# Assessing the Energy, Indoor Air Quality, and Moisture Performance for a Three-Story Building Using an Integrated Model, Part Two: Integrating the Indoor Air Quality, Moisture, and Thermal Comfort

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## Abstract

**:**

_{2}, PM

_{2.5}, and VOCs obtained by CONTAM; the simulated indoor relative humidity (RH), predicted percentage of dissatisfied (PPD), and predicted mean vote (PMV) obtained by WUFI; and those obtained by the integrated model are compared separately for all scenarios in Montreal, Vancouver, and Miami. Finally, the optimal scenarios are selected. The simulated results of the optimal scenarios with the integrated model method (−28.88% to 46.39%) are different from those obtained with the single models. This is due to the inability of the single models to correct the airflow variables.

## 1. Introduction

## 2. Methodology

#### 2.1. Coupling Method of CONTAM and WUFI

^{−1}), natural ventilation–infiltration air–volume flow rate (m

^{3}/s), building net volume (m

^{3}), normalized leakage, effective leakage area, floor area (m

^{2}), and building height (m), respectively.

^{3}), heat flow from natural ventilation–infiltration (W), specific enthalpy internal air (J/kg), specific enthalpy external air (J/kg), moisture content of external air (kg/kg), internal air temperature (°C), and external air temperature of (°C), respectively.

^{3}/(s·Pa

^{n})), reference pressure difference (Pa), flow exponent, predicted airflow rate at $\Delta {P}_{r}$ (m

^{3}/s) (from curve fit to pressurization test data), and discharge coefficient. There are two sets of reference conditions for the discharge coefficient: ${C}_{d}=1\mathrm{and}\Delta {P}_{r}=4\left(\mathrm{Pa}\right)$ or ${C}_{d}=0.6\mathrm{and}\Delta {P}_{r}=10\left(\mathrm{Pa}\right)$ [39]. Additionally, the effective leakage area is used in ContamW at a pressure difference ($\Delta {P}_{r}$) of 4 Pa, flow exponent (n) of 0.65, and discharge coefficient (${C}_{d}$) of 1 [37]. According to Figure 1, both WUFI and CONTAM models use the simulated airflow rate simulation data instead of the assumed input variable of airflow rate. Consequently, the co-simulation for this main control variable is completed.

^{−1}), and removal coefficient of contaminant $\alpha $ in zone i (kg/s), respectively [35].

^{2}), heat transfer resistance interior (m

^{2}·K/W), internal room air temperature (°C), and interior surface temperature (°C), respectively.

^{2}), long-wave radiation balance of interior surface (W/m

^{2}), Stefan Boltzmann constant 5.67⋅10

^{−8}(W/m

^{2}⋅K

^{4}), temperature of the exterior surface (K), heat transfer resistance, exterior (m

^{2}⋅K/W), heat transfer resistance, interior (m

^{2}⋅K/W), heat transfer coefficient of the entire window (W/m

^{2}·K), and total surface area (window frame + glazing) (m

^{2}), respectively. In Equation (15), short-wave solar radiation (${\dot{q}}_{solar}$) (W) is calculated by the summation of ${\dot{q}}_{solar,i}$ and ${\dot{q}}_{solar,c}$, which are solar-gain for the internal air or interior furnishing (W), and solar-gain for the components surface (W), respectively.

^{2}), diffuse solar radiation (W/m

^{2}), shading coefficient direct radiation, shading coefficient diffuse radiation, frame coefficient (percentage of transparent area), direct solar heat gain coefficient (depending on angle), solar heat gain coefficient of the diffuse radiation, and window area (m

^{2}), respectively. Convective heat sources in the room (${\dot{q}}_{Internal}$) are calculated according to Equation (19) by the summation of all individual convective heat sources.

^{3}·s·Pa), partial water vapor pressure in zone (Pa), and partial water vapor pressure on component surface (Pa), respectively. The moisture source in the room (${\dot{w}}_{internal}$) is calculated based on Equation (23).

- the outward contaminant α flow rate from zone i with the rate of $\sum}_{j}{\dot{m}}_{air-outwar{d}_{\left(i,j\right)}}\xb7{C}_{i}^{\alpha};$
- the contaminant α removal in zone i with the rate of ${R}_{i}^{\alpha}\xb7{C}_{i}^{\alpha}$; and
- the first-order chemical reactions with contaminant β at the rate of ${m}_{ai{r}_{i}}{\displaystyle \sum}_{\beta}{K}_{i}{}^{\alpha ,\beta}\xb7{C}_{i}^{\beta}$.

#### 2.2. Description of the Case Study

^{2}, volume: 9.72 m

^{3}), an exercise room (area: 18.65 m

^{2}, volume: 55.95 m

^{3}), parking (area: 12.97 m

^{2}, volume: 38.91 m

^{3}), and a staircase (area: 0.81 m

^{2}, volume: 2.43 m

^{3}) with the first level total area of 35.67 m

^{2}and volume of 107.01 m

^{3}. The main floor includes zones of the living room with a kitchen (area: 34.88 m

^{2}, volume: 104.64 m

^{3}), a washroom (area: 1.62 m

^{2}, volume: 4.86 m

^{3}), and a staircase (area: 1.62 m

^{2}, volume: 4.86 m

^{3}) with the second level total area of 38.12 m

^{2}and volume of 114.36 m

^{3}. The bedrooms floor includes three bedrooms (area: 18.10 m

^{2}, volume: 54.30 m

^{3}), two bathrooms (area: 3.78 m

^{2}, volume: 11.34 m

^{3}), a hall (area: 12.43 m

^{2}, volume: 37.29 m

^{3}), and a staircase (area: 1.62 m

^{2}, volume: 4.86 m

^{3}) with the third level total area of 35.93 m

^{2}and volume of 107.79 m

^{3}. The floor-to-floor height is assumed to be 3 m for all levels.

