Question

A country needs to build new power plants to meet

the increasing demand for electric power. One possibility is
to build coal-fired power plants, which cost $1300 per kW
to construct and have an efficiency of 40 percent. Another
possibility is to build clean-burning Integrated Gasification
Combined Cycle (IGCC) plants where the coal is subjected to
heat and pressure to gasify it while removing sulfur and particulate matter from it. The gaseous coal is then burned in a
gas turbine, and part of the waste heat from the exhaust gases
is recovered to generate steam for the steam turbine. The construction of IGCC plants costs about $1500 per kW, but their
efficiency is about 48 percent. The average heating value of
the coal is about 28,000,000 kJ per ton (that is, 28,000,000 kJ
of heat is released when 1 ton of coal is burned). If the IGCC
plant is to recover its cost difference from fuel savings in five
years, determine what the price of coal should be in $ per ton.

Answer 1

To determine the price of coal that would allow the IGCC plant to recover its cost difference from fuel savings in five years, we first need to calculate the cost savings of the IGCC plant compared to the coal-fired power plant. The IGCC plant costs $1500 per kW to construct and has an efficiency of 48 percent, while the coal-fired power plant costs $1300 per kW to construct and has an efficiency of 40 percent. The cost savings of the IGCC plant can be calculated as follows:

$1500/kW - $1300/kW = $200/kW

We can then calculate the total cost savings of the IGCC plant over a five-year period by multiplying the cost savings per kW by the total number of kW the plant will generate in five years. For this calculation, we will assume that the plant will generate 1,000 kW of power.

$200/kW * 1000 kW = $200000

Next, we need to calculate the amount of coal that the IGCC plant would need to burn over a five-year period to generate 1,000 kW of power. We know that the average heating value of coal is 28,000,000 kJ per ton, and that the efficiency of the IGCC plant is 48 percent. We can calculate the amount of coal the IGCC plant would need to burn as follows:

1,000 kW / (28,000,000 kJ/ton * 0.48) = 10.7 tons

Finally, we can calculate the price of coal that would allow the IGCC plant to recover its cost difference from fuel savings in five years by dividing the total cost savings by the amount of coal the plant would need to burn over the same period.

$200000 / 10.7 tons = $18,661.04/ton

Therefore, the price of coal that would allow the IGCC plant to recover its cost difference from fuel savings in five years is $18,661.04/ton.