RISK is a multi-room model based on an earlier models, INDOOR (2) and EXPOSURE (3). RISK allows calculation of pollutant concentrations based on source emission rates, room-to-room air movement, air exchange with the outdoors, and indoor sink behavior.
Each room is considered to be well mixed. The validity of the well mixed assumption was verified in several experiments in the EPA IAQ test house (3,4), and by data reported by Maldonado (5).
A mass balance for each room gives:
VidCi/dt = CiINQiIN - CiOUTQiOUT + Si - RI (1)
where
Vi = the volume of the room
Ci = the pollutant concentration in the room
CiIN = the concentration entering the room
QiIN = the air flow into the room
CiOUT = the concentration leaving the room
QiOUT = the air flow leaving the room
Si = the source term
Ri = the removal term
and the subscript i refers to room i for a room in a set of multiple rooms, i = 1,2,.. N where N is the number of rooms. The removal term, Ri, includes pollutant removal by air cleaners and sinks.
From the well mixed assumption COUT equals Ci. Equation (1) can be rewritten as:
VidCi/dt = CiINQiIN - CiQiOUT + Si - Ri(2)
Equation (2) is one of a set of similar equations that must be solved simultaneously in a multiple room model. RISK uses a fast discrete time step algorithm developed by Yamamoto et al. (6) to solve the series of equations. The method is stable for all time steps and is accurate for sufficiently small time steps. (The size of the time step depends on how rapidly concentrations are changing. In general a time step of 1 minute is small enough when concentrations are changing rapidly, and time steps of several minutes to hours are adequate when concentrations are near steady state.) The time step must be small enough to capture the changing behavior of the ventilation system, the sources, the sinks, and the individual activity patterns.