# Infiltration Models in EnergyPlus: Empirical Assessment for a Case Study in a Seven-Story Building

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}tracer gas, were conducted to establish coefficients for the models. Then, they were evaluated in three independent periods according to the criteria established in the American Society for Testing Material D5157 Standard. Those models that only used in situ coefficients consistently met the standard across all three periods, demonstrating for both equations their accurate performance and reliability. For the best model derived from tracer gas data, the R

^{2}and NMSE values are 0.94 and 0.019, respectively. In contrast, the model developed using blower door test data and EnergyPlus default values presented a 64% reduction in accuracy compared to the best one. This discrepancy could potentially lead to misleading energy estimates. Although other software options exist for estimating infiltration, this study specifically targets EnergyPlus users. Therefore, these findings offer valuable insights to make more informed decisions when implementing the infiltration models into energy simulations for high-rise buildings using EnergyPlus.

## 1. Introduction

#### 1.1. Calibration Methodology

#### 1.2. Literature Review

^{2}year of heating loads. Additionally, air infiltration calculation methods can be derived in higher or lower energy demand [31]. Happle et al. have found that using an Equilibrium Pressure Model (EPM) calculation with dynamic values of infiltration rate, which depend on wind pressures and air temperatures, can reduce the annual heating demand, in comparison to using a Simple Infiltration Model (SIM) calculation with static values of infiltration rate [32].

- The blower door test, which gives an average infiltration value after the building has undergone pressurization and depressurization with high-pressure differences between indoor and outdoor (e.g., 10 to 300 Pa) [51].
- Tracer gas experiments that can determine the air change rate without necessarily requiring knowledge of the airflow pathways [52]. The experiment consists of introducing a tracer gas, for example, ${\mathrm{CO}}_{2}$, into space at normal conditions (e.g., 3–4 Pa) and can be performed using one of the following three methods: constant concentration, constant injection, and decay. In the last one, the decay equation can be used for the calculation of the infiltration value [16].

#### 1.3. Originality of the Research

^{2}), the normalized mean square error (NMSE), and the line of regression. In this investigation, the ASTM D5157 Standard is applied by analogy to ${\mathrm{CO}}_{2}$ concentrations. Considering the influence of infiltration on the decay curve, it becomes feasible to assess infiltration models based on standard criteria. As stated in the documents, a main prerequisite for performing the evaluation is the independence of the data used for the construction of the model. For that reason, in the present study, the summer period is used for training the model, and the other two are used as checking periods.

## 2. Methodology

#### 2.1. Infiltration Model Equations

- ${F}_{Schedule}$ represents a value from a schedule defined by the user;
- c: Flow coefficient. Units: ${\mathrm{m}}^{3}/\left(\mathrm{s}{\mathrm{Pa}}^{\mathrm{n}}\right)$;
- ${C}_{s}$: Coefficient for stack-induced infiltration. Units: ${\left(\mathrm{Pa}/\mathrm{K}\right)}^{\mathrm{n}}$;
- $\Delta T$: Absolute difference between the average dry bulb temperature within the zone and the average exterior dry bulb temperature. Units: °C;
- n: Pressure exponent. Dimensionless;
- ${C}_{w}$: Coefficient for wind-induced infiltration. Units: ${(\mathrm{Pa}{\mathrm{s}}^{2}/{\mathrm{m}}^{2})}^{\mathrm{n}}$;
- s: Shelter factor. Dimensionless;
- $WS$: Local wind speed. Units: m/s.

- ${F}_{Schedule}$ represents a value from a schedule defined by the user;
- ${A}_{L}$: Effective air leakage area corresponding to a 4 Pascal (Pa) pressure differential. Units: cm
^{2}; - ${C}_{s}$: Coefficient for stack-induced infiltration. Units: ${(\mathrm{L}/\mathrm{s})}^{2}/\left({\mathrm{cm}}^{4}\mathrm{K}\right)$;
- $\Delta T$: Absolute difference between the average dry bulb temperature within the zone and the average exterior dry bulb temperature. Units: °C;
- ${C}_{w}$: Coefficient for wind-induced infiltration. Units: ${\left(\mathrm{L}/\mathrm{s}\right)}^{2}/\left({\mathrm{cm}}^{4}{\left(\mathrm{m}/\mathrm{s}\right)}^{2}\right)$;
- $WS$: Local wind speed. Units: m/s.

#### 2.2. Test Site Description

^{2}living room situated in the loft of a residential building in the north of Spain, which has a southeast, a northwest, and a southwest façade. The fourth façade is shared with the adjacent building (Figure 2). The reasons for choosing this space are the following:

- The authors had access to monitoring it and to carry out in situ tests;
- Since it is a real space, there are imperfections in the thermal envelope. Three of its façades are exterior and exposed to weather conditions; only the east side adjoins the building’s vertical circulation lobby;
- The test site is located at the top of a high-rise building, which is surrounded by other constructions with different heights: 25 m from the southeast, 27 m from the west, and 55 m from the northwest façade, approximately;
- The dwelling was unoccupied during the on-site experiments.

