Plug flow reactor Damkohler number

Reactor conversion for the PFPVMR configuration as a function of the modified Damkohler number. Da, for various values of the parameter Q, is shown in Fig. 5.23. The line for Q=0 represents the conversion of a conventional plug-flow reactor (PFR). 

In a conventional isothermal plug-flow reactor (PFR), two important rates govern its performance - the rate of reaction and the rate of reactant feed per catalyst volume to the reactor. The ratio of these gives the Damkohler number, = (reactor volume)(maximum reaction rate per volume)/(inlet flow rate), which also involves reactor tube dimensions. The membrane reactor brings in at least one additional rate, the permeation rate of the fastest gas. The ratio of these has been labelled differently by various authors we will follow Bernstein and Lund and term it the Damkohler-Peclet product, DaPe = (maximum reaction rate per volume)/(maximum permeation rate per volume). For proper perfor-... 

A minimum conversion ofX = 0.75 is required. For a second order reaction the conversion in an ideal plug flow reactor depends on the first Damkohler number. Dal, as shown in Equation 5.52 (see Chapter 2) ... 

The effectiveness factor E is evaluated for the appropriate kinetic rate law and catalyst geometry at the corresponding value of the intrapellet Damkohler number of reactant A. When the resistance to mass transfer within the boundary layer external to the catalytic pellet is very small relative to intrapellet resistances, the dimensionless molar density of component i near the external surface of the catalyst (4, surface) IS Very similar to the dimensionless molar density of component i in the bulk gas stream that moves through the reactor ( I, ). Under these conditions, the kinetic rate law is evaluated at bulk gas-phase molar densities, 4, . This is convenient because the convective mass transfer term on the left side of the plug-flow differential design equation d p /di ) is based on the bulk gas-phase molar density of reactant A. The one-dimensional mass transfer equation which includes the effectiveness factor. 

As illustrated in Sections 30-1 and 30-2, all intrapellet resistances can be expressed in terms of f-A, surface a, intrapeiiet and Ea mtrapeiiet approaches zero near the central core of the catalyst when the intrapellet Damkohler number is very large. For small values of the intrapellet Damkohler number, effectiveness factor calculations within an isolated pellet allow one to predict Ca, intrapeUet in terms of CA,sur ce via the dimensionless molar density profile. All external transport resistances can be expressed in terms of Ca, buit gas — Ca, surface, and integration of the plug-flow mass balance allows one to calculate the bulk gas-phase concentration of reactant A. The critical step involves determination of Ca, surface via effectiveness factor formalism. Finally, a complete reactor design strategy is... 

The simplest flow-sheet for the reaction Aj o Aj is the RD column sequence with an external recycling loop shown in Fig. 5.1. The system as a whole is fed with pure Aj. According to the assumed relative volatility of the two components a > 1, the reaction product A2 is enriched in the column distillate product whereas the bottom product contains non-converted reactant Aj, which is recycled back to the reactor (continuous stirred tank reactor, CSTR, or plug flow tube reactor, PFTR). The process has two important operational variables the recycling ratio cp = B/F, that is the ratio of recycling flow B to feed flow rate F, and the reflux ratio of the distillation column R = L/D. At steady-state conditions, D = F since the total number of moles is assumed to be constant for the reaction Aj A2. As principal design variables, the Damkohler number. 

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