The Design Equations

The temperature and composition of the contents of an ideal batch reactor are uniform at any instant, but the concentration changes with time. Since the composition is uniform, the mass balance may be performed over the whole reactor. 

batch reactors are almost always used to carry out reactions involving only condensed phases and, in such cases, the volume of the reactants does not change significantly. Then, eqn. (5) becomes 

If the volume of reactants does change, then the volume at any stage is linked to the fractional conversion and the parameter e by the equation 

It is important to include any inerts present in the calculation of e. Then 

To use the design equation in either form, it is necessary to know the dependence of r on reactant concentration. 

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Entrance andExit SpanXireas. The thermal design methods presented assume that the temperature of the sheUside fluid at the entrance end of aU tubes is uniform and the same as the inlet temperature, except for cross-flow heat exchangers. This phenomenon results from the one-dimensional analysis method used in the development of the design equations. In reaUty, the temperature of the sheUside fluid away from the bundle entrance is different from the inlet temperature because heat transfer takes place between the sheUside and tubeside fluids, as the sheUside fluid flows over the tubes to reach the region away from the bundle entrance in the entrance span of the tube bundle. A similar effect takes place in the exit span of the tube bundle (12). 

For the air—water system, the Lewis relation shows that r = 1. Under these conditions, the two parenthetical terms on the right-hand side of equation 33 ate enthalpies, and equation 33 becomes the design equation for humidification operations ... 

The simplification of equation 33 to equation 34 is possible only if r = 1 that is, foi simple monoatomic and diatomic gases. Foi other systems the design equation can be obtained by a direct rearrangement of equation 33. 

Thermal design concerns itself with sizing the equipment to effect the heat transfer necessaiy to cany on the process. The design equation is the familiar one basic to all modes of heat transfer, namely,... 

Pickiug up the solids at the bottom of the tank depends upon the eddies and velocity fluctuations in the lower part of the tank and is a different criterion from the flow pattern required to keep particles suspended and moving in various velocity patterns throughout the remainder of the vessel This leads to the variables in the design equation and a relationship that is quite different when these same variables are studied in relation to complete uniformity throughout the mixing vessel. 

D. Caleulate the eomponent values and ratings from the design equations using your partieular set of operating eonditions. 

Application of the Design Equations to Packed Liquid Chromatography Columns and Open Tubular Gas Chromatography Columns... 

The type of optimum reaetor that will proeess 200 m /hr is a eon-tinuous flow stirred tank reaetor (CFSTR). This eonfiguration operates at the maximum reaetion rate. The volume V[ of the reaetor ean be determined from the design equation ... 

For the ideal reactors considered, the design equations are based on the mass conservation equations. With this in mind, a suitable component is chosen (i.e., reactant or product). Consider an element of volume, 6V, and the changes occurring between time t and t + 6t (Figure 5-2) ... 

Considering an nth order iiTeversible reaetion represented by A —> bB with (-r ) = kC, the design equation is... 

The design equations for plug flow in eoneentration and fraetional eonversion are ... 

Fig ure 5-30. Graphioal representation of the design equations for a plug flow reaotor. 

The design equations for both bateh and plug flow systems show that at eonstant density, = 0, tpi g and are identieal, and either of these equations ean be used interehangeably. Where systems ehange in density, there is no direet relationship between the bateh and plug flow equations. In sueh eases, the eorreet equation must be applied for the partieular problem. 

Assuming that the reaetion is seeond order, the design Equation 5-307 for a plug flow reaetor is... 

Substituting Equations 5-330 and 5-331 in the design Equations 5-328 and 5-329, values of exit conversions Xj, Xj, and the composition of die components are computed for various values of V/E. 

By comparing the design equations of batch, CFSTR, and plug flow reactors, it is possible to establish their performances. Consider a single stage CFSTR. 

For a well-mixed batch reactor, the design equation is... 

For the plug flow reaetor, the design equation at 10% eonversion Xa = 0.1 is... 

The design equations for a CFSTR with perfeet mixing, eonstant fluid density, and steady state operation are as follows. If u is the volumetrie flowrate and K = kj/kj, relative reaetion rate eonstant, where kj, kj, and kj are the speeifie reaetion rate eonstants for reaetions 5-357, 5-358, and 5-359. The rate expressions of A, B, R, S, and T are... 

The design equations and parameters for the different hoods are quite different, which is the main reason for describing each of these hood types separately. 

The design equations for pressure drops can also be used for evaluation procedures (Section 10..5. ... 

The position of the worker could be inside or outside the booth. In some ca.ses, the worker is no longer necessary because of automation. The essential types of emission processes are described in the Design Equations and/or Parameters section. 

The design equations may also be used to infer nueleation kineties from eontinuous erystallizer performanee data. 

Recall the design equations for the MSMPR Slurry density Mt =... 

Note that estimating maximum acceptable differs from the design equations for Wg and W. ... 

To select the proper sizing equation, determine whether the flowing conditions are sonic or subsonic from the equations. When the absolute pressure downstream or exit of the throat is less than or equal to the critical flow pressure, P., then the flow is critical and the designated equations apply [33a]. WTien the downstream pressure exceeds the critical flow pressure, P,., then sub-... 

The purpose of these 3 volumes is to present techniques of process design and to interpret the results into mechanical equipment details. There is no attempt to present theoretical developments of the design equations. The equations recommended have practically all been used in actual plant equipment design, and are considered to be the most reasonable available to the author, and still capable of being handled by both the inexperienced as well as the experienced engineer. A conscious effort has been made to offer guidelines to judgment, decisions and selections, and some of this will be found in the illustrative problems. 

For most gases over a wide range of temperature and pressure, Cppjk is constant and the Prandtl group may often be omitted, simplifying the design equations for the calculation of film coefficients with gases. 

Using V, we can write the design equations for a batch reactor in very compact form ... 

Chapter 2 developed a methodology for treating multiple and complex reactions in batch reactors. The methodology is now applied to piston flow reactors. Chapter 3 also generalizes the design equations for piston flow beyond the simple case of constant density and constant velocity. The key assumption of piston flow remains intact there must be complete mixing in the direction perpendicular to flow and no mixing in the direction of flow. The fluid density and reactor cross section are allowed to vary. The pressure drop in the reactor is calculated. Transpiration is briefly considered. Scaleup and scaledown techniques for tubular reactors are developed in some detail. 

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