The following article will guide you about how to calculate the calorific value of fuels. Learn about:- 1. Meaning of Calorific Value of Fuels 2. Theoretical Determination of Calorific Value of Fuel 3. Experimental Determination of Calorific Value of a Fuel 4. Determination of Calorific Value of Fuels Using Bomb Calorimeter 5. Calorific Value of Liquid Fuel 6. Calorific Value of Gaseous Fuels.
Contents:
- Definition of Calorific Value of Fuels `
- Theoretical Determination of Calorific Value of Fuel
- Experimental Determination of Calorific Value of a Fuel
- Determination of Calorific Value of Fuels Using Bomb Calorimeter
- Calorific Value of Liquid Fuel
- Calorific Value of Gaseous Fuels
How to Calculate Calorific value of Fuel? – Answered!
1. Meaning of Calorific Value of Fuels:
The calorific value or the heat value of a solid, liquid or gaseous fuel is defined as the number of heat units developed by the complete combustion of unit mass or unit normal volume of a given fuel. It may be expressed as kJ/kg or kJ/normal m3.
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Sometimes it is also expressed by the name calorific power. In combustion work the term calorific intensity is used which means the maximum temperature attained in a given combustion. For gaseous fuels the calorific value is expressed as kJ/m3 measured at STP.
Any fuel containing available hydrogen will form water vapour during the process of combustion. If, in cooling the products of combustion back to initial temperature, usually room temperature or near it, all of the water vapour formed during combustion is condensed and thus we shall abstract from the products of combustion the maximum heat energy possible.
This is known as the higher, gross or total heat value of the fuel. If during the cooling process to room temperature none of the water vapour formed by the combustion of fuel is condensed, we shall abstract from the products of combustion an amount of heat less than the higher heat value by the quantity of heat carried away by the uncondensed vapour. This smaller heat value is called the lower or net heat value of the fuel.
The calorific value of a fuel can be determined:
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(i) By calculations when the composition of fuel by mass is known.
(ii) By actual experiment.
2. Theoretical Determination or how to calculate Calorific Value of Fuel:
Let C, H, O and S % be the carbon, hydrogen, oxygen and sulphur contents of the fuel respectively.
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Let us consider 100 kg of fuel.
The quantity of heat evolved due to combustion of carbon is C × 35000 kJ, when burnt to CO2.
The quantity of heat evolved due to combustion of hydrogen is –
The assumption is made that any oxygen present in the fuel is already wholly in combination with hydrogen. Since it is known that in water 8 parts by mass of oxygen are combined with 1 part of hydrogen, it is customary to deduct from the total hydrogen an amount equal to 1/8 of the oxygen present, calling the remainder available hydrogen.
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The quantity of heat evolved due to the combustion of sulphur is S × 9160 kJ.
Example:
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A fuel oil consists of 85% carbon, 12.5% hydrogen and the rest is incombustible material. Estimate the higher calorific value and the lower calorific value of this fuel, taking the specific enthalpy of the water vapour formed by combustion to be 2442 kJ/kg.
Solution:
One kg of carbon burning to CO2 liberates 35000 kJ, and one kg of hydrogen liberates 143000 kj, when the products of combustion are cooled down to 25°C.
Higher calorific value = 0.85 × 35000 + 0.125 × 143000
= 47750 kJ/kg.
Lower calorific value = 47750 – 9 × 0.125 × 2442
= 45000 kJ/kg.
3. Experimental Determination or how to calculate Calorific Value of a Fuel:
An apparatus which is used for determining the calorific value of a fuel is known as a fuel calorimeter.
The principle of all the calorimeters is the transference of heat of combustion of the given mass of fuel to water and the vessel. From the observed rise of temperature of the water and the container the calorific value of the fuel can be determined by equating the heat given out by the fuel to the heat taken by the water and the container. In order to know the heat taken by the container, water equivalent of the container should be known.
In this method of determining the calorific value of a fuel the following conditions should be satisfied:
(i) The combustion of the fuel must be complete.
(ii) The heat must be transferred completely to the water.
(iii) Cooling losses from the calorimeter must be corrected.
(iv) The rise of temperature of water must be correctly determined because the mass of the fuel is very small in comparison with the quantity of water heated.
Calorimeters may be classified as follows:
(i) Where combustion is achieved by admixture of fuel with a solid oxidizing agent such as sodium peroxide and mixture of potassium chlorate and potassium nitrate
(ii) By combustion with oxygen at ordinary pressure
(iii) By combustion with oxygen at high pressures.
The results obtained by combustion with oxygen at high pressure are correct and therefore they are used for determining the calorific value of solid and liquid fuels.
When a solid or liquid fuel is burnt, the energy release due to combustion of the fuel is measured in an isothermal constant volume reaction performed in a special combustion chamber known as a bomb.
The energy release, when a gaseous fuel is burned, is measured in an isothermal constant pressure reaction.
If a fuel is burnt at constant volume the energy evolved will all go into the stock of internal energy of the products of combustion produced, since no external work is done.
