Ser m

B92 no. 177

SENS TTTV X TY 01: R E S I IIENTIAL HEATING ENERGY

TO BUILDING ENVELOPE THERMAL CONDUCTANCE

by

M.R. Bassctt*

INTRODUCTION

The "Measures far Energy Conservation in N e w B u i l d i n g s , 19781q' contains

t a b l e s o f minimum thermal resistances for var ious components of t h e building

construction. These values were derived from a life c y c l e cos t analysis that

endeavoured to determine the m i n i m u m value fo r the sum of t h e c o s t of supplying

and installing t h e i n s u l a t i o n and of t h e present worth o f t h e heating energy

consumed wer a given pe r iod of years. Studies of t h i s type2 have been based

upon the best estimates of many factors - t h e p e r i o d of time to be considered,

the cos t of money ( in teres t ra te) , the cos t of energy and t h e escalation

in the cost of energy, t h e seasonal efficiency of the heating equipment, t h e

incremental cos t of increasing the thermal resistance and, of course, t h e

change i n t h e quan t i t y of heat ing energy required unde r var ious climatic con-

d i t i o n s resulting f rom a change i n the thermal resistance of t h e component.

This study was carr ied out with the objective of quan t i fy ing t h i s l a s e i t e m

more precisely.

COMPUTER SIMULATIONS

3 The ENCORE computer program was used t o simulate t h e energy consumption

of a house with f ou r d i f f e r e n t levels of insulation under t e n d i f f e r e n t climatic

conditions. The model building chosen is a common t ype of b u i l d i n g found in 2

Canada. It is a two-storey detached house with 124 m of above-grade f loor

a rea and occupied by a family of three. Detailed thermal and dimensional

details are given in Appendix A.

The factors a f fec t ing space heating demand can be summarized as follows.

The occupants gcncrate about 30 kl.h/day d i r e c t l y and through energy-demanding

ac t i v i t i e s , and the r a t e of below-grade heat loss from t h e f u l l y heated base-

ment i s a constant 1 kW. Window areas were chosen for daylighting and

appearance r a t h e r than f o r optimum solar assistance to space h e a t i n g , and

CLIMATIC DATA

Hour-by-hour climatic records fo r the locations l i s t ed in t he following

t a b l e were used in t h i s s t u d y ,

Location

Vancouver

Summer land

Toronto

St. John's

Montreal

O t t a w a

SuffieId

S w i f t Current

Winnipeg

Edmonton

Year

Annual Degree-Days Computed EOT t h e Particular Year

(base 18"~)

These locat ions were selected to include the main centres of population,

the f u l l range o f climatic severi ty measured in degree-days, t he maritime

and in land climate types.

represent 9.6 per cent of t h e floor arca. A i r leakage openings i n t h e

envelope allow approximately 0.2 a i r changelhour of infilsration in winte r

climatic conditions.

T l ~ c envelope thermal conductance was increased i n t h ~ c e s teps t o c rca te

a se r i e s of f o u r buildings l abe l l ed A, R , C and D- Bui ld ing A h a s RSI 2 . 7 5 2

r n 2 ~ / w walls and RSI 4 . 1 m K/W roof. It l i e s at fhe low end of recommendations

i n t h e Measures f o r Energy Conservation i n New Buildings, 1978. Buildings

B , C and D arc insulated to progressively h igher levels w i t h an upper limit 2

of triple glazing, RSI 6.5 m K/W walls and RSI 11 r o o f .

SAVINGS IN PURCHASED SPACE HEAT

The results of the 40 s imula t jons show t h a t at each location the energy

consumption (E ) is proportional t o t h e above-grade thermal conductance (C)

e x c l u d i n g infiltration. Figure 1 shows t h i s relationship fo r seven of t h e

loca t ions . It does not matter that ventilation and basement heat loss a r c

not included in t h e conductance a t t h i s stage since t h e y remain constant fo r

a l l t e n locations and a l l four b u i l d i n g t ypes. Hence the change in energy

consumption (AE) as a result of a change in conductance (AC) as given by t h e

s lope of t h e l i n e s i n Figure 1 has a r e l a t i o n s h i p of the form

where t h e valuc of t h e constant k depends upon t h e climate. The only ex-

ccption i s a small amount of d iminished r e t u r n f o r b u i l d i n g n i n Vancouver,

but this i s not considered any f u r t h e r ; r a t h e r i t is l e f t as a warning

t h a t t h e d a t a may not be extrapolated to more h i g h l y i n s u l a t e d b u i l d i n g s in

1 ocations with fewer degree-days than Vancouver.

