Posted by: @bobtskutter

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But I guess that's the problem you're trying to solve.

I should add that there is another problem we have been trying to solve, so far without success, the question of how much setbacks (eg an overnight setback for 6 hours) save energy/money with compromising comfort. The empirical evidence is they do save some money, in some situations, but not as much as you might expect, because you need a recovery boost after the setback that uses more energy during that recovery than you would have used without the setback. @jamespa has been trying to produce a model to do this that takes account of the energy flows in to and out from the fabric of the building, and has got close to an answer, but so far a definitive model has eluded him. I think that is where he might welcome and appreciate your input. 

Here's an interim chart for the last week, with key events added (CC3->CC1 is the secondary circulating pump setting):

I think the energy balance model of setback I posted a few days ago (attached again) is not a bad approximation and certainly exhibits all of the qualitative behaviours I would expect intuitively.  However there is definitely scope for improvement.

Part of the problem with setbacks is to define the problem.  This is an area where I do think I have made some (significant) progress over the last few days.

In my models of setback I approximate the cooling phase by a linear drop in temperature, which is a reasonable approximation for temperature falls which are small relative to the difference between IAT and OAT.  The (re)heating phase however is exponential, asymptotically approaching the equilibrium temperature, and a linear approximation is not adequate in this case.

For some while I have struggled with how to deal with 'asymptotically approaching' in the model.  My struggle is not just with the maths (which is difficult enough) but with what 'boundary conditions' to impose such that the model represents what we need to do in reality.  I think I have now worked the latter out!

Since we are talking about a setback that occurs every 24hrs, the requirement (for the model and the house) is that the house temperature returns to the starting temperature (which we will call the design temperature) 24hrs after the heating was turned off (so the cycle starts again from the same point).  This defines the flow temperature required in the setback case, which will be higher than the flow temperature required to maintain the design temperature if the heating were constant.  At this higher flow temperature the COP will be lower, the latter is the penalty of part time heating, to be offset against the savings from reduced loss to the outside world.

Since the house is never in equilibrium at the design temperature the second consideration is the period during which the house temperature is sufficiently close to the design temperature for the occupants to be comfortable.  To assess this we can define a temperature 'tolerance' (which might be 0.5-1C) and from that can work out for how much time the IAT is within the tolerance.  We can call this the 'acceptability time' t_a.  Unless we have a 'timed boost' mechanism we cant control this independently, so for now I will be content simply to work out how long ta is once the stage above is completed and, since few will have a timed boost, I don't currently think its necessary to go further to get a very good insight into behaviours.

if we work out t_a and energy use during the reheat time under the above conditions, we have, I think, an adequate and usable model of the setback case which is better than the simple model in the spreadsheet I have posted.  There is scope to argue whether the 'control' against which the setback case is compared should be a house heated constantly to the 'design temperature' as defined above, or to a the slightly lower value design temperature-tolerance/2.  This wont affect the model materially, but in the latter case the parameter space where setback is beneficial will be smaller

Solving this should give us a robust model for the one setback in 24hrs case.  Once that is solved 2 setbacks in 24hrs should be a fairly simple extension.

The attached sketch illustrates these concepts

I have some equations describing the performance but need to collect them together together with the proofs, refine them, and then solve them (with the help of those here, ChatGPT or another tool).  Unfortunately as we want a representation which explores the behaviour over a range of parameter values (like the cruder model in the spreadsheet) we cant easily use excel to integrate/differentiate, we need some formulae.  Since the underlying behaviour is exponential and both the integral and derivative of exponential functions is known, that shouldn't be beyond the wit of man (but it may be beyond the wit of me!).

I may take a break from this for a day or so for sanity, but will return.

Evening...I got the spreadsheet.  Blimey, there aren't many people I know who know how to use named ranges - very nice 😉

It'll take me a while to go through it, life gets in the way.

Have you got a specific forum thread somewhere for this discussion?

