First fractional conversions

Oxidation of cumene to cumene hydroperoxide is usually achieved in three to four oxidizers in series, where the fractional conversion is about the same for each reactor. Fresh cumene and recycled cumene are fed to the first reactor. Air is bubbled in at the bottom of the reactor and leaves at the top of each reactor. The oxidizers are operated at low to moderate pressure. Due to the exothermic nature of the oxidation reaction, heat is generated and must be removed by external cooling. A portion of cumene reacts to form dimethylbenzyl alcohol and acetophenone. Methanol is formed in the acetophenone reaction and is further oxidized to formaldehyde and formic acid. A small amount of water is also formed by the various reactions. The selectivity of the oxidation reaction is a function of oxidation conditions temperature, conversion level, residence time, and oxygen partial pressure. Typical commercial yield of cumene hydroperoxide is about 95 mol % in the oxidizers. The reaction effluent is stripped off unreacted cumene which is then recycled as feedstock. Spent air from the oxidizers is treated to recover 99.99% of the cumene and other volatile organic compounds. 

Example (h) In terms of fractional conversion,/ = 1 — C/Cj, the material and energy balances for a first-order CSTR are ... 

Nc = 0.0 gmol, Nq = 0.0 gmol, respectively. A mixture of A and B is charged into a 1-liter reactor. Determine the holding time required to achieve 90% fractional conversion of A (X = 0.9). The rate constant is k = 1.0 X 10 [(liter) /(gmoP min)] and the reaction is first order in A, second order in B and third order overall. 

For a cascade of N CFSTRs of equal volume, Vr, in which the first order forward reaction A—occurs with a throughput u, show that the system fractional conversion is... 

The first order reaction is represented by (-r ) = kC, and applying the mass balance Equation 6-120 and the heat balance Equation 6-121, respectively, gives the fractional conversion in terms of the mass balance equation ... 

Fig ure 6-32. Fractional conversion versus T pt for a first order reversible reaction A R. 

Consider the reversible first order reaction A R. It is possible to determine the minimum reactor volume at the optimum temperature Tgp( that is required to obtain a fractional conversion X, if the feed is pure A with a volumetric flowrate of u. A material balance for a CESTR is... 

Example 3.5 A 1-in i.d coiled tube, 57 m long, is being used as a tubular reactor. The operating temperature is 973 K. The inlet pressure is 1.068 atm the outlet pressure is 1 atm. The outlet velocity has been measured to be 9.96 m/s. The fluid is mainly steam, but it contains small amounts of an organic compound that decomposes according to first-order kinetics with a half-life of 2.1s at 973 K. Determine the mean residence time and the fractional conversion of the organic. 

Solution The first-order rate constant is 0.693/2.1=0.33 so that the fractional conversion for a first-order reaction will be 1 — exp(—0.227) where f is in seconds. The inlet and outlet pressures are known so Equation (3.27) can be used to And t given that [L/Mom ] = 57/9.96 = 5.72s. The result is f = 5.91 s, which is 3.4% higher than what would be expected if the entire reaction was at Pout- The conversion of the organic compound is 86 percent. 

Figure 5.46. A burst of warm feed at 310 K for the first 1400 seconds causes the system to shift into a higher temperature and higher conversion steady state. The fractional conversion curves A and C are for normal startup and B and D are for the startup with a warm feed period.

In Illustrations 8.3 and 8.6 we considered the reactor size requirements for the Diels-Alder reaction between 1,4-butadiene and methyl acrylate. For the conditions cited the reaction may be considered as a pseudo first-order reaction with 8a = 0. At a fraction conversion of 0.40 the required PFR volume was 33.5 m1 2 3, while the required CSTR volume was 43.7 m3. The ratio of these volumes is 1.30. From Figure 8.8 the ratio is seen to be identical with this value. Thus this figure or equation 8.3.14 can be used in solving a number of problems involving the... 

Each of these reactions is first-order in A and first-order in S. The inlet concentration of A is equal to 5 moles/liter. The reactor combination is to be operated under conditions such that the fraction conversion of A based on the inlet concentration is 0.4 leaving the first reactor and 0.6 leaving the second reactor. 

If converted into plots of fraction conversion versus time, these forms give rise to a characteristic S shape. These plots first rise, showing autoacceleration as the rate increases, then pass through an inflection point as the rate reaches a maximum, and finally taper off so that the fraction conversion approaches unity or its equilibrium value as the time approaches infinity. 

The fraction conversion in the effluent from the first reactor can be determined from equation C and the definition of the fraction conversion. 

The fraction conversion at the CSTR exit for this first-order reaction is given by... 

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. 

