Tidbit - Simple method to estimate reservoir pressure from two rate points

[vinomarky]

All - just a quick and simple tidbit that works quite well to help fill the gaps between pressure build up tests during production. When you have historical production and can identify two distinct stabilized rate points over a relatively narrow time window along with their respective bottom hole flowing pressures, then the application of simple Darcy equation can yield the reservoir pressure.

Example below for oil (Oilfield units, pseudo steady state), but you can do the same exercise for gas using the pressure squared Darcy flow equation for gas;

q1 = 7.08e-3 kh (Pr-Pwf1)/(mu.B.[Ln(re/rw)+S-0.75]) can be rearranged as;

(mu.B.[Ln(re/rw)+S-0.75])/(7.08e-3 kh) = (Pr-Pwf1)/q1, where for a narow time window everything on the left is constant. Seeing as it is constant, a different rate point, with a different Pwf will then reveal Pr as follows;

(Pr-Pwf1)/q1 = (Pr-Pwf2)/q2, therefore;

Pr = (Pwf1.q2 - Pwf2.q1)/(q1 - q2)

Simple! - No skin, external reservoir radius or kh assumptions needed - you don't even have to use standard rate & pressure units as long as they are consistent both sides of the equation. As mentioned, same can be done for gas where you end up with an equation with a square root.

From this, you can also infer change in effective perm or skin over time with appropriate additional assumptions. Quite useful

Enjoy.

[bayan]

Thank you I would like to inquire if the result of Pr will be close BU test result for avarage reservoir pressure.

[petengr]

useful, and quick calculation, for quick look. Before conducting those calculation, check-up to the allocated rates is essential, just to make sure that the allocation done appropriately. Especially, when "stabilized rate points over a relatively narrow time window" is observed.

regards!

[vinomarky]

bayan: Yes, it should approximate a PBU pressure. That is not to say that it is a replacement for PBU tests, nor that single points in isolation should be trusted implictly, but a succession of scatter points over time should represent a reliable trend that can be used to fill the blanks in areas with sparse information. I've done some quick checks against a simple Eclipse model and was getting ~5% error.

petengr: a valid comment, although part of the beauty of this approach is that if back allocation would be accomplished through application of identical simple (ratio) correction factors for both rates, then back allocation becomes irrelevant as the correction fractions will cancel each other.

[petengr]

Thank you!