Payback time

One of the major issues of energy policy is EROEI, Energy Return On Energy Invested.  If something consumes more energy than it produces (without some other advantage like portability or compatibility), it isn't worth using.  The greater the EROEI, the better the investment.

Some investments use energy to produce on-going savings.  These have to be measured by a different standard; the investment is up front but the return is over a span of time, so both the rate and duration of the return are important.  The payback may be measured in months to decades.  This complicates matters.  (Fiscal rather than energetic payback is a further complication; prices of some forms of energy are rising faster than the discount rate, which makes future returns more valuable than today's investment rather than less.  I will not try to analyze the price of energy and will restrict this to physics rather than economics.)

The housing stock of the USA varies in efficiency with some of it being fairly good and some being notoriously inefficient (early houses with balloon framing and no insulation, or the cheap stock built in the 1960's being examples).  If these buildings are to be updated, the energy invested in the process must be returned during the remaining lifespan and the faster the better.  But how do you measure either the return or the investment?

When in doubt, guesstimate.  It usually gets to the ballpark, and guesstimates can be refined when you get more data.

The standard for residential construction used to be the exterior wall with 2x4 studs (actually 3-1/2 inches thick) on 16-inch centers with fiberglass insulation and skins of plywood outside and sheetrock inside; it was rated at a nominal R-11¹, with its actual insulating value being quite a bit lower due to thermal bridging via the studs.  The typical wall actually gets about R-9 per various authorities.  The question becomes, if we have such a wall and want to reduce our net energy consumption, what is the best thing we can do to it?

Insulate the living daylights out of it, of course.  I did some calculations of the heat loss of an unimproved 2x4 stud wall versus the improvements which could be added by re-skinning the house with various thicknesses of solid foam insulation.  (I also just, as in Thursday night, made a pass through Home Depot to check current retail prices and the R-values claimed for the materials.)  If the foam monomer is produced from natural gas and the efficiency of production (weight of foam per weight of gas) is 50%, this table sums up what I got for extruded polystyrene (not beadboard) foam insulation:

Base insulation R-value:	9
Insulation value, R/inch	5
Insulation weight, lb/ft3	1.5
Mfgr efficiency, %	50
Heating value of nat. gas, BTU/lbm	23875
	Foam thickness, inches	0	1	2	3	4	5	6	7	8
	Foam weight, lbm/ft2	0	0.13	0.25	0.38	0.5	0.63	0.75	0.88	1
	Wall R-value	9	14	19	24	29	34	39	44	49
Heating degree-days		Heat loss per square foot of wall, BTU/year
2000		5333	3429	2526	2000	1655	1412	1231	1091	980
3000		8000	5143	3789	3000	2483	2118	1846	1636	1469
4000		10667	6857	5053	4000	3310	2824	2462	2182	1959
Heating degree-days			Energy payback time, years
2000			3.13	4.25	5.37	6.49	7.61	8.73	9.85	10.97
3000			2.09	2.84	3.58	4.33	5.07	5.82	6.57	7.31
4000			1.57	2.13	2.69	3.25	3.81	4.36	4.92	5.48

Types of foam insulation

Polyisocyanurate board is a better insulator than extruded EPS (about R-6.5/inch after aging compared to R-5) and weighs about 2 lbs/ft³ to XEPS's 1.5.  This makes it roughly equal in insulating value to an XEPS board 4/3 as thick; 6 inches of polyisocyanurate is almost exactly equivalent in insulating value to 8 inches of XEPS.  They are also amazingly close in retail price; the optimum cost XEPS board was $17.64 for 4 cubic feet (4 foot by 8 foot by 1.5 inches, R-7.5) while the best-buy polyisocyanurate was $12.34 for 2.67 cubic feet (4 foot by 8 foot by 1 inch, R-6.5).  The polyisocyanurate is very slightly cheaper for the same insulating value, at least in quantity 1.  Which one you'd choose for a given installation would depend more on the immediate price situation and other details (like property taxes from increased "square footage") rather than the specific R-values.

Spray-on urethane does not appear to be even remotely competitive for similar applications.  The kits I found cost around $700 for 50 cubic feet of foam, roughly $14 per cubic foot.  The insulating value is not good enough to justify this cost, but it can be used where rigid board cannot.  Since it is incommensurable with the other two types I will not consider it further.

I did some research on the synthesis of styrene (the monomer for polystyrene) and found that it's derived more from coke-oven products than petroleum per se.  It appears that the raw material for polystyrene may not be affected much by shortages of natural gas or oil.  I had difficulty even finding the molecular structure of isocyanurate monomer (see here), though the nitrogen-carbon ring at the center looked unusual to me; I did not find any hints regarding the typical raw materials for its manufacture.

The payoff

As you can see, the calculated energy payback from the invested fuel is very good; even 8 inches of foam takes a mere 11 heating seasons to pay back its energy of manufacture in an area with 2000 heating degree-days, and just 5 and a half where it's cold enough to make 4000 degree-days.  Unfortunately, the fiscal payback is nowhere near as attractive.  Slapping R-40 of XEPS onto a wall costs roughly $2.94/ft²; under the most severe climactic conditions it would only save about 8700 BTU/year, or 0.087 therms.  If the price of natural gas rises to $1.50/therm it would take over 22 years to pay for itself, exclusive of the cost of structural skins and re-siding.  Even at today's low interest rates, this is not a very attractive investment.  Half that thickness (4 inches, R-20) would save about 11¢/ft²/year at a cost of $1.47/ft²; this would pay off in a bit over 13 years.  At current interest rates, this is moderately attractive.  Greater levels of insulation may pay off faster if combined with a smaller, cheaper heating plant or other economies made possible by the reduced heating load, and tax deductibility of mortgage interest versus operating expenses also adds a bias towards insulation.  This is not a simple calculation.

Conclusion

On a straight EROEI basis, retrofits of foam insulation appear to be a very good investment.  Even the thickest (near-superinsulation) applications will pay off the chemical energy invested in them many times over the life of the structure, and in just a few years in the coldest climates.  The fiscal payback is not nearly so attractive even for the raw materials sans installation costs (at least at retail), unless other factors are considered.

Footnotes:

1. R-value is a measure of resistance to heat transmission, in feet-squared hours degrees-F per BTU.  Divide the temperature difference by the R-value, and you get the heat transmission in BTU per square foot per hour.  The R-value is 1 over the U-value, and vice versa. (back)

¶ 2/17/2006 02:07:00 AM