#### 2.3. Monitored Data

- P_1_T: Training period of 9 days in summer: from 20 June 2021 to 2 July 2021;
- P_2_C: Checking period 01 of 11 days in spring: from 10 December 2021 to 9 January 2022;
- P_3_C: Checking period 02 of 11 days in spring: from 24 March 2022 to 24 April 2022.

#### 2.4. Tracer Gas Test

- ${C}_{p}$: Estimated ${\mathrm{CO}}_{2}$ concentration at time, t;
- ${\overline{C}}_{o}$: Average of measured interior ${\mathrm{CO}}_{2}$ concentration;
- ${\overline{C}}_{bg}$: Daily average of measured exterior ${\mathrm{CO}}_{2}$ concentration;
- t: Time, s;
- I: Infiltration of each time-step determined through IFC or ELA methods.

- The injected ${\mathrm{CO}}_{2}$ has an homogeneous distribution;
- All the living room’s exterior openings are closed, interior doors are properly sealed, and the area is not occupied; therefore, there is only air exchange with the outside;
- The outside air needs to be adequately blended throughout the test area.

#### 2.5. Blower Door Test

#### 2.6. Coefficients of the Equations

#### 2.6.1. Off-the-Shelf Coefficients

^{+}) provides predefined coefficients values for both models: Flow Coefficient (Equation (1)) and Effective Leakage Area (Equation (2)). ASHRAE (2017) establishes some specific values for stack (${C}_{s}$) and wind (${C}_{w}$) coefficients, as well as the shelter factor (s), determined by factors such as the number of floors in the building, the presence of a crawl space or a basement with or without a flue, and the shelter class. For this particular test site, the value for the maximum number of stories (3) was selected, since there is no coefficient for a seven-story area. A crawlspace lacking a flue and a shelter class of 3 were the other coefficients chosen. Although the coefficient names may sound alike in both equations, it is crucial to note that they are not interchangeable.

#### 2.6.2. In Situ Coefficients

^{3}/(sPa

^{n}) at depressurization mode), and one to the ELA model (${A}_{L}$ of 75.60 cm

^{2}at 4 Pa). Table 2 presents all models with the source of their coefficients.

#### 2.7. Model Validation

^{2}, NMSE, and the line of regression. Also, two additional statistical indices are applied for assessing bias: the normalized or fractional bias of the mean concentration (FB) and the fractional bias based on the variance (FS). The values that they should comply with are shown in Table 3.

- n: Number of time-steps of each period;
- ${{C}_{o}}_{i}$: Observed ${\mathrm{CO}}_{2}$ concentration in ppm;
- ${\overline{C}}_{o}$: Mean observed ${\mathrm{CO}}_{2}$ concentration in ppm.

^{2}) should be above 0.90 and the root mean square error (RMSE) should be as low as possible. This analysis justifies the fulfillment of the requirements explained in Section 2.4.

- The uniformity of ${\mathrm{CO}}_{2}$ dispersion is illustrated by the fact that sensors 4 and 5, placed in distinct areas within the living room, exhibited the same deviation from the average (Table 5).
- ${\mathrm{CO}}_{2}$ concentration curves from from each sensor were analyzed using the R
^{2}value. All the values were higher than 0.94 and 80% were higher than 0.96. That means that the different measured curves were similar, indicating that outside air was infiltrating evenly into the room.

## 3. Results and Discussion

_{L}value is established at 4 Pa, which is a normal pressure condition that could align with the conditions during the tracer gas test.

^{+}” and “BWD+E

^{+}” for both models, IFC and ELA. The second ELA model (“REG + E

^{+}”) nearly complied with the standard requirements (b/${\overline{C}}_{o}$ equal to 28.83% and R

^{2}equal to 0.72), which confirms the methodology of finding appropriate coefficients for the room. In addition, despite having values found at natural conditions in the ELA, the “BWD + E

^{+}” shows the highest NMSE value of 2.735 and the lowest R

^{2}value of 0.60, being the least precise model in representing dynamic infiltration across both equations.

_{2}concentrations from the eight models. In all periods, we can conclude that the IFC and ELA equations are efficient for accurately predicting air leakage in this test case in a high-rise multi-family building, particularly when employing in situ coefficients. Particularly, the “REG” models in both IFC and ELA fit the measured ${\mathrm{CO}}_{2}$ curve with an accuracy of 0.94 R

^{2}, making it unable to discern the green curve in the graphs.

^{+}”, in ELA. This value could lead to misleading energy estimations since infiltration significantly impacts energy demand and consumption.

## 4. Conclusions

^{2}and 0.018 of NMSE in the training period. On the other hand, the combination of blower door results with the off-the-shelf coefficients of EnergyPlus represents only an accuracy of 60% of R

^{2}. The obtained results are consistent across the three analyzed periods, demonstrating the robustness of the models.

^{2}of 0.94 during the training period. Nevertheless, these coefficients might not be universally accessible across all building types. Therefore, it was pertinent to analyze the performance of the blower door values along with off-the-shelf coefficients. This combination led to a 64% decrease in accuracy based on R

^{2}.

#### Limitations and Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

GHG | Greenhouse Gas Emissions |

DT | Digital Twin |

NZEB | Net Zero Energy Buildings |

BEM | Building Energy Model |

BMS | Building Management System |

BEPG | Building Energy Performance Gap |

ASHRAE | American Society of Heating, Refrigerating and Air-Conditioning Engineers |

EPM | Equilibrium Pressure Model |

SIM | Simple Infiltration Model |

CFD | Computational Fluid Dynamics |

HVAC | Heating, Ventilation, and Air Conditioning |

AFN | AirFlowNetwork |

IFC | DesignFlowRate |

ELA | ZoneInfiltration:EffectiveLeakageArea |

ASTM | American Society for Testing Material |

IAQ | Indoor Air Quality |

NMSE | Normalized Mean Squared Error |

TRL | Technology Readiness Level |

°C | Celsius Degrees |

m | Meter |

T | Temperature |

t | Time |

I | Infiltration |

WS | Wind Speed |

m/s | Meters per Second |

% | Percentage |

REG | Multi-variable Regression |

E^{+} | EnergyPlus |

BWD | Blower Door |

MAE | Mean Absolute Error |

IPMVP | International Performance Measurement and Verification Protocol |

## References

- European Commission and Directorate-General for Energy. Clean Energy for All Europeans; Technical Report; European Commission: Brussels, Belgium, 2019. [Google Scholar] [CrossRef]
- European Commission. COM(2020) 562 Final: Stepping up Europe’s 2030 Climate Ambition. Investing in a Climate-Neutral Future for the Benefit of Our People; Technical Report; European Commission: Brussels, Belgium, 2020.
- Hou, L.; Wu, S.; Zhang, G.; Tan, Y.; Wang, X. Literature review of digital twins applications in construction workforce safety. Appl. Sci.
**2020**, 11, 339. [Google Scholar] [CrossRef] - Liu, M.; Fang, S.; Dong, H.; Xu, C. Review of digital twin about concepts, technologies, and industrial applications. J. Manuf. Syst.
**2021**, 58, 346–361. [Google Scholar] [CrossRef] - Tahmasebinia, F.; Lin, L.; Wu, S.; Kang, Y.; Sepasgozar, S. Exploring the Benefits and Limitations of Digital Twin Technology in Building Energy. Appl. Sci.
**2023**, 13, 8814. [Google Scholar] [CrossRef] - Borowski, P.F. Digitization, digital twins, blockchain, and industry 4.0 as elements of management process in enterprises in the energy sector. Energies
**2021**, 14, 1885. [Google Scholar] [CrossRef] - Kaewunruen, S.; Rungskunroch, P.; Welsh, J. A digital-twin evaluation of Net Zero Energy Building for existing buildings. Sustainability
**2019**, 11, 159. [Google Scholar] [CrossRef] - Qian, Y.; Leng, J.; Wang, H.; Liu, K. Evaluating carbon emissions from the operation of historic dwellings in cities based on an intelligent management platform. Sustain. Cities Soc.
**2024**, 100, 105025. [Google Scholar] [CrossRef] - Zaidi, N.H.M.; Haw, L.C. Decarbonization of tropical city using digital twin technology: Case study of Bertam city. Iop Conf. Ser. Mater. Sci. Eng.
**2023**, 1278, 012012. [Google Scholar] [CrossRef] - Opoku, D.G.J.; Perera, S.; Osei-Kyei, R.; Rashidi, M. Digital twin application in the construction industry: A literature review. J. Build. Eng.
**2021**, 40, 102726. [Google Scholar] [CrossRef] - Coakley, D.; Raftery, P.; Keane, M. A review of methods to match building energy simulation models to measured data. Renew. Sustain. Energy Rev.
**2014**, 37, 123–141. [Google Scholar] [CrossRef] - De Wilde, P. The gap between predicted and measured energy performance of buildings: A framework for investigation. Autom. Constr.
**2014**, 41, 40–49. [Google Scholar] [CrossRef] - Ruiz, G.R.; Bandera, C.F.; Temes, T.G.A.; Gutierrez, A.S.O. Genetic algorithm for building envelope calibration. Appl. Energy
**2016**, 168, 691–705. [Google Scholar] [CrossRef] - Fernández Bandera, C.; Ramos Ruiz, G. Towards a new generation of building envelope calibration. Energies
**2017**, 10, 2102. [Google Scholar] [CrossRef] - González, V.G.; Ruiz, G.R.; Bandera, C.F. Empirical and comparative validation for a building energy model calibration methodology. Sensors
**2020**, 20, 5003. [Google Scholar] [CrossRef] - American Society of Heating Refrigerating and Air-Conditioning Engineers. The 2017 ASHARE Handbook Fundamentals; ASHRAE: Atlanta, GA, USA, 2017. [Google Scholar]
- Zhang, Y.; Korolija, I. Performing complex parametric simulations with jEPlus. In Proceedings of the SET2010-9th International Conference on Sustainable Energy Technologies, Shanghai, China, 24–27 August 2010; pp. 24–27. [Google Scholar]
- Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput.
**2002**, 6, 182–197. [Google Scholar] [CrossRef] - Du, H.; Bandera, C.F.; Chen, L. Nowcasting Methods for Optimising Building Performance; ORCA, Online Research @ Cardiff: Cardiff, UK, 2019. [Google Scholar]
- Lucas Segarra, E.; Du, H.; Ramos Ruiz, G.; Fernández Bandera, C. Methodology for the quantification of the impact of weather forecasts in predictive simulation models. Energies
**2019**, 12, 1309. [Google Scholar] [CrossRef] - Hong, T.; Lee, S.H. Integrating physics-based models with sensor data: An inverse modeling approach. Build. Environ.
**2019**, 154, 23–31. [Google Scholar] [CrossRef] - Liddament, M.W. Air Infiltration Calculation Techniques: An Applications Guide; Air Infiltration and Ventilation Centre: Berkshire, UK, 1986. [Google Scholar]
- Lozinsky, C.H.; Touchie, M.F. The limitations of multi-zone infiltration algorithms in whole building energy simulation engines. In Proceedings of the eSim 2018, the 10th Conference of IBPSA-Canada, Montréal, QC, Canada, 9–10 May 2018; pp. 367–374. [Google Scholar]
- Walker, I.S.; Less, B.D.; Lorenzetti, D.; Sohn, M.; Casquero-Modrego, N. Compartmentalization and Ventilation System Impacts on Air and Contaminant Transport for a Multifamily. In Proceedings of the ASHRAE Buildings XV, Clearwater Beach, FL, USA, 5–8 December 2022. [Google Scholar]
- Meiss, A.; Feijó-Muñoz, J. The energy impact of infiltration: A study on buildings located in north central Spain. Energy Effic.
**2015**, 8, 51–64. [Google Scholar] [CrossRef] - Kalamees, T.; Kurnitski, J.; Korpi, M.; Vinha, J. The distribution of the air leakage places and thermal bridges of different types of detached houses and apartment buildings. In Proceedings of the 2nd European BlowerDoor-Symposium Tight Building Envelope, Thermography and Dwelling Ventilation, Kassel, Germany, 16–17 March 2007; pp. 71–81. [Google Scholar]
- Goldwasser, D.; Ball, B.; Farthing, A.; Frank, S.; Im, P. Advances in calibration of building energy models to time series data: Preprint. In Proceedings of the ASHRAE and IBPSA-USA Building Simulation Conference, Chicago, IL, USA, 26–28 September 2018. [Google Scholar]
- Han, G.; Srebric, J.; Enache-Pommer, E. Different modeling strategies of infiltration rates for an office building to improve accuracy of building energy simulations. Energy Build.
**2015**, 86, 288–295. [Google Scholar] [CrossRef] - Jokisalo, J.; Kurnitski, J.; Korpi, M.; Kalamees, T.; Vinha, J. Building leakage, infiltration, and energy performance analyses for Finnish detached houses. Build. Environ.
**2009**, 44, 377–387. [Google Scholar] [CrossRef] - Feijó-Muñoz, J.; Pardal, C.; Echarri, V.; Fernández-Agüera, J.; de Larriva, R.A.; Calderín, M.M.; Poza-Casado, I.; Padilla-Marcos, M.Á.; Meiss, A. Energy impact of the air infiltration in residential buildings in the Mediterranean area of Spain and the Canary islands. Energy Build.
**2019**, 188, 226–238. [Google Scholar] [CrossRef] - Hurel, N.; Leprince, V. VIP 46: Building Airtightness Impact on Energy Performance (EP) Calculations. Air Infiltration and Ventilation Centre (AIVC VIP 46). 2023, pp. 1–18. Available online: https://www.aivc.org/resource/vip-46-building-airtightness-impact-energy-performance-ep-calculations (accessed on 3 January 2024).
- Happle, G.; Fonseca, J.A.; Schlueter, A. Effects of air infiltration modeling approaches in urban building energy demand forecasts. Energy Procedia
**2017**, 122, 283–288. [Google Scholar] [CrossRef] - Cardoso, V.E.; Pereira, P.F.; Ramos, N.M.; Almeida, R.M. The impacts of air leakage paths and airtightness levels on air change rates. Buildings
**2020**, 10, 55. [Google Scholar] [CrossRef] - Hayati, A.; Mattsson, M.; Sandberg, M. Evaluation of the LBL and AIM-2 air infiltration models on large single zones: Three historical churches. Build. Environ.
**2014**, 81, 365–379. [Google Scholar] [CrossRef] - Choi, K.; Park, S.; Joe, J.; Kim, S.I.; Jo, J.H.; Kim, E.J.; Cho, Y.H. Review of infiltration and airflow models in building energy simulations for providing guidelines to building energy modelers. Renew. Sustain. Energy Rev.
**2023**, 181, 113327. [Google Scholar] [CrossRef] - Warren, P.; Webb, B. The relationship between tracer gas and pressurization techniques in dwellings. In Proceedings of the Proc. First Air Infiltration Center Conference, Windsor, ON, USA, 6–8 October 1980; pp. 245–276. [Google Scholar]
- Sherman, M.; Grimsrud, D. Measurement of Infiltration Using Fan Pressurization and Weather Data; Technical Report; Lawrence Berkeley National Lab. (LBNL): Berkeley, CA, USA, 1980. [Google Scholar]
- Walker, I.S.; Wilson, D.J. Field validation of algebraic equations for stack and wind driven air infiltration calculations. HVAC&R Res.
**1998**, 4, 119–139. [Google Scholar] - Dols, W.S.; Emmerich, S.J.; Polidoro, B.J. Coupling the multizone airflow and contaminant transport software CONTAM with EnergyPlus using co-simulation. In Building Simulation; Springer: Berlin/Heidelberg, Germany, 2016; Volume 9, pp. 469–479. [Google Scholar]
- Bae, Y.; Joe, J.; Lee, S.; Im, P.; Ng, L. Evaluation of Existing Infiltration Models Used in Building Energy Simulation; Technical Report; Oak Ridge National Lab. (ORNL): Oak Ridge, TN, USA, 2021. [Google Scholar]
- González, V.G.; Bandera, C.F. A building energy models calibration methodology based on inverse modelling approach. In Building Simulation; Springer: Berlin/Heidelberg, Germany, 2022; pp. 1–16. [Google Scholar]
- Lee, S.H.; Hong, T. Validation of an inverse model of zone air heat balance. Build. Environ.
**2019**, 161, 106232. [Google Scholar] [CrossRef] - Gu, L. Airflow network modeling in EnergyPlus. In Building Simulation; Springer: Berlin/Heidelberg, Germany, 2007; Volume 10. [Google Scholar]
- DoE, U. EnergyPlus Engineering Reference: The Reference to EnergyPlus Calculations; Lawrence Berkeley National Laboratory: Berkeley, CA, USA, 2021. [Google Scholar]
- McLeod, R.S.; Swainson, M.; Hopfe, C.J.; Mourkos, K.; Goodier, C. The importance of infiltration pathways in assessing and modelling overheating risks in multi-residential buildings. Build. Serv. Eng. Res. Technol.
**2020**, 41, 261–279. [Google Scholar] [CrossRef] - Monari, F.; Strachan, P. Characterization of an airflow network model by sensitivity analysis: Parameter screening, fixing, prioritizing and mapping. J. Build. Perform. Simul.
**2017**, 10, 17–36. [Google Scholar] [CrossRef] - Ng, L.C.; Persily, A.K.; Emmerich, S.J. Improving infiltration modeling in commercial building energy models. Energy Build.
**2015**, 88, 316–323. [Google Scholar] [CrossRef] - Sherman, M.H.; Grimsrud, D.T. Infiltration-pressurization correlation: Simplified physical modeling. In Proceedings of the Conference of the American Society of Heating, Refrigeration and Air Conditioning Engineers, Denver, CO, USA, 3–7 February 1980. [Google Scholar]
- Persily, A.; Linteris, G. A comparison of measured and predicted infiltration rates. ASHRAE Trans.
**1983**, 89, 830640. [Google Scholar] - Zheng, X.; Mazzon, J.; Wallis, I.; Wood, C.J. Airtightness measurement of an outdoor chamber using the Pulse and blower door methods under various wind and leakage scenarios. Build. Environ.
**2020**, 179, 106950. [Google Scholar] [CrossRef] - Shrestha, S.; Hun, D.; Moss, C. Modeling Whole Building Air Leakage and Validation of Simulation Results against Field Measurements. In Whole Building Air Leakage: Testing and Building Performance Impacts; ASTM International: West Conshohocken, PA, USA, 2019. [Google Scholar]
- de Gids, W.; Sherman, M.; Janssens, A.; Delmotte, C.; Walker, I.; Borsboom, W.; Jones, B.; Linares, P.; Wahlgren, P.; Kolokotroni, M.; et al. AIVC Technical Note 70–40 years to Build Tight and Ventilate Right: From Infiltration to Smart Ventilation; INIVE EEIG: Brussels, Belgium, 2022; pp. 1–95. ISBN 2-930471-62-4. [Google Scholar]
