Hydraulic fracturing to determine $S_3$

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Hydraulic fracture initiation in vertical well

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$$ \sigma_{\theta \theta}^{min} = 3 S_{hmin} - S_{Hmax} - 2 P_p - \Delta P - \sigma^{\Delta T} = -T_0 $$

Leakoff test (mini-frac, FIT, XLOT)

© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 7.2, pp. 211)

Must add the pressure in the wellbore due to the column of wellbore fluid. Always preferable to measure pressure downhole.

FBP - unstable fracture growth away from wellbore FPP - should be close to LOP and min. principle stress in absencse of excess fluid resistance from high viscosity fluids or turbulent flow.

$S_3$ from instantaneous shut-in pressure

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© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 7.3, pp. 213)

© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 7.3, pp. 213)

Step-rate test

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© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 7.5, pp. 216)

Be careful!

When $S_3 \sim S_v$ integrate density logs

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© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 7.4, pp. 214)

What about $S_{Hmax}$?

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$$ \Delta P = P_b - P_p $$

so

$$ S_{Hmax} = 3 S_{hmin} - P_b - P_p + T_0 $$

or

$$ S_{Hmax} = 3 S_{hmin} - P_b(T=0) - P_p $$

Does it work?

Consider a system with compressibility $\beta_s$

$$ \beta_s = \frac{\Delta V_s}{V_s} \frac{1}{\Delta P} $$

$$ \Delta P = \frac{1}{\beta_s V_s} \Delta V_s $$

$$ \frac{\Delta P}{\Delta t} = \frac{1}{\beta_s V_s} \frac{\Delta V_s}{\Delta t} $$

Answer: Not very well.