^{2}and a volume of 107.01 m

^{3}, second level a total area of 38.12 m

^{2}and volume of 114.36 m

^{3}, and third level a total area of 35.93 m

^{2}and volume of 107.79 m

^{3}. This three-story house is commonly built in many locations in North America. However, the present integrated model can also be used to assess the indoor air quality, moisture, and thermal comfort performances of other types of one, two, and three-story houses. Most recently, the EnergyPlus model was successfully coupled with the present integrated model developed in this study so as to simultaneously assess the energy, indoor air quality, moisture, and thermal comfort performances for the same three-story house considered in this study, subjected to the climatic conditions of Montreal, Vancouver, and Miami [42].

_{2}, indoor PM

_{2.5}, and indoor VOCs. The only source for indoor CO

_{2}is assumed to be the respiration of the occupants. The source of indoor PM

_{2.5}is in the kitchen through cooking and in the living room through kitty litter. Indoor VOCs are available through the dining table, sofa, desk chair, bedside table, and cabinet. VOCs are assumed to include benzene, toluene, ethylbenzene, xylene, and styrene.

^{3}/s. In this AHS, a typical furnace filter of MERV (minimum efficiency reporting value) with the rating of 4 in a single pass is used. The maximum space heating capacities of 5.2 kW, 5.2 kW, and 7 kW, and also the maximum space cooling capacities of 18.16 kW, 15.10 kW, and 10.59 kW for Montreal, Vancouver, and Miami, respectively, have been used [43,44]. An exhaust fan with a capacity of 24 L/s is considered in on or off positions. In addition, the minimum and maximum zone temperatures of 20 °C and 26 °C, and the minimum and maximum relative humidity (RH) of 30% and 70%, respectively, are assumed as the design conditions.

^{2}·K/W, 10.671 m

^{2}·K/W, and 5.241 m

^{2}·K/W; below grade wall of 5.445 m

^{2}·K/W, 3.695 m

^{2}·K/W, and 0.695 m

^{2}·K/W; above grade wall of 7.070 m

^{2}·K/W, 7.070 m

^{2}·K/W, and 4.445 m

^{2}·K/W; intermediate floor–ceiling of 6.801 m

^{2}·K/W, 6.801 m

^{2}·K/W, and 0.651 m

^{2}·K/W; roof of 10.488 m

^{2}·K/W, 10.488 m

^{2}·K/W, and 4.678 m

^{2}·K/W; reflected double glazed windows of 0.366 m

^{2}·K/W, 0.366 m

^{2}·K/W, and 0.277 m

^{2}·K/W; external door of 0.350 m

^{2}·K/W, 0.350 m

^{2}·K/W, and 0.350 m

^{2}·K/W; and interior wall of 1.2 m

^{2}·K/W, 1.2 m

^{2}·K/W, and 1.2 m

^{2}·K/W in Montreal, Vancouver, and Miami, respectively, have been assumed.

_{2}, indoor PM

_{2.5}, and indoor VOCs, as well as the relative humidity (RH), predicted percentage of dissatisfied (PPD), and predicted mean vote (PMV). Output-simulated indoor CO

_{2}, indoor PM

_{2.5}, and indoor VOCs are assumed as daily values, while relative humidity (RH), predicted percentage of dissatisfied (PPD), and predicted mean vote (PMV) are assumed to be hourly values.

#### 2.3. Verification of the Developed Integrated Model

_{2}concentration and relative humidity (RH) were selected as indoor air quality and moisture data, respectively. The simulated and actual values of these data for the three-story house case of the leaky-fan on in Vancouver are shown in the Table 3 and Table 4.

_{2}concentration data for the case of the leaky-fan on in Vancouver for the 15th day of each month for 2020. The simulated data is calculated by the integrated model and the actual data is measured by the CO

_{2}meter monitor.

_{2}concentration and relative humidity (RH) are 0.14212 and 1.07103, respectively (being > half mean difference), with the significance level of 0.608 and 0.513, respectively (being > 0.05). As such, there are no significant differences between the simulated and actual data for indoor CO

_{2}concentration and relative humidity (RH).

_{2}concentration and indoor relative humidity (RH) are 0.965 and 0.997, respectively (being > 0.5), with the significance level of <0.05. Thus, the simulated and actual data are significantly correlated and in good agreements.

## 3. Results

#### 3.1. Results of the Single Model of CONTAM

_{2}percentage difference, (2) results related to indoor PM

_{2.5}percentage difference, and (3) results related to indoor VOCs percentage difference according to Figure 3, Figure 4 and Figure 5. Each of these results is also simulated daily for the three different climatic regions of Montreal, Vancouver, and Miami for a period of one year (Figure 3, Figure 4 and Figure 5). In each of Figure 3, Figure 4 and Figure 5, the results of four scenarios listed in Table 7 are simulated using CONTAM. To assess the indoor air quality performance for these scenarios, the percentage difference method was used to compare indoor contaminants’ concentration with the acceptable level of ASHRAE Standard 62.1 [60]. The results of this percentage difference of indoor CO

_{2}, PM

_{2.5}, and VOCs with ASHRAE Standard 62.1 are shown in Figure 3, Figure 4 and Figure 5, respectively.

