5.8 Pressure Buildup Tests Preceded by Two Different Flow Rates

Pressure buildup behavior preceded by two different flow rates can be described as

where

Eq. 5-76 can be used, when the producing rate is changed a short time before the buildup test begins, so that there is not sufficient time for Horner's approximation to be valid. All production before time t ₁ is at rate q ₁ for time t _p1 and production just before the test to have been at rate q ₂ for time t _p2. Upon simplification, Eq. 5-76 becomes

Hence a plot of

on Cartesian coordinates should give a straight line of slope, m, from which

Extrapolation of this line to zero will give p _ws = p _i to calculate the skin factor, s; note that at the end of the flow period just before shut-in

The equation of the MTR line on the buildup test plot is

Subtracting Eq. 5-80 from Eq. 5-79, we get

Assuming t _p1 + t _p2 + ?t = t _p1 + t _P2 and t _P2 + ?t = t _P2 for small ?t (e.g., ?t = 1 hr), then p _ws p _wf = m(log ?t + s).

If we choose ?t = 1 hr, p _ws = p1u _r (on the MTR line) and, for t _p2 >...