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# Membrane Reactor for an Equilibrium-Limited Reaction

A porous membrane tube is used as a plug flow reactor containing a catalyst. This membrane reactor combines reaction with separation to obtain higher conversions for an equilibrium-limited reaction by selectively removing one of the products. The reversible reaction is , and product is selectively removed from the reactor by permeating through the membrane. The membrane is assumed to only permeate product , and the permeate pressure of is assumed to be zero. When the membrane permeance (which you can vary) is low, the reaction is equilibrium limited for large enough rate constants for the forward reaction. Increasing the permeance shifts the equilibrium to the right to obtain higher conversions. Increasing the reactor diameter decreases the conversion because the permeation area per reactor volume decreases. The molar flow rate divided by the cross sectional area of the reactor is plotted to make the comparison easier when the reactor diameter changes. You can also change the equilibrium constant.

### DETAILS

= molar flow rate of reactant
= molar flow rate of reactant
= molar flow rate of product
= molar flow rate of product
= total molar flow rate
= total initial molar flow rate
= initial molar flow rate of reactant
= initial molar flow rate of reactant
= reactor cross-sectional area
= reactor diameter
= volumetric flow rate
= initial volumetric flow rate
= rate of reaction (moles/time/volume)
= rate permeating
= reaction rate constant
= equilibrium constant
= membrane permeance, based on concentration difference

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