Permeablity & Compression: 2018 #61

Problem 61. A new 4.892-inch diameter well flows at 439 BOPD for 72 hours, after which a PBU is performed. Oil viscosity is 0.32 cp. The formation is 68 ft thick, with 28% porosity and 27% water saturation. Compressibility (water and formation) are 2.57E-6 and 3.05E-6 1/ psi, respectively. 

The FVF is 1.369, 1.376, 1.362, and 1.360 at pressures of 2230, 2572, 2910, and 3000 psia, respectively. PBU pressures are measured at 0, 0.25, 0.5, 1, 2, 4, 8, 24, and 48 hours showing 2234, 2342, 2456, 2582, 2748, 2825, 2840, 2871, and 2882 psia, respectively. 

The reservoir permeability (md) and total compression (1/psi) are most nearly: (A) 5.7 & 16E-6; (B) 6.7 & 15E-6; (C) 7.7 & 16E-6; (D) 8.7 & 15E-6.

Solution: Guidebook 12 WLT 12, 13 RES 3; A Guide to Professional Registration for PEs, SPE, 1991.
dt = 4, 8, 24, 48 becomes t+dt/dt = 19, 10, 4, 2.5…at….2825, 2840, 2871, 2882 psia.

1. p* = 2910 from graph
2. pave=0.5(p*+pwf)=0.5(2910+2234)=2572.
3. Bo=B at pave or 2572=1.369 (given).
4. k=(162.6q uo Bo)/(mh) = [162.6(439)0.322(1.369)]/[(69)68] = 6.7 md.
5. co = (Bo-Boi)/(Boi(Pr-pwf)) = (1.376 - 1.362)/[1.362(2910 - 2234)].
    co = 0.014/[(1.362)(676)] = 15.21E-6.
6. ct = coSo+cwSw+cf = (15.21*0.73)+(2.57*0.27)+3.05][10E-6]=14.85E-6 1/psi.

This one is long and ugly; I might skip it on an exam. Making good judgements here is often the difference between P or F.