As a first approximation consider no heat transfer to or from the tank.
Second approximation, the pressure as a function of time is equally distributed thoughout the tank.
Third, neglect KE of the components in the tank
The change in internal energy of the liquid and vapors in the tank
DELTA{(Mf*Ef)+(Mv*Ev)}=integral of Wf*Hf*dt
where Wf is the liqid flow rate
Hf is the specific enthalpy of the liquid in the tank
t is the time.
On a simple numerical integration,given a pressure in the tank, the orifce flow should be known. Use that flow over a small increment of time.
This allows calc of change of internal energy in tank.
With the change of internal energy of that time, calculate a new pressure (if two phase, one component-the problem is greatly simplified)
The new pressure and temp allows calc of new orifice flow.
repeat process.
One must check to see if orifice flow is restriced by flashing, choking, etc.
With P vs time known, repeat calc with a smaller time increment, until P vs time is reasonably repeative.
I'd hate to do this simplified problem by hand.