PBU: 2005 #16 & #68 (similar)

The standard pressure buildup (PBU) question wants skin, pressure drop, or radius of investigation (ROI). 12 WLT 12:

Variables:
B FVF bbl/STB
ct compressibility 1/psi
h thickness reservoir ft
k permeability md
MTR middle time region
p pressure psia
pwf pressure well flow psia
q flow rate well last STB/hr
ri radius investigation ft
rw radius wellbore ft
tp time produced pre-SI hr
Δt time new well SI after tp hr
ϕ porosity x.xx
μ viscosity cp

Example: q = 100 BO/D, h = 50 ft, Bo = 1.4 RB/STB, μ = 0.8 cp, & a graph of psi vs (tp-Δt)/Δt with an MTR of m = 300 psi (use one log cycle):

k = [162.6(100 BO/D)1.4 rb/STB(0.8 cp)]/[300*50 ft] =  2.25 md

From here, the ROI from SI pressure transient (say after 2 days) calculates from a simple equation on 12 WLT 6. A few more variables like ϕ (say 12%) and ct (say 4E-6 /psi) are needed:

ri = [2.25 md(48 hr)]/[948(0.12)(0.8 cp)4.3E-6 psi]^0.5 = 540 ft

Skin is calculated using tp (say 72 hr) and PBU data (tp+Δt)/Δt. Use Δt = 1 hr (easier division); this means (tp+Δt)/Δt = (72 hr+1 hr)/1 hr = 73 hrs. Now: back-extrapolate MTR to 73 hrs for pressure; 2,500 psi is a typical value. Subtract from given Pwf for drawdown (say 1,000 psi) and then divide by slope m over one log cycle.This is the skin equation's first term. 6.5 would be typical.

Using our our prior data, plus the well diameter (assume 4 in diameter) we can calculate skin:

s = 1.151[(P1hr-Pfbhp)/m]-log[k/[(por)(vis)ct(rw^2)]+3.23
   = 1.151[6.5-log[2.25[(0.12*0.8*4.3E-6*0.125^2]+3.23
   = 1.151[6.5-6.7+3.23] = 3.5