Isothermal Piston Flow Reactors

Chapter 1 treated PFRs with constant axial velocity. The design equations for this type of PFR are directly analogous to the design equations for a constant-density batch reactor. What happens in time in the batch reactor happens in space in the PFR, and the transformation t = zfu converts one design equation to the other. For component A, 

All the results obtained for isothermal, constant-density batch reactors apply to isothermal, constant-density (and constant-cross-section) PFRs. Just replace t with z/u, and evaluate the outlet concentration at z = L. Equivalently, leave the result in the time domain and evaluate the outlet composition at time t = L/u. For example, the solution for component B in the competitive reaction sequence 

Chemical Reactor Design, Optimization, and Scaleup, Second Edition. By E. B. Nauman Copyright 2008 John Wiley Sons, Inc. 

The extension to multiple reactions is done by writing Equation 3.1 (or the more complicated versions of Equation 3.1 that will soon be developed) for each of the Ncomponents. The component reaction rates are found from Equation 2.8 in exactly the same ways as in a batch reactor. The result is an initial-value problem consisting of N simultaneous, first-order ODEs that can be solved using your favorite ODE solver. The same kind of problem was solved in Chapter 2, but the independent variable is now z rather than t. 

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Example 3.2 Consider the reaction 2A B. Derive an analytical expression for the fraction unreacted in a gas-phase, isothermal, piston flow reactor of length L. The pressure drop in the reactor is negligible. 

If the pilot reactor is turbulent and closely approximates piston flow, the larger unit will as well. In isothermal piston flow, reactor performance is determined by the feed composition, feed temperature, and the mean residence time in the reactor. Even when piston flow is a poor approximation, these parameters are rarely, if ever, varied in the scaleup of a tubular reactor. The scaleup factor for throughput is S. To keep t constant, the inventory of mass in the system must also scale as S. When the fluid is incompressible, the volume scales with S. The general case allows the number of tubes, the tube radius, and the tube length to be changed upon scaleup ... 

Consider the reaction B — 2A in the gas phase. Use a numerical solution to determine the length of an isothermal, piston flow reactor that achieves 50% conversion of B. The pressure drop in the reactor is negligible. The reactor cross section is constant. There are no inerts. The feed is pure B and the gases are ideal. Assume bin = F and =0, Ui = 1, and k = n some system of units. 

The reaction A — B — C is occurring in an isothermal, piston flow reactor that has a mean residence time of 2 min. Assume constant cross section and physical properties and... 

Chapter 3 Isothermal Piston Flow Reactors is given by Equation 2.22 for a batch reactor ... 

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