Wednesday, November 25, 2009

Propane Use and the Power Conversion Number

In the prior co-generation posts an important number I've used to calculate the propane to power factor via the Ecopower. That number is 5.82 KWH/gallon of propane (plus about twice that amount in heat produced which is also used). That number comes from the Ecopower spec-sheet that has the rate of 4.7KW with a fuel rate of 3.42 lbs/hr, and using 4.24 lbs/gal, the weight of propane, you get the 5.82 number above.

I've been putting off the analysis of trying to check the power conversion number, mainly because it meant aggregating my propane bills and importing the numbers into a spreadsheet. Well I did that finally and this post goes through the estimation.

Our propane tank has a 500 gallon capacity, and about once a month the propane truck shows up and fills the tank to some level near the top. Exactly where it gets filled to, I don't know, but I know it isn't to full capacity. They always leave a little room for vapor expansion and such, so there is potentially some jitter there on a month-to-month basis. I will make the assumption that the tank is filled to the same level each time, and the amount of power generated from fill-to-fill is related to the amount put into the tank.

Another complicating factor is that we also use propane for cooking, and the amount of cooking isn't necessarily a constant, so if we just take the amount of propane used and divide that into the amount of KWH generated, the result will be an under-estimate of the conversion efficiency, and there will be a fill-to-fill variation depending upon how much stove top usage there is. The only way to get a more accurate number would be to put a flow meter on the co-generator fuel line, and I may request that, but the soonest that would be done is January, 2010.

The useful data is comprised of 16 periods starting with a fill on July 22, 2008 to the latest fill on November 9, 2009. The following figure shows the daily propane usage for the periods where each box represents one fill.



The red line in the figure is an estimate of the baseline propane use, and at just under 4 gallons per day. I'm going to call it 3.9 gallons/day baseline which is where the line is drawn. That sure is a lot of fuel just to heat hot water. When we were using heating oil, we used about 1.9 gallons per day for hot water use which is still quite a lot, and it continues to bother me.

At any rate, how do the numbers compare? For starters, we have to compare with similar heat content. A gallon of heating oil, if burned, releases 139,000 BTUs of heat while a gallon of propane releases 91,333 BTUs, so heating oil has 1.52 times more energy than propane, gallon for gallon, which means that if magically we could run the Ecopower on heating oil (or diesel for that matter), we would be using 2.56 gallons of heating oil--still above the 1.9 gal/day old use.

Well, we are close to our heating oil use, but we have one more adjustment before a proper comparison. Because we are co-generating electricity, we using 27% more than we would normally use in heat production, and if we divide 2.56 by 1.27, we get 2.02 gallons per day of heating oil boiler equivalent--close to our old baseline rate, so that's good on a consistency basis. It is a little bit high, though, and that could in part be explained by the cooking use. Let's keep that in mind as we continue on our goal, the propane-to-power conversion number.

The other great thing about the Ecopower is that it keeps track of how much power has been generated, and I've been logging that information too. The next figure shows the KWH generated per gallon of propane for the 16 periods. The blue points are the raw numbers without any adjustment. The x-axis has the number of days between fills, partly as a way to separate the estimates, and partly to look for a bias that would show the cooking use. The red line is the advertised value from Marathon Engine, 5.82 KWH/gal.



Looking at the data scatter, one can argue that there is an average daily use, and it works out to about 0.28-0.29 Gal/day cooking use. This number is determined iteratively. Frankly, I haven't thought much about cooking use, so I don't know how to interpret that value, but that value would give an agreement with the old baseline heating oil use of about 1.9 gal/day (in fact, it overcorrects!). The blue line shows the least-squares fit to the data, and it intercepts out at 5.62 KWH/gal which is the number that should be compared to the advertised value. The error estimate on that is 0.1 KWH/gal (from a bootstrap technique for any geeks reading this).

One has to be careful over-interpreting these data. The two points out near 80 days between fills were early on. After those points were taken, a leak in the system was found. Was the leak present during those points, and later use has less of an effect? Also, the laggards at 20 days and near or below 5 KWH/gal can be selected out, because my in-laws were in town, and my mother-in-law loves to cook. Could she have been using 4 times as much propane per day we normally use in cooking? Seems easy to believe, and it can't be ruled out at the moment. If you discard those two laggards, you get to the 5.82 value, and it would raise the daily cooking use to about 0.4 gal/day. All sorts of data adjustments are possible. I'll leave the values as I found them for now which is the appropriate thing to do.

This post has tried to test the Ecopower propane-to-power conversion number advertised by Marathon Engine. The value I get using the number of gallons reported to me by the propane delivery company and the number of KWH reported by the Ecopower is 5.62 KWH/gal plus or minus 0.1 KWH/gal, and I estimate we are using 0.29 gal/day of propane in stove top cooking (our oven is electric). The measured propane to KWH number is lower than advertised by about 3%, but it is within the statistical error range and probably within the possible systematic errors, the bulk of which would bias our estimate to be too low.

Note: The daily cooking rate number was originally calculated incorrectly, and I have corrected that from an earlier version of this post and adjusted the text appropriately.

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