinary mass transport between the fluid and the solid. The treatment of this type of transport is quite similar to fluid-solid mass transfer found in other types of operations such as fixed beds and agitated tank reactors. This mechanism of mass transfer is not always significant in fluidized beds and can be totally neglected in some cases. 

Fluid-solid mass and heat transfer in particulate fluidization... 

Here, qmax is in mass of solute per unit mass of solid and CQ is in mass of solute per unit volume of fluid. For practical use, the infinite series IA and IB are shown in Figure 4.25. 

Why adsorption, ion exchange and heterogeneous catalysis in one book The basic similarity between these phenomena is that they all are heterogeneous fluid-solid operations. Second, they are all driven by diffusion in the solid phase. Thus, mass transfer and solid-phase diffusion, rate-limiting steps, and other related phenomena are common. Third, the many aspects of the operations design of some reactors are essentially the same or at least similar, for example, the hydraulic analysis and scale-up. Furthermore, they all have important environmental applications, and more specifically they are all applied in gas and/or water treatment. 

It should be noted that the introduction of fluid/solid interaction has no effect on the macroscopic equations since F2jt exists only at the fluid/solid interface. The relaxation time, tk, is estimated based on the viscosity and mass density representations given by Eqs. (20) and (21) of the Mi component and is detailed in Ref. [37, 43, 44], This model has been shown to satisfy Galilean invariance.44 Furthermore, in this interparticle potential model, the separation of a two-phase fluid into its components is automatic.37... 

The various volumetric mass-transfer coefficients are defined in a manner similar to that discussed for gas-liquid and fluid-solid mass transfer in previous sections. There are a large number of correlations obtained from different gas-liquid-solid systems. For more details see Shah (Gas-Liquid-Solid Reactor Design, McGraw-Hill, 1979), Ramachandran and Chaudhari (Three-Phase Catalytic Reactors, Gordon and Breach, 1983), and Shah and Sharma [Gas-Liquid-Solid Reactors in Carberry and Varma (eds.), Chemical Reaction and Reactor Engineering, Marcel Dekker, 1987],... 

A special type of fluid-solid catalyzed reaction is obtained when either the reaction rate is so fast that the reactants become completely exhausted at the external catalyst surface (i.e. at very high reaction temperatures) or when the catalyst is nonporous. Then, pore diffusion and effective heat conduction inside the pellet need not be considered. Thus, the problem is reduced to a treatment of the coupled interphase heat and mass transport. 

To use the various criteria given in the previous section, some experimental data on the reacting system are necessary. These are the effective diffusivity of the key species in the pores of the catalyst, the heat and mass transfer coefficients at the fluid-solid interface, and the effective thermal conductivity of the catalyst. The accuracy of some of these parameters, which are usually obtained from known correlations, may sometimes be subject to question. For example, under labo-... 

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