Fluid-solid reactors relations

In this chapter, we develop matters relating to the process design or analysis of reactors for fluid-solid noncatalytic reactions that is, for reactions in which the solid is a reactant. To construct reactor models, we make use of ... 

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. 

In bubble columns and gas-liquid stirred reactors, the estimation of parameters is more difficult than in gas-solid or liquid-solid fluidized beds. Solid particles are rigid, and hence the fluid-solid interface is nonde-formable, whereas the gas-liquid interface is deformable. In addition, the effect of surface-active agents is much more pronounced in the case of gas-liquid interfaces. This leads to uncertainties in the prediction of all major parameters, such as the terminal bubble rise velocity, the bubble diameter, the gas holdup, and the relation between the bubble diameter and the terminal bubble raise velocity. 

It is well known that during liquefaction there is always some amount of material which appears as insoluble, residual solids (65,71). These materials are composed of mixtures of coal-related minerals, unreacted (or partially reacted) macerals and a diverse range of solids that are formed during processing. Practical experience obtained in liquefaction pilot plant operations has frequently shown that these materials are not completely eluted out of reaction vessels. Thus, there is a net accumulation of solids within vessels and fluid transfer lines in the form of agglomerated masses and wall deposits. These materials are often referred to as reactor solids. It is important to understand the phenomena involved in reactor solids retention for several reasons. Firstly, they can be detrimental to the successful operation of a plant because extensive accumulation can lead to reduced conversion, enhanced abrasion rates, poor heat transfer and, in severe cases, reactor plugging. Secondly, some retention of minerals, especially pyrrhotites, may be desirable because of their potential catalytic activity. 

The performance of a reactor for a fluid (A) + solid (B) reaction may be characterized by /B obtained for a given feed rate (FBo) and size of reactor the latter is related to the holdup (WB) of solid in the reactor, whether the process is continuous or batch (fixed... 

After introducing some types of moving-particle reactors, their advantages and disadvantages, and examples of reactions conducted in them, we consider particular design features. These relate to fluid-particle interactions (extension of the treatment in Chapter 21) and to the complex flow pattern of fluid and solid particles. The latter requires development of a hydrodynamic model as a precursor to a reactor model. We describe these in detail only for particular types of fluidized-bed reactors. 

The design of a reactor is connected to certain preferred parameters and it is useful to know how they are related to each other. For instance, it is very important to use the appropriate terms in order to conelate the reactor volume to the fluid and solid volumes. In Table 3.1, the most important ratios per reactor are presented. VR denotes the total volume of the reactor, Vs denotes the volume of the solid, and VL is the fluid volume in two-phase systems and the liquid-volume in three phase systems. 

Except for continuous weighing, control of the flow of solids is less precise than that of fluids. Several devices used for control of feed rates are shown schematically in Figure 3.7. They all employ variable speed drives and are individually calibrated to relate speed and flow rate. Ordinarily these devices are in effect manually set, but if the solid material is being fed to a reactor, some property of the mixture could be used for feed back control. The continuous belt weigher is capable ordinarily of 1% accuracy and even 0.1% when necessary. For processes such as neutralizations with lime, addition of the solid to process in slurry form is acceptable. The slurry is prepared as a batch of definite concentration and charged with a pump under flow control, often with a diaphragm pump whose stroke can be put under feedback control. For some applications it is adequate or necessary to feed weighed amounts of solids to a process on a timed basis. 

A number of industrial reactors involve contact between a fluid (either a gas or a liquid) and solids. In these reactors, the fluid phase contacts the solid catalyst which may be either stationary (in a fixed bed) or in motion (particles in a fluidized bed, moving bed, or a slurry). The solids may be a catalyst or a reactant (product). Catalyst and reactor selection and design largely depend upon issues related to heat transfer, pressure drop and contacting of the phases. In many cases, continuous regeneration or periodic replacement of deteriorated or deactivated catalyst may be needed. 

The second major reactor type that requires much further quantification is the fluid-bed chemical reactor, which is of tremendous industrial importance, as indicated by Table 1. A related reactor is the fluid-bed combustor that is employed for combustion of relatively coarse solids with reduced emissions. 

For a conventional mechanically agitated biological reactor, the information provided for aqueous gas-liquid and gas-liquid-solid systems in Sections II, III, and VII is applicable here. For power consumption, the most noteworthy works are those by Hughmark (1980) (see Eqs. (6.15) and (6.16)) and Schiigerl (1981). For gas-liquid mass transfer, the relationship kLaL = (P/V, ug) is applicable for biological systems. The relationships (6.19) and (6.20) are also valuable, and their use is recommended. The most generalized relation for kLaL is provided by Eq. (6.18). The intrinsic gas-liquid mass transfer coefficient is best estimated by Eq. (6.23). For liquid-solid mass transfer, the use of the study by Calderbank and Moo-Young (1961) (Eqs. (6.24)-(6.26)) is recommended. For viscous fluids, Eq. (6.27) should be used. 

Ergun [25] developed a useful pressure drop equation caused by simultaneous kinetic and viscous energy losses and applicable to all types of flow. Ergun s equation relates the pressure drop per unit of bed depth to dryer or reactor system characteristics, such as, velocity, fluid gravity, viscosity, particle size, shape, surface of the granular solids and void fraction. The original Ergun equation is ... 

When concentration polarization occurs, permeate fluxes become invariant with the transmembrane pressure, and increases in the permeation rate can be achieved only by enlarging the membrane surface area or by improved fluid management. The design of the UF membrane unit in the polarized regime must relate the flux to the optimal level of reactor VSS or total suspended solids (TSS) according to Michaels gel theory, to give... 

This section deals with problems that bear considerable relation to those dealt with in Chapter 11 on fixed bed catalytic reactors with a single fluid phase, the main difference being in the hydrodynamics, because of the existence of two fluid phases. In addition, the mass and heat transfer phenomena are more complex, since resistances in the gas phase, the liquid phase, and the solid catalyst, where the reaction takes place, have to be considered. Figure 14.3.b-l illustrates concentration and partial pressure profiles around a catalyst particle and defines the notation. A is the reacting component of the gas phase, B that of the liquid phase. 

The latter model type describes the experimentally determined relations between dependent and independent variables with the help of statistical methods and neglects the known physicochemical relations. Such models are primarily used on reactor types difficult to describe deterministically. The cell models are composed of specific networks of mixing cells (e.g. stirred reactor cascades) or of combinations of mixing cells and transport cells (ideal tube reactors). The so-called continuum models, however, handle each phase as a continuum. The continuum models are further distinguished as homogeneous and heterogeneous reactor models. In the heterogeneous reactor model, the fluid phases and the solid phase (catalyst) are considered and mathematically described as individual items. 

MSRs have numerous potential advantages over solid fuel reactors. Most benefits relate to the fluid nature of the fuel form. It is this fluid nature which at first may be a point of concern for those solely familiar with solid fuels. The listed benefits below will of course vary between MSR concepts but are generally universal in nature. 

Thus as the interstitial, linear velocity of the bulk fluid increases, 6 decreases. And, as 6 decreases, reactant and product molecules spend less time traversing the stagnant film surrounding each solid-supported catalyst pellet, which increases Aroveraii- We can relate 6 to since the fluid density, fluid viscosity, and reactor diameter remain constant during the velocity change. Thus... 

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