Question

A diesel engine with an engine volume of \(4.0 \mathrm{L}\) and an engine speed of 2500 rpm operates on an air-fuel ratio of \(18 \mathrm{kg}\) air/kg fuel. The engine uses light diesel fuel that contains 750 ppm (parts per million) of sulfur by mass. All of this sulfur is exhausted to the environment where the sulfur is converted to sulfurous acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{3}\right)\). If the rate of the air entering the engine is \(336 \mathrm{kg} / \mathrm{h}\), determine the mass flow rate of sulfur in the exhaust. Also, determine the mass flow rate of sulfurous acid added to the environment if for each kmol of sulfur in the exhaust, one kmol sulfurous acid will be added to the environment.

Short answer

Answer: The mass flow rate of sulfur in the diesel engine exhaust is 0.014 kg/h and the mass flow rate of sulfurous acid formed in the environment is 0.0359 kg/h.

Step-by-step solution

Calculate the mass flow rate of fuel

Since we know the rate of air entering the engine and the air-fuel ratio, we can calculate the mass flow rate of the fuel. The formula for the mass flow rate of fuel is: Mass flow rate of fuel = (Mass flow rate of air) / (Air-fuel ratio) Given, Mass flow rate of air = 336 kg/h and Air-fuel ratio = 18 kg air/kg fuel. Calculate the mass flow rate of fuel: Mass flow rate of fuel = (336 kg/h) / 18 = 18.67 kg/h

Calculate the mass flow rate of sulfur

We are given that the diesel fuel contains 750 ppm of sulfur by mass. It means there is 750 grams of sulfur in every million grams of fuel. We can use this information to find the mass flow rate of sulfur in the exhaust: Mass flow rate of sulfur = (Mass flow rate of fuel) * (Sulfur content in fuel) Convert the sulfur content from ppm to mass fraction: Sulfur content (mass fraction) = 750/1000000 = 0.00075 Now, calculate the mass flow rate of sulfur: Mass flow rate of sulfur = (18.67 kg/h) * (0.00075) = 0.014 kg/h

Determine the mass flow rate of sulfurous acid

We are given that for each kmol of sulfur in the exhaust, one kmol of sulfurous acid is added to the environment. To find the mass flow rate of sulfurous acid, we first need to find the mass fraction of sulfur in sulfurous acid. Using the molar mass of sulfur (M_S = 32.065 g/mol) and the molar mass of sulfurous acid (M_H2SO3 = 82.07 g/mol), we can find the mass fraction: Mass fraction of sulfur in sulfurous acid = M_S / M_H2SO3 = 32.065 / 82.07 = 0.3904 Now, we can find the mass flow rate of sulfurous acid using the mass flow rate of sulfur: Mass flow rate of sulfurous acid = (Mass flow rate of sulfur) / (Mass fraction of sulfur in sulfurous acid) Mass flow rate of sulfurous acid = (0.014 kg/h) / (0.3904) = 0.0359 kg/h So the mass flow rate of sulfur in the exhaust is 0.014 kg/h, and the mass flow rate of sulfurous acid added to the environment is 0.0359 kg/h.

Key concepts

Mass Flow Rate Calculation

Understanding the mass flow rate calculation is essential when analyzing engine performance and its impact on emissions. The mass flow rate represents the amount of mass passing through a given point per unit time. Typically measured in kilograms per hour (kg/h) for engine applications, this allows engineers to estimate fuel consumption and forecast the output of exhaust products.

When dealing with diesel engine emissions, one first calculates the mass flow rate of air entering the engine and, using the air-fuel ratio, deduces the fuel mass flow rate. Applying the formula \( \text{Mass flow rate of fuel} = \frac{\text{Mass flow rate of air}}{\text{Air-fuel ratio}} \) we find the proportional amount of fuel consumed for a given amount of air. This step is crucial for predicting fuel efficiency and the subsequent generation of exhaust components, including pollutants.

Air-Fuel Ratio

The air-fuel ratio plays a significant role not only in the efficiency of a diesel engine but also in the production of emissions. It is defined as how much air is used to burn a unit mass of fuel and is usually expressed as a mass ratio (kg air/kg fuel).

The optimal air-fuel ratio is essential for complete combustion; if the ratio is too low (rich mixture), there will be unburnt fuel, whereas a high ratio (lean mixture) may result in excess oxygen, leading to the formation of nitrogen oxides (NOx). The balance is crucial for minimizing the environmental impact while maintaining engine performance.

In the context of the exercise, knowing the air-fuel ratio allows us to compute the quantity of fuel used, which then helps us determine the quantity of pollutants, such as sulfur, that will be emitted from the exhaust.

Environmental Impact of Engine Exhaust

The impact of diesel engine exhaust on the environment is significant due to the emission of various pollutants, including sulfur compounds, nitrogen oxides, particulate matter, and greenhouse gases. Sulfur, when present in diesel fuel, transforms into sulfurous acid upon combustion, contributing to acid rain and respiratory problems in humans and wildlife.

By calculating the mass flow rate of sulfur emissions using the previously determined sulfur content in fuel, one can estimate the extent of the environmental impact. In our exercise, we used the formula \( \text{Mass flow rate of sulfurous acid} = \frac{\text{Mass flow rate of sulfur}}{\text{Mass fraction of sulfur in sulfurous acid}} \) to determine the amount of sulfurous acid added to the environment. This understanding helps in designing emission control strategies such as using low-sulfur fuels and implementing exhaust after-treatment systems like sulfur traps or scrubbers.