Reactor models ideal batch

Often the kinetics of the chemical reaction and whether or not the reaction rate is affected by transport limitation are not known a priori. Lab-scale experimental reactors are structured such that they are operated isothermally and can be described by one of three ideal reactor models (ideal batch, CSTR, and plug flow). Isothermal operation is achieved by providing a large beat-transfer surface and maintaing the reactor in a constant-temperature bath. Experiments are conducted at different initial (or inlet) reactant proportions (to determine the form of the rate expression) and at different temperatures (to determine the activation energy). 

We derived the species-based design equations for three ideal reactor models ideal batch reactor, plug-flow reactor, and CSTR. 

In this chapter the most important operation modes of reactors are considered. Models are developed by combining simple reaction kinetics for single-phase reactions with mass balances for five ideal model reactors the ideal batch reactor the semi-batch reactor the plug flow reactor the perfectly mixed continuous reactor and the cascade of perfectly mixed reactors. For isothermal conditions, conversions can be calculated on the basis of chemical kinetics only. 

As with continuous processes, the heart of a batch chemical process is its reactor. Idealized reactor models were considered in Chapter 5. In an ideal-batch reactor, all fluid elements have the same residence time. There is thus an analogy between ideal-batch reactors and plug-flow reactors. There are four major factors that effect batch reactor performance ... 

A simulation model needs to be developed for each reactor compartment within each time interval. An ideal-batch reactor has neither inflow nor outflow of reactants or products while the reaction is carried out. Assuming the reaction mixture is perfectly mixed within each reactor compartment, there is no variation in the rate of reaction throughout the reactor volume. The design equation for a batch reactor in differential form is from Chapter 5 ... 

In this chapter, we describe several ideal types of reactors based on two modes of operation (batch and continuous), and ideal flow patterns (backmix and tubular) for the continuous mode. From a kinetics point of view, these reactor types illustrate different ways in which rate of reaction can be measured experimentally and interpreted operationally. From a reactor point of view, the treatment also serves to introduce important concepts and terminology of CRE (developed further in Chapters 12 to 18). Such ideal reactor models serve as points of departure or first approximations for actual reactors. For illustration at this stage, we use only simple systems. 

Our treatment of Chemical Reaction Engineering begins in Chapters 1 and 2 and continues in Chapters 11-24. After an introduction (Chapter 11) surveying the field, the next five Chapters (12-16) are devoted to performance and design characteristics of four ideal reactor models (batch, CSTR, plug-flow, and laminar-flow), and to the characteristics of various types of ideal flow involved in continuous-flow reactors. Chapter 17 deals with comparisons and combinations of ideal reactors. Chapter 18 deals with ideal reactors for complex (multireaction) systems. Chapters 19 and 20 treat nonideal flow and reactor considerations taking this into account. Chapters 21-24 provide an introduction to reactors for multiphase systems, including fixed-bed catalytic reactors, fluidized-bed reactors, and reactors for gas-solid and gas-liquid reactions. 

A more quantitative analysis of the batch reactor is obtained by means of mathematical modeling. The mathematical model of the ideal batch reactor consists of mass and energy balances, which provide a set of ordinary differential equations that, in most cases, have to be solved numerically. Analytical integration is, however, still possible in isothermal systems and with reference to simple reaction schemes and rate expressions, so that some general assessments of the reactor behavior can be formulated when basic kinetic schemes are considered. This is the case of the discussion in the coming Sect. 2.3.1, whereas nonisothermal operations and energy balances are addressed in Sect. 2.3.2. 

In Chaps. 5 and 6 model-based control and early diagnosis of faults for ideal batch reactors have been considered. A detailed kinetic network and a correspondingly complex rate of heat production have been included in the mathematical model, in order to simulate a realistic application however, the reactor was described by simple ideal mathematical models, as developed in Chap. 2. In fact, real chemical reactors differ from ideal ones because of two main causes of nonideal behavior, namely the nonideal mixing of the reactor contents and the presence of multiphase systems. 

