Compensating for the Lag in Flammable Vapor Concentration Meters

Abstract

There are many industrial and experimental reasons to have the abili ty to measure the time -varying concentration of flammable vapors. Several companies have developed and marketed instruments that serve this function, but no gas concentration meter has an instantaneous response; all such meters have a lag in their respons e. These instruments are reliable indicators of steady state vapor concentrations, but the readings they provide can be misleading if they are exposed to a time -varying vapor concentration environment. Because the vapor concentration meters are first ord er systems, they respond according to an exponential relationship; the reading on the meter will asymptotically approach the actual concentration to which the meter is exposed. Testing of vapor concentration meters confirmed that the meters tested behaved as a simple linear system; therefore, the meter readings at any given time are the result of the step inputs for all time prior to the measurement time. Using the mathematical behavior of linear systems, the time history of actual concentrations can be d etermined from the time history of meter readings and the known lag in the instrument. This paper presents mathematical relationships that enable the reconstruction of the actual vapor concentration history for several simplifying assumptions and shows se veral theoretical and actual examples of the reconstruction methodology.