Scientific sizing of a buffer tank

[JamesPa]

I know this general topic has been covered before, but I'm trying to understand the scientific formula for sizing a buffer tank, as opposed to various 'rules of thumb'.

 

Assuming that the sole purpose of the buffer tank in question is to avoid short cycling (its obviously a different calculation if the objective is thermal storage) then I think that the requirement is that the volume of water in the system be able to absorb the excess power generated by the heat pump (relative to the demand) for at least the minimum time for which the heat pump should be on, and do so without heating up by more than the variation acceptable in flow temperature. 

 

This leads to

 

Vb = (Pmin-Dmin)*Tmin/(Hmax*4.2)-Vs (or zero if this yields a negative number)

 

Where

 

Vb is the required buffer volume

Pmin is the minimum output that the heat pump is capable of modulating down to at the temperature where the heat demand is lowest (most likely about 16C, ie just before you would switch off heating altogether)

Dmin is the demand generated (at the same ambient temperature) by the rooms which are still heated when anything in the system that can shut off (eg due to zone or thermostatic valves) has done so.

Tmax is the minimum time the heatpump should switch on before it should turn off again (generally about 10 mins) 

Hmax is the maximum variation you are prepared to permit in the output buffer temperature

4.2 is the specific heat capacity of water (in kJ/kgK) (substitute the appropriate lower value if the system is glycol filled)

and Vs is the system volume when anything that can shut off (eg due to zone or thermostatic valves) has done so

 

So for example

 

• if the heat pump can modulate down to 4kW, the minimum heat demand (eg at 16C) is 2kW, you allow a flow temp variation of 2C and the minimum system volume is 100l, and a min ‘on’ time of 10 minutes you need a buffer tank of 142-100=42l
• With the same system and an allowed flow temp variation of 3C, you don’t need a buffer at all (the formula yields a negative number)

 

Is this formula correct?  

 

If it is correct then I think it points to design/control tweaks to avoid a buffer tank in cases where there isn't sufficient space or a buffer is not desired for some other reason.

[JohnMo]

MCS give this as formula with a worked example. Looking at the system volume.

 

Example:

A 12kW nominal inverter controlled heat pump unit (at 7oC ambient and 35oC water flow) can provide an output of 4kW at maximum turn down (minimum output) at an ambient of 12oC and weather compensated flow temperature of 30oC.

What is the minimum water content to ensure cycling does not exceed six starts per hour?

Assume acceptable temperature drop of fluid is 5oC and the fluid has a SHC of 4 [kJ/oC kg] because it has antifreeze in it (normally 4.18[kJ/oC kg])

 

Total heat energy required:

4 [kW = kJ/s x 60/6] [minutes/number]

x 60 [secs/min] = 2,400 [kJ]

Mass of water required [kg] = 2400 [kJ]/(4 [kJ/oC kg] x 5 [oC] = 120 [kg]

 

Assume 1 kg of water = 1 litre, therefore 120 litres required.

[Marvin]

🙄I will have to check my own system now.....

[JamesPa]

Thanks for the MCS formula, but it ignores the load unless I am mistaken.  So in the MCS world you still might need a buffer tank with a heat pump that can modulate continuously down to the minimum system demand. 

 

I suppose MCS is thinking that people might turn the heating on when the outside temperature is, say, 19C so that, in effect, the minimum system demand is (almost) zero, but in the real world most wouldn't. 

 

Or am I missing something?

Edited August 18, 2022 by JamesPa

[JamesPa]

Having said what I said (perhaps hastily) - the MCS formula is in essence the same as that which wrote, just that MCS ignores the load (arguably justifiable, arguably not).  Thanks therefore for confirming!

[JohnMo]

Another way I found was (in US units)

 

V= t(Qhsmin – Qloadmin)/500(delta T)

 

V = minimum buffer tank volume (gallons) 
t = minimum heat source on time (minutes) 
Qhsmin = minimum stable heat output of heat source (Btu/hr) 
Qloadmin = minimum concurrent heating load when heat source is on (Btu/hr) 
ΔT = change in average tank temperature during minimum heat source on time (ºF) 
 

[JamesPa]

17 minutes ago, JohnMo said:

Another way I found was (in US units)

 

V= t(Qhsmin – Qloadmin)/500(delta T)

 

V = minimum buffer tank volume (gallons) 
t = minimum heat source on time (minutes) 
Qhsmin = minimum stable heat output of heat source (Btu/hr) 
Qloadmin = minimum concurrent heating load when heat source is on (Btu/hr) 
ΔT = change in average tank temperature during minimum heat source on time (ºF) 
 

Thanks for this. 

 

It is, I think, essentially the same (assuming that 500 is the specific heat capacity of water in some US units) but, unlike MCS, allows for a minimum load yet ignores the minimum system volume. 

 

That pretty much convinces me that my formula is correct, its just that MCS differs by choosing to ignore one factor and the 'American' one by choosing to ignore another.

 

It strikes me that, at minimum load, one could possibly (in principle) be quite a bit more tolerant with flow temperature variation than when the demand is high so one could, again in principle, get away with a smaller (or no) buffer tank in more situations than any of the formulae indicate.  However, so far as I know, there isn't a heat pump that allows you to vary the permitted deviation from 'ideal' flow temperature according to ambient.  Further scope, perhaps, for smart control engineers to come up with heat pump controllers which simplify installation (like the self-learning ones we are beginning to hear about), thus driving down installed system cost and complexity particularly in retrofit applications.  Its a pity that the heating market (and in particular the heating control market) moves at such a glacial pace - its going to need to move a lot faster if there are to be glaciers left to compare its speed of movement to!

 

 

 

[ReedRichards]

It seems to me that the formula is only scientific if the input parameters are derived scientifically.  Is there a scientific basis for a minimum cycle time of 10 minutes or could it just as easily be 5 minutes or 20 minutes?  

[SteamyTea]

To be more scientific, the thermal losses from the buffer have to be taken into account.  These losses may be useful i.e. heat the house, or they may not i.e. overheat a section of the house.

 

My fridge, which is just a heat pump, comes on for about 10 minutes every house.  Been reliable so far.

[Marvin]

HI @SteamyTea 

Where's that report you had about buffer tanks? 

[SteamyTea]

6 hours ago, Marvin said:

HI @SteamyTea 

Where's that report you had about buffer tanks? 

There was a report about buffers, was not posted up by me.

But I think I downloaded it.

 

hot_water_cylinders_buffer_tanks_heat_pumps.pdf

[Marvin]

Hi @JamesPa

 

in the above report, page 62 to 68 (as shown on the bottom of the pages) cover buffer tank sizing and cycling. 

[Marvin]

FHi @JamesPa

 

In the above report, page 62 to 68 (as shown on the bottom of the pages) cover buffer tank sizing and cycling, and figure 51 on page 64 is used as a decision guide. Also depends if the emitters are controlled as one or divided and therefore the flow is divided.

Edited August 19, 2022 by Marvin
Further info

[JamesPa]

Thanks to all for the ongoing discussion and for posting the report, which is certainly interesting.  Some comments:

 

On 18/08/2022 at 21:42, ReedRichards said:

It seems to me that the formula is only scientific if the input parameters are derived scientifically.  Is there a scientific basis for a minimum cycle time of 10 minutes or could it just as easily be 5 minutes or 20 minutes?  

 

Sometimes there is a manufacturers recommendation and 10 mins is often quoted.   The graph on page 56 of the KIWA report helps, it shows (for the configuration tested) that COP flattens out around a min on time of 10 mins, and is about 10% down at a min on time of 5 mins. 

 

Lets face it all of central heating design is very approximate but that doesn't stop us or invalidate doing calculations, it just means that you have to be aware of the uncertainty on the result.

 

On 18/08/2022 at 23:01, SteamyTea said:

To be more scientific, the thermal losses from the buffer have to be taken into account.  These losses may be useful i.e. heat the house, or they may not i.e. overheat a section of the house.

Fair enough, I didn't want to make the formula too complicated (or iterative, which this refinement would make it) and hopefully the heat loss from the buffer is relatively small (particularly if its outside the insulated envelope).

 

On 19/08/2022 at 08:12, Marvin said:

FHi @JamesPa

Also depends if the emitters are controlled as one or divided and therefore the flow is divided.

That's taken into account by defining Vs in the formula as 'the system volume when anything that can shut off (eg due to zone or thermostatic valves) has done so'

 

On 19/08/2022 at 08:12, Marvin said:

FHi @JamesPa

 

In the above report, page 62 to 68 (as shown on the bottom of the pages) cover buffer tank sizing and cycling, and figure 51 on page 64 is used as a decision guide. Also depends if the emitters are controlled as one or divided and therefore the flow is divided.

