Background

Indoor air pollution models provide estimates of indoor concentrations of contaminants derived from external and/or internal sources.  Models have mainly been developed for the purpose of building design, but have variously been adopted and adapted for use in epidemiological and health impact studies. 

A range of models have been applied in this context.  The most widely used are dilution (or ventilation) models.  These simulate changes in concentrations of contaminants under the influence of atmospheric mixing within a room, and air exchange with the outdoor environment and/or between rooms.  

Two main approaches to dilution modelling may be identified: mass balance models and computational fluid dynamic (CFD) models.  The simplest (mass balance) models apply for a single compartment (i.e. a room where the source, ventilation and the exposed target occur), steady state conditions and complete mixing.  Multi-zone models are also available to simulate more complex situations, with several interconnected compartments.  The most advanced (CFD) models deal with dynamic conditions, including changing or intermittent release and ventilation, multiple interconnected compartments and displacement ventilation.  Indoor air chemistry, sedimentation and absorption (deposition) of pollutants indoors can also be incorporated into the models.

Principles

Dilution models are mechanistic in that they are based on simplified physical mixing, yet often semi-empirical - i.e. adjusted by empirical correction factors for different air ingress and egress configurations and room characteristics.  The models are deterministic: with appropriate input data, the same model applies for any indoor space – usually the home or workplace of an individual. If, however, full ranges and distributions of the input data are available (e.g. for the rooms in a large office building, or homes in a suburb), dilution models can be run for probabilistic simulation of the whole range of indoor exposure concentrations for the target population. 

For general modeling of exposure to contaminants released into the indoor air, dilution models often lack important terms: decay, e.g. absorption to room surfaces and furnishings; removal, e.g. filtration by air cleaning devices; medium transfer, e.g. sedimentation and absorption from air to dust; and contact rate/time. 

In the simplest formulations, with assumptions of steady state conditions and complete mixing, the indoor concentration (C) is seen as the product of a constant source term (m) (mass/time) and ventilation rate (Q) (volume/time)

C = m/Q

Incomplete mixing is dealt with by a dimensionless empirical correction factor (0 < c < 1.0), in which c = 1.0 would indicate complete mixing:

C = m/c۰Q

Displacement ventilation is often used in large rooms.  This avoids mixing fresh and used indoor air, and instead gently flows fresh cool air below the used and warmed up room air, pushing it upwards to exhaust vents.  In dilution modeling this is treated simply by giving the empirical correction factor a value higher than 1.0 (c ≥ 1.0).

A source release starting at time t = 0 leads to an indoor concentration (in room of volume V) that asymptotically changes towards the steady state.

C(t) = m۰e^-(V/Q۰t)^/c۰Q

Stopping the source release at any point of time leads to a similar concentration decay towards zero.  Instantaneous releases are incompatible with complex mixing: in reality, mixing is not instantaneous.  Indoor concentrations from instantaneous releases can therefore be modeled only from the time required for complete mixing (t~cm~).  If the source release and/or ventilation rate can be expressed as mathematical function(s) of time, the most complicated single compartment model thus becomes:

C(t) = m(t)۰e^-(V/Q(t)۰t)^/c۰Q(t)

The contribution of pollution from outdoor air to indoor exposure can be incorporated simply by adding the outdoor air concentration, corrected if necessary by an indoor/outdoor removal term. 

More complicated cases of dynamic releases and ventilation, multiple interconnected compartments, incorporation of decay and removal by indoor air chemistry or pollutant deposition on indoor surfaces require increasingly complicated and often numerical dilution models.

The figure below summarises the main factors and processes affecting indoor concentrations of particulates.  

Recommended models for indoor air pollution are given in ventilation handbooks and the legally binding ventilation codes. The National Institutes for Standards and Technology (NIST), the American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) and the Air Infiltration and Ventilation Centre (AIVC) are examples of organisations with ventilation modelling resources.

Further details on mass balance models are given in the downloadable document (appended), and detailed factsheets for (and access to) specific models are available via the links in See also, below.