ENERGY LOSSES AND OPERATIONAL COSTS OF
RADON MITIGATION SYSTEMS
L. Moorman, Ph.D.
Radon Home Measurement and Mitigation, Inc.
Fort Collins, CO
ABSTRACT
Energy losses and operational costs of radon mitigation systems in typical locations
within the various heating zones in the USA have been calculated that include a
modeling of seasonal and daily temperature variations.
Two types of energy losses are compared with the electrical energy consumption for
various ventilators that will be presented graphically. These energy losses will also be
compared with the losses for higher quality radon mitigation systems, where the yearly
energy losses are designed to be minimal. Optimization does not lead to the same results
for all locations. The results will also be presented as all inclusive formulas for
operational energy losses and costs including altitude corrections. The applicability of
these calculations will be discussed and the case will be made that the knowledge of
these issues may help an individual radon mitigation company to improve its
competitiveness.
ENERGY LOSS TYPES RELEVANT TO
RADON MITIGATION SYSTEMS
Operational energy costs of radon mitigation systems are either ignored or merely
partially taken into account when various mitigation systems are compared. The cost
that is typically recognized is (1) the direct electrical cost to operate the ventilator, but
consists also of (2) conductive thermal losses and (3) convective warm and cool air
losses. In the winter due to the operation of a furnace the additional operational energy
costs consist of thermal conduction through the boundaries of the building (referred to
later as W2), and warm air lost by convective replacement of warm air with cold air
from outside the building (W3). In the summer, when an air conditioner or other cooling
system exists, additional energy losses consist of conductive thermal losses (S2)
conductions through the boundaries of the building and cooled air lost by convective
replacement of cooled air with warm air from outside the building (S3). In calculating
the total energy burden the efficiencies of equipment to effectively heat the replaced air
in the winter and cool air in the summer must be included, and when operational cost
rates to the occupant are calculated typical utility energy cost rates have to be included.
265
The direct electrical yearly energy to operate the fan (1) is easiest to measure or
estimat. Measuring pressure differences across the ventilator can be accomplished
directly with a digital micro-manometer that can be combined with the information from
the fan curves of the manufacturer. From this information the operational volumetric
flow rate can be calculated for each section of pipe. The electrical energy costs of
ventilators can be approximated by its rating. Although the actual operation point for a
ventilator will be below this rated power, the operational electrical energy used will be
close to the maximum energy rating when large air flow rates are observed.
Conductive energy losses (W2 and S2) are hard to measure and exist in the
winter as cooling of the bottom of the concrete slab by air movement caused by the
system under the slab and thermal diffusion from the warm top to cold bottom of the
slab (or membrane in case of a crawlspace) and vice versa in the summer. In general
wooden residential buildings with floating slabs in the dryer climates are constructed
with conductive losses much smaller than convective losses and it is estimated that the
additional conductive losses fall within the uncertainty of the calculations of the
convective losses that will follow.
Convective energy losses (W3 and S3) during heating and cooling seasons
generated by a radon system, are caused by gaps and openings in concrete slabs of
basements, sump pit openings, and between improperly sealed membrane-to-foundation
wall boundaries, and at overlaps of membrane sections. The effect of this is not
negligible and is not often included in an energy calculation.
There are two potential exceptions to radon systems causing additional
convective energy losses. One exception (A) is when the additional convective air loss
by the radon mitigation system from the building has the effect to reduce the loss of a
fraction of air loss elsewhere from the building envelope for example by raising the zero
pressure plain inside the building. This effect has been noticed in another study but
Fig. 1: Energy (dashed) and Air flow (solid) diagram for a radon system
extracting warm air from the house in the winter. Energy: Top of diagram, Air flow
bottom of diagram, Inside vs. outside the house is represented by the left vs right side of
the diagram.
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and in that study did not completely reverse the effective flow in the upstairs [1].
Another exception (B) is when a fraction of the air loss that the radon system is
exhausting is unconditioned air that entered the building before it had a chance to fully
mix with warm air and reach a new thermal equilibrium [2], which can be the case in a
cold crawlspace. In both cases the fraction of exhausted cold air mass does not
contribute to additional energy losses compared to what the building would have
suffered without the radon mitigation system. In this paper we will assume that both of
these cases do not apply to the situation that will be discussed. The reason for this is that
in most houses with a furnace or conventional boiler or heater, by Code, one or two
required make-up fresh-air openings in the basement exist preventing back drafting of
the furnace, but also allowing most of the additional evacuated air by the radon
mitigation system to be drawn in at this location and be mixed with the interior basement
air. Thus in the generic situation the air that entered mixes fully with inside air before it
is removed from the house by the radon system. However residences entirely operating
on electrical appliances, or Solar or Green houses with their specific energy
circumstances may have to be investigated separately.
In Figure 1 an energy-air-flow diagram is shown for a radon mitigation system in
the winter. The bottom half of the diagram indicates the relevant air flow movement and
top half the energy flow. In addition items in the left side of the diagram are events
occurring inside the house and in the right side of the diagram outside of the house. The
diagram indicates that the system draws in warm air from the inside of the building that
bypasses the lowest slab of a house through its openings in the winter.
Thus the first line of defense against convective heat losses is to seal all openings
from the interior of the house through and around concrete slabs to the soil with a
durable caulk. The caulk has to have enough elasticity to allow for small movements of
components it is adhered to without breaking, such as in the case of floating slab to
foundation wall joints. Therefore special caulks are applied and insulating foams are
rarely used successfully because they do not have the elastic durability,
Fig. 2: Energy/Air-flow diagram for a radon mitigation system extracting cool air from
the house in the summer.
267
resistive porosity, and adherent quality we need for radon mitigation systems.
A better sealing of these openings results in lower convective energy losses. Given the
examples mentioned an effective estimate of 50% convective energy losses is a good
first guess for calculation purposes in sub-slab situations with gravel as is prescribed in
certain Codes.
Finally a distinction must be made between heating and cooling losses when
various energy sources are being used. In these calculation we assume that in the winter
a normal gas fired furnace or boiler with 70% efficiency is used and in the summer a
whole house air conditioning unit is used with moderate energy efficiency whose
compressor does work and uses electrical energy.
MEASURING AN AIR REMOVAL RATE FROM A BUILDING
AND THE EFFECT OF SEALING THE SLAB
An unfinished basement was constructed with floating slab and gravel as sub-slab
material, and an interior drain tile pipe and all openings through the slab were
appropriately sealed during this research. Openings included all expansion joints near
floor and walls, control joints interior to the slab in 10x10 square foot sections, whether
it had cracked yet or not, to provide protection for future cracking, openings around
plumbing pipes, rough-in openings, and all additional cracks visible in the slab. The
existing sump pit opening was sealed with a hard cover transparent polycarbonate
material to accommodate future visual inspection. Figure 3 shows the results of
localized, single point, measurements of the sub-slab difference pressure across the
thickness of the concrete slab material at different distances from the radon extraction
cavity that were made before the sealing process was initiated. After the sealing process
was completed the measurements were repeated the base pressure drop at the cavity can
be roughly translated into an effective flow rate through the radon system. Using the
published ventilator curves from the manufacturer of this ventilator the effective air
removal rate can be estimated. In this case an effective removal rate of 280 cfm was
reduced to 143 cfm just by complete sealing of the slab. This means that an effective
additional air removal rate of 137 cfm is taken from this basement by the radon
mitigation system with this ventilator when the basement remained unsealed compared
to when the basement was sealed. This derivation was rough and ignores all other parts
of the mitigation system. A more sophisticated analysis [3] taking the friction of the
equivalent length of the piping in this 1-branch system into account allowed a modeling
of the proper sub-slab cavity pressures resulting in flow rates of 167 cfm and 97.8 cfm
The resulting cavity resistance change that was used to model this was 6.65 10-6 min/cf
and 3.65 10-5 min/cf. This demonstrates what size changes of cavity resistance can be
accomplished by sealing alone. The total effective flow rate change was 69.2 cfm.
This type of data should have a consequence for new home construction design. If
RRNC building techniques require gravel (or gravel is chosen) and these systems do not
require sealing of the slab at the same time, or sealing is not properly inspected by the
municipal inspector, basements have been observed to be finished immediately during
construction or later without appropriate sealing of the slab, despite new home building
268
Codes that require it. This will have the consequence that the building occupant will be
burdened with additional indoor air losses of a similar magnitude as we just presented
when radon systems are installed while proper sealing is no longer possible because
openings and gaps are not reachable any more. Moreover, expansion joints of 40 year
old homes have been observed to have been completely deteriorated, which will affect
the operation of currently installed radon systems well into the future when such joints
could not be sealed during installation. Techniques to seal expansion joints of finished
basements are either very costly (remove drywall and plates to reach the joints) or messy
(clean, vacuum and caulk the joint through the drywall) and satisfactory methods are not
existing at this moment, but will be needed in the future when advanced diagnostic
methods will show which houses have unacceptably high energy losses for the occupants
living in them in the future. This is a current challenge for the radon industry to solve.
This paper will address the question what magnitude of energy losses and costs
can be expected in these situations. If control grooves in slabs are not caulked, or are
sealed with the wrong caulk material that tends to harden too much and crack later, or
grooves are not properly cleaned and vacuumed before caulking and caulk has been
observed to peal loose with time, a significant additional operational air removal loss can
be introduced by activation of passive radon removal systems, even when they are
Fig. 3: Effect of sealing an unfinished basement on the radon pressures and
system air removal flow from the building with large gravel and interior perimeter drain
under slab. The reduction in air removal rates based on complete simulation of the
system [1] shows that in this case a removal rate of 69.2 cfm air is prevented from the
building, when complete sealing is applied before finishing the basement (Ventilator
power is 150 W).
269
activated much later. An obvious advantage is that once the floor is sealed a ventilator
with smaller power can be chosen to mitigate the same building, reducing air losses even
further as well as reducing direct electrical costs and Air Conditional losses in the
summer. As an additional benefit this causes a lower noise burden on the living area.
If in the example of figure 3 all of the remaining air flow through the radon
mitigation system came from the sub-slab material under the building that ultimately
came from the surrounding outside soil a reduced energy loss for this radon removal
system would have been introduced. As a second example we show in Figure 4 a similar
situation with pea-size gravel and no interior perimeter drain. It can be seen that the subslab resistance for air flow is reduced and is not symmetric around the cavity because of
the two data points near 27 ft distance that have quite different values. When sand and
clay are used the heating losses are reduced even more because of the low porosity of the
material; however when low resistance channels exist in the sub-slab materials cracks
and expansion joints can be reached and can provide significant pathways with higher
flow with similar concern for operational energy and cost losses for the system.
Fig. 4: Effect of sealing an unfinished basement on the radon pressures and system air
removal flow from the building with sand and pea gravel under the slab and with no
interior perimeter drain. The reduction in air removal rates based on the complete
systems analysis shows that in this case a removal rate of 28.2 cfm air is prevented from
the building, when complete sealing is applied before finishing the basement (Ventilator
rating is 83 W).
