Mole balances design

In the following sections we will examine the following three reactor types and develop the mole balance/design equations for each ... 

We now must determine the ratio F/Fq a function of volume V or the catalyst weight, W to account for pressure drop. We then can combine the concentration, rate law, and design equation. However, whenever accounting for the effects of pressure drop, the differential form of the mole balance (design equation) must be used. 

In order to determine design characteristics of chemical reactors, we have to formulate mole balance equations. 

From the above mole balance equation we can develop the design equation for various reactor types. By solving the design equation we can then determine the time required for a batch reactor system or a reactor volume for a continuous flow system to reach a specific conversion of the reactant to products. 

Integrating the mole balance equations gives us the design equations for the different reactor types ... 

At this design stage, the mole balance model of the plant is given by the following equations, where the reactor and separation performances are described by the reaction extents and ( 2 and the recoveries pP and pl respectively. 

From this general mole balance equation we can develop the design equations for the various types of industrial reactors batch, semibatch, and continuous-flow. Upon, evaluation of these equations we cau determine the time (batch) or reactor volume (continuous-flow) necessary to convert a specified amount of the reactants to products. 

Des n equatioiis. The general mole balance equations (design equatiova) bvtsed... 

Before entering into discussions of the conditions that affect chemical reaction rates and reactor design, it is necessary to account for the various chemical species entering and leaving a reaction system. This accounting process is achieved through overall mole balances on individual species in the... 

The first chapter focused on the general mole balance equation die balance was applied to the four most common types of industrial reactors, and a design equation was developed for each reactor type. In Chapter 2 we first define con-version and then rewrite the design equations in terms of conversion. After car rying out this operation, we show how one may size a reactor i.e., determine the reactor volume necessary to achieve a specified conversion) once the relationship between reaction rate, r, and conversion is known. 

Now that we have a relationship [Equation (2-10)] between the molar flow rate and conversion, it is possible to express the design equations (i,e., mole balances) in terms of conversion for the flow reactors exantinMi in Chapter 1,... 

Dibular Flow Reactor (PFR). After multiplying both sides of the tubular reactor design equation (1-10) by -1, we express the mole balance equation for species A in the reaction given by Equation (2-2) as... 

When using measures other than conversion for reactor design, the mole balances are written for each species in the reacting mixture ... 

To design slurry reactors we simply couple this rate law with the appropriate mole balance" (see Chapters 1 and 2). 

In phase equilibrium, mole fraction in each of the phases is the most common way to express composition that goes along with mole balances around the system being studied. There is also the possibility to use mass fraction for defining composition. Mass balances around the system can then be made. For some situations, absorption column design, for example, the composition may be expressed as mass of solute per mass of solvent. 

The equation we will use to design PFRs at steady. state can he developed in two ways 0) directly from Equation (1-4) by differentiating with respect to voKime K or (2) from a mote balance on species./ in a differential segment of the reactor volume it. Let s choose the second way tti airive at the differential form of the PER mole balance. The differential volume. AV. shown in Figure MO. will be chosen sufficiently small such that there are no spatial variations in reaction rate within this volume. Thus the generation term. is... 

In ihe three idealized types of reactors just discussed (the perfectly mixed batch reactor, the plug-fiow tubular reactor (PFR). and the perfectly mixed con-tinuous-siirred tank reactor (CSTR), the design equations (i.e.. mole balances) were dei doped based on reactor volume. The deris ation of the design equation for a packed-bed catalytic reactor (PBR) will be carried out in a manner analogous to the development of the tubular design equation. To accomplish this derivation. we simply replace the volume coordinate in Equation (MO) with (he catalyst weight coordinate H (Figure - 4). 

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