Volumentric Average Pressure in Semisteady-state Flow equation

Hallo everyone,

I want to ask about the semisteady-state flow equation in the Reservoir Engineering Handbook by Tarek Ahmed that I captured in this image.
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I wonder about the constant 0.5 that include in the equation with initial reservoir pressure and the constant 0.75 in the equation with average reservoir pressure.

How to convert the equation with initial reservoir pressure to average reservoir pressure that make this constant changed from 0.5 to 0.75?

thanks for your help.

Jami hello!

Since average reservoir pressure found at distance 0.61re then ln0.61re/rw is going to be instead of lnre/rw ...and mathamatically ln0.61re/rw is equal to lnre/rw-0.5 so this minus 0.25 you then get lnre/rw-0.75 for boundary dominated flow or pesudo steady state flow.

Regards

Wow thx a lot, do you have references book or paper about that?

Regards,

You are welcomed...there are lots of references explaining the fluid flow..I advice you if you are fresh learner to start with tarek ahmed reservoir engineering books also it is good to have some idea about the more practical books like Slider book and applied reservoir engineering by craft.

Thanks for your advice,

when I looking for the references for average pressure in pseudo steady state flow condition is about 47% of re, 61%re is for steady state condition.

You are totally right ln0.47re/rw which is equal to lnre/rw-0.75 sorry for the not accurate answer.

Strictly speaking, the -0.5 is not for 'initial reservoir pressure', rather it is for when you are using the external radius pressure for evaluating the pressure differential. When using the average reservoir pressure, you use -0.75

At initial conditions, when external radius pressure = average reservoir pressure, then pseudo steady state conditions have not been met and you'd need to use transient formulations / approach.