RADON REMOVAL EFFECTIVENESS IN
VERY LOW ENERGY LOSS SYSTEMS
The two examples presented before indicate the importance of proper sealing when
leaky slabs are encountered. Although improvements can be made in existing homes
there is no substitute for being able to work the problem from the ground up. In the
example we will look at in this section a Radon Risk Evaluation had been performed on
270
a location where the house was going to be constructed. The basement had been
excavated and the concrete foundation walls poured. The Radon Risk Evaluation
indicated that the finished house would have had a radon concentration of approximately
150 pCi/L (See Fig. 5). We were asked to install our most effective and energy efficient
radon mitigation system that the owners preferably would like to see work as a passive
system, to avoid any noises added to the house and surroundings. A double barrier
passive system was installed that resulted after completion in a measured radon
concentration (2 day short term test, closed house conditions) of approximately 25
pCi/L. During this time the plumber had left an 8 inch slit in the crawlspace membrane
near the water heater. After repair and activation of the membrane very low levels were
reached. A follow up measurement operating the system as a passive system measured a
level of 5.2 pCi/L.
Additional measurements with a Continuous Radon Monitor (femtotech CRM
510) were done by operating various fans and electronically operating fans at various
Fig. 5: Radon Risk Evaluation and double barrier passive and active operation of high
energy efficient combined ASD and membrane radon mitigation system.
rotational speed. Pressures across the fan were measured whose flow rates had been
compared with measurements in a bench set up elsewhere. From figure 5 it can be seen
that the measured radon levels at different flow rates had a background. A theoretical fit
based on a volume theory resulting in a hyperbolic shape showed a fit as shown that
indicated a background of 0.85 pCi/L. This background was reached for an extra
271
powerful fan operating at its full power at 150 Watt which with the low frictions in this
two-branch mitigation system was at flow rates of 150 cfm.
Similarly we found that even at very small flow rates the radon level did not rise above 2
pCi/L even at a flow rate of as little as 20 cfm. The ventilator used was a 12 V-DC fan
drawing a power of 3.2 Watt. The physical dimensions of the ventilator was a 2 inches
diameter axial fan that was inserted inside the 4-inch PVC pipe on a perpendicular
polycarbonate holder that allowed leakage for water around it through the pipe.
From this graph we can conclude that with limited testing not much benefit
seems to be indicated to run a 150 cfm 150 Watt commercial radon ventilator compared
to a 3.2 Watt ventilator. However it must be kept in mind that the membrane system was
hermetically double-sealed below the slab and a full interior perimeter drainpipe was
inserted in the gravel under the double membrane, which treatment can only be done
during new home construction.
Thus the question is if it is possible to reduce energy losses through sealing and reducing
the power of the ventilator while maintaining a high radon removal efficiency. A
theoretical fit curve of the data indicates that to minimize the radon concentration a
maximum power of the ventilator would be required. The theoretical fit shows a
Fig 6 Short term radon tests in the house after installation of a high energy efficient
radon mitigation system allowing a number of ventilators to run at different power.
Ventilator powers range from 3.2 W (20 cfm) to 150 W (150 cfm).
background of 0.85 pCi/L that is not affected by the flow rate. Its interpretation is
that this background is caused by a combination of radon in the outside air around the
building and the combined sources of building materials inside the building.
The choice of maximum air flow through the system would add unnecessary energy
losses and additional noise to the house to the extent that a homeowner may not want to
272
live with. This is an example in support of the fact that the requirement in the author’s
opinion for a ‘higher quality’ radon mitigation system is not to uniquely ‘maximize’ the
radon reduction, but to ‘optimize’ a number of variables. The four desired variables to
optimize simultaneously are (1) maximizing radon removal, (2) minimizing energy
losses, (3) minimizing the noise burden on the most sensitive living areas, and (4)
minimizing visibility of the system. The latter is added such as not to affect curb appeal
and visibility from a backyard and low visibility through the most frequently visited
areas in a house. Systems installed in this way will be functional and avoid adding a
burden to the house. When done well in new home construction by conscientious
mitigators passive mitigation systems can be designed optimally in this sense and
provide for an uncomplicated activation, if radon tests show the need later.
A MODEL FOR EXTERIOR TEMPERATURES
In order to calculate which energy losses a radon mitigation system adds to the utility
costs of an occupied residence we must first define the baseline, which is the outside
environment with which the house exchanges air.
In the industry and academics a useful measure in terms of heating and cooling
degree days has been used for decades [4]. Limitations of the method are that it only
takes into account temperatures due to space heating, not when solar heating becomes
important. In this Sense the CDD has limitations. It assumes the Heat Loss is
proportional to the temperature difference. In most cases cooling is applied only in a few
rooms which limits
Fig. 7: Example of a match of a three parameter model that fits the seasonal cycle of
temperatures for thirty year average monthly Heating Degree Days and Cooling Degree
Days for Fort Collins CO. February’s shorter month causes a seeming irregularity.
273
the usefulness of the method. [5]
A single heating degree day based on the reference temperature 65 degrees
Fahrenheit is defined by the average temperature during one day to be 1 degree
Fahrenheit below 65 degrees, relating to the assumption that the occupant would want to
heat the residence during that day by an average of 1 degree to bring it from 64 to 65 oF.
Five different Climate Zones are classified for the HVAC industry in which specific
recommendations for use and operation of furnaces and air conditions may vary across
the Climate Zones.
Based on the information of thirty year averages of heating degree days (19712001) [6] and cooling degree days (1961-1990) [7] a model for exterior temperatures can
be made with an average amplitude describing the seasonal temperature cycle, and a
number of days shift from January 1, can be made that approximates best the
temperature for each day during the year. The consistency of this three parameter fit
with the heating degree days curve as well as the cooling degree curve is shown in figure
7. The curve can be captured remarkably well with these three parameters.
On top of this seasonal cycle a daily cycle is chosen with a temperature
amplitude based on average high-low temperature differences within the day. The
resulting model can be considered a reasonable approximation of the average hourly
temperatures that we can give with a total of only four parameters.
Fig. 8 Hourly modeling of outside temperatures in Fort Collins CO where the daily
highs and lows are taken 17 oF up and down from the average temperature (black line).
Heating of the house is set at the point where the outside temperature is below 68 F (red
line) and cooling starts when the outside temperature is above 72 oF (blue line).
The daily modeling parameters for outside temperatures in Fort Collins, CO,
throughout the year are exemplified in figure 8. The outside temperatures vary between
the two extremal green curves with black curve being the daily average The red
horizontal line in this figure indicates the outside temperature 68 oF below which heating
274
Table 1 Locations across various Climate Zones with Fit parameters to the 30 year
averaged HDD and CDD data
City
Index
KEY WEST
SAN DIEGO
CHARLSTON AP
ATLANTA
NASHVILLE
NEW YORK C.PARK
INDIANAPOLIS
FORT COLLINS
SIOUX FALLS
SAINT CLOUD
CARIBOU
ANCHORAGE
DILLON
KW
SD
Charl.
Atl
Na
NY
Ind.
FC
SiFa
SntCl
Car
An
Dil
State Climate HDD
Zone
FL
CA
SC
GA
TN
NY
IN
CO
SD
MN
ME
AK
CO
5
4
5
4
4
3
2
2
1
1
1
1
1
64
1063
1973
2827
3658
4744
5521
6587
7746
8812
9505
10470
11208
CDD Temperature Seasonal
O
( F)
variation
O
( F)
4798
87
7
984
64.7
7.8
2266
66
17
1667
62
18
1616
59
21
1096
55
22
1014
52
23
571
48.5
25
744
44
27
417
43
30
131
39
28
0
36
22
0
35
21
Shift Daily
(days) Ampl.
O
( F)
210
5
216
10
199
17
200
17
202
17
204
17
200
17
200
17
197
17
200
17
201
17
194
17
206
17
of the inside air in the house is chosen. The blue horizontal line gives the temperature
72 oF above which cooling of the inside air in the house is chosen.
The Climate Zones follow the classification for heating zones. HDD is an abbreviation
of Heating Degree Days and CDD for Cooling Degree Days which are often chosen with
a reference temperature of 65 oF. Classification boundaries are shown in Table 2.
Temperature, Seasonal Variation, in degrees Fahrenheit, and Shift in number of days
with respect to January 1, are the best three parameter fit that was found to simulate both
HDD and CDD based on their 12 monthly average recorded values over several decades
at each City’s location. Daily amplitude is a reasonable guess based on location, with
locations near coasts and equator assumed to have smaller daily variations than all other
locations.
Table 2: The definition of Climate Zones in Cooling Degree Days and Heating Degree
Days with a reference temperature of 65 oF is used in the heating and cooling industry.
Locations in all zones are represented in our calculations, see Table 1.
1
2
3
4
5
Fewer than 2,000 CDD and more than 7,000 HDD
Fewer than 2,000 CDD between 5,500 to 7,000 HDD
Fewer than 2,000 CDD and between 4,000 to 5,499 HDD
Fewer than 2,000 CDD and fewer than 4,000 HDD
between 2,000 CDD and 4,000 CDD
275
NUMERICAL CALCULATIONS OF OPERATIONAL COSTS
The outside temperature simulations at each location are used in an hour by hour method
to numerically calculate the convective heating and cooling losses:
"Q perhour = C p , m n!T
(1)
The heating energy needed is expressed in Joule and Cp,m is the molar heat capacity of
air at constant pressure, n is the number of molecules measured in moles of air
(Avogadro: 6.022 1023molecules/mol) and ΔΤ is the temperature difference in Kelvin
we need to accomplish in heating or cooling the gas. The molar heat capacity, Cp,m at
constant pressure for a diatomic ideal gas, which is appropriate for heating dry air at
atmospheric pressure, can be expressed in Ru, the universal gas constant, whose
numerical constant is 8.314 Joule/mol K, as follows:
7
C p , m = Ru =29.085 J/(Mol K)
(2)
2
which can be converted in values we will recognize in other formulas later. The heat
capacity at constant pressure can be converted to a volumetric quantity:
C p ,m = 5.6815 10-6 kWhr/(ft3 oF)
(3)
3o
= 0.019375 Btu/(ft F)
The later value is well known in the heating industry as approximately 0.02 Btu/(ft3 oF).
Using the ideal gas law, PV=nRuT the heat added to an air mass of n mole in volume V
that is drawn into the house and that is increased by temperature ΔΤ can be written as:
7 ' PV $
)Q perhour = C p , m n!( = %
(4)
"!T
2& T #
This means that a volume of cold air drawn to the inside, V, every hour is the product of
a fractional loss, f, and the volumetric rate R moved by the ventilator through any cross
section of the main radon vent pipe, which when expressed in cubic feet per minute
(cfm) must be multiplied with 60 to calculate the air volume per hour and with
0.30483=0.02831687, which is the volume of 1 cubic foot expressed in m3.
The temperature difference as calculated per hour and converted from degrees
Fahrenheit, t, to absolute units in Kelvin, T, can be written as
5& ,
t )#
(5)
.T = $ti - * to - t A cos(2/ '!
9% +
24 ("
The average temperature T at which the energy is heated, in equation 4, is taken to be the
freezing point of water, which is 273 Kelvin, and is a good approximation for the
average temperature of the air when winter air is heated, introducing only a small error.
The outside daily average temperature in degrees Fahrenheit is simulated by:
t
to = t Avg + tSeasonalA cos(2! )
(6)
24
Converting the expressed energy from Joule to kWhr requires a factor 2.78 10-7 kWhr/J.
The energy efficiency of the method to generate a unit of air volume must be included
by dividing through the efficiency of the device that we choose to use.
For a gas fired furnace the efficiency, g, will be taken here to be 70%, as was also
indicated in figure 1.
