Question

Calculate the higher and lower heating values of a coal from Illinois which has an ultimate analysis (by mass) as 67.40 percent \(\mathrm{C}, 5.31\) percent \(\mathrm{H}_{2}, 15.11\) percent \(\mathrm{O}_{2}, 1.44\) percent \(\mathrm{N}_{2}, 2.36\) percent \(\mathrm{S},\) and 8.38 percent ash (non- combustibles). The enthalpy of formation of \(\mathrm{SO}_{2}\) is \(-297,100 \mathrm{kJ} / \mathrm{kmol}\).

Short answer

Question: Calculate the higher heating value (HHV) and lower heating value (LHV) of a coal sample from Illinois with the following ultimate analysis: C (67.40%), H (5.31%), S (2.36%). Answer: TheHigher Heating Value (HHV) of the coal sample is -2986.93 kJ per 100 g of coal and the Lower Heating Value (LHV) is -2871.18 kJ per 100 g of coal.

Step-by-step solution

Determine the molar composition of the coal

To determine the molar composition of the coal, convert the percent composition by mass to moles. Assume we have 100 g of coal sample, then we can calculate the moles of each component as follows: - Moles of C: \(\dfrac{67.40\,\text{g}}{12.01\,\text{g/mol}} = 5.61\,\text{moles}\) - Moles of H₂: \(\dfrac{5.31\,\text{g}}{2.02\,\text{g/mol}} = 2.63\,\text{moles}\) - Moles of S: \(\dfrac{2.36\,\text{g}}{32.06\,\text{g/mol}} = 0.0736\,\text{moles}\) (We don't need the moles of O₂, N₂ and ash for this calculation since they don't affect the heating values)

Calculate the heat released by the combustion of individual components

The heat released by the combustion of individual components can be calculated as follows: - Heat released by C (coal) combustion: \(5.61\,\text{moles} \times \dfrac{-394,520\,\text{kJ}}{\text{kmol}} = -2213.01\,\text{kJ}\) - Heat released by H₂ combustion: \(2.63\,\text{moles} \times \dfrac{-285,830\,\text{kJ}}{\text{kmol}} = -752.08\,\text{kJ}\) - Heat released by S combustion: \(0.0736\,\text{moles} \times \dfrac{-297,100\,\text{kJ}}{\text{kmol}} = -21.84\,\text{kJ}\) The negative signs indicate that heat is released (exothermic reactions).

Calculate the higher heating value and lower heating value

To find the Higher Heating Value (HHV), simply add the heat released by the combustion of individual components: HHV \(= (-2213.01\,\text{kJ}) + (-752.08\,\text{kJ}) + (-21.84\,\text{kJ}) = -2986.93\,\text{kJ}\) per 100 g of coal. To determine the Lower Heating Value (LHV), we need to account for the heat loss due to vaporization of water formed during the combustion of H₂. The heat loss can be calculated by multiplying the moles of H₂O formed with the enthalpy change of vaporization of water at 25°C (44,010 kJ/kmol): Heat loss due to H₂O vaporization \(= 2.63\,\text{moles} \times \dfrac{44,010\,\text{kJ}}{\text{kmol}} = 115.75\,\text{kJ}\) Thus, the Lower Heating Value (LHV) is: LHV \(= \text{HHV} - \text{Heat loss due to H₂O vaporization} = -2986.93\,\text{kJ} - (-115.75\,\text{kJ}) = -2871.18\,\text{kJ}\) per 100 g of coal.

Key concepts

Ultimate Analysis of Coal

The ultimate analysis of coal is a critical examination that quantifies the various elemental constituents within a coal sample, namely carbon (C), hydrogen (H), oxygen (O), nitrogen (N), sulfur (S), and ash (incombustible residue). This detailed composition is usually presented as a percentage by mass. Understanding these elemental distributions is crucial for several applications, including combustion processes and the calculation of heating values. By knowing the exact percentages of these elements, we can compute the amount of heat energy (heating values) that the coal will release upon burning.

For the practical application of ultimate analysis in our exercise, a coal sample from Illinois was analyzed. The composition found was primarily carbon, which is typical for coal, along with smaller amounts of hydrogen, oxygen, nitrogen, sulfur, and ash. These findings form the basis for determining the heating values of the coal, which is an essential parameter for energy generation and efficiency calculations.

Enthalpy of Formation

Enthalpy of formation describes the change in enthalpy when one mole of a compound is formed from its constituent elements under standard conditions (typically 1 atm pressure and 25°C). For an exothermic reaction, where heat is released, the enthalpy of formation is negative. Conversely, for endothermic reactions, where heat is absorbed, the value is positive.

In the context of our coal analysis exercise, the enthalpy of formation of sulfur dioxide (SO₂) is a critical value. It is provided as -297,100 kJ/kmol, indicating that when sulfur from the coal combines with oxygen during combustion to form SO₂, a significant amount of heat is released. This is an important consideration when calculating the higher heating value (HHV) because it contributes to the total heat released during coal combustion.

Higher Heating Value (HHV)

The Higher Heating Value (HHV), also known as the gross calorific value, is a measure defining the total amount of heat energy that can be obtained from combusting a given quantity of fuel when the water produced is condensed to a liquid state. This value is essentially the maximum energy yield from a fuel. HHV takes into account not just the heat generated from the combustion of the carbon and hydrogen in the fuel but also other combustible elements like sulfur.

Calculating the HHV for our coal sample involved summing the heat released from the combustion of carbon, hydrogen, and sulfur. This comprehensive approach ensures all available energy in the coal is accounted for, making HHV a key metric for industries where energy content directly translates to fuel efficiency and power generation capacity.

Lower Heating Value (LHV)

The Lower Heating Value (LHV), or the net calorific value, is the effective energy that can be derived from a fuel when the water generated from combustion remains as vapor. Unlike HHV, LHV does not include the heat that could be recovered from condensing this water vapor, a step which requires additional processes or technologies. LHV is a more practical measure of the heat produced in regular combustion systems such as furnaces and engines where water remains in the gaseous state.

For our coal analysis, the LHV was found by subtracting the heat associated with the vaporization of water from the HHV. This adjusted value is lower than the HHV, as it reflects the real-world scenario where the energy used to vaporize the water does not contribute to the heating process. LHV is especially relevant for power plants and heating systems that operate under these normal conditions.