The change i n energy consumption w i t h a change in conductance (dE/dC)

t aken from Figure 1 a r e p lo t t ed againsr annual degree-days t o base 18'~

(D l&) i n Figure 2 . T h e r e is some scatter around a s t r a i g h t line drawn through

t h e da t a but this is expected becausc degree-days havc never been considered

t o encompass a l l climatic variables. The scatter i s random, however, and the

straight l i n e cannot be significantly improved with a h i g h e r order r e l a t i o n -

sh ip .

The in tercept a t zero degree-days i s dEJdC = (-3*90] k h p K a l t h o u g h we - - . 1 . . . .I-.- .- C . ~ J C I A ~ +n Fnl I n ~ r r thi rial-ticr~la~ t r end

The s l o p e {[dE/dC)fD) = ZU h with a 95 per cen t confidence i n t e rva l of

a h o u t 2 h. T h i s uncertainty in thc slope follows from desc r ib ing t h e

climate w i t h n s ing le variable.

Assembling these observations i n t o a s ing le package gives t h e following

relaeionship between a change in t h e purchased space hea t ing energy, t he

change i n envelopc conductance and thc c l i m a t i c s e v e r i t y i n degree-days.

TOTAL ENERGY PREDICTIONS

Having reached the objec t ive of t h i s study, it i s o f interest to continue

f u r t h e r and derive an equation r e l a t i n g absolute h e a t i n g energy to D and t he

total above-grade conductance including i n f i l t r a t i o n , G . When the seasonal

furnace energy is plo t ted aga in s t annual degree-days [Figure 3) the following

po in t s emerge.

(a) S t r a i g h t lines drawn through thc data f o r each building

cannot be use fu l ly improved by a h i g h e r order relationship.

(h] Intersection of t he degree-day axis occurs around 500 d - K o r

at about t h e number o f degree-days accumulated while the

h e a t i n g system i s turned o f f (June, July, August).

(c) The s lopes measured i n units kW-hJd-K a re as follows:

Building A R C D

Slope k ~ * h / d - ~ 2.86 2.19 1 . 8 6 1.58

These slopes are the product of the degree-day constant and effective

envelope conductance. Unravelling t h e two i s greatly simplified by

observing that t h e mean i n f i l t r a t i o n ra te can be considered independent

of D and building t y p e (A, B,C,D) . The mean i n f i l t r a t i o n r a t e i s 0.18 a i r

change,/hour with a between bui lding va r i a t ion of standard dev ia t ion 0 . 0 1 a i r

changelhour and locality to local i ty variation of standard devia t ion 0.02 a i r

change/hour. Values for G are as follows:

Building A B C D

and t h e seasonal furnace energy can be calculated from:

E = 20.G (D-d)

*-. . .

above-grade conductance

G, W J K

where d = t h e number o f degree-days accumulated while the furnace

i s shut down.

143 109 9 3 79

COblPARISON WITH THE DEGREE- DAY MODEL

THE ASHRAE MODIFIED DEGREE-DAY MODEL

The modified degree-day procedure given i n the 1980 ASHRAE System

4 Handbook can be written as follows:

where E = t h e energy consumed during a h e a t i n g season

HL = t h e design heat loss , W

D = t h e number of degree-days to base 1 8 % during the

h e a t i n g season, O C days

AT = t h e design temperature difference, "C

n = an efficiency factor which includes t h e effects of part

load performance, full load efficiency, o v e r s i z i n g , and

energy conserving devices

V = h e a t i n g value of fue l , consistent with HL and E

CD = a correction factor

Earlier experience with utility hills showed that the annual h e a t

requirement fo r a well i n s u l a t e d house falls s h o r t o f (H by about L . D.24