- Roberti, F.; Oberegger, U.F.; Gasparella, A. Calibrating historic building energy models to hourly indoor air and surface temperatures: Methodology and case study. Energy Build.
**2015**, 108, 236–243. [Google Scholar] [CrossRef] - Taddeo, P.; Ortiz, J.; Salom, J.; Segarra, E.L.; González, V.G.; Ruiz, G.R.; Bandera, C.F. Comparison of experimental methodologies to estimate the air infiltration rate in a residential case study for calibration purposes. In Proceedings of the 39th AIVC 2018-Smart Ventilation for Buildings, Juan-les-Pins, France, 18–19 September 2018; p. 68. [Google Scholar]
- Weather-driven infiltration and interzonal airflow in a multifamily high-rise building: Dwelling infiltration distribution. Build. Environ.
**2020**, 181, 107098. [CrossRef] - Bastos Porsani, G.; Casquero-Modrego, N.; Echeverria Trueba, J.B.; Fernández Bandera, C. Empirical evaluation of EnergyPlus infiltration model for a case study in a high-rise residential building. Energy Build.
**2023**, 296, 113322. [Google Scholar] [CrossRef] - ASTM D5157-2019; Standard Guide for Statistical Evaluation of Indoor Air Quality Models. American Society for Testing and Materials: West Conshohocken, PA, USA, 2019.
- Pourkiaei, S.M.; Romain, A.C. Exploring the Indoor Air Quality in the context of changing climate in a naturally ventilated residential Building using CONTAM. In Proceedings of the Indoor Air 2022, Kuopio, Finland, 18 February 2022. [Google Scholar]
- Emmerich, S.; Howard-Reed, C.; Nabinger, S. Validation of multizone IAQ model predictions for tracer gas in a townhouse. Build. Serv. Eng. Res. Technol.
**2004**, 25, 305–316. [Google Scholar] [CrossRef] - Manning, C.G. Technology Readiness Levels. 2023. Available online: https://t.ly/sC2iK (accessed on 27 December 2023).
- Cui, S.; Cohen, M.; Stabat, P.; Marchio, D. CO
_{2}tracer gas concentration decay method for measuring air change rate. Build. Environ.**2015**, 84, 162–169. [Google Scholar] [CrossRef] - Li, H.; Li, X.; Qi, M. Field testing of natural ventilation in college student dormitories (Beijing, China). Build. Environ.
**2014**, 78, 36–43. [Google Scholar] [CrossRef] - ASTM E779-2019; Standard Test Method for Determining Air Leakage Rate by Fan Pressurization. American Society for Testing and Materials: West Conshohocken, PA, USA, 2019.
- ASTM E741-11(2017); Standard Test Method for Determining Air Change in a Single Zone by Means of a Tracer Gas Dilution. American Society for Testing and Materials: West Conshohocken, PA, USA, 2017.
- Sherman, M.H. Tracer-gas techniques for measuring ventilation in a single zone. Build. Environ.
**1990**, 25, 365–374. [Google Scholar] [CrossRef] - ISO 9972:2015; Thermal Performance of Buildings, Determination of Air Permeability of Buildings, Fan Pressurization Method. ISO: Geneva, Switzerland, 2015.
- Emmerich, S.J.; Nabinger, S.J.; Gupte, A.; Howard-Reed, C. Validation of CONTAM predictions for tracer gas in a townhouse. In Proceedings of the 8th international IBPSA Conference, Eindhoven, The Netherlands, 11–14 August 2003; IBPSA: Eindhoven, The Netherlands, 2003; pp. 299–306. [Google Scholar]
- International Performance Measurement and Verification Protocol: Concepts and Options for Determining Energy and Water Savings; Technical Report; National Renewable Energy Lab.: Golden, CO, USA, 2018; Volume I, pp. 1–85. Available online: https://www.nrel.gov/docs/fy02osti/31505.pdf (accessed on 7 December 2023).
- Few, J.; Elwell, C.A. Applying the CO
_{2}concentration decay tracer gas method in long-term monitoring campaigns in occupied homes: Identifying appropriate unoccupied periods and decay periods. Int. J. Build. Pathol. Adapt.**2023**, 41, 96–108. [Google Scholar] [CrossRef]

