Mass and Heat Balance

Mass Balance

A pass-through distillation installation must involve three main pieces of equipment: an evaporator, a gas absorber, and a regenerator for the absorption fluid. These are configured as shown in the block diagram below.

A liquid feed stream is fed to an evaporator vessel. A portion of it is turned to vapour and leaves the evaporator through a port near its top. The unevaporated portion leaves the vessel through a port near its bottom.

The vapours from the evaporator are drawn through an absorber vessel where it contacts an absorbent fluid ( labelled brine). Most or all of the vapours are absorbed into the fluid and leave the vessel at the bottom as part of a diluted brine solution.

The diluted absorbent fluid is fed to the regenerator which is a conventional still. It boils out the volatile substances taken in by the brine in the absorber. In most commercial plants the regenerator will have multiple effects to save energy.

Figure 1

The mass balance for this system is very simple. Referring to the diagram below:

A) The mass flow rate of vapour leaving the evaporator, M3, is equal to the feed M1 minus the bottoms M2.

M3 = M1 – M2

B) The mass flow of vapours collected by the brine is equal to the vapours entering the absorber, M3, minus those leaving the absorber and entering the vacuum pump, M7. The material collected by the brine adds to its mass flow.

M3 – M7 = M5 – M4

C) In order to keep the inventory of circulating absorbent fluid at a steady level, it is imperative that 100% of the material absorbed by the brine in the absorber be boiled out and condensed by the regenerator. So the product stream M6 must be equal to evaporator vapours M3 minus the amount lost to the vacuum system.

M6 = M3 – M7

Figure 2

Heat Balance

Understanding the heat balance is best accomplished by first considering a simple case involving some constraints. First, the evaporator and absorber are essentially at the same absolute pressure. This corresponds well to experimental reality where vapour ducts are suitably sized and the vessel internals are properly designed.

Secondly, both the feed entering the evaporator and the concentrated brine entering the absorber are saturated. That is to say, both these fluids are at their boiling point with respect to the system pressure. For example, If the system pressure is 30 Torr, the boiling point of a solution comprising mostly water will be roughly 30 degrees Celsius. That then will be the temperature of the feed. A brine however does not boil at the same temperature as water; boiling point elevation (BPE) causes it to boil at a higher temperature. If the brine happens to be a concentrated Lithium salt solution the BPE may exceed 30 Celsius degrees.

Finally, we will assume that all the vapours entering the absorber chamber were in fact absorbed and that no gases pass on into the vacuum pump. Under this assumption, the vacuum pump was used to bring the system to its desired absolute pressure then valved off and shut down.

Figure 3

With the assumptions above the heat that must be added to the evaporator is simply the vapour flow rate M3 times its latent heat of evaporation. Also, ignoring second order effects, the heat that must be withdrawn from the absorber to make it operate is the very same quantity.

The regenerator must boil the same amount of material boiled by the evaporator, but it will use less heat to do so if it is a multiple effect distillation (MED) apparatus. A triple effect regenerator will use less than half the energy of a single effect evaporator.

Figure 4

In the diagram above, we show PTD with heat integration. The absorber operates at a higher temperature than the evaporator. In the restricted case we are considering, the magnitude of the heat thrown off by the absorber matches the heat needed by the evaporator. If some clever heat exchange device can be built to do the job, then the evaporator/absorber combination becomes a passive device requiring no external heating or cooling.

From a functional standpoint, the diagram above shows something very much like ordinary distillation. A feed stream was boiled generating a bottoms stream depleted of volatile components and a condensed liquid product stream comprising the materials boiled out of the feed stream. There are two very important differences. 1) PTD did the job at lower temperature and 2) PTD used less energy.

Drystill Technologies has invented a heat and mass exchanger that integrates the heat according to Figure 4. They call the device a SAM (Stripper/Absorption Module). You may learn more about this on the Drystill website.

But now, what happens if we relax the simplifying assumptions we made for this analysis. What if there is a non-zero mass flow into the vacuum pump? What if we fail to control pressures and temperatures so that the absorber and evaporator feeds are perfectly saturated? What about the effects of parasitic heat loss? How about the heat of mixing when the brine absorbs water?

These questions are beyond the scope of this article. Answers can be sought with Aspen Pus modelling and through direct experimentation. But the answers will depend heavily on the composition of the feed, the absorbent fluid selected, and various application-specific constraints.