(hT m 25 per cen t and t h a t t h e appropriate value of C was 0.75(*). A number of D explanations can b e g iven f o r t h e origin o f C as follows: n

[I) By meastrring t h e n u m b e ~ of degree-days to base 18'C ra ther than

from t h e thermostat s e t point T STAT

and allowance E is made far f

internal heat gains f rom people, appliances and sunlight:

where - 'f - ( T ~ ~ ~ ~ - l a ) H~ D. 24

- * -

AT rlv

If t h e indoor temperature a t which the internal gains balance t h e

losses is less than 1 8 " C , then t h e allowance made in the modified

degree-day expression will be inadequate and t h e seasonal energy

h i g h . A value of C u c l would bc appropriate i n this case.

(2) The design conductance H ]AT has traditionally been calculated L from outdoor temperatures and a i r infiltration rates c lose t o the

annual extreme values. The mean i n f i l t r a t i o n rate aver a hea t i ng

season w i l l be rather less than the peak value, indicating that

HL/AT generally overestimates t he representative building con-

ductance. Once again, a value o f C ~1 is called f o r . a

Modified Degree-day Model compared with Simulations

Equation ( 2 ) can be used to calculate t h e seasonal heating energy consumed

by the particular building described in Appendix A. There are, however, t w o

important differences hetween t h i s relationship and the modified degree-day

expression.

( 4 ) The building conductance G includes t h e season average a i r

infiltration rate rather t h a n the design value.

( 2 ) Below-grade heat loss has been held constant fo r a l l locations.

It has been accounted for in the analysis along with internal

gains as follows:

Net internal gain = T o t a l internal gains - below-grade loss

I n the modified degree-day model, t h e term IIL/AT includes

below-grade heat loss which implies that it scales with

degree-days.

If t h c conductance G in Equation 12) were replaced with the des ign value

H /AT, then a smaller value of CD would he required to balance the degree- L

day type expression. This explains, in par t , why the numerical value 20 for

t h e f ac to r k i n Equation (23 is h i g h e r t h a n t h e expected C D -

A Variable Base Degree-Day Approach

The factor CD is known to depend on the comparative s ize of internal g a i n s 4

and t h c heat last from t h e bui lding. The ASHRAE Handbook i n d i c a t e s ( F f g . 1,

p. 4 3 . 8 ) how CD depends on t h e number of degree-days. The range of C D

attributed to different building t y p e s and occupancies Is indicated by a span

o f one standard deviation. This means that the 63 per cent confidence i n t e r v a l

f o r C in Canadian climates is approximately 0.25. D

Various attempts have been made t o eliminate t h e need f o r C by adjus t ing D the degree-day base temperature to su i t each particular building. I t is worth

considering the possibility for t h e buildings described in t h i s r epor t . A

va r i ab l e base degree-day equation can t a k e t h e following Eorm.

where T* = The outdoor temperature at which t h e heating

system t u r n s on (the balance temperature) "C

G = The above-grade envelope conductance including

air infiltration and excluding below-grade heat

l o s s (W/K)

The balance t e q e r a t u r e can be estimated using t h e following equation:

( T s ~ ~ ~ ~

- T*) = S + E - B (41 Cr

T~~~~ = thermostat setpoint, ' 6

S = mezn s o l a r h e a t g a i n , W

F = heat gain from occupancy, W

0 = basement heat loss, W

Annual degree-days are n o t widely available f o r a variety of base temperatures.

For the locations l i s t e d on page 2 , t h e y were computed from degree-hours f o r

t he base temperatures 1 2 , 14, 16 , 18 and 20°C. A r e l a t i o n s h i p between the

impor tant variables D and T* has been developed which accounts f o r about 1 8

90 per cent of t h e variance i n D T* - The remaining error has a s t a n d a r d

deviation of degree-days [C) for each degree removed from base 1 8 ° C - The value

of DTP can be calculated from D and T* as follows: 18

provided t h a t T* fa l l s within t h e range 20 > T* > 1 2 . Substituting i n Eq. (33

E 24 2

= G - (D + (T* - 18) ~ 3 0 8 + (T* - 18) x 5 ) VV 18

where

Of immediate note in a slope dE ( 1 = 24

Applying these equations ta building A gives the following:

Figure 3 shows the predicted energy plotted against D as a dashed line. 18 Agreement w i t h the simulation impravcs in colder climates but t h i s is expected

because in t e rna l gains are more likely t a be utilized. In reality, in ternal

gains are no t as steady as assumed by t h e base temperature selection process,

and as the h e a t l o s t through t he envelope fs reduced by adding insulation or

moving to a warmer climate, internal ga ins mare frequently exceed t he demand

far heat and are partly wasted by higher conduction losses because of higher

i n s i d e temperatures and by d e l i b e r a t e ventilation. In addition, the buildings

s i ~ I I l :~ tcd i n t f a i s pirl~cr hnvc m u l t i 111 c zorlcs :ln(I t h c ma j n r Jntcrnnl gni n s

rclcasucl on the f i r s t and secorld f l o u r s c;trlnot tjc t radcd for heat l o s t from

t h e basement.

Thcse observations h igh l5gh t one of t h e major difficulties encountered by

simplified energy predictive methods: the problem o f determining how much of

t h e heat released by occupants, appliances and window s o l a r gains contribute

towards reducing demand from t h e furnace . In t h e degree-day method and its

variations, these d i f f icu l t ies are cu r r en t l y accounted f o r by a f a c t o r de t e r -

mined from experience w i t h utility h i 1 1s.

A two-storey housc w i t h basement was modeled using t h c ERGORE computer

program under climatic conditions of 10 Canadian locations and w i f h four

dif ferent l eve l s o f insulation i n each l oca t i on . The r e s u l t s of t h e 40

simulations can be expressed in terms of t h e above-grade envelope conductance

C (excluding i n f i l t r a t i o n ) and the cl imatic severity in degree-days (D)

as follows:

(1) Changes to t h e seasonal purchased energy attributed to changes

in abovc-grade envelope conductancc follow t h e t r e n d :

(2) To ta l seasonal purchased energy can be estimated using t h e

following expression:

E = 20.G CD18 '0°1

T h i s carrelation could not be reproduced u s i n g a variable base

temperature degree-dzy equation unless t he utilization of i n t e r n a l gains

is more accurately accounted f o r .

These observations havc simplicitjr i n common with t h e modified degree-

day model but t he re is an important difference. Thc '"design load" canduct-

ance term i n t h e modified degree-day ctluntion i s n o t t h e same as t h e season

averaged above-grade conductance used here. Consequently t h e factor

hE ,, ;" CnlrnJ -r P Y T I P ~ ~ P ~ . t.n he ra ther hinher t h a n t h e commonly accepted

REFERENCES

1) Measures fo r Energy Conservation in New Buildings, 1978. Issued by the Associate Committee on the National Building Code. National Research Council o f Canada, Ottawa. NRCC 16574.

23 Stephenson, D-G., Determining the Optimum Resistance for Malls and Roofs. National Research Council of Canada, Division of Building Research, Bldg. Res. Note 105. January 1976-

3) Konrad, A . , Description of t he Encore-Canada Building Energy Use Analysis Computer Program. National Research Council of Canada, Divis ion of Building Research, Computer Program No. 46. April 1980.

4) ASHME Handbook; 1980 Systems Volume. American Society of Heating, Refr igerat ion and Air-Conditioning Engineers. New Ysrk, U . S . A .

5) Ilanion, V.S. and Juchymenko, A . , Energy Usage and Relative Utilization Efficiencies of O i l , Gas, and Electric-Heated Single-Family Homes. Ontario Hydro Survey,

ACKNOWLEDGEMENTS

The co-operasive e f f o r t of the Building Research Association of New Zealand and the Div i s ion of Building Research, Nat iona l Research Council of Canada i s acknowledged in supporting t h i s project. h e acknowledgement must go to J . K . Latta who initiated this study and added many he lp fu l s u g g e s t i o n s .

APPEND I X A

B U I L D I N G DETAILS

Floor P l a n

A lmi l d i n g of t h e following f l o o r p l ; ~ n has heen modeled :is f i v e e q u : ~ l l ~ ' thermostatted h e a t i n g t o n e s .

