## How Long Will My Generator Run?

Hurricane Irene just wandered up the east coast and once again my house was spared from any significant problems. We lost power for about 11 hours, but that was nothing compared to my neighbors, many of whom were without power for days. Luckily, I have a 12 KW whole-house generator. And because Verizon kept the FiOS TV and Internet going full speed for the entire storm I spent the day watching Looney Tunes with my daughter and surfing the net for information. My neighbors spent it manually bailing water out of their basements.

The day after the storm traffic to my generator article doubled. Go figure … I suspect generator sales will increase too. But one reader made left an interesting comment: “I never see anyone say how large their propane tanks are and how long the generator (a 17kva, let us say) can run on a certain quantity of LPG. Thanks!” That’s a good point. The reason is probably because the calculations can be complicated, but decent estimates can be made. Here’s how I figure it all out.

## Step 1 – How Much Fuel Does Your Generator Need?

This should be a relatively straight-forward answer. Though it depends on the load at which the generator is running, ultimately this is a straight power calculation. In AC electrics, power is expressed as kilovolt-amperes or kVA. In some instances one kVA = one kilowatt or kW. But for some types of loads (capacitive rather than resistive like a motor versus a light bulb) something called a “power factor” must be taken into consideration. In these cases, 1 kVA may equal more than 1 kW. Why does this matter? Because the fuel your generator consumes depends on the load or the number of kVAs it is driving at any time. But most generators are rated in Watts. If you are really concerned you can look at the specification plates on all your appliances and add up the kVA loads and do a conversion to kW. Or you can assume that the overall power factor for your appliances will be pretty close to 1 and just assume 1 kVA = 1kW. That’s what I do. Ultimately you could calculate the power required to run what you want to run, add a bit for the inefficiency of the engine and alternator, and then calculate how much fuel is required to deliver that much power.

The easier way is to let the generator’s engineers do this for you. Somewhere in your generator’s manual there will be a chart that shows fuel consumption versus load. Mine looks like this (found on the second page of my manual at http://www.kohlerpower.com/onlinecatalog/pdf/g4097.pdf):

Load (%) | Fuel Requirement (Propane) | BTU / hour Required |
---|---|---|

25% (~3 kVA) | 45 ft^{3} / hour | 72,500 BTU/hour |

50% (~6 kVA) | 60 ft^{3} / hour | 90,000 BTU/hour |

75% (~9 kVA) | 75 ft^{3} / hour | 112,500 BTU/hour |

100% (~12 kVA) | 81 ft^{3} / hour | 180,000 BTU/hour |

Then it’s just a matter of figuring out your load, converting the cubic foot measurements to gallons, and voilà, that’s how much fuel you will burn. Except it’s not really that easy … the exact expansion of a gallon of liquid propane to a volume of gas is governed by things like temperature and pressure (remember the Ideal Gas Law from high school physics? PV=NkT? This is why you should have paid attention.) Since propane techs have better things to do than run around with cheat sheets listing the Boltzmann Constant and Avagadro’s Number, they take temperature and pressure out of the equation and work with the actual energy requirements needed rather than volumes. These are listed in column 3 of my chart and are based on the approximate energy value of a cubic foot of propane listed in the Kohler manual.

Thus, at 100% load (the worst case scenario) my generator needs 180,000 BTU per hour to run. The National Propane Gas Association lists one gallon of propane having 91,502 BTU. Thus my generator will need to vaporize and burn approximately 2 gallons per hour at full load. (Or, a bit more accurately, 1.97 gallons per hour.)

## Step 2 – How Much Gas Do You Have?

This seems like a simple question, but it isn’t. My installation has two 125 gallon tanks (420 lbs. capacity each). So it might seem like they could hold a combined 250 gallons. Which, at the approximate 2 gallon / hour rate calculated above would mean that my generator should be able to run at 125 hours (~5 days) at full load on two full tanks. But that isn’t even close.

Propane is stored as a liquid. It must become vapor before it can be used. To do this, it must absorb heat and then transition from the liquid to the gas phase. Gasses occupy many times the volume of liquids, so in order for this vaporization to occur, the gas needs a space into which it can expand. In a gas cylinder, this is called “headspace,” and it means that my 125 gallon bottles can never be filled to the top. Some room must be left for the gas to expand.

As a general rule, propane cylinders are only filled to 80% of their maximum capacity to allow for expansion of the liquid and enough headspace for the gas. Thus, each cylinder can only hold a maximum of 100 gallons of propane (125 gallons * .8 = 100). So when the fill gauges are pegged at 80% I have 200 gallons to work with or approximately 100 hours at 2 gallons per hour full load. See, we already lost a day of runtime. 100 hours is approximately four days, if we could drain the tanks completely dry.

But guess what – we can’t drain the tanks dry. There are a number of reasons for this. In ideal conditions, there comes a point where the empty volume of the cylinder is so large compared to the amount of propane left that even if it were to all vaporize it wouldn’t generate sufficient pressure to push out of the cylinder. And this can be exacerbated if the temperature drops as it does here in a Massachusetts winter.

So another rule of thumb is that you will never draw a cylinder down below 10% of its rated volume. Thus my 125 gallon tanks will always run out with about 12.5 gallons left in them. If they only start with 100 gallons each, and we can only draw until 12.5 are left, that leaves 87.5 gallons of usable propane in each tank or 175 gallons of total usable propane. That means that in a perfect world I have 87.5 hours running at full load, or just over 3.5 days.

## Step 3 – Can You Really Generate the Gas Needed?

If you live someplace warm, the answer to this question is yes. Those of you in Tampa Florida can pretty much stop reading now. Just divide the amount of gas you have by the consumption per hour and there you go – that’s your runtime. But those of us who live in cold climates have an additional concern. The factors here are complicated, but essentially come down to this:

Can your gas system absorb enough heat on a very cold day to vaporize the amount of propane needed to run your generator at full load?

What factors determine this? Two mainly.

- The “wetted surface area” of your tanks. The wetted area is the surface area of the tank exposed to the liquid propane contained within the tank. Obviously the wetted area decreases as propane is withdrawn, another reason why tanks can’t be drawn much past 10% capacity; on a cold day there’s simply not enough surface area available to absorb heat from the environment.
- The ambient temperature outside the tank. Buried tanks have a distinct advantage in the winter versus tanks exposed to the weather.

This may help to answer an obvious question: why does my installation have two 125 gallon tanks rather than a single 250 gallon tank? The answer is that two 125 gallon tanks have a greater surface area, and a greater wetted area per unit of propane volume, than a single larger tank. This helps ensure that my system can generate the necessary gas volume even on the coldest day.

How can you figure out if your system will generate enough? Rego Products is a company that makes propane regulators and fittings among other things. They publish a handbook for propane installers which has some handy equations. The most useful appears on page 7 which lists the “rule-of-thumb” for calculating propane vaporization rates and correcting for temperature and cylinder volume (wetted area).

It looks like this:

Vaporization rate (in BTU / hour ~~at 0°F~~) = cylinder diameter in inches * length/height in inches * percent volume correction constant * temperature multiplier.

**Update (10/2/2012):** I built a simple online calculator that will do this math for you. Enter your cylinder sizes and it’ll tell you how much energy your system can deliver at a given temperature and gas level.

## Part 4 – My Particular Situation

In the summertime I don’t have much to worry about. I’ll get the 3.5 days at full load without trouble, and much more if I am careful with the appliances. In winter, the concerns are different. Rather than list all the constants and corrections here, please visit the Rego book and see for yourself. I will calculate the worst case scenario: -5°F weather and a full generator load all the time.

With full a full cylinder my calculation is:

2 * (30″ * 54.5″) * 100 * .75 = 245,240 BTU / hour generated. This is well above the 180,000 BTU / hour required at full load we calculated above. So, with full tanks, we know my generator will run at full load for some amount of time even if it’s -5°F out. What about at the end of a tank though?

Repeating the same calculation for a cylinder only 10% full I get:

2 * (30″ * 54.5″) * 45 * .75 = 110,362 BTU / hour. Uh-oh. My generator can’t run at full load at -5°F when the cylinder is at 10%. But a quick look at the original chart says this is still enough to run at 50% to 60% load.

If I raise the temperature to 0°F and 10% tank volume my result is 147,350 BTU / hour, well above 75% load capacity.

The good news is that the temperature in this equation is a 24 hour average and it rarely gets below zero for even a full day where I live. On all but the coldest days of winter my generator can run for at least 3.5 days at full load. Since I can be careful about the appliances I run I rarely approach full load in winter when its cold out (I have oil heat for example). So my generator can run for more than that. How much more? A rough calculation says that at a constant 75% load I should be able to run for six days on a full set of tanks no matter how cold it gets outside.

That is a comforting thought.

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