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Gas and Liquid Injection Rates 199

The in situ formation stresses are expressed as
2 3
0 0
σ H
σ fg = 4 0 σ h 0 5 (9.43)
0 0 σ V

in which σ H = the maximum horizontal stress; σ h = the minimum hori-
zontal stress; and σ V = the vertical stress. The vertical stress can be esti-
mated using density log numerically:
D g n
σ V = 1 ∫ gρdz ≈ ∑ ρ Δz i (9.44)
i
144
0 144 1
The minimum horizontal stress can be determined from mini-frac test-
ing. The procedure for conducting a mini-frac test in a vertical borehole is
shown in Figure 9.16. Hydraulic pressure is applied to the borehole by
injecting water through the DST string until a mini-fracture is created. If a
near-vertical fracture is created, the fracture is expected to break down the
bottomhole. Oriented coring of the bottomhole should give the informa-
tion about the fracture orientation. The fracture should be oriented in the
direction of the maximum horizontal stress or opened against the mini-
mum horizontal stress. The magnitude of the minimum horizontal stress
can be determined from the pressure data recorded during the mini-frac
testing. Figure 9.17 shows a typical shape of the pressure curves recorded
in mini-frac tests. The magnitude of the initial shut-in pressure (ISIP) is
taken as an approximation of the minimum horizontal stress.

DST Packer
Open Hole

Perf Tailpipe

Oriented Mini-Fracture
Core Edge

Figure 9.16 DST string for mini-frac testing.