- How big a heat pump do I need?
- What will it cost to operate?
- How often will it need to run?
- How many emissions will I be saving?
This is a little tricky for a few reasons. Heat pump water heaters, aka hybrid water heaters, have two heating elements. One is an efficient heat pump and the other is a less efficient resistance heating element. You don’t know how often each will run. Heat pump space heaters have variable speed motors, so you don’t know how much power they will use (they have a big range). Heat pumps also lose efficiency as it gets colder because it’s harder to extract heat from cold air, making power consumption weather-dependent. So I make some assumptions here as you will see. These rough calculations are intended to get ballpark answers for the questions listed above.
Let’s start simply, by understanding the behavior of a gas tank water heater that you might already own. If you take a look at your gas bill, especially in the spring and summer months when you aren’t heating your home, you can estimate how much gas you are using to heat water. (Most is for heating water, though some might be for a gas dryer or stove.) Let’s say that you estimate that you are using about 20 therms/month for heating water. Since one therm costs about $1.90 in Palo Alto these days (1), the monthly cost of heating your water is about $38 (20 therms * $1.90/therm).
The specifications for some typical gas tank water heaters are shown below. You can find specifications for your specific tank on a label, in a manual, or online. For this example we’ll use the first water heater in the table, a 50-gallon version.
Specifications for some Rheem gas tank water heaters (Source: Rheem)
How often does the water heater run? You can see in the sixth column that it burns gas at 40,000 BTUs/hour = 0.4 therms/hour. (2) Since your water heater is burning 20 therms/month or 0.67 therms/day, the water heater is running about 1.7 hours/day (0.67 therms/day / 0.4 therms/hours).
Another interesting thing about this water heater, as you can see in the last column, is that only 64% of the gas coming into the heater is used to heat water. The rest of the gas is wasted. (Maybe it warms up the garage a little.) That is pretty typical for gas tank water heaters. In this case, every day, although the water heater burns 68,000 BTUs of gas (40,000 BTUs/hour * 1.7 hours), it is using only 64% of that, or 43,520 BTUs, to heat the water.
How does this compare to a heat pump water heater?
Rheem offers a variety of heat pump water heaters. If you owned the gas tank heater described above, you might choose to replace it with a 65-gallon, 30-amp model, the third row in the table below, because it’s readily available and the functional capacity is similar to your gas tank water heater.
Specifications for some Rheem heat pump (“hybrid”) water heaters (Source: Rheem)
You can see from the “First hour” column in each of the two tables that both the gas and the heat pump water heater can deliver about 75 gallons of hot water when starting from a full tank. Since you’ve been happy with your gas-fired water heater, we know that the 75 gallons is plenty for your household’s morning routine. It will refill during the day and be ready for the evening’s use.
The chart above also has information about the water heater’s two heating elements. One is an “electric resistance” element that uses 4,500 watts. The other is a heat pump that outputs 4,200 BTUs/hour. How do these compare with the 40,000 BTUs/hour gas tank? Well, the heat pump seems puny in comparison. And the 4,500 watt element translates to about 15,400 BTUs/hour (there are 3.412 BTUs/watt-hour). That also seems pretty small. How can this heater possibly keep up with gas?
Well, it is slower to reheat, which is why it’s important to make sure the first hour metric is sufficient. How much slower is it? If we assume that the heat pump is used 95% of the time and the resistance element only 5%, then the average output of the two heating elements is 0.95 * 4,200 BTUs/hour + 0.05 * 15,400 BTUs/hour = 4,758 BTUs/hour.
Compare that with the 40,000 BTU/hour of gas input to the other water heater, which wastes 36% of its energy. It is heating with only 0.64 * 40,000 = 25,600 BTUs/hour. The hybrid water heater’s effective power is less than 20% that of the gas heater. While the gas heater runs for about 1.7 hours each day to generate the 43,520 BTUs/day needed for heating water, the hybrid will run for about 9.1 hours/day (43,520 BTUs/day / 4,758 BTUs/hour) to heat the water. That will typically be split between a midday re-heat and an overnight re-heat. (3)
The hybrid water heater is slower, but it is fast enough (for most homes and uses). The great thing about it is that it is extremely efficient. Unlike gas water heaters, these water heaters don’t have a large exhaust chamber running up the middle that is constantly losing heat. Very little energy is wasted, and much additional energy is extracted from heat in the surrounding air. The UEF rating in the last column captures the efficiency of this hybrid water heater in real-world conditions. The rating of 3.85 means that the water heater produces 3.85 times more energy than it uses.
