Step-rate test

${}$

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

Be careful!

When $S_3 \sim S_v$ integrate density logs

${}$

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

What about $S_{Hmax}$?

${}$

$$ \Delta P = P_b - P_p $$

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.

Occurance of both drilling induced tensile fractures and breakouts

Allows for estimate of rock strength in-situ

Recall: $S_{Hmax}$ from breakout data

$$ S_{Hmax} = \frac{(C_0 + 2 P_p + \Delta P + \Delta \sigma^T) - S_{hmin}(1 + 2 \cos(\pi - w_{bo}))}{1 - 2 \cos(\pi - w_{bo})} $$

Recall: From Kirsch solution

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

Geomechanical case study: Cook Inlet Alaska

To case or not to case?

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© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 10.21, pp. 334)

Emperical strength model from cores

$${}$$$$ C_0 = 1.745 \times 10^{-9} \rho V_p^2 -21 $$$${}$$$${}$$

© Cambridge University Press Zoback, Reservoir Geomechanics (Table 4.1, Eq. 5, pp. 113)

Pressure drawdown and sand production

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500 psi slow drawdown $\sim 60^\circ$ breakouts
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1000 psi rapid drawdown $> 90^\circ$ breakouts

© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 10.22, pp. 335)

Preventing sand production by limiting production rate

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© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 10.23, pp. 336)

Preventing sand production with perforation orientation

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© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 10.24a, pp. 337)

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© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 10.25, pp. 338)

Preventing sand production with azimuth changes

Considering fixed horizontal perforations

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© Cambridge University Press Zoback, Reservoir Geomechanics (Fig. 10.24b, pp. 337)