RESULTS AND METHODOLOGY OF THE LIFE-CYCLE COST ANALYSIS FOR

RESIDENTIAL WATER HEATER EFFICIENCY STANDARDS

Submitted to the

U.S. Department of Energy

Office of Codes and Standards (OCS)

November 3, 1998

ADDENDUM

pages 73-86

EE-RM-97-900 COMMENT 38VV
Temperature Derivations

The temperatures for water heater thermostat setpoint, inlet water temperature, and

temperature of the air surrounding the water heater are based on the outdoor air temperature.

RECS provides data on heating and cooling degree days, but not air temperatures, for

each household in the sample. To assign a physical location to each RECS household from which

outdoor air temperatures could be derived, three steps were taken:

1. The continental United States was divided into 42 different climate zones. Each zone is

associated with a particular city.22 Figure 5.5.3 shows the 42 climate zones. The cities are listed

below.

Birmingham, AL Chicago, IL Las Vegas, NV Nashville, TN

Phoenix, AZ Lake Charles, LA Reno, NV El Paso, TX

Fresno, CA Boston, MA Buffalo, NY Ft. Worth, TX

Los Angeles, CA Portland, ME New York, NY San Antonio, TX

San Diego, CA Minneapolis, MN Cincinnati, OH Salt Lake City, UT

San Francisco, CA St. Louis, MO Oklahoma City, OK Burlington VT

Denver, CO Great Falls, MT Portland, OR Seattle-Tacoma, WA

Miami, FL Raleigh, NC Philadelphia, PA Cheyenne, WY

Jacksonville, FL Bismarck, ND Pittsburgh, PA Washington DC

Atlanta GA Omaha, NE Charleston, SC

Boise, ID Albuquerque, NM Memphis, TN

Climate Zones for LCC Analysis

Sealtq

San FrOmeh

Los A.. > Id li )/rh 3

Sanb- \»fAluenieI M oms Bminlhm

Figure 5.5.3 Map of Climate Zones

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2. NOAA provides daily outdoor air temperatures and cooling and heating degree days for

each of the 42 cities. Cooling degree days are the number of degrees the average temperature is

above a base temperature. Heating degree days are the number of degrees the average temperature

is below a base temperature. The base temperature used in this study is 65°F.

3. RECS reports heating and cooling degree days for each housing record. Every RECS

household was assigned to the climate zone within its reported census region with the closest

number of heating and cooling degree days for 1993.

Once each RECS household is associated with a climate zone, other temperature

assignments are made from the 30 year average annual temperatures from NOAA.

To assign thermostat setpoints for RECS households, an equation was derived from a

California Energy Commission (CEC) study that measured hot and cold water temperatures. 3

The CEC study examined single-family houses built between 1984 and 1988 to assess the

accuracy of the California Title 24 Energy Efficiency Standards modeling assumptions. As a part

of the study, hot and cold water temperatures were measured. The CEC assumed that hot water

temperatures were equal to the water heater thermostat setpoint and the cold water temperatures

were equal to the inlet water temperatures.

The graph of the CEC data displayed in Figure 5.5.4 shows the correlation between the

thermostat setpoint and the inlet water temperature. The data show that people with colder inlet

water tend to set their water heaters to higher setpoint temperatures to avoid using a greater

proportion of hot water to cold to get their desired water temperature. Often what motivates people

to increase the setpoint is frequently running out of hot water.

The equation that was derived from the CEC data is shown below. If the inlet water

temperature for the household is 58°F, then the water heater's setpoint temperature is 134.1°F. As

the inlet water temperature gets warmer, the setpoint temperature decreases.

Ttank = 134.1 + 0.55* (58 - T7n)

RECS households were given setpoint temperatures based on their inlet water temperatures

using this equation. Since individual households maintain a wide range of thermostat settings, a

random error with a mean of 0OF and a standard deviation of 13°F was added to account for this

variability.

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Hot vs Cold Water Temperature

from CEC data for California

200-

u 180 1

G o I

1 160-

I140 -"''' .......... ... ...... I

X- *- B * *m E E- *nn I · B *" **-*.......

- 20 .....

O 100-

80--

40 45 50 55 60 65 70 75 80

Cold Water Temperature (deg F)

Figure 5.5.4 Comparison of Setpoint and Inlet Water Temperatures

Inlet water temperature was assumed to equal the ground water temperature, which varies

according to geographic region. Ground water temperatures are assumed to be slightly warmer than

air temperatures. Two degrees were added to the NOAA average annual outdoor air temperature

data2 4. The estimates were compared to the National Well Water Association's published annual

average ground water temperatures for various regions in the country25. The comparison shows

that, in the majority of cases, the difference between the two estimates is less than 2°F.

A set of assumptions to determine air temperature around the water heater was developed

based on calls to fifty water heater installers from around the country regarding the typical

locations for water heater installation.

1. RECS reports the presence or absence of basements and, if there is a basement,

whether or not it is heated. If the house had a basement, it was assumed the water

heater was located in the basement. For unheated basements, the assigned

temperature was the average between the outdoor air temperature for that climate

zone and a house air temperature of 72°F (22.2°C).

2. If the basement is reported as a heated space, then the temperature of the air around

the water heater is assumed to be the temperature of the house: 72°F (22.2°C).

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3. If the house had no basement but did have a garage or carport, it was assumed that

the water heater was in the garage or carport. The temperature assigned was 5°F

(2.8°C) higher than the outside air temperature for that house.

4. In the absence of a basement, garage, or carport, it was assumed that the water

heater was in the house (in the kitchen or a utility closet) and a temperature of 72°F

(22.2°C) was assigned.

Table 5.5.6 shows the percentages of assigned water heater locations.

Table 5.5.6 Water Heater Location Percentages

Water Heater Location Percentage

(%)

unheated basement 20.9

heated basement 26.0

garage 24.7

house 28.3

The volume of hot water drawn in 24 hours is calculated using the Hot Water Draw Model

discussion in Section 5.6.

5.5.5 Energy Analysis Results

Electric Water Heater Energy Use

Table 5.5.7 lists the average annual energy use for electric water heaters and the average

daily energy savings for each design option.

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Table 5.5.7 Energy Consumption for Electric Water Heaters

Design Option Average Electricity Use Average Energy Savings

(kWh/yr) (Btu/day)

0 Analytic Baseline 3503

1 0 + Heat Traps 3408 884

2 1 + 2" Jacket Insulation 3362 1312

3 1 + 2.5" Jacket Insulation 3318 1726

4 3 + Plastic Tank 3276 2121

5 3 + Insulated Tank Bottom 3296 1936

Figure 5.5.5 shows, for each design option, the cumulative frequency of the difference of

energy consumption compared to analytic baseline electric water heaters.

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Delta Daily Energy Consumption of Heat Trap Delta Daily Energy Consumption of 2' Jacket

Water Heater compared to Analytic Baseline Insulation Water Heater compared to Analytic

(Btu/Day) Baseline (Btu/Day)

3000 100 % 1 2500 - -.. 100%

! S.80% s " 2000 80% S

2000 60% I 1500 60%

10 Z _iB |L 20% X20% E 1 500 20% 2- : 0 _ 0% 0 _==::::I 0% o

o 0000000000 o n o oOOO O CD - COD N o 0 v a-O CD a o e14 0 i .o 0 0 ' O0 NC 0 O CDCN 0COD * - to ou o c _

BTU/Day BTU/Day

Delta Daily Energy Consumption of 2.5" Jacket Delta Daily Energy Consumption of Plastic Tank

Insulation Water Heater compared to Analytic Water Heater compared to Analytic Baseline

Baseline (Btu/Day) (Btu/Day)

2500 100% 2000 100% > 2000 80% o i 3 1500 o -80% 

s1500 60% 60% - lOO1000. n40% ! 10 0 0 ~1000 40%5~ ~ C 40%

o500 20% = 500 20% E

00000000000)oooo~~~~ !O CD l)o ioo 

.....0..l 0 ~ 0 C? - 0 ;! T :D0 I? I? Cm CN(C? CN N

BTU/Day BTU/Day

Delta Daily Energy Consumption of Tank

Bottom Insulation Water Heater compared to

Analytic Baseline (Btu/Day)

2000 _- 100%

1500 80% *

| 1000 BH60%

e 500 20%

" 0 o 0% o

0 OON OO o ooo

BTU/no Day BTU/Day

, Frequency Cumulative %

Figure 5.5.5 Differences in Energy Consumption by Design Option - Electric Water Heaters

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Gas-fired Water Heater Energy Use

Table 5.5.8 lists the average annual energy use for gas-fired water heaters and the average

daily energy savings for each design option.

Table 5.5.8 Energy Consumption for Gas-Fired Water Heaters

Design Option Average Energy Use Average Energy

Savings

(MCF/yr) (kWh/yr) Btuday)

(Btu/day)

0 Analytic Baseline 22.32 0

1 0 + Heat Traps 21.72 0 1671

2 1 + 2" Jacket Insulation 20.58 0 4886

3 1 + 2.5" Jacket Insulation 20.34 0 5567

4 3 + Side Arm Heater 17.37 23 13719

5 2 + Improved Flue Baffle 20.04 0 6422

Figure 5.5.6 shows, for each design option, the cumulative frequency of the difference of

energy consumption compared to analytic baseline gas-fired water heaters.

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EE-RM-97-900 COMMENT 38VV
Delta Daily Energy Consumption of Heat Trap Delta Daily Energy Consumption of 2' Jacket

Water Heater compared to Analytic Baseline Insulation Water Heater compared to Analytic

(Btu/Day) Baseline (Btu/Day)

1000 100% : 5000 100%

800 80% > 4000 80%

600 660% Z : 3000- 60% Z

" 400 40% & 2000 40%

e 200 20% " E 1000 0 20%

0 0% L 0 0%

C(0 _" N C(D 1- 0 ON 0 _ N ( 0 0 0N ( 

0 I _ 1 N r 00 N o _ N 0 N N N N ' N N Nr N _ r

BTU/Day BTU/Day

Delta Daily Energy Consumption of 2.5' Jacket Delta Daily Energy Consumption of Side-Arm

Insulation Water Heater compared to Analytic Design (w/ Metal Tank) Water Heater compared

Baseline (Btu/Day) to Analytic Baseline (Btu/Day)

5000 100% 3000 - - - 100%

; 4000 -80% , I 2500- 80

0 3000 60% _ c 2000 60% i

1000 20% 500 20% . 0 0% 0 _ .... 0% %

oL___ o ooo 0CD 0C N (0 0( N (0 N 0(0 NC 0CD > 0 N0 NC

N Nt - , , N N N N - ' '

BTU/Day BTU/Day

Delta Daily Energy Consumption of Improved

Flue Baffle Water Heater compared to Analytic

Baseline (BtulDay)

4000 100%

' 3000 80% 1

80% I; 200060% a.o~~~ 4-~~40% 1000 20% E

L 0 0%

to o o oo o o 0 N - N 'q (0 _ 0, ON

BTU/Day

r-- Frequency Cumulative %

Figure 5.5.6 Differences in Energy Consumption by Design Option - Gas-fired Water Heaters

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5.6 Hot Water Draw Module

5.6.1 Introduction to Hot Water Use

Hot water use varies widely between households because it is dependent on the household

and water heater characteristics including: the number and age of the people who live in the home,

the presence of hot water-using appliances, the tank size and thermostat setpoint of the water

heater, and the climate in which the home is situated. By accounting for these five types of

characteristics, the draw model estimates average daily hot water draw volume26 .

There is a degree of uncertainty in this estimation of hot water use. Uncertainty is caused

not only by variability in the demographic and climatic inputs but also by uncertainties attached to

the weighting factors, i.e., the estimated coefficients in the equation. The uncertainties in the

coefficients are defined using normal distributions with the parameters provided in the original

regression analysis2 7.

5.6.2 Equation for Hot Water Use

The Hot Water Draw Model equation is expressed as follows:

vol = { sea_coef + (peroef* per) + (agel_coef* agel) + (age2_coef* age2) +

[age34_coef * (age3 + age4)] + (T,ancoef * (Tank + Ttanerr)) +

(Tankszcoef * Tanksz) + T7,coef * T) + (Tarcoef* Tar) +

(home_coef * athome) - [(0.692 *per + 1.335 * /(per) * no_dw] -

[(1.1688 *per + 4.7737 * /(per)) * no_cw } * (senior_mf * no_pay)

where:

vol = hot water consumption, gal (L)/day

per = total number of persons in household

agel = number preschool children, age 0-5 yrs

age2 = number of school age children, age 6-13 yrs

age3 = number of adults, age 14-64 yrs

age4 = number of adults, age 65 yrs and over

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Tank = water heater thermostat setting, °F (°C)

Tanksz = water heater nominal tank size, gal (L)

Tn = water heater inlet water temperature, °F (°C)

Tair = outdoor air temperature, °F (°C)

athome = presence of adults at home during day

nodw = absence of a dishwasher

no cw = absence of a clothes washer

senior_mf = senior-only household in a multi-family building

no_pay = household does not pay for hot water

Ttankerr = estimation error for the thermostat setpoint (normal distribution)

sea_coef = coefficient for seasonal effects (normal distribution)

per_coef = coefficient for total number of persons in household (normal distribution)

agel_coef = coefficient for "agel" (normal distribution)

age2_coef = coefficient for "age2" (normal distribution)

age34_coef = coefficient for "age3" + "age4" (normal distribution)

home_coef = coefficient for "athome" (normal distribution)

Tanksz_coef = coefficient for water heater tank size (normal distribution)

Tankcoef = coefficient for water heater setpoint (normal distribution)

Te,_coef = coefficient for water heater inlet temperature (normal distribution)

Tircoef = coefficient for average outdoor temperature (normal distribution)

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5.6.3 General Description of Key Variables

Number of People in Household (per). The total number of household members.

Number of Preschool Children (agel). The number of infants and young children up through age

5.

Number of School-Age Children (age2). The number of children age 6 through 13.

Number of Adults 14-64 (age3). The number of adults age 14 to 64.

Number of Adults 65+ (age4). The number of adults age 65 or more.

Thermostat Setpoint (Tank). The thermostat setting of the heating element of the water heater.

Water Heater Tank Size (Tanksz). The nominal size of the water heater tank.

Outside Air Temperature (Tair). The average annual outdoor air temperature.

Inlet Water Temperature (Tn). The temperature of the water entering the water heater.

Unemployed Household Member (athome). The presence of a household member at home

during the day.

Dishwasher (no_dw). Absence of a dishwasher in the household.

Clothes Washer (no_cw). Absence of a clothes washer in the household.

Senior Only (senior_mf). A senior-only (age 65 or more) household in a multi-family building.

No-Pay Household (no_pay). A household that does not pay to heat water.

5.6.4 General Description of Sources of Data

RECS provides data on the number, age, and employment status of household occupants,

presence of a clothes washer or dishwasher, and form of payment to fuel utilities.

The derivations of the three temperature variables are discussed in Section 5.5.4.

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RECS reports three ranges of water heater tank size -- small, medium, and large; for this

analysis however, specific sizes are needed. By matching the three RECS ranges with the standard

sizes, an exact water heater size was assigned to each RECS house.

Table 5.6.1 shows, by fuel type, the RECS water heater volumes and the corresponding

selections for this analysis.

Table 5.6.1 Water Heater Volumes Selected for LCC Analysis

RECS Selection for LCC Analysis

(gal) (liters)

Electric Small 30 (110)

Medium 40 (150)

Large 50 (190)

65 (250)

80 (300)

Gas Small 30(110)

Medium 40 (150)

Large 50 (190)

75 (280)

Oil Small

Medium 32 (120)

Large 50(190)

Terms and values for no_dw, no_cw, senior_mf, and no_pay were developed by LBNL for

the draw model.

Standard errors for the coefficients used in the equation were reported in the original hot

water consumption model. These values were used to develop the normal distributions for the

coefficients.

5.6.5 Results of Hot Water Use Calculations

Figure 5.6.1 shows estimated daily hot water use for households with electric water heaters

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as a histogram. For these households average daily use is 44.3 gallons. Figure 5.6.2 shows the

equivalent chart for households with gas-fired water heaters. For those households the average

daily use is 48.9 gallons of hot water.

Daily Hot Water Use

(Gal/Day)

2500 ----- A--- 100%

>, 2000 t -t80% !

c g1500]- 60%

1000o 40% E

500 20%

0 !__In La - 20Hann___ 0%

Gal/Day

Figure 5.6.1 Frequency Chart of Hot

Water Use - Households with Electric Water Heaters

Daily Hot Water Use

(gal/day)

3000 . ......- 100%

>2500 t-80%

* 2000 2 1000 , E- 4 0% E

[L 500 20%

0 :In I__ 0%

Gal/Day

Figure 5.6.2 Frequency Chart for Hot Water Use - Households with Gas-Fired Water Heaters

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References

1. Lawrence Berkeley National Laboratory (LBNL), 1998. Engineering Analysis

Methodology and Results for Residential Water Heater Efficiency Standards, 1998.

Intermediate report to U.S. DOE, Berkeley, CA. October 1.

2. LBNL, 1998. LBNL Water Heater Cost Database. [Microsoft Excel spreadsheet.]

Berkeley, CA. August.

3. Lutz, J.D., C.D. Whitehead, A. Lekov, D. Winiarski, G.J. Rosenquist, 1998. "WHAM: A

Simplified Energy Consumption Equation for Water Heaters." In: Proceedings of the

ACEEE 1988 Summer Study on Energy Efficiency in Buildings, August 23-28, 1998.

American Council for an Energy-Efficient Economy, Washington, DC.

4. Gas Appliance Manufacturers Association (GAMA), 1998. Consumers' Directory of

Certified Efficiency Ratings for Residential Heating and Water Heating Equipment.

Prepared for GAMA by Intertek Testing Services, Cortland, NY. April.

5. U.S. DOE, Energy Information Administration, 1997. Annual Energy Outlook 1998.

DOE/EIA-0383(98). Washington, DC. December.

6. Gas Research Institute (GRI), 1998. 1998 Edition of the GRI Baseline Projection.

Arlington, VA.

7. U.S. DOE, Energy Information Administration, 1995. Household Energy

Consumption and Expenditures 1993. DOE/EIA-0321(93), Washington, DC.

October.

8. Whirlpool Corporation comments to the Department of Energy, December 12, 1990,

Docket No. CE-RM-90-201, p. 1&2, Attachment #1.

9. "The Life Expectancy/Replacement Picture." 1998. Appliance Magazine. 55:9, 71.

September.

10. National Oceanic and Atmospheric Administration (NOAA), 1998.

<http://www.ncdc.noaa.gov/ol/climate/online/ccd/meantemp.html >

(last accessed: July 17, 1998).

11. Stanonik, F., 1998. Manufacturing Cost Data for Residential Gas and Electric Storage

Water Heaters. GAMA, Arlington, VA. Letters to DOE, June 19 and July 17.

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