Unless Im missing something fig 51 neglects any ability of the heat pump to modulate down and assumes that there is no zoning.  Since most of the better heat pumps have at least 3 to 1 modulation, I would question its real-world value as a sizing tool unless very carefully interpreted.  

 

The 'Recommendations' (page 68) of the report are interesting, starting with 'Buffer tanks are unlikely to be required when the heat pump can modulate (i.e. if the heat pump is not fixed speed)' and the obvious one 'Buffer tanks should not be installed in unheated spaces'.  All four of the 'MCS' quotes I have received violated both of these, which, in part, explains my interest in the science!

 

Its worth bearing in mind that we are aiming for minimum energy consumption not maximum HP efficiency.  A large buffer tank may improve efficiency at either end of the heating season, when the HP cant modulate down to match the (low) demand, but wont do anything for HP efficiency during the coldest months of the year, when the heat pump can precisely match the demand.  If its in an unheated space (because there is nowhere else convenient) it will still be losing heat throughout the season, and that may well offset the efficiency gains at either end of the season.  So far as I can see its best to design out if at all possible, or design small enough to put inside the house if not.

 

Edited August 20, 2022 by JamesPa

[JohnMo]

I read Stiebel Eltron ASHP manual a while ago, it went in to exactly what the min flow and system volume you were to provide for their heat pump.  If you could not provide both the flow and system volume you had to add a buffer to meet or exceed those requirements.  Making the sizing or need of a buffer pretty easy.

 

May be worth finding a Stiebel Eltron  manual for size heat pump and see what it says.

[JamesPa]

On 18/08/2022 at 17:42, JamesPa said:

I know this general topic has been covered before, but I'm trying to understand the scientific formula for sizing a buffer tank, as opposed to various 'rules of thumb'.

 

Assuming that the sole purpose of the buffer tank in question is to avoid short cycling (its obviously a different calculation if the objective is thermal storage) then I think that the requirement is that the volume of water in the system be able to absorb the excess power generated by the heat pump (relative to the demand) for at least the minimum time for which the heat pump should be on, and do so without heating up by more than the variation acceptable in flow temperature. 

 

This leads to

 

Vb = (Pmin-Dmin)*Tmin/(Hmax*4.2)-Vs (or zero if this yields a negative number)

 

Where

 

Vb is the required buffer volume

Pmin is the minimum output that the heat pump is capable of modulating down to at the temperature where the heat demand is lowest (most likely about 16C, ie just before you would switch off heating altogether)

Dmin is the demand generated (at the same ambient temperature) by the rooms which are still heated when anything in the system that can shut off (eg due to zone or thermostatic valves) has done so.

Tmin is the minimum time the heatpump should switch on before it should turn off again (generally about 10 mins) 

Hmax is the maximum variation you are prepared to permit in the output buffer temperature

4.2 is the specific heat capacity of water (in kJ/kgK) (substitute the appropriate lower value if the system is glycol filled)

and Vs is the system volume when anything that can shut off (eg due to zone or thermostatic valves) has done so

 

So for example

 

• if the heat pump can modulate down to 4kW, the minimum heat demand (eg at 16C) is 2kW, you allow a flow temp variation of 2C and the minimum system volume is 100l, and a min ‘on’ time of 10 minutes you need a buffer tank of 142-100=42l
• With the same system and an allowed flow temp variation of 3C, you don’t need a buffer at all (the formula yields a negative number)

 

Is this formula correct?  

 

If it is correct then I think it points to design/control tweaks to avoid a buffer tank in cases where there isn't sufficient space or a buffer is not desired for some other reason.

In this formula Tmin is expressed in seconds not minutes.  Sorry for any confusion!

[Nickfromwales]

Ok. This seems to be as good a place as any;

 

Sparked by a recent discussion here;

 

 

@JohnMo's comments set the old grey matter a-working.

 

If a PH dwelling has an ASHP, and EV / other favourable ToU electricity tariff earmarked, then does it not make sense to massively oversize the buffer tank?

 

Thoughts are; allow dirt cheap heat energy to be harvested and then drip-fed into the house during peak rate / winter absence of PV etc?

 

So, set the ASHP to run for ( lets say for example ) the 5 hours of Octopus go faster ( lets run with that for this example and NOT Cosy tariff ) and heat up a bulk of stored hot water in a buffer ( lets say a 500L buffer double-sprayed with insulation ( circa 110mm thick ) storing at 50oC for this exercise ), and then laminate this with also heating, in parallel, the ( assumed ) passive raft heated slab, thus 'charging' the house thermally for the day ahead.

