In sulfuric acid production, the conversion rate of each section in the converter is a critical production indicator, indirectly reflecting both the efficient utilization of raw materials and product yield. Currently, most sulfuric acid plants calculate conversion rates by measuring gas concentrations in each section. Alternatively, conversion rates can be determined using empirical formulas based on inlet and outlet gas temperatures to calculate λ, where λ values can be obtained from reference tables. This paper introduces a method for calculating conversion rates using heat balance. It aims to provide industry professionals with an alternative approach for assessing conversion efficiency.

The calculation requires the gas composition and inlet/outlet temperatures for the specific section. Treating the reactor as a closed system, the conversion process considers only exothermic reactions without other heat interferences. Changes in gas temperature thus indicate the extent of reaction. We now calculate the conversion rate using the first section as an example.

Given confirmed inlet and outlet temperatures, the heat converted can be calculated by multiplying the heat capacity by the temperature difference, then multiplying by the molar quantity of flue gas. However, since flue gas consists of four components—sulfur dioxide, sulfur trioxide, oxygen, and nitrogen—the heat capacity of the entire flue gas cannot be directly derived from a single component's heat capacity. Therefore, separate calculations are required. The specific heat capacities for each gas are shown in the figure below. This method employs average temperature as the calculation metric to minimize error.

Assuming inlet and outlet temperatures of 415°C and 617°C, respectively, with gas concentrations of 0.1067 for sulfur dioxide, 0.0032 for sulfur trioxide, 0.0985 for oxygen, and 0.7916 for nitrogen. Calculating the specific heat capacities yields the following results, where temperatures are expressed in Kelvin and thus require adding 273.15 during computation:

Average Temperature = (Inlet Temperature + Outlet Temperature) / 2 = (415 + 617) / 2 + 273.15 = 789.15

Average specific heat capacity of sulfur dioxide = 26.04 + 5.8 × 10⁻² × average temperature - 38.1 × 10⁻⁶ × average temperature² + 0.861 × 10⁻⁸ × average temperature³ = 52.31500887

Average specific heat capacity of sulfur trioxide = 15.09 + 15.2 × 10⁻² × average temperature - 120.7 × 10⁻⁶ × average temperature² + 3.62 × 10⁻⁸ × average temperature³ = 77.66440599

Average specific heat capacity of oxygen = 26.04 + 1.3 × 10⁻² × Average Temperature - 3.86*10⁻⁶*Average Temperature² = 33.89510519

Average Specific Heat Capacity of Nitrogen = 27.48 + 0.591*10⁻²*Average Temperature - 0.338*10⁻⁶*Average Temperature² = 31.93338439

For convenience, the gas flow rate is now set to 10000Nm³/h. Multiplying the gas flow rate by the corresponding gas concentration and dividing by 22.4 yields the molar quantity of each gas.

The heat required per 1°C temperature increase can be calculated:

Heat required per 1℃ temperature rise = Average heat capacity of sulfur dioxide × Molar amount of sulfur dioxide + Average heat capacity of sulfur trioxide × Molar amount of sulfur trioxide + Average heat capacity of oxygen × Molar amount of oxygen + Average heat capacity of nitrogen × Molar amount of nitrogen = 15378.42522

For the reaction of sulfur dioxide with oxygen to form sulfur trioxide, each mole of sulfur dioxide released generates 99227.2 J of heat.

Multiplying the temperature increase of 617 - 415 = 202°C by the heat required per 1°C temperature rise yields the total heat released by the reaction. Dividing this heat by the reaction heat of 99,227.2 J determines the amount of sulfur dioxide consumed. Dividing this amount by the input volume for the section gives the conversion rate for that section.

Amount of SO₂ reacted = (Exit temperature - Entry temperature) × Heat required per 1°C temperature rise / 99,227.2 = 31.30635445 First-stage conversion rate = Amount of SO₂ reacted × 100 / Molar quantity of SO₂ entering first stage = 65.72280597

Since the molar quantity of SO₂ entering the first stage correlates with gas volume, the gas volume is effectively canceled out during calculations. Therefore, the conversion rate remains unaffected whether using formula 1 or 10000.

This method calculates conversion rates using heat balance. For other stages, calculate the corresponding gas concentration using the preceding stage's conversion rate, then apply the above method. A simplified formula can be established in Excel. Each time it is used, simply input the gas concentration and corresponding temperature to obtain the corresponding conversion rate. There is no need to measure gas concentrations across multiple stages or consult tables to calculate λ values. However, due to the complexity of actual production and the varying operating conditions of different reactors, this method can provide a reference but cannot fully account for on-site conditions. It requires adjustment for practical application.