,

,

where

is conversion,

is volume (

),

is the reaction rate,

is the molar flow rate of component

(kmol/hr) that converts velocity of feed to molar flow rate of feed,

is the velocity of component

(m/s),

is the radius of the inner tube (cm),

and

are the densities of the reactant and coolant (

), and

is the molar mass of

(kg/kmol).

,

,

,

where

and

are the forward and reverse rate constants (1/hr),

is a pre-exponential factor (1/hr),

and

are the activation energies for the forward and reverse reactions (J/mol),

is the ideal gas constant (J/[mol K]),

is temperature (K),

is the heat of reaction (kJ/mol), and

is the inlet concentration of

(

).

,

,

,

where

is the heat transfer coefficient (

),

is the heat exchange area per unit volume of reactor (1/m),

is the temperature of the heat transfer fluid (K),

is the average molar heat capacity of reacting mixture (kJ/[kmol K]),

is the coolant heat capacity (kJ/[kg K]),

is the mass flow rate of coolant (kg/hr) which converts velocity of heat transfer fluid to mass flow rate and

is the coolant velocity (m/hr).