The principles and methods of scale-up can be applied to chemical reactors. In the absence of significant thermal effects, i.e., when the ratio <2r/ Vr may be considered negligible, ideal batch reactors do not show any problem of scale-up, because the volume Vr does not appear in the mathematical model (2.17), so that their performance is only determined by chemical kinetics (see Sect. 2.3). On the contrary, a very complex behavior is expected for real reactors in fact, this behavior cannot be analyzed in terms of mathematical models, and the design procedures must be largely based on semi-empirical rules of scale-up. 

The state of mixing in a given reactor can be evaluated by RTD experiments by means of inert tracers, by temperature measurements, by flow visualization and, finally, by studying in the reactor under consideration the kinetics of an otherwise well-known reaction (because its mechanism has been carefully elucidated from experiments carried out in an ideal reactor, the batch reactor being generally chosen as a reference for this purpose). From these experimental results, a reactor model may be deduced. Very often, in the laboratory but also even in industrial practice, the real reactor is not far from ideal or can be modelled successfully by simple combinations of ideal reactors this last approach is of frequent use in chemical reaction engineering. But... 

Equation (7-60) is identical to that of the ideal batch reactor, Eq. (7-47), and the two reactor systems can be modeled in identical fashion. 

Reactors may be divided into three simple, idealized model categories batch reactor, tubular or plug flow reactor, and the continuous stirred tank reactor (CSTR). 

Hot spring pools are usually well stirred by thermal convection and rising gas bubbles, so they can be modeled as ideal batch reactors and the volume of water in the pool can be determined using a tracer spike. 

The first step in developing a mass balance model is to compute the difference in the concentration of each element between the final and initial solution. In an ideal batch reactor this difference is the result of reactions between the solution and the solid phases. The next step is to postulate reactions that might have caused those changes in the solution composition and to construct a set of linear equations to represent the effect of each reaction. Finally, the linear equations are solved to determine the extent of each of the reactions that must have occurred. If a reasonable solution is not found, the postulated reactions are revised imtil a fit is found between the reactions and the changes in solution chemistry. This means that the model may not produce a unique fit to the data. 

We consider the TAP reactor as a basic kinetic device for systematic studies of reaction-diffusion systems. In this chapter, we are going to (i) present and analyze models of different TAP configurations with a focus on their possibilities with respect to characterizing active materials and unraveling complex mechanisms, and (ii) demonstrate relationships between TAP models and other basic reactor models, that is, models for the ideal continuous stirred-tank reactor (CSTR), batch reactor (BR) and plug-flow reactor (PER). In some situations, the TZTR can be considered a simple building block for constracting the various models. 

Ideal reactors have idealized flow patterns. Four cases are important, the uniformly mixed batch reactor, the plug flow reactor (PFR), the continuous stirred tank reactor (CSTR), and a cascade of CSTRs. Real reactors are arbitrarily complicated, but can be regarded as composed of elements of ideal reactors. Modeling is possible, if we know how to account for non-ideal flow. 

In all three models the rate of mixing of the reactants is assumed not to influence the rate of the chemical reactions. In the ideal batch reactor, the reactants are mixed before they react in the plug flow reactor the reactants are mixed immediately with each other, and in the perfectly mixed CSTR the entering reactants are mixed immediately with the reactor contents. In addition we present two other reactor models that approach reactor types that are frequently used in practice ... 

In this chapter we have made the jump from molecular models to reactor models. These were developed for various operation modes, batch, semi-batch, continuous with plug flow, continuous and well mixed and a cascade of continuous well mixed reactors. Each reactor model was based on a combination of mass balances and equations for chemical kinetics. These were all models of ideal reactors therefore the modelling was uncomplicated and quite straightforward. The reactor models are called "ideal" because of the following assumptions ... 

The hquid-phase chlorination of benzene is an ideal example of a set of sequential reactions with varying rates from the single-chlorinated molecule to the completely chlorinated molecule containing six chlorines. Classical papers have modeled the chlorination of benzene through the dichlorobenzenes (14,15). A reactor system may be simulated with the relative rate equations and flow equation. The batch reactor gives the minimum ratio of... 

Reactor design usually begins in the laboratory with a kinetic study. Data are taken in small-scale, specially designed equipment that hopefully (but not inevitably) approximates an ideal, isothermal reactor batch, perfectly mixed stirred tank, or piston flow. The laboratory data are fit to a kinetic model using the methods of Chapter 7. The kinetic model is then combined with a transport model to give the overall design. 

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