#### 3.2. Result of the Single Model of WUFI

#### 3.3. Results of the Integrated Model

_{2}percentage difference, (2) indoor PM

_{2.5}percentage difference, (3) indoor VOCs percentage difference, (4) indoor relative humidity (RH) percentage difference, (5) predicted percentage of dissatisfied (PPD), and (6) predicted mean vote (PMV). These results are shown in Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 similarly to the results of the single models for the three different climate cities of Montreal, Vancouver, and Miami on a daily basis for one year. Along with the results obtained by the integrated model, all three ASHRAE standards of 62.1, 160, and 55 [6,60,61] have been used in order to calculate the percentage difference between the simulated parameters with the acceptable level of ASHRAE standards. Therefore, the results of the simulated performances for all four scenarios are comparable to each other as well as to the other results (Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14).

## 4. Discussion

_{2}, PM

_{2.5}, and VOCs with ASHRAE Standard 62.1 was used to evaluate indoor air quality performance. The obtained results for the Montreal, Vancouver, and Miami climates are shown in Figure 3a,b,c, respectively. As shown in these figures for the simulated indoor CO

_{2}concentration results, the minimum values on the scenarios’ curves have the highest negative percentage difference with the level of ASHRAE Standard 62.1 (indoor CO

_{2}< 6300 mg/m

^{3}) [60] and have the highest performances. For scenarios 1, 2, 3, and 4, this percentage difference in Montreal resulted in values of −80.85, −81.13, −84.13, and −84.30%, respectively; in Vancouver, in values of −80.49, −80.87, −82.93, and −83.15%, respectively; and in Miami, in values of −80.96, −81.41, −81.82, and −81.98%, respectively.

_{2.5}concentration simulation, the minimum values on the scenarios’ curves have the lowest percentage difference with the level of ASHRAE Standard 62.1 (indoor PM

_{2.5}< 15 µg/m

^{3}) [60] and have the highest performances. For scenarios 1, 2, 3, and 4, this percentage difference in Montreal resulted in values of 432.26, 406.69, 378.39, and 369.03%, respectively; in Vancouver, in values of 432.26, 420.65, 432.18, and 420.65%, respectively; and in Miami, in values of 485.81, 474.27, 479.11, and 474.27%, respectively.

^{3}) [60]. For scenarios 1, 2, 3, and 4, this percentage difference in Montreal resulted in values of −21.65, −22.77, −32.13, and −32.89%, respectively; in Vancouver, in values of 42.45, 41.12, 35.94, and 34.98%, respectively; and in Miami, in values of −32.13, −32.89, −35.90, and −36.47%, respectively.

_{2}, PM

_{2.5}, and VOCs concentrations are presented in Figure 9, Figure 10 and Figure 11. In the second group, the results of indoor relative humidity (RH), predicted percentage of dissatisfied (PPD), and predicted mean vote (PMV) are shown in Figure 12, Figure 13 and Figure 14.

_{2}concentration results, Figure 9a–c show that the minimum values on the scenarios’ curves have the highest performances based on the percentage difference with ASHRAE Standard 62.1 [60]. For scenarios 1, 2, 3, and 4, this percentage difference in Montreal resulted in values of −84.88, −84.18, −85.55, and −84.98%, respectively; in Vancouver, in values of −83.61, −84.11, −84.25, and −84.29%, respectively; and in Miami, in values of −82.31, −84.64, −82.53, and −84.65%, respectively. Whereas for the simulated indoor PM

_{2.5}concentration, minimum values on the scenarios’ curves have the highest performances based on the percentage difference with ASHRAE Standard 62.1 [60]. For scenarios 1, 2, 3, and 4, this percentage difference in Montreal resulted in values of 342.98, 316.53, 303.31, and 317.42%, respectively; in Vancouver, in values of 411.21, 324.11, 377.02, and 324.11%, respectively; and in Miami, in values of −463.31, 377.74, 455.97, and 377.74%, respectively (see Figure 10a–c).

_{2}concentration, in Montreal, scenarios 1, 2, 3, and 4 resulted in average values of −79.17, −79.62, −80.95, and −81.25% by CONTAM, and −81.51, −83.34, −82.13, and −83.53% by the integrated model, respectively; in Vancouver, scenarios 1, 2, 3, and 4 resulted in average values of −79.08, −79.59, −80.66, and −80.96% by CONTAM, and −81.17, −83.33, −81.64, and −83.41% by the integrated model, respectively; and in Miami, scenarios 1, 2, 3, and 4 resulted in average values of −79.63, −80.14, −80.29, and −80.65% by CONTAM, and −80.63, −83.86, −80.80, and −83.85% by the integrated model, respectively.

_{2.5}concentration, in Montreal, scenarios 1, 2, 3, and 4 resulted in average values of 465.31, 438.50, 452.92, and 440.76% by CONTAM, and 450.39, 339.15, 423.43, and 339.77% by the integrated model, respectively; in Vancouver, scenarios 1, 2, 3, and 4 resulted in average values of 465.31, 452.59, 465.23, and 452.59% by CONTAM, and 464.63, 346.59, 457.48, and 346.59% by the integrated model, respectively; and in Miami, scenarios 1, 2, 3, and 4 resulted in average values of 518.94, 506.19, 516.77, and 506.19% by CONTAM, and 509.56, 400.13, −505.07, and 400.13% by the integrated model, respectively.

- Scenario 4 resulted in the optimal scenario for the indoor CO
_{2}performance in both the CONTAM model and the integrated model methods in Montreal and Vancouver. The integrated model calculates the indoor CO_{2}performance for Scenario 4 in Montreal and Vancouver by differences of 2.80% and 3.02%, respectively, more than the CONTAM model. The reason for this difference is because in the CONTAM model method, the effective leakage area of 0.3 m^{2}and exhaust fan airflow of 24 L/s are defined by the users as airflows input data. In contrast, the airflows in the integrated model method are corrected by the co-simulation mechanism for CONTAM–WUFI. - To calculate indoor CO
_{2}performance in Miami, the results of Scenario 4, the optimal scenario using the integrated model method, are 3.98% different from the results of Scenario 2, the optimal scenario using the CONTAM model method. The reason for this difference is that the calculation of indoor CO_{2}performance in Scenario 2 is defined by the user based on the effective leakage area of 0.04 m^{2}and exhaust fan airflow of 24 L/s. The integrated model method in Scenario 4 calculates indoor CO_{2}performance based on the corrected airflows using the co-simulation mechanism of CONTAM-WUFI. - In calculating the indoor PM
_{2.5}performance, the results of Scenario 2, the optimal scenario by the integrated model method, are −22.65% different from the CONTAM model method. The reason for this difference is that in the CONTAM model method, effective leakage area of 0.04 m^{2}and exhaust fan airflow of 24 L/s are defined as input airflows data by the user. Thus, in the integrated model method, with the help of the co-simulation mechanism of CONTAM–WUFI, the airflows values have been corrected. - Scenarios 2 and 4 are predicted for both Vancouver and Miami in the optimal level of indoor PM
_{2.5}performance. The indoor PM_{2.5}performance values calculated for these scenarios by the integrated model method are −23.4% and −20.95% different from the CONTAM model method for Vancouver and Miami, respectively. The reason for this difference is that in the CONTAM model method, the effective leakage areas of 0.04 m^{2}and 0.3 m^{2}and exhaust fan airflow rate of 24 L/s for Scenarios 2 and 4, respectively, are defined as input data airflows by the user. In contrast, the corrected airflows variables have been used by the integrated model method based on the co-simulation mechanism for CONTAM–WUFI. - The values of the indoor VOCs performance for Scenario 4, the optimal scenario by the integrated model method, are 31.54% and −22.70% different from the CONTAM model method for Montreal and Vancouver, respectively. The reason for this difference is that in the CONTAM model method, the effective leakage area of 0.3 m
^{2}and exhaust fan airflow of 24 L/s are defined as airflows input data by the user. In the integrated model, the airflows variables are corrected by the co-simulation mechanism of CONTAM–WUFI. - To calculate the indoor VOCs performance in Miami, the results of Scenario 2, the optimal scenario through the integrated model method, are 25.86% different from Scenario 4, the optimal scenario through the CONTAM model method. The reason for this difference is that the effective leakage area of 0.3 (m
^{2}) and exhaust fan airflow of 24 L/s for Scenario 4 are defined by the user as the input airflows data in the CONTAM model method. As in the integrated model method in Scenario 2, the corrected airflows data is used by the co-simulation mechanism of CONTAM–WUFI. - In Montreal, for the calculation of the indoor relative humidity (RH) performance, the results of Scenario 3, the optimal scenario through the integrated model method, are 7.39% different from the results of Scenario 4, the optimal scenario based on the WUFI model method. Therefore, the reason for this difference is that in the WUFI model method, infiltration of 3.2 h
^{−1}and mechanical ventilation of 0.3 h^{−1}for Scenario 4 are defined as airflows input data by the user. In addition, in the integrated model method for Scenario 3, corrected airflows are used by the co-simulation mechanism of CONTAM–WUFI. - The results of Scenario 4, the optimal scenario in calculating indoor relative humidity (RH) performance through the integrated model method, are 2.55% and −28.8% different from the WUFI model method results for Vancouver and Miami, respectively. The reason for this difference is that the infiltration of 3.2 h
^{−1}and mechanical ventilation of 0.3 h^{−1}are defined by the user as the input airflows data in the WUFI model method. In the integrated model method, the airflows data is corrected by the co-simulation mechanism of CONTAM–WUFI. - In calculating the indoor percentage of dissatisfied (PPD) performance, the results of Scenario 1, the optimal scenario through the integrated model method, resulted in a 39.58, 29.39, and 23.99% difference in Montreal, Vancouver, and Miami, respectively, from the WUFI model method. The reason for this difference is that the infiltration of 0.4 h
^{−1}is defined as the input airflow data by the user in the WUFI model method. In contrast, in the integrated model method, air flow data corrected by the co-simulation mechanism of CONTAM–WUFI are used. - In calculating the indoor predicted mean vote (PMV) performance, Scenario 1, the optimal scenario through the integrated model method, resulted in a 52.98, 32.41, and 40.18% difference in Montreal, Vancouver, and Miami, respectively, from the WUFI model method. The reason for this difference is that the infiltration of 0.4 h
^{−1}is defined as airflow input data by the user in the WUFI model method. However, the airflow data is corrected through the co-simulation mechanism of CONTAM–WUFI in the integrated model method.

## 5. Conclusions

_{2}, PM

_{2.5}, and VOCs concentrations, as well as indoor air quality measures, indoor relative humidity (RH) as moisture measures, percentage of dissatisfied (PPD), and predicted mean vote (PMV) as thermal comfort measures were provided in this study. The results of indoor CO

_{2}, PM

_{2.5}, and VOCs simulated by CONTAM were compared with the integrated model, and the results of indoor relative humidity (RH), percentage of dissatisfied (PPD), and predicted mean vote (PMV) by WUFI were compared with the integrated model, as well.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Co-simulation mechanism for CONTAM and WUFI. Abbreviations: ACH: air change rate; PRJ: project file; XLSX: Excel Microsoft Office open XML format spreadsheet file (XML: extensible markup language); ELA: effective leakage area; CONTAM: contaminant transport analysis; IDF: input data file; and WPS: WUFI plugin in SketchUp file.

**Figure 3.**Results of CONTAM for the IAQ performance based on the comparison of the indoor CO

_{2}percentage difference on the acceptable level of ASHRAE Standard 62.1 for Montreal, Vancouver, and Miami.

**Figure 4.**Results of CONTAM for the IAQ performance based on the comparison of the indoor PM

_{2.5}percentage difference on the acceptable level of ASHRAE Standard 62.1 for Montreal, Vancouver, and Miami.

**Figure 5.**Results of CONTAM for the IAQ performance based on the comparison of the indoor VOCs percentage difference on the acceptable level of ASHRAE Standard 62.1 for Montreal, Vancouver, and Miami.

**Figure 6.**Results of WUFI for the moisture performance based on the comparison of the indoor relative humidity (RH) on the acceptable level of ASHRAE Standard 160 for Montreal, Vancouver, and Miami.

**Figure 7.**Results of WUFI for the thermal comfort performance based on the comparison of the predicted percentage of dissatisfied (PPD) on the acceptable level of ASHRAE Standard 55 for Montreal, Vancouver, and Miami.

**Figure 8.**Results of WUFI for the thermal comfort performance based on the comparison of the predicted mean vote (PMV) on the acceptable level of ASHRAE Standard 55 for Montreal, Vancouver, and Miami.

**Figure 9.**Results of the integrated model for IAQ performance based on the comparison of the indoor CO

_{2}percentage difference on the acceptable level of ASHRAE Standard 62.1 for Montreal, Vancouver, and Miami.

**Figure 10.**Results of the integrated model for IAQ performance based on the comparison of the indoor PM

_{2.5}percentage difference on the acceptable level of ASHRAE Standard 62.1 for Montreal, Vancouver, and Miami.

**Figure 11.**Results of the integrated model for IAQ performance based on the comparison of the indoor VOCs percentage difference on the acceptable level of ASHRAE Standard 62.1 for Montreal, Vancouver, and Miami.

**Figure 12.**Results of the integrated model for moisture performance based on the comparison of the indoor relative humidity (RH) on the acceptable level of ASHRAE Standard 160 for Montreal, Vancouver, and Miami.

**Figure 13.**Results of the integrated model for thermal comfort performance based on the comparison of the predicted percentage of dissatisfied (PPD) on the acceptable level of ASHRAE Standard 55 for Montreal, Vancouver, and Miami.

**Figure 14.**Results of the integrated model for thermal comfort performance based on the comparison of the predicted mean vote (PMV) on the acceptable level of ASHRAE Standard 55 for Montreal, Vancouver, and Miami.

**Table 1.**The list of all assumptions’ input data parameters to each of the CONTAM and WUFI models as well as the integrated model as a coupling method.

Program | Parameter | Values |
---|---|---|

Weather Data | Montreal, Vancouver, and Miami: CONTAM (WTH file); WUFI (database) | |

CONTAM | Envelope Effective Leakage Area (m^{2} @4 Pa, Exponent: 0.65, Discharge Coefficient: 1) [37] | Airtight = 0.04 Leaky = 0.3 |

Exhaust Fan (L/S) | Fan On = 24, Fan Off = 0 | |

Number of Envelope Paths | 42 | |

Number of Zones | 15 | |

Contaminants, 3 | CO_{2}, PM_{2.5}, and VOCs | |

Outdoor Contaminant Concentration (mg/m^{3}) [47,48,49,50] | CO 665.8 (Montreal), 665.8 (Vancouver), and 630 (Miami). _{2}:PM 0.027 (Montreal), 0.027 (Vancouver), and 0.035 (Miami). _{2.5}:VOCs: 0.132 (Montreal), 0.322 (Vancouver), and 0.100 (Miami) | |

Number of Indoor Contaminant Source Elements | 21 | |

Indoor CO_{2} Source Generation Rate (mg/s) [48] | Awake: [11 (adult male), 9.8 (adult female), 8.6 (child 13 years old), 6.8 (child 10 years old), and 3.8 (child 4 years old)]. Sleeping: [6.6 (adult male), 6.2 (adult female), 5.2 (child 13 years old), 4.1 (child 10 years old), and 2.3 (child 4 years old)] | |

Indoor PM_{2.5} Source Generation Rate (mg/h) [51,52] | Kitchen cooking: [65.45 (breakfast), 40.90 (lunch), and 8.18 (dinner)]. Living room: [5.5 (kitty litter)] | |

Indoor VOCs Source Generation Rate (mg/h·unit) [53] | 10 (dining table), 3 (sofa), 2 (desk-chair), 1 (bedside table), and 0.5 (cabinet) | |

Filtration-Minimum Efficiency Reporting Value (MERV) rating | 4 | |

Occupants | 5 (An adult male, adult female, and three children of ages 4, 10, and 13 years old) | |

Air Handling System (AHS) Airflow Rate (m^{3}/s) | 0.35 (supply), 0.35 (return) | |

WUFI | Geometry | Total floor area 109.72 (m^{2}), net volume 329.16 (m^{3}), floor-to-ceiling height 2.7 (m), orientation 0°–180°,and window-to-wall ratio: S, E, N, 40% |

Component Assembly RSI (m^{2}·K/W) [44] | Montreal: 13.221 (ground floor), 5.445 (below grade wall), 7.070 (above grade wall), 6.801 (intermediate floor–ceiling), 10.488 (roof), 0.366 (reflected double glazed windows), 0.350 (external door), and 1.2 (interior wall)Vancouver: 10.671 (ground floor), 3.695 (below grade wall), 7.070 (above grade wall), 6.801 (intermediate floor–ceiling), 10.488 (roof), 0.366 (reflected double glazed windows), 0.350 (external door), and 1.2 (interior wall)Miami: 5.241 (ground floor), 0.695 (below grade wall), 4.445 (above grade wall), 0.651 (intermediate floor–ceiling), 4.678 (roof), 0.277 (reflective aluminum frame-fixed windows), 0.350 (external door), and 1.2 (interior wall) | |

Internal Load Category | Family household (5 persons) | |

Design Temperature (℃) | 20 | |

Infiltration and Ventilation Rates (h^{−1}) [37] | Airtight: 0.4 (fan off) and 0.7 (fan on); Leaky: 3.2 (fan off) and 3.5 (fan on) | |

HVAC Load Capacity [43,44] | Montreal: 18.16 (heating load) and 5.2 (cooling load); Vancouver: 15.10 (heating load) and 5.2 (cooling load); and Miami: 10.59 (heating load) and 7 (cooling load) | |

HVAC Airflow Capacity (m^{3}/s) [54] | 0.4 (Montreal), 0.365 (Vancouver), and 0.377 (Miami) | |

Building Envelope Conditions (outside to inside) | Ground floor: XPS surface skin (heat conductivity: 0.03 W/mK; bulk density: 40 kg/m^{3}; porosity: 0.95; specific heat capacity: 1500 J/kgK; water vapor diffusion resistance factor: 450; and typical built-in moisture: 0 kg/m^{3}); XPS Core (heat conductivity: 0.03 W/mK; bulk density: 40 kg/m^{3}; porosity: 0.95; specific heat capacity: 1500 J/kgK; water vapor diffusion resistance factor: 100; and typical built-in moisture: 0 kg/m^{3}); XPS surface skin, concrete (w/c: water-cement-ratio of 0.5; heat conductivity: 1.7 W/mK; bulk density: 2308 kg/m^{3}; porosity: 0.15; specific heat capacity: 850 J/kgK; water vapor diffusion resistance factor: 179; and typical built-in moisture: 100 kg/m^{3}); PVC roof membrane (heat conductivity: 0.16 W/mK; bulk density: 1000 kg/m^{3}; porosity: 2E-4; specific heat capacity: 1500 J/kgK; water vapor diffusion resistance factor: 15000; and typical built-in moisture: 0 kg/m^{3}); EPS (except for Miami) (heat conductivity: 0.04 W/mK; bulk density: 30 kg/m^{3}, porosity: 0.95; specific heat capacity: 1500 J/kgK; water vapor diffusion resistance factor: 50; and typical built-in moisture: 0 kg/m^{3}); and gypsum-fiberboard (heat conductivity: 0.32 W/mK; bulk density: 1153 kg/m^{3}; porosity: 0.52; specific heat capacity: 1200 J/kgK; water vapor diffusion resistance factor: 16; and typical built-in moisture: 35 kg/m^{3}). Below grade wall: mineral plaster (stucco, A-value: 0.1 kg/m^{2}h^{0.5}; heat conductivity: 0.8 W/mK; bulk density: 1900 kg/m^{3}; porosity: 0.24; specific heat capacity: 850 J/kgK; water vapor diffusion resistance factor: 25; typical built-in moisture: 210 kg/m^{3}; reference water content: 45 kg/m^{3}; free water saturation: 210 kg/m^{3}; and water absorption coefficient: 0.0017 kg/m^{2}s^{0.5}); oriented strand board (heat conductivity: 0.13 W/mK; bulk density: 630 kg/m^{3}; porosity: 0.6; specific heat capacity: 1400 J/kgK; water vapor diffusion resistance factor: 650; and typical built-in moisture: 95 kg/m^{3}); wood-fiber board (heat conductivity: 0.05 W/mK; bulk density: 300 kg/m^{3}; porosity: 0.8; specific heat capacity: 1400 J/kgK; water vapor diffusion resistance factor: 12.5; and typical built-in moisture: 45 kg/m^{3}); EPS (except for Miami); polyethylene-membrane (poly; 0.07 perm; heat conductivity: 2.3 W/mK; bulk density: 130 kg/m^{3}; porosity: 0.001; specific heat capacity: 2300 J/kgK; water vapor diffusion resistance factor: 50000; and typical built-in moisture: 0 kg/m^{3}); chipboard (heat conductivity: 0.11 W/mK; bulk density: 600 kg/m^{3}; porosity: 0.5; specific heat capacity: 1400 J/kgK; water vapor diffusion resistance factor: 70; and typical built-in moisture: 90 kg/m^{3}); and gypsum board (heat conductivity: 0.2 W/mK; bulk density: 850 kg/m^{3}; porosity: 0.65; specific heat capacity: 850 J/kgK; water vapor diffusion resistance factor: 8.3; and typical built-in moisture: 6.3 kg/m^{3}). Above grade wall: mineral plaster (stucco, A-value: 0.1 kg/m^{2}h^{0.5}); oriented strand board; wood-fiber board; EPS; polyethylene-membrane; chipboard; and gypsum board. Intermediate floor–ceiling: oak-radial (heat conductivity: 0.13 W/mK; bulk density: 685 kg/m^{3}; porosity: 0.72; specific heat capacity: 1400 J/kgK; water vapor diffusion resistance factor: 140; and typical built-in moisture: 115 kg/m^{3}); air layer 40 mm (heat conductivity: 0.23 W/mK; bulk density: 1.3 kg/m^{3}; porosity: 0.999; specific heat capacity: 1000 J/kgK; water vapor diffusion resistance factor: 0.38; and typical built-in moisture: 0 kg/m^{3}); EPS (except for Miami); softwood (heat conductivity: 0.09 W/mK; bulk density: 400 kg/m^{3}; porosity: 0.73; specific heat capacity: 1400 J/kgK; water vapor diffusion resistance factor: 200; and typical built-in moisture: 60 kg/m^{3}); and gypsum board. Roof: 60 min building paper (heat conductivity: 12 W/mK; bulk density: 280 kg/m^{3}; porosity: 0.001; specific heat capacity: 1500 J/kgK; water vapor diffusion resistance factor: 144; and typical built-in moisture: 0 kg/m^{3}); mineral insulation board (heat conductivity: 0.043 W/mK; bulk density: 115 kg/m^{3}; porosity: 0.95; specific heat capacity: 850 J/kgK; water vapor diffusion resistance factor: 3.4; and typical built-in moisture: 4.5 kg/m^{3}); softwood; vapor retarder (1 perm) (heat conductivity: 2.3 W/mK; bulk density: 130 kg/m^{3}; porosity: 0.001; specific heat capacity: 2300 J/kgK; water vapor diffusion resistance factor: 3300; and typical built-in moisture: 0 kg/m^{3}); air layer 40 mm; wood-fiber insulation board (heat conductivity: 0.042 W/mK; bulk density: 155 kg/m^{3}; porosity: 0.981; specific heat capacity: 1400 J/kgK; water vapor diffusion resistance factor: 3; and typical built-in moisture: 19 kg/m^{3}); polyethylene-membrane (poly; 0.07 perm); and softwood. |

