# How many BTU required to heat air

Good Day folks,  this is my first posting to HEPF although I used to regularly participated in the LinkedIN group.  I am approaching year 6 on my build of a single family home.  Been quite the journey.

Anyway, I need some advise regarding the best approach to offset the cooling created by a Heat Pump Water heater.  I requested and received some data from RHEEM re their 80 Gal Rheem Hybrid DHW tanks.  The unit pumps out 4000 BTUH of cooling into a room.  If the exhaust was ducted to the outdoors, the flow would be 150 CFM.  And they do not recommend ducting the intake to the outdoors where the outdoor ambient temp can drop below 50F (so that option is not on the table for me as we get down below 14F in winter)

I will be placing this unit in a 3312 cuft (414 ft2) below grade room that is well insulated on all 6 sides and separated from the main dwellings building envelope.

I need to see what makes the most sense, not ducting the exhaust and just heating the room an additional 4000 BTUH   OR   Ducting the exhaust and heating the required makeup air from outside.  I just need to understand how to do the calculation.

I used this site https://www.simplex.ca/en-CA/btu-calculator and entered a room size of 1x1x150 to simulate the makeup air volume.  It uses ºC so I used -5 and 20.  This gave me a needed BTU of 210 which would be per Minute as that is the air flow scale.  So this would be 12,600 BTUH.  Right??

In this case it is obviously cheaper to not duct the unit and just heat the room the extra 4000 BTUH.

If this calculation is correct, there would not really be a time when it made sense to duct the unit. The only time that the makeup air heating requirement was equal to the 66 BTUH (4000 BTUH / 60 minutes), was when the outside air was within 1 degree of the inside set point. And when the outside air is warmer, then obviously the cooling of the heat-pump is a beneficial reduction on the cooling load.

Are these calculations correct?? Any insight would be appreciated.

Tags: BTU, Calcs, Hot, Hybrid, Tank, Water, air, heating, make, up

Views: 496

### Replies to This Discussion

Based on

https://www.ruppair.com/documents/white-papers/Actual%20Air%20Densi... the advise is to use the formula

BTU Output = Temperature Rise (∆ T) x CFM x 1.08

I am close enough to sea level and will be using 70F. So this should be more than close enough for me.

Based on this formula and using 14F winter air temp, and 150 CFM, I end up with 9072 BTUH, so still better to not vent during coldest winter period.

Using this formula does however change the break even point. At 45F outside temp, the BTUH are the same for not venting and venting scenarios.  Between 45F and 70F, I would be better off to vent.  So looks like I should vent exhaust and put an interlocked damper on make up air vent and exhaust vent that shuts both down when outside air temp is less then 45F  (7C).

Does this make sense?  Have I understood the formula and factors properly?

Don't waste your time with that BTU calculator, it's not intended for what you're trying to do. Your followup post is spot-on. Allow me to summarize...

It should be self evident that ducting the exhaust air makes sense whenever outside air temp > exhaust air temp. Given the numbers you cite, we can estimate the evaporator delta-T at 25F (4000 / 1.08 / 150 CFM), which works out to 45F exhaust air if ambient is 70F, as you have already determined. So you would only want to divert the exhaust to the outside when ODT > 45F. You would want to verify the exhaust air temp in situ, which is easy enough.

Rather than using 70F for the upper cutoff, I suggest exhausting to the inside whenever the makeup air is warm enough to create an actionable cooling load, which might be a bit higher than 70 depending on the time of year. For example, in early spring, you might welcome 75F makeup air.

Although this all makes sense on paper, I would question whether it's worth the effort. You'll need to come up with a makup air system that prevents unwanted leakage when the water heater is off, and reasonably matches exhaust CFM when it's operating. Not sure if you're thinking active or passive, but either way is not straightforward. My assumption is that you don't want to let the exhaust induce 150 CFM of infiltration through your shell.

Moreover, you'll need some sort of control to interlock the two, and also a custom damper to divert exhaust air from inside to outside, also under some sort of control. Wow.

Keep in mind that the more efficient your heating system is, the less benefit you'll get from all this complexity. But sometimes we have to journey down the path before we realize it's a dead end. Ask me how I know that ;-)

The bigger question in my mind is whether a HPWH makes sense in your climate. Do you not have access to natural gas service?  Or, are you intentionally trying to avoid any combustion appliances?

- thanks for confirming this is the right formula

- The plan was for a dampered 8" passive vent for makeup air.

The setup for my range hood has broan-nutone-make-up-air-damper-slave for the passive makeup and Broan-MD8TU-Universal-Make-Up-Damper for the exhaust. I would plan something similar for the DHW

- The HPWH will be in a room totally isolated from the rest of the dwelling (including being air tight).  This is a room underneath the garage, created by using a suspended slab for garage floor.  Their is a foundation wall between this room and the rest of the dwelling, so all sides of this room are concrete, and I have installed an air tight 'ext' door to enter.  I believe this makes a passive approach for make-up workable, because the only 'suction' on the passive vent will be the air flow through the exhaust duct.  Right??  This isolated room was the only way I would accept a HPWH as I did not want the noise of operation heard in the main dwelling and also wanted to limit the 'cooling effect'.

- Yes I have natural gas service and even have it coming to property to use for the backup generator and BBQ.  But I do not plan to connect to house.  I originally planned on using the SpacePak heat pump for both space conditioning and DHW, before it was determined that it really was not suitable for DHW production.  But I did not find that out till the building envelope was complete.  I do not have any location where I could run any combustion exhaust on the dwelling at this point (even low temp).  I also did want to avoid combustion devices in general as a heat pump will always be more efficient and much easier to bring the house towards a Net-0 situation, with roof top PV, vs gas.

- This leaves the custom damper to dump HPWH exhaust to interior when beneficial.  For now it can be manual, and I will put my mind to figuring out a temp controlled variant.  Yes I will have an efficient heat pump space conditioning system (outdoor heat pump connected to ThermAtlantic's DX2W).  BUT, for a majority of the year, I expect the system to be dormant (no heat or cooling required) do to internal gains taking care of the 'heating' needs during the shoulder months.

SO - I really do not want to have to fire up the Space Conditioning system, and heat up the 120 gal buffer tank, just to pump some heat into the room containing the HPWH, if I can avoid this by dumping the HPWH exhaust to the exterior.  This WOULD be worth the extra cost and complexity in my view, to avoid.

There is one more level of complexity.  The 8" passive intake and 8" exhaust I plan to utilize for the HPWH was actually installed to service a exhaust fan I will have in that room to extract welding fumes, as this room would be my metalwork shop.  So I will need to figure out the best way to 'share' the exhaust with these two tasks.  Obviously, will need back-draft dampers.  That may be all.??

Thanks again David and also congratulations again for the phenomenal performance of your new home!

Regarding ducted exhaust control: "For now it can be manual..."

Think about what that means... For much of the time when it's useful, you'll need to switch modes twice daily, perhaps at inconvenient times. But given the scenario you describe (space conditioning system less likely to be active during these milder times of the year, buffer tank that would need to be charged), I understand your desire to avoid space conditioning for just that room.

But you also should consider the economic trade-off between a conventional electric heater and the HPWH + multiple dampers and possibly a custom controller that could end up costing more than than the water heater. Depending on how much hot water you guys use and the marginal cost of electricity, I'm thinking the lifecycle cost of a straight electric heater may actually be less. Perhaps a lot less.

What you want to avoid is another lookback where the future you has to caveat your design rationale with "I did not find that out until..."

I suggest you get a handle on the entire system cost before you journey any further down the path. Hopefully you haven't installed the HPWH yet?

Hi David,  Thanks for follow up.

Your first paragraph I believe is biased by your location. We do not get significant diurnal temp changes here.  The switch between out and in would be more seasonal for me.

The costs between the HPWH and 100% resistance electric HWT definitely are heavily in the favour of the heat pump.  The house is designed for 5 occupants, and based on this, the payback will be less than 5 years from what I have seen with online reviews and calcs (kind of hard to estimate the water use of a family).  For the two of us, it will be a bit longer, but I am a bath guy so not that big of a reduction, and we also do not intend to be living here that long once complete (hope to be someplace warm with sandy beaches in less than 10 years).

There is the fractional increase in heating cost for that room.  I do not think I have enough data to estimate this, but don't believe it would be significant (unless I had to start heating the room during shoulder months).

So this leaves the temp controlled damper. Something like this could work https://www.instructables.com/id/Smart-Thermostat-Controlled-HVAC-D...  I would not expect to pay more than \$500 for the setup and probably a lot less if I built my own using a digital thermistor (I have hundreds on hand for the instrumentation I am putting into the science labs) and an Arduino controller.

I have the 8" passive intake and the exhaust already in place, and had planned on the interlocked dampers for that room anyway, so these would not be added costs, plus they are cheap.

Am I over simplifying this?

Not sure how a locational bias plays into this... it doesn't take much of a swing for daily temps to bracket a given temperature. I just ran a quick script on Vancouver Intl. temp data. Over the last 365 days, daily highs & lows bracketed 45F by at least 1 degree 92 times. I'm guessing well over half of those would clearly be actionable. An automated system makes that irrelevant of course. I'm just sayin' you'll be motivated to get it done sooner than later ;-)

As for your justification for a HPWH, your 10-year estimated occupancy isn't much different than the heater's life expectancy so it doesn't make sense to think of payback in terms of 5 occupants.  OTOH, with just the two of you, you may be able to disable the supplemental heat element, depending on size of your bath tub and whether your usage patterns are favorable for hp recovery. For such a large investment, it's a shame you don't have historical DHW consumption data so you could actually do an economic comparison instead of winging it.

