Continuous fractional conversions

For a simple A -t- B —> C reaction in a continuous stirred-tank reactor, as shown in Fig. 5.134, in terms of fraction conversion of the reactant A, the balance... 

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. 

Figures 7-9 show the fractional conversion of methanol in the pulse as a function of temperature for the three catalysts and the three methanol feeds. Evidently the kinetic isotope effect is present on all three catalysts and over the complete temperature range, indicating that the rate limiting step is the breaking of a carbon-hydrogen bond under all conditions. From these experiments, the effect cannot be determined quantitatively as in the case of the continuous flow experiments, but to obtain the same conversion of CD,0D, the temperature needs to be 50-60° higher. This corresponds to a factor of about three in reaction rate. The difference in activity between PfoCL and Fe.(MoO.), is larger in the pulse experiments compared to tHe steady stateJ results.

The process design of a batch reactor may involve determining the time (t) required to achieve a specified fractional conversion (/A, for limiting reactant A, say) in a single batch, or the volume (V) of reacting system required to achieve a specified rate of production on a continual basis. The phrase continual basis means an ongoing operation,... 

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. 

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. 

For a simple system, the continuity equation 21.6-1 may be put in forms analogous to 21.5-2 and 21.54 for the axial profile of fractional conversion, fA, and amount of catalyst, W, respectively ... 

A batch reactor and a single continuous stirred-tank reactor are compared in relation to their performance in carrying out the simple liquid phase reaction A + B —> products. The reaction is first order with respect to each of the reactants, that is second order overall. If the initial concentrations of the reactants are equal, show that the volume of the continuous reactor must be 1/(1 — a) times the volume of the batch reactor for the same rate of production from each, where a is the fractional conversion. Assume that there is no change in density associated with the reaction and neglect the shutdown period between batches for the batch reactor. 

One might intuitively expect that infinite recycle rates associated with a system as described by eqn. (61) would produce a completely well-mixed volume with concentration independent of location. This is indeed so and under these conditions, the performance tends to that of an equal sized CSTR. At the other extreme, when R is zero, PFR performance pertains. Fractional conversions at intermediate values of R may be determined from Fig. 14. The specific form of recycle model considered is thus seen to be continuously flexible in describing flow mixing between the PFR and CSTR extremes just as was the tanks-in-series model. The mean and variance of this model are given by eqns. (62) and (63) and these may be used for moments matching purposes of the type illustrated in Example 6. 

The example is concerned with a batch chlorination process. At the beginning, the fresh toluene charged to the reactor will contain no dissolved chlorine. After bubbling of the chlorine has commenced, a period of time will need to elapse before the concentration of the dissolved chlorine rises to a level that just matches the rate at which it is being removed from the solution by reaction. To avoid such a complication in this example, calculations are carried out for the stage when, after chlorine bubbling has continued at a steady rate, the fractional conversion of the toluene has reached a value of 0.10. It is then assumed that, at any instant in time, the rate of mass transfer of chlorine from the gas phase is just equal to the rate at which it reacts in the bulk of the liquid, i.e. the rate is given by equation 4.17. 

The extent of reaction (or conversion) at any stage can be expressed by the fraction of total reactive sites that have been consumed. Reactive sites usually display the same reactivity regardless of the size of the molecule to which they are linked. The polymerization process has the characteristics of a statistical combination of fragments. In this way, a distribution of products from the monomer to a generic n-mer is obtained (Table 2.1), with average molar masses increasing continuously with conversion. 

For the simple network 5.26 and a reaction with no fluid-density variation, the magnitude of the effect is easily calculated The cumulative selectivity of conversion to P (moles of A converted to P per mole of A consumed, see definition 1.11) in batch and continuous stirred-tank reactors as a function of fractional conversion,/A, is... 

At the initial stage the dependence of fractional conversion F on (Fo) is linear. The exchange rate is dependent on the value of ag/Cg and independent of Dy. This is in accordance with the analytical solution (11) for the rectangular isotherm of the B counterion. The greatest spread of concentration profiles appears in situations where both factors act together to spread the concentration distribution of the B ion i.e., at Df/ Dg < 1 and Kg /Kgg < 1 (Fig. 3, Vg, curve Il.e). In this instance the diffusion of the A ion is slower than the diffusion of the B ion (D, < Dg) and this results in accumulation of the A ion (Fig. 3, curve Il.e). The accumulation is partially attenuated due to the effect of the selectivity factor when Kg /Kgs < 1 continues to prevail (compare concentration profiles in variants II and Il.e). Co-ion Y also enters the bead (Fig. 3, Cy, curve Il.e) although not as vigorously as in the case with variant II. 

The reaction between ethylene and hydrogen bromide to form ethyl bromide is carried out in a continuous reactor. The product stream is analyzed and found to contain 51.7 mole% C2HsBr and 17.3% HBr. The feed to the reactor contains only ethylene and hydrogen bromide. Calculate the fractional conversion of the limiting reactant and the percentage by which the other reactant is in excess. If the molar flow rate of the feed stream is 165 mol/s, what is the extent of reaction (Give its numerical value and its units.)... 

The synthesis of methanol from carbon monoxide and hydrogen is carried out in a continuous vapor-phase reactor at 5.00 atm absolute. The feed contains CO and H2 in stoichiometric proportion and enters the reactor at 25 C and 5.00 atm at a rate of 17.1 m /h. The product stream emerges from the reactor at 127 C. The rate of heat transfer from the reactor is 17.05 kW. Calculate the fractional conversion achieved and the volumetric flow rate (m /h)of the product stream. (See Example 9.5-4.)... 

However, the stopped-flow FIA technique allows the fractional conversion to be measured experimentally for any FIA system by resolving the contribution of the dispersion process and of chemical kinetics. By stopping the flow (cf. Sections 2.4.3 and 4.3) any element of the dispersed sample zone can be selected and arrested in the flow cell, where the change of response with time [i.e., rf(response)/[Pg.81]

In many cases of metal-ion removal, there is a need to maintain a very high fractional conversion in a continuous flow-through reactor. This situation may be accomodated via a number of reactors in series flow both CSTR s [36, 37] and PFR s [45] have been considered. The important requirement of design simplicity often dictates the use of a static cathode geometry incorporating porous, 3-dimensional electrode materials [46], One example is reticulated vitreous carbon which has been extensively investigated in our laboratories [45-49] and elsewhere, e.g. [50, 51]. 

From kinetic investigation of the curing of macro-triisocyanates (MTI) based on L-3003, P-2200, and their mixtures, kinetic curves of the polymerization process were obt uned at 298 K. Kinetic curves for the curing of polyurethane prepolymer mixtures obtained by reaction of TDI with L-3003, P-2200, and various mixtures with a double excess of NCO groups with respect to OH groups are linear. These dependences show that NCO group reactions continue until high fractional conversions comply with the second-order equation... 

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