Consider the gas container shown in Figure 3-4, the container sinking as a buffer or surge tank in a process. It is assumed that the process takes place isothermally, at a temperature T, and that the flow through the outlet valve is expressed by

where R_v = resistance to flow at the valve, psi/scfm. We are interested in knowing how the pressure in the tank responds to changes in the inlet flow, q_i(t), and in the valve outlet pressure, p_2(t).

For this process the required relationship is given by a steady state mass balance:

1 equation, 2 unknowns (qo(t), m(t))

where:

m(z) = mass of the gas in the tank, Ib

= gas density at standard conditions of 14.7 psia and 60F, lb/(ft^3).

If the pressure in the tank is low, the relationship between the mass of the gas and the pressure is established with the equation of state for perfect gases:

2 equations, 3 unknowns (p(t))

T = absolute temperature in the tank, R

V = volume of tank, ft^3

M = molecular weight of gas

R = perfect gas constant =10.73 (ft3*psia)/(lb mol* R)

qo(t)=Rip(t)R1p(t)p2(t) qi(t)qo(t)=dtdm(t) p(t)=VMRTm(t)