Electrolytic reactor model

The following scheme was suggested as a possible network model to describe a real electrolytic processes. Reactors 1 and 2 are continuous-flow stirred-tank electrolytic reactors (CSTER), reactor 3 is a reactor for the recycling electrolyte and reactor 4 is collector in which no electrolytic process takes place. 

Process models are also important components of reactor control schemes. Kiparissides et al. [17] and Penlidis et al. [16] have used reactor models for control simulation studies. Particle number and size characteristics are the most difficult latex properties to control. Particle nucleation can be very rapid and a strong function of the concentration of free emulsifier, electrolytes and various possible reagent impurities. Hence the control of particle number and the related particle surface areas can be a difficult problem. Even with on-line light scattering, chromatographic [18], surface tension and/or conversion measurements [19], control of nucleation in a CSTR system can be difficult. The use of a pre-made seed or an upstream tubular reactor can be utilized to avoid nucleation in the CSTR and thereby imjHOve particle number control as well as increase the number of particles formed [20-22]. Figures 8.6 and 8.7 illustrate open-loop CTSR systems for the emulsion polymerization of methyl methacrylate with and... 

Let us construct a reactor model that will predict the effects of conversion, current density, and electrolyte circulation rate on the chemical yield and run time of a cell for the production of -anisidine (see Clark et al., 1988 for details). The electrolytic cell used will be assumed to be of the narrow gap filter press type with total recirculation of... 

Recently, our group developed and validated a reactor model suitable for design calculations in a thin-gap single-pass high-conversion electrochemical cell [23, 24). The model is based on electrolyte plug flow and includes electrochemical kinetics and mass transfer limitations. It has been developed for the case of three consecutive electrochemical reactions, with the key product formed by the second reaction, but can easily be modifled in order to be used for other reaction schemes, such as parallel reactions or solvent oxidation. 

An electrolytic reactor or cell is a device in which one or more chemical species are transformed to alternative states with an associated energy change. There are many kinds of reactors selection of an appropriate one is dealt with in Chapter 5. The form a reactor takes depends largely on the number of phases involved and the energy requirements. The size depends on the rate of reaction we shall see that a reactor model can provide important answers about this rate. The reaction rate of an electrolytic reactor is defined by the possible current density, expressed in terms of reaction models in Chapter 3. 

THE PROBLEM Construct a reactor model that will predict the effect of conversion, current density, and electrolyte recirculation rate on the chemical yield and run-time of a pilot plant cell producing p-anisidine. 

Change in the scale of a reactor will change its performance. This calls for suitable allowances in process design knowledge of the probable variation in performance of units on a change of scale is required. For this we need mathematical models supported by key experimental trials. This section describes the procedures necessary to scale up an electrolytic reactor. 

Scale- Up of Electrochemical Reactors. The intermediate scale of the pilot plant is frequendy used in the scale-up of an electrochemical reactor or process to full scale. Dimensional analysis (qv) has been used in chemical engineering scale-up to simplify and generalize a multivariant system, and may be appHed to electrochemical systems, but has shown limitations. It is best used in conjunction with mathematical models. Scale-up often involves seeking a few critical parameters. Eor electrochemical cells, these parameters are generally current distribution and cell resistance. The characteristics of electrolytic process scale-up have been described (63—65). 

The first study on the oxidation of arylmethanes used this reaction as a model to show the general advantages of electrochemical micro processing and to prove the feasibility of an at this time newly developed reactor concept [69]. Several limits of current electrochemical process technology hindered its widespread use in synthetic chemistry [69]. As one major drawback, electrochemical cells stiU suffer from inhomogeneities of the electric field. In addition, heat is released and large contents of electrolyte are needed that have to be separated from the product. 

Filtration of Liquids Depending on the specific electrochemical reactor type, the filtration rate of a liqnid electrolyte throngfi tfie separator should be either high (to secure a convective snpply of snbstances) or very low (to prevent mixing of the anolyte and catholyte). The filtration rate that is attained under the effect of an external force Ap depends on porosity. For a separator model with cylindrical pores, the volnme filtration rate can be calcnlated by Poiseuille s law ... 

The Kolbe electrolysis of acetate to ethane and carbon dioxide was modeled for a parallel-plate reactor. Three zones were considered in the model a turbulent bulk region, and a thin diffusion layer at each electrode [184b]. The same authors describe the electrolysis of gaseous acetic acid in a polymer electrolyte membrane (PEM) reactor. Platinized... 

In this configuration, a CSTER is imbedded between two perfectly-mixed reactors 1 and 3 in the forward loop. As in model A above, electrolyte recycling is represented by a perfectly-mixed reactor 4 in the feedback loop shown in Fig.5.2-3(6). Electrolysis takes place in reactor 2 and the collector is reactor 5. 

For low pressures (a few atmospheres and lower) we can apply the ideal gas model for gases and ideal mixture models for liquids. This formulation is very common in reactor technology. In some cases at higher pressures, the pressure effect on the gas phase is important. A suitable model for these systems is to use an EOS for the gas phase, and an ideal mixture model for liquids. However, in most situations at low pressures the liquid phase is more non-ideal than the gas phases. Then we will rather apply the ideal gas law for the gas phase, and excess properties for liquid mixtures. For polar mixtures at low to moderate pressures we may apply a suitable EOS for gas phases, and excess properties for liquid mixtures. All common models for excess properties are independent of pressure, and cannot be used at higher pressures. The pressure effect on the ideal (model part of the) mixture can be taken into account by the well known Poynting factor. At very high pressures we may apply proper EOS formulations for both gas and liquid mixtures, as the EOS formulations in principle are valid for all pressures. For non-volatile electrol3d es, we have to apply a suitable EOS for gas phases and excess properties for liquid mixtures. For such liquid systems a separate term is often added in the basic model to account for the effects of ions. For very dilute solutions the Debye-Htickel law may hold. For many electrolyte systems we can apply the ideal gas law for the gas phase, as the accuracy reflected by the liquid phase models is low. 

Electrolytic gas evolution can be discussed on two scales of length. The macroscopic or process scale is important to the overall design of equipment and includes modeling the overall distribution of gas in the reactor and the effects of gas bubbles on the gross electrolyte flow pattern. The microscopic scale is where the details of bubble events and their consequences are found. In this review, I concentrate on the latter, microscopic scale. 

From the correlations given above it is also evident that the liquid composition has an important effect on the interfacial area. All other conditions being equal, the area may be a factor 10 larger in electrolytes than in pure liquids. Evidently, the design and scaling up of stirred gas-liquid reactors still relies on model experiments involving the liquids actually used in the reaction. 

Equation 21.51a or b is the design equation for a stirred tank batch reactor with recirculation of electrolyte. It can be solved by combining it with the reaction model given by Equation 21.41 or 21.42 to obtain A as a function of conversion, current density, and other system parameters. The current efficiency can be calculated from and (as in Example 21.1). 

Two model fuel cell reactors, the stirred tank reactor- polymer electrolyte membrane fuel cell and the segmented anode parallel channel fuel cell, have been shown to be effective in the study of PEM fuel cell dynamics. Simplified... 

The leaching model (Figure 2) consists of a number of leaching stages and Thickener 4 , where the ZIC is filtered and recovered. The whole leaching and neutralization circuit is summarised in one reactor for the model. Calcine is leached with spent electrolyte. From this sub-model of Model 1, an accurate estimate could be made for the ount of spent electrolyte required to leach one tonne of calcine. This value will later be used to develop a model for predicting the amoimt of produced ZIC. In addition, unmeasured streams were estimated. 

We use the hydrolysis of A into P and Q as an illustration. Examples are the hydrolysis of benzylpenicillin (pen G) or the enantioselective hydrolysis of L-acetyl amino acids in a DL-mixture, which yields an enantiomerically pure L-amino acid as well as the unhydrolysed D-acetyl amino acid. In concentrated solutions these hydrolysis reactions are incomplete due to the reaction equilibrium. It is evident that for an accurate analysis of weak electrolyte systems, the association-dissociation reactions and the related phase behaviour of the reacting species must be accounted for precisely in the model [42,43]. We have simplified this example to neutral species A, P and Q. The distribution coefficients are Kq = 0.5 and Kp = K = 2. The equilibrium constant for the reaction K =XpXQ/Xj = 0.01, where X is a measure for concentration (mass or mole fractions) compatible with the partition coefficients. The mole fraction of A in the feed (z ) was 0.1, which corresponds to a very high aqueous feed concentration of approximately 5 M. We have simulated the hydrolysis conversion in the fractionating reactor with 50-100 equilibrium stages. A further increase in the number of stages did not improve the conversion or selectivity to a significant extent. Depending on the initial estimate, the calculation requires typically less than five iterations. 

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