Not being familiar with the components you intend to use, I can't say if you're oversimplifying the challenge, but the bugaboos typically show up at integration. If you're capable of doing this by yourself (including setup and coding the Arduino), then my hat's off to you. But I discourage my clients from adding complexity to the mechanical system, especially when it comes to controls. I'm thinking... who's going to maintain that system after you move on to those sandy warm beaches?

Thanks David,  Was just thinking we do not have the large swings in the summer that I think you have in Arizona ( I remember visiting my dad there, it would be 30+ during day and cold enough at night I needed a blanket), I was also not thinking that the 45F would have to be a hard set rule, just when warming and cooling trends happen for weeks.  But yes you're right, I will probably be motivated to automate sooner than later.

Yes historical data for old house would be nice, but we had gas that did both the boiler and the HWT, so no way to break out how much each were.  I was looking at a \$5K Sanden heat pump at one point, and at another was looking at a preheat buffer and final tank, so the \$2500 CAD for the RHEEM 80 gal seems a bargain.  Of course an electric would be cheaper still, but the research I have done shows that the payback for the RHEEM would be well within the lifespan of the unit.

Also, yes I would run the unit in Hybrid only mode providing the best savings.

Looking at the Energuide, and similar first hour gal available units, the estimated yearly cost for the electric would be \$419 and the Hybrid would be \$110.   The Electric unit would cost  \$550 and the Hybrid \$2400. So the premium for the hybrid would be \$1850 and would pay back in 6 years based on the usage used for Energuide.

I have calculated I would need around 114,600 gals of hot water yearly for the two of us. Our energy costs around \$.012 per KWH, but I have no idea how to translate this to yearly cost for both devices or how this use relates to the use used in EnerGuide (I was not able to find the volume they base their calcs on).

I am flexible  to using strictly resistance HWT if it can be shown to save me money, I just have not seen anything so far that suggests it would.

you wrote: "I have calculated I would need around 114,600 gals of hot water year"

Huh? That's not a credible number. It would cost close to \$2,200/yr to heat that much water with an electric storage tank @ 12 cents/kWh (formulas to follow).

I've reviewed more than a few client water bills over the years and I have to say that consumption is all over the map. But I'd be very surprised if your TOTAL water consumption for 2 people is anywhere close to 114k gal/yr, let alone your hot water consumption!

When we had metered water service we averaged ~3,000 gallons per month or 36,000 annually, about a third of that heated. Admittedly, our consumption is on the low side, but not by a factor of 2 less than most examples I've seen)

Do you have water bills from your old house that would at least put some bounds on DHW consumption?

Here's an interesting factoid from the 2015 EIA Household Site End-Use Consumption report (see pgs 5-7):

2-person households with electric water heaters consume on average 9.1 million BTU's of energy on water heating. 9.1 MBTU = 91 therms = 2,665 kWh

NOTE: to convert BTU's to kWh's, divide by 3414

To put this in perspective, let's work backwards from this number to see how many gallons of hot water 9.1 MBTU represents, roughly. Let's assume a 55 degree rise (avg draw temp less avg entering water temp) and 88% efficiency to account for standby and distribution losses:

9,100,000 BTU / 8.33 lbs per gal / 55 degrees * .88 = 17,500 gallons per year

NOTE: it takes 1 BTU to heat 1 lb of water 1 degreeF

Hi David, No we did/do not have water metering.

My estimate had a mistake in formulas- SORRY.  It is actually 47.6K Gal.  Let me share my estimate numbers (some of which could actually be low).  I allowed for the following:

Baths - 35 gal per, 8 per week (these are therapeutic for my very bad back - cheaper than physio - I have them hot, almost straight hot water)

Shower - 15 gal per, 9 per week (some me, some spouse)

Dishwasher - 4 gal per, 2 per week

Clothes washer - 20 gal per, 1 hot water load per week

Lavatory - 2.5 gpm, avg 15 min per day (again, generally are using hot to probably a 75% mixture.)

Kitchen Sink - 3 gpm, avg 10 mins daily (again fairly hot mix)

This bath and shower will reduce somewhat once all of the construction is complete, but this will be well after we move in as I will still have 2 years of landscaping after we move in.

