where

is the molar flow rate of component

(mol/min),

is the total molar flow rate (mol/min),

is the initial total molar flow rate (mol/min),

and

are the initial molar flow rates of reactants

and

(mol/min),

is the reactor cross-sectional area (

),

is the reactor diameter (m),

and

are the volumetric flow rates down the reactor and initially (

),

is rate of reaction (

),

is the rate

permeating (mol/min),

is the reaction rate constant (

),

is the equilibrium constant (unitless), and

is the membrane permeance, based on concentration difference (

).