Conversion of Reaction Rate Coefficient k or Pre-Exponential factor k0The reaction rate coefficient k or pre-exponential factor k0 estimated per unit of catalyst mass, volume or surface area to the units corresponding to the reaction rates in [kmol/ (m3*s)] may be converted as described below:

1. In CSTR model the rate of reaction is assumed to be in [mole fraction / s] or in [kmol/ (m3*s)]. The CSTR model does take into account directly the mass, volume or surface area of the catalyst. If the user has the reaction rate coefficient k or pre-exponential factor k0 estimated per unit of catalyst mass, kg, catalyst volume, m3, or surface area, m2, these values should be converted to the units per m3 of the reactor volume.

If the concentration of the reactants and products in the kinetic equation for the reaction over the solid catalyst are in kmol/ m3 or kPa (this is the typical case in industrial applications) then the transformation is straightforward – to multiply the given constant with the converting factor:

Wcat /V - if rate coefficient k or pre-exponential factor k0 estimated per unit of catalyst mass,

Vcat /V - if rate coefficient k or pre-exponential factor k0 estimated per unit of catalyst volume,

Scat /V - if rate coefficient k or pre-exponential factor k0 estimated per unit of catalyst mass;

where,

V - reactor volume m3

Vcat - volume of catalyst in the reactor

Wcat - mass of catalyst in the reactor kgcat

Scat - catalyst surface area

2. The reaction rate coefficient k or pre-exponential factor k0 estimated per unit of catalyst mass, volume or surface area to the units corresponding to the reaction rates in [kmol/ (m3*s)] has one of the following units of the reaction rate for the reaction over the solid catalyst:

- kmol/(kgcat s) = rate rW is the reaction rate per unit mass of catalyst , (choice 1)

- kmol/(m3cat s) = rate rV is the reaction rate per unit volume of catalyst, (choice 2)

- kmol/(m2cat s) = rate rS is the reaction rate per unit surface area of catalyst, (choice 3)

3. Then the value of the reaction rate coefficient k or pre-exponential factor k0 should be entered in the units, compatible with the choice, made in step 2, and the values of

o Wcat and V for choice 1

o Vcat and V for choice 2

o Scat and V for choice 3

4. The resulting coefficient, matching to reaction rates in [kmol/ (m3*s)] is calculated then by multiplying the value of coefficient k or pre-exponential factor k0, entered at step 3, by Wcat/V, Vcat /V, or Scat/V, respectively.

5. In some cases, the modeler can have the data on the reaction rate over the solid catalyst, for instance:

rS is the reaction rate per unit surface area of catalyst, kmol/( m2cat s), and the design catalyst characteristics that typically include the following;

sm is the surface area per unit of the catalyst mass in (m2cat / kgcat );

pcat is the density of the catalyst pellet in (kgcat/ m3cat); and

ecat is the fraction of the reactor space occupied by the catalyst in (m3cat/ m3react). Usually, the value ecat is about 0.6.

Then conversion from rS in kmol/( m2cat s) to r in kmol/ (m3*s) is as follows: