Conversion design equations using

Design Equations Using Conversion. Recall from Section... 

In reality, will a reactor designed using the above equations achieve the specified conversion Xjif Definitely not, because the design equations used here are applicable to ideal... 

This is the packed tower design equation used for calculating the height of the packed bed required to achieve a specified conversion XAf... 

The basic design equation for a plug flow reactor (equation 8.2.7) may be used to describe the steady-state conversion achieved in the plug flow element of the recycle reactor ... 

In the case of isothermal operation the material and energy balance equations are not coupled, and design equations like 10.2.1 can be solved readily, since the reaction rate can be expressed directly as a function of the fraction conversion. For operation in this mode, an energy balance can be used to determine how the heat transfer rate should be programmed to keep the system isothermal. For this case equation 10.2.12 simplifies to the following expression for the heat transfer rate... 

Equation 10.3.6, the reaction rate expression, and the design equation are sufficient to determine the temperature and composition of the fluid leaving the reactor if the heat transfer characteristics of the system are known. If it is necessary to know the reactor volume needed to obtain a specified conversion at a fixed input flow rate and specified heat transfer conditions, the energy balance equation can be solved to determine the temperature of the reactor contents. When this temperature is substituted into the rate expression, one can readily solve the design equation for the reactor volume. On the other hand, if a reactor of known volume is to be used, a determination of the exit conversion and temperature will require a simultaneous trial and error solution of the energy balance, the rate expression, and the design equation. 

This example illustrates the use of the design equations to determine the volume of a batch reactor (VO for a specified rate of production Pr(C), and fractional conversion (/A) in each batch. The time for reaction (0 in each batch in equation 12.3-22 is initially unknown, and must first be determined from equation 12.3-21. 

The space velocity for a given conversion is often used as a ready measure of the performance of a reactor. The use of equation 1.25 to calculate reaction time, as if for a batch reactor, is not to be recommended as normal practice it can be equated to VJv only if there is no change in volume. Further, the method of using reaction time is a blind alley in the sense that it has to be abandoned when the theory of tubular reactors is extended to take into account longitudinal and radial dispersion and other departures from the plug flow hypothesis which are important in the design of catalytic tubular reactors (Chapter 3, Section 3.6.1)... 

To achieve desired conversions predicted by ideal design equations, plug flow is required. This implies turbulent flow and higher energy costs if packing is used. Mass transfer can also be a problem. Axial diffusion or dispersion tends to decrease residence time in the reactor. High values of the length-to-diameter ratios (L/D > 100) tend to minimize this problem and also help heat transfer. 

Most reactors used in industrial operations run isother-mally. For adiabatic operation, principles of thermodynamics are combined with reactor design equations to predict conversion with changing temperature. Rates of reaction normally increase with temperature, but chemical equilibrium must be checked to determine ultimate levels of conversion. The search for an optimum isothermal temperature is common for series or parallel reactions, since the rate constants change differently for each reaction. Special operating conditions must be considered for any highly endothermic or exothermic reaction. 

The presence of the internal discontinuities makes the use of the standard design equations impossible. Therefore it is necessary to know at what degree of conversion will the discontinuity occur. Then the design equation will tell us at what point in the reactor this happens. 

Rather than using Simpson s rule we could have used the data in Table 2-2 to fu — rj X) to a polynomial and then used POLYMATH to integrate the design equation to obtain the conversion profile,... 

In Chapter 2 we showed how it was possible to size CSTRs, PFRs, and PBRs using the design equations in Table 3-1 if the rate of disappearance of A is known as a function of conversion, X ... 

With these additional relationships, one observes that if the rate law is given and the concentrations can be expressed as a function of conversion, then in fact we have as a function ofX and this is all that is needed to evaluate the design equations. One can use either the numerical techniques described in Chapter 2, or, as we shall see in Chapter 4, a table of integrals. 

PSC>1 A packed-bed reactor was used to study the reduction of nitric oxide with ethylene on a copper-silica catalyst [ln Eng. Chem. Process Des. Dev., 9, 455 (1970)]. Develop the integral design equation in tenns of the conversion at various initial pressures and temperatures. Is there a significant discrepancy between the experimental results shown in Figures 2 and 3 in the article and the calculated results based on (he proposed rate law If so, what is the possible source of this deviation ... 

We note that for adiabatic conditions the relationship between temperature and conversion is the same for batch reactors, CSTRs, PBRs, and PFRs. Once we have T as a function of X for a batch reactor, we can construct a table similar to Table E8-5.1 and use techniques analogous to those discussed in Section 8.3.2 to evaluate the design equation to determine the time necessary to achieve a specified conversion. 

Derive the equation of a first-order reaction using the segregation model when the RTD is equivalent to (a) an ideal PFR, and (b) an ideal CSTR. Compare these conversions with those obtained from the design equation. 

Because each globule acts as a batch reactor of constant volume, we use the batch reactor design equation to arrive at the equation giving conversion as a function of time ... 

When a single chemical reaction takes place, we can readily express the design equation in terms of the conversion of the limiting reactant using Eq. 2.6.5 ... 

The solution is Zout =/a = 0.680. Hence, if the wrongly specified reactor voltrme is used, only 68% conversion is obtained, e. To attain 80% conversion on the 67.1-L reactor, flie feed flow rate should be reduced. From the design equation (e), t = 2.42. Using Eq. 7.1.3 to determine the feed rate. 

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