Plug fractional conversions

Consider j plug flow reactors connected in series and let/i,/2,/3, -fh >/ represent the fraction conversion of the limiting reagent, leaving reactors 1, 2, 3,. J. For each of the reactors considered above, the appropriate design equation is 8.2.7. For reactor z,... 

This volume is appreciably larger than the volume of plug flow reactor calculated in Illustration 8.3 for the same reaction conditions and fraction conversion. However, the cost of such a reactor would be considerably less than the cost of a tubular reactor of the size determined in Illustration 8.3. 

The relationship between the temperature and the fraction conversion at a particular point in the plug flow reactor can be obtained by setting Sa2 = Sa and TieavingPFR equal to T. Thus,... 

The F(t) curve for a system consisting of a plug flow reactor followed by a continuous stirred tank reactor is identical to that of a system in which the CSTR precedes the PFR. Show that the overall fraction conversions obtained in these two combinations are identical for the case of an irreversible first-order reaction. Assume isothermal operation. 

For the gas phase reaction, A => 2B, in a plug flow reactor, find the relation between fractional conversion and the quantity kVr/VQ, when starting with pure A. 

The feed consists of a mols of steam per mol of butene. Derive the equation for the volume of a plug flow reactor in terms of the fractional conversion, x, of butene. 

In eqn. (62), which is the basic form of the design equation for a plug-flow reactor, V is the reactor volume, G is the total mass flow through the reactor, Cao is the concentration of A at inlet in moles per unit mass of feed, Xa is the fractional conversion of A and r is the reaction rate. 

Consider N plug flow reactors connected in series, and let X2,.. . , be the fractional conversion of component A leaving reactor 1, 2,.. . , A. Basing the material balance on the feed rate of A to the first reactor, we find for the /th reactor from Eq. 5.18... 

The basic equation for a tubular reactor is obtained by applying the general material balance, equation 1.12, with the plug flow assumptions. In steady state operation, which is usually the aim, the Rate of accumulation term (4) is zero. The material balance is taken with respect to a reactant A over a differential element of volume 8V, (Fig. 1.14). The fractional conversion of A in the mixture entering the element is aA and leaving it is (aA + SaA). If FA is the feed rate of A into the reactor (moles per unit time) the material balance over 8V, gives ... 

For a typical packed bed, take the value of the Peclet number (udp/eDl) as 2. Dl is the dispersion coefficient in a packed tube. Then show that for a fractional conversion of 0.99 and a ratio of dp L of 0.02, the length L of the reactor with axial dispersion exceeds the length of the simple ideal plug-flow reactor by only 4.6 per cent where dp is the diameter of the particles. 

The design equations for plug flow in concentration and fractional conversion are ... 

The Microsoft Excel spreadsheet program REACTOR.xls was used to compute the volumes of the CFSTR, plug flow reactors, and the ratio of the volumes for fractional conversions of 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 95% for a first order reaction. Table 5-14 shows the volumes of the CFSTR, plug flow reactors, and the ratio of the volumes at given conversion levels. 

Yield-Based Reactor Fractional Conversion Reactor Combined Specification Model Well-Stirred Reactor Model Plug Flow Reactor Model Two Phase Chemical Equilibrium General Phase and Chemical Equilibrium... 

Laboratory experiments on the irreversible, homogeneous gas-phase reaction 2A + B = 2C have shown the reaction rate constant to be 1 x 105 (g mol/L)-2 s 1 at 500°C(932°F). Analysis of isothermal data from this reaction has indicated that a rate expression of the form — rA = kCAC2B provides an adequate representation for the data at 500°C and 101.325 kPa (1 atm) total pressure. Calculate the volume of an isothermal, isobaric plug-flow reactor that would be required to process 6 L/s (0.212 ft3/s) of a feed gas containing 25% A, 25% B, and 50% inserts by volume if a fractional conversion of 90% is required for component A. 

For this case it will be necessary to calculate the steady-state temperature and fractional conversion profiles along the length of the tubular reactor. For a plug flow reactor the appropriate differential material balance for the reaction at hand is... 

Figure 4.1. A differential volume element (dVr) in a tubular (or plug flow) reactor with F and f being the flow rate and fractional conversion, respectively, of the limiting reactant A.

For a given flow rate Q and inlet reactant concentration the outlet concentration may be decreased by raising ki or A, The fractional conversion over the plug flow reactor may be stated from equation (2.120) as ... 

A set of quality control tests is run on each batch of catalyst One of these tests, designed to measure catalyst activity, is earned out as follows. Exactly SO g of catalyst are charged to a small tubular reactor. The reactor operates isotheimally at 300 °Candcan be characterized as an ideal, plug-fiow reactor. A mixture of A and N2 is fed to the reactor at 300 °C and 1 atm total pressure. At these conditions, the inlet concentration of A, Cao, is 0.008S8 g-mol/l and the total volumetric feed rate is SOO 1/h. Transport resistances are negligible. In order to pass the activity test, a catalyst sample must produce a fractional conversion jca of 0.50 0.01. 

The integral method of analysis can be used when the available data are in the form of concentration (or fractional conversion) versus time or space time (or V/Fao or W/Fao)-As pointed out earlier in this chapter, this kind of data are obtained when an ideal batch reactor or an ideal plug-flow reactor is used. For these two reactors, use of the integral method avoids the need for numerical or graphical differentiation. 

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