1. Interfacial Mass Transfer in Gas-Liquid Reactors
Consider a metal-catalyzed hydrogenation of a non-volatile olefin (liquid-phase). A semi-batch process is used, wherein hydrogen is replenished to maintain the reactor pressure.
An autoclave is charged with the olefin solution, pressurized with hydrogen and allowed to equilibrate at the reaction temperature.
The liquid phase is saturated with hydrogen,
[H2] = [H2]eq @ P, T.
Hydrogenation is started by charging catalyst to the autoclave. H2 is consumed in the liquid phase as a result of the reaction:
[H2] < [H2]eq
This deviation from equilibrium initiates mass transfer of H2 from the vapour phase to the liquid. H2
Catalyst
t=0, [H2] = [H2]eq
t>0, [H2] < [H2]eq
CHEE 323

2. Interfacial Mass Transfer in Gas-Liquid Reactors
Hydrogenation in a gas-liquid contactor involves:
1. Physical adsorption of H2 across the gas-liquid interface into the
bulk liquid phase.
2. Catalytic hydrogenation within the liquid phase.
If r1 >> r2, then the overall rate is that of the catalytic process.
Kinetic Control, [H2][H2]eq
If r1 << r2, then the rate equals the rate of interfacial mass transfer.
Mass Transfer Limited, [H2]0
CHEE 323

3. Quantifying Interfacial Mass Transfer
In all gas-liquid contactors, mass transfer takes place under forced convection, meaning the gas and liquid phases are mixed.
Physical adsorption brings the system towards an equilibrium condition.
It is known from experiment that the farther the system is from an equilibrium condition, the faster the rate of mass transfer.
Define the rate of H2 transfer across a gas-liquid interface, FH2:
where,
FH2 = interfacial transfer rate: mole/s
kl = convective mass transfer coefficient: m/s
A = gas-liquid interfacial area: m2
[H2]* = equilibrium H2 concentration of liquid: mole/m3
[H2] = H2 concentration of liquid: mole/m3
CHEE 323

4. Measuring klA in a Stirred-Tank Contactor
It is difficult to determine both kl and A by experiment, as measuring interfacial area can be tedious if not impossible in some cases. However, the product kl A is more accessible.
Mass transfer in a stirred tank can be quantified quite easily:
Equilibrate the system at low pressure under static conditions
Raise the reactor pressure several bar
At t=0, start the agitator and measure the amount of H2 required to maintain constant pressure as a function of time.
1. Equilibrate
at low P
[H2] =
Plow T
2. Raise P under static conditions
[H2] =
Phigh T
3. Start agitator
Maintain pressure
[H2] 
Phigh T H2
CHEE 323

5. Measuring klA in a Stirred-Tank Contactor
When the agitator is started, transport of H2 across the gas liquid interface commences, the rate of which is governed by:
where nH2 is the number of moles of H2 in the liquid phase.
Dividing by the volume of liquid, V, yields an expression in terms of molar concentration:
which can be integrated using the initial condition, t=0: [H2] = [H2]o to yield:
which expresses the concentration of H2 in the liquid phase as a function of time during the system’s approach towards equilibrium.
CHEE 323

6. Measuring klA in a Stirred-Tank Contactor
The integrated expression for the rate of physical adsorption of H2 into a stirred solution:
fits the experimental data quite well.
The intensity of agitation, as measured by the stirring rate is seen to have a significant effect on the mass transfer rate.
CHEE 323

7. Design Considerations
Whether a process operates under kinetic (chemical) control or mass transfer control depends on the rates of reaction and interfacial transfer.
If our catalytic reaction is first order with respect to hydrogen:
: mole/s m3
and the rate of interfacial mass transfer (NH2 = FH2/V) is:
then at steady state, these rates are equal, giving us: or
CHEE 323

8. Flow and Mixing Regimes in Gas-Liquid Reactors
klA/V s-1
CHEE 323

9. Factors Influencing Mass Transfer Efficiency
Design parameters influence mass transfer efficiency by altering the convective mass transfer coefficent, kl A/V.
Factors influencing kl (film thickness, surface renewal rate) and interfacial area:
large and small-scale “mixing intensity”
liquid viscosity
gas diffusivity
Selection and design of a multi-phase reactor requires careful consideration of vessel configuration and reactant properties.
Find mass transfer data collected under conditions as close to your proposed design as possible
Be conservative in your estimates of mass transfer coefficients
Bench-scale data must be collected under kinetic control
Mass transfer effects should be handled at the pilot-scale, not bench-scale.
CHEE 323

10. Heat Transfer: Design Considerations
The rate of heat removal under convective heat transfer is described as:
where, q = heat transfer rate: watts (W)
h = convective heat transfer coefficient: W/m2K
A = heat transfer area: m2
DT = temperature difference between the surface and
the fluid : K
The heat released by hydrogenation is:
where, qrn = rate of heat generation: watts (W)
rhdgn = hydrogenation rate: mole/s
DHrn = Enthalpy of reaction: J/mole
To avoid a runaway reaction, adequate heat removal capacity (quantified by hA) must be designed into the reactor configuration.
CHEE 323