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(Edited to provide additional info)

My wife is looking to buy an old house (I'm guessing 19th century) that'll need a lot of renovating, including the heating system. Renovation works will include (some) insulation and modernisation of the electric system. Actually the part in which we'll be living seems to have been a farm building; what appear to be the old living quarters are in a small attached house that hasn't seen occupation for at least 40y, from the looks of it. Both are built with local limestone (probably raw-hewn "stones" behind a layer of plaster), meaning there's only so much wall insulation you can install without losing precious internal space. But the obligatory energy-loss assessment is surprisingly good, despite the fact there are no double-glass windows except in the attic (thanks, Velux!).

Currently there is a central heating system that runs on fuel oil which also provides the hot water (except in the kitchen), backed up by a fireplace insert (one of those sealed things) in one of the rooms, plus an electric radiator here and there. We're currently in a rented house which also has individual electric heaters. We are used to in-house temperatures that peak at 20°C at most, 18°C being the more usual average; we wouldn't even want it hotter and having to put on 2 extra layers of clothing plus coat before going outside.

Most likely we will be wanting to get rid of the fuel boiler, either ASAP after getting the house or in the year or so following the acquisition. A single fuel delivery is around 1000€ which corresponds to about the number of individual electric heaters we'd need. It would also cover much of the price of an electric replacement for the fuel boiler, depending on whether we'd opt for a model that also provides hot sanitary water (we'd want a hot water boiler anyway).

I've been reading up on the topic and while electric boilers are clearly the least expensive to buy and install (and maintain) they're apparently the most expensive in use, compared to other energy sources for central heating.

I have not found a single text that compares them to a system with individual space heaters. Can anyone here help with that question? In particular, will a central heater burn more energy if you do not heat all rooms all the time (shut off radiators, manually or via a local thermostat)? Will individual heaters heat the room more efficiently for instance because they get hotter (e.g. oil-based ones that are safer and give less dry heat)?

Our budget doesn't really allow for other alternatives that are more economic in use (or greener), like those using wood pellets or a heat pump. I know running costs of such systems will be lower in the long run but you have to be able to finance the initial investment.

Thanks!

RJVB
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To answer the main question, an electric boiler is exactly as efficient at turning electricity into heat as individual electric heaters. However, individual electric heaters allow per-room heating setups; if you only rarely use a room, you can turn the heat down. However, an oil boiler will almost always be cheaper to run than either, unless you live near a nuclear power plant or dam. (Although an oil delivery is expensive, you don't need oil delivered that often.)

However, with this specific property, having a central boiler, plus a fireplace insert, plus individual heaters, tells me that the central boiler is probably not able to keep up with the heat demands of the house. (Side note: relying on a fireplace for heating is a terrible idea. They leak most of their heat to the outside, and add a large draft to the house.) It sounds like the house was made when it was expected that people would wear a sweater while indoors during winter, with the house not being heated to "room temperature". So, the individual heaters were added in order to provide an extra boost, but comfort is still not going to be great, and you'll probably be paying a lot for heating unless you're willing to use the sweater method.

My suggestion would be to keep the boiler for now. Those things have a service life, and you might as well let that service life run out. In the meantime, you should upgrade the sealing and insulation of the house to at least close to modern standards. This will increase comfort and decrease heating load.

(Side note: some houses have in-ground oil storage. These are expensive to deal with, and you do not want that. Make sure you know where the fuel oil is stored.)

user3757614
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TCO

I am big on Total Cost of Ownership. In this case, it includes the cost of the equipment and also the ongoing cost of fuel. In many areas, electricity costs quite a bit more than fossil fuels (oil or gas) for heating - both space heating and water heating (and combined like a boiler).

Essentially, you have to figure out how much heat you get from 1000€ of fuel oil and how much the equivalent will cost with electric heat. If electricity will also cost 1000€ then the difference is paying it month-by-month instead of a lump sum. If electricity will actually cost you 1500€ then fuel oil starts to make a lot of sense.

All electric heating will cost nominally the same. Electricity in, BTUs out. Comfort may vary depending on how the heat is distributed through the house, but the basic cost doesn't vary much.

Scotty, We Need More Power!

There is also an additional cost to keep in mind if you switch from oil to electric heat and hot water: Upgrading your electric service. An older house designed for oil heat may not have a large enough electric feeder (and panel, etc.) to support full house electric heat and electric hot water. And if you need a meter/feeder/panel upgrade then you may find that you now have to add AFCI, GFCI, etc. to circuits that until now have been grandfathered under old rules. So the cost of installing that inexpensive electric boiler may turn out to be quite significant.

manassehkatz-Moving 2 Codidact
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If you're renewing the building, I strongly suggest to go heat-pump, unless outside temperatures plum in winter under -15°C for long periods.

If climate is mild air-air heat pump (split system) are the best (cool in summer heat in winter and only in desired rooms), if heating is more important than cooling, underfloor with air-water heat pump will be better (you could pass an icy day running on thermal inertia of the building)

For water heating go with a heatpump-fired storage kind water heater, at least 100L/person because heatpump-only mode is quite slow in heating but with traditional backup elements installed (in case HP engine fail), you could get a boiler with also 'auxiliary heat' inlet and hook it up to thermo-solar panel just not to use EE in summer to heat water.

DDS
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Heat pumps work better when they interchange with groundwater instead of ambient air. Air is very light, so you have to move a Lot of air to interchange with much mass of it. That's why air heat pumps sound like jet engines.

For one thing, air is always on the wrong side of your desired temperature, so you’re always having to pump heat "uphill". Imagine the day is 35C and you are trying to air condition to 25C. You have to chill the Freon down to 15C to get it to cool your house's air, and it rises to 25C... then you have to "pump it up" to 40C to get the heat to move into the 35C air. This is inefficient, so you have to move a lot of air.

Whereas, you take your 25C warmed Freon and interchange it with 10C ground water. It moves freely. You don't even need Freon and the enthalpy cycle, any coolant would do because you're "pumping downhill".

On the other side, you're better off heating from 10C groundwater than -5C air - it's uphill, but less uphill. There's just more heat to extract.

If you want to do heat-only and use it for water radiators and household heating, then I guess you'd need a water-water heat pump. But if you can get air radiators, you can do air conditioning.

Harper - Reinstate Monica
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