Question 1 of 8: Seasonal heating fuel, and a gas furnace against an air-to-air heat pump in Winnipeg

Question 1: Seasonal heating fuel, and a gas furnace against an air-to-air heat pump in Winnipeg (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A commercial building in Winnipeg with a design heating load of 150 kW sensible and 15 kW latent, held at 22 °C against a −33 °C outdoor design temperature, presently heated by an 83 % efficient natural-gas warm-air furnace; the proposed alternative is an air-to-air heat pump of rated COP 3.6 with an 82 % efficient compressor motor, supplied from a coal-fired grid of 32 % overall efficiency.

Find. The annual natural-gas consumption of the existing furnace, and whether the proposed air-to-air heat pump is defensible for this location on energy, cost and carbon grounds.

Approach. Convert the design load into a seasonal energy requirement with the modified degree-day method, divide by the furnace efficiency to obtain fuel, then compare the heat pump with the furnace on three independent yardsticks — delivered cost, primary (fuel) energy and carbon — rather than on COP against efficiency, which are not comparable numbers.

1. Reduce the design load to a building conductance. The sensible load is proportional to the indoor-to-outdoor temperature difference, so $$UA=\frac{q_s}{t_i-t_o}=\frac{150\ \text{kW}}{22-(-33)} =\frac{150}{55}=2.727\ \text{kW/K}$$ This conductance lumps envelope transmission and infiltration together; it is the only building property the degree-day method needs.
2. Convert degree-days into equivalent full-load hours. The modified degree-day method writes the seasonal heat requirement as $Q=24\,UA\,\mathrm{DD}\,C_D$. Dividing by the design temperature difference expresses the same thing as the number of hours the plant would run at full output, $$\mathrm{EFLH}=\frac{24\,\mathrm{DD}\,C_D}{t_i-t_o} =\frac{24\times 5670\times 0.70}{55}=1,732\ \text{h}$$ About 1730 hours of full-load operation in a 5670 degree-day climate is the expected order for a commercial building; a residence with a larger internal gain fraction would show fewer.
3. Seasonal heat delivered to the space. Multiplying the design outputs by the equivalent hours, $$Q_{space}=q_s\,\mathrm{EFLH}=150\times 1,732 =259,789\ \text{kWh/yr}$$ $$Q_{hum}=q_l\,\mathrm{EFLH}=15\times 1,732 =25,979\ \text{kWh/yr}$$ The latent term is the duty of the humidifier, which in a warm-air system is a separate electrically fed appliance rather than part of the furnace output; it is carried separately from here on and charged to electricity in both options, so it does not bias the comparison.
4. Fuel input to the furnace. Dividing the delivered space heat by the seasonal efficiency, $$Q_{fuel}=\frac{Q_{space}}{\eta_f}=\frac{259,789}{0.83} =312,999\ \text{kWh}=1,126,796\ \text{MJ}$$ and at a higher heating value of 37.5 MJ/m³, $$\boxed{\;V_{gas}=\frac{1,126,796}{37.5} =30,048\ \text{m}^3\ \text{of natural gas per year}\;}$$ which at CAD 0.30/m³ is about CAD 11,612 per year once the humidifier electricity is added.
5. Refer the heat-pump COP to the electricity meter. A COP quoted at the compressor shaft has not yet paid for the motor. The useful figure for an energy comparison is $$\mathrm{COP}_{el}=\mathrm{COP}_{sh}\,\eta_m=3.6\times 0.82 =2.95$$ so the seasonal electricity, taken at the rated COP and therefore as a best case, is $$W_{hp}=\frac{Q_{space}}{\mathrm{COP}_{el}} =\frac{259,789}{2.95}=88,004\ \text{kWh/yr}$$
6. Compare on primary energy, not on COP. A COP of 2.95 and a furnace efficiency of 0.83 are not comparable numbers, because a kilowatt hour of electricity from a 32 % coal plant costs about three kilowatt hours of fuel. Putting both on the same basis with a 7 % transmission and distribution loss, $$\mathrm{PER}_{hp}=\mathrm{COP}_{el}\,\eta_p\,\eta_{td} =2.95\times 0.32\times 0.93=0.879 \qquad \mathrm{PER}_{furnace}=\eta_f=0.83$$ $$\boxed{\;\mathrm{PER}_{hp}=0.879\ \text{against}\ \mathrm{PER}_{furnace}=0.83\;}$$ The heat pump wins by under 6 % on primary energy — and only if it achieves its rated COP in every hour of a Winnipeg winter, which it cannot.
7. Compare on carbon and on cost. With the emission factors stated above, $$m_{CO_2,gas}=30,048\times 1.886+25,979\times 1.142=86,351\ \text{kg/yr}$$ $$m_{CO_2,hp}=(88,004+25,979)\times 1.142 =130,223\ \text{kg/yr}$$ and on operating cost, CAD 11,612 per year for the furnace against CAD 11,398 per year for the heat pump — a difference of well under 2 %, which is inside the uncertainty of the tariff assumptions.

