Adiabatic PFR

As a numerical example, we consider a gas-phase exothermic irreversible reaction with two reactants and one product that occurs in a PFR packed with a solid catalyst  

The rate of reaction depends on the partial pressures of the reactants and is expressed as kmol per second of C generated per kilogram of catalyst. 

The ordinary differential equations describing a steady-state adiabatic PFR can be written with axial length z as the independent variable. Alternatively the weight of catalyst w can be used as the independent variable. There are three equations a component balance on the product C, an energy balance, and a pressure drop equation based on the Ergun equation. These equations describe how the molar flowrate of component C, temperature T, and the pressure P change down the length of the reactor. Under steady-state conditions, the temperature of the gas and the solid catalyst are equal. This may or may not be true dynamically  

A is the heat of reaction (kJ/kmol), Fj is the molar flowrate of component j at any axial position, and cpj is the molar heat capacity of component j 

e is the catalyst porosity and Re is the particle Reynolds number (Re = DpVp/fi) and i is viscosity (kg m-1 s-1). The pressure and temperature change with axial position, so the friction factor changes somewhat down the length of the reactor. 

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The next example treats isothermal and adiabatic PFRs. Newton s method is used to determine the throughput, and Runge-Kutta integration is used in the Reactor subroutine. (The analytical solution could have been used for the isothermal case as it was for the CSTR.) The optimization technique remains the random one. 

Example 6.4 Find the best combination of reaction temperature and volume for the example reaction using isothermal and adiabatic PFRs. 

The above computation is quite fast. Results for the three ideal reactor t5T)es are shown in Table 6.3. The CSTR is clearly out of the running, but the difference between the isothermal and adiabatic PFR is quite small. Any reasonable shell-and-tube design would work. A few large-diameter tubes in parallel would be fine, and the limiting case of one tube would be the best. The results show that a close approach to adiabatic operation would reduce cost. The cost reduction is probably real since the comparison is nearly apples-to-apples. ... 

In an adiabatic PFR the product is recycled after cooling to the 350 fC temperature of the fresh feed. The reaction is 2A => B. Fresh feed concentration is Ca0 = 2. The specific rate is... 

Show that the Equation (3.34) is valid if the large and small reactors have the same value for jl and that this will be true for an isothermal or adiabatic PFR being scaled up in series. 

Example 6.7 Determine optimal reactor volumes and operating temperatures for the three ideal reactors a single CSTR, an isothermal PFR, and an adiabatic PFR. 

All other things being equal, as they are in this contrived example, the competitive reaction sequence of Equation (6.6) is superior for the manufacture of B than the consecutive sequence of Equation (6.1). The CSTR remains a doubtful choice, but the isothermal PFR is now better than the adiabatic PFR. The reason for this can be understood by repeating Example 6.5 for the competitive reaction sequence. 

The above kinetic equations have been tested by the simulation of an adiabatic PFR. For an inlet temperature of 160 °C, a benzene/propylene ratio of 7 and a spatial time WHSV of 10 a total conversion of propylene may be reached with selectivity around 90%. In conclusion, the kinetic data corresponds to a fast industrial catalyst and may be reasonably used in design. 

In a first attempt, we simulate the reactor as an adiabatic PFR. We consider a diameter of 1.3 m and a total length of 7 m, which ensure propylene conversion over 99.9%. The feed consists of lOOkmol/h propylene at molar benzene/... 

Table 6.9 The performance of an adiabatic PFR function of inlet temperature and excess of benzene.

Figure 6.6 Profile of concentrations and temperature in an adiabatic PFR for cumene synthesis.

The simulation of the ethylene chlorination can be done as an adiabatic PFR with a liquid superficial velocity between 0.1 and 0.3 m/s. The results obtained by Aspen Plus [19] by using a scheme such as that shown in Figure 7.3(a) with the kinetic equations (7.1) and (7.2) is in good agreement with the industrial practice. 

Equation (9.4.4) relates the conversion to the temperature for an adiabatic PFR. If the reactor is operated isothermally, then ... 

Steady-State Nonisothermat Reactor Design Chap. 8 Table 8-2a, Adiabatic PFR/PBR Algorithm... 

Tb relale temperature and conversion we apply the energy balance to an adiabatic PFR. If all species enter at the same temperature, 3% = Ti,. 

From these three case.s. (I) adiabatic PFR and CSTR, (2) PFR and PBR with heat effects, and (3) CSTR with heat effects, one can see how one couples the energy balances and mole balances. In principle, one could simply use Table 8-1 to apply to different reactors and reaction systems w ithout further discussion, However, understanding the derivation of the.se equations w ill greatly facilitate their proper application and evaluation to various reactors and reaction systems. Ctmsequenily, the following Sections 8.2. 8.3, 8,4. 8.6, and 8,8 will derive the equations given in Table 8-1. 

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