The calorific value in this case is, therefore, sometimes called the internal energy of combustion or the internal energy of reaction.
If, however, a fuel is burnt at constant pressure then the calorific value will be modified as a function of whether there is an increase in volume, the volume remains the same or if there is a volumetric contraction after combustion.
If there is an increase in volume then some energy will be used up in performing the work of expansion. In this case the calorific value will be decreased.
If there is no change of volume, the calorific value of the fuel remains unchanged.
If there is a volume contraction then the calorific value is increased by an amount equal to the contraction work.
If either case, however, the process being at constant pressure will mean that the energy liberated due to combustion of the fuel will appear a change of enthalpy.
The calorific value in this case is, therefore, sometimes called the enthalpy of combustion or the enthalpy of reaction.
4. Determination of Calorific Value of Fuels Using Bomb Calorimeter:
In a bomb calorimeter, oxygen is employed at about 25 atmospheric pressure. No products escape during the experiment and since the bomb which is the combustion vessel is immersed almost completely in water the whole of the heat is transferred to the water. This type of calorimeter is as perfect as possible but its high cost has allowed certain inferior types to compete with it.
Description:
The bomb calorimeter consists of a strong steel shell known as the bomb which has a capacity of 650 c.c. and is designed to withstand a pressure of 200 atmospheres. It is lined with enamel to prevent corrosion due to the action of gases formed during the combustion of the fuel and the exterior of the bomb is nickel plated.
A cover and cap screws at the bottom of the bomb are made perfectly gas tight by means of a spanner. The top has a valve for the introduction of oxygen. The bottom cover is provided with insulated firing plug and platinum nickel supports for the crucible and magnesium wire. The crucible is made of silica and quartz.
The mass of the fuel taken depends upon the type of calorimeter and mass of water used. The quantity of the fuel should be so taken that the temperature rise of water is limited to 3°C because the thermometer can read upto 5°C temperature rise. The bomb is placed in a water container in which a known quantity of water is taken.
Surrounding this water container is a water jacket. An air space is left between the water container and the water jacket. An outer cover is also provided which encloses the water container and through this cover suitable stirring arrangement passes through for stirring the water. Besides a hole is provided for a thermometer which can read upto 1/100 degree centigrade. Terminals are provided for electrical connections at the bottom.
A known quantity of the fuel is taken and a pillet is formed from it. It is placed in the crucible and fusible wire surrounds this pillet. The bomb cover is screwed in position and oxygen at a high pressure is admitted into the bomb until the pressure on the gauge indicates 25 to 30 atmospheres. The screw valve is closed and the bomb is disconnected from the tube supplying oxygen and also from the pressure gauge.
The bomb is then connected to the electric wires. A known mass of water is poured in the container. The cover is now placed in position and an interval of about 10 minutes is allowed for the equalization of temperature of the bomb and the water container.
During the interval stirring is carried out continuously and the temperature readings are taken at regular intervals and when the indicated temperature is constant the fuel is ignited. The combustion is very rapid, and the heat generated is transferred from the wall of the bomb to the water.
The stirring of the water is continued at the uniform rate and the temperature of water is recorded at regular intervals. The temperature will rise initially and reach to a maximum value and then begins to fall gradually due to cooling losses of the instrument. By noting this decrease in temperature the rate of cooling can be obtained.
Let C be the calorific value of fuel in calories, M be the water taken in gm, m be the water equivalent of the container in gm, θ°C be the corrected rise in temperature of the water and container and x be the mass of fuel burnt in gm.
Then heat given by the fuel = x × C
Heat taken by the water = θ (M + m) C,
where C is the specific heat of water.
By equating the above two heat quantities, assuming that there is no loss during the transfer of heat, we get –
In order to find out the water equivalent (m) of the bomb and the calorimeter, chemical compounds of known calorific values are taken.
The following are the compounds generally used:
(i) Naphthalene- Calorific value = 40.57 MJ/kg
(ii) Benzoic acid- Calorific value = 26.489 MJ/kg
(iii) Cane sugar- Calorific value = 16.564 MJ/kg.
One of the above compounds is burnt in a bomb and the rise in temperature as indicated by the thermometer is observed. The amount of heat given out by the fuel is known and so water equivalent of the bomb and calorimeter can be calculated with the usual formula. The equation for the determination of water equivalent of the bomb is given as –
This value of water equivalent is to be taken for calculating the calorific value of the fuel.
Example:
A bomb calorimeter was used to determine the calorific value of a sample of coal and the following readings were recorded:
When the fuel is fired in a boiler, the calorific value given by bomb cannot be realised in furnace because the water vapour cannot give up its enthalpy as it does in the bomb. Also the bomb works at constant volume while boiler furnace works at constant pressure.
5. Calorific Value of Liquid Fuel:
The calorific value of non-volatile fuels may be determined in bomb calorimeter in the same manner as with solid fuels. The liquid fuel is weighed in the crucible and ignition is effected by a cotton thread attached to the platinum ignition wire and dipping in the sample.
