Page 229 - Fundamentals of Gas Shale Reservoirs

GEOMECHANICS AND NATURAL FRACTURE BASICS FOR APPLICATION TO HYDRAULIC FRACTURING 209
blocks in fault zones. For this reason, we will follow the
10.2 GEOMECHANICS AND NATURAL FRACTURE common geomechanical convention that gives compressive
BASICS FOR APPLICATION TO HYDRAULIC stress a positive sign. We will refer to the principal stresses
FRACTURING
as Smax, Sint, and Smin for the maximum, intermediate, and
minimum principal stresses.
10.2.1 Basics of Earth Stress and Strain
Another common stress terminology refers to the stress
An elementary understanding of stress and strain is required axes that are mutually orthogonal and parallel and perpen­
to discuss seismic phenomena produced by hydraulic frac­ dicular to earth’s surface. The use of this nomenclature usu­
turing and to develop a basic understanding of the natural ally assumