The Temperature Map

Almost every chemical plant has a boiler and an evaporative cooling tower. The boiler sources heat at a particular temperature. A portion of that heat is wrought into the the goods the plant produces, and the remainder (usually most of it) is dissipated into the environment by the cooling tower at a lower temperature. The source and sink temperatures, sometimes referred to as the “temperature rails”, are very important. They determine the plant’s capabilities.

The lower “rail”, the plant cooling water temperature, varies with the season and the weather. Plants must be designed to operate even in the hottest summer days, so the design value of the cooling water is often a near-worst-case value. We will use 30C.

While the plant’s “upper rail” is the steam temperature, evaporators may have a much lower temperature limit. We are going to consider one with a maximum allowable heating temperature of 85C. If we were to ask why the limit was set at that value, we would likely discover that it was a compromise. People responsible for product quality, equipment maintenance and production scheduling want low temperatures where delicate molecules don’t degrade and heaters don’t foul. But low temperatures are a costly luxury. The 85C limit is probably the point where product quality is only mildly affected and the fouling of the heater is just on the edge of acceptability.

single effect2

FIGURE 1 Single Effect Temperature Map

The diagram or “Temperature Map” above represents a single effect distillation heated by 85C steam and cooled by 30C water. The pink block represents the heater and the green block the condenser. The horizontal line at the 57C mark represents the phase change from liquid to vapour in the evaporator and from vapour to liquid in the condenser (in this example boiling and condensing take place at the same temperature). The two heat exchangers here are well matched so they share the 55 Celcius degree temperature difference equally. The delta T of each is 27.5 C. This is a generous amount. For a given heat flow, the surface area required is inversely proportional to the delta T, so both heater and condenser are fairly small and inexpensive. But we want to see if we can save energy costs through the use of multiple effect distillation.

four effect2

Figure 2 MED Temperature Map

As we add effects, the delta T of each heat exchanger diminishes. If they are well matched, the five heat exchangers in the four effect unit will each have a delta T of 11 Celsius degrees. Each heat exchanger must therefore be larger and costlier than ones in a single effect plant of the same capacity, roughly by a factor of 27/11 or 2.5.

Fig 2 shows an idealized version of multiple effect distillation (MED). In real life there is always a gap between the temperature of the boiling liquid and the temperature of the condensing vapour. One cause of this is pressure drop through ducts and passages of real equipment. The other cause is boiling point elevation BPE), a difference in temperature between the boiling liquid and the vapour it produces.

Process and equipment designers work together to minimize the problem. To minimize pressure drop, huge vapour ducts are provided to convey gases from stage to stage. Boiling point elevation is a thermodynamic property of the fluid that cannot be mitigated. It dictates the kind of of process that may be considered. For example, if the fluid in the 4 effect process under discussion had a BPE of 10C, then each heat exchanger would have a delta T of only 1C. That plant would be an impractical monster, each heat exchanger having grown by a full order of magnitude. peel iphone 8 case If the boiling point elevation were 11C, four effect distillation would be utterly impossible between the temperature rails specified.

PASS-THROUGH DISTILLATION TEMPERATURE MAP

Pass-through Distillation involves two independent pieces of equipment: a SAM and a multiple effect desorber. We’re going to consider first the desorber, shown below.

Desorber four effect

FIGURE 3 Four Effect Desorber Temperature Map

The first thing to notice is that since the desorber does not see any temperature sensitive process fluid, it is not bound by the 85C process temperature limit. I set an arbitrary metallurgical limit of 230C. (Above that temperature low cost alloys suffer excessive corrosion when exposed to the absorbent fluid in this study, but with different alloys or absorbent fluids the temperature limit could be greatly extended.)

The next thing to notice is that there are white spaces between the blocks representing heat exchangers. This is because the absorbent fluid, unlike the hypothetical process liquid of the previous example, has a strong boiling point elevation.

At the top of the map is the steam temperature of 230C. The heater has a 16C delta T. The boiling temperature is 214C. But the vapours do not condense at that temperature. There is roughly a 30C gap, and the condensation occurs in the first interstage heat exchanger at 185C. The pattern of a 16C delta T across a heat exchanger alternating with a 30C gap repeats until the bottom of the chart heat is discharged into the 30C cooling water.

Although there are other absorbent fluids available, Lithium Bromide and water is the one we will consider. It is widely used in the chiller industry. Its boiling point elevation is mainly a function of concentration,as shown on the Duhring Plot below. Every point on the chart represents a system state in which the lithium bromide solution is in equilibrium with the saturated water vapour surrounding it. A common way of expressing this is to say that the liquid is at its boiling point. At any such point the addition of heat will cause some of the water in the solution to become part of the vapour (i.e. iphone 8 case hot pink boil) while removal of heat will cause some of the vapour to be absorbed into the liquid.

ashrae duhring plot

FIGURE 4 Duhring Plot

The magnified portion of the chart shown below has been marked with a red horizontal line to represent system pressure of 200 Torr (that would read 22″HG on a vacuum gauge). Since the gas in the vapour space is pure water, we know from the saturated steam tables that its temperature is 66C. The chart tells us that if that this gas is in equilibrium with a 50% lithium bromide solution, the temperature of that solution will be 93C. It will also be in equilibrium with a 60% solution if that solution temperature is 115C. The boiling point elevation (BPE) values for these two cases are 27C and 49C respectively.

