Tutorial 11 summary for lecture 11 Convective mass transfer – two fluids in contact
Here we look at this mass transfer process between two fluids in contact from an alternative angle – The two-resistance theory.
We have gone through the lecture recording and notes, and have already got basic idea about the theoretical treatment of mass transfer from one fluid phase to the other (contacting) fluid phase. The theoretical treatment is based on a scenario of NH3 transfer from an oil phase to water phase; it considers the phase equilibria and the division of the interface region into two films.
In this Q&A session, we shall consider a scenario where mass transfer occurs from a gas phase to a liquid phase.
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The interface transfer involves the following three processes:
1) Convective mass transfer from the bulk of phase 1 (gas) to the interface;
2) (Diffusive) transfer across the interface into the 2nd phase (liquid);
3) convective transfer from the interface region into the bulk of the 2nd phase.
These processes are shown in Figure 1.
Assumptions
Steady state:
– concentrations at any position in the mass transfer equipment (e.g. tower) do not change with time.
Sharp boundary:
– interface between the gas and the liquid phase is clear and sharp (no mixing zone or a third phase)
– mass transfer inside the films on both sides of the interface is through molecular diffusion. Equilibrium:
– at the interface (not in the whole film), concentrations on the two contacting phases are in equilibrium;
– (diffusive) mass transfer resistance across the interface is negligible, equilibrium concentration relations can be applied.
No chemical reaction:
– Rate of diffusion across the gas-phase film must be equal to the rate of diffusion into the liquid-phase film
In Lecture 11, we have seen that the strategy of calculating the mass transfer flux from the left to the right fluid phase must be linked to the bulk concentration of the transferring component A, so as to avoid the difficulties in determining interfacial concentrations pA,i and cA,i.
In this example (illustrated in Figure 1), we have a similar problem and will take the same strategy.
When “A” transfers through the bulk gas phase to the interface, it has a transfer resistance RA,G; similarly, it has a transfer resistance when transferring from the interface to the bulk liquid phase, RA,L. These resistances are the individual resistances. In the two-resistance theory we assume that the diffusive resistance in the two-film region is far smaller than the convective resistances, therefore negligible. We can also consider that when A transfers from bulk gas to bulk liquid phase, it has an overall resistance, Rtotal. From Figure 1, we know that the overall convective mass transfer resistance is equal to the sum of RA,G, and RA,L :
Rtotal = RA,G, + RA,L
The resistance in mass transfer has the same mathematical form as the heat transfer resistance in heat transfer. In heat transfer, the overall heat transfer coefficient is U, the corresponding overall heat transfer resistance is 1/U. Below is a quick recap of the relationship between the heat transfer coefficients of a process and the corresponding heat transfer resistances.
In heat transfer through a wall formed by two materials of different thicknesses, l1 and l2, we need to consider the two different thermal conductivities, k1 and k2, and two convective heat transfer coefficients of the two outer surfaces of the wall, h(inf),0 and h(inf),3:
Rewrite the above eqn, we have
Then we have
The overall heat transfer resistance is the reciprocal of the heat transfer coefficient. Their relationship can be summarised by the following eqns
Now, let’s return to the two-resistance theory of Mass Transfer; first, let’s look at the math relationships between the individual MT resistances and the overall MT resistance.
Individual convective mass transfer flux equations for the gas and liquid phases:
The Overall convective mass transfer flux (NA) equation can be written using the overall mass transfer coefficient (KG or KL) and the driving force:
Next, we find out the equilibrium conditions to specify pA* and CA*. But first let’s read Figure 2 to understand our system; then in Figure 3 we read out all the driving forces and do the final derivation of the mass transfer resistance equation.
When reading Figure 2, consider the following eqns. Our objective is to understand why the driving forces can be drawn in such a way as shown in Figure 2.
From Figure 3 we read out all the driving forces and do the final derivation of the mass transfer resistance equation.
In the example of lecture 11 recording, we derived the relations of mass transfer coefficients of NH3 between the oil and water phases, and obtained
These eqns for mass transfer in liquid-liquid situation can be obtained using the same approach shown above for gas -liquid situation.
The thickness of the water film is small, therefore, the cylindrical water film can be assumed as a flat film.
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