Case B Tubular Reactor

The basic concepts of the above lumped parameter and distributed parameter systems are shown in Fig. 1.7. 

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The solution of Equations (5.23) or (5.24) is more straightforward when temperature and the component concentrations can be used directly as the dependent variables rather than enthalpy and the component fluxes. In any case, however, the initial values, Ti , Pi , Ui , bj ,... must be known at z = 0. Reaction rates and physical properties can then be calculated at = 0 so that the right-hand side of Equations (5.23) or (5.24) can be evaluated. This gives AT, and thus T z + Az), directly in the case of Equation (5.24) and imphcitly via the enthalpy in the case of Equation (5.23). The component equations are evaluated similarly to give a(z + Az), b(z + Az),... either directly or via the concentration fluxes as described in Section 3.1. The pressure equation is evaluated to give P(z + Az). The various auxiliary equations are used as necessary to determine quantities such as u and Ac at the new axial location. Thus, T,a,b,. .. and other necessary variables are determined at the next axial position along the tubular reactor. The axial position variable z can then be incremented and the entire procedure repeated to give temperatures and compositions at yet the next point. Thus, we march down the tube. 

In a simple tubular reactor, the concentration of both reactants will be high at the inlet and the question is whether the disadvantage of a high concentration of B outweighs the advantage of a high concentration of A. This is nearly always the case because the relative p kp CA... 

In these equations it is understood that CA may be (a) the concentration of A at a particular time in a batch reactor, (b) the local concentration in a tubular reactor operating in a steady state, or (c) the concentration in a stirred-tank reactor, possibly one of a series, also in a steady state. Let St be an interval of time which is sufficiently short for the concentration of A not to change appreciably in the case of the batch reactor the length of the time interval is not important for the flow reactors because they are each in a steady state. Per unit volume of reaction mixture, the moles of A transformed into P is thus 9LAP6t, and the total amount reacted (9lAP + 3tAQ)St. The relative yield under the circumstances may be called the instantaneous or point yield will change (a) with time in the batch reactor, or (b) with position in the tubular reactor. 

As our first example, we consider the case of a first-order homogeneous reaction A -> B in a laminar flow tubular reactor for which the global equation is linear in c (i.e. r( c)) — (c)) and is therefore completely closed. To obtain the range of convergence of the two-mode model, we need to consider only the local equation. In this specific case, the reduced model equations to all orders of p are then given by... 

The stirred-tank reactor and the tubular reactor are two basic reactors used for continuous processes, so much of the experimental and theoretical studies pubhshed to date on continuous emulsion polymerization have been conducted using these reactors. The most important elements in the theory of continuous emulsion polymerization in a stirred-tank reactor or in stirred-tank reactor trains were presented by Gershberg and Longfleld [330]. They started with the S-E theory for particle formation (Case B), employing the same assumptions as stated in Sect. 3.3, and proposed the balance equation describing the steady-state number of polymer particles produced as ... 

The following configuration is in some aspects similar to the previous one. It simulates a flow pattern in a tubular reactor [21, p.334, case b] in the presence of side feedings. 

Cases a and b in Fig.4.4-3a demonstrate the effect of q. By increasing q, i.e. the by-pass stream, the mean residence time in the tubular reactor tp is increased from 0.1 to 0.5 time units. Case a and c demonstrate the effect of Xi = X2- By increasing this quantity from 10 to 500, the mean residence time in the perfectly mixed reactor is decreased, and the response becomes instantaneous. In the computations. At = 0.002 for q = 1 and 0.01 for q = 5. 

Under smooth fluidization the motion, heat capacity, and small size of the particles result in a remarkably uniform temperature throughout the bed. Radial gradients, so important in fixed beds, are negligible. The transfer of heat to or from the reactor can be considered by assuming that a finite heat-transfer coefficient exists at the wall, and that the temperature across the bed is uniform. This situation is depicted in Fig. 13-18, where curve c applies to the fluidized bed. For comparison, curve b represents a homogeneous tubular reactor in turbulent flow, where the temperature profile is not so flat as in the fluidized bed but is still more uniform than for the packed bed, case (a). ... 

The comparison between the homogeneous tubular reactor and the packed-bed case depends on the velocity level and dpjd. It is possible for the temperature profile in the packed bed to be more uniform than the profile shown for case b). 

Determine the yield of a second order reaction, A -F B — prodnct with ai = bm in an isothermal tubular reactor governed by the axial dispersion model. Specifically, plot fraction unreacted versus aiJd for a variety of Pe. Be sure to show the limiting cases that correspond to a PER and a CSTR. 

We turn now to the plug flow reactor. Here, as we have said, there is absolutely no mixing in the direction of flow but perfect mixing perpendicular to it, that is, between the centerline and the walls. This special case of a tubular reactor can be operated transiently or in the steady state, but it is the latter mode that is most often considered for kinetics and design. Consider the reactor shown in Figure 4 in which A is converted to B irreversibly and with linear kinetics. 

The shape of the response curve for an impulse function f t) is shown in Fig. 3.3b for various residence time distribution functions. Figure 3.4c, shows the response curves F t) for a step function. The limiting cases of an ideal stirred vessel and an ideal tubular reactor are shown in both b and c. To quantify RTD curves, two fundamentally different models are used (a) the so-called one-dimensional dispersion model, primarily used for tubular reactors with low backmixing, and (2) the so-called cell model ( tanks in series model ) which was primarily intended for stirred vessel reactors but is of general validity. 

Consider the second case (b)—a tubular flow reactor followed by a CSTR—and... 

Tubular flow reactors (TFR) deviate from the idealized PFR, since the applied pressure drop creates with viscous fluids a laminar shear flow field. As discussed in Section 7.1, shear flow leads to mixing. This is shown schematically in Fig. 11.9(a) and 11.9(b). In the former, we show laminar distributive mixing whereby a thin disk of a miscible reactive component is deformed and distributed (somewhat) over the volume whereas, in the latter we show laminar dispersive mixing whereby a thin disk of immiscible fluid, subsequent to being deformed and stretched, breaks up into droplets. In either case, diffusion mixing is superimposed on convective distributive mixing. Figure 11.9(c) shows schematically the... 

Reactor 1. Stirred tank 2. Tubular a. packed-bed b. Trickle-bed c. fluidized bed d. bubble column Reaction 1. Gas-liquid-solid or gas-liquid 2. In most cases solid with gas and/or liquid 0-300 psi, 50-200°C... 

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