Oh...not sure how my Chemical Engineering brain stacks up against a Doctor and a Physicist, but I'll try and help.

Bob

Posted by: @bobtskutter

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Blimey, there aren't many people I know who know how to use named ranges - very nice

And then just look at them there formulas!

Posted by: @bobtskutter

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not sure how my Chemical Engineering brain stacks up against a Doctor and a Physicist, but I'll try and help

I think the benefit is all three of us understand how science works, but from different viewpoints.

Inevitably posts on the subject are now scattered among various forum threads, including this one. The original thread which still contains a lot of the discussion is "Do setbacks save energy without compromising comfort?" but it is a long one (843 posts over 71 pages) and much of the discussion is now historic, though definitely worth reading my original post since that sets the scene. The basic problem is how to describe (model in modern language) heat flow through a building in various states in such a way that the results match the empirical results. Very quickly you get into 'well, it depends' territory, eg it depends very much on the thermal characteristics of the building - and that's why we are still hammering away at it! It's partly an academic challenge because certainly I and I think @jamespa enjoy such challenges for their own sake but it also has the potential to provide very useful answers on whether a particular setback regime will save you money, and if so, how much, or even whether, counter-intuitively, some setbacks may even cost you more money.       

Posted by: @bobtskutter

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Evening...I got the spreadsheet.  Blimey, there aren't many people I know who know how to use named ranges - very nice 😉

 

I haven't used named ranges either more than a couple of times previously, but I found following the formulae with eg d23^d22*d2/2 difficult to follow, so I thought Id give it a try.  Having done it I rather like it so will reuse.

My aim now, following the advances over the past few days, is now to solve the 'problem' illustrated in the scanned sketch, building in the real world effects listed in the spreadsheet, and then present it in a format similar to the results page of the spreadsheet.  I plan to do this over a currently unspecified period.   

This would be a bit of an advance on the spreadsheet as it currently stands, because it models recovery more accurately and has an objective definition of when recovery has taken place.   I think this should be a tolerably robust model, but of course still doesn't take into account (a) the fact that the house is not monolithic, (b) plate heat exchangers, buffer tanks and llhs and various other things.  Modelling (a), and in particular the air in the house vs the house fabric, would definitely be useful, but too challenging at present and for the foreseeable future.  I don't think its worth modelling (b) given our stance against such things (understanding of course that they can work) and anyway I wouldn't know how to.

Yes I do enjoy such 'academic' challenges, it keeps my brain active.  However I also have to be aware that spending too much time on heat pumps is not good for me!

Ideas on how best to go about this welcome!

Posted by: @jamespa

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Ideas on how best to go about this welcome!

Anyone here with an AI background? 😉 

Plenty of data with which to develop an appropriate model.

So, I'm thinking out loud here - this is a way I often approach solving complex problems:

I've got a house at 10C and I turn on the heating.  Where does the energy go that I'm paying for?

If it's gas/oil some of the energy is lost out the combustion appliance flue pipe.

I'm billed for my gas based on Higher Heating Value and I don't have a condensing boiler, so I'm loosing energy as steam out the flue pipe.

Energy is needed to:

* heat the water in the circulating system.

* heat the metal work in the circulating system.

* heat the DHW tank if there is one.

* dry out the fabric of the building and it's contents because it's very cold and has probably absorbed damp.

* dry out the external walls if they're very wet because of heavy rain.

Energy will be absorbed by:

* fixtures and fittings

* the heavy / dense building materials

* the air inside the building

Energy will be lost by:

* conduction through the walls / roof / floor

* radiation from the walls / roof

* draughts carrying warm air away

* forced ventillation (extractor fans)

Now I turn off the heating, where does the energy go?

* conduction / convection / radiation through the walls / floor / roof

* draughts blowing the warm air away

What about accumulation?

* Everything in the building contains energy which will be given up to the surroundings which will help maintain the air temperature.

Anything else?

* When does damp start to penetrate in to the building fabric?  Below 16C?

