Gas-phase tubular reactors

In gas-phase reactors, the volume and volumetric flow rate frequently vary, owing to the molar changes caused by reaction and the effects of temperature and pressure on gas phase volume. These influences must be taken into account when formulating the mass and energy balance equations. 

The Ideal Gas Law can be applied both to the total moles of gas, n, or to the moles of a given component of the gas mixture nj, where 

Here P is the total pressure of the system, pi is the partial pressure of component i, V is the volume of the system, T is temperature and R is the Ideal Gas Constant. 

This can also be expressed in terms of the molar flow rate Ni, and the volumetric flow rate G, where, 

The steady-state material balance, for a volume element, AV, as shown in Fig. 4.9, for reactant A, is given by 

---

The emphasis in this chapter is on the generalization of piston flow to situations other than constant velocity down the tube. Real reactors can closely approximate piston flow reactors, yet they show many complications compared with the constant-density and constant-cross-section case considered in Chapter 1. Gas-phase tubular reactors may have appreciable density differences between the inlet and outlet. The mass density and thus the velocity down the tube can vary at constant pressure if there is a change in the number of moles upon reaction, but the pressure drop due to skin friction usually causes a larger change in the density and velocity of the gas. Reactors are sometimes designed to have variable cross sections, and this too will change the density and velocity. Despite these complications, piston flow reactors remain closely akin to batch reactors. There is a one-to-one correspondence between time in a batch and position in a tube, but the relationship is no longer as simple as z = ut. 

Example 3.4 Find the mean residence time in an isothermal, gas-phase tubular reactor. Assume that the reactor has a circular cross section of constant radius. Assume ideal gas behavior and ignore any change in the number of moles upon reaction. 

The terms space time and space velocity are antiques of petroleum refining, but have some utility in this example. The space time is defined as F/2, , which is what t would be if the fluid remained at its inlet density. The space time in a tubular reactor with constant cross section is [L/m, ]. The space velocity is the inverse of the space time. The mean residence time, F, is VpjiQp) where p is the average density and pQ is a constant (because the mass flow is constant) that can be evaluated at any point in the reactor. The mean residence time ranges from the space time to two-thirds the space time in a gas-phase tubular reactor when the gas obeys the ideal gas law. 

The first of the relations in Equation (4.9) is valid for any flow system. The second applies specifically to a CSTR since p = pout- It is not true for a piston flow reactor. Recall Example 3.6 where determination of t in a gas-phase tubular reactor required integrating the local density down the length of the tube. 

Figure 4.9. Mass balancing for a gas-phase, tubular reactor.

Figure 4.10. Information flow diagram for a gas-phase tubular reactor with molar change.

Chemical Kinetics, Tank and Tubular Reactor Fundamentals, Residence Time Distributions, Multiphase Reaction Systems, Basic Reactor Types, Batch Reactor Dynamics, Semi-batch Reactors, Control and Stability of Nonisotheimal Reactors. Complex Reactions with Feeding Strategies, Liquid Phase Tubular Reactors, Gas Phase Tubular Reactors, Axial Dispersion, Unsteady State Tubular Reactor Models... 

We turn now to the case of a gas phase, tubular reactor in which the pressure drop is significant. An ODE for pressure must be added to those for the component... 

Mean Residence Time in Gas Phase Tubular Reactor... 

Suppose A —> B 4- C in an isothermal, gas phase, tubular reactor that operates at atmospheric pressure with negligible pressure drop. The molecular weights are 100, 48, and 52 for A, B, and C, respectively. The input gas velocity is 10 m s . The reactor is 10 m long. The entering gas is pure A. The temperature is 700°C. The reaction is first order with a rate constant of 2 s. Determine (tout, and Wom. 

Now, the coupled mass and thermal energy balances can be combined and integrated analytically to obtain a linear relation between temperature and conversion under nonequilibrium (i.e., kinetic) conditions because it is not necessary to consider the temperature and conversion dependence of (Cp mixture)- At high-mass-transfer Peclet numbers, axial diffusion can be neglected relative to convective mass transfer, and the mass balance is expressed in terms of molar flow rate F, and differential volume dV for a gas-phase tubular reactor with one chemical reaction ... 

For adiabatic performance of a variable-volume gas-phase tubular reactor, the first term on the right-hand side of (3-37) is identically zero, and the second term vanishes if the gas mixture behaves ideally. Hence, the coupled plug-flow mass and thermal energy balances are... 

Benzene is hydrogenated to cyclohexane in a series of two gas-phase tubular reactors. A stoichiometric feed of benzene and hydrogen enters the first reactor. The reversible elementary chemical reaction is... 

Possible problem The reaction may not be going to completion (not consuming all of the chlorine) in the gas phase tubular reactor, thereby allowing gas phase chlorine to enter the fractionating column and react with refluxing acetone, as shown schematically in Figure 13-19. 

---