APPENDIX 7-B. HOT WATER DRAW MODEL

TABLE OF CONTENTS

7-B.1 INTRODUCTION ................................................................................................. 7-B-1

7-B.2 SEASONAL EFFECT ADJUSTMENTS.............................................................. 7-B-1

7-B.3 CLOTHES WASHER AND DISHWASHER ADJUSTMENTS ......................... 7-B-2

7-B.4 HOT WATER DRAW MODEL COEFFICIENTS AND VARIABLES.............. 7-B-2

7-B.5 SAMPLE CALCULATION USING THE HOT WATER DRAW MODEL ....... 7-B-4

7-B.6 REGIONAL AVERAGE DAILY HOT WATER USE VOLUMES .................... 7-B-6

LIST OF TABLES

Table 7-B.2.1 Summary of EPRI Analysis Results for Seasonal Coefficients................. 7-B-1 Table 7-B.2.2 Summary of Seasonal Values .................................................................... 7-B-1 Table 7-B.3.1 Impact of Clothes Washer and Dishwasher Adjustments.......................... 7-B-2

Table 7-B.4.1 Variable Definition and Value Derivations ............................................... 7-B-3

Table 7-B.4.2 Coefficient Definitions............................................................................... 7-B-4 Table 7-B.5.1 Sample Hot Water Draw Model Calculation for a 40-Gallon Water

Heater......................................................................................................... 7-B-5

LIST OF FIGURES

Figure 7-B.5.1 Average Daily Hot Water Use for Sample Calculation............................. 7-B-5 Figure 7-B.6.1 Regional Average Daily Hot Water Use for Gas-Fired Storage Water

Heaters ....................................................................................................... 7-B-6 Figure 7-B.6.2 Regional Average Daily Hot Water Use for Electric Storage Water

Heaters ....................................................................................................... 7-B-6 Figure 7-B.6.3 Regional Average Daily Hot Water Use for Oil-Fired Storage Water

Heaters ....................................................................................................... 7-B-7 Figure 7-B.6.4 Regional Average Daily Hot Water Use for Gas-Fired Instantaneous

Water Heaters............................................................................................. 7-B-7

7-B-iAPPENDIX 7-B. HOT WATER DRAW MODEL

7-B.1 INTRODUCTION

DOE developed a modified Hot Water Draw Model 1 as an improvement on a previously existing model. The Hot Water Draw Model estimates the average daily volume of hot water used by various households by accounting for the key characteristics described below.

DOE modified the Hot Water Draw Model to be able to calculate seasonal hot water use. DOE also adjusted the Hot Water Draw Model to account for changes in hot water use by clothes washers and dishwashers due to the updated Federal energy conservation standards for these products.

7-B.2 SEASONAL EFFECT ADJUSTMENTS

The seasonal coefficients for spring, summer, fall, and winter were derived using the linear regression results in the EPRI study found in appendix A of Modeling Patterns of Hot

Water Use in Households. 1 Table 7-B.2.1 provides the detailed seasonal coefficients by hour. To obtain the total values, number of hours was multiplied by the coefficients.

Table 7-B.2.1 Summary of EPRI Analysis Results for Seasonal Coefficients

hour # hours Weekday (I-P units) Weekend (I-P units)

a10 a11 a12 a13 a10 a11 a12 a13
(spring) (summer) (fall) (winter) (spring) (summer) (fall) (winter)

11-6 7 0 0 0 0.1459 0.0907 0.1675 0 0.1696

6-8 2 0 -3.593 0 0 0 -1.569 -0.6553 0

8-11 3 0 0 -0.432 0.5654 1.2574 0 0 1.3516

11-1 2 0 0 -0.4447 0.4012 0 -1.2638 0 1.4804

1-5 4 0 0 0 0.683 0 -0.9405 0 1.1756

5-7 2 0 -0.9736 0 0.9658 0 -1.4838 0 1.6384

7-9 2 0 -2.1273 -0.8588 0 0.8262 -0.9764 0 0

9-11 2 0 -0.8922 -0.9381 0 0 0 -0.3788 0

Total 0 -15.1722 -5.7792 8.1835 6.0595 -13.1755 -2.0682 16.182

To obtain the daily average values (see Table 7-B.2.2) the coefficients were weighted by the number of days in the week which are weekend and weekday.

Table 7-B.2.2 Summary of Seasonal Values

Seasonal Coefficient Average Value Standard Deviation Spring 1.731286 0.52
Summer -14.6017 4.35
Fall -4.71891 1.41
Winter 10.46879 3.12

7-B-17-B.3 CLOTHES WASHER AND DISHWASHER ADJUSTMENTS

The Hot Water Draw Model incorporates the parameters for clothes washer and dishwasher hot water use. These parameters reflect assumptions about clothes washer and dishwasher water use as they existed in the 1990s. Since that time, there has been a considerable change to clothes washer and dishwasher technology that has resulted in lower hot water use. In particular, updated Federal energy conservation standards for clothes washers that became

effective in 2007 2 and for dishwashers that will become effective in 2010 3 have a significant impact on clothes washer and dishwasher hot water use.

The baseline water use for clothes washers in the 1990s was 39.2 gallons/cycle and the water use calculated based on the 2007 standard is 21.0 gallons/cycle. 2 The baseline water use for dishwashers in the 1990s was 8.2 gallons/cycle and the water use calculated based on the 2010 standard is 6.5 gallons/cycle. 4 Therefore, DOE updated the draw model to account for the reduced hot water use by adjusting the dishwasher and clothes washer water use variables to account for the new standards. The results are shown in Table 7-B.3.1. For example, the impact on gas-fired storage water heaters was a reduction of the average daily water use by 10.7 percent.

Table 7-B.3.1 Impact of Clothes Washer and Dishwasher Adjustments

Product Classes Average Hot

Water Use (not Adjusted) Average

Hot Water

Use (Adjusted) Change in

Hot Water

Use Percent Change

gal Gal gal % Gas-fired (Storage) Water Heater 50.7 45.3 -5.4 -10.7

Electric Water Heater 47.5 43.1 -4.4 -9.3

Oil-fired Water Heater 48.2 43.0 -5.2 -10.8 Gas (Instantaneous) Water Heater 51.3 46.4 -4.9 -9.6

7-B.4 HOT WATER DRAW MODEL COEFFICIENTS AND VARIABLES

The Hot Water Draw Model uses an equation that is expressed as follows:

vol = { sea

_ coef + ( per

_ coef * per ) + ( age 1

_ coef * age 1 ) + age 2

_ ceof * age 2 +

[ age 34 _ coef *( age 3 + age 4) + ( T

_ coef * T ) + ( Tanksz

_ coef * Tanksz ) + tank tank ( T

_ coef * T ) + ( T

_ coef + T ) + (hom e

_ coef * at hom e )

−

in in air air [(0.692 * per + 1.335* per ) * dw

_ adj

− [(1.1688* per + 4.7737 * per ) * cw

_ adj ]}*

( senior

_ mf

_ coef * senior

_ mf ) *( no

_ pay

_ coef * no

_ pay )

Table 7-B.4.1 lists the variables used in the equation as well as the definition and

derivation of the value for each RECS household

7-B-2Table 7-B.4.1 Variable Definition and Value Derivations

Variable Definition Value Derivation

per total number of persons in

household =NHSLDMEM*

age1 number of preschool children, age 0-5 yrs =PRESCHOOLCHILDREN**

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

age3 number of adults, age 14-64 yrs =ADULTS**
age4 number of adults, age 65 yrs and

over =SENIORS**

T

tank water heater thermostat setting, o F Uniform distribution from contractor survey (See Ch. 7)

Tank sz water heater nominal tank size, gal Derived using WHEATSIZ and methodology described in Ch. 7

T

in water heater inlet water
temperature, o F Calculated (See Ch.7)

T

air outdoor air temperature, o F Derived using HD65 and CD65 variables, using the methodology described in appendix 7-D

athome presence of adults at home during day =ATHOME*

dw_adj adjustment factor to account for

the differences due to the current energy conservation standard for

dishwasher and for the cases of

households with no dishwasher = IF DISHWASH*=1 then .207

IF DISHWASH* ≠ 1 then 1

cw_adj adjustment factor to account for

the differences due to the current energy conservation standard for

cloth washers and for the cases of

households with no cloth washers = IF CWASHER*=1 then .464

IF CWASHER* ≠ 1 then 1

senior

_ mf senior-only household in a multifamily building = IF TYPEHUQ*=4 or 5 AND NHSLDMEM*=YEAR4*, then 1; = IF TYPEHUQ* ≠ 4 or 5 OR

NHSLDMEM* ≠ YEAR4*, then 0

no_pay household does not pay for hot

water = IF (PGASHTWA, LPGPAY, PELHOTWA, or FOPAY)*=1 then 0 = IF (PGASHTWA, LPGPAY,

PELHOTWA, or FOPAY)* ≠ 1 then 1

* RECS 2005 variable. See appendix 7-A for definitions.

** Values derived from RECS 2005 variables.

7-B-3Table 7-B.4.2 lists the coefficients used in the equation as well as the definition and normal distribution parameters for each RECS household

Table 7-B.4.2 Coefficient Definitions

Coefficient Definition Normal Distribution

Parameters Average

Value Standard

Deviation sea_coef coefficient for seasonal effects See Table D.2.2 per_coef coefficient for total number of persons in household 0.974 0.09 age1_coef coefficient for age1 6.393 0.71 age2_coef coefficient for age2 10.518 0.63 age34_coef coefficient for age3 + age4 15.305 0.67 home_coef coefficient for athome 10.219 1.44

Tank
sz _coef coefficient for tank size 0.144 0.03

T

tank _coef coefficient for water heater setpoint -0.128 0.02

T

inlet _coef coefficient for water heater inlet temperature -0.179 0.05

T

air

_coef coefficient for average outdoor temperature 0.512 0.06 senior_mf_coef coefficient for senior-only household in a multifamily building 1.00 0.2

no_pay_coef coefficient for household does not pay for hot water 1.00 0.2

7-B.5 SAMPLE CALCULATION USING THE HOT WATER DRAW MODEL

Table 7-B.5.1 and Figure 7-B.5.1 provide a sample calculation and results for a 40-gallon

water heater and common values for the hot water draw model variables.