Climate Characteristics | |||
---|---|---|---|

Parameters | Montreal | Vancouver | Miami |

Altitude (m) | 27 | 4 | 5 |

Latitude | 45°30′ N | 49°11’ N | 25°45′ N |

Longitude | 73°25′ W | 123°10′ W | 80°23′ W |

Average Annual Max. Temperature (°C) | 11 | 14 | 28 |

Average Annual Temperature (°C) | 6 | 10 | 24 |

Average Min. Temperature (°C) | 1 | 6 | 21 |

Average Annual Precipitation (mm) | 1017 | 1167 | 1420 |

Annual Number of Wet Days | 166 | 164 | 132 |

Average Annual Sunlight (hours/day) | 5 h 05′ | 5 h 01′ | 8 h 03′ |

Average Annual Daylight (hours/day) | 12 h 00′ | 12 h 00′ | 12 h 00′ |

Annual Percentage of Sunny Daylight Hours (cloudy) | 42 (58) | 42 (58) | 67 (33) |

Annual Sun Altitude at Solar Noon on the 21st day | 44.8° | 41.1° | 64.5° |

**Table 3.**Daily indoor CO

_{2}concentration data of the 15th day of each month in 2020 for the case of the leaky-fan on in Vancouver.

Data ((kg/kg) × 10 ^{−4}) | Month | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

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

Simulated | 8.24 | 8.79 | 8.82 | 8.29 | 8.84 | 8.85 | 8.35 | 8.87 | 8.87 | 8.33 | 8.83 | 8.78 |

Actual | 8.44 | 8.72 | 8.74 | 8.48 | 8.75 | 8.75 | 8.50 | 8.75 | 8.73 | 8.45 | 8.68 | 8.61 |

**Table 4.**Hourly relative humidity (RH) data of the 15th day of each month in 2020 for the case of the leaky-fan on in Vancouver.

Data (%) | Month | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

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

Simulated | 21.02 | 32.11 | 44.45 | 26.88 | 45.70 | 46.56 | 60.63 | 59.06 | 56.17 | 30.39 | 35.31 | 19.53 |

Actual | 22.39 | 31.04 | 43.51 | 27.92 | 44.65 | 47.55 | 60.79 | 60.01 | 55.61 | 29.77 | 33.38 | 18.68 |

**Table 5.**Paired samples’ differences t-test results between the simulated and actual data for indoor CO

_{2}concentration and indoor relative humidity (RH) in 2020 for the case of the leaky-fan on in Vancouver.

Simulated versus Actual Data | Paired Differences | ||||||||
---|---|---|---|---|---|---|---|---|---|

Mean | Standard Deviation | Standard Error Mean | 95% Confidence Interval of the Difference | t-Statistic | df | Significance (Two-Tailed) | |||

Lower | Upper | ||||||||

1 | Indoor CO_{2} concentration ((kg/kg) × 10^{−4}) | 0.02167 | 0.14212 | 0.04103 | −0.06863 | 0.11196 | 0.528 | 11 | 0.608 |

2 | Indoor relative humidity (%) | 0.20917 | 1.07103 | 0.30918 | −0.47133 | 0.88966 | 0.677 | 11 | 0.513 |

**Table 6.**Paired samples’ correlations t-test results between the simulated and actual data for indoor CO

_{2}concentration and indoor relative humidity (RH) in 2020 for the case of the leaky-fan on in Vancouver.

