FE Environmental Energy and Environment Practice Problems

The current FE Environmental specification assigns 4-6 of the 110 exam questions to Energy and Environment. Form A contains 4 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A regional grid generates 3,200 GWh from coal at 0.95 t CO $_{2}$ /MWh, 4,800 GWh from natural gas at 0.42 t CO $_{2}$ /MWh, and 2,000 GWh from zero-emitting renewables in one year. The carbon intensity of the delivered electricity is most nearly:

(A)457 kg CO $_{2}$ /MWh
(B)506 kg CO $_{2}$ /MWh
(C)590 kg CO $_{2}$ /MWh
(D)632 kg CO $_{2}$ /MWh

Show worked solution

Answer: (B)

Fossil generation emits 5.06 million tonnes across the year, and spreading that over all 10,000 GWh delivered gives about 506 kg CO $_{2}$ per MWh.

Only the two fossil sources emit, each contributing its generation times its own emission factor.

m_{coal} = (3.2 \times 1 0^{6} MWh) (0.95) = 3.04 \times 1 0^{6} t

m_{gas} = (4.8 \times 1 0^{6} MWh) (0.42) = 2.016 \times 1 0^{6} t

Renewable output carries no emissions but still reaches customers, so it belongs in the denominator, where it dilutes the fossil contribution.

I = \frac{5.056 \times 1 0 ^{6} t}{10 \times 1 0 ^{6} MWh} = 0.5056 t/MWh

I = 506 kg CO_{2} /MWh

FE Reference Handbook — Energy and Environment: Emission Factors and Carbon Intensity of Electricity Generation

Why the other choices appear

(A)Averaging the three emission factors without weighting them by generation, $(0.95 + 0.42 + 0) /3 = 0.457$ t/MWh, gives 457 kg CO $_{2}$ /MWh.
(C)Interchanging the coal and gas generation shares, $0.48 (0.95) + 0.32 (0.42) = 0.590$ t/MWh, gives 590 kg CO $_{2}$ /MWh.
(D)Dividing the same emissions by fossil generation alone, $5.056 \times 1 0^{6} /8 \times 1 0^{6} = 0.632$ t/MWh, gives 632 kg CO $_{2}$ /MWh and describes the fossil fleet rather than the delivered mix.

FE Environmental Energy and Environment Practice Problems

Free FE Environmental problems in the other knowledge areas