NIST Technical Note 1829

An improved method of modeling 

infiltration in commercial

building energy models

Lisa C. Ng

Steven J. Emmerich

Andrew K. Persily

http://dx.doi.org/10.6028/NIST.TN.1829

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

EnergyPlus air change rate (h-1)

CONTAM air change rate (h-1)

Stand Alone Retail

System on (Improved method)

System off (Improved method)
NIST Technical Note 1829

An improved method of modeling 

infiltration in commercial

building energy models

Lisa C. Ng

Steven J. Emmerich

Andrew K. Persily

Energy and Environment Division

Engineering Laboratory

http://dx.doi.org/10.6028/NIST.TN.1829

April 2014

U.S. Department of Commerce 

Penny Pritzker, Secretary

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director 
Certain commercial entities, equipment, or materials may be identified in this

document in order to describe an experimental procedure or concept adequately.

Such identification is not intended to imply recommendation or endorsement by the

National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Technical Note 1829

Natl. Inst. Stand. Technol. Tech. Note 1829, 41 pages (April 2014) 

http://dx.doi.org/10.6028/NIST.TN.1829

CODEN: NTNOEF
iii

ABSTRACT

As building envelope performance and HVAC equipment efficiencies are increasingly improved

to reduce building energy use, a greater percentage of the total energy loss of a building can

occur through envelope leakage. Although the energy impacts of unintended infiltration on a 

building’s energy use can be significant, current energy simulation software and design methods 

are generally not able to accurately account for envelope infiltration and the impacts of improved 

airtightness. New strategies to incorporate airflow calculations into building energy calculations

are proposed, which are more accurate than current approaches in energy simulation software

and easier to apply than multizone airflow modeling. The new strategies are based on

relationships between infiltration rates calculated using multizone airflow models, building 

characteristics, including envelope airtightness, weather conditions, and HVAC system 

operation.

Keywords: airflow modeling, commercial buildings, CONTAM, energy modeling, EnergyPlus, 

infiltration
1

1. INTRODUCTION

Heating, ventilating, and air conditioning (HVAC) systems in buildings are designed to maintain 

acceptable thermal comfort and indoor air quality (IAQ). The operating cost of these HVAC 

systems is often a large percentage of the total energy cost of buildings, which constitutes 40 % 

of the primary energy consumed in the U.S. (DOE 2010). Due to the current emphasis on 

reducing energy consumption and greenhouse gas emissions, the use of energy simulation 

software has increased to investigate different design options and their impacts on building 

energy use. One design option to reduce building energy use is the improvement of building 

envelope airtightness. Existing data show that unless efforts are made to design and build tight

building envelopes, commercial buildings are actually much leakier than typically assumed

(Emmerich et al. 2007; Emmerich and Persily 2013). As a result, the energy impacts of 

uncontrolled infiltration are also greater than assumed. Nevertheless, current energy simulation 

software and design methods generally do not accurately account for envelope infiltration, and

therefore the impacts of improved airtightness on energy may not be fully captured.

A review of the airflow analyses capabilities of the most widely used energy simulation software

tools found that many of the empirical infiltration models employed in these tools are based on 

calculation methods developed for low-rise, residential buildings (Ng and Persily 2011). These 

methods are not generally appropriate for other types of buildings, particularly mechanically 

ventilated commercial buildings as well as taller buildings, which have more airtight separations 

between floors and vertical shafts. Also, these empirical infiltration models require the user to 

specify air leakage coefficients that are best obtained from building pressurization tests (ASTM 

2010), and only limited air leakage data are available for commercial buildings (Emmerich and 

Persily 2013). Many energy simulation software users simply assume constant infiltration rates, 

which do not reflect known dependencies on indoor-outdoor conditions and ventilation system 

operation. Airflow calculations using existing theory and methods (Walton 1989) are the only 

technically sound means of determining the airflow rates for analyzing energy use as well as 

indoor air quality.

Considering the few energy simulation software tools that are able to simulate airflow using 

multizone airflow models, the capabilities are often limited and can be difficult for users to 

employ. The AIRFLOW NETWORK model in EnergyPlus is based on an early version of the 

National Institute of Standards and Technology’s (NIST) multizone airflow and contaminant 

transport model CONTAM (Walton and Dols 2013) with restrictions on the type of analyses that 

it can perform. DesignBuilder implements limited capabilities of the EnergyPlus AIRFLOW 

NETWORK model. McDowell et al. (2003) describe a partial coupling of the multizone airflow 

model, CONTAM, with the transient system simulation program TRNSYS. More recently, NIST 

has updated the TRNSYS/CONTAM coupling to include the full multizone airflow and IAQ 

capabilities of CONTAM (available at http://www.bfrl.nist.gov/IAQanalysis/software/). The 

application of modeling approaches that couple airflow and thermal or energy analyses in actual 

building design, however, is limited.

Empirical approaches to estimating infiltration rates have the advantage of ease of use relative to 

multizone building airflow models. These empirical approaches employ algebraic equations that 

relate simple building features, such as height and envelope leakage, as well as weather 

conditions to calculate infiltration rates. One of the earliest such approaches was developed by 
2

Shaw and Tamura (1977), which had one equation for stack induced infiltration, one for wind 

driven, and another to combine the two into the total building infiltration rate. More recently, 

Gowri et al. (2009) proposed a method to account for infiltration in commercial buildings that 

was developed using a square medium-size office building and a building envelope airtightness 

value, such as one obtained by a pressurization test. Assuming a constant indoor-outdoor 

pressure difference of 4 Pa, Gowri calculated an infiltration rate to be input into EnergyPlus 

using an approach that accounts for wind but not temperature effects. Note that those 

temperature effects can be important particularly in taller buildings and colder climates. Gowri 

recommends that this leakage rate be multiplied by a wind speed adjustment and by a factor of 

0.25 in EnergyPlus when the HVAC system is on and 1.0 when the HVAC system is off. 

Overall, the method greatly simplifies the interaction of building envelope airtightness, weather, 

HVAC system operation, and infiltration. 

In summary, the ways in which infiltration are currently accounted for in energy simulations are 

not typically based on well-developed airflow theory relating building envelope airtightness, 

HVAC system operation, and weather (Walton 1989). In those few energy simulation programs 

where airflow can be more accurately modeled, the features are often limited and cumbersome to 

employ and are rarely used in design. New strategies to more accurately, and more simply,

incorporate physically-based infiltration calculations into energy software are proposed in this 

paper. These strategies are based on relationships developed between infiltration rates calculated 

by multizone airflow modeling, building characteristics, HVAC system operation, weather 

conditions, and building envelope airtightness. The strategies are described for implementation 

in EnergyPlus but are applicable to other energy simulation software.
3

2. METHODS

Sec. 2.1 describes how infiltration is currently incorporated into EnergyPlus, though the 

approach is applicable to other energy simulation software. Sec. 2.2 describes new strategies for 

estimating infiltration in mechanically ventilated commercial buildings based on detailed 

multizone airflow simulations in buildings. Sec. 2.2.1 describes a building-specific strategy, and 

Sec. 2.2.2 describes a generalized one. In the building-specific strategy, the results of multizone 

airflow simulations are fit to an empirical relationship between infiltration rates and weather 

conditions for individual buildings. For the generalized strategy, the coefficients of the empirical 

relationships calculated in Sec. 2.2.1 are related to general building characteristics, such as 

building height, in order to derive expressions for calculating empirical coefficients for any given 

building.

2.1. Current strategy for modeling of infiltration in EnergyPlus

EnergyPlus uses the following empirical equation to calculate infiltration:

Infiltration = Idesign•Fschedule [A + B|ΔT| + C•Ws + D•Ws

2

] (1)

where Idesign is defined by EnergyPlus as the "design infiltration rate", which is the airflow 

through the building envelope under design conditions. Its units are selected by the user and can 

be h-1, m3/s•m2or m3/s. To apply this infiltration approach in EnergyPlus, a value of Idesign is 

assigned to each zone, with the option of each zone being assigned a different Idesign value.

Fschedule is a factor between 0.0 and 1.0 that can be scheduled, typically to account for the impacts 

of fan operation on infiltration. |ΔT| is the absolute indoor-outdoor temperature difference in °C, 

and Ws is the wind speed in m/s. A, B, C, and D are constants, for which values are suggested in 

the EnergyPlus user manual (DOE 2013). However, those values are based on studies in low-rise 

residential buildings. Given the challenges in determining valid coefficients for a given building, 

a common strategy used in EnergyPlus for incorporating infiltration is to assume fixed 

infiltration rates. In other words, assume A=1 and B=C=D=0. However, this strategy does not 

reflect known dependencies of infiltration on outdoor weather and HVAC system operation. 

