9.4 Temperature profile in an evaporator
Let us consider the case of long-tube vertical evaporator heated by steam. After boiling and flashing of the superheated liquid, the disengagement of the vapor and liquid occur in vapor space of the evaporator and the recycled liquid flows down the external pipe. A part of this concentrated liquid is withdrawn as a product and the remaining part get mixed with a feed and again enter the evaporator tube. If TBP is the boiling of the liquid in the evaporator as the prevailing pressure, then the temperature of the liquid in the tube will be TBP. The temperature of the recycled stream entering the tubes will then also be TBP, if the feed is sufficiently hot. Now, we will imagine how the temperature is changing in the tube. Let us see that when the liquid flows up in the tube, its temperature rises because at the bottom of the tube the pressure is higher (vapor chamber pressure + hydrostatic pressure + frictional loss) as compared to the top of the tube. Therefore, a liquid starts boiling at a level when its temperature rises to its saturation temperature at the pressure at that point. After the boiling in between the tube, as liquid goes up in the tube, the local temperature drops because of the reduction in the local pressure. It may also be mentioned that as the liquid moves up it gets concentrated and thus the boiling point of the solution also increases as the liquid traversed up in the tube. The liquid temperature profile in the tube is shown in the fig.9.4 for low (plot i) and high (plot ii) liquid velocity. The liquid temperature in the tubes increases up to certain height and then the temperature decreases due to the loss of superheat. At higher velocity the temperature raise is less and the liquid boils near the top of the tube. The plot (iii) shows the shell side temperature profile where steam is heating the tube. As can be seen, the slightly superheated steam enters the shell and soon the temperature of the steam losses its sensible heat and then condenses on the tubes and provide the latent heat of condensation (at temperature Tsteam) to the tube and before boiling from the shell may get slightly sub-cooled. The plot (iv) is the boiling temperature of the water (Tw) at the pressure in the vapor chamber. Thus, the BPE=TBP-Twand the true temperature during force is the difference between the plot (iii) and the plot (i) or (ii).
It can be understood with the help of the discussion and fig.9.4 that the temperature changes all along the length of the tube. Thus, the real temperature driving force will be the difference in steam temperature and liquid temperature always the high. However, it is practically not easy to determine the temperature profile in the tube. Therefore, the driving force can be taken as (Tsteam - TBP) for the design purpose.
9.5 Heat transfer coefficient
The correlation used in the boiling and condensation may be used here. If the evaporator operates at very high liquid velocity so that the boiling occurs at the top end of the tube, the following correlation (eq. 9.1) may be used,
where, D is the inner diameter of the tube, k is the thermal conductivity of the liquid or solution.
Fig.9.4: Temperature profiles in an evaporator
Fouling is a concern in the evaporator; therefore the following equation (eq.9.2) may be used for the overall heat transfer coefficient with time,
where, t is the time for where the evaporator is the operation, α is a constant for a particular liquid, Udirty and Uclean all the overall heat transfer coefficient of the dirty and clean evaporator.
9.6 Method of feeding: Multiple effect evaporators
The fig.9.5, 9.6, 9.7, and 9.8 show the four different feeding arrangement of feed to the evaporators. In the fig.9.5 the liquid feed is pumped into the first effect and the partially concentrated solution is sent to the second effect and so on. The heating steam is also sent through the first effect to another effect. This particular strategy is known as forward feed. In the forward feed the concentration of the liquid increases from first effect to the subsequent effects till the last effect. It may be noted that the first effect is that in which the fresh steam is fed, whereas the vapour generated in the first effect is fed to the next evaporator (connected in series with the first effect) is known as second effect and so on.
The forward feed requires a pump for feeding dilute solution to the first effect. The first effect is generally at atmospheric pressure and the subsequent effects are in decreasing pressure. Thus, the liquid may move without the pump from one effect to another effect in the direction of decreasing pressure. However, to take out the concentrated liquid from the last effect may need a pump.
The backward feed arrangement is very common arrangement. A triple-effect evaporator in backward arrangement is shown in the fig.9.6. In this arrangement the dilute liquid is fed to the last effect and then pumped through the successive effects to the first effect. The method requires additional pumps (generally one pump in between two effects) as shown in the fig. 9.6. Backward feed is advantageous and gives higher capacity than the forward feed when the concentrated liquid is viscous, because the viscous fluid is at higher temperature being in the first effect. However, this arrangement provides lower economy as compared to forward feed arrangement.
The combination of forward-feed and backward-feed is known as mixed feed arrangement. In mixed feed the dilute liquid enters in between effects, flows in forward feed to the end of the effect and then pumped back to the first effect for final concentration. Figure 9.7 shows triple effect mixed feed arrangement. This mixed feed arrangement eliminates the need of a few of the pumps. Moreover, it still passes the most concentrated liquid through the first effect, which is having higher temperature among all the effect (being at highest pressure compared to other effects).
Another common evaporator arrangements, which is more common in crystallization is parallel feed where feed is admitted individually to all the effects. Figure 9.7 shows such arrangement.
Fig.9.5: Forward feed arrangement in triple-effect evaporator (dotted line: recycle stream)
Fig.9.6: Backward feed arrangement in triple-effect evaporator (dotted line: recycle stream)
Fig.9.7: Mixed feed arrangement in triple-effect evaporator (dotted line: recycle stream)
Fig.9.8: Parallel feed arrangement in triple-effect evaporator