So based on your provided formula (thank you) and using an 70 degree rise (120 out, 40 intake in winter and 60 in summer), \$0.12/KWH, this would be \$1100/yr based on .88 efficiency and only \$315 with hybrid assuming efficiency of 3.1. This makes payback 5.9 years

Your consumption numbers seem rather high if not unrealistic, especially sink draws, which add up to > 24,000 gals of hot water per year... wow!  I don't have anything close at hand to cite but I think this is way out of line with research done by Oak Ridge, Gary Klein, etc, especially for 2 people.  Three things jump out at me:

Faucets Part 1: Today's vanity faucets are rated 1.2 to 1.5 gpm. Kitchen/utility faucets are rated at 1.8 to 2.0 gpm. I had to dig to find a 2.2 gpm faucet for our kitchen sink, but I never fully open the hw side unless I'm filling the sink basin to hand-wash some dishes. The main reason I like having a high flow faucet is to fill a large pot or container but that's always from the cold tap. (I guess you know to never draw hot water for anything you intend to consume.)

Faucets Part 2: Your minutes-per-day sink estimates also seem high (as do many online calculators).  10 or 15 minutes over the course of a day may not seem like much but most hw lavatory & sink draws are typically on the order of a few seconds.

Faucets Part 3: Although you acknowledge less than 100% hot water mix for faucet draws, your 70F rise assumption ignores this reality. If you actually do fully open your hot water tap on every draw (as reflected in your calculations), and you do that for 25 minutes a day for real, then I'd say you have some VERY low hanging fruit to harvest!

Still, given your bath/shower requirements, your hw usage will no doubt range higher than the typical 2-person household. But 8 baths & 9 showers weekly appears to be a peak condition resulting from heavy/dirty construction work. I can't imagine these conditions aren't interrupted at times by intervening priorities, bad weather, illness, etc.  In other words, one should not base a payback analysis on peak load conditions!

Moreover, you acknowledge that bath/shower consumption will subside in a couple of years, which can't be ignored. Finally, I can't imagine an 80 gallon heater would support the loads you describe without supplemental heat, calling the 3.1 COP assumption into question.

Bottom line, with everything else you have on your plate, I'd say you have bigger 'value' propositions to focus on than to chase possibly a few hundred dollars 'profit' a HPWH MAY deliver 8 to 10 years down the road. Or it could swing for a loss. I would instead be thinking about reducing your hot water consumption ;-)

I'm hammering on this because I've been down this path many times before and learned some tough lessons when all was said and done. But I'll admit it's sometimes easier to analyze another person's dilemma than to follow one's own advice.

Thanks for follow up David, Valid comments.  The facet flow is high, I was basing on current faucets I am using and not the low flow ones that will be put in the new house. The duration per day is probably a bit high, but not significantly and is based on current observations (I will pay more attention to measuring the duration of use per day). I have a family member that leaves them on for long periods.  And as I mentioned, I typically will wash my hands 10-15 times per day (sucks loving a pet you are very allergic to), but as you allude to, this is only for 7-10 seconds or so a time.  Mix is about 50%, so I will put 3.5 seconds X 10 for me.  The baths and showers is actually normal use.  I have at least one hot bath a day which can increase to two or more (which I have not added to estimate) to ease the pain of destroyed lumbar discs.  And as the water cools down, I am typically refiling with straight hot water again till the tank is empty.  This is far from a sustainable practice I know, but as I said is cheaper (and more effective) than physio etc. The other household member has a shower daily.  The extra 2 showers will be me when coming in from a dirty or dusty task and these will disappear once construction is complete.   Fortunately, the uses seldom overlap.  There is usually at least 2-3 hours between the major draws (showers and baths) based on our schedules. Also the hand washing for me is spread out all day. The current Rheem claims 4 back to back showers with the 80 Gal tank.  Obviously the new house with modern low flow fixtures will help both the shower and the lavatory numbers. But we will always be at a higher than average 2 person volume.  I am also not too concerned at duration of payback.  As long as it does not COST me money in the end, I am more than willing to invest in the technology.

I do appreciate the public accountability that this discussion has caused for me.   I went back and tweaked the numbers based on revised flow rates and also halved some to indicate a 50/50 hot cold mix.  This drops the load significantly down to 30,100 Gals. Drops payback closer to a wash for savings. So certainly something to think about.

Another factor on the + side, is that the heat pump uses les electricity at any given time vs resistance and therefore the PV is able to meet more of the demand at any given time.  This does not matter on a yearly cost bases as I should have net metering, but it does set best practice for reducing the demand on the grid and delaying need for more generation capacity if adopted by more consumers.

Final comment - if it makes anyone feel better about our water usage.  Our COLD water use will be much lower than even larger families.  All of our irrigation (including two neighbours) and exterior water uses (car, etc), and the water for our toilets will all be non-potable water I am collecting around the foundation footings and pumping into a 1000 gal cistern.

Also one last point on the final benefit.  Although we do not have time of day energy rates, we do have tiered thresholds.  Based on the current energy use at site (a 30A electric construction heater), I am already in tier 2.  This bumps my rate from \$0.12 up to \$0.167/KWH.  I am sure that the resistance heating option would also put me into that category.

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