Material balance Ideal batch reactor

Consider the ideal batch reactor illustrated in Figure 3.2.1. If it is assumed that the contents of the reactor are perfectly mixed, a material balance on the reactor can be written for a species i as ... 

In an ideal continuous stirred tank reactor, composition and temperature are uniform throughout just as in the ideal batch reactor. But this reactor also has a continuous feed of reactants and a continuous withdrawal of products and unconverted reactants, and the effluent composition and temperature are the same as those in the tank (Fig. 7-fb). A CSTR can be operated under transient conditions (due to variation in feed composition, temperature, cooling rate, etc., with time), or it can be operated under steady-state conditions. In this section we limit the discussion to isothermal conditions. This eliminates the need to consider energy balance equations, and due to the uniform composition the component material balances are simple ordinary differential equations with time as the independent variable ... 

Equations (3-S)-(3-7) are alternative forms of the design equation for an ideal batch reactor with a homogeneous reaction taking place. Despite the somewhat pretentious name, design equations are nothing more than component material balances, i.e., molar balances on i , A , etc. 

The concentration of reactant A in a packet that was in the reactor for a time r is Cpft). This concentration can be calculated by solving the design equation for an ideal batch reactor, if a single reaction is taking place, or by solving the appropriate set of material balances (design equations), if multiple reactions are taking place. 

Ridelhoover and Seagrave [57] studied the behaviour of these same reactions in a semi-batch reactor. Here, feed is pumped into the reactor while chemical reaction is occurring. After the reactor is filled, the reaction mixture is assumed to remain at constant volume for a period of time the reactor is then emptied to a specified level and the cycle of operation is repeated. In some respects, this can be regarded as providing mixing effects similcir to those obtained with a recycle reactor. Circumstances could be chosen so that the operational procedure could be characterised by two independent parameters the rate coefficients were specified separately. It was found that, with certain combinations of operational variables, it was possible to obtain yields of B higher than those expected from the ideal reactor types. It was necessary to use numerical procedures to solve the equations derived from material balances. 

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. 

An ideal isothermal single-phase batch reactor in which a general reaction network takes place nas the following general material balance equation ... 

In the analysis of batch reactors, the two flow terms in equation (8.0.1) are omitted. For continuous flow reactors operating at steady state, the accumulation term is omitted. However, for the analysis of continuous flow reactors under transient conditions and for semibatch reactors, it may be necessary to retain all four terms. For ideal well-stirred reactors, the composition and temperature are uniform throughout the reactor and all volume elements are identical. Hence, the material balance may be written over the entire reactor in the analysis of an individual stirred tank. For tubular flow reactors the composition is not independent of position and the balance must be written on a differential element of reactor volume and then integrated over the entire reactor using appropriate flow conditions and concentration and temperature profiles. When non-steady-state conditions are involved, it will be necessary to integrate over time as well as over volume to determine the performance characteristics of the reactor. 

In this section, we develop a simplistic model of beer fermentation. This model is based upon the work of Engasser (1981) and Gee and Ramirez (1987). The fermentation medium is assumed to contain three major sugars. These are glucose, maltose, and maltotriose and are the limiting nutrients. The fermentation is carried out in a batch reactor which can be considered to be ideally mixed. The material balance relations for each sugar are... 

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