Heat Capacity with Dissolved Solids

You are working on some design problem where a concentrated salt solution is under consideration and you are looking for its heat capacity. In such situation, will you use it to be equal to water Or it will be significantly different.

Yes, the answer is that it will be significantly different than water depending on its concentration. The deviation goes higher & higher if concentration increases.

The discussed equations are very useful for heat transfer calculations for slurry systems as well as solid handling systems.

So how to calculate it? Find out the easy way to calculate it.

A quick estimation method was proposed by Dimoplon in 1972. The proposed expression is:

Cpsoln = W1 x Cps + W2 x Cpw

Where Cpsoln = Specific heat of soluion mix.
Cps = Specific heat of solids
Cpw = Specific heat of water
W1 = Wt% of solids
W2 = Wt% of water (Usually 1 - W1)

The equation is valid for a given T. So if T changes you need to change the values accordingly.

Following chart / table is very important for above equation.



Example
Calculate the heat capacity of a 20-wt% Na2CO3 solution at 150 °F

Solution
Step-1
Look up the heat capacity of this solid from table. If it is not available, apply Kopp's Rule, which says

Cp(Na2CO3) = 2 x Cp(Na) + 1 x Cp(C) + 3 x Cp(O)

From Table, we read the values at 150 °F (339 K). Notice that the heat capacity for oxygen is given as O2 (it's natural form). This value must be divided by two to get the heat capacity for one atom of oxygen.

So,
Cp(Na) = 28.5612 KJ/Mole/K
Cp(C) = 11.6364 KJ/Mole/K
Cp(O) = 14.0611 KJ/Mole/K

So by Kopp's Rule

Cp (Na2CO3) = 2 x 28.5612 + 11.6364 + 3 x 14.0611
= 110.9421 KJ/Mole/K

Step-2
Now since our Dimoplon equation uses only weight basis, we need to divide this figure by molecular weight of compound. So,

Cp (Na2CO3) = 110.9421 / 105.9 = 1.0476 KJ/Kg/K

Now if you convert to Kcal then it becomes = 1.0476 x 0.23886 = 0.25 Kcal/Kg/K

Step-3
Now note down the heat capacity of water at 150 F which is 0.9975 Kcal/Kg/K.

Step4
Now finally apply Dimoplon rule as,
W1 = 0.2 (20%)
W2 = 0.8 (80%)
Cpw = 0.9975
Cps = 0.25

Hence,
Cps = 0.2 x 0.25 + 0.8 x 0.9975
Cps = 0.848 Kcal/Kg / K

Result
The literature data for this system is reported as 0.850, SO there is a variation of only 0.2%. Thus Dimoplon rule gives a very good estimate of specific heat of solutions with dissolved solids.

The equations are useful for slurry systems where impacts are significant.
Also it can be used for identification of specific heats of solids, where solid handling systems are involved with heat transfer.

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Thumb Rules for Tray Towers

Similar to my previous post, here I am putting few good thumb rules for Tray towers also.

Again be careful while using these thumb rules.

1. For ideal mixtures, relative volatility can be taken as the ratio of pure component vapor pressures.


2. Tower operating pressure is most often determined by the cooling medium in condenser or the maximum allowable re-boiler temperature to avoid degradation of the process fluid.


3. Perform the easiest separation first (least trays and lowest reflux) while sequancing columns


4. If relative volatility, nor feed composition vary widely, take products off one at a time as the overhead.


5. If the relative volatility of components do vary significantly, remove products in order of decreasing volatility.


6. If the concentrations of the feed vary significantly but the relative volatility does not, remove products in order of decreasing concentration.


7. The most economic reflux ratio usually is between 1.2 Rmin and 1.5 Rmin.


8. The most economic number of trays is usually about twice the minimum number of trays.


9. Typically, 10% more trays than are calculated are specified for a tower.


10. Tray spacing should be from 18 to 24 inches, with accessibility in mind.


11. Peak tray efficiencies usually occur at linear vapor velocities of 2 ft/s (0.6 m/s) at moderate pressures, or 6 ft/s (1.8 m/s) under vacuum conditions.


12. A typical pressure drop per tray is 0.1 psi (0.007 bar)


13. Tray efficiencies for aqueous solutions are usually in the range of 60-90% while gas absorption and stripping typically have efficiencies closer to 10-20%.


14. The three most common types of trays are valve, sieve, and bubble cap. Bubble cap trays are typically used when the low-turn down is expected or a lower pressure drop than the valve or sieve trays can be provided.


15. The most common weir heights are 2 and 3 inch and the weir length is typically 75% of the tray diameter.


16. Reflux pumps should be at least 10% over designed.


17. The optimum Kremser absorption factor is usually in the range of 1.25 to 2.00.


18. Reflux drums are almost always horizontally mounted and designed for a 5-min holdup at half of the drum capacity.


19. For towers that are at least 3 ft (0.9 m) in diameter, 4 ft (1.2 m) should be added to the top for vapor release and 6 ft (1.8 m) should be added to the bottom to account for the liquid level and reboiler return.


20. Limit tower heights to 175-ft (53 m) due to wind load and foundation considerations.


21. The length / diameter ratio of a tower should be no more than 30 and preferably below 20.


22. A rough estimate of reboiler duty as a function of tower diameter is given by:

Q = 0.5 D2 for pressure distillation.
Q = 0.3 D2 for atmospheric distillation.
Q = 0.15 D2 for vacuum distillation.

