Phase Tubular Reactors

Assuming the case of a first-order chemical reaction (rA=-kCA) and a non-compressible liquid system, the generalised mass and energy balance equations reduce to 

The general solution approach, to this type of problem, is illustrated by the information flow diagram, shown in Fig. 4.8. The integration thus starts with the initial values at Z = 0, and proceeds with the calculation of rA, along the length of the reactor, using the computer updated values of T and CA, which are also produced as outputs. 

The simultaneous integration of the two continuity equations, combined with the chemical kinetic relationships, thus gives the steady-state values of both, CA and T, as functions of reactor length. The simulation examples BENZHYD, AN-HYD and NITRO illustrate the above method of solution. 

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 ni, where 

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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. 

TABLE 5.1 Scaleup Factors for Liquid-Phase Tubular Reactors. 

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... 

One of the critical units in the production of paper is a reactor called a digester. In the kraft process this reactor is a two-phase tubular reactor in which the lignin that binds the wood chips together is broken down through a combination of chemical and thermal effects. The white liquor (aqueous solution of sodium hydroxide and hydrosulfide) and solid wood chips flow countercurrently in some zones and co-currently in others. The residence time of the pulp is about 10 h. 

Two-phase tubular reactors offer opportunities for temperature control, accommodate wide ranges of T and P, and approach plug flow, and the high velocities prevent settling of slurries or accumulations on the walls. Mixing of the phases may be improved by helical... 

The optimal control of the two-phase tubular reactors had been formulated by Kassem (1977). A distributed minimum principle was presented and the necessary conditions for optimality were derived. Based on these conditions for optimality a functional gradient aigorichm for synthesizing boundary and distributed controls were deduced. 

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... 

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