Results for the Hawthorne system-continue

Table 1. Sample data and calculated results for the Hawthorne AAP steam system

Figure 3. Adjusted average makeup flow rate as a function of degree days

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The steam use due to leaks in the steam distribu-

system will undergo much less variation. For this

tion piping is basically only a function of the pres-

reason we will assume that the heat losses from the

sure in the steam supply pipe. Since the supply

steam pipe are constant over the heating season.

pressure at the inlet to the distribution system is

This allows us to lump the steam use due to these

maintained at a reasonably constant level, the rate

heat losses with the steam use due to leaks.

of steam leakage is also fairly constant. When higher

The remaining steam load on the system, that

loads are experienced at the buildings, the increased

due to the space heating requirements of the build-

steam flow rate will result in greater pressure losses

ing, will vary substantially with the outdoor air

and thus the pressure will be lower under the higher

temperature and thus the degree days accumulated.

load conditions. This effect will of course increase as

In fact, if our degree-day model were an exact repre-

the distance from the plant increases. The Haw-

sentation, this load would disappear when the av-

thorne AAP system is a relatively small system with

erage outdoor air temperature for the day reached

18.3C (65F), the point at which no degree days

the longest distance along the pipe from plant to

consumer being about 1035 m (3400 ft). For this

would be accumulated for the day. In reality this is

reason, the amount of steam used due to leaks will

not true for several reasons, the primary one being

be assumed to be essentially independent of the

inadequate control of the heating system in the build-

space heating load.

ings. Some of the building heating systems at

Steam use resulting from heat losses in the distri-

Hawthorne AAP do not shut off completely when a

bution system is a function of the temperature of the

specified indoor temperature level is achieved. This

surroundings, and thus it is also correlated with the

is a common problem in steam-heated buildings,

degree days accumulated. This function is basically

resulting primarily from leaking valves that do not

proportional to the temperature difference between

completely close. Thus, some portion of the load

the steam in the pipe and the adjacent surround-

due to space heating at the buildings is residual

ings. Since most of the main steam lines are con-

after degree days are no longer being accumulated.

tained in concrete trenches whose covers are at grade

This must be lumped with the "fixed" portion of the

level, there is little time lag between the time of an

load on the system, resulting from steam leaks and

air temperature change and the time at which the

heat losses from the steam distribution piping.

steam system experiences heat losses proportional

A linear function has been regressed onto the

to the new temperature. The dependence of the rate

data of Figure 2 as shown. The slope of the re-

gressed line is 0.0445 kg/sC-day (0.0545 lbm/

of heat loss from the steam pipe on the ambient air

sF-day) and the intercept is 0.663 kg/s (1.46

temperature is not nearly as dramatic as that of the

building heating load. Since the elevated tempera-

lbm/s). Based on the discussion presented above,

ture of the steam pipe results in a large temperature

the intercept would represent the sum of the loads

difference between itself and the environment, the

due to steam leaks, heat losses from the steam

changes in this temperature difference due to

piping, and residual heating of the building due

changes of the environmental temperature are rela-

to inadequate building control systems. The slope

tively small. For example, during the 1987/88 heat-

of the regressed line would represent the rate of

ing season the largest temperature difference be-

increase of steam use as a function of increasing

tween the mean ambient air temperature and the

degree days. One measure of the efficiency of the

steam pipe occurred on 25 December when the tem-

distribution system is the ratio of the useful heat

perature difference was 177.20C (170 to 7.2) (319F).

delivered to the total heating energy that leaves

By contrast this temperature difference was at its

the plant. We can find the useful heat delivered

lowest value during the 1987/88 heating season on

using the slope of the regressed line from above.

27 October when it was 154.4C (170 to 15.6) (278F).

To do so we multiply the slope value from the

Thus, this temperature difference is only 12.8% less

regressed function by the length of a day and

at its minimum than when at its maximum. The rate

then in turn multiply the resulting value by the

of heat loss will vary by a somewhat lesser amount,

total number of degree days for the heating sea-

since the thermal mass and thermal resistance of the

son. For the period of the 1987/88 heating season

concrete trench and surrounding soil will tend to

under study, the total accumulation of the

weighted average degree days was 2026.5C-days

dampen the effective temperature difference be-

(3647.7F-days). Thus, the total useful steam de-

tween the steam pipe and the environment. Hence,

during this period when the space heating load

livered was 7,791,000 kg (17,176,000 lbm). The

would range from essentially zero to its maximum

total steam delivered will include, in addition to

value, the heat losses from the steam distribution

this useful steam, that which was consumed due

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