...just my thought process.

Bob

@bobtskutter Thats about how I understand it.

To simplify it down, as well as a loss from conduction (to the outside air) and ventilation, the various fabric elements are often said to have a thermal mass.  What that really means is that they have a heat capacity.  They slowly heat up when you turn the heating on, and slowly cool (losing energy to the outside air) when you turn the heating off.  In the simple model of a house thats it.  More sophisticated models might consider the air separately from the rest of the building and the heat capacity within and outside the main insulation layer.  The heat capacity of the building becomes apparent as soon as you start working with a dynamic OAT (ie reality) and is one of the reasons why making measurements of loss based on a short period of time is doomed to failure (the dynamic elements and the heat capacity dominate).

Stuff lost up the flue etc can often just be rolled up into an efficiency figure for the heating system, but that can fall down with passive house levels of insulation, where the fixed load from pumps etc can start to become significant.

There are times when the heat capacity can be ignored in modelling, but anything to do with dynamic behaviour will have it in there somewhere, albeit possibly masquerading as a rate of change in temperature.

The weather over the last week has included some 'useful' cold spells which have provided an opportunity to assess how my hear pump behaves in more demanding conditions: 

Throughout the period shown, it has been running with all secondary circuit valves including lock shield valves fully open, on CC1 (the lowest 'constant curve setting) on the secondary circuit water pump. The first bottom line (in the upper chart) is the IAT (indoor air temperature) which has been OK. The slight rise on the 1st Feb is because I had family round for lunch, more people and more cooking. By coincidence, the OAT was at the point where my heat pump is above defrost cycling and below modulation cycling, meaning it managed mostly continuous running for almost 24 hours (the big spike at 1300 is the DHW heating).

The second 'bottom line' on the lower chart, the green energy in bars, is probably less satisfactory, as the energy use in the cold spells is extremely high (>4kWh per hour, equivalent to >100kWh over 24 hours). This is offset by the much lower use in milder temperatures (and the COP also improves significantly). I have yet to determine how my bills will be affected over the long term (need a longer period to assess this).

At present, with all the lock shield valves fully open, the radiators are unbalanced. Despite this, most rooms are OK, warm but not over warm and at similar temperatures. The two exceptions are the two rads/room at the ends on the pipe runs, the main bedroom upstairs (rad barely tepid) and the living room downstairs (rad stone cold). The latter has been problematic from day one (of the heat pump installation). It is at the end of a longish run of presumably 15mm (its buried in a solid floor) pipe, and also has its fair share of 90 elbows (the new K3 was too large to fit where the old K2 was, and so the pipe work had to be extended to an adjacent wall that was large enough to take it). A while back I briefly tried closing most of the lock shields except the one on this problem rad and it still didn't warm up properly (only got tepid). If I bleed the rad, I get a normal flow of water, confirming the pipe work isn't totally blocked, but I suppose it might be partially blocked, open enough to allow bleeding, but not open enough to allow normal heating water flow. If only there was a simple and accurate and non-invasive way of measuring water flow in a particular pipe! I think it can be done with ultrasound, but as I recall it, the equipment is expensive.

Not sure what to do. If I balance the rads to get some warmth in the living room (and main bedroom), I will almost certainly compromise the system flow. Perhaps I just have to live with it. Being the living room in an old cottage, it does have a fireplace... 

I was wondering how you were getting on.

Are the pipes to living room radiator in a concrete floor? Do they have insulation?  You're probably loosing heat into the slab.

You might want to set your pump back to CC3 just to see if makes any difference.

Regards

Bob

@cathoderay I’m really pleased to read you have some sense (not 100% as you want/need) but making progress, thanks to your persistence and @bobtskutter ‘s expertise.

A heating pipe embedded into an un insulated slab would certainly make sense of a stone cold radiator, does the water even come out warm when you bleed it? Silly question is there any possibility of being piped to something other than the outward flow pipe? eg both sides piped to the return?