 

Setting aside the space required for such a vessel, but looking at this on the basis that a ( say 150L ) buffer is going to be bought and installed anyway; so this just needs a few more quid and some more height to facilitate, then what's not to like, please? Low-ish storage temp vs high volume + high level of insulation = low standing losses, so also assuming here that any 'waste' heat would be adventitious.

 

Fire away.

[JamesPa]

12 minutes ago, Nickfromwales said:

Ok. This seems to be as good a place as any;

 

Sparked by a recent discussion here;

 

 

@JohnMo's comments set the old grey matter a-working.

 

If a PH dwelling has an ASHP, and EV / other favourable ToU electricity tariff earmarked, then does it not make sense to massively oversize the buffer tank?

 

Thoughts are; allow dirt cheap heat energy to be harvested and then drip-fed into the house during peak rate / winter absence of PV etc?

 

So, set the ASHP to run for ( lets say for example ) the 5 hours of Octopus go faster ( lets run with that for this example and NOT Cosy tariff ) and heat up a bulk of stored hot water in a buffer ( lets say a 500L buffer double-sprayed with insulation ( circa 110mm thick ) storing at 50oC for this exercise ), and then laminate this with also heating, in parallel, the ( assumed ) passive raft heated slab, thus 'charging' the house thermally for the day ahead.

 

Setting aside the space required for such a vessel, but looking at this on the basis that a ( say 150L ) buffer is going to be bought and installed anyway; so this just needs a few more quid and some more height to facilitate, then what's not to like, please? Low-ish storage temp vs high volume + high level of insulation = low standing losses, so also assuming here that any 'waste' heat would be adventitious.

 

Fire away.

Basically a thermal store to load shift into cheap rate periods...  

 

Lets do some crude math.  1cum (1000l) of water heated by say 20C would store 4.2*1000*20kJ = 23kWh, a decent amount of energy at least in the shoulder season, or for a well insulated house, so in principle yes.  You would have to think about the flow temp/capacity of the HP and how the low temperature water (which will cool as the day goes on) gets distributed, also I suspect it would be best to plumb it specifically for a storage function not as a 'buffer tank.  It would be a lot cheaper than 23kWh of battery storage, albeit that it wouldn't store excess PV in the summer.  

 

Now where is that IBC container I had kicking around?

[RobLe]

On 20/08/2022 at 08:35, JamesPa said:

Sometimes there is a manufacturers recommendation and 10 mins is often quoted. 

I've seen that before - so far as I'm aware it used to be to do with heatpump lifetime.  Every time a fixed non inverter compressor turns on there is a considerable mechanical jolt, which stresses the brazed joints to the compressor, and eventually these will fatigue fail.  I think 10mins, so 6/hour, is a "rule of thumb" - systems turning on/off more than this are increasingly likely to fail in an unacceptably short time, leaking out the magic gasses.  I accept that this may be a bogus explanation for todays A2A/A2W inverter designs - surely they slowly ramp up, entirely avoiding this jolt, so it won't matter at all?  I think it's a legacy still from older non-inverter heatpumps, and is only likely to really apply to non inverter mostly W2W units.  Rapidly turning on/off is likely to not give great efficiency; but neither is using the ridiculous immersion often built into the heatpump!

The minimum water volume for an ASHP is more now to do with coping with defrost so far as I'm aware - the heatpump "reverses" briefly, sucking heat out of the circulating water to rapidly defrost.

[JohnMo]

29 minutes ago, RobLe said:

surely they slowly ramp up, entirely avoiding this jolt, so it won't matter at all?  I think it's a legacy still from older non-inverter heatpumps, and is only likely to really apply to non inverter

Not sure I really agree.  A modulating heat pump can only modulates so far.  So let's use an example a media 4kW monobloc (staying low energy house)

 

So my house at -5 needs say 3.5kW and at +10 needs a heat input of 0.5kW, flow temps equate to 30 and 25.

 

-5 HP output ranges from 1.3 to 5.2kW, so all ok with the world, I need 3.5kW so mid range.

 

+10 output is just under 2kW, I need 0.5kW.  So on/off operation.  To allow the hp to run for 10 mins you need just over 50L of water engaged for the heat pump to work on.

