## July 29, 2009

### Latent Heat Calculation

The most used & ever needed property is the latent heat of vaporization which is critical also for various calculations. A process engineer must understand it properly.

This is one of the property of a pure fluid or a mixture which is never available to you when you need it most specially when you need it urgently. That time you are never able to recall the source where did you see it last time.

So don't worry now. There are few easy methods available which can give you quick & accurate estimate of this be it for pure fluid or for a liquid mixture.

The first method I am discussing is Riedel's Correlation.
This method is limited to calculating latent heat at normal boiling point only. However, this is a property which can be used for the derivation of other properties also. We will see it in future & coming posts.

Hvb = 1.093 R Tc [ Trb x {Ln(Pc)-1}/{0.930 - Trb}]

Where
Hvb = Latent heat at normal boiling point. (Remember this is an important definition)
Trb = Tb / Tc Reduced Boiling Point Ratio in Kelvin
Pc = Critical Pressure atm

Hvb Unit is Lit-Atm/Gm-mole
R = Gas Constant in Lit-Atm/Gm-mole/K

So change R value in different unit & you will get Hvb in desired unit accordingly, because the value in parantheses is unitless.
Also note that 1 Lit-Atm/Gm-mole is equal to 24.12 Cal/gm-mole

The second method I am discussing is Pitzer's Correlation.
This method is applicable for a wide range from normal boiling point to critical point.

The equation given is as below.

(Hv / R Tc) = 7.08 ( 1 - Tr)^0.354 + 10.95 * omega ( 1 - Tr)^0.456

Hv = Latent heat at t °C.
Tr = (t+273.15)/Tc
omega is accentricity factor - a std property

The third method I am discussing is Watson's Correlation.
This method is most useful for the fluid where you know the latent heat at a given temperature & want to calculate it at another temperature, or using some simulation where accurate estimate is required so instead of using basic equations you can use this escalation equation.

Hv2 = Hv1 [ (1 - Tr2) / (1 - Tr1)]^0.378

Hv1 = latent heat at T1
Hv2 = latent heat at T2

Units are same as described in first method.

List of other property estimation methods on this Blog.

## July 21, 2009

### Vapor Pressure Vs Temperature

Generally we search too many things for frequently used properties like the vapor pressure or saturation temperature at given condition which is the most common among all.

Though the famous & simplest correlation of Antoine is available but many a times we do not find correlation constants A, B & C for a given compound. Therefore, I always prefer methods which uses its own thermodynamic property e.g. critical parameters for calculation of any derived property.

So this post is giving a method which uses Tc, PC atc for calculating vapor pressure, though the method is somewhat tedious but can be used once formulated in Excel or in any other program.

The method used in this case is called Gomez - Nieto & Thodos which is based on critical properties.

The equation is

Ln (Pvr^5) = beta [ (1/ Tr^m)-1] + gamma (Tr^n - 1)

Where
Pvr is basically reduced vapor pressure i.e. Pv / Pc
Tr is as usual reduced temperature at T i.e. T/Tc

m = [0.78425 exp (0.089315 * S)] - [8.5217 / exp (0.74826 * S)]
n = 7
beta =-4.267-[221.79/{(S^2.5)(exp(0.03848 S^2.5))}]+[3.8126 / exp(2272.44 /S^3)]
gamma = a * S + b * beta

a = [(1/Trb)-1]/(1-Trb^7)
b = [(1/Trb^m)-1]/(1-Trb^7)
S = Tb * Ln (Pc)/ (Tc - Tb)

Here Pc is in atm & Pvr is in mmHg.

List of other property estimation methods on this Blog.

## July 13, 2009

### Cooling Tower - Audit & Efficiency

I have written three posts & one audit report on this topic of cooling towers calculations. Recently one of our reader suggested that I should go for posting an article on how to identify different components of cooling tower performance. Therefore, I decided to provide the details on how to establish different factors contributing to the inefficiencies in case of a cooling tower.

The article & report I have earlier published are here.

Factors affecting cooling tower & how to find out the impact of each of them.