As a result, the water heater uses surprisingly little electricity. When it is generating 4,758 BTUs/hour, it is using only about 4,758 / 3.85 = 1,236 BTUs/hour to do that. That means the heat pump water heater is drawing just 286 watts (1,236 BTUs/hour / 4.312 BTUs/watt-hour). That is similar to a small kitchen appliance.
This is great for your energy bill. This water heater is six times more efficient than its comparable gas heater (UEF 3.85 / UEF 0.64 = 6). If the gas heater is using 20 therms/month, this heater will need only the equivalent of 20/6 = 3.33 therms/month. That translates to 98 kWh/month (there are 29.3 kWhs/therm). At Palo Alto’s tier 2 rate of $0.194/kWh, this water heater costs about $19/month to heat the water (98 kWh * $0.194/kWh), or about half the cost of the gas water heater. In one year, you will save about $230 with the heat pump water heater. At times when you want it to be somewhat less efficient but faster, for example if you have house guests, there are settings that allow you to do that.
What about space heating?
You can do similar calculations for space heating. (You are excited about that, right?)
Let’s start with an existing gas furnace again. Suppose you look at your gas bill and estimate that on an average winter day you use about 2 therms of gas for space heating. You are using about 60 therms per winter month at a cost of $114/month (60 therms * $1.90/therm).
Let’s say you have a 60,000 BTU/hour furnace that is very efficient, maybe 95%. Each hour it burns 60,000 BTUs of gas and generates 57,000 BTUs of heat. On the average winter day, it runs for 3.3 hours (2 therms = 200,000 BTUs / 60,000 BTUs/hour). On a particularly cold day, it might use 300,000 BTUs and run for 5 hours.
What kind of heat pump will comfortably heat this house, what will it cost, and how long will it need to run?
Let’s take a look at this “3-ton” (36,000 BTU) Mitsubishi heat pump. We know we need about 0.95 * 200,000 = 190,000 BTUs on an average day and about 0.95 * 300,000 = 285,000 BTUs of heat on a cold day. Can we get that with this heater?
Specifications for a 3-ton Mitsubishi heat pump space heater (Source: eComfort)
The average winter day in this spec is set to be 47F and the cold day 17F. Since it doesn’t get to 17F here, I think we can assume from the ranges shown that this heater can comfortably generate 30,000 BTUs/hour on an average winter day here, and 22,000 BTUs/hour on a particularly cold day (say 25F). That means it might run for 6.3 hours on an average winter day (190,000 BTUs / 30,000 BTUs/hour), and 13 hours on a cold day (285,000 BTUs / 22,000 BTUs/hour). This assumes the indoor units convey the full benefit of the heat pump. In practice, they may need to run somewhat longer.
If you don’t have a spec like that, you can also get an idea of this from the documented efficiency metrics.
Specifications for a 3-ton Mitsubishi heat pump space heater (Source: eComfort)
The COP or Coefficient of Performance is very similar to the UEF metric used for water heaters -- it is a ratio of output energy to input energy. The HSPF metric is a seasonal version of that, though it is multiplied by 3.412 (because it uses units of BTUs in part). (4) The HSPF of 11 for ductless mini-splits translates to a seasonal COP of about 3.2 (11 / 3.412). In our temperate area, I will assume a COP of 3.5 for an average winter day and a COP of 2.9 for a cold winter day.
The maximum power this heat pump uses is about 3,000 watts, from the first table above. Let’s assume it’s running at 2,500 watts, since the motor is variable speed. That will generate 3.5 * 2,500 watts = 8,750 watts of heat on an average winter day and 2.9 * 2,500 watts = 7,250 watts of heat on a cold day. Translating to BTUs/hour (multiply watts by 3.412), that is about 30,000 BTUs/hour on an average winter day and 25,000 BTUs/hour on a cold day, which is close to what we were figuring above.
What is it going to cost to heat the home with this heater? We know we need about 57 therms for an average winter month. We are guessing the seasonal COP is about 3.5 for an average winter day in our climate. So the heater will consume the equivalent of 16.2 therms each month (57 therms / 3.5). That translates to 477 kWh per month (16.2 therms * 29.3 kWh/therm), which at $0.194/kWh costs about $93. The heat pump is a little cheaper to operate than the gas furnace’s $114/month. Given the rough assumptions, it is at least in the ballpark.
What about emissions?
If your gas bill runs about 500 therms/year, which is typical for a single family home in Palo Alto, then your gas-powered home heating is generating around 3.5 metric tons of emissions each year. (5) To physically capture that amount from the atmosphere and store it currently costs individuals $1000/ton, but the price is anticipated to drop to closer to $100/ton as the technology reaches scale. That is also in the (very large) ballpark of the social cost of carbon. So each year your home produces (say) $350 worth of emissions. Over the 10-20 year lifetime of these appliances, that is $3500-$7000. The benefit of fuel-switching, though, extends beyond the appliance lifetime to the lifetime of the house.
The heat pump space heater gets even more interesting when you consider the value of the air conditioning it provides. Many of us don’t have cooling now, but with the warmer and smokier summers the air conditioning will only add to the value of your home.
So, eesh, this was a lot of math. But I thought it was useful to explain some of the specifications on these appliances and go over how to use them to answer real-world questions. Please add a comment if you have any questions about electrifying your heating. Next week we’ll move onto another topic.
Notes and References
0. Thank you to Tom Kabat for his careful review of this blog post.
1. You can find the rates for gas and electricity in Palo Alto. Other nearby towns have more expensive electricity, so you can plug in your own values. I am using the Tier 2 rates because if you change out one of these you are probably eliminating Tier 2 for gas and adding Tier 2 for electricity. If you change out both, you end up eliminating some Tier 1 gas, which is cheaper.
2. Some conversions for units of energy are:
1 therm = 100,000 BTUs
1 therm = 29.3 kWh
1 watt-hour = 3.412 BTUs
1 ton = 12,000 BTUs/hour
In case you are curious:
- 1 BTU is the energy needed to change the temperature of 1 pound of water by 1 degree F.
- 1 ton applied for 24 hours is the energy needed to melt 1 ton of ice. Or melting one ton of ice provides 1 ton of cooling power for 24 hours.
3. The gas water heater can heat 40 gallons per hour from 35 F to 125 F (the “Recovery” column). The HPWH, even with its 4500 watt element (see “Element wattage” column), can only do about half that (see table here).
In our area, since the ground water comes in at around 65 F and not 35 F, the resistance element can heat about 33 gallons per hour to 120 F. A 15-amp heater would do half that rate. More generally, it’s useful to know that it takes about 460 BTUs to heat up 1 gallon of water from 65 F to 120 F. The heat pump on its own, generating around 4,200 BTUs/hour of heat, can heat about 9 gallons of water per hour from 65 F to 120 F. That is fast enough to refresh morning use during the day and evening use overnight. For days when you need more concentrated hot water use, you can set the tank to use only resistance heating.
4. The SEER metric is just like HSPF but for cooling. That is, it’s a seasonal metric that when divided by 3.412 gives the ratio of output energy to input energy averaged over a season.
5. Burning a therm of gas generates 12-13 pounds of emissions, but I am rounding that up to a conservative 15 pounds because of the upstream methane leaks.
Current Climate Data (September 2021)
Global impacts, US impacts, CO2 metric, Climate dashboard (updated annually)
Climate statistic of the week, from this Bloomberg article on methane leaks: “The French satellite-analytics company Kayrros SAS estimates that the Permian basin (an oil-and-gas-producing area in Texas) has emitted more than 2 million tons of methane this year through September, equivalent to the annual emissions from at least 40 million passenger cars.”
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