Duhring detail

FIGURE 5 Duhring Plot Detail

Referring back to the desorber temperature map (Fig. 3), we now know what the white blocks represent: the boiling point elevation (BPE) of the LiBr solution. We have seen that BPE is around 30C at 50% concentration and 50C at 60%. The process designer can choose the value of BPE by specifying the working concentration of the absorbent fluid. Now we will examine what will be affected elsewhere in the pass-through distillation process.

PASS-THROUGH DISTILLATION AND BPE

Fig. 6 below shows the schematic of a pass-through distillation plant comprising a SAM and a desorber. A feed liquid enters the top of the left hand chamber, splashes over warm tubes and exits the chamber at the bottom. The absolute pressure in the SAM and the feed temperature are matched such that the liquid is at its boiling point upon entering. All the heat added to the liquid by the warm tubes causes evaporation to occur. In this example the feed liquid is an aqueous slurry for which the boiling liquid and the vapour share the same temperature (i.e. the feed liquid has no BPE) and the vapour generated is saturated water vapour.

SAMptd2

FIGURE 6 Pass-through distillation Schematic

The blue arrows indicate the path of the vapours from the left hand (evaporation) chamber to the bottom of the right hand (absorption) chamber. As the vapours rise they are absorbed into the Lithium Bromide solution as it splashes downward over relatively cool tubes. The latent heat of evaporation carried by the vapours is imparted to the liquid but immediately removed by the cool tubes. As the solution descends its LiBr concentration drops, but at all points it is in equilibrium with the vapour, and its state can therefore be found on the Duhring plot.

There pressure drop in both chambers of the SAM is negligible, so the pressure and temperature of the vapour will be the same throughout. In the evaporation chamber the temperature of the liquid and vapour are equal. In the absorption chamber the temperature of the of the liquid solution is that of the vapour plus the boiling point elevation (BPE). Thus the BPE is the delta T which drives heat from the absorption chamber into the evaporation chamber. The tubes are heat pipes, which conduct the heat with very little thermal resistance.

Figure 7 below shows a temperature map for a SAM. This map is a little different from the ones we have seen so far. While the others were merely one dimensional bar charts, this one reflects the fact that as the LiBr solution falls through the absorber, its concentration and temperature drop.

SAMtempMAP1

FIGURE 7 SAM Temperature Map

Point 1 on the map corresponds to the brine entering the SAM while point 2 is the brine leaving it. iphone 7 cases blue marble The difference in the two temperatures depends upon the ratio of the mass flow rate of the brine to the mass flow rate of the water vapour it absorbs. At infinite brine flow the concentration would be unchanged and the equilibrium temperatures would likewise be unchanged. In practical systems point 2 will always be a few degrees lower than point 1. I arbitrarily chose to show a 5 degree drop.

Points 3 and 4 are the in and out temperature of the feed liquid respectively. In this example they are assumed to be equal.

The length of the vertical line between points 1 and 3 is the BPE of the absorption brine when it is in its regenerated state. In Fig.7 it is shown larger than the 30C of our example for the sake of legibility. Even so, the temperature map of the SAM touches neither the Process Limit of 85C nor the cooling water rail of 30C. That prompts the obvious question “How does the SAM temperature map relate to the plant temperature map?” The answer may surprise you: the two are independent.

Figure 8 below shows the same SAM with the same absorbent liquid operated at two different pressures. This time the maps are to scale for 30C BPE.

SAMtempMA21

FIGURE 8 Operating Pressure Dependency

It is the vacuum train that determines the position the SAM’s temperature map. The lower the absolute pressure of operation, the lower the temperature at which the feed liquid will boil. but whatever that temperature happens to be, the absorbent fluid will absorb the vapours at a temperature higher by the amount of the BPE.

At this point in the discussion, people with plant experience are likely to protest that 17 Torr is impractical for industrial distillations. That is true when industrial distillations involve condensers cooled by normal cooling water. Below 100 Torr the condensers may do an imperfect job, and process vapours will overwhelm the vacuum pump. In some plants where low temperature distillation is needed and the business can support the added operating cost, chilled water is fed to the condenser and lower operating pressures are obtained. Generally, any technique that minimizes the flow of uncondensed gas makes inexpensive vacuum equipment capable of very low plant operating pressures. iphone 8 plus battery case 10000mah Using a version of pass-through distillation, I ran a commercial pervaporation plant for several years at pressures normally below 20 Torr and sometimes below 10 Torr.

SUMMARY

A temperature map is a useful tool in visualizing how pass-through distillation differs from conventional distillation. PTD is a two step process. One of these is a conventional multiple effect distillation applied to an absorbent fluid. It is tied to the plant “temperature rails” in the same way as any other distillation. iphone 6 cool cases for boys The other step is transfer of volatile components from the feed liquid to the absorbent fluid through evaporation and absorption.

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