Consider a pressure surge system to reduce the effect of pressure variations at a compressor outlet on the pressure in a compressed gas header. We want to develop a two-tank model and evaluate the form of the resulting transfer function for the two-tank process shown in figure.

(a) Develop a dynamic model that can be used to solve for the gas flow rate, w3 (t), to the header given known pressures at the compressor, Pc (t), and in the header, Ph(t). Determine the degrees of freedom.

Available Information:

(i) The three valves operate linearly with resistances R1, R2, R3.

(ii) The tank volumes (V1 and V2) are constant.

(iii) The Ideal Gas Law holds.

(iv) The molecular weight of the gas is M.

(v) Operation is isothermal.

(b) Develop the model (linearize, Laplace transform, etc.) just to the point where you can identify the following characteristics of the transfer function

(i) Order of the denominator?

(ii) Order of the numerator?

(iii) Any integrating elements present?

(iv) Gain equals one?

w3 w2 Im Ph To header R3 P2 P1 Pe R2 R1 Surge tank 2 Surge tank 1