 

So in this case the heat pump runs fine without a buffer.  But it only works if I don't split the system in to zones.  If zone down the system capacity a buffer would be required as I only have 56L of water in the floor.

 

A 6kW hp would need a buffer in my case.

 

 

[JamesPa]

35 minutes ago, JohnMo said:

Not sure I really agree.  A modulating heat pump can only modulates so far.  So let's use an example a media 4kW monobloc (staying low energy house)

 

So my house at -5 needs say 3.5kW and at +10 needs a heat input of 0.5kW, flow temps equate to 30 and 25.

 

-5 HP output ranges from 1.3 to 5.2kW, so all ok with the world, I need 3.5kW so mid range.

 

+10 output is just under 2kW, I need 0.5kW.  So on/off operation.  To allow the hp to run for 10 mins you need just over 50L of water engaged for the heat pump to work on.

 

So in this case the heat pump runs fine without a buffer.  But it only works if I don't split the system in to zones.  If zone down the system capacity a buffer would be required as I only have 56L of water in the floor.

 

A 6kW hp would need a buffer in my case.

 

 

Hence Vb = (Pmin-Dmin)*Tmin/(Hmax*4.2)-Vs (or zero if this yields a negative number) !

 

where Vs is the system volume when anything that can shut off (eg due to zone or thermostatic valves) has done so (and everything else is as described at the start of this thread).

 

RobLee is (I think) saying that Tmin can arguably be set to zero with modern inverter HPs.  The formula doesn't consider the energy reserve needed for defrost however.

Edited January 5, 2023 by JamesPa

[JohnMo]

500L buffer. Let's use a working range of 28 to 50 degs.  So 7kWh an average nighttime temp of 5 degs.

 

Flow temp of 55 and outside air temp of 7 should give a CoP of 2.5.  Say you pay 10p kWh, that 4p per kWh delivered.  Using the same hp as above it puts out 5kW.

 

So you dump in to cylinder and floor for 6 hrs at 5kW, so 30kWh in total, so that's cost £1.20

 

Doing a similar 30kWh but slowly into the floor at 30 degs across the day at normal 34p per kWh.

 

Let's spread heat dump into floor at hp min output at 7 degs, so that takes 13hrs but CoP is 5.9.  34p/5.9=5.8p per kWh.  So total cost is now £1.74.

 

Let's say heating season is 180 days, that's £90 per day saving.  But you would need add in extra day time rate and increased standing charges etc. 

 

By a way of comparison for gas. Currently getting 110% efficiency out of the boiler so about as good as you can.

10.7p kWh / 1.1 =9.7p

 

30 x 9.7p =£2.90.

 

Gas is a lot more expensive!

 

 

 

[RobLe]

1 hour ago, JohnMo said:

2 hours ago, RobLe said:

surely they slowly ramp up, entirely avoiding this jolt, so it won't matter at all?  I think it's a legacy still from older non-inverter heatpumps, and is only likely to really apply to non inverter

Not sure I really agree.  A modulating heat pump can only modulates so far.

I agree that inverter ashp generally steady-state operates around 30% to 100%.  But I expect that the 0%->30% or 0%->100% transition will be gentle; the inverter will almost certainly ramp the frequency and voltage up from 0Hz 0V to 50Hz 240V over a second or so (rather than ~50ms for an old non inverter unit) - it's normal procedure for an inverter driven AC motor, it's one of the primary advantages of having an inverter, to avoid the clunky turnon.  If it did just startup at 30% instantly it would put a strain on the compressor, and a strain on the inverter.

I think we might be talking slightly cross purposes though?

 

I think:

10min cycle time:  Old issue to do with non inverter heatpumps

Buffer volume:  issue to do with A2x heatpumps needing to defrost AND reducing short cycling for better efficiency

 

 

 

[JohnMo]

You don't need a buffer to defrost, as long as the open capacity in the heating system is acceptable. 

 

Yes soft starts of inverter put less strain on things, but that not the whole story.

 

Short cycling just uses way more power that it needs to, doesn't matter if it a heat pump or a boiler.  Short run time use loads of energy just heating up steel work, it stops, everything cools, starts, heat the metal work -cools, repeat.  10 stop starts is 10x heating up up stuff that not inside the house. 3 stop start 3x heating stuff outside the house. Long runs good, short runs bad.  The worst case is lots of start, no heat put in the house to any useful degree.