I know, I have seen your picture somewhere else.
I think there is something to be gained by insulating and I can’t see any harm in doing so, some of it is already insulated, and not in a particularly special way.
I think it is important to consider very carefully what is going on.
In my case, and I would expect the same in all other cases of this heat pump with a BUH, R2T is the LWT coming into the house.
There is a higher water temperature at R1T but that is not where it leaves the heat pump, it is where is leaves the heat exchanger.
We could reduce and possibly eliminate the heat loss between R1T and R2T but it won’t make the temperature at R2T higher, it will make the temperature at R1T lower.
That would be a good thing at anything over minimum electrical input as it will improve efficiency.
Insulating those pipes between R1T and R2T won’t increase the temperature at R2T though as R2T is the LWT requested by the MMI and delivered at the outlet of the heat pump.
In my example when R2T is 35.0c and R1T is 36c the saving and increase in efficiency, if we were able to eliminate the heat loss in full, would be the additional electricity required for the heat pump to produce water at 36.0c instead of 35.0c
Somehow I doubt it is very much electricity in reality, which is perhaps why it is constructed as it is.
I’m sure we could work out how much electricity would be consumed by the compressor in raising the water temperature by 1c at a flow of 11 lpm at a COP of 5, probably not much, the loss is pretty small in reality.
The actual loss in efficiency caused by the temperature drop is nothing like the apparent heat loss shown by using R1T as LWT instead of the actual LWT at R2T.
The heat pump is not using 14% more of the total reported electricity consumption (as the electricity use includes other things like the circulation pump) to heat the water to 36.0c instead of only 35.0c
It takes 1.2w to increase the temperature of 1 litre of water by 1c
So if the flow rate is 11 litres per minute the heat loss between R1T and R2T needs an extra 792wh of energy which at a COP of 5 is electricity consumption of 158.4wh.
Quite a lot really.
Is my maths correct?