Drawing No. EH–705 // Thermal / Energy Systems
A reactor rejects roughly twice as much heat as it sells as electricity. This model asks what it would cost to pipe some of that heat into a city instead — comparing three supply concepts, the distance you can afford to move heat, and how to cover the coldest days of the year.
Everything updates live. There is no run button — move any control and the whole 8760-hour year is recalculated, along with the schematic, the six headline figures and all four charts. Nothing is hidden behind a submit step.
1. Choose a supply concept. The three options differ in where the heat comes from and therefore in what it costs you. Click the small i on any concept for its description and its performance at your current settings. Start with steam extraction, then switch to the others and watch which cost line dominates change completely.
2. Describe the city and the link to it. Pick a climate, set the annual heat delivered and how far the plant sits from the city. Supply and return temperatures matter more than most people expect — they set the mass flow, and therefore the pipe diameter and most of the pipeline capital. Try dragging the return temperature down and watch the pipe cost fall.
3. Size the capacity mix. Nuclear heat capacity is expressed as a share of peak load, not of energy. Because the load duration curve falls steeply, plant sized at half the peak still supplies most of the annual heat. Everything else — storage, heat pumps, electric boilers, fuel boilers — exists to cover the last few percent that only occurs for a handful of hours. Make sure the shares add to at least 100% of peak, or the model will report unmet heat.
4. Check the market assumptions. The defaults are representative recent European values, but the answer is often more sensitive to the electricity price or the cost of capital than to any engineering choice. Change them and see whether your conclusion survives.
What to read where. The six figures at the top are the headline result. The three panels beneath the controls break down energy, transmission and money. The charts answer four separate questions: which plant runs when, where the cost actually comes from, how far you can afford to move heat, and how much nuclear capacity is worth building.
A good first experiment. Leave everything at default and note the cost of heat. Now push the distance from 25 km to 100 km — the cost rises steeply because pipeline capital scales with length. Bring it back, and instead raise nuclear capacity from 55% to 90% of peak. The cost improves at first and then stops, because you are buying capacity for hours that barely exist. Those two experiments cover most of what the model has to teach.
Save your work with the buttons below the diagram. Save writes every parameter and a summary of the results to a file on your computer; Load restores them. Reset returns every control to its default.
Defaults are representative recent European values. Change them to test how sensitive the answer is to the market rather than the engineering.
Optional reading — open any section below.
A nuclear station converts roughly a third of its heat into electricity and rejects the rest, typically at 30–40 °C, into a river, the sea or the air. A 900 MWth reactor throws away around 600 MW of heat continuously. Meanwhile the city next door burns gas to warm buildings to 20 °C.
The obvious question is why not use one to do the other, and the answer is that the heat is in the wrong place at the wrong temperature. Condenser heat is far too cold to push through a district heating network directly, and moving heat any distance is expensive in a way that moving electricity is not. Both problems are solvable; the model is about what solving them costs.
This is not speculative. Nuclear district heating has operated for decades in Switzerland, Russia, Ukraine, Slovakia, Hungary, China and elsewhere, and several Nordic and Central European utilities have studied large schemes seriously.
Nuclear district heating is not a new idea awaiting demonstration. It has been supplying real customers for more than forty years, and the operating record is a useful corrective to both enthusiasm and dismissal — the technology works, and it has still been deployed far less than its advocates expected.
Switzerland — Beznau and the REFUNA network. The most cited Western European example. Eleven municipalities in the lower Aare valley voted in 1983 to form a company to build a regional heat network fed by the Beznau plant's two pressurised water reactors, and the extraction system was commissioned in 1983–84. It supplies roughly 75–80 MW of heat through about 35 km of transmission main plus some 85 km of local distribution, serving around 20,000 inhabitants and delivering on the order of 140 GWh per year. It has run essentially without incident for four decades. Notably, the operators reported that unusually low return temperatures left considerable spare transport capacity in the main pipeline — the same return-temperature effect this model exposes.
Switzerland — Gösgen. A different use of the same idea. Since December 1979 the Gösgen plant has diverted about 1% of its live steam to supply roughly 45 MW of process heat to a nearby cardboard factory through a short steam line, extended in 1996 with a small district heating network. It is a reminder that industrial process heat is often an easier first customer than a city: closer, steadier, and contracted.
Czech Republic — Temelín to České Budějovice. The most relevant recent European build. A roughly 25 km transmission pipeline, begun in 2019, delivering on the order of 750 TJ per year — about 30 MW on average. By late 2023 it was reported to supply around 30% of the city's district heat and to avoid roughly 80,000 tonnes of CO₂ annually. Its distance and scale sit squarely within the range this model covers, so it is a good sanity check on your own inputs.
Central and Eastern Europe. Several plants built under CMEA-era planning supply nearby towns — Bohunice in Slovakia, Paks in Hungary, and a number of Russian and Ukrainian stations. Heat supply was often designed in from the start, because district heating was already the normal way of heating cities. The pattern is instructive: nuclear district heating spread where dense heat networks already existed and was largely abandoned where they did not.
China — the largest current programme by far. The Haiyang plant in Shandong began supplying heat in 2020 through the network marketed as "Warm Nuclear No. 1". By November 2022 it was reported to be using around 345 MW of thermal output to heat roughly 200,000 homes, displacing twelve coal-fired heating plants. It has since expanded to neighbouring cities, serving on the order of 400,000 people, with proposals to extend towards Qingdao roughly 130 km away — a transmission distance well beyond anything attempted in Europe.
Where it has not happened, and why. The counter-examples matter as much. Sweden's Ågesta reactor supplied a Stockholm suburb in the 1960s and early 1970s and was then shut down. Finland studied piping heat from Loviisa to Helsinki, a distance of roughly 75–80 km, and did not proceed. Swiss plans to add heat extraction at further plants were dropped. The obstacles have rarely been technical. They are the ones this model makes visible: the capital cost of a long pipeline committed before any heat is sold, the value of the electricity given up, and the difficulty of underwriting a forty-year asset against uncertain future heat demand — compounded by the fact that many schemes were proposed against cheap gas.
Reading the model against this record. Industry sources note that more than sixty reactors worldwide are technically capable of supplying heat, while only a handful actually do. If your inputs produce a comfortably attractive cost of heat, it is worth asking why the real-world uptake has been so much narrower than the engineering would suggest. The usual answers are the electricity price assumption, the cost of capital, and the assumption that the customers are already connected.
Sources. IAEA INIS, "75 MW heat extraction from Beznau nuclear power plant (Switzerland)" and the accompanying conference paper on the REFUNA system; POWER Magazine, "District Heating Supply from Nuclear Power Plants" (2022); Leurent et al., "Regress in nuclear district heating: the need for rethinking cogeneration"; CBC, "Nuclear heat keeps people warm in many countries" (2026). Figures are as reported by these sources and have not been independently verified.
Steam extraction takes steam from the turbine before it has finished expanding, at a pressure high enough to reach network temperature directly. It is thermally straightforward and the heat is immediately usable. The cost is electricity: every megawatt-hour of heat costs roughly 0.12–0.20 MWh of lost generation, because that steam no longer expands through the low-pressure turbine. At European electricity prices that lost revenue is usually the single largest line in the whole business case, and it scales directly with the supply temperature you demand.
Condenser latent heat recovery takes the heat that would have been rejected anyway. The catch is temperature: at a normal 35 °C the heat is useless for district heating. The plant must run its condenser deliberately warmer, which costs some output through raised backpressure, and heat pumps must lift the rest of the way. The electricity penalty per unit of heat is far smaller than extraction, but the heat pumps cost capital and consume power. This is the concept that gets most interesting as networks move to lower supply temperatures.
A dedicated heat-only source sidesteps the trade entirely. With no turbine there is no generation to sacrifice, and the reactor can run at lower pressure and temperature. The catch is that the whole capital cost lands on the heat business, rather than being a modest addition to a power station that was being built anyway. This concept lives or dies on capital cost and utilisation.
Switch between them and watch the cost breakdown chart: the three concepts fail and succeed for completely different reasons.
Electricity travels well; heat does not. The reason is simple geometry. A transmission line can carry gigawatts on a structure a metre wide, whereas heat needs a pipe sized for the mass flow:
ṁ = Q / (cp · ΔT)
The model sizes the pipe for the peak flow at a sensible design velocity, and the cost per metre scales with diameter. A large scheme needs DN800–DN1200 twin buried pipe, which runs to roughly 1.5–3 million euros per kilometre before crossings, and the cost is unavoidable capital spent before a single megawatt-hour is sold.
Losses matter less than people expect. A well-insulated large transmission pipe loses around 0.3–0.9 W per metre per kelvin, so even 50 km typically loses only a few percent. Distribution inside the city loses considerably more, which is why the model separates the two — the transmission line is usually a capital problem rather than a thermal one.
The return temperature is the lever most people miss. Widening the difference between supply and return means less mass flow for the same heat, a smaller pipe, lower pumping power and cheaper capital. Drag the return temperature down and watch the pipe diameter and pipeline cost fall. This is precisely why the district heating industry has spent decades pushing return temperatures down.
How the pumping power is calculated. Head loss and pumping power use the Darcy–Weisbach equation, which is general enough to apply to any single-phase fluid, not just water. The friction factor is not a fixed assumption: it is calculated from the Reynolds number and the pipe's internal roughness using the Swamee–Jain approximation to the Colebrook–White equation, so a rougher or narrower pipe genuinely costs more to pump. Water viscosity is evaluated at the average network temperature, so a hotter network (lower viscosity) pumps slightly more easily than a cooler one at the same flow. The Hazen–Williams equation, used elsewhere on this site for simpler water-only pipe-flow problems, is not used here: it is a water-specific empirical correlation with a fixed roughness coefficient that does not respond to Reynolds number, so it is less suitable once the friction factor itself is being modelled explicitly. For other fluids, or where higher accuracy matters than a screening model can offer, use Darcy–Weisbach with site-specific roughness data rather than either of these general-purpose approximations.
Heat demand is far peakier than electricity demand. A cold snap can double the load for a few days, and the annual peak may occur for only a handful of hours. Sizing nuclear capacity for that peak would be absurd — expensive plant sitting idle most of the year.
Instead the base plant is sized well below peak. Because the load duration curve falls steeply, nuclear capacity equal to only 50–60% of peak still supplies around 90% of annual heat energy. Look at the load duration chart: the base band is short but very wide.
The remaining few percent is covered by cheap capacity that runs rarely:
Thermal storage is usually the best value. A large accumulator lets the base plant run flat while the city load swings through the day, shaving daily peaks for a capital cost measured in single euros per kilowatt-hour. It does nothing for a week-long cold spell.
Heat pumps deliver several units of heat per unit of electricity, so they are efficient, but they cost real capital and their advantage shrinks as the source cools — exactly when you need them. Watch the coefficient of performance fall as you lower the source temperature.
How the COP is estimated. No heat pump can beat the Carnot limit, which depends only on the absolute temperatures of the heat source and the network it is delivering into:
COPCarnot = Tsink / (Tsink − Tsource) (absolute temperature, kelvin)
Real machines fall well short of this theoretical ceiling because compression and heat exchange are irreversible. This model assumes a large heat pump achieves 48% of the Carnot COP, a figure representative of well-designed large-scale ammonia or water vapour compression heat pumps used in district heating — smaller or older units typically do worse, the best modern units somewhat better. The result is clamped between 1.6 and 8: below 1.6 a heat pump is rarely worth building over an electric boiler, and above 8 the temperature lift is so small (within about 2 K of the network temperature) that the number stops being physically meaningful, so the model treats it as a practical ceiling instead. The live COP figure updates next to the heat pump source temperature slider so you can see the trade-off directly: a 12 °C source feeding a 95 °C network gives a very different COP to the same source feeding a 70 °C low-temperature network.
Electric boilers are almost free to install and terrible to run, converting expensive electricity one-for-one into heat. That is precisely right for something used a hundred hours a year, and they can also soak up cheap surplus power.
Fuel-fired peak boilers remain the cheapest insurance per kilowatt, at the cost of emissions and carbon price exposure. Raise the CO₂ price and watch them become unattractive.
Try pushing nuclear capacity above about 70% of peak: the cost of heat stops improving, because you are now buying expensive capacity to serve hours that barely exist.
Costs are annualised with a standard capital recovery factor at the chosen cost of capital, over asset lives of 40 years for pipeline, 30 for plant and storage, 25 for boilers and 22 for heat pumps. The capital recovery factor is:
CRF = r(1+r)n / [(1+r)n − 1]
where r is the cost of capital (the "Cost of capital" slider in Market Assumptions) and
n is the asset's life in years. Multiplying CRF by a capital cost spreads it into a level
annual payment over that asset's life, in the same way a mortgage payment spreads a lump sum into equal
instalments. Divided by heat actually delivered to customers, that gives a levelised cost of heat in
euros per megawatt-hour.
Representative European assumptions, all adjustable: pre-insulated twin pipe at roughly 420 € plus 2.35 € per millimetre of diameter per metre of trench; heat pumps at 720 €/kW; electric boilers at 95 €/kW; gas boilers at 65 €/kW; large thermal storage from a few euros per kilowatt-hour upward.
The result is usually dominated by two lines, and which two depends on the concept. Extraction is dominated by lost electricity revenue, so it is sensitive to power prices and to your supply temperature. A dedicated source is dominated by capital, so it is sensitive to the cost of capital and to utilisation. Change the electricity price and watch the ranking of the three concepts change with it — there is no single right answer, only an answer for a given market.
For context, heat production costs in European district heating systems commonly fall in the range of roughly 30–70 €/MWh before distribution margins, taxes and retail costs. Results in that band are plausible; results far outside it should make you check your inputs.
This is a screening model. It deliberately omits a great deal that a real project would have to resolve:
No city distribution network cost. The model assumes a network already exists and charges only for its heat losses. Building one from scratch in an existing city can easily exceed the cost of everything modelled here.
No route engineering. Pipeline cost is a linear function of distance and diameter. Real routes involve river and road crossings, rock, existing services, land acquisition and consent, none of which are linear or predictable.
Simplified thermodynamics. The electricity lost per unit of heat comes from a fitted correlation anchored to typical extraction data, not from a heat balance of a specific turbine. A real assessment uses the machine's own expansion line and extraction points.
No licensing or safety case. Coupling a reactor to a public heat network raises real questions about pressure boundaries, isolation, contamination monitoring and intermediate circuits. These add cost and, more importantly, time.
No demand risk. Heat networks depend on customers connecting, and the model assumes the load simply exists. In practice, connection rates and building efficiency improvements are among the largest uncertainties in any scheme.
Synthetic weather. One seeded year from a smooth climate model, not measured data, and no extreme-year analysis.
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