7-B-4Table 7-B.5.1 Sample Hot Water Draw Model Calculation for a 40-Gallon Water

Heater

Variable Values Coefficients GallonsSpringSummerFallWinterSpringSummerFallWinterSpringSummerFallWinter

Sea_coef 1.73 -14.60 -4.72 10.46 1.7 -14.6 -4.7 10.5

per 3 0.974 2.9 age1 0 6.393 0 age2 1 10.518 10.5 age3 2 15.305 30.6 age4 0 15.305 0

T

tank 120 o F -0.128 -15.4

Tank sz 40 gal 0.144 5.8

T

in 56.0 68.7 64.2 51.2 -0.179 -10.0 -12.3 -11.5 -9.2

T

air 55.3 74.1 57.9 37.5 0.512 28.3 37.9 29.7 19.2

athome 1 10.219 10.2 dw_adj 1 -.207 *(0.692 * per + 1.335 * √ per) -0.9 cw_adj 1 -.464*(1.1688*per +4.7737 * √ per) -5.4

senior

_ mf 0 1 1

no_pay 0 1 1
Total Gallons per Day 58.3 49.4 51.8 58.8

48 50 52 54 56 58 60

1 2 3 4 5 6 7 8 9 10 11 12

MonthDaily Hot Water Use (gallons / day)

Figure 7-B.5.1	 Average Daily Hot Water Use for Sample

Calculation

7-B-57-B.6 REGIONAL AVERAGE DAILY HOT WATER USE VOLUMES

Figures 7-B.6.1 to 7-B.6.4 show the range of average daily hot water use volumes for each product class and region. For oil-fired storage water heaters, data was only available for the listed regions.

Gas-Fired Storage Water Heaters, Average Daily Hot Water Draw
Median; Box 25%-75%; Whisker: 5%-95%

0 20 40 60 80 100 120

1 2 3 4 5 6 7 8 9 10 11 12 13

RegionGallons median
Average

Figure 7-B.6.1 Regional Average Daily Hot Water Use for GasFired Storage Water Heaters

Electric Storage Water Heaters, Average Daily Hot Water Draw
Median; Box 25%-75%; Whisker: 5%-95%

0 20 40 60 80 100 120

1 2 3 4 5 6 7 8 9 10 11 12 13

RegionGallons median
Average

Figure 7-B.6.2	 Regional Average Daily Hot Water Use for Electric Storage Water Heaters

7-B-6Oil Storage Water Heaters, Average Daily Hot Water Draw
Median; Box 25%-75%; Whisker: 5%-95%

0 20 40 60 80 100 120

1 2 5 10

RegionGallons median

Average

Figure 7-B.6.3 Regional Average Daily Hot Water Use for Oil- Fired Storage Water Heaters

Gas-Fired Instantaneous Water Heaters, Average Daily Hot Water Draw
Median; Box 25%-75%; Whisker: 5%-95%

0 20 40 60 80 100 120 140 160

1 2 3 4 5 6 7 8 9 10 11 12 13

RegionGallons median
Average

Figure 7-B.6.4 Regional Average Daily Hot Water Use for GasFired Instantaneous Water Heaters

7-B-7REFERENCES

1. Lutz, J. D., X. Liu, J. E. McMahon, C. Dunham-Whitehead, L. J. Shown, and Q. T. McGrue, Modeling Patterns of Hot Water Use in Households , 1996. Lawrence Berkeley National Laboratory. Berkeley, CA. Report No. LBNL-37805 Rev.

2. U.S. Department of Energy-Office of Building Research and Standards, Final Rule Technical Support Document (TSD): Energy Efficiency Standards for Consumer

Products: Clothes Washers , 2000. U.S. Department of Energy. Washington, DC. Report

No. LBNL-47462.

< http://www.eren.doe.gov/buildings/codes_standards/reports/cwtsd/index.html >

3. United States Cong. House. 110th Congress, H. R. 6 Energy Independence and Security Act of 2007 . 2007. http://frwebgate.access.gpo.gov/cgi

bin/getdoc.cgi?dbname=110_cong_bills&docid=f:h6enr.txt.pdf

4. U.S. Department of Energy - Energy Efficiency & Renewable Energy, Technical Support Document: Energy Efficiency Program for Consumer Products and Commercial and Industrial Equipment, Residential Dishwashers, Dehumidifiers, and Cooking Products,

and Commercial Clothes Washers , 2007. Washington, DC.

7-B-8