Equations tank-type chemical reactor

The Balance Equations for a Tank-Type Chemical Reactor, 779... 

THE BALANCE EQUATIONS FOR A TANK-TYPE CHEMICAL REACTOR... 

The CRE approach for modeling chemical reactors is based on mole and energy balances, chemical rate laws, and idealized flow models.2 The latter are usually constructed (Wen and Fan 1975) using some combination of plug-flow reactors (PFRs) and continuous-stirred-tank reactors (CSTRs). (We review both types of reactors below.) The CRE approach thus avoids solving a detailed flow model based on the momentum balance equation. However, this simplification comes at the cost of introducing unknown model parameters to describe the flow rates between various sub-regions inside the reactor. The choice of a particular model is far from unique,3 but can result in very different predictions for product yields with complex chemistry. 

The various types of reactors employed in the processing of fluids in the chemical process industries (CPI) were reviewed in Chapter 4. Design equations were also derived (Chapters 5 and 6) for ideal reactors, namely the continuous flow stirred tank reactor (CFSTR), batch, and plug flow under isothermal and non-isothermal conditions, which established equilibrium conversions for reversible reactions and optimum temperature progressions of industrial reactions. 

We turn now to consider the principal types of reactors and derive a set of equations for each that will describe the transformation 5 of the state of the feed into the state of the product. The continuous flow stirred tank reactor is one of the simplest in basic design and is widely used in chemical industry. Basically it consists in a vessel of volume V furnished with one or more inlets, an outlet, a means of cooling and a stirrer which keeps its composition and temperature essentially uniform. We shall assume that there is complete mixing on the molecular scale. It would be possible to treat of other cases following the work of Danckwerts (1958) and Zweitering (1959), but the corresponding transformation is much less wieldy. If the reactants flow in and out at a constant rate q, the mean residence time T/g is known as the holding time of the reactor. 

It is possible to express Eq. (3-10) for isothermal operation in simpler forms when assumptions such as constant density are permissible. These will be considered in Chap. 4. The constant-density form of Eq. (3-10) was used in Chap. 2 to calculate rate constants from measured conversions or concentrations as a function of time (see, for example. Sec. 2-7). It is important to recall that we could determine the rate equation for the chemical step from a form of Eq. (3-10) because the reactor is assumed to be an ideal stirred-tank type, with no physical resistances involved. 

For each of the chemical species participating in the mechanism, a mass balance equation must be written. The appropriate form of the mass balance for the specific type of reactor at hand must be used. Two of the most common types of reactors used in industry are the CSTR (continuous stirred tank reactor) and the tubular reactor. The corresponding mathematical models for their idealized forms, based on transport phenomena equations and available in any standard chemical reactor text [17, 18], are the ideal CSTR and the ideal model for the plug flow tubular reactor (PFR). The ideal CSTR model is given by Equation 12.1 ... 

For a basic understanding of chemical reactor design, start with Sections 4.10.1 and 4.10.2, where different ideal and isothermal reactor types are introduced and the respective performance equations are derived. You should then study the behavior of real reactors (non-ideal flow and residence time distribution, Section 4.10.4) and the simplest model to account for deviations of real systems from ideal reactors, the tanks-in-series model (Section 4.10.5). 

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