The arithmetic answers the contractor's proposal directly, but the climate answers it more forcefully. Is this a good solution for this location? No. An air-to-air machine must lift heat out of air at the −33 °C design condition. Three things happen together as the outdoor temperature falls: the suction density collapses, so the mass flow the compressor can move falls roughly in proportion; the pressure ratio rises, so the work per unit mass rises; and the building load rises linearly with the temperature difference. Capacity and demand therefore diverge, and the two curves cross at the balance point, typically near −8 to −12 °C for equipment sized to a mild-climate rating. Below it every additional kilowatt comes from resistance backup at a COP of 1. Most conventional units also carry a low-ambient cut-out near −20 to −25 °C, above the Winnipeg design temperature, and lose a further 5 – 10 % of seasonal output to defrost cycles. The seasonal COP will therefore be far below the rated 3.6, and the 6 % primary-energy margin computed above is erased before the coldest month even begins.

Other types of heat pump. The limitation is the source, not the cycle, so the useful alternatives all change what the evaporator draws from. A ground-source (geo-exchange) machine takes heat from vertical boreholes or horizontal loops where the ground stays near 4 – 8 °C all winter; the source temperature is then almost independent of weather, the seasonal COP holds near 3.5 – 4.0, there is no defrost penalty, and capacity does not fade when the load peaks. A water-source machine on a building loop, a lake or a sewer main behaves similarly. An air-to-water machine feeds hydronic terminals and suits a retrofit with existing radiators, although the higher sink temperature costs COP. Exhaust-air heat pumps recover from the building's own relief air, which is at room temperature but limited in quantity. Absorption (gas-fired) heat pumps deliver a heating COP near 1.3 –1.6 on gas alone and sidestep the generation penalty entirely. CO₂ transcritical machines maintain capacity at low ambient and give high water temperatures, at the price of very high operating pressures.

Advice to the owner. Do not install the air-to-air machine as proposed. Ranked by risk-adjusted return: first, replace the 83 % furnace with a condensing unit at 95 % seasonal efficiency, which is a low-capital, no-risk 13 % cut in gas with no change to the distribution system; second, if the site can accept a borehole field, a ground-source heat pump is the only electric option whose seasonal COP is high enough to beat a modern gas furnace on all three yardsticks; third, a dual-fuel hybrid — air-source above the balance point, gas below — captures the shoulder-season savings without exposing the building to a −33 °C day on resistance heat. In every case, the air-side measures come first: reducing the 2.727 kW/K conductance with envelope and infiltration work shrinks whatever plant is finally chosen.

Comment on the coal-fired grid. The 32 % figure is the whole argument. A heat pump is a device for moving heat, so its environmental merit is inherited entirely from the electricity it moves it with: at 32 % generation and 7 % delivery loss the primary-energy ratio is 0.879, and the carbon result is worse still — 130,223 kg CO₂ per year against 86,351 kg for the furnace, a 51 % increase — because coal emits roughly twice as much carbon per unit of fuel energy as natural gas. On this grid the machine would have to reach an electrical COP of about 3.4 merely to break even with the furnace on primary energy, and far higher to break even on carbon. It is worth stating the converse, because it is the real engineering lesson: Manitoba's actual grid is more than 97 % hydro, and on that grid the same heat pump would cut carbon by well over 90 %. The technology is not good or bad in itself — it is exactly as clean as the generation behind it.