1. In HW#4 you estimated the amount of gasoline (ie, gallons per year) you use for automotive transportation. Now your task is to estimate the amount of pollution you cause through our dependency on the automobile.

Assume a chemical formula of C₈H₁₅ for gasoline. Based on this formula, prove that complete combustion of 1 kg (kilogram) of gasoline results in the emission of 3.17 kg of CO₂.

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Assume one US gallon of gasoline has a mass of 2.85 kg. Assume the vehicle travels (on average) 25 miles per gallon. Based on this information, prove that the CO₂ emission is 360 grams per mile.

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The CO emission limit for automobiles sold in the USA (set by the USEPA) is about 1% of the CO₂ emission determined above (it is 3.4 grams per mile). Based on your personal dependency on the automobile, how much CO₂ (as kg per year) and how much CO (as kg per year) do you emit?

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Find the US emission limits for UHC and NOx from automobiles. Determine your emissions of UHC (as kg per year) and NOx (as kg per year) from your dependency on the automobile.

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2. Now let’s consider pollution from the combined cycle combustion turbine, which is becoming important for electricity generation in the Pacific Northwest. The fuel is natural gas. Large state-of-the-art combined cycle power plants have a rated electrical power output of 250 MW and an overall (fuel to electricity) efficiency of 58%. Assume the combined cycle power plant runs at rated power 8000 hours per year (that is, its capacity factor is 8000/8760 = 0.91).

We need to know the heating value of the natural gas. On p. 3:7, Bodansky gives this as 1033 BTU per scf. A standard cubic foot of natural gas has a mass of about 0.022 kg. Converting BTU to kJ and scf to kg, gives a heating value of about 49,500 kJ/kg. We’ll assume 50 MJ/kg. Unfortunately, this is the Higher Heating Value (HHV), which assumes the H₂O in the exhaust gases is condensed. However, most combustion equipment does not condense the exhaust H₂O – it goes up the stack (or out the tail pipe) as gas. The heat of condensation is not captured! Engines, including combined cycle power plants are rated on the basis of the fuel’s Lower Heating Value (LHV). This assumes the H₂O remains as a gas. For natural gas, LHV @ 0.9 x HHV. Thus, for this problem, the heating value we use is LHV = 45 MJ/kg.

Determine the kg of natural gas burned per year by the combined cycle power plant.

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The combustion chambers of the combined cycle (in the gas turbine engine) burn the natural gas with a large excess of air. This reduces the flame temperature, greatly curtailing the formation of NOx. Early on we learned high efficiency requires the heat to be added at high temperature. This is still true! However, the T_H is the temperature of the burnt gases entering the turbine of the gas turbine engine. And this temperature is limited by the turbine blade material properties and the turbine blade cooling methods used. Current technology limits T_H to a maximum of about 1700K (2600 deg F), and many engines run no hotter than about 1500K (2240 deg F) at the turbine inlet. The flame on the other hand, will produce minimal NOx if it is maintained not much hotter than 1800K. This requires an air-fuel ratio for the flame of about double that for chemically correct burning. The excess air is the diluent. The combustor is lean and premixed.

The chemical equation below is for a combined cycle running with 225% excess air (some of the excess air is added after the flame, so the flame doesn’t get so lean it blows out). The natural composition is CH_3.8.

CH_3.8 + (1.95)(1+225/100)O₂ + 3.773(1.95)(1+225/100)N₂ ®

CO₂ + 1.90H₂O + (1.95)(225/100)O₂ + 3.773(1.95)(1+225/100)N₂

Calculate the kg of CO2 emitted per year.

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Measurements of exhaust emissions are done on dry, molar basis. Thus, by the chemical equation, the exhaust measurements of CO₂ and O₂ would be:

3.4% CO₂ and 15% O₂. Verify these values.

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The CO and NOx exhaust measurements for this combined cycle power plant are: CO = 0.001% and NOx = 0.001%. Find the annual emissions of CO and NOx (as kg per year for each pollutant). NOx is assumed to have the mass of NO₂.

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Additional comment: It is useful to compare emissions on the basis of the fuel burned and the work done. This comparison is made in the table below, assuming 1 kg of fuel.

Note 1: The combined cycle assumed in this HW has state-of-the-art low-NOx (and low-CO) combustors. Systems of a few years ago had CO and NOx emissions of about 0.0025% each. Several of these systems installed exhaust emission control catalysts to reduce the CO and NOx to under 0.001% each. (This caused an ammonia emission of about 0.001%. Ammonia is used since it chemically reduces NOx: NH₃ + NOx ® N₂ + …)

Note 2: Most combined cycle power plants are on interruptable natural gas service. The price is lower, but the supplier can cut off the supply, especially in the winter when the gas is badly needed for residential and commercial heating. Thus, most combined cycle systems are equipped to run on oil (#2 diesel oil) if necessary. This increases emissions! A month of running on oil can significantly impact the annual CO, NOx, SO₂, and particulate emissions of the power plant. During running on oil, the combustors may need to be injected with water to control the NOx (by cooling the flame). This adds capital and operating costs.