276
Thus putting all factors together we can calculate the heating energy needed per hour
expressed in kWhr per hour, by writing equation 4 as:
7 . 60 / 0.028317 / fR + ( 5 .
t +% 2.78 " 10!7
(7)
1Q perhour = , P
) & , ti ! (t0 ! t A cos(20 )) )#
2273
24 *$ 0.70
*' 9 Using the value for 1 atmosphere, P=101,325 Pa, and by combining the constant factors
we find for the energy loss in kWhr per hour by a simple rearrangement of the factors:
60 % 5.681 $10#6
t
"Q perhour =
fR(ti # (t0 # t A cos(2! )))
(8)
0.70
24
where the efficiency 0.70 shall be replaced by the Coefficient of Performance when we
will be considering cooling of air instead of heating later.
The hourly energy rate loss could be easily analytically integrated if this formula
was valid during the entire year but this would not be realistic. To simulate the behavior
that is closer to reality we use a criterion that switches the furnace on and off depending
on the outside temperature condition. In these calculations we use the criterion that for
all outside temperatures below the ti=68 oF the furnace will maintain the house to this
target interior temperature by heating the air that is drawn in from the outside. Similarly
for all values above 72 oF in the summer our simulation describes to cool the outside air
with an electrical air conditioner. In case we are cooling outside air entering the house
in the summer we will replace the furnace efficiency 0.70 by the Coefficient of
Performance. The Coefficient of Performance is dimensionless and indicates how much
heat energy (in any unit) can be removed from the cold reservoir of the air conditioner
per unit energy work done by the unit. This was also indicated in figure 2.
A typical air conditioner used these days in homes (not the newer high efficient type)
with an energy efficiency rating (EER) of 8 Btu/Whr will have a Coefficient of
Performance (COP) of 2.343. This is the value we will be using in this paper yet it can
be easily adapted if a different COP is known in the final presentation of the results.
In Figure 9 we have displayed the daily energy losses due to the operation of a
radon mitigation system calculated based on the hourly modeling of exterior
temperatures in Fort Collins. The horizontal scale starts on January 1. This simulation
shows that for this location the energy losses predominantly are from the heating, next
the electric loss form running the ventilator and the energy losses through cooling are
smallest.
The energy losses are converted to dollar costs based on the cost rate for the
utility applicable i.e. Natural Gas cost rate for low outside temperatures during heating
periods, and Electrical cost rate for air conditioning cooling when outside temperatures
are too warm. The current cost Rates for energy sources are given in the table 3, and
were calculated from the billings of local energy providers for 2009: Future estimated
277
Fig 9.: Energy losses due to operation of a radon mitigation systems calculated based on
the hourly modeling of exterior temperatures indicated in Fig. 7 for Fort Collins, CO
(Ventilator: 150 W ventilator, 120 cfm,, Internal losses: 60 cfm).
rates are including expected rate increases within the next decade. It should be clear that
depending on location and cost rates the ranking of importance of the three components
in Figure 8 for the occupant in dollars spent may vary.
Using these Energy cost rates and the previously discussed convective loss efficiency of
50% (LE=0.5) and Furnace or boiler efficiency of 70% (FE=0.7) and for the AC unit an
EER of 8 Btu/Whr (COP of 2.343) we can calculate the operational costs per year for
various ventilator configurations and locations.
Table 3: Local utility energy rates in 2009 in comparison to future expected rates that
were used in these calculations
Energy source
Natural Gas
Electricity
Local Current
Energy Cost Rate (2009)
3.0 c/kWhr
7.8 c/kWhr
Future Estimated Energy
Cost Rate
4.0 c/kWhr
12.0 c/kWhr
A large variation of operational costs was found with location. Total radon mitigation
operational costs were found to vary from less than $225 per year at the warmest regions
to $500 per year in the coldest regions considered for the largest air-losses considered in
the calculations and using heating by gas. The largest contributor to operational costs
was generally the heating cost, except for the warmest regions.
278
Figure 10: Additional Energy Cost calculated by using hourly computer model following
parameters and abbreviations defined in Table 1 and the future estimated energy rates
from table 2.
THE BEST FIT FORMULA ACROSS LOCATIONS AND SYSTEMS
In general the three most significant contributions to the energy losses are the electrical
power operating the fan continuously and the two convective losses causing outside air
to be heated in winter and cooled in summer. Rather than the detailed derivation from
first principles shown in the previous section we will look here to start the description
from the point of view of proportionalities that can be expected on reasonably grounds
and using the numerical data we calculated in the previous section we will try to obtain
effective proportionality constants for the largest range of realistic parameters. When
this is accomplished and the range of variables for which the simplified formula is a
good approximation this formula can be used within its validity ranges to calculate
additional results with a reasonable degree of accuracy, without having to resort to
additional numerical calculations. However it must be kept in mind that there is no
guaranty this formula will be describing all data points correctly with a single set of
279
effective parameters. On the other hand if we wanted to we could have derived a single
set of exact parameters for each individual location.
Since the ventilator operates throughout the year the energy loss over the year is
proportional to the power, P, with a proportionality constant, a:
(9)
! = aP
If we draw a fractional volume rate of air, f, from the interior of the house and the rest
from the soil under the house, given a certain air removal rate by the ventilator, R, the
energy loss due to heating or cooling will on the average be linear with the rate at which
the air is removed from the interior, fR. When heating of the air is needed the energy loss
rate is approximated to be proportional to the number of heating degree days for any
given location, H, and inverse proportional to the efficiency, g, with which this heating
occurs.