Therefore, new strategies are proposed in the following sections that can more accurately 

estimate infiltration in EnergyPlus and other energy simulation tools.

2.2. Proposed strategies for improved modeling of infiltration in EnergyPlus

2.2.1. Method 1 – Building Specific

Method 1 is a building-specific strategy for determining A, B, C, and D values in Equation (1) by

using the results of multizone airflow simulations. Seven commercial reference buildings (DOE 

2011) were selected for testing this strategy: Full Service Restaurant, Hospital, Large Office, 

Medium Office, Primary School, Stand Alone Retail, and Small Hotel. These particular buildings 

were selected based on their being representative of different types of occupancy and HVAC 

systems in commercial buildings. 

Models of these buildings have previously been created in the multizone airflow and 

contaminant transport model CONTAM (Walton and Dols 2013). Details of the CONTAM 

building models can be found in Ng et al. (2012) and (2013). In order to test the new strategies

for modeling infiltration, Energy Plus models of the buildings were used. Details of the 
4

EnergyPlus building models can be found in DOE (2011). The building zoning was different 

between the CONTAM and EnergyPlus models in instances where the CONTAM models needed 

additional zones to support realistic airflow analyses. Zones that were added to the CONTAM 

models included restrooms, stairwells, elevator shafts, and storage rooms. Modeling all building 

zones, or at least more of the zones than are typically needed for energy analyses, is important 

for airflow and IAQ analyses in order to properly capture pressure relationships and airflow 

patterns in buildings. Though the number of zones and some zone floor areas are different 

between the CONTAM and EnergyPlus models, the total building floor areas and volumes are 

consistent. The CONTAM and EnergyPlus models employed the same occupancy and system 

operation schedules and outdoor air ventilation requirements. In addition, the outdoor air 

economizers and night-cooling options in EnergyPlus were disabled for all of the buildings since 

these capabilities were not implemented in the CONTAM models. 

Hourly infiltration rates for one year were simulated for each building using weather data for 

Chicago (DOE 2011). Chicago weather was selected since there are a relatively high percentage 

of buildings in the U.S. in this climate zone (Deru et al. 2011) and because Chicago covers a 

wide range of outdoor temperatures and wind speeds. A building envelope effective leakage area 

of 5.27 cm2/m2 at a reference pressure of 4 Pa was used in the CONTAM models. This value was 

based on available airtightness data in U.S. commercial buildings (Emmerich and Persily 2005). 

Based on a constant indoor-outdoor pressure of 4 Pa and a pressure exponent of 0.65, this 

leakage area corresponds to a building envelope leakage value of 0.00137 m3/s•m2 for use in 

Energy Plus. In this discussion, infiltration includes the outdoor air entering through 

unintentional building envelope leakage only. It does not include any outdoor air entering the 

building through mechanical ventilation systems.

The results of CONTAM simulations for each building are fit to Equation (1) to determine A, B, 

C, and D values for the seven buildings. Note that the outdoor temperature EnergyPlus uses to 

calculate |ΔT| in Equation (1) is not the temperature from the weather file. Instead, EnergyPlus 

uses the zone (or local) outdoor dry-bulb, Tlocal, which is calculated as a function of zone height

(DOE 2012):

Tlocal = Tambient + -0.0065•Hlocal (2)

where Tambient is the ambient temperature from the weather file, and Hlocal is the height of a zone 

above ground level. The tallest building simulated in this paper was the Large Office (50.4 m), 

resulting in less than a 0.5 °C difference between Tlocal and Tambient when calculated using 

Equation (2). Thus, when fitting CONTAM infiltration rates and weather data to Equation (1), it 

was assumed that Tlocal=Tambient for all buildings. The indoor temperature setpoint in the 

EnergyPlus models was set to 20 °C when the system was on. The indoor temperature in the 

CONTAM models was set to be 20 °C all the time.

It should also be noted that the wind speed in Equation (1) that EnergyPlus uses is not the wind 

speed from the weather file. EnergyPlus uses a zone (or local) wind speed, Ws, which is 

calculated as a function of zone height (DOE 2012):
5

Ws = Wmet �

δmet

zmet

�

αmet �

z

δ

�

α

(3)

where Wmet is the wind speed measured at the meteorological station, δmet is the wind speed 

profile boundary layer thickness at the meteorological station, zmet is the height of the wind speed 

sensor at the meteorological station, αmet is the wind speed profile exponent at the meteorological 

station, z is the height of a zone above ground level, α is the wind speed profile at the site, and δ 

is the wind speed profile boundary layer thickness at the site. Equation (3) is used to scale the 

wind speed measured at a meteorological station off-site to the wind speed at the top of a 

building or higher, with this scaling dependent on nearby obstructions. Below the building 

height, the wind speed is a complex function of the geometry of the building and nearby 

buildings, limiting the accuracy of the adjustments in Equation (3) (ASHRAE 2009).

For each building, it was assumed that the meteorological station was located in "open, flat"

terrain and the building was located in "city" terrain. The wind speed profile boundary layer 

thickness and wind speed profile exponent for flat terrain are 270 m and 0.14, respectively, and 

for city terrain are 460 m and 0.33, respectively (ASHRAE 2009). Thus, Equation (3) can be 

simplified to:

Ws = 0.2096•Wmet•z

0.33 (4)

For buildings with multiple floors, EnergyPlus uses the value of z for each floor in Equation (4). 

In order to simplify the fitting of CONTAM infiltration rates and weather data to Equation (1),

an average "local wind speed adjustment" was calculated for each building. The "local wind 

speed adjustment" for each zone is defined using Equation (4) with z equal to the zone height. 

For example, the heights of the zones in the Full Service Restaurant are 1.53 m and 3.89 m, and 

the two local wind speed adjustments are 0.2412 and 0.3282. The average local wind speed 

adjustment for the building is therefore 0.2847. Thus, Ws=0.2847•Wmet in Equation (1) for the 

Full Service Restaurant. The average local wind speed adjustments for all seven buildings are 

listed in Table 1.

Table 1. Average local wind speed adjustments

Building Average Local Wind Speed Adjustments

Full Service Restaurant 0.2847

Hospital 0.4346

Large Office 0.5823

Medium Office 0.3705

Primary School 0.2636

Stand Alone Retail 0.3030

Small Hotel 0.3642

Using a spreadsheet program, CONTAM infiltration rates and the corresponding weather data 

over one year were fit to Equation (1) to calculate A, B, C, and D values for each of the seven 

buildings. Since wind pressure on the surface of a building is a function of the square of wind 

speed (Walton and Dols 2013), a separate set of A, B, and D values were calculated with C set to 

0.
6

The calculated A, B, C, and D values (not shown) and Idesign=0.00137 m3

/s•m2were input into the 

EnergyPlus ZoneInfiltration:DesignFlowRate object, which implements Equation (1) for 

calculating infiltration. It was found that the infiltration rates calculated by EnergyPlus, whether 

C was non-zero or zero, were similar. Therefore, to simplify the subsequent analyses, C was set 

equal to 0. The calculated A, B, and D values, assuming Idesign = 0.00137 m3/s•m2, for each of the 

seven buildings are listed in Table 2. It was assumed that A = 0 when the HVAC system was off 

because when |ΔT| and Ws are zero, the system-off infiltration rate should be zero. There are no 

system-off values for the Hospital and Small Hotel because the HVAC systems in these 

buildings were always on. 

The Hospital, Large Office, and Medium Office had negative A values. The rest of the A, B, and 

D values were positive. Independent of the sign, all of the buildings have A, B, and D values that 

are of the same magnitude except for the Full Service Restaurant. Its A, B, and D values were

about five to ten times greater than in the other buildings. This may be due to its large negative 

net system flow (discussed later in conjunction with Table 4), while the other buildings have 

positive net system flow. It may also be due to the presence of an attic space, which the other 

buildings do not have.

