HP1.1 · Useful heat, temperature and electrification pathways

Learning objectives

• Define useful MW_th/MWh_th separately from electrical and fuel inputs.
• Explain direct heating, heat recovery and heat-pump energy balance.
• Check temperature quality, source availability and electrical headroom.

Allow 30–45 minutes including derivations and exercises. All numerical values are teaching assumptions.

1. Describe the actual production service

Start at the process user: what fluid or product must be heated, to which supply temperature or steam condition, at what flow, for how long and with what permitted interruption? Return temperature, pressure, phase change, hygiene and contamination limits can change the supply technology. A yearly fuel total does not identify the peak service or its temperature quality.

Place the useful-heat meter after the relevant heat exchanger or distribution boundary. For a stable single-phase fluid, heat rate can be estimated from mass flow, specific heat and temperature difference if the properties and measurements are appropriate. Steam or phase-changing processes need the corresponding enthalpy states rather than a casual temperature-difference shortcut. [H1]

For a single-phase liquid, the simplified balance is Q̇ = ṁ × c_p × (T_supply − T_return). With a fictional water-like c_p of 4.2 kJ/(kg·K), a 50 kg/s stream heated through 10 K receives 2,100 kJ/s, or 2.1 MW_th. The kJ/s-to-kW conversion is essential. This example assumes approximately constant properties and excludes phase change; for steam, use the relevant specific enthalpy difference Q̇ = ṁ × Δh and define pressure, dryness or superheat as applicable.

2. Distinguish three energy quantities

MW_e describes electrical power and MWh_e its energy over time. MW_th describes useful heat rate and MWh_th the delivered heat quantity. Fuel MWh is an input on a stated lower- or higher-heating-value basis. The boiler efficiency and fuel price must use a compatible basis; otherwise the apparent saving can be a bookkeeping error.

A 2 MW_th service for six hours requires 12 MWh_th. A hypothetical 85% boiler needs 12 / 0.85 = 14.1176 MWh of fuel input. At 40 currency units per fuel MWh, the duty energy cost is 564.7059. This excludes capital, maintenance and other charges. A six-hour example is not automatically an annual operating profile.

3. Direct heating converts work into useful heat

With an assumed 98% electricity-to-useful-heat efficiency at the declared boundary, 12 MWh_th requires 12.2449 MWh_e. Constant electrical demand is 2 / 0.98 = 2.0408 MW_e. The grid interface must support that coincident import after other site loads and any reserve margin. A low energy price does not create physical headroom.

Resistance, electrode and other electric process-heating technologies have distinct process interfaces and operating ranges. Do not transfer one efficiency to every temperature and load point. The useful service may still require a heat exchanger, circulation, water treatment, pressure control or a legacy backup path whose energy and costs must be included consistently.

4. A heat pump combines work with source heat

Heating COP equals useful heat divided by electrical input at specified conditions. For 2 MW_th and COP 2.5, electrical input is 0.8 MW_e and the simplified balance requires 1.2 MW_th from the source. Over six hours these become 4.8 MWh_e and 7.2 MWh_th. COP above one does not create energy: the remaining heat arrives from the source. [H2]

Source temperature, recoverable heat flow and time availability matter alongside sink temperature and part load. If only 0.8 MW_th can be extracted from the source under the stated COP, the theoretical heat-output ceiling from that source is 0.8 / (1 − 1/2.5) = 1.3333 MW_th. Additional electrical headroom alone does not establish the requested 2 MW_th in that operating mode.

A common vapour-compression heat pump circulates a working fluid through four main functions. An evaporator absorbs heat from the source; a compressor raises the vapour pressure using electrical work; a condenser or relevant high-side heat exchanger releases useful heat; and an expansion device lowers pressure before the next source-side pass. Source and process fluids commonly exchange heat across surfaces rather than mixing. Each exchanger needs a temperature difference, so equipment temperatures and process delivery temperatures are distinct. This is a functional explanation, not a refrigerant-selection or pressure-system design. [H2, H4]

Temperature lift describes the separation between source and sink operating temperatures. A larger lift generally increases compressor work per unit of useful heat, but a real COP must come from a performance map or test at the actual temperatures, flow rates and load. An ideal heating-cycle upper bound uses absolute temperatures: COP_ideal = T_hot / (T_hot − T_cold). It excludes practical irreversibilities and auxiliaries and must not be entered as an equipment guarantee. The whole-system boundary must include pumps, fans and any backup heat consistently when comparing alternatives.

5. Match heat quality before comparing money

A device verified to deliver at 120°C does not establish a 150°C process service. Check the guaranteed useful outlet condition after the relevant exchanger, including source changes, pinch/approach requirements, steam quality and start/ramp behaviour. A hot refrigerant or storage core temperature is not automatically the delivered process temperature.

For an electricity price of 100 per MWh_e, the illustrative heat-pump duty energy cost is 480, compared with the boiler’s 564.7059. This apparent advantage is conditional on the temperature, source heat and electrical checks. IEA’s industrial discussion [H3] also identifies site integration and energy prices as important project conditions.

Worked answers and reasoning

Attempt the exercises before opening each answer.