Derivative and Reverse Responses of Differential Pressure Gas Flow Meter

Abstract

Routine operation of differential pressure type gas flow meters for industrial purpose, has revealed various abnormal phenomena, e.g., (1) over-flow of mercury from the U-tube manometer to the transmission lines, (2) instability of the flow control system caused by choking of the transmission lines, (3) inserting the artificial restrictions into the lines for preventing hunting of recording and control, etc..
For the purpose of obtaining the common answers for the above mentioned cases, the abnormal responses of the differential pressure gas flow meter were analysed theoretically and experimentally.
When the time-constant in the one side of two transmission lines becomes much larger than the other side and the differential pressure at taps p_d is changed in step-function, then the transient responses of the applying differential pressure to the transmitter p_d' are indicated as follows:
p_d'/p_d=1-(1-a)e^-t/T₂ (T₁<<T₂)
p_d'/p_d=1-ae^-t/T₁ (T₁>>T₂)
when, T₁ and T₂ are the time-constants of the upstream and downstream transmission lines.
Process parameter a is the slope of the static pressure-differential pressure diagram of the gas flow system and is equivalent to dp₁/dp_d. (a>0: manipulated by the upstream valve, a<0: manipulated by the downstream valve)
The transient responses of p_d' become either derivative or reverse responses according with the sign of a and the peak values of responses at start-up are dependent on |a|.
When two time-constants of both lines are same, the transient responses of p_d' become the single-capacity type responses independent on a, i.e.,
p_d'/p_d=1-e^-t/T (T₁=T₂=T)
To summarize, the conclusions are that the line time-constant of the same side to the manipulating valve or disturbance causes the reverse response of p_d' and the one of the opposite side causes the derivative response.