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.
Educational demonstration only. A screening-level techno-economic model with representative
European cost assumptions. Climate determines the hourly load shape; the selected annual heat
demand independently scales that profile. Dispatch follows a fixed priority order rather than a
least-cost optimisation. It is not a feasibility study, a bankable cost estimate, or a substitute
for site-specific engineering.
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 the plant-side peak duty, including network and transmission losses, not of annual 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.
Levelised cost of heat——
Total capital cost——
Peak heat load——
Nuclear share of heat——
Electricity sacrificed——
CO₂ avoided——
Supply Concept
City & Network
A wider temperature difference means less flow, a smaller pipe and lower pumping power.
Capacity Mix
As a share of plant-side peak duty, including distribution and transmission losses. Base plant sized below peak can still cover most annual energy.
—
Hours of peak load. A large accumulator lets the base plant run flat while the city load swings.
Energy Balance
Heat delivered to customers—
Nuclear heat supplied—
Heat pumps—
Electric boilers—
Peak boilers—
Transmission losses—
Distribution losses—
Unmet heat—
Storage cycles—
Transmission
Pipe diameter—
Peak mass flow—
Pipeline cost—
Cost per metre—
Standing heat loss—
Pumping power at peak—
Friction factor / Reynolds no.—
Economics
Annualised capital—
Lost electricity revenue—
Nuclear heat cost—
Electricity for HP / boilers—
Peak fuel + carbon—
Total annual cost—
Market Assumptions
Defaults are representative recent European values. Change them to test how sensitive the answer is to the market rather than the engineering.
Low end: large pit or tank accumulator. High end: pressurised steel vessels.
Sets the friction factor together with the Reynolds number. ~0.045–0.05 mm is typical for new steel pipe; older or scaled pipe can be several times rougher.
Load duration curve and supply stack
Where the cost comes from
Cost of heat versus distance
Effect of nuclear capacity share
Cost of heatNuclear share of annual energy
Background
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.
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 are part of the base heat interface, require dedicated capital and consume substantial electricity. 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:
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.
What is this model intended for?
It is an educational and preliminary screening model for comparing nuclear district-heating concepts,
transmission distance, capacity mix, storage and market assumptions. It is not a feasibility study,
hydraulic network design or bankable cost estimate.
How is the annual heat-demand profile generated?
The model creates an 8,760-hour synthetic load profile from the selected climate and then scales that
profile to the annual heat delivered entered by the user. Climate therefore changes the shape,
seasonality and peak-to-average ratio, while annual demand sets the total energy.
Does the model optimise the lowest-cost supply mix?
No. It uses a transparent fixed-priority dispatch order: nuclear heat, storage, heat pumps, electric
boilers and then fuel-fired peak boilers. The controls are intended for sensitivity studies rather
than mathematical least-cost optimisation.
Why does condenser heat recovery require a heat pump?
Condenser heat is normally available at a temperature too low for direct use in a conventional
district-heating network. The model therefore includes a dedicated large heat pump, its electricity
consumption, capital cost and maintenance, as well as the assumed effect of elevated condenser
temperature on plant electricity output.
Why can a long transmission pipeline still have moderate percentage heat loss?
A large insulated pipe can carry hundreds of megawatts while its external surface area grows much
more slowly than the transported heat. The percentage loss can therefore remain modest even though
the absolute heat loss and pipeline capital cost are significant. The model is a screening
approximation and does not replace a manufacturer-specific EN 13941 calculation.
Why can the levelised cost of heat display INVALID?
The model suppresses the headline LCOH when the selected capacities leave meaningful heat demand
unmet. Otherwise an undersized system could appear artificially inexpensive because it serves only
the easiest part of the annual load.
What does nuclear heat capacity as a percentage mean?
It is the installed nuclear heat capacity as a share of the calculated plant-side peak duty,
including distribution and transmission losses. It is not the share of annual heat energy. Because
the load-duration curve falls steeply, capacity below the peak can still supply most of the annual
energy.
Can these results be used for a real investment decision?
No. A real project requires measured demand data, route and geotechnical studies, detailed hydraulic
network modelling, turbine and heat-pump performance data, safety and licensing analysis, commercial
arrangements and a project-specific cost estimate.