Furthermore the heating energy will be proportional to the mass in the air at a certain
volumetric rate that is replaced, thus it will be proportionally to the density of the air at
the altitude where the house is located, which is proportional to the barometric altitude
formula. This can be described as an exponential factor, where in a good approximation
the pressure drops a factor 2 due to an altitude increase of 5.5 km, for which the
parameter L will be used. Defining a proportionality constant, b, that will be interpreted
later, leads to the simple relationship for all excess connecting heating energy loss due to
an operating ASD radon mitigation system in units of energy:
A
" =b
HfR ! L
2
g
(10)
Similarly, the excess convection cooling energy loss is approximated to be proportional
to the number of cooling degree days for any given location, C, and inverse proportional
to the efficiency, e, with which this cooling is accomplished by the Air Conditioning
unit. Defining an effective proportionality constant, c, that will be interpreted later,
leads to the simple relationship for all heating losses in units of energy:
A
CfR ! L
" =c
2
e
(11)
Thus the total energy loss to the occupant of the house due to the radon mitigation
system per year can be described by adding the three contributions:
A
!
H
C
L
" = aP + (b + c ) fR 2
(12)
g
e
The energy make-up efficiency in terms of heating of the air was included in the
simulations, thus the proportionality constant, b, does not include the efficiency factor
for a natural gas furnace (g=0.70), indicating how much energy of the source energy it
280
takes to produce a unit energy of heated air. For example when an electric heating
element would be used this parameter would be 100% (g=1.0).
When using the air conditioner, the efficiency is equal to that of a reversed heat
pump with efficiency larger than 1. For an air conditioner with an Energy efficiency
Ratio (EER) equal to 8, the coefficient of performance (COP) is 2.343, which means that
for every Joule electrical energy used by the air conditioner 2.343 kWhr of heat is
transported from the interior of the building to the outside.
Figure 11: Best fit for largest group of data by adjusting the defined effective
proportionality constants. Key West and to a lesser degree Dillon are the only
significant deviations when these effective values of the parameters are used.
The electrical cost of operating the ventilator can now be calculated by
multiplying the first factor containing the power directly with the electrical energy cost
rate factor, ε. The cost rate factor for the heating energy loss term is given by the energy
cost rate of the source energy,γ, which although it differs in case natural gas, electric, oil
or propane are used, can be accounted for easily using the formula.
In addition to the Future estimated energy cost rates shown in table 3 we have
chosen the following set of parameters in the formulas consistent with our earlier
numerical calculations:
ε = $ 0.12 /kWhr
γ = $0.04 /kWhr
g = 0.70
e = 2.343
A=0 ft
The only parameter that is not realistic in many locations is the altitude, A, which is
chosen to be the value at sea level for all locations (1 atmosphere= 101,325 Pa). This is
281
done since the pressure in the numerical simulations we compare with in equation 7 is
also taken tot be 101,325 Pa. We will comment on altitude effects later.
The complete formula for the operational cost to the home owner or occupant of
operating a radon mitigation system with using natural gas to heat the house is thus:
A
U = a"P + (b#
!
H
C
+ c" ) fR 2 L
g
e
= uP + (vHfR + wCfR )2
!
(13)
A
L
All quantities are known except for the proportionality constants, a , b and c.
The proportionality constant a can exactly be calculated because the ventilator is
running all the time throughout the year. By expressing the utilities rate costs, U , in $/yr
and the power P in Watts, the proportionality constant is simply the number of 1000
hours in a year (khr/yr). This number is 8.759.
Since both b and c are effective parameters, their value can be determined by
fitting the theoretical behavior to the simulated numerical data.
The proportionality constant b is the costs in dollars per year for a unit of air. This
method on the simulated data leads to the following best fit values excluding for Key
West and Breckenridge, the extremal data points.
Energy parameters
a
b
c
Cost parameters
u
v (for natural gas)
w
Fit Values
8.759
0.009283
0.01760
Future
Current
1.051
0.6831
0.0005380 0.0004035
0.0004570 0.0002971
Units
(kWhr/yr)/W=k hr/yr
kWhr/(HDD cfm yr)
kWhr/(CDD cfm yr)
($/(W yr)
$/(HDD cfm yr)
$/(CDD cfm yr)
Table 3: Effective parameters that fit data well, except for Key West.
The energy costs across Zones for various air removal rates at the projected source
energy rates are given as data points in the following figure:
The parameters b, c, v, w can be reinterpreted by writing them in terms of the
heat capacity of air at constant pressure at 1 atmosphere pressure, as was introduced in
equation (3) in kWhr/ft3 oF. This can be done by factoring out a few trivial factors.
Because we are converting the quantity from unit cfm which has the time unit minute in
it to HDD which has the unit day in it, the number of minutes in a day has to be factored
out and we the result are written in terms of effective, dimensionless f-parameters.
For the energy parameters this is:
b = f b " 24 # 60 # 5.6815 " 10!6 kWhr /(HDD cfm yr)
c = f c " 24 # 60 # 5.6815 " 10!6 kWhr /(CDD cfm yr)
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Similarly, for the operation cost parameters, it makes sense to factor out the cost rate and
efficiency of the utilities energy conversion:
v = f v ! 24 " 60 " 5.6815 !10#6 ! 0.04 / 0.7
w = f w ! 24 " 60 " 5.6815 !10#6 ! 0.12 / 2.343
The resulting dimensionless f-parameters introduced in these equations are the various
effective proportionalities close to unity. The following are the best result using the
linear least square fitting method:
Table 4: Least square fitted, best values of the dimensionless fit parameters that describe
the numerical operational heating and cooling energy losses and costs.
1.134
fb
fc
2.15
fv
1.15
fw
1.09
Figure 12.: Energy Cost formula compared to numerical simulation for various
ventilator of various strengths and simulated air vent losses fans and scenarios. In
addition to the data introduced in Fig. 10, three data points for New York were
calculated for electric heat and the low power fan in Fort Collins.
