Conversion in Laminar Flow Reactor

Each one of the fluid elements, which is a completely segregated cluster of fluid molecules, can be treated as a micro-batch reactor. The residence time 0 of a fluid element is taken as the batch reaction time to determine the conversion achieved in the fluid element. Consider a first-order reaction A—carried out in the laminar flow reactor, (-ni) = kCA is the kinetic rate equation. The rate of change of reactant concentration in a single fluid element (treated as a batch reactor) is given by 

Integrating this equation from time f = 0 to f = 0 (0 is the residence time of the fluid element), as the concentration Ca of 1 in the fluid element changes from inlet feed concentration Qio to exit concentration Ab 

The fractional conversion x b(0) achieved in the fluid element having a residence time of 9 in the reaction vessel is 

the fractional conversion achieved in a fluid element is a function of residence time 0 of the fluid element in the reaction vessel. Given the RTD E(0), the average value of conversion achieved in all the fluid elements leaving the reaction vessel at any time is calculated and it is taken as the final conversion Thus 

This equation is a general equation for the calculation of conversion in any segregated flow reactor. For a laminar flow reactor, that is modelled as a segregated flow reactor, we get an equation for XAfhy substituting Equations 3.369 and 3.365 in 3.370  

---

CHEMICAL CONVERSION IN LAMINAR FLOW REACTORS Single w-th Order Reactions... 

Example 3.4 Conversion in laminar flow tubular reactors. 

Figure 8.1 includes a curve for laminar flow with 3>AtlR = 0.1. The performance of a laminar flow reactor with diffusion is intermediate between piston flow and laminar flow without diffusion, aVI = 0. Laminar flow reactors give better conversion than CSTRs, but do not generalize this result too far It is restricted to a parabolic velocity profile. Laminar velocity profiles exist that, in the absence of diffusion, give reactor performance far worse than a CSTR. 

Determine the fractional conversion /A of A for a zero-order reaction (A - products) in a laminar flow reactor, where c o = 0.25 mol L 1, jfcA = 0.0015 mol L-1 s-1, and t = 150 s. Compare the result with the fractional conversion for a PFR and for a CSTR 16-4 Using equation 16.2-18, develop a graph which shows the fractional conversion /A as a function of the dimensionless reaction number MAo for a zero-order reaction, where Mao = kt/cAo< equation 4.3-4. what are the real limits on Mao ( e > values f°r which reasonable values of /A are obtained) Explain. 

A reaction with rate equation rc = C/(1+0,2C) is conducted in a laminar flow reactor. Evaluate the ratio of the mean laminar conversion to the plug flow conversion for a range of residence times. 

Figure 8-6 Plots of the ratio of conversions in a tubular reactor with laminar flow to that in a perfect PFTR for first- md second-order kinetics. The lower pmd shows the percent loss in conversion from l nin flow comp ed to plug flow.

Before proceeding to show how the RTD can be used to estimate conversion in a reactor, we shall derive E t) for a laminar flow reactor. For laminar flow in a tubular reactor, the velocity profile is parabolic, with the fluid in the center of the tube spending the shortest time in the reactor. A schematic diagram of the fluid movement after a time t is shown in Figure 13-9. The figure at the left shows how far down the reactor each concentric fluid element has traveled after a time t. 

Example 6-4 Consider the laminar-flow reactor described in Sec. 6-4 and calculate the conversion for a first-order reaction for which k- = 0.1. sec and 0 = 10 sec. 

For calculating conversion in this laminar-flow reactor the RTD for a stirred-tank reactor is more appropriate than that for a plug-flow reactor. This is not apparent from a comparison of the three RTDs shown in Fig. 6-7. 

Denbigh has provided useful guidelines for deciding when deviations (in conversion) from ideal tubular-flow performance are significant. In laminar flow, molecular diffusion in the axial direction causes little deviation if the reactor is reasonably long with respect to its diameter. Molecular diffusion in the radial direction may be important, particularly for gases, but it serves to offset the deviation from ideal performance caused by the velocity distribution. That is, radial diffusion tends to make the reactor... 

Calculate the conversion for the laminar-flow reactor of Prob. 6-7, using the stirred-tanks-in-series model to represent the RTD. 

Reconsider the system in Prob. 6-7, with all conditions the same, except that volumes of different reactors required to obtain the same conversions (for the same flow rate) will be compared. Calculate the ratio of the volumes required for a laminar-flow reactor and a plug-flov/ reactor for several conversion levels between 0 and 100%. Do the results depend on the feed concentrations and the rate constant ... 

Figure 8.1 gives conversion curves for an isothermal, first-order reaction in various types of reactor. The curves for a PFR and CSTR are from Equations 1.38 and 1.49. The curve for laminar flow without diffusion is obtained from Equation 8.14 and the software of Example 8.2. Without diffusion, the laminar flow reactor performs better than a CSTR but worse that a PFR. Add radial diffusion and the performance improves. This is illustrated by the curve in Figure 8.1 that is between those for laminar flow without di ffusion and piston flow. The intermediate curve is one member of a family of such curves that depends on theparameter f// . IfL // is small, <... 

Chapter 8 ignored axial diffusion, and this approach would predict reactor performance like a PFR so that conversions would be generally better than in a laminar flow reactor without diffusion. However, in microscale devices, axial diffusion becomes important and must be retained in the convective diffusions equations. The method of lines ceases to be a good solution technique, and the method of false transients is preferred. Application of the false-transient technique to PDFs, both convective diffusion equations and hydrodynamic equations, is an important topic of this chapter. 

The second-order irreversible reaction 2A B + C is being carried out in the gas phase in a laminar-flow reactor, 1 in. in internal diameter and 8 ft long. The feed rate of A is 0.1 Ibmol-h at 1 atm, and conversion of A is 53%. In an attempt to increase conversion at the same temperature and molar flow rate it proposed to increase operating pressure to 10 atm. Determine the conversion under the new conditions. 

If k /k is 0.8, the laminar-flow reactor would have to be 1/0.8, or 1.25, times longer than a plug flow reactor with the same conversion. Values of k jk are given in Table 6.1. 

J. M. Castro, S. D. Lipshitz, and C. W. Macosko [AIChE J., 28, 973 (1982)] modeled a thermosetting polymerization reaction in a laminar flow reactor under several different operating conditions. Demonstrate your ability to simulate the performance of a plug flow reactor for this reaction under both isothermal and adiabatic reaction conditions. In particular, determine the reactor space times necessary to achieve 73% conversion for both modes of operation and the following parameter values for a (3/2)-order reaction (r = kc - ). 

---