Table 2. Method 1: A, B, and D values of simulated buildings (Idesign=0.00137 m3

/s•m2)

Full 

Service 

Restaurant

Hospital Large 

Office

Medium 

Office

Primary 

School

Small 

Hotel

Stand 

Alone 

Retail

A on 0.1413 -0.0535 -0.0412 -0.0283 0.0173 0.0374 0.0181

B on 0.0197 0.0065 0.0012 0.0031 0.0047 0.0078 0.0074

D on 0.1033 0.0151 0.0087 0.0280 0.0364 0.0275 0.0322

A off 0 NA 0 0 0 NA 0

B off 0.0255 NA 0.0141 0.0138 0.0068 NA 0.0099

D off 0.1189 NA 0.0153 0.0315 0.0433 NA 0.0364

Note: The Hospital and Small Hotel HVAC systems are always scheduled to be on.

The A, B, and D values from Table 2 were then input into the EnergyPlus 

ZoneInfiltration:DesignFlowRate object. Aon, Bon, and Don were used with Fschedule = 1.0 during 

system-on hours and Fschedule = 0.0 during system-off hours. Aoff, Boff, and Doff were used with 

Fschedule = 1.0 during system-off hours and Fschedule = 0.0 during system-on hours. Annual energy 

simulations were then performed using EnergyPlus for the same Chicago weather used in the 

CONTAM predictions. Hourly infiltration rates were then compared between CONTAM and 

EnergyPlus. The mean of the CONTAM and EnergyPlus infiltration rates are listed in Table 3, 

along with the standard error, standard error as a percentage of the CONTAM mean rate (or 

"relative standard error"), and coefficient of determination, R2

, of the EnergyPlus infiltration 

rates compared with the CONTAM rates.

The average system-on and system-off R2 value for the seven buildings shown in Table 3 is 0.80. 

Excluding the Hospital and Large Office, which have the smallest mean infiltration rates among 

the buildings, the average system-on relative standard error of the other buildings is 24 % and the 

average system-off relative standard error is 15 %. As expected, the R2 values and relative 

standard error of the EnergyPlus infiltration rates compared with CONTAM are relatively good 

using Method 1 because the A, B, and D values were specifically calculated for each building. 

However, using Method 1 requires infiltration rate data, such as those generated using 
7

CONTAM or measured values, which may not necessarily be available in a given building. In 

order to address this limitation, a general method to calculate A, B, and D in any building is 

described in Section 2.2.2.

Table 3. Comparison of CONTAM and EnergyPlus infiltration rates using A, B, and D

values from Table 2 (Idesign=0.00137 m3

/s•m2)

Restaurant Hospital Large 

Office

Medium 

Office School Hotel Retail

System on

CONTAM mean 

infiltration rate (h-1) 0.53 0.02 0.03 0.11 0.25 0.26 0.23

EnergyPlus mean 

infiltration rate (h-1) 0.48 0.06 0.03 0.14 0.24 0.29 0.24

Standard error of 

EnergyPlus rates (h-1) 0.09 0.02 0.02 0.04 0.06 0.06 0.05

(% of CONTAM mean) (17 %) (87 %) (65 %) (35 %) (25 %) (22 %) (20 %)

Coefficient of 

determination, R2 0.83 0.87 0.78 0.75 0.83 0.82 0.88

System off

CONTAM mean 

infiltration rate (h-1) 0.50 NA 0.14 0.27 0.29 NA 0.26

EnergyPlus mean 

infiltration rate (h-1) 0.43 NA 0.12 0.23 0.23 NA 0.23

Standard error of 

EnergyPlus rates (h-1) 0.07 NA 0.02 0.05 0.05 NA 0.03

(% of CONTAM mean) (14 %) (15 %) (18 %) (18 %) (12 %)

Coefficient of 

determination, R2 0.83 NA 0.76 0.75 0.68 NA 0.88

Note: The Hospital and Small Hotel HVAC systems are always scheduled to be on. The standard error of 

EnergyPlus rates and R2 values were based on the comparison between EnergyPlus and CONTAM results.

2.2.2. Method 2 – General

Method 2 is a generalized strategy for determining A, B, and D values in Equation (1) based on

key building characteristics. The building characteristics considered are: building height (H in 

m), exterior surface area to volume ratio (SV in m2

/m3), and net system flow (i.e., design supply 

air minus design return air minus mechanical exhaust air) normalized by exterior surface area (Fn

in m3

/s•m2). The values for these characteristics for each of the seven buildings are listed in

Table 4. It should be noted that only the Full Service Restaurant has a large negative net system 

flow (Table 4), while the other buildings have positive net system flows.

Table 4. Building characteristics of seven simulated buildings

Full 

Service 

Restaurant

Hospital Large 

Office

Medium 

Office

Primary 

School

Small 

Hotel

Stand 

Alone 

Retail

H (m) 4.7 23.8 50.4 12 4 11.6 6.1

SV (m2/m3) 0.17 0.11 0.09 0.18 0.34 0.23 0.24

Fn (m3/s•m2) × 10-3 -2.6 1.0 1.3 0.56 0.02 0.50 0.21

In order to determine values of A, B and D for any given building, the following relationships 

between these constants and the building characteristics (H, SV, and Fn) were considered:
8

A = MA∙H + NA∙SV + PA∙Fn (5)

B = MB∙H + NB∙SV + PB∙Fn (6)

D = MD∙H + ND∙SV + PD∙Fn (7)

where M, N, and P are constants, and their subscripts distinguish them between A, B, and D. 

Using a spreadsheet program, the building-specific A, B and D values calculated using Method 1 

(Table 2) and the building characteristics of the seven buildings (Table 4) were fit to Equations 

(5) through (7) to calculate M, N, and P. Equations (8) through (13) show the results for systemon and system-off conditions. It was assumed that A = 0 and the net system flow is zero (Fn = 0) 

when the system is off.

Aon = 0.0001∙H + 0.0933∙SV + -47∙Fn (8)

Bon = 0.0002∙H + 0.0245∙SV + -5∙Fn (9)

Don = 0.0008∙H + 0.1312∙SV + -28∙Fn (10)

Aoff = 0 (11)

Boff = 0.0002∙H + 0.0430∙SV (12)

Doff = -0.00002∙H + 0.2110∙SV (13)

In Method 2, one would use Equations (8) through (13) to determine A, B and D values for any 

given building based on its specific characteristics (H, SV and Fn). A, B, and D were calculated 

for each of the seven reference buildings using these equations and are listed in Table 5. As was 

the case with Method 1 (Table 2), the Hospital, Large Office, and Medium Office have negative

A values. Using Method 2, the Small Hotel also had a negative A value. While there are 

differences between the A, B, and D values in Table 2 and Table 5, the corresponding values are 

generally on the same order of magnitude. In some cases they are quite close to one another. 

Table 5. A, B, and D values of simulated buildings using Equations (8) through (13) 

(Idesign=0.00137 m3/s•m2)

Full 

Service 

Restaurant

Hospital Large 

Office

Medium 

Office

Primary 

School

Small 

Hotel

Stand 

Alone 

Retail

A on 0.1424 -0.0349 -0.0466 -0.0082 0.0310 -0.0008 0.0137

B on 0.0186 0.0014 0.0040 0.0036 0.0088 0.0050 0.0059

D on 0.1004 0.0049 0.0160 0.0177 0.0468 0.0256 0.0311

A off 0 NA 0 0 0 NA 0

B off 0.0086 NA 0.0155 0.0106 0.0154 NA 0.0119

D off 0.0427 NA 0.0175 0.0437 0.0710 NA 0.0515

Note: The Hospital and Small Hotel HVAC systems are always scheduled to be on.
9

3. EVALUATING METHOD 2

Method 2 is a general approach to improving infiltration calculations in EnergyPlus. In this 

section, the method is tested using the seven reference buildings and three other buildings, and 

using different building envelope effective leakage area values, or Idesign.

3.1. Evaluation in the seven simulated buildings

The calculated A, B, and D values in Table 5 and Idesign=0.00137 m3/s•m2 (referred to as the 

"original Idesign" value since this value is changed in subsequent analyses) were input into the 

EnergyPlus ZoneInfiltration:DesignFlowRate object for each of the seven reference buildings

simulated previously. Annual EnergyPlus simulations were performed using EnergyPlus for the 

same year of Chicago weather used previously. The calculated hourly infiltration results were 

then compared between CONTAM and EnergyPlus. The mean of the CONTAM and EnergyPlus 

infiltration rates are listed in Table 6, along with the standard error, relative standard error, and 

R2

of the EnergyPlus infiltration rates compared with the CONTAM rates. Some R2 values in 

Table 6 are negative because the relationship between the CONTAM and EnergyPlus rates is not 

linear in these cases. Table 6 shows that, excluding the Hospital and Large Office, the average 

system-on difference in mean infiltration rates is 18 % and the average system-off difference is 

30 %. Those two buildings have the smallest mean infiltration rates among the buildings, leading 

to larger percentage errors. The Medium Office CONTAM and EnergyPlus system-on mean

infiltration rates agree within about 1 %, and the Large Office CONTAM and EnergyPlus 

system-off mean infiltration rates differ by only 6 %. 