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These are displayed as dashed lines in the figures 11 for energy losses and 12 for
energy costs. There are two reasons why the f-parameters are different from unity. This
is because (1) the exterior temperature model takes into account daily variations, and (2)
the switch-on temperatures of heating and cooling equipment was taken at 68 oF and 72
o
F, respectively, which is different from he 65 oF for which the HDD and CDD values
can be found in each location. Thus comparing with the HDD and CDD with reference
base 65 oF at any location, we are working with somewhat misalligned variables.
However this problem is taken care of by introduction of these f-parameters following
from a least square fit across most of the HDD range..
A few additional data points are shown in Figure 12 both as numerically
evaluated and using the formula, in order to see how accurate the formula works for a
variety of situations. The three dashed data points were calculated by the simulation
method for each of the three ventilator loss situations in New York and shifts are
indicated to higher costs. In addition one data point for Fort Collins with the lowest
energy fan introduced in chapter 3 is also shown in this Figure. Its’ volumetric rate was
20 cfm, but because of the special sealing applied, we estimate it to take no more than 5
cfm from the house. The energy efficiency of this system as a whole is shown to be
impressively low compared to any other data point in the Figure.
The formula was next applied for all data points and it can be seen that a good
approximation of the formula to the three data points was obtained for electric heat.
This shows reliability of the formula in predicting a variety of circumstances. The solid
numerical data points are identical to the previous figure.
ENERGY LOSSES RELATIVE TO ELECTRICAL COSTS
In Figure 13 it is interesting to compare the ratio between heating and electrical
Fig.13: The ratio of heating and electrical Costs across the HDD values.
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cost to run the ventilator for each of the three considered mitigation scenarios:
C
b"HfR
(14)
Rh = h =
Ce
a!gP
In general cooling contributes less than the electrical costs as shown in figure 14 and in
zones 1,2 and 3 less than 40% of the electrical costs. In Caribou we see a value over
50%. Only in Key West we calculate a fraction above 60% of the electrical costs which
has to be ignored due to its known inaccuracy of these parameters for Key West.
Rc =
C c cCfR
=
Ce
aeP
(15)
Fig.14 The ratio of cooling and electrical costs across the explored HDD range
Whereas heating contributes to most of the costs. For heating zones 4 and 5 with values
under 2000 HDD the cooling can contribute equal or more than heating.
In terms of the yearly total energy costs relative to the yearly electrical costs as shown in
figure 15 for the midrange and more powerful ventilator considered we calculated a
factor of 3 for Dillon, Colorado, but the moderate zones 2 and 3, this factor is calculated
to be twice the electrical costs.. For the warmest regions, heating Zones 4 and 5 the total
energy costs to electrical cost ratio is calculated to be generally smaller than a factor
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2.5. The least powerful ventilator had the highest factors across the entire HDD range
which were up to a factor 4.5 in the coolest climate of Zone 1.
Rtot = 1 + Rh + Rc
(16)
Fig.15 The ratio of Total energy costs calculated and electrical Costs across the HDD
values
THE EFFECT OF ALTITUDE
The effect of altitude on convective energy losses is directly related to the pressure at
which the volume of air is extracted by the mitigation system from the house. The
barometric altitude formula describes the pressure loss as a function of altitude due to a
layer of air carrying all air above it while the layer itself is carried by all air below within
the constant gravitational field of the earth. The exponentially decreasing formula with
increasing altitude that results is known as the barometric altitude formula and can be
written as:
!
z
P ( z ) = P0 e ! #z = P0 " 2 L
(17)
with β a known constant and P0 equal to 1 atmosphere at Sea level (at z=0 ft). The value
of β allows us to write this formula alternatively as indicated with L approximately 5.5
km, the altitude increase where the pressure assumes half its value.
As an example figure 16 indicates the relative change over the pressure range relevant to
altitudes in most residential locations of the US. As an example for Fort Collins at 5100
ft altitude this value results in a relative pressure loss of 17.8%. Extreme locations, such
as Twin Lakes, CO can go up to 41.6% loss of pressure compared to 1 atmosphere.
From equation 4 we see that the heat added for the same volume at the same temperature
at different altitudes is proportional with pressure, P, thus the same factor was taken into
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account into the fitting formulas in equations 10-13 to describe the heat lost for a fixed
volume rate fR at various altitudes.
Fig 16: Relative pressure loss as a function of altitude following the barometric altitude
formula for the altitude range of most homes in the USA. Fort Collins is at 5100 ft with
17.8% atmospheric pressure loss. Radon installations in Twin Lakes, CO were harder to
accomplish than in Fort Collins.
ENERGY LOSSES FOR ALTERNATIVE RADON MITIGATION SYSTEMS
ERV/HRV systems are subject to similar type of heat losses as discussed, but the
calculations here cannot be applied for the ventilation rates caused by these systems
because in ERV/HRV systems a large fraction of the energy is recovered by an energy
exchange medium, e.g. in the winter between a warm stream of air that is discharged out
of the house to a cold stream of air that is pulled into the house.
The air exchange medium makes the calculation we have done here not applicable on
that type of situation.
High energy efficient and electrostatic filtration to mitigate Radon Decay
Products directly, not radon, do not exchange additional air with the outside
environment, thus do not add additional energy losses beyond the already existing
natural ventilation of the home. Thus from an energy efficiency point of view this
technique maybe the most energy efficient method. However the number and power of
ventilators may be very different from a radon ventilator in an ASD system and regular
replacement costs of filters must be taken into account to determine operational costs.
A more in depth analyses for each situation separately is necessary to reach a
valid conclusion.
