Material balance expressions batch reactors

Rates of reaction can be expressed in terms of process variables associated with a given reactor type via relationships generated by material balances on that reactor. Because rate measurements are essentially always made in a reactor, a discussion of the rate of reaction can be initiated by considering a well-mixed, closed reactor system typically referred to as a batch reactor. In this system, the advancement of the reaction is measured by the molar extent of reaction, and the reaction rate is equivalent to the rate of change of the molar extent of reaction, i.e.. 

The semibatch reactor is a cross between an ordinary batch reactor and a continuous-stirred tank reactor. The reactor has continuous input of reactant through the course of the batch run with no output stream. Another possibility for semibatch operation is continuous withdrawal of product with no addition of reactant. Due to the crossover between the other ideal reactor types, the semibatch uses all of the terms in the general energy and material balances. This results in more complex mathematical expressions. Since the single continuous stream may be either an input or an output, the form of the equations depends upon the particular mode of operation. 

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... 

Insert the rate expression into batch-reactor material balance. A transient material balance for the NaOH on an isothermal batch reactor becomes (NaOH in) — (NaOH out) + (net NaOH generation) = NaOH accumulation. For this system,... 

Equation (7-54) allows calculation of the residence time required to achieve a given conversion or effluent composition. In the case of a network of reactions, knowing the reaction rates as a function of volumetric concentrations allows solution of the set of often nonlinear algebraic material balance equations using an implicit solver such as the multi variable Newton-Raphson method to determine the CSTR effluent concentration as a function of the residence time. As for batch reactors, for a single reaction all compositions can be expressed in terms of a component conversion or volumetric concentration, and Eq. (7-54) then becomes a single nonlinear algebraic equation solved by the Newton-Raphson method (for more details on this method see the relevant section this handbook). 

Its importance lies in the fact that the changes in composition in a reactor are not haphazard, but are of two distinct kinds. First, there are the advective changes due to material brought into the system or removed from it this may be by forced flow, convection, or diffusion. Second, there is the internal change of composition by reaction this change would be seen in a well-stirred batch reactor, for example, where advection has been deliberately eliminated. The advection will have to be expressed by certain terms in the material balance for a particular reactor, but the reactive changes are common to all types and deserve study first. 

The fed-batch reactor model is commonly built using classical thermal and mass balance differential equations [11], Under isothermal conditions, the material balance for each measured component in the H KR of epichlorohydrin with continuous water addition is expressed by one of the following equations (Eqs. 12-17). These equations can be solved using an appropriate solver package (Lsoda, Ddassl [12]) with a connected optimization module for parameter estimation. 

Section 1.2 developed rate expressions for elementary reactions. These expressions are now combined with the material balances of Section 1.1 to develop reactor design equations, that is, equations to predict final concentrations in a batch reactor or outlet concentrations in a flow reactor. Since reaction rate expressions have units of concentration per time, it may seem that is identical to da/dt. This is true only for... 

For a weU-agitated reactor being used to carry out the culture of a microorganism in a working volume (V) during the feeding stage of fed batch operation, the material balance equation for total mass can be expressed as... 

One way of expressing the material balance on the total mass of snbsirate present in the reactor during the fed batch mode of operation is... 

Because of the similarity between the PFR and the batch reactor, we can by analogy develop an expression of the material balance, which is based on conversion ... 

There are five primary reactor designs based in theory batch, semibatch, continuous-stirred tank, plug flow, and fluidized bed. The operating expressions for these reactors are derived from material and energy balances, and each represents a specific mode of operation. Selected reactor configurations are presented in Fig. 1. 

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