# Solar Thermal heat gain formula converted to CO2e and trees saved

We have invented a solar thermal heating system with interseasonal storage, recently patented. I want to display the trees saved and carbon offset on the control display based on temperatures coming down from the solar panels and that flow rate.

The pump station/controller has many sensors and we have added a flow meter. I can read the temperature rise (in from solar vs out to solar), & judge the flow rate (2-25L/Min) accurately. Typically the DeltaT is 15c but can vary wildly based on actual insolation. Flow rate is typically 15L/Min

I am trying to build an algorithm to show CO2e offset. I need to calculate in energy terms (kWt or Mj) the energy injected into the heating system based on temps and flow rate. From that I can calculate the CO2e and trees saved.

• There is a building in Switzerland with a 100 tonne insulated water tank which does all-year-round heating and hot water... The building was built around the tank and this was completed and in operation several years ago... – Solar Mike Oct 17 '18 at 16:16
• @SolarMike tell that to the patent bureau as prior art. – ratchet freak Oct 17 '18 at 16:24
• @ratchetfreak any decent or competent search will find it... – Solar Mike Oct 17 '18 at 16:26
• @SolarMike With a google of the username I found his company's site, apparently the thermal buffer mass will no be water but some kind of aggregate under the slab. – ratchet freak Oct 17 '18 at 16:35

You can get the energy gained from heating by multiplying the heat capacity with the temperature difference and the amount of medium heated.

Assuming you use water as a medium with a specific heat capacity of $$4.2~J/(g~K)$$ and mass density of $$1000~g/l$$ your typical situation as you described ($$\Delta T =15~K$$, flow = $$15~l/min$$) would come out to be

$$15~K \times 15~l/min \times 1000~g/l \times 4.2~J/(g~K) = 945000~J/min = 15750~W$$

How many trees per time unit that saves depends on who you talk to.

• Thanks for the feedback @Solarmike ratchetfreak. Our inter-seasonal storage is indeed encapsulated in an insulated GEO storage system with very specific design, heat injection and extraction. The question surrounds understanding the heat injected into the system for any use including storage, after the transport and H/E losses incurred from the EvT panels to the pump station. Can you please clarify the unclear letters (g over l, J over gK,) to allow me to better understand this. I did ask Mr. Google but as per normal my query strings were poorly accepted. – R. Theaker CD Oct 17 '18 at 19:02
• I edited the post to improve the unit display. It should be clear now. – Jeffrey J Weimer Oct 18 '18 at 3:37
• @R.TheakerCD they are units: g = grams, l = liter, J is Joules, K is Kelvin, W is Watts – ratchet freak Oct 18 '18 at 8:04
• Appreciate the update from both of you. One aspect still not clear is where 1000 g/l comes from. And: It was my understanding to achieve an energy output we need 2 things: DeltaT of the flow temps (T1-T2) and velocity of fluid (L/Min). And while the flow rate is incorporated the temperature differential doesn't seem to be. In my case heat is injected into the load(s) and the return fluid pumped back to the Solar system for re-heating. The DeltaT of this is predicated on the flow rate and insolation at the panels. – R. Theaker CD Oct 18 '18 at 14:29
• @R.TheakerCD 1000 g/l is the density of water to convert it's volume to mass. – ratchet freak Oct 18 '18 at 16:21