287
TOTAL AVERAGE COST COMPARISONS OVER LIFETIME OF SYSTEM
Using a lifetime of a system of 40 years and for Fort Collins, Colorado which is in the
middle of the HDD scale, the formula is used to calculate various components using
equation 13 and the future variables for u , v, w from table 3. Durability of the
ventilators is taken to have an average lifetime of 10 years. Installation costs are taken
into account based on actual systems installed by us or others. In the histogram with the
cost comparisons and power levels indicated along the base, the left four data each
represent a system in Fort Collins without sealed slab or with finished basement that
could not be sealed. The last data point represents the high energy efficient system
presented as part of figure 6. The first data represent a system with the altitude
correction. The second data represent a system without the altitude correction (sea level
simulation), the effect is less than 19% because only a fraction of the energy losses
involve air. It is clear that after 40 years the total cost per year to the home owners is
lowest for the lowest power system, even when higher installation costs are included.
In Figure 19 we have shown the cost development for the home owner including
operational costs and ventilator replacement (proportionally taken into account) of each
of these systems (calculated at sea level) accumulated over the years after installation.
The open circles describe the cost tipping points where the occupant will have earned
back their investment of the higher installation costs, after which it is clear that the
system with lowest power ventilator will be most cost effective for the home owner.
Radon levels are somewhat higher as indicated in figure 6. However even if higher
Figure 18 Four systems are compared on their 40 year total costs to the consumer. The
left four represent non-sealed systems, the right-most data represent a high energy
efficient system (See Fig. 6) system hermetically sealed with a double membrane under
the slab. Left two data differ only in that the actual altitude of Fort Collins (5100 ft) was
taken into account in the calculation for operational costs of the first data point..
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power ventilators are used in the high efficiency systems they would not draw as much
air from the basement as the system characteristics used in this calculation. From figure
19 we conclude that savings of radon mitigation systems are determined by how well
they are installed, rather than any other parameter, specifically, they are not determined
by the savings on installation costs.
Figure 19 Comparison of accumulated costs in time to find out cross points for return
on investment of a double membrane, completely sealed high energy efficient system
compared to lower quality unsealed systems that have higher energy loss rates.
CONCLUSIONS
We considered various operational energy losses for radon mitigation systems. The
convective heating, cooling losses and electrical costs were found to be the main energy
losses. Measurements of air losses were discussed when gravel is applied below the
concrete slab. It was concluded that substantial convective energy losses can be added
to a house when proper sealing is not accomplished, or cannot be accomplished when the
basement is finished. A case with an energy efficient system was discussed. It was
concluded that although increased ventilation rates generate increased radon reduction,
very satisfactory radon removal can be accomplished with extremely low power radon
systems provided a high energy efficient passive radon mitigation system is installed
during new home construction by conscientious mitigators.
In order to perform numerical calculations for a variety of locations in the United States
and across all climate zones, fit parameters for outside air temperature conditions
describing a modulation with a yearly cycle and a daily cycle were evaluated for each
location. Numerical calculations were performed of additional operational energy losses
and costs employing realistic utility cost rates for the next decade. A large variation of
operational costs was found as a function of location. Total radon mitigation operational
costs for the midrange and highest power ventilators were calculated to vary from less
than one and one half times, in the warmest locations, to up to three times the electrical
costs in the coldest locations considered. The smallest power commercially available
289
ventilator considered had the largest loss ratios to electrical costs across all regions
which reached up to four and a half in the coldest location. General formulas were
derived with effective parameters to describe the numerical operational energy loss and
cost data in an effective way across the largest possible fraction of the heating zones and
ventilator powers. The effective parameters in the formulas derived by a least square fit
method compared well with the numerical data except for the most extreme weather
locations. The operational costs formula was also employed to look at alternatives such
as electrical heating and high energy efficient systems and this was compared to a
normal heating system using natural gas. These results evaluating the formula also
compared well with direct numerical calculations. It was shown that altitude effects
which had been left out of all numerical calculations on purpose can be taken into
account by using the barometric altitude formula. The size of these effects was
evaluated. Energy losses of alternative radon mitigation such as ERV systems were
discussed, and it was concluded that the formulas derived here do not apply to HRV and
ERV systems due to the nature how they recover energy. Similarly it was concluded that
RDP mitigation systems cause less energy losses but add operational costs due to
frequent filter replacements.
A cost comparison over the lifetime of various systems in one location was made
showing that over a forty year lifespan the costs saved by installing the highest energy
efficient system during new home construction can be a four digit dollar amount. In this
paper a case was made that for the highest quality radon mitigation systems one should
look for the simultaneous “optimization” of four parameters, maximizing radon
reduction, minimizing additional energy losses, minimizing noise effects and minimizing
visual impact.
REFERENCES
290
[1] B.Turk, J. Hughes. “Exploratory Study of Basement Moisture During Operation of
ASD Radon Control Systems”, Revised 3/10/08 U.S. Environmental Protection Agency
Indoor Environments Division Washington, http://www.epa.gov/radon/pubs/index.html
[2] J. Bartholomew, Private Communication
[3] L. Moorman, “Solving turbulent flow dynamics of complex, multiple branch radon
mitigation systems”, AARST International Symposium Proceedings, 2008, Las Vegas,
http://www.aarst.org/proceedings/2008
[4] J. Akauder, S Alvarez, G Johannesson, “Energy Normalization Techniques” p 59, in
Energy Performance of residential buildings: a practical guide for energy rating and
efficiency, edited by M Santamouris (2005), ISBN 1-902916-49-2
[5] J. E. Piper, “Operations and Maintenance Manual for Energy Management”. Jones E.
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[6]Comparative Climatic Data", National Climatic Data Center, NOAA, 2001. Heating
Degree Days, Normals 1971-2000 Years given by month;
http://www.ncdc.noaa.gov/oa/climate/online/ccd/nrmavg.txt
[7] Cooling Degree Days: Normals 1961-1990 Years given by month by NRCC
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291