Mixing ideal

The thermodynamics of relatively ideal mixed films can be approached as follows. It is convenient to define... 

Figure 8.1 The entropy of mixing (in units of R) as a function of mole fraction solute for ideal mixing and for the Flory-Huggins lattice model with n = 50, 100, and 500. Values are calculated in Example 8.1.

Reac tors that are nominally CSTRs or PFRs may in practice deviate substantially from ideal mixing or nonmixing. This topic is developed at length in Sec. 23, so only a few summary statements are made here. More information about this topic also may be found in Nauman and Buffham (Mixing in Continuous Flow Systems, Wiley, 1983). 

Real reactors may conform to some sort of ideal mixing patterns, or their performance may be simulated by combinations of ideal models. The commonest ideal models are the following ... 

The intensity funetion of two or more identieal, ideally mixed vessels in series starts from the origin and inereases monotonieally to an asymptotie value (A —> n), whieh is equal to the number of vessels. 

An Excel spreadsheet (Example8-7.xls) was used to determine the various RTD functions and the computer program PROGS 1 was used to simulate the model response curve with the experimental data. The results show the equivalent number of ideally mixed stages (nCSTRs) for the RTD is 13.2. The Gamma distribution function from Equation 8-143 is ... 

This result is nearly equal to 4.87 J K hmoT. the value that would be calculated for the entropy of mixing to form an ideal solution. We will show in Chapter 7 that the equation to calculate AmixSm for the ideal mixing process is the same as the one to calculate the entropy of mixing of two ideal gases. That is. AmixSm = -R. Vj ln.Yj. 

Establish ideal flow patterns This is usually assumed to be the case for plug-flow and continuously stirred tank reactors, but are all conditions for ideal mixing fulfilled For example, a rule of thumb is that the diameter d of the PFR should be at least lOx the diameter of the catalyst particles to eliminate the influence of the reactor wall. Also, the amount of catalyst should be sufficient to avoid axial gradients. Another rule is that the ratio of the bed length L to the reactor diameter d, i.e. L/d, should be >5-10. Higher values are preferable, but these may cause other problems such as temperature gradients and pressure drops. 

In a certain range of process conditions, column reactors for multiphase processes behave as a tubular reactor with respect to gaseous reactants and as an ideally mixed tank reactor with respect to condensed phases. 

CSTR steady-state V / ji r j F V.our Ci F V.in Cijn Ideal mixing assumed... 

Semibatch reactors are often used to mn highly exothermic reactions isothermally, to run gas-liquid(-solid) processes isobarically, and to prevent dangerous accumulation of some reactants in the reaction mixture. Contrary to batch of)eration, temperature and pressure in semibatch reactors can be varied independently. The liquid reaction mixture can be considered as ideally mixed, while it is assumed that the introduced gas flows up like a piston (certainly this is not entirely true). Kinetic modelling of semibatch experiments is as difficult as that of batch, non-isotherma experiments. 

The mass and energy balance equations for ideally mixed components where zero-order reaction proceeds are ... 

Other model representations of flow mixing cases in chemical reactors are described by Levenspiel (1972), Fogler (1992) and Szekely and Themelis (1971). Simulation tank examples demonstrating non-ideal mixing phenomena are CSTR, NOSTR, TUBMIX, MIXFLO, GASLIQ and SPBEDRTD. 

Zero temperature gradients in the bulk phases (ideal mixing in the boiler). 

Figure 5.112. The fraction conversion for the system, X3, is lower than the ideally-mixed situation, curve X4.

Non-ideal mixing conditions in a reactor can often be modelled by combinations of tanks and tubes. Here, three, stirred tanks are used to simulate the tubular, by-passing condition. 

CAIM = (PO (CAO-CAIM))/Vtot-K CAIM n Ideally-mixed... 

Figure 5.115. Here for second-order reaction the ideally-mixed tank has a larger conversion.

The dispersion coefficients can be increased to observe an approach to ideal mixing, and setting them to zero should give the best performance. 

The module system consists of three ideally mixed sections, separated by two membranes. Overall steady-state balances can be used to check the solution and are as follows ... 

For the melt, Landwehr et al. (2001) adopted a model of ideal mixing of six-oxygen [Al206] units, similar to that of Wood and Blundy (1999) and Blundy et al. (1995) ... 

In practice, it is often possible with stirred-tank reactors to come close to the idealized mixed-flow model, providing the fluid phase is not too viscous. For homogenous reactions, such reactors should be avoided for some types of parallel reaction systems (see Figure 5.6) and for all systems in which byproduct formation is via series reactions. 

Due to the elevated contaminant mass load a contaminant balance also has to be included in the wastewater storage constraints. This is given in constraint (8.54), where the contaminant mass present in a storage vessel at a time point is the contaminant mass from the previous time point and the difference between the contaminant mass entering and exiting the vessel. Each storage vessel is assumed to be ideally mixed, hence the concentration within the vessel is uniform. 

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