Use the F(t) curve generated in Illustration 11.1 to determine the fraction conversion that will be achieved in the reactor if it is used to carry out a first-order reaction with a rate constant equal to 3.33 x 10 3 sec-1. Base the calculations on the segregated flow model. 

D. Use fA = 0.008 as a first estimate of the average fraction conversion for the second increment in... 

The first column lists all the species involved (including inert species, if present). The second column lists the basis amount of each substance (in the feed, say) this is an arbitrary choice. The third column lists the change in the amount of each species from the basis or initial state to some final state in which the fractional conversion is fA. Each change is in terms of fA, based on the definition in equation 2.2-3, and takes the stoichiometry into account. The last column lists the amounts in the final state as the sum of the second and third columns. The total amount is given at the bottom of each column. 

A second-order reaction may typically involve one reactant (A -> products, ( -rA) = kAc ) or two reactants ( pa A + vb B - products, ( rA) = kAcAcB). For one reactant, the integrated form for constant density, applicable to a BR or a PFR, is contained in equation 3.4-9, with n = 2. In contrast to a first-order reaction, the half-life of a reactant, f1/2 from equation 3.4-16, is proportional to cA (if there are two reactants, both ty2 and fractional conversion refer to the limiting reactant). For two reactants, the integrated form for constant density, applicable to a BR and a PFR, is given by equation 3.4-13 (see Example 3-5). In this case, the reaction stoichiometry must be taken into account in relating concentrations, or in switching rate or rate constant from one reactant to the other. 

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. 

For a constant-density system, several simplifications result. First, regardless of the type of reactor, the fractional conversion of limiting reactant, say fA, can be expressed in terms of molar concentration, cA ... 

Calculate the ratio of the volumes of a CSTR and a PFR ( Vst pf) required to achieve, for a given feed rate in each reactor, a fractional conversion (/A) of (i) 0.5 and (ii) 0.99 for the reactant A, if the liquid-phase reaction A - products is (a) first-order, and (b) second-order with respect to A. What conclusions can be drawn Assume the PFR operates isothermally at the same T as that in the CSTR. 

In Table 17.2, fA (for the reaction A products) is compared for each of the three flow reactor models PFR, LFR, and CSTR. The reaction is assumed to take place at constant density and temperature. Four values of reaction order are given in the first column n = 0,1/2,1, and 2 ( normal kinetics). For each value of n, there are six values of the dimensionless reaction number MAn = 0, 0.5, 1, 2, 4, and °°, where MAn = equation 4.3-4. The fractional conversion fA is a function only of MAn, and values are given for three models in the last three columns. The values for a PFR are also valid for a BR for the conditions stated, with reaction time t = t and no down-time (a = 0), as described in Section 17.1.2. 

PF, to model the effect of earliness or lateness of mixing, depending on the sequence, on the performance of a single-vessel reactor. The following two examples explore the consequences of such series arrangements-first, for the RTD of an equivalent single vessel, and second, for the fractional conversion. The results are obtained by methods already described, and are not presented in detail. 

The hydrolysis of methyl acetate (A) in dilute aqueous solution to form methanol (B) and acetic acid (C) is to take place in a batch reactor operating isothermally. The reaction is reversible, pseudo-first-order with respect to acetate in the forward direction (kf = 1.82 X 10-4 s-1), and first-order with respect to each product species in the reverse direction (kr = 4.49 X10-4 L mol-1 S l). The feed contains only A in water, at a concentration of 0.050 mol L-1. Determine the size of the reactor required, if the rate of product formation is to be 100 mol h-1 on a continuing basis, the down-time per batch is 30 min, and the optimal fractional conversion (i.e., that which maximizes production) is obtained in each cycle. 

A (desired) liquid-phase dimerization 2A -> A2, which is second-order in A0"a2 = for a), is accompanied by an (undesired) isomerization of A to B, which is first-order in A(rB = 1 Ca). Reaction is to take place isothermally in an inert solvent with an initial concentration Ca0 = 5 mol L-1, and a feed rate (q) of 10 L s 1 (assume no density change on reaction). Fractional conversion (/a) is 0.80. 

If both reactions are first order (a = j8 = 1), then micromixing is irrelevant yield, selectivity, and fractional conversion depend solely on the RTD. If, however, either a or /3 is not equal to 1, then the degree of micromixing can have a significant impact upon performance, as illustrated in the following example. 

In Figure 21.7(a), it is assumed that fAo = 0, and T0 < Tmax. T0 is first increased to Tmax in a preheater, and operation in the FBCR is then isothermal until intersects with (-rA)max, after which it follows (- rA)max until a specified final value of fractional conversion, fAi0Ut, is reached. This last part requires appropriate adjustment of T at each point, and is thus nonadiabatic and nonisolhetmal. Such precise and continuous adjustment is impractical, but any actual design path attempts to approximate the essence of this. 

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