Batch reactor description

The reactions are still most often carried out in batch and semi-batch reactors, which implies that time-dependent, dynamic models are required to obtain a realistic description of the process. Diffusion and reaction in porous catalyst layers play a central role. The ultimate goal of the modehng based on the principles of chemical reaction engineering is the intensification of the process by maximizing the yields and selectivities of the desired products and optimizing the conditions for mass transfer. 

A detailed description of hardware, software and mathematical analysis of the computer controlled batch reactor system is... 

In this chapter the simulation examples are presented. They are preceded by a short description of simulation tools and the MADONNA program in particular. As seen from the Table of Contents, the examples are organised according to thirteen application areas Batch Reactors, Continuous Tank Reactors, Tubular Reactors, Semi-Continuous Reactors, Mixing Models, Tank Flow Examples, Process Control, Mass Transfer Processes, Distillation Processes, Heat Transfer, Biological Process Examples and Environmental Process Examples. There are aspects of some examples that make them relevant to more than one application area, and this is usually apparent from their titles. Within each section, the examples are listed in order of their degree of difficulty. 

A set of first order differential equations descriptive of the molar concentrations for polymeric species is given. Species, less than size n, are saturated and, therefore, accmulate only within the batch reactor and do not participate in branch/cross-llnk reactions. Molecules greater in size than n are unsaturated and will experience the reaction described by branch formation. 

Glaze, H.W. and Kang, J.W., Advanced oxidation process. Description of a kinetics model for the oxidation of hazardous materials in aqueous media with ozone and hydrogen peroxide in a semi-batch reactor, Ind. Eng. Chem. Res,. 28, 1573-1579, 1989a. 

Equations 7.4 and 7.5 form a system of differential equations for which no analytical solution is known. Thus, the description of the behavior of the semi-batch reactor with time requires the use of numerical methods for the integration of the differential equations. Usually, it is convenient to use parameters which are more process-related to describe the material balance. One is the stoichiometric ratio between the two reactants A and B ... 

Briggs and Haldane [8] proposed a general mathematical description of enzymatic kinetic reaction. Their model is based on the assumption that after a short initial startup period, the concentration of the enzyme-substrate complex is in a pseudo-steady state (PSS). For a constant volume batch reactor operated at constant temperature T, and pH, the rate expressions and material balances on S, E, ES, and P are... 

Although the yields and total growth rate are useful parameters, it is the state variables like the concentrations of biomass, substrate and product, and the culture parameters like the specific rates of growth, substrate uptake, etc., that provide a complete description of the bioreactor. One attempt in estimating these variables from R and the yields consisted of integrating the governing differential equation with known initial conditions and the measured values for R and the yields (9). For a batch reactor, for example, b was estimated by integrating... 

When such a stirring is absolutely absent in a continuous flow system, as it takes place in the piston reactor (PR), regularities of the batch processes with the same residence time 0 are realized. This implies that in order to describe copolymerization in continuous PR one can apply all theoretical equations known for a common batch process having replaced the current time t for 0. As for the equations presented in Sect. 5.1, which do not involve t al all, they remain unchanged, and one can employ them directly to calculate statistical characteristics of the products of continuous copolymerization in PR. It is worth mentioning that instead of the initial monomer feed composition x° for the batch reactor one should now use the vector of monomer feed composition xin at the input of PR. In those cases where copolymer is being synthesized in CSTR a number of specific peculiarities inherent to the theoretical description of copolymerization processes arises. 

In this section, we attack the problem of kinetics in multicomponent mixtures, and we dedicate attention mostly to the case where one is only interested in, or may only be able to determine experimentally, some overall concentration of species of a certain class, such as sulfurated compounds in an oil cut during a hydrodesulfurization process. The presentation is given in terms of a continuous description special cases of the corresponding discrete description are discussed as the need arises. Instead of working with the masses of individual species, we will work with their mass concentration distribution c x). In the case of a batch reactor, the distinction is irrelevant, but in the case of a plug flow reactor the concentration-based description is clearly preferable. The discussion is presented in purely kinetic terms for, say, a batch reactor. 

We now move to the general case of a continuous description the pragmatical usefulness of such a type of description in real-life kinetic problems has been discussed by Krambeck (1991a,b). Let c(x,0) be the initial distribution of reactant concentrations in the batch reactor, and let c(x,t) be the concentration distribution at any subsequent (dimensional) time t. We assume that both the label x and the concentration c have already been normalized so that = = 1. Furthermore, we assume that a (dimensional) frequency factor k(x) can be identified, and that x has been normalized so that k(x) = k x, where k is the average value of k(x) at r = 0. One then normalizes the time scale as well by defining the dimensionless time t as k t. The overall concentration C(t) is defined with a weighting function that is identical to unity, C(t) = , 0(0) = 1. 