**Figure 3.**Living room 3D view. Numbers indicate the height of the ${\mathrm{CO}}_{2}$ sensor above the ground, measured in meters.

**Figure 4.**IFC model results: ${\mathrm{CO}}_{2}$ concentrations curves (measured and estimated) during P_1_T. h means hours.

**Figure 5.**IFC model results: ${\mathrm{CO}}_{2}$ concentrations curves (measured and estimated) during P_2_C. h means hours.

**Figure 6.**IFC model results: ${\mathrm{CO}}_{2}$ concentrations curves (measured and estimated) P_3_C. h means hours.

**Figure 7.**ELA model results: ${\mathrm{CO}}_{2}$ concentrations curves (measured and estimated) during P_1_T. h means hours.

**Figure 8.**ELA model results: ${\mathrm{CO}}_{2}$ concentrations curves (measured and estimated) during P_2_C. h means hours.

**Figure 9.**ELA model results: ${\mathrm{CO}}_{2}$ concentrations curves (measured and estimated) during P_3_C. h means hours.

Data | Sensor Model | Unity | Precision | Range | Resolution |
---|---|---|---|---|---|

${\mathrm{CO}}_{2}$ | Delta OHM HD37VBTV.1 | ppm | ±50 ppm | 0 to 5000 ppm | 1 ppm |

EXTECH CO210 | 0 to 9999 ppm | ||||

Temperature | HOBO ZW-006 | °C | ±2% | −20 to 50 °C | 0.02 °C |

Wind Speed | AHLBORN FVA 615-2 | m/s | ±0.5 m/s | 0 to 50 m/s | 0.1 m/s |

Model | IFC Coefficients | ELA Coefficients | ||||||
---|---|---|---|---|---|---|---|---|

$\mathit{c}$ | $\mathit{s}$ | ${\mathit{C}}_{\mathit{s}}$ | ${\mathit{C}}_{\mathit{w}}$ | $\mathit{n}$ | ${\mathit{A}}_{\mathit{L}}$ | ${\mathit{C}}_{\mathit{s}}$ | ${\mathit{C}}_{\mathit{w}}$ | |

1. REG | REG | REG | REG | REG | REG | REG | REG | REG |

2. REG + E^{+} | REG | E^{+} | E^{+} | E^{+} | REG | REG | E^{+} | E^{+} |

3. BWD + REG | BWD | REG | REG | REG | BWD | BWD | REG | REG |

4. BWD + E^{+} | BWD | E^{+} | E^{+} | E^{+} | BWD | BWD | E^{+} | E^{+} |

Index | Description | Limitation |
---|---|---|

R^{2} | Square of the correlation of predictions and measurements | ≥0.90 |

NMSE | Normalized mean square error | ≤0.25 |

m | Slope of the line of regression | 0.75 ≤ m ≤ 1.25 |

FB | Normalized or fractional bias of the mean concentration | ≤0.25 |

FS | Fractional bias based on the variance | ≤0.50 |

**Table 4.**Standard deviation ($\sigma $) and mean (µ) values for each measured data point in every period.

Parameter | Index | P_1_T | P_2_C | P_3_C |
---|---|---|---|---|

${\mathrm{CO}}_{2}$ | $\sigma $ (ppm) | 316.80 | 378.57 | 278.47 |

µ (ppm) | 613.75 | 561.14 | 629.78 | |

ΔT | $\sigma $ (°C) | 10.29 | 3.17 | 3.85 |

µ (°C) | 4.80 | 13.08 | 11.26 | |

Wind speed | $\sigma $ (m/s) | 0.33 | 0.11 | 0.16 |

µ (m/s) | 0.18 | 0.13 | 0.13 |

**Table 5.**Results from the uncertainty analysis reveal the variation between the average data employed in the calculus of infiltration and the concentration of ${\mathrm{CO}}_{2}$ recorded by every sensor.

Sensor Number and Model | R^{2} | RMSE |
---|---|---|

1. Delta OHM | 0.99 | 0.23 |

2. Delta OHM | 0.99 | 0.23 |

3. EXTECH | 0.98 | 0.39 |

4. EXTECH | 0.98 | 0.46 |

5. EXTECH | 0.96 | 0.46 |

**Table 6.**Results of IFC models following the ASTM D5157 Standard. (Models and values not in compliance with the standard are highlighted in red).

Model | Period | ${\overline{\mathit{C}}}_{\mathit{o}}$ (ppm) | ${\overline{\mathit{C}}}_{\mathit{p}}$ (ppm) | R^{2} | m | b | b/${\overline{\mathit{C}}}_{\mathit{o}}$ (%) | NMSE | FB | FS |
---|---|---|---|---|---|---|---|---|---|---|

1. REG | P_1_T | 613.87 | 637.80 | 0.94 | 1.05 | −4.96 | −0.81 | 0.019 | 0.037 | 0.149 |

P_2_C | 559.27 | 382.23 | 0.96 | 1.00 | −179.76 | −32.14 | 0.177 | −0.376 | 0.027 | |

P_3_C | 627.72 | 577.88 | 0.94 | 1.09 | −107.86 | −17.18 | 0.026 | −0.083 | 0.121 | |

2. REG + E^{+} | P_1_T | 613.87 | 637.80 | 0.72 | 0.81 | 163.71 | 26.67 | 0.077 | 0.069 | −0.100 |

P_2_C | 559.27 | 305.98 | 0.91 | 0.94 | −219.32 | −39.22 | 0.452 | −0.585 | −0.014 | |

P_3_C | 627.72 | 511.22 | 0.89 | 1.11 | −182.63 | −29.09 | 0.079 | −0.205 | 0.156 | |

3. BWD + REG | P_1_T | 613.87 | 637.80 | 0.94 | 1.05 | −7.86 | −1.28 | 0.021 | 0.037 | 0.164 |

P_2_C | 559.27 | 398.97 | 0.96 | 1.00 | −160.78 | −28.75 | 0.139 | −0.335 | 0.019 | |

P_3_C | 627.72 | 551.07 | 0.93 | 1.11 | −142.57 | −22.71 | 0.040 | −0.130 | 0.136 | |

4. BWD + E^{+} | P_1_T | 613.87 | 637.80 | 0.64 | 0.86 | −86.69 | −14.12 | 0.276 | −0.333 | 0.141 |

P_2_C | 559.27 | 174.57 | 0.74 | 0.72 | −226.69 | −40.53 | 1.895 | −1.048 | −0.181 | |

P_3_C | 627.72 | 286.59 | 0.76 | 1.01 | −346.58 | −55.21 | 0.785 | −0.746 | 0.147 |

**Table 7.**Results of ELA models following the ASTM D5157 Standard. (Models and values not in compliance with the standard are highlighted in red).

