Tubular reactor with dispersion

As can be seen from Eqn. (13.17), the time delay is also present here and incoming changes 

The next type of reaction that will be considered is the equilibrium reaction with a rate constant k for the forward reaction and a rate constant 2 for the backward reaction. 

Both equations have to be solved simultaneously. Taking the boundary conditions into account, the solution for the product concentration can be given as  

As can be seen, the response is again characterized by a gain and a time delay. 

The component balance for component A is given by Eqn. (13.6), the balance for component B is given by Eqn. (13.19). Since Eqn. (13.6) ordy depends on ca it can be solved independently. The solution for the transfer function from Sc Am to Scb, taking the appropriate boundary conditions into account, can be written as  

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Tubular Reactor with Dispersion An alternative approach to describe deviation from ideal plug flow due to backmixing is to include a term that allows for axial dispersion De in the plug flow reactor equations. The reactor mass balance equation now becomes... 

The model is referred to as a dispersion model, and the value of the dispersion coefficient De is determined empirically based on correlations or experimental data. In a case where Eq. (19-21) is converted to dimensionless variables, the coefficient of the second derivative is referred to as the Peclet number (Pe = uL/De), where L is the reactor length and u is the linear velocity. For plug flow, De = 0 (Pe ) while for a CSTR, De = oo (Pe = 0). To solve Eq. (19-21), one initial condition and two boundary conditions are needed. The closed-ends boundary conditions are uC0 = (uC — DedC/dL)L=o and (dC/BL)i = i = 0 (e.g., see Wen and Fan, Models for Flow Systems in Chemical Reactors, Marcel Dekker, 1975). Figure 19-2 shows the performance of a tubular reactor with dispersion compared to that of a plug flow reactor. 

Tubular Reactor with Dispersion As discussed earlier, a multistage CSTR model can be used to simulate the RTD in pilot and commercial reactors. The dispersion model, similar to Fick s molecular diffusion law with an empirical dispersion coefficient De replacing the diffusion coefficient, may also be used. 

There are two sections on the FEMLAB ECRE CD. The first one is Heat effects in tubular reactors." and the second section is Tubular reactors with dispersion." In the first section, the four examples focus on the effects of radial velocity profile and external cooling on the performances of isothermal and noni.soihermal tubular reactors. In the second section, two examples examine the di,spersion effects in a tubular reactor. 

This equation indicates that the conversion in the tubular reactor with dispersion will always be less than that in the plug flow reactor (Q dispersion > plug). For the case where one Axes the effluent composition instead of the reactor size, equations (11.2.13) and (11.2.14) can be manipulated to show that for small Vi/uL at the same conversion,... 

SHOOTING TECHNIQUES TUBULAR REACTOR WITH DISPERSION... 

Figure 7.2 Information—Flow Diagram for Tubular Reactor with Dispersion.

Figure 7.4b Tubular Reactor with Dispersion Profiles.

Let us use the generalized shooting technique to solve for the backward integration of the tubular reactor with dispersion. The describing differential equations and boundary conditions are given by equations (7.1.9) to (7.1.12). The state functions are... 

NONLINEAR TUBULAR REACTOR WITH DISPERSION QUASILINEARIZATION SOLUTION... 

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