There isn't a spring rate per say. Compression and expansion of the air will be controlled by the water inlet and outlet rate. First because it is the water entering the tank that will compress the air, and the water's flowrate is limited by the tank entrance nozzle connection (Cd coefficient). So, if that's a spring constant, it isn't one in the classical sense, and its nonlinear at best since its doubtful that water entrance and exit rate will be constant for long. Air can't be compressed faster than the air volume in the tank can change by the water volume entering. As air pressure builds, the water inlet rate will decrease until pressures equalize. As the surge pressures in the water decrease, once the surge wave is reflected, the water will begin exiting, as the air pressure in the tank is above the lessened surge pressure. That exit rate of the water is once again limited by the tank discharge nozzle Cd.
What you describe above is exactly what I would expect for a 30" pipeline, although you didn't mention the normal operating pressure at the tank, such a pipeline when surging would be expected to reach or exceed (within code allowables) the normal operating pressure when properly designed. I would guess that the surge tank volume is pretty much correct.
As for what you're asking about the air volumes in the tank, the critical point will be whether the tank is larger than the surge volume of water expected to enter or not. That is what will increase the pressure of the air and consequently the internal pressure of the tank and surrounding piping. If the predicted surge volume is more than expected, the pressures will rise higher than expected. That's what you need to avoid. As long as there is enough air in the tank to accomodate all surge water entering without reaching a pressure higher than the pipe and tank allowable pressure, you're OK. That would indicate that this system should be checked at the coldest operating temperature it is likely to have, since that would also be when you would have the minimum volume of air in the surge tank.
Let me know when you want to take it to detailed analysis.
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"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that
99% for pipeline companies)