If the fuel does not ignite, it may be absorbed in three or four paper discs whose mass is known. The heat received by the water will be due to combustion of fuel plus the paper discs or the sample of thread.
By making allowance for the combustion of paper discs or thread, calorific value of oil fuel can be determined.
With very volatile liquids such as motor spirits, etc. bomb calorimeters are dangerous and special precautions must be taken. During the period when the initial temperature readings are taken the spirit volatilizes and an explosive mixture is formed which may detonate with violence. Another difficulty occurs in weighing spirits into platinum crucible due to losses by evaporation tending to give low results. Several methods have been adopted in order to overcome both these difficulties.
These are:
(i) Covering crucible with a piece of thin rubber sheet,
(ii) Enclosing spirit in a glass bulb, and
(iii) Use of celluloid capsules.
Of all the three methods, the last one would be most satisfactory if only capsules of uniform calorific values were obtainable.
Another method of obtaining the calorific value of spirits is to vaporize them and burn the vapour in a gas calorimeter. Suitable arrangement is provided to weigh the liquid which has been evaporated.
Example:
In an experimental determination of the calorific value of oil having hydrogen content of 14% the following data were obtained:
Mass of oil 0.579 gm; mass of water 1400 gm; water equivalent of calorimeter 500 gm; rise in temperature of water 2.912°C; cooling correction 0.058°C; mass of cotton used in igniting oil 0.005 gm; calorific value of cotton is 16750 J/gm. Find the higher and lower calorific values of the fuel. Specific heat of water may be taken as 4.1868 J/gm-K.
6. Calorific Value of Gaseous Fuels:
The calorific value of a gas may be determined in a bomb calorimeter but many calorimeters of suitable types are available so that bomb calorimeter is not employed.
The most suitable form of calorimeter is one in which constant flow of water is used for cooling. From the volume of gas burnt, the rise of temperature of water and mass of water heated, the calorific value is obtained.
The heat entering the calorimeter is:
(i) Calorific value of the fuel,
(ii) Sensible heat in air and gas supplied to the calorimeter, and
(iii) Sensible heat of water entering the calorimeter.
The heat leaving the calorimeter is:
(i) Sensible heat of water leaving the calorimeter,
(ii) Sensible heat in the products of combustion,
(iii) Sensible heat in the condensate produced from the hydrogen in the fuel and the moisture in the gas and air, and
(iv) Heat due to radiation.
When the calorimeter is properly run, the products of combustion leave the apparatus at the same temperature as inlet air. When the temperature range is small the radiation losses are eliminated.
The following readings are to be taken:
(i) Time of run
(ii) Pressure of gas supply in mm of water
(iii) Temperature of gas supply
(iv) Barometer reading
(v) Amount of gas consumed
(vi) Temperature of entering water
(vii) Temperature of leaving water
(viii) Quantity of water circulated
(ix) Amount of condensate collected.
The above calorific value will be the higher calorific value of fuel at a given pressure and temperature which can be converted to STP conditions by gas law PV/T = constant. From the amount of condensate collected the lower calorific value can be obtained.
In order to have low temperature of products of combustion, a specific relationship should exist between –
(i) The rate at which gas is burnt,
(ii) The rate of flow of circulating water, and
(iii) The temperature rise of circulating water.
The board of Referries in England have recommended a meter speed of 1/10 of 1 ft3/min for a test occupying 4 minutes during which 2100 ± 50 c.c. of water should be circulated and the temperature rise should be about 20°C.
A gas pressure regulator is used to damp out the pulsation in the gas supply which would affect adversely the results. A weir is provided to ensure a uniform supply of circulating water while to avoid air bubbles which would affect the specific heat of water, the water should be drawn from a tank in preference to mains.
In order to calculate the calorific values of gaseous fuels, a complete chemical analysis is made to find its composition. By reckoning the sum of the calorific values of all the constituent combustible gases when burnt separately as free gas, an estimate is made of the heat evolved by the complete combustion of the m3 of the gaseous mixture and in the subsequent cooling of the burnt products. The complete analysis requires skillful chemical manipulation in the separation and determination of the quantity of heavy hydrocarbons present.
The chemical analysis gives the volume of each gas present in the compound or mixture but affords no clue as to the chemical constitution or the way in which the elements are held together or how the constituent gases interact during combustion at the high temperature.
If we know the calorific values of carbon and hydrogen, in order to estimate the calorific values of hydrocarbon present it is assumed that the calorific values of hydrocarbons such as CH4 and C2H6 are equal to the sum of the calorific values of carbon and hydrogen present as free elements in them when separately burnt, without knowing either the amount of heat energy used up in the decomposition of the gases or interaction that may take place between the different gases in the process of combustion. The calorific value of hydrocarbon gaseous fuels is given in table 8-5.
The method of calculating the calorific value of a composite gaseous fuel is explained in the illustrative example 1.
Example:
