Page 120 - Reservoir Geomechanics

104 Reservoir geomechanics

wellbore stability (Chapter 10), for example, practical experience has shown that for
relativelystrongrocks,eithertheMohr–CoulombcriterionortheHoek–Browncriterion
yield reliable results. In fact, when using these data to fit the polyaxial strength data
shown in Figure 4.8, the two criteria worked equally well (Colmenares and Zoback
2002). However, because the value for the parameter m in the Hoek–Brown criterion is
rarely measured, it is usually most practical to use the Mohr–Coulomb criterion when
considering the strength of relatively strong rocks. Similarly, in weaker rocks, both the
modified Lade and the modified Wiebols–Cook criteria, both polyaxial criteria, seem
to work well and yield very similar fits to the data shown in Figure 4.8 (Colmenares
and Zoback 2002). The modified Lade criterion is easily implemented in practice as
it is used with the two parameters most commonly measured in laboratory tests, µ i
and C 0 .

Strength and pore pressure

As mentioned in Chapter 3, pore pressure has a profound effect on many rock properties,
including rock strength. Figure 4.11 shows conventional triaxial strength tests on Berea
sandstone and Mariana limestone by Handin, Hager et al.(1963). In Figures 4.11a and c,
the strength tests are shown without pore pressure in the manner of Figure 4.3b where
the strength at failure, S 1 ,is shown as a function of confining pressure, S 3 .As discussed
above, S 1 depends linearly on S 3 such that
(4.31)
S 1 = C 0 + nS 3
where C 0 , n and µ i are 62.8 MPa, 2.82 and 0.54 for Berea sandstone and 40.8 MPa,
3.01 and 0.58 for Marianna limestone, respectively. Rearrangement of equation (4.31)
yields the following
(4.32)
S 1 − S 3 = C 0 + (1 − n)P p − (1 − n)S 3
Assuming that it is valid to replace S 1 with (S 1 − P p ) and S 3 with (S 3 − P p )in equation
(4.31), it would mean that strength is a function of the simple form of effective stress
(equation 3.8). Figures 4.11b,c show that the straight lines predicted by equation (4.32)
fit the data exactly for the various combinations of confining pressures and pore pres-
sures at which the tests were conducted. In other words, the effect of pore pressure on
rock strength is described very well by the simple (or Terzaghi) form of the effective
stress law in these and most rocks. One important proviso,however, is that this has
not been tested in a comprehensive way in the context of wellbore failure, a topic of
considerable interest. Hence, more research on this topic is needed and points to a clear
need for investigating the strength of a variety of rocks (of different strength, stiffness,
permeability, etc.) at range of conditions (different loading rates, effective confining
pressures, etc.).