Where Q is in Million Btu/hr and D is lower diameter in feet.

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Thumb Rules for Packed Towers

Here are some thumb rules for Packed Towers which are compiled from various internet sources.

These rules are just for preliminary checks & estimates and should not be followed as design criteria, because design criteria is always different from thumb rules depending on specific conditions & detailed design calculations.

1. Packed towers almost always have lower pressure drop than comparable tray towers.


2. Packing is often retrofitted into existing tray towers, to increase capacity or separation. Thus same size of packed towers can handle more than tray towers.


3. For gas flow rates of 500 ft3/min (14 m3/min) use 1 in (2.5 cm) packing, for gas flows of 2000 ft3/min (57 m3/min) or more, use 2 in (5 cm) packing.


4. Ratio of tower diameter to packing diameter should usually be less than 15.


5. Due to the possibility of deformation, plastic packing should be limited to an unsupported depth of 10-15 ft (3-4 m) while metallic packing can withstand 20-25 ft (6-7.5 m).


6. Liquid distributor should be placed every 5-10 tower diameters along the length for pall rings and every 20 ft (6.5 m) for other types of random packing.


7. Packed columns should operate near 70% flooding.


8. Height Equivalent to theoretical stages (HETS) for vapor liquid contacting is 1.3-1.8 ft for 1in pall rings and 2.5-3 ft for 2.0 in pall rings.


9. Design pressure drop should be as follows

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Understand the Boiler Efficiency

Energy Savings do not always mean efficiency improvement for Boilers.

This is with reference to my previous post long back on How much do you know your boiler efficiency?

Understand the formula
The general efficiency equation is as below

Efficiency = Absorbed heat / Energy Input

But it doesn’t say anything about useful heat. For example blow down is absorbing heat but it is not “useful”. Thus, if you increase the blow down the heat absorption will increase but your efficiency goes down.

In other words, energy in the blow down is not useful energy or is not utilized for useful work i.e. steam generation in case of boilers and hence we should revise the above formula as below

Efficiency = Useful energy / Energy Input
= 1 - Energy wasted / Energy Input

Now even with this formula, should I consider the blow down as a factor / component in energy efficiency calculation.

Factors affecting efficiency
First we have to define the system. Boiler is only furnace & water tube part. If you consider convection section preheater, fans, motors etc. they do not affect the boiler efficiency. They are the part of steam generation system & affect the overall effectiveness or efficiency of “Steam Generation System”.

Most of the people do vice versa even some standards do not considering blow down, steam pressure, steam temperature, condensate return temperature etc as the part of boiler efficiency. In fact they consider combustion air temperature as part of factors affecting efficiency. This is totally illogical from my side.

Let us understand them one by one.

Combustion air
Combustion air temperature entering into the furnace do not affect the Boiler efficiency (It affects the fuel savings or overall steam generation system efficiency but not the boiler part) as its temperature is very low (~200°C max) compared to furnace temperature of ~1200-1400°C. therefore, the changes in the temperature potential (see it equivalent to LMTD) for heat transfer across water tubes is not at all significantly affected.

There is no increase in boiler efficiency even if you preheat combustion air in the economizer in convection section. It is rather heat recovery from the system & not the increase in boiler efficiency.

Condensate return & its temperature
This also does not affect boiler efficiency. The temperature of return condensate is usually very low ~80°C or less compared to steam drum temperature of >200°C. therefore, practically there is no change in temperature potential again.

Similarly, the quantity of return condensate does not alter the total water flow to the boiler drum, which is usually preheated in economizers, & hence practically there is no visible change in heat transfer in the radiation zone of the furnace.

Blow down
Generally, we can assume 2% blow down in the large boilers. This can reduce the drum temperature by ~1.5% of the boiling temperature i.e. if drum temperature is 200°C it will reduce to ~197°C. it will positively affect the heat transfer in the furnace but overall system efficiency goes down. However, it is not considered in the efficiency due to the fact that most of the make up boiler feed water goes to the drum through preheater and therefore, practically drum temperature will not get affected.

Boiler efficiency
So what is the boiler efficiency? Is it really 75-92% depending on the fuel fired & boiler design? Or is it system efficiency for steam generation system?

In fact, what we are generally reading in the books or practically following in the plants is neither boiler (furnace) efficiency nor it is the efficiency of the steam generation system because……….

• We need to consider only furnace part for efficiency calculation of boilers which should be in the range of ~55-60%, as it is usually the case with fired heaters. Therefore, fuel consumption varies based on this efficiency and not based on 80 or 90%. This is the reason that practical savings are always either very less or very high compared to prediction based on 80-90% efficiency.


• We are considering heat recovery in the convection section when we consider final stack gas temperature of 150-200°C without giving credit for other streams being preheated. (Streams not used for boilers e.g. DM water, Air etc. used for other purpose in the plant)


• We are not considering the total station approach e.g. the power used for different motors like ID fan or FD fan, efficiency of other equipments like pumps etc to call it the efficiency of “Steam Generation System” (SGS).


• What we are doing / calculating is the efficiency of package unit supplied by the vendor as “BOILER”.

The objective of this paper is to make it clear in simple language to the young engineers & plant personnel what they are doing and what are the consequences of it. They are not doing anything wrong but one should be clear in what they are doing.

This will explain you the difference in the efficiency from 75-80% on coal to ~85-90% on gas in the same boiler. How it is possible? Is it just because of heat content of ash / fly ash or something else?

Invite your comments if you want to learn more.

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