Simulated Versus Actual Data | Measurers | |||
---|---|---|---|---|

N | Correlation | Level of Significance | ||

1 | Indoor CO_{2} concentration ((kg/kg) ×10^{−4}) | 12 | 0.965 | 0.000 |

2 | Indoor relative humidity (%) | 12 | 0.997 | 0.000 |

Status | Airtight | Leaky | Fan Off | Fan On | |
---|---|---|---|---|---|

1 | Scenario 1 | Yes | No | Yes | No |

2 | Scenario 2 | Yes | No | No | Yes |

3 | Scenario 3 | No | Yes | Yes | No |

4 | Scenario 4 | No | Yes | No | Yes |

**Table 8.**Comparison of the average percentage difference of each indoor air quality (IAQ) performance between the single and integrated model.

IAQ | Indoor CO_{2} | Indoor PM_{2.5} | Indoor VOCs | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Cities | Montreal | Vancouver | Miami | Montreal | Vancouver | Miami | Montreal | Vancouver | Miami | |||||||||

Models | CONTAM Model | Integrated Model | CONTAM Model | Integrated Model | CONTAM Model | Integrated Model | CONTAM Model | Integrated Model | CONTAM Model | Integrated Model | CONTAM Model | Integrated Model | CONTAM Model | Integrated Model | CONTAM Model | Integrated Model | CONTAM Model | Integrated Model |

S1 | −79.17% | −81.51% | −79.08% | −81.17% | −79.63% | −80.63% | 465.31% | 450.39% | 465.31% | 464.63% | 518.94% | 509.56% | −19.65% | −26.40% | 43.92% | 38.55% | −30.17% | −34.55% |

S2 | −79.62% | −83.34% | −79.59% | −83.33% | −80.14% | −83.86% | 438.50% | 339.15% | 452.59% | 346.59% | 506.19% | 400.13% | −21.10% | −33.11% | 42.34% | 30.26% | −31.67% | −43.70% |

S3 | −80.95% | −82.13% | −80.66% | −81.64% | −80.29% | −80.80% | 452.92% | 423.43% | 465.23% | 457.48% | 516.77% | 505.07% | −24.51% | −28.69% | 39.99% | 36.92% | −33.67% | −35.05% |

S4 | −81.25% | −83.53% | −80.96% | −83.41% | −80.65% | −83.85% | 440.76% | 339.77% | 452.59% | 346.59% | 506.19% | 400.13% | −25.58% | −33.65% | 38.89% | 30.06% | −34.78% | −43.67% |

**Table 9.**Comparison of the average percentage difference of each moisture and thermal comfort performance between the single and integrated model.

Moisture | Indoor Relative Humidity (RH) | Predicted Percentage of Dissatisfied (PPD) | Predicted Mean Vote (PMV) | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Cities | Montreal | Vancouver | Miami | Montreal | Vancouver | Miami | Montreal | Vancouver | Miami | |||||||||

Models | WUFI Model | Integrated Model | WUFI Model | Integrated Model | WUFI Model | Integrated Model | WUFI Model | Integrated Model | WUFI Model | Integrated Model | WUFI Model | Integrated Model | WUFI Model | Integrated Model | WUFI Model | Integrated Model | WUFI Model | Integrated Model |

S1 | −12.19% | −41.06% | −8.36% | −32.23% | 12.01% | 0.73% | 9.75% | 13.54% | 9.90% | 12.81% | 4.21% | 5.22% | 36.19% | 52.98% | 38.07% | 50.41% | 10.65% | 14.93% |

S2 | −25.62% | −41.04% | −19.58% | −32.34% | 9.21% | 0.69% | 10.68% | 13.72% | 10.86% | 12.87% | 4.55% | 5.24% | 39.87% | 54.07% | 42.09% | 50.67% | 12.28% | 14.98% |

S3 | −40.30% | −40.62% | −31.44% | −32.539% | 0.99% | 0.65% | 12.57% | 14.73% | 12.59% | 13.26% | 5.15% | 5.25% | 48.34% | 60.75% | 49.55% | 52.32% | 14.64% | 15.04% |

S4 | −40.59% | −40.50% | −31.71% | −32.543% | 0.90% | 0.64% | 12.72% | 14.85% | 12.65% | 13.34% | 5.17% | 5.26% | 49.00% | 61.50% | 49.76% | 52.73% | 14.72% | 15.07% |

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**MDPI and ACS Style**

Heibati, S.; Maref, W.; Saber, H.H.
Assessing the Energy, Indoor Air Quality, and Moisture Performance for a Three-Story Building Using an Integrated Model, Part Two: Integrating the Indoor Air Quality, Moisture, and Thermal Comfort. *Energies* **2021**, *14*, 4915.
https://doi.org/10.3390/en14164915

**AMA Style**

Heibati S, Maref W, Saber HH.
Assessing the Energy, Indoor Air Quality, and Moisture Performance for a Three-Story Building Using an Integrated Model, Part Two: Integrating the Indoor Air Quality, Moisture, and Thermal Comfort. *Energies*. 2021; 14(16):4915.
https://doi.org/10.3390/en14164915

**Chicago/Turabian Style**

Heibati, Seyedmohammadreza, Wahid Maref, and Hamed H. Saber.
2021. "Assessing the Energy, Indoor Air Quality, and Moisture Performance for a Three-Story Building Using an Integrated Model, Part Two: Integrating the Indoor Air Quality, Moisture, and Thermal Comfort" *Energies* 14, no. 16: 4915.
https://doi.org/10.3390/en14164915