Model | Period | ${\overline{\mathit{C}}}_{\mathit{o}}$ (ppm) | ${\overline{\mathit{C}}}_{\mathit{p}}$ (ppm) | R^{2} | m | b | b/${\overline{\mathit{C}}}_{\mathit{o}}$ (%) | NMSE | FB | FS |
---|---|---|---|---|---|---|---|---|---|---|

1. REG | P_1_T | 613.87 | 637.80 | 0.94 | 1.03 | 8.64 | 1.41 | 0.018 | 0.039 | 0.111 |

P_2_C | 559.27 | 470.40 | 0.99 | 1.03 | −106.68 | −19.07 | 0.038 | −0.173 | 0.038 | |

P_3_C | 627.72 | 601.13 | 0.94 | 1.08 | −75.83 | −12.08 | 0.019 | −0.043 | 0.109 | |

2. REG + E^{+} | P_1_T | 613.87 | 637.80 | 0.72 | 0.80 | 176.98 | 28.83 | 0.077 | 0.080 | −0.129 |

P_2_C | 559.27 | 390.62 | 0.96 | 1.00 | −166.81 | −29.83 | 0.159 | −0.355 | 0.019 | |

P_3_C | 627.72 | 541.76 | 0.90 | 1.10 | −146.86 | −23.40 | 0.053 | −0.147 | 0.144 | |

3. BWD + REG | P_1_T | 613.87 | 637.80 | 0.94 | 1.03 | 8.61 | 1.40 | 0.018 | 0.039 | 0.111 |

P_2_C | 559.27 | 470.39 | 0.99 | 1.03 | −106.68 | −19.07 | 0.038 | −0.173 | 0.038 | |

P_3_C | 627.72 | 601.13 | 0.94 | 1.08 | −75.84 | −12.08 | 0.019 | −0.043 | 0.109 | |

4. BWD + E^{+} | P_1_T | 613.87 | 637.80 | 0.60 | 0.81 | −172.89 | −28.16 | 0.651 | −0.612 | 0.099 |

P_2_C | 559.27 | 143.27 | 0.68 | 0.64 | −213.84 | −38.24 | 2.735 | −1.184 | −0.252 | |

P_3_C | 627.72 | 231.27 | 0.70 | 0.92 | −347.35 | −55.34 | 1.278 | −0.923 | 0.097 |

**Table 8.**IFC coefficients. (Highlighted in bold are those provided in the EnergyPlus Input Output Document).

Model | IFC Coefficients | ||||
---|---|---|---|---|---|

c | s | ${\mathit{C}}_{\mathit{s}}$ | ${\mathit{C}}_{\mathit{w}}$ | n | |

1. REG | 9.9 × 10^{−3} | 1.29 | 0.038 | 0.344 | 0.600 |

2. REG + E^{+} | 0.00500 | 0.70 | 0.098 | 0.151 | 0.600 |

3. BWD + REG | 0.00788 | 1.26 | 0.041 | 0.382 | 0.704 |

4. BWD + E^{+} | 0.00788 | 0.70 | 0.098 | 0.151 | 0.704 |

**Table 9.**ELA coefficients. (Highlighted in bold are those provided in the EnergyPlus Input Output Document).

Model | ELA Coefficients | ||
---|---|---|---|

${\mathit{A}}_{\mathit{L}}$ | ${\mathit{C}}_{\mathit{s}}$ | ${\mathit{C}}_{\mathit{w}}$ | |

1. REG | 104.46 | 0.00002 | 0.00197 |

2. REG + E^{+} | 27.31 | 0.00044 | 0.00027 |

3. BWD + REG | 75.60 | 0.00003 | 0.00377 |

4. BWD + E^{+} | 75.60 | 0.00044 | 0.00027 |

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## Share and Cite

**MDPI and ACS Style**

Bastos Porsani, G.; Fernández-Vigil Iglesias, M.; Echeverría Trueba, J.B.; Fernández Bandera, C.
Infiltration Models in EnergyPlus: Empirical Assessment for a Case Study in a Seven-Story Building. *Buildings* **2024**, *14*, 421.
https://doi.org/10.3390/buildings14020421

**AMA Style**

Bastos Porsani G, Fernández-Vigil Iglesias M, Echeverría Trueba JB, Fernández Bandera C.
Infiltration Models in EnergyPlus: Empirical Assessment for a Case Study in a Seven-Story Building. *Buildings*. 2024; 14(2):421.
https://doi.org/10.3390/buildings14020421

**Chicago/Turabian Style**

Bastos Porsani, Gabriela, María Fernández-Vigil Iglesias, Juan Bautista Echeverría Trueba, and Carlos Fernández Bandera.
2024. "Infiltration Models in EnergyPlus: Empirical Assessment for a Case Study in a Seven-Story Building" *Buildings* 14, no. 2: 421.
https://doi.org/10.3390/buildings14020421