The question that arises is that of the description of the intrinsic kinetics, that is, of the constitutive equation for c,(x,t) in a batch reactor (we indicate partial derivatives with a subscript). Special cases that have been dealt with in the literature are discussed later. 

The description of the nonisothermal batch reactor then involves Equation (9.3.1) and either Equation (9.3.9) or (9.3.11) for nonisothermal operation or Equation (9.3.12)... 

A 800 g sample of the milled wood was pyro lysed in a batch reactor under vacuum run G72). A detailed description of the batch pyrolysis reactor system used in this work has been described elsewhere. Two vacuum pumps in series were used to achieve a total pressure of 0.7 kPa and three dry-ice-in-limonene condensers ( 72 C) were used to trap the pyrolysis vapours. When the maximum pyrolysis temperature was reached, it was held for I hour prior to cooling to room temperature. After the pyrolysis in each step, the system was kept under nitrogen until the next pyrolysis step was started. Each pyrolysis step was carried out by using the solid residue from the previous step. Table 1 shows the different pyrolysis steps and product yields. The pyrolysis oils which were... 

Conditions (1) and (2) imply that, from the point of view of the mathematical description, the circulating system will behave as a stirred batch reactor. Then, the initial rate of reaction, v0, in the reactor is... 

We shall recapitulate the governing equations in the next section and discuss the economic operation in the one following. The results on optimal control are essentially a reinterpretation of the optimal design for the tubular reactor. We shall not attempt a full derivation but hope that the qualitative description will be sufficiently convincing. The isothermal operation of a batch reactor is completely covered by the discussion in Chap. 5 of the integration of the rate equations at constant temperature. The simplest form of nonisothermal operation occurs when the reactor is insulated and the reaction follows an adiabatic path the behavior of the reactor is then entirely similar to that discussed in Chap. 8. 

For non-isothermal or non-linear chemical reactions, the RTD no longer suffices to predict the reactor outlet concentrations. From a Lagrangian perspective, local interactions between fluid elements become important, and thus fluid elements cannot be treated as individual batch reactors. However, an accurate description of fluid-element interactions is strongly dependent on the underlying fluid flow field. For certain types of reactors, one approach for overcoming the lack of a detailed model for the flow field is to input empirical flow correlations into so-called zone models. In these models, the reactor volume is decomposed into a finite collection of well mixed (i.e., CSTR) zones connected at their boundaries by molar fluxes.4 (An example of a zone model for a stirred-tank reactor is shown in Fig. 1.5.) Within each zone, all fluid elements are assumed to be identical (i.e., have the same species concentrations). Physically, this assumption corresponds to assuming that the chemical reactions are slower than the local micromixing time.5... 

Figure l-Sfb) Batch reactor mixing patterri.s. Further descriptions and photos of the batch reactors can he found in both the Visual Encyclopedia of Eguipnieal and in the Pm/essional Reference Shelf on the CD-ROM. 

Equations 14.2-3 and 14.2-4 bear a striking resemblance to the mass and energy balances for a batch reactor, Eqs. 14.1-13 and 14. There is, in fact, good physical reason why these equations should look very much alike. Our model of a plug-flow reactor, which neglects diffusion and does not allow for velocity gradients, assumes that each element of fluid travels through the reactor with no interaction with the fluid elements before or after it Therefore, if we could follow a small fluid element in a tubular reactor, we would find that it had precisely the same behavior in time as is found in a batch reactor. This similarity in the physical situation is mirrored in the similarity of the descriptive equations. 

For the batch reactor of Example 1.3, the qualitative control objective is the maximization of the profit. The quantitative description of this objective is rather complex. It requires the solution of a maximization problem, which will yield the value of the steam flow rate, Q(t), at each instant during the reaction period. 

The rate equations of Chapter 1 were given, for the most part, as they pertain to homogeneous batch reactions. While the purpose there was to treat descriptive kinetics, the results obtained pertain also to the operation of homogeneous batch reactors. One of the features of such a reactor was said to be that all the molecules in the reactor at a given time of reaction had been there for the same amount of time in other words, they had the same age. A second feature implied in the treatment was the intimate association, on a molecular scale, of all species contained in the reactor. 

For each phase of the growth cycle, we first provide a qualitative description of the biological phenomena involved in that phase in a stirred-tank reactor and then indicate how one can quantitatively characterize both the number of viable microorganisms present in this batch reactor and the rates at which products are created during the normal course of events. 

---