B A S E M E N T G R O U N D F L O O R S E C O N D F L O O R

'A Building Dimensions

Toral floor area including basement 182.6 m2

Building volume including basement 411.6 m3

Average construction weight approximately 146 kg/m2 of f l o o r area

Window areas and orientations:

THERMAL PROPERTIES OF COMPONENTS

Bui ld ing

Exte r io r wall above-grade 2 2.75

thermal resistance, m K / W

Roof thermal resistance, 2

m K /If 4.10

Basement above-grade walls 2

thermal resistance, m K/IV 1 ,34

External door s thermal 2

resistance, m K / W

T o t a l window conductance,

N/K, 36.34

Above-grade envelope

condtrctance excluding

infliltration, W/K

roof solar absorptivity = 0.9

external wall solar absorptivity = 0.4

external door solar absorptivity = 0.4

above-grade basement w a l l solar absorptivity= 0.75

SPACE HEATING MEASURES AND TEMPERATURE CONTROL

Adequate electric heating capacity was installed in each zone and

controlled to the following se tpoin ts with 0.5"C dead band.

Time Thermostat s e t t i n g

Excess heat was s p i l l e d to prevent t h e indoor temperature. of any of the zones

exceeding 26.7 '~ .

BASEMENT HEAT LOSS

The basement heat lass remained unchanged from locality to locality f o r

t h e following two reasons.

[a) In practice the below-grade heat l o s s depends on fac to r s

which are d i f f i c u l t to account for v i z ground water movement

and t h e conductivity of back f i l l ed soil. These appear to vary

as much within t he localities chosen far climate modeling as

from one climatic zone to the next.

(b ) A t t h i s t i m e , there are very few reliable measurements o f below-

grade heat loss.

A steady heat lass of approximately 1 kW based on measurements by the

Divis ion of Building Research was chosen for a l l localities.

INFILTRATION

In the ENCORE simulation, hourly infiltration rates are calculated from

t h e specif ied leakage openings in t h e envelope and t h e driving forces o f wind

and temperature. The procedure is described by Konrad e t al.*

The mean heat ing season infiltration rate was 0.18 a i r changeJhour.

Variation between buildings at each l o c a l i t y caused by h i g h e r mean indoor

temperatures i n the b e t t c r insulated cases was less t h a n 0-01 a i r change/

hour. Variation f r o m locality to locality amounted to a standard deviat ion

of 0.02 a i r change/hour .

CASUAL HEAT

The h e a t released by t h r e e occupants has been modeled as a series of hourly schedules for:

Sensible and l a t e n t heat

Elect r ic appliances

Contribution from h o t water

Electric lights

There are holiday and workday schedules f o r each of these consisting of hourly

average values. Elec t r i c l i g h t s are t u rned on when called f o r by the schedule

or when insufficient daylight i s available. The amount o f hot water heat ing

energy f i n a l l y made available as space heat includes the standby losses and

50 per cent of energy to h e a t water.

* Konrad, A . , Larsen, B.T. and Shaw, C.Y. Programmed Computer model of a i r

infiltration in small residential buildings with oil furnace. Procs, Third

In terna l S p p . Use o f Computers f o r Environmental Engineering Related t o

Buildings, Ban f f , Alberta, May 1978, p . 637-644 (NRCC 176643.

The following table gives mean d a i l y contributions to space heat .

The annual total electrical consumption breaks down to around 8000 k1V.h for hot water and 3800 kW.h f a r lights and appliances. The total of 11,800 kW,h l i e s close to t h e mean annual electrical consumption f i g u r e s c i t e d in a survey o f single family homes by Ontario ~ ~ d r o '

'

$cns ib l e and la tent heat

Electric appliances

Approximate Mean Daily Contribution

to Space Heat

7.3 kW.h/d

6 . 3 kW.h/d

Hot water system

Electric lights

I Total.

14.3 kw.hJd

2.9 klVlh/d

3 0 . 8 kw.hJd

0 0 20 40 60 80 100 120 140 1.60

ABOVE-GRADE CONDUCTANCE l EXCLUDl NG I NFILTRATION1. WIK

e c s A B U I L D ~ N G I I I

F I G U R E I