Table 6 shows that the Stand Alone Retail and Small Hotel generally have the lowest relative 

standard errors and highest R2 of the buildings. This is also shown in Figure 1, in which the 

infiltration rates predicted with EnergyPlus are plotted against the rates predicted with 

CONTAM. Similar plots are presented below as an indication of the relative agreement between 

the two sets of predictions. Each point corresponds to a single hour in the year, with the 

uncertainty of each infiltration rate a function of the predictive accuracy of each model. The 

accuracy of each model is largely a function of the uncertainties in the model inputs. Since these 

buildings do not exist in reality, there is no uncertainty in the input values. The relative 

uncertainty in the predictions of the two calculation approaches are captured by the statistics 

contained in the Table 6 and other similar tables shown below.

Figure 1 shows that the CONTAM and EnergyPlus infiltration rates for the Stand Alone Retail 

and Small Hotel fall close to lines of perfect agreement. For the Medium Office, Table 6 shows 

that the system-on relative standard error of the EnergyPlus infiltration rates is among the highest 

of the buildings, but the R2 value is also among the highest. Nevertheless, Figure 2(a) shows 

good agreement between the CONTAM and EnergyPlus infiltration rates for the Medium Office.

For the Primary School, Table 6 shows that the system-off relative standard error of the 

EnergyPlus infiltration rates is among the highest of the buildings, and the R2 value among the 

lowest. However, the system-on relative standard error of the EnergyPlus infiltration rates and

the R2 value are both among the lowest. Figure 2(b) shows the CONTAM versus EnergyPlus 

infiltration rates for the Primary School.
10

For the Full Service Restaurant, Table 6 shows that the system-off relative standard error of the 

EnergyPlus infiltration rates is comparable with the other buildings though the R2 value is the 

lowest. However, the system-on relative standard error of the EnergyPlus infiltration rates is 

among the lowest and R2 value is among the highest of the buildings. Figure 4 shows good 

agreement between the CONTAM and EnergyPlus infiltration rates for system-on but not for 

system-off for the Full Service Restaurant.

For the Large Office, the system-on relative standard error of the EnergyPlus infiltration rates is 

among the highest of the buildings, and the R2 value the lowest. However, the system-off relative 

standard error of the EnergyPlus infiltration rates is among the lowest and the R2 value is among 

the highest of the buildings. Figure 3(a) shows the CONTAM versus EnergyPlus infiltration rates 

for the Large Office, where the better agreement with the system off is evident. For the Hospital, 

the system-on relative standard error of the EnergyPlus infiltration rates is the highest of the 

buildings and the R2 value among the lowest. However, the mean infiltration rate is the lowest of 

the buildings, which means the absolute standard error is also low. Figure 3(b) shows that the 

CONTAM rates are underestimated by EnergyPlus for the Hospital. 

Table 6. Comparison of CONTAM and EnergyPlus infiltration rates (original Idesign)

Restaurant Hospital Large 

Office

Medium 

Office School Hotel Retail

System on

CONTAM mean 

infiltration rate (h-1) 0.53 0.02 0.03 0.11 0.25 0.26 0.23

EnergyPlus mean 

infiltration rate (h-1) 0.46 0.01 0.08 0.11 0.34 0.19 0.21

Standard error of 

EnergyPlus rates (h-1) 0.09 0.02 0.02 0.04 0.07 0.06 0.05

(% of CONTAM mean) (17%) (130%) (68%) (36%) (26%) (24%) (20%)

Coefficient of 

determination, R2 0.80 -0.23 -1.74 0.83 0.31 0.61 0.83

System off

CONTAM mean 

infiltration rate (h-1) 0.50 NA 0.14 0.27 0.29 NA 0.26

EnergyPlus mean 

infiltration rate (h-1) 0.15 NA 0.13 0.23 0.44 NA 0.29

Standard error of 

EnergyPlus rates (h-1) 0.08 NA 0.02 0.06 0.15 NA 0.03

(% of CONTAM mean) (15%) (16%) (23%) (18%) (13%)

Coefficient of 

determination, R2 -1.47 NA 0.81 0.57 -0.90 NA 0.78

Note: The Hospital and Small Hotel HVAC systems are always scheduled to be on. The standard error of 

EnergyPlus rates and R2 values were based on the comparison between EnergyPlus and CONTAM results.
11

(a)

(b)

Figure 1: EnergyPlus vs. CONTAM infiltration rates for (a) Stand Alone Retail and 

(b) Small Hotel (original Idesign)
12

(a)

(b)

Figure 2: EnergyPlus vs. CONTAM infiltration rates for (a) Medium Office and 

(b) Primary School (original Idesign)
13

(a)

(b)

Figure 3: EnergyPlus vs. CONTAM infiltration rates for (a) Large Office and 

(b) Hospital (original Idesign)
14

Figure 4: EnergyPlus vs. CONTAM infiltration rates for Full Service Restaurant

(original Idesign)

In general, buildings with the lowest infiltration rates, the Hospital and two offices, also have the 

highest system-on relative standard errors. However, since the absolute infiltration rates are 

relatively low for these three buildings, the absolute errors in the infiltration rates are also low. 

Thus, despite high relative standard errors, Figure 2 and Figure 3 show good agreement between 

CONTAM and EnergyPlus rates for the Hospital and two offices. For all of the buildings except 

the Hospital and Full Service Restaurant, there is good agreement between the system-on and 

system-off infiltration rates calculated by CONTAM and EnergyPlus as shown in Figure 1

through Figure 4. Though the average system-on and system-off R2 values for the seven 

buildings is only 0.08, the average system-on relative standard error, excluding the Hospital and 

Large Office, is 25 % and the average system-off relative standard error is 17 %. Note that these 

analyses are based on the original value of Idesign. Additional simulations are discussed below in 

which this value is varied.

3.2. Evaluation of Method 2 in other buildings

Method 2, as embodied in Equations (8) to (13), was used to calculate system-on and system-off 

A, B, and D values (not shown) for three additional buildings based only on their building 

characteristics. The buildings were the Small Office building from the DOE reference buildings, 

and two actual buildings on the NIST campus, the Administration and the TRF Buildings. The 

building height, exterior surface area to volume ratio, and net system flow normalized by exterior 

surface area for these buildings are listed in Table 7. The height and surface area to volume ratio 

of the Small Office is similar to the Full Service Restaurant, and its normalized net system flow 

is similar to the Medium Office. For more details on the Small Office, see Ng et al. (2012). The 

NIST Administration Building is almost as tall as the Large Office, has the smallest surface to 
15

volume ratio and largest normalized net system flow of the buildings considered in this paper. 

The height and surface area to volume ratio of the NIST TRF Building is similar to the Primary 

School, and its normalized net system flow is similar to the Small Hotel. For more details on the 

NIST buildings, see Persily et al. (2007).

Table 7. Building characteristics of three additional buildings

Small

Office

NIST

Administration

NIST

TRF

H (m) 4.3 46.6 4.0

SV (m2/m3) 0.18 0.05 0.36

Fn (m3/s•m2) × 10-3 0.61 0.85 0.51

The average local wind speed adjustments for the Small Office and two NIST buildings are listed 

in Table 8. An EnergyPlus model was available for the Small Office (DOE 2011), but not for the 

two NIST buildings. Thus, rather than using EnergyPlus, infiltration rates for the NIST buildings 

were calculated using a spreadsheet that implemented Equation (1) with C=0, where Ws was 

calculated using Equation (4) and the wind speed adjustments listed in Table 8.

Table 8. Average local wind speed adjustments (other buildings)

Building Average Local Wind Speed Adjustment

Small Office 0.2818

NIST Administration Building 0.4650

NIST TRF Building 0.2784

For the Small Office, Table 9 shows that the system-on relative standard error of the EnergyPlus 

infiltration rates is one of the highest and the R2 value the lowest relative to the seven other 

reference buildings in Table 6. The system-off relative standard error and R2 value of the 

EnergyPlus infiltration rates are both low compared to the other seven buildings. Figure 5 shows 

that EnergyPlus underestimates the infiltration rates when compared to CONTAM for the Small 

Office for both system-on and system-off conditions. As in the case of the Full Service 

Restaurant, the Small Office has an attic space that may contribute to the low infiltration

estimates.

For the NIST Administration Building, Table 9 shows that the system-on relative standard error 

of the calculated infiltration rates are in the middle of the range seen in the seven reference 

buildings in Table 6, but the R2 value is one of the lowest. The system-off relative standard error 

of the calculated infiltration rates is among the lowest and the R2 value lower than all seven 

buildings (Table 6). Figure 6(a) shows that the calculated infiltration rates are lower than the 

values calculated by CONTAM for the Administration Building. 

For the NIST TRF Building, Table 9 shows that the system-on relative standard error of the 

calculated infiltration rates is also in the middle of the range seen in the seven buildings in Table 

6, but the R2 value is one of the highest. Both the system-off relative standard error of the 

calculated infiltration rates and the R2 value are among the lowest relative to the seven buildings. 

Nevertheless, Figure 6 (b) shows good agreement between the calculated and CONTAM 

infiltration rates for the NIST TRF Building.
16

Table 9. Comparison of CONTAM and EnergyPlus and calculated infiltration rates

Small Office NIST

Administration1

NIST

TRF1

System on

CONTAM mean 

infiltration rate (h-1) 0.33 0.17 0.29

EnergyPlus or calculated mean 

infiltration rate (h-1) 0.02 0.04 0.29

Standard error of 

EnergyPlus rates or calculated rates (h-1) 0.08 0.05 0.09

(% of CONTAM mean) (23 %) (33 %) (30 %)

Coefficient of determination, R2 -2.59 -0.67 0.82

System off

CONTAM mean 

infiltration rate (h-1) 0.37 0.34 0.43

EnergyPlus or calculated mean 

infiltration rate (h-1) 0.13 0.05 0.59

Standard error of 

EnergyPlus or calculated rates (h-1) 0.06 0.05 0.08

(% of CONTAM mean) (17 %) (14 %) (18 %)

Coefficient of determination, R2 -1.30 -3.06 -0.05

Figure 5: EnergyPlus vs. CONTAM infiltration rates for Small Office (original Idesign)
17

(a)

(b)

Figure 6: Calculated vs. CONTAM infiltration rates for (a) NIST Administration Building 

and (b) NIST TRF Building

0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

Calculated air change rate (h-1)

CONTAM air change rate (h-1)

NIST Admin Bldg

System on

System off

0.0

0.5

1.0

1.5

2.0

0.0 0.5 1.0 1.5 2.0

Calculated air change rate (h-1)

CONTAM air change rate (h-1)

NIST TRF Bldg

System on

System off
18

As noted earlier, EnergyPlus models were not available for the NIST buildings, thus, infiltration 

was calculated using a spreadsheet and may not reflect the rates that EnergyPlus would calculate. 

This is due to the fact that EnergyPlus applies a different wind speed adjustment to each zone 

depending on its height. In contrast, the infiltration calculated by the spreadsheet uses a single 

average local wind speed adjustment for the entire building (Table 8). This could explain the 

underestimated infiltration rates in the NIST Administration Building, which was one of the 

taller buildings. Using an average local wind speed adjustment may neglect the impacts of wind 

on infiltration on the highest floors.

3.3. Evaluation of Method 2 for other Idesign values

Additional analyses were performed to investigate how well Method 2 performed for different 

envelope airtightness values than that used to derive Equations (8) through (13). As noted above, 

these equations were developed using a building envelope effective leakage area of 5.27 cm2

/m2

at 4 Pa (i.e., Idesign = 0.00137 m3

/s•m2, referred to as "original Idesign"). Method 2 was applied 

using two other Idesign values by running both CONTAM and EnergyPlus simulations with these 

new values. CONTAM simulations were re-run with building envelope effective leakage areas of 

1.18 cm

2

/m2 at 4 Pa and 20.96 cm2/m2 at 4 Pa, which were respectively four times lower and four 

times higher than the original Idesign value. EnergyPlus simulations were re-run with

corresponding Idesign values of 0.000304 m3/s•m2 (or "low Idesign") and 0.0054 m3/s•m2 (or "high 

Idesign") respectively. In these EnergyPlus simulations, the Idesign values changed, but the A, B, and 

D values remained the same as those determined using the original Idesign value, shown in Table 

5. The calculated hourly infiltration rates were then compared between CONTAM and 

EnergyPlus.

As was the case for the original Idesign value, Table 10 shows that the Stand Alone Retail and 

Small Hotel generally have the lowest relative standard errors and highest R2 of the buildings for 

both system-on and system-off conditions with the low Idesign value. The relative standard errors 

of the EnergyPlus infiltration rates using the low Idesign value are higher than they were using the 

original Idesign value (Table 6), and the system-on R2 value for the Stand Alone Retail is lower. 

Nevertheless, Figure 7(a) and (b) show that the CONTAM versus EnergyPlus infiltration rates 

fall close to lines of perfect agreement for the Stand Alone Retail and Small Hotel.

For all of the remaining buildings, either or both the system-on and system-off R2 values are 

negative for the low Idesign value. The system-off relative standard errors of the EnergyPlus 

infiltration rates using the low Idesign value are comparable to those using the original Idesign value

(Table 6), but the system-on relative standard errors are higher, with the exception of the Full 

Service Restaurant. Table 10 shows that the buildings with positive R2 values are the Medium 

Office with system off, Full Service Restaurant with system on, and Large Office with systemoff. Figure 8(a) and Figure 9(a) show that for the Medium Office and Large Office, the systemoff EnergyPlus rates agree well with CONTAM, but the system-on rates are overestimated by 

EnergyPlus. In contrast, Figure 8(b) shows that for the Full Service Restaurant, the system-on 

EnergyPlus rates agree well with CONTAM, but the system-off rates are underestimated by 

EnergyPlus. 
19

Table 10. Comparison of CONTAM and EnergyPlus infiltration rates (low Idesign)

Restaurant Hospital Large 

Office

Medium 

Office

Small 

Office School Hotel Retail

System on

CONTAM mean 

infiltration rate (h-1) 0.12 0.0001 0.00003 0.002 0.05 0.02 0.03 0.03

EnergyPlus mean 

infiltration rate (h-1) 0.10 0.0023 0.02 0.03 0.01 0.08 0.04 0.05

Standard error of 

EnergyPlus rates (h-1) 0.02 0.0006 0.0003 0.01 0.02 0.01 0.01 0.01

(% of CONTAM mean) (17%) (720%) (881%) (258%) (40%) (60%) (34%) (35%)

Coefficient of 

determination, R2 0.78 -23 -5880 -11 -1.08 -3 0.66 0.29

System off

CONTAM mean 

infiltration rate (h-1) 0.11 NA 0.03 0.06 0.08 0.07 NA 0.06

EnergyPlus mean 

infiltration rate (h-1) 0.03 NA 0.03 0.05 0.03 0.11 NA 0.07

Standard error of 

EnergyPlus rates (h-1) 0.02 NA 0.00 0.01 0.01 0.01 NA 0.01

(% of CONTAM mean) (16%) (15%) (22%) (17%) (18%) (12%)

Coefficient of 

determination, R2 -1.44 NA 0.81 0.63 -1.26 -1.88 NA 0.68

Note: The Hospital and Small Hotel HVAC systems are always scheduled to be on. The standard error of 

EnergyPlus rates and R2 values were based on the comparison between EnergyPlus and CONTAM results.

Table 10 shows that the buildings with negative R2 values for both system-on and system-off 

conditions using the low Idesign value are the Small Office, Primary School, and Hospital. Figure 

9(b) shows that for the Small Office, both the system-on and system-off rates are underestimated 

by EnergyPlus. In contrast, Figure 10(a) and (b) show that for the Primary School and Hospital, 

the rates are overestimated by EnergyPlus.

The summary statistics using the high Idesign value in Table 11 show that the relative standard 

errors of EnergyPlus infiltration rates are not as high as for the low Idesign value (Table 10). While 

there are still a few cases where the R2 value is negative, they are not as low as the values in 

Table 10. Similarly, the summary statistics in Table 11 are sometimes better than those seen in 

Table 6 for the original Idesign value. 

As was the case for the original and low Idesign values, Table 11 shows that the Stand Alone Retail 

and Small Hotel generally have the lowest relative standard errors and highest R2 of the buildings

for the high Idesign value. The Large Office also has relative standard errors among the lowest and 

R2 values among the highest of the buildings listed in Table 11 for the high Idesign value. The 

statistical measures for the Large Office for the high Idesign value were much better than those 

with the original and low Idesign values. Figure 11(a) and (b) and Figure 12 show that the 

CONTAM versus EnergyPlus infiltration rates fall close to lines of perfect agreement for the 

Stand Alone Retail, Small Hotel, and Large Office.

For the remaining buildings, Table 11 shows that the buildings with all positive R2 values are the 

Primary School and Medium Office. From Figure 12(b) and Figure 13(a), shows good agreement 

between CONTAM and EnergyPlus rates for the Primary School and Medium Office. 
20

Table 11. Comparison of CONTAM and EnergyPlus infiltration results (high Idesign)

Restaurant Hospital Large 

Office

Medium 

Office

Small 

Office School Hotel Retail

System on

CONTAM mean 

infiltration rate (h-1) 2.05 0.51 0.36 0.77 1.38 1.14 1.21 1.04

EnergyPlus mean 

infiltration rate (h-1) 1.82 0.04 0.30 0.43 0.10 1.35 0.77 0.82

Standard error of 

EnergyPlus rates (h-1) 0.35 0.19 0.08 0.17 0.26 0.27 0.27 0.20

(% of CONTAM mean) (17 %) (37 %) (23 %) (22 %) (19 %) (24 %) (23 %) (19 %)

Coefficient of 

determination, R2 0.81 -2.18 0.78 0.26 -3.51 0.60 0.27 0.70

System off

CONTAM mean 

infiltration rate (h-1) 1.95 NA 0.53 1.01 1.39 1.16 NA 1.04

EnergyPlus mean 

infiltration rate (h-1) 0.54 NA 0.47 0.80 0.49 1.45 NA 1.00

Standard error of 

EnergyPlus rates (h-1) 0.29 NA 0.09 0.25 0.24 0.22 NA 0.16

(% of CONTAM mean) (15 %) (17%) (25 %) (17 %) (19 %) (15 %)

Coefficient of 

determination, R2 -1.59 NA 0.77 0.45 -1.45 0.26 NA 0.86

Note: The Hospital and Small Hotel HVAC systems are always scheduled to be on. The standard error of 

EnergyPlus rates and R2 values were based on the comparison between EnergyPlus and CONTAM results.

Table 11 shows that the Full Service Restaurant has only one negative R2 value using the high 

Idesign value. Nevertheless, the system-on EnergyPlus rates are in good agreement with 

CONTAM as shown in Figure 13(b). The Hospital and Small Office have all negative R2 values. 

Figure 14(a) and (b) show that the CONTAM rates are underestimated by EnergyPlus for the 

Hospital and Small Office. The relative standard error of the EnergyPlus rates is higher in the 

Hospital than in the Small Office because its infiltration rates are lower.

As seen in Table 10 and Figure 7 through Figure 10, using a value of Idesign that is one-quarter of 

the value used to develop Method 2 resulted in comparable agreement between the EnergyPlus 

and CONTAM infiltration rates in most buildings tested. The exceptions were the Large and 

Small Offices, Primary School, and Hospital. The level of agreement between CONTAM and 

EnergyPlus infiltration rates is better using the high Idesign value (Table 11 and Figure 11 through 

Figure 14) relative to using the low Idesign value for the buildings tested test cases in this paper. 

No studies using different Idesign values for the NIST buildings were performed because 

EnergyPlus models were not available to make those comparisons. These results show that as 

Method 2 is developed further, it will be important to identify a range of Idesign values over which 

it can be applied without introducing excessive errors.
21

(a)

(b)

Figure 7: EnergyPlus vs. CONTAM infiltration rates for (a) Stand Alone Retail and 

(b) Small Hotel (low Idesign)
22

(a)

(b)

Figure 8: EnergyPlus vs. CONTAM infiltration rates for (a) Medium Office and (b) Full 

Service Restaurant (low Idesign)
23

(a)

(b)

Figure 9: EnergyPlus vs. CONTAM infiltration rates for (a) Large Office and (b) Small 

Office (low Idesign)
24

(a)

(b)

Figure 10: EnergyPlus vs. CONTAM infiltration rates for (a) Primary School and (b) 

Hospital (low Idesign)
25

(a)

(b)

Figure 11: EnergyPlus vs. CONTAM infiltration rates for (a) Stand Alone Retail and 

(b) Small Office (high Idesign)
26

(a)

(b)

Figure 12: EnergyPlus vs. CONTAM infiltration rates for (a) Large Office and 

(b) Primary School (high Idesign)
27

(a)

(b)

Figure 13: EnergyPlus vs. CONTAM infiltration rates for (a) Medium Office and 

(b) Full Service Restaurant (high Idesign)
28

(a)

(b)

Figure 14: EnergyPlus vs. CONTAM infiltration rates for (a) Hospital and (b) Small Office 

(high Idesign)
29

3.4. Comparing CONTAM rates to fixed infiltration rates in EnergyPlus 

The EnergyPlus models of the reference buildings developed by DOE (2011) implemented an

infiltration modeling approach that simplified the required assumptions and reduced simulation 

times (Deru et al. 2011). The building envelope leakage was assumed to be 1.18 cm

2

/m2 at a 

constant indoor-outdoor pressure of 4 Pa, based on a then-proposed addendum to ASHRAE 

90.1-2004 for an air barrier requirement. This building envelope leakage is equivalent to an 

airflow rate at 4 Pa of 0.000302 m3

/s•m2 of exterior surface area, 22 % of the original Idesign value 

used in the simulations described above. In those EnergyPlus models, A=1, B=C=D=0 in 

Equation (1), and Fschedule equaled 1.0 during system-on hours and was reduced to 0.25 or 0.5

during system-off hours. In other words, those models used a fixed infiltration rate that depended 

only on whether the system was on or off and did not consider weather effects.

It should be noted that an air barrier requirement was added to ASHRAE 90.1-2010 (ASHRAE 

2010), but it does not contain a quantitative whole building airtightness requirement. Instead the 

standard contains material and assembly tightness requirements. Note also that the value of 

1.18 cm

2

/m2 used in the DOE models is not necessarily consistent with expectations for 

buildings built in the two decades based on existing airtightness data (Emmerich and Persily 

2005). However, the value of 5.27 cm

2

/m2 used in the CONTAM models (Section 2.2.1) is 

supported by consideration of these data. In addition to the building leakage value, a more 

important difference is that CONTAM calculates the indoor-outdoor pressure difference across 

the exterior envelope, while the DOE models assumed it to be a constant 4 Pa. Assuming a 

constant pressure difference does not reflect known dependencies of infiltration on indooroutdoor pressure differences. 

Table 12. Comparison of CONTAM and DOE fixed infiltration results (original Idesign)

Restaurant Hospital Large 

Office

Medium 

Office

Small 

Office School Hotel Retail

System on

CONTAM mean 

infiltration rate (h-1) 0.53 0.02 0.03 0.11 0.33 0.25 0.26 0.23

EnergyPlus mean 

infiltration rate (h-1) 0.10 0.03 0.02 0.05 0.05 0.18 0.13 0.14

Standard error of 

EnergyPlus rates (h-1) 0.20 0.04 0.04 0.10 0.14 0.13 0.12 0.14

(% of CONTAM mean) (38 %) (233 %) (145 %) (90 %) (43 %) (51 %) (46 %) (58 %)

Coefficient of 

determination, R2 -2.64 -0.24 0.74 0.56 -2.35 -0.22 -0.83 -0.49

System off

CONTAM mean 

infiltration rate (h-1) 0.50 NA 0.14 0.27 0.37 0.29 NA 0.26

EnergyPlus mean 

infiltration rate (h-1) 0.19 NA 0.09 0.20 0.20 0.35 NA 0.27

Standard error of 

EnergyPlus rates (h-1) 0.18 NA 0.05 0.08 0.12 0.11 NA 0.09

(% of CONTAM mean) (36 %) (34 %) (31 %) (31 %) (37 %) (34 %)

Coefficient of 

determination, R2 -1.50 NA 0.81 0.17 -1.04 -0.20 NA 0.00

Note: The Hospital and Small Hotel HVAC systems are always scheduled to be on. The standard error of 

EnergyPlus rates and R2 values were based on the comparison between EnergyPlus and CONTAM results.
30

Summary statistics comparing use of a fixed infiltration rate in the DOE models and infiltration 

rates calculated by CONTAM are presented in Table 12. For most of the buildings, the 

infiltration rates assumed in the DOE models are less than those calculated by CONTAM, which 

is largely a reflection of the different building leakage values used in the two approaches. The 

exceptions are the Hospital and Large Office, where the infiltration rates are very low and the 

difference is only 0.01 h-1

, but the relative standard error is more than 100 %. Also, the systemoff infiltration rate assumed in the DOE model of the Stand Alone Retail is similar to the mean

infiltration rate calculated by CONTAM. Nevertheless, the relative standard errors using fixed 

infiltration rates in the DOE models are higher than they were using the Method 2 (Table 6). 

There are also more negative R2 values when using assuming constant infiltration rates than there 

were using Method 2.

3.5. Comparing Method 2 to PNNL approach

As described in the Introduction to this paper, Gowri et al. (2009) proposed a method (referred to 

as the PNNL approach in this paper) to account for infiltration in commercial buildings. 

Assuming a constant indoor-outdoor pressure difference of 4 Pa, this approach calculates an 

infiltration rate to be input into EnergyPlus, accounting for wind but not temperature effects 

using the following equation:

Infiltration = F•Idesign•0.224•Ws (14)

where F is 0.25 when the HVAC system is on and 1.0 when the HVAC system is off. 

Compared with Method 2 using the original Idesign value, the relative standard error of the 

EnergyPlus infiltration rates were higher when calculated using the PNNL approach with the 

same original Idesign value as shown in Table 13. For instance, the system-on relative standard 

error of the EnergyPlus infiltration rates for the Stand Alone Retail was 20 % for Method 2 

(Table 6) but increases to 38 % using the PNNL approach (Table 13). Figure 15(a) shows that 

the system-on infiltration rates calculated using the PNNL approach underestimate those 

calculated by CONTAM. The system-off relative standard error of the EnergyPlus infiltration 

rates for the Stand Alone Retail was 13 % for Method 2 (Table 6). This error increased to 35 % 

using the PNNL approach (Table 13). Figure 15(a) shows more scatter at the lower values of the 

system-off infiltration rates calculated using the PNNL approach.

The system-on relative standard error of the EnergyPlus infiltration rates for the Hospital was 

130 % (Table 6) and 208 % for the PNNL approach (Table 13). The R2 value also decreased 

from -0.23 (Table 6) to -6.67 (Table 13). Figure 15(b) shows that the system-on infiltration rates 

calculated using the PNNL approach overestimate those calculated by CONTAM. 

Compared with Method 2, the R2 value of the EnergyPlus infiltration rates calculated using the 

PNNL approach were negative in more buildings. Using Method 2, two of the system-on cases 

had negative R2 values, compared with seven of the eight system-on cases for the PNNL 

approach. Also, two of the system-off cases had negative R2 values for Method 2, whereas four

of the six system-off cases did using the PNNL approach.
31

The differences between the infiltration rates calculated using CONTAM, Method 2, and the 

PNNL approach are more evident when the infiltration rates are plotted against indoor-outdoor 

temperature differences (ΔT). From Figure 16, it is clear that the infiltration rates calculated 

using the PNNL approach have no temperature dependency. For the Stand Alone Retail in Figure 

16(a), the infiltration rates calculated using Method 2 agree fairly well with those calculated 

using CONTAM. For the Hospital in Figure 16(b), the infiltration rates calculated using Method 

2 underestimate those calculated using CONTAM. Nevertheless, a small amount of temperature 

dependency is reflected in the infiltration rates calculated using Method 2. More scatter is 

observed in the infiltration rates calculated using the PNNL approach when compared with the 

infiltration rates calculated using CONTAM or Method 2.

When using the low Idesign value and the PNNL approach, Table 14 shows that the system-on 

relative standard errors of the calculated infiltration rates are higher than when using the original 

Idesign value (Table 13). On the other hand, Table 14 shows that the system-off relative standard 

errors of the calculated infiltration rates are relatively close to those for the original Idesign value 

(Table 13). Nevertheless, both the system-on and system-off relative standard errors of the 

infiltration rates calculated using the PNNL approach are higher than for Method 2 (Table 10). 

When using the high Idesign value and the PNNL approach, Table 15 shows that both the systemon and system-off relative standard errors of the infiltration rates are similar to the errors when 

using the original Idesign value. The only exception is for the Hospital, where the relative standard 

error decreased significantly from 208 % (Table 13) to 47 % (Table 15). As was the case when 

using the low Idesign value, both the system-on and system-off relative standard errors of the 

infiltration rates calculated using the PNNL approach are higher than when using Method 2 

(Table 11).

Table 13. Comparison of CONTAM and EnergyPlus infiltration rates using PNNL 

approach (original Idesign)

Restaurant Hospital Large 

Office

Medium 

Office

Small 

Office School Hotel Retail

System on

CONTAM mean 

infiltration rate (h-1) 0.53 0.02 0.03 0.11 0.33 0.25 0.26 0.23

EnergyPlus mean 

infiltration rate (h-1) 0.04 0.19 0.05 0.08 0.04 0.09 0.09 0.08

Standard error of 

EnergyPlus rates (h-1) 0.17 0.04 0.02 0.05 0.12 0.09 0.10 0.09

(% of CONTAM mean) (33%) (208%) (91%) (47%) (36%) (36%) (38%) (38%)

Coefficient of 

determination, R2 -3.23 -6.67 -0.70 0.57 -2.27 -0.72 -1.02 -1.02

System off

CONTAM mean 

infiltration rate (h-1) 0.50 NA 0.14 0.27 0.37 0.29 NA 0.26

EnergyPlus mean 

infiltration rate (h-1) 0.14 NA 0.18 0.26 0.15 0.30 NA 0.25

Standard error of 

EnergyPlus rates (h-1) 0.17 NA 0.05 0.10 0.13 0.09 NA 0.09

(% of CONTAM mean) (33%) (33%) (36%) (36%) (31%) (35%)

Coefficient of 

determination, R2 -1.72 NA -3.13 -0.57 -1.30 0.42 NA 0.42

Note: The Hospital and Small Hotel HVAC systems are always scheduled to be on. The standard error of 

EnergyPlus rates and R2 values were based on the comparison between EnergyPlus and CONTAM results.
32

(a)

(b)

Figure 15: EnergyPlus (Method 2 and PNNL approach) vs. CONTAM infiltration rates for 

(a) Stand Alone Retail and (b) Hospital (original Idesign)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

E+ air change rate (h-1)

CONTAM air change rate (h-1)

Stand Alone Retail

System on (Method 2)

System off (Method 2)

System on (PNNL)

System off (PNNL)

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5

E+ air change rate (h-1)

CONTAM air change rate (h-1)

Hospital

System on (Method 2)

System on (PNNL)
33

(a)

(b)

Figure 16: EnergyPlus (Method 2 and PNNL approach) and CONTAM infiltration rates 

vs. indoor-outdoor temperature for (a) Stand Alone Retail and (b) Hospital (original Idesign; 

wind speeds < 2 m/s)
34

Table 14. Comparison of CONTAM and EnergyPlus infiltration results using PNNL 

approach (low Idesign)

Restaurant Hospital Large 

Office

Medium 

Office

Small 

Office School Hotel Retail

System on

CONTAM mean 

infiltration rate (h-1) 0.12 0.0001 0.00003 0.002 0.05 0.02 0.03 0.03

EnergyPlus mean 

infiltration rate (h-1) 0.01 0.0467 0.01 0.02 0.01 0.02 0.04 0.02

Standard error of 

EnergyPlus rates (h-1) 0.04 0.0007 0.0003 0.01 0.02 0.01 0.01 0.01

(% of CONTAM mean) (33 %) (799 %) (936 %) (293 %) (41 %) (58 %) (34 %) (49 %)

Coefficient of 

determination, R2 -3 -4880 -3260 -7 -0.77 0.49 0.66 0.37

System off

CONTAM mean 

infiltration rate (h-1) 0.11 NA 0.03 0.06 0.08 0.07 NA 0.06

EnergyPlus mean 

infiltration rate (h-1) 0.03 NA 0.05 0.07 0.04 0.08 NA 0.06

Standard error of 

EnergyPlus rates (h-1) 0.04 NA 0.011 0.02 0.03 0.02 NA 0.02

(% of CONTAM mean) (33 %) (33 %) (36 %) (36 %) (31 %) (35 %)

Coefficient of 

determination, R2 -1.51 NA -2.81 -0.45 -1.06 0.19 NA 0.34

Note: The Hospital and Small Hotel HVAC systems are always scheduled to be on. The standard error of 

EnergyPlus rates and R2 values were based on the comparison between EnergyPlus and CONTAM results.

