Steady-State Tubular Reactor Dispersion Model

7 Steady-State Tubular Reactor Dispersion Model 

Letting the element distance AZ approach zero in the finite-difference form of the dispersion model, gives 

At steady state, aCA/9t can be set to zero, and the equation becomes an ordinary second-order differential equation, which can be solved using ISIM. 

Again the entrance and exit boundary conditions must be considered. Thus the two boundary conditions at Z = 0 and Z = L are used for solution, as shown in Fig. 4.15. Note, that these boundary conditions refer to the inner side of the tubular reactor. A discontinuity in concentration at Z = 0 is apparent in Fig. 4.16. 

Balancing the mass flows at the inlet gives a relation for the boundary conditions at Z=0 

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First we introduce the reader to the principles of such problems and their solution in Sections 5.1.2 and 5.1.2. As an educational tool we use the classical axial dispersion model for finding the steady state of one-dimensional tubular reactors. The model is formulated for the isothermal case with linear kinetics. This case lends itself to an otherwise rare analytical solution that is given in the book. From this example our students can understand many characteristics of such systems. 

In Section 11.1.3.1 we considered the longitudinal dispersion model for flow in tubular reactors and indicated how one may employ tracer measurements to determine the magnitude of the dispersion parameter used in the model. In this section we will consider the problem of determining the conversion that will be attained when the model reactor operates at steady state. We will proceed by writing a material balance on a reactant species A using a tubular reactor. The mass balance over a reactor element of length AZ becomes ... 

In this form, the two-mode model is identical to the classical steady-state two-phase model of a tubular catalytic reactor with negligible axial dispersion. There is also a striking structural similarity between the two-mode models for homogeneous reactions and two-phase models for catalytic reactions in the practical limit of Per 1. This could be seen more clearly when Eqs. (137) and (138) are rewritten as... 

In particular cases simplified reactor models can be obtained neglecting the insignificant terms in the governing microscopic equations (without averaging in space) [9]. For axisymmetrical tubular reactors, the species mass and heat balances are written in cylindrical coordinates. Himelblau and Bischoff [9] give a list of simplified models that might be used to describe tubular reactors with steady-state turbulent flow. A representative model, with radially variable velocity profile, and axial- and radial dispersion coefficients, is given below ... 

In Sec. 6-5 a non-steady-state mass balance for a tubular-flow reactor (plug flow except for axial dispersion) was used to evaluate an effective diffusivity. Now we consider the problem of calculating the conversion when a reaction occurs in a dispersion-model reactor operated at steady-state conditions. Again a mass balance is written, this time for steady state and including reaction and axial-dispersion terms. It is considered now that the axial diffusivity is known. 

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