Solid/fluid systems

The area of colloids, surfactants, and fluid interfaces is large in scope. It encompasses all fluid-fluid and fluid-solid systems in which interfacial properties play a dominant role in determining the behavior of the overall system. Such systems are often characterized by large surface-to-volume ratios (e.g., thin films, sols, and foams) and by the formation of macroscopic assembhes of molecules (e.g., colloids, micelles, vesicles, and Langmuir-Blodgett films). The peculiar properties of the interfaces in such media give rise to these otherwise unlikely (and often inherently unstable) structures. 

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

A reactor model based on solid particles in BMF may be used for situations in which there is deliberate mixing of the reacting system. An example is that of a fluid-solid system in a well-stirred tank (i.e., a CSTR)-usually referred to as a slurry reactor, since the fluid is normally a liquid (but may also include a gas phase) the system may be semibatch with respect to the solid phase, or may be continuous with respect to all phases (as considered here). Another example involves mixing of solid particles by virtue of the flow of fluid through them an important case is that of a fluidized bed, in which upward flow of fluid through the particles brings about a particular type of behavior. The treatment here is a crude approximation to this case the actual flow pattern and resulting performance in a fluidized bed are more complicated, and are dealt with further in Chapter 23. 

The grade efficiency reflects the properties of the particles exploited in the separation. It is influenced by the nature of the fluid/solid system, and by the operating conditions which determine the magnitude of the separating effect, and the period during which particles are subjected to it. Such details should, therefore, accompany any experimental data on G(d). The concept is widely applied to separations using hydrocyclones as discussed in Section 1.5.4. 

Commonly, the fuel-bed system of PBC systems is referred to as a fixed bed [11,19]. However, this classification refers to the interparticle distance (bed expansion) in the fluid-solid (bed) system as a function of air velocity, according to the classification by Kunii and Levenspiel [36]. Figure 25 shows the classification of updraft fluid-solid systems with respect to bed expansion as function of air velocity. 

Figure 25 The classification of fluid-solid systems with respect to bed expansion as function of air velocity [36]...

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

The concept of micro- and macrofluids is of particular importance in heterogeneous systems because one of the two phases of such systems usually approximates a macrofluid. For example, the solid phase of fluid-solid systems can be treated exactly as a macrofluid because each particle of solid is a distinct aggregate of molecules. For such systems, then, Eq. 2 with the appropriate kinetic expression is the starting point for design. 

Batch Operations. The reaction and dissolution of a batch of solid in a batch of fluid, such as the acid attack of a solid, is a common example of batch operations. Analysis and design of fluid-solid systems are greatly simplified if the composi-... 

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... 

The above analysis and Fig. 19-25 provide a theoretical foundation similar to the Thiele-modulus effectiveness factor relationship for fluid-solid systems. However, there are no generalized closed-form expressions of E for the more general case ofa complex reaction network, and its value has to be determined by solving the complete diffusion-reaction equations for known intrinsic mechanism and kinetics, or alternatively estimated experimentally. 

Lee, C. H. Holder, G. D., Use of Supercritical Fluid Chromatography for Obtaining Mass Transfer Coefficients in Fluid-Solid Systems at Supercritical Conditions, Ind. Eng. Chem. Res., 1995, 34, 906-914... 

In fluid-solid systems the interparticle gradients - between the external surface of the particle and the adjacent bulk fluid phase - may be more serious, because the effective thermal conductivity of the fluid may be much lower than that of the particle. For the interparticle situation the heat transfer resistances, in general, are more serious than the interparticle mass transfer effects they may become important if reaction rates and reaction heats are high and flow rates are low. Hie usual experimental test for interparticle effects is to check the influence of the flow rate on the conversion while maintaining constant the space velocity or residence time in the reactor. This should be done over a wide range of flow rates and the conversion should be measured very accurately. 

Fluid-solid systems, especially in situations where the fluid is a gas, are very frequently encountered in various important industrial processes such as packed-bed reactors, moving-bed reactors, fluidized-bed reactors, and entrained reactors. 

We will now stop and consider reactor design for a fluid-solid system with decaying catalyst. To analyze these reactors we only add one step to our algoritlhm, that is, determine the catalyst decay law. The sequence is shown below. 

The mesoscale models for momentum transfer between phases differ quite substantially depending on the multiphase system under investigation, and different semi-empirical relationships have been developed for different systems. Since the nature of the disperse phase is particularly important, the available mesoscale models are generally divided into those valid for fluid-fluid and those valid for fluid-solid systems. The main difference is that in fluid-fluid systems the elements of the disperse phase are deformable particles (i.e. bubbles or droplets), whereas in fluid-solid systems the disperse phase is constituted by particles of constant shape. Typical fluid-fluid systems for which the mesoscale models reported below apply are gas-liquid, liquid-liquid, and liquid-gas systems. The mesoscale models reported for fluid-solid systems are valid both for gas-solid and for liquid-solid systems. As a general rule, the mesoscale model for Afp should be derived starting from a single-particle momentum balance ... 

Summarizing the forces introduced above, tests carried out in different multiphase systems have shown that the order of importance of the different forces involved typically ranks buoyancy and drag in the first positions and then lift and virtual-mass forces for fluid-solid systems and virtual-mass and lift forces for fluid-fluid systems (see, for example, the studies on non-drag forces by Diaz et al (2008) and Barton (1995)), whereas the most common values for the corresponding constants are Cl = 0.25 and Cv = 0.5 both for fluid-fluid and for fluid-solid systems. Naturally, since it is straightforward to implement all the forces in a computational code (Vikas et al, 201 lb), it is best to include them all for the sake of generality. 

Symposium on Dynamics of Fluid Solid Systems, Ind. Eng. Chem. 41, 1099... 

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