Question 7 of 8: Seasonal heating fuel, and a gas furnace versus an air-source heat pump

Question 7: Seasonal heating fuel, and a gas furnace versus an air-source heat pump (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 small commercial building in Toronto with a known design heating load and design temperature difference, heated by a gas furnace of stated efficiency, and a proposed air-source heat pump alternative.

Find. The yearly heating fuel requirement; a schematic of an air-to-air heat pump serving this load; an account of other heat-pump types; and advice to the owner on cost and environmental impact.

Approach. Convert the design load and design temperature difference into an overall building conductance, apply the modified degree-day method to get the seasonal heat delivered, divide by the furnace efficiency to get fuel input, and convert to cubic metres of gas. Then repeat the seasonal calculation with the heat pump's system COP and compare cost and emissions on the stated assumptions.

1. Building conductance at design. The whole design load must be met by the heating plant, so the effective overall conductance including infiltration is$$UA = \frac{\dot{Q}_s + \dot{Q}_l}{t_i - t_o} = \frac{75 + 12}{22 - (-20)} = \frac{87}{42} = 2.0714 \text{ kW/K}$$
2. Seasonal heat delivered, by the modified degree-day method. Toronto has about 3520 °C·days below 18 °C. The correction factor $C_D$ accounts for the fact that internal and solar gains carry part of the load and that the plant does not run at design efficiency all season; 0.70 is the usual value for a commercial building at these temperatures:$$\dot{Q}_{del} = UA \times \text{HDD} \times 24 \times C_D = 2.0714 \times 3520 \times 24 \times 0.70$$$$\dot{Q}_{del} = 122496 \text{ kWh/year} = 441 \text{ GJ/year}$$
3. Fuel input to the furnace. At 85% efficiency,$$\dot{Q}_{fuel} = \frac{\dot{Q}_{del}}{\eta_f} = \frac{122496}{0.85} = 144113 \text{ kWh} = 518.8 \text{ GJ}$$
4. Yearly natural gas requirement. At a higher heating value of 37.5 MJ/m$^3$,$$V_{gas} = \frac{518.8 \times 10^3 \text{ MJ}}{37.5 \text{ MJ/m}^3} = \boxed{13835 \text{ m}^3\text{/year}}$$ At the assumed delivered price of CAD 0.32/m$^3$ this costs about CAD 4427 per year.
5. Heat pump: system coefficient of performance. The contractor's 3.56 is a shaft-work COP; the electricity actually purchased must also cover the motor losses, so$$\text{COP}_{sys} = \text{COP} \times \eta_m = 3.56 \times 0.82 = 2.919$$$$E_{hp} = \frac{\dot{Q}_{del}}{\text{COP}_{sys}} = \frac{122496}{2.919} = \boxed{41962 \text{ kWh/year}}$$ At CAD 0.13/kWh that is about CAD 5455 per year.
6. Compare operating cost. On these assumptions the heat pump costs about CAD $1028$ more per year than the furnace — roughly $23$ % more — despite moving heat about three times more efficiently than the furnace burns it. The reason is entirely the price ratio: electricity at CAD 0.13/kWh is $0.13 \div (0.32 \times 3.6/37.5) = 4.2$ times the cost of the same delivered energy in gas, so a COP of about $3.6$ is needed merely to break even. A resistance-heated building would spend CAD $15924$, so the heat pump is still far better than electric baseboards.
7. Compare environmental impact. Natural gas emits about 1.921 kg CO₂e per cubic metre burned, whereas Ontario's electricity grid is largely nuclear and hydro with an intensity of roughly 30 g CO₂e/kWh:$$\text{gas: } 13835 \times 1.921 = 26577 \text{ kg CO}_2\text{e/y} \qquad \text{heat pump: } 41962 \times 0.030 = 1259 \text{ kg CO}_2\text{e/y}$$ a reduction of about $95$ %, or $25.3$ tonnes of CO₂e per year. This is the decisive difference between the two options, and it is a feature of the Ontario grid specifically — the same comparison in Alberta or Saskatchewan would favour the heat pump far less.
8. Other types of heat pump. Heat pumps are classified by the source and sink they exchange with. An air-to-air unit, as drawn above, is the cheapest to install but suffers exactly where this building needs it most: capacity and COP both fall as outdoor temperature drops, and periodic defrost cycles impose a further penalty. An air-to-water unit rejects into a hydronic loop and suits buildings with fan-coil or radiant distribution. A ground-source (geothermal) heat pump, water-to-air or water-to-water, exchanges with vertical boreholes, horizontal loops or a pond; because the ground stays near the annual mean temperature, seasonal COP is both higher and far more stable, at the cost of substantial drilling. A water-source machine uses a lake, river, well or a building's own condenser-water loop, and in the water-loop form allows heat rejected by one zone to serve another. Wastewater and sewer-source heat pumps exploit a warm, stable urban resource and are in service in several Canadian district-energy schemes. Finally, absorption heat pumps are driven by heat rather than shaft work and are worth considering where waste heat or cheap gas is available.
9. Advice to the owner. Four points, in order of importance. First, verify the COP claim at the design condition. A COP of 3.56 is a rating-point or seasonal figure; no ordinary air-source machine achieves it at −20 °C, where COP typically falls to 1.5–2.0 and capacity to roughly half of nameplate. The contractor should be asked for certified capacity and COP tables at −8, −15 and −20 °C. Second, do not remove the furnace. A dual-fuel (hybrid) installation — heat pump as the lead source, existing gas furnace as backup below a changeover temperature chosen on cost or emissions — captures most of the emissions benefit, keeps the design-day capacity the building already has, and avoids the electrical service upgrade that resistance backup would demand. Third, be candid that the operating cost will probably rise. On the assumptions above the heat pump costs about CAD 1028 a year more; the case for it is environmental and, increasingly, regulatory, not financial at today's Ontario price ratio. The owner should test the sensitivity to future carbon pricing and to time-of-use electricity rates before committing. Fourth, look at the envelope first. A 2.07 kW/K conductance on a small commercial building is high; air sealing, attic insulation and glazing upgrades reduce the load for every option simultaneously, and they also let a smaller and cheaper heat pump cover a larger fraction of the season.