Table 15. Comparison of CONTAM and EnergyPlus infiltration results using PNNL 

approach (high Idesign)

Restaurant Hospital Large 

Office

Medium 

Office

Small 

Office School Hotel Retail

System on

CONTAM mean 

infiltration rate (h-1) 2.05 0.51 0.36 0.77 1.38 1.14 1.21 1.04

EnergyPlus mean 

infiltration rate (h-1) 0.17 0.75 0.21 0.41 0.18 0.35 0.35 0.31

Standard error of 

EnergyPlus rates (h-1) 0.65 0.24 0.11 0.25 0.43 0.38 0.43 0.38

(% of CONTAM mean) (32 %) (47 %) (32 %) (33 %) (31 %) (33 %) (35 %) (36 %)

Coefficient of 

determination, R2 -3.29 -0.62 0.54 -0.10 -3.09 -1.21 -1.66 -1.44

System off

CONTAM mean 

infiltration rate (h-1) 1.95 NA 0.53 1.01 1.39 1.16 NA 1.04

EnergyPlus mean 

infiltration rate (h-1) 0.54 NA 0.72 1.38 0.60 1.22 NA 0.99

Standard error of 

EnergyPlus rates (h-1) 0.63 NA 0.16 0.35 0.48 0.36 NA 0.37

(% of CONTAM mean) (32 %) (30 %) (34 %) (35 %) (31 %) (35 %)

Coefficient of 

determination, R2 -1.69 NA -3.69 -0.76 -1.14 0.41 NA 0.42

Note: The Hospital and Small Hotel HVAC systems are always scheduled to be on. The standard error of 

EnergyPlus rates and R2 values were based on the comparison between EnergyPlus and CONTAM results.
35

4. SUMMARY AND DISCUSSION

Though modelers can account for infiltration and improved envelope airtightness with current 

energy simulation software, the simplified approaches employed ignore the effects of weather, 

system operation, and envelope leakage, or at best do not account for them very well. 

Oftentimes, zero, constant or scheduled infiltration rates are input into energy simulation 

software due to a lack of understanding of how to more accurately account for infiltration. Also, 

the infiltration equations currently included in energy simulation software and guidance for input 

variables are based largely on research for low-rise, residential buildings. However, the 

interaction of weather, system operation, and envelope leakage in determining infiltration rates is 

fundamentally related to pressure, but the physics of these interactions are not typically or easily 

modeled in current energy simulation software. Multizone airflow modeling is the accepted 

approach to calculating infiltration, however, the current means of doing so in energy simulation 

programs are limited and can be cumbersome to implement.

Strategies to incorporate the effects of weather, system operation, envelope leakage, and building 

characteristics on infiltration are presented in this paper. Method 1 is a building-specific strategy 

for determining coefficients in an empirical equation available in EnergyPlus to calculate 

infiltration. The method improves the accuracy of the infiltration rates in EnergyPlus simulations 

by using the results of detailed multizone airflow simulations to calculate the coefficients in the 

empirical equation for a given building. When applying this method to seven of the DOE 

reference buildings, the average system-on and system-off R2 value for the seven buildings is 

0.80, when comparing the rates from the CONTAM and EnergyPlus simulations. Excluding the 

Hospital and Large Office, which have the smallest mean infiltration rates among the buildings, 

the average system-on relative standard error of the other buildings is 24 % and the average 

system-off relative standard error is 15 %. However, Method 1 requires infiltration rate data, 

such as those generated using CONTAM or measured values, which may not necessarily be 

available. In order to address this limitation, Method 2 is presented. Method 2 calculates the 

coefficients in the EnergyPlus empirical equation using key building characteristics. For all of 

the buildings except the Hospital and Full Service Restaurant, there is good agreement between 

the system-on and system-off infiltration rates calculated by CONTAM and EnergyPlus using 

Method 2. Though the average system-on and system-off R2 values for the seven buildings is 

only 0.08, the average system-on relative standard error, excluding the Hospital and Large 

Office, is 25 % and the average system-off relative standard error is 17 %.

Method 2 was also tested on buildings other than the seven used to develop it. Using Method 2 

for the Small Office reference building, EnergyPlus underestimated the CONTAM infiltration 

rates (Section 3.1). Method 2 was also tested on two NIST buildings in Section 0. The calculated 

rates were lower than the CONTAM infiltration rates for the NIST Administration Building, but

there was good agreement between the calculated and CONTAM infiltration rates for the NIST 

TRF Building.

In Section 0, Method 2 was tested using two different building envelope airtightness values, 

25 % and four times a baseline value used to develop the method. For the eight buildings for 

which EnergyPlus models were available, Method 2 performed better for the higher building 

leakage value than for the lower one. 
36

Lastly, in Section 3.4, Method 2 was compared with the approach proposed by PNNL (Gowri et 

al. 2009). For all values of building envelope airtightness tested, it was found that the relative 

standard errors of the infiltration rates calculated using the PNNL approach were higher than 

when using Method 2. This was partly due to the infiltration rates calculated by the PNNL 

approach having no temperature dependence. 

4.1. Future work

The proposed methods for estimating infiltration rates based on weather, system operation, 

building envelope airtightness, and building characteristics were developed using hourly 

infiltration rates from CONTAM for seven commercial building models. It is possible that these 

methods could be made more robust by considering other buildings, such as the complete 

collection of fifteen commercial building models available from DOE (2011). Also, the building 

models developed by DOE (2011) are based on data from real buildings, but are not actual 

buildings. Future work could include using building envelope airtightness values and 

measurements of infiltration from real buildings to further evaluate these methods. Also, 

Method 1 and Method 2 were developed by performing CONTAM simulations using Chicago 

weather data only. Future work could include the use of weather data for other climates.

In addition, future work should be considered to develop guidance on how to use both methods

in EnergyPlus, or other energy simulation software. However, depending on the building, 

occupancy use type, building envelope airtightness, and its location, the methods may still not 

yield infiltration rates that are sufficiently accurate. In these situations, CONTAM or other 

airflow simulation program would be recommended.

4.2. Recommendations to EnergyPlus

Based on the physics of airflow in mechanically ventilated buildings, as reflected in the 

CONTAM simulation results, infiltration rates are not necessarily symmetrical around an indooroutdoor temperature difference of zero when fans are on. In such cases, the absolute value of 

indoor-outdoor temperature difference (|ΔT=0|) in the infiltration equation used in EnergyPlus 

will not accurately account for infiltration at negative indoor-outdoor temperature differences. 

This limitation could be overcome by allowing for negative indoor-outdoor temperature 

differences in the calculation of infiltration in EnergyPlus.

In addition, EnergyPlus assumes that the local wind speeds at various heights acting on the 

building can be calculated using a scaling factor for the wind measured at a meteorological 

station. However, the physics of airflow at heights close to the ground and between buildings is 

complex and most accurately determined by wind tunnel experiments or computational fluid 

dynamic (CFD) simulations. From experiments or CFD simulations, local wind pressure 

coefficients (Cp) can be determined and used to more accurately calculate local wind pressure on 

buildings.
37

5. CONCLUSIONS

Due to an increased emphasis on energy consumption and greenhouse gas emissions, the 

potential savings from energy efficiency measures are often analyzed using energy simulation 

software. However, the impact of implementing some efficiency measures is oftentimes 

incomplete because building envelope infiltration is not properly accounted for. Many of the 

airflow estimation approaches implemented in current energy software tools are inappropriate for 

large buildings or are otherwise limited. Based on the relationship between building envelope 

airtightness, building characteristics, weather, and system operation, methods are presented in 

this paper to calculate infiltration rates that are comparable to performing multizone calculations.

These methods show better accuracy when compared with existing approaches to estimating

infiltration in commercial building energy calculations.

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