THE RUDOLF REPORT

GERMAR RUDOLF · THE RUDOLF REPORTThis turns (15) intodv–a =(dt · dV)(16)After the time t = V·dtdv, the complete volume is exchange one time.Therefore, a is the reciprocal of the air exchange time:1a =exchange time . (17)After a single air exchange, the concentration is:c i (t) = c o· e −1 ≈ 0.37 · c o . (18)For the 1 /x-value period (time period in which the concentrationdrops to 1 /x) the following applies accordingly:t 1 /x = ln(1 / x )–a . (19)Example: If it is required to lower the value down to 1% of the initialvalue (12 g per m3, 1 Vol.%, down to 120 mg hydrogen cyanide perm3, 0.01 Vol.%), i.e., down to 1/100 of the initial value, this results to:222t 1 /100 = ln(1 / 100 )–aThe half-value period is:≈ 4.6 × air exchange time. (20)t ½ ≈ 0.693–a . (21)Therefore, the concentration has dropped down to half afterroughly 2/3 of a complete air exchange. This is true, if the fresh andthe old air are mixed perfectly. However, this is not necessarily thecase, as there are two other possible scenarios:1. Exchange of old gas only (linear, laminar flow along the entirecross-section of the room): air exchange time roughly identicalwith ventilation time: Technically not given in the facilities underconsideration.2. Exchange of mainly fresh gas (exhaust close to intake), areas ofold gas partly not involved: ventilation time is a multiple of what