Utilizing Diffusion Theory to predict carbon dioxide concentration in an indoor environment

This research details a new method of relating sources of carbon dioxide to carbon dioxide concentration in a room operating in a reduced ventilation mode by utilizing Diffusion Theory. The theoretical basis of this research involved solving Fick's Second Law of Diffusion in spherical coordinates for a source of carbon dioxide flowing at a constant rate and located in the center of an impermeable spherical boundary. The solution was developed using a Laplace Transformation. A spherical diffusion test chamber was constructed and used to validate and benchmark the developed theory. The method was benchmarked by using Dispersion Coefficients for large carbon dioxide flow rates due to diffusion induced convection. The theoretical model was adapted to model a room operating with restricted ventilation in the presence of a known, constant source of carbon dioxide. The room was modeled as a sphere of volume equal to the room and utilized a Dispersion Coefficient that is consistent with published values. The developed Diffusion Model successfully predicted the spatial concentration of carbon dioxide in a room operating in a reduced ventilation mode in the presence of a source of carbon dioxide. The flow rates of carbon dioxide that were used in the room are comparable to the average flow rate of carbon dioxide from a person during quiet breathing, also known as the Tidal Breathing. This indicates the Diffusion Model developed from this research has the potential to correlate carbon dioxide concentration with static occupancy levels which can lead to energy savings through a reduction in air exchange rates when low occupancy is detected.