Effect of Water Temperature
The impact of return water temperature is that the cooling approach must change by ~50% of the difference in the design & actual return water temperature. For example: If a tower is designed for 4°C approach for the cooling of water from 44°C to 34°C and actual return water temperature is 42°C then you must get an approach of 3°C instead of 4°C. The range of cooling will be 9°C against design value of 10°C. Thus, if your return water temperature is 42°C against design value of 44°C and you are getting design approach of 4°C that means your cooling tower is operating inefficiently.

Effect of Wet Bulb
Similarly, In this case, the approach of cooling will go up by ~50% of the difference between design & actual wet bulb, if wet bulb is lower than design value. However, total range of cooling will also increase in this case by ~50% of the difference in actual & design wet bulb i.e. 44°C to 33°C means range of cooling will increase from 10°C to 11°C.

Yes, one should not infer from these two examples that the thumb rules expressed here are valid for any changes in the temperatures. Instead, it is always governed by the equilibrium conditions & for larger changes one should go for proper evaluation procedure as described later in this article.

Cooling towers are normally supplied in standard modules called tower cells. Therefore, the cooling water is distributed equally on each cell in parallel configuration. However, in actual operation it deviates from what it should be (Average water flow/cell). This causes for example 80% water on one cell & total water flow being the same it will be 120% on the other. Even the same cell might have different water loading on both sides of distribution deck. This much deviation may result in ~5-10% rise in cooling approach.

Effect of Air Distribution
Similarly, the imbalance in air loading in each side of every cell may cause 1.5 times more negative impact as compared to effect of disturbed water loading. Thus, 20% deviation in air distribution may cause ~10-15% rise in cooling approach.

Effect of Air Short Circuiting
By now it is clear that operators has to regularly monitor the performance of their cooling tower especially at different loads & at different ambient conditions. More appropriately, the comparison of actual approach with the design approach is not a good & actual indicator of its performance

NTU Calculation
For the identification of actual differences in the performance calculation of a cooling tower & for identifying the impact of each factor, NTU calculation method is the most useful & recommended one based on my experience.

As Promised earlier in the performance calculation - II, I am giving here the method for using this NTU for prediction of performance.

Step - 1
Start with how much is approximate difference in inlet & exit temperature from cooling tower & divide them in equal parts with say an increment of 0.2°C or so.

Start from first row & column A with some approx t temperature & make diff in column G as zero. (This all is explained in above linked article on this Blog)

Since all other rows are linked with same increment of 0.2 till last row, finally you should get your inlet temperature in last row & column A. If it is less or more change it in first row to get same.

With each change all rows in column G should have zero value as difference.

Step - 2
Once you get all zero in column G and inlet temperature in last row of Column A, the first row in column A should give you the exit temperature, but wait.

Now you need to check the sum of NTUL in column K or NTUG in column N. This value should be equal to your design NTU. (Yes, design NTU is also found in similar manner)

Example, so if you want to evaluate the impact of change in wet bulb compared to design, first consider all data of design & find out NTUG in design.

Now change wet bulb & you will see that ha in column F is changed, so you need to change t in column A to make difference in column G = 0.

Finally you will find the changed temperature figure at the exit by keeping NTUG same.

## July 06, 2009

### Ultimate Analysis of Biomass

Heating value & ultimate analysis of any fuel be it biomass or fossil fuel is correlated long back by Du-Long in 19th Century.

Most recently a Mr. S. A. Channiwala 1992 thesis, The Indian Institute of Technology, Bombay) collected data on over 200 species of biomass and fitted the following equation to the data:

HHV (in kJ/g) = 0.3491C + 1.1783 H - 0.1034 O - 0.0211 A + 0.1005 S -0.0151 N

Where C is the weight fraction of carbon; H of hydrogen; O of oxygen; A of ash; S of sulfur and N of nitrogen appearing in the sltimate analysis.

This equation fitted the experimental data with an average error of 1.45%, typical of the error of most measurements. This equation permits using heat values in calculations and models of biomass processes.

However, I am giving here the table for fuels indicating their ultimate analysis & HHV.

Source: - BioMass Energy Website