Reactive Distillation Using Arc Length Continuation

Consider a mixture of four components , , , and with relative volatilities , , and . This mixture is subject to an equilibrium-limited chemical reaction with reaction rate , where the user can set the value of the equilibrium constant . This mixture is fed to a reactive distillation column such that the total number of plates is 17. The feed stage location is stage number 10, the reactive stages are from stage 6 to stage 14, and the feed composition is equimolar in and (i.e. the feed is composed of 50 mole % and 50 mole % ). The feed, a saturated liquid, has a flow rate of 100 kmol/hr. For simplicity, constant molal overflow (CMO) is assumed and heat effects are neglected.
This Demonstration plots the purities of the distillate and bottom (mole fractions of at the top of the column and at the bottom of the column) versus the Damköhler number. This dimensionless number is defined by , where is the liquid hold-up in a plate, is the reaction rate constant, and is the liquid flow rate in each section of the column. The numerical technique used to compute the solution of a system of nonlinear algebraic equations, where is a parameter, is based on arc length continuation.
In addition, the liquid phase compositions versus plate number for components , , , and (in red, blue, green, and magenta, respectively) are given. The reactive zone is shown in light blue, while the stripping and rectifying zones are indicated in light red and light green, respectively. Here, one can set the values of the Damköhler number.
When , one recovers the case where no reaction is taking place, shown in the last snapshots, with no or components in the column.
If is very large, the simulation represents a situation close to reaction equilibrium (i.e., ).
The first snapshot shows good conditions where almost pure and exit the column. Hence, this reactive distillation setup can achieve conversions near 100% in addition to the simplification of the operation scheme: no reactor followed by separation units and no recycling of unreacted and components.

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