Page 229 - Reservoir Geomechanics

210 Reservoir geomechanics

The other issue addressed by Hubbert and Willis (1957)is the manner of hydraulic
initiation at the wellbore wall. They were the first to note that a tensile wall fracture will
be induced when equation (6.7) equals −T 0 , the tensile strength of the rock. Because
T 0 ∼ 0, a tensile fracture will form at the wellbore wall when the hoop stress goes
into tension, as in the formation of a drilling-induced tensile fracture. As mentioned
in Chapter 6, what distinguishes a drilling-induced tensile fracture from a hydraulic
fracture is the fact that during hydraulic fracturing, the fluid pressure in the wellbore is
above the magnitude of the least principal stress so that the fracture will propagate away
from the wellbore. In some cases, the wellbore pressure required to initiate a tensile
fracture is greater than the least principal stress so that the pressure drops after fracture
initiation. In other cases, the fracture initiation pressure is significantly lower than
the least principal stress such that the wellbore pressure slowly climbs to the value
of the least principal stress after a tensile fracture initiates at the wellbore wall (see
Hickman and Zoback 1983). This point should now be obvious in the context of the
formation of drilling-induced tensile fractures discussed in Chapter 6.Itisobvious
that if the interval being hydraulically fractured already has drilling-induced tensile
fractures present, no additional pressurization is needed to initiate them.
A schematic pressure–time history illustrating an XLOT or mini-frac is shown in
Figure 7.2 (modified after Gaarenstroom, Tromp et al. 1993). In the schematic example
shown in Figure 7.2, the pumping rate into the well is constant. Thus, the pressure
should increase linearly with time as the volume of the wellbore is fixed. At the pres-
sure where there is a distinct departure from a linear increase of wellbore pressure
with time (referred to as the LOP, the leak-off point) a hydraulic fracture must have
formed. The reason for this is that there cannot be a noticeable decrease in the rate of
wellbore pressurization unless there is a significant increase in the volume of the sys-
tem into which the injection is occurring. In other words, the pressure in the wellbore
must be sufficient to propagate the fracture far enough from the wellbore to increase
system volume enough to affect the rate of wellbore pressurization. Thus, there must
be a hydraulic fracture propagating away from the wellbore, perpendicular to the least
principal stress in the near-wellbore region, once there is a noticeable change in the
pressurization rate. Thus, a clear LOP (a distinct break-in-slope) is approximately
equal to the least principal stress (as shown in Figure 7.2) although the wellbore pres-
sure may also reflect some near-wellbore resistance to fracture propagation. If the
hydrofrac is being made through perforations in a cased and cemented wellbore (as
is the case in mini- or micro-fracs), the tortuosity of the perforation/fracture system
may cause the pressure to increase in the wellbore above the least principal stress.
The same is true if the injection rate is high or if a relatively high viscosity fluid is
used.
It should be noted that Figure 7.2 represents pressure at the surface during a mini-frac
or LOT (note that the pressure is zero at the beginning of the test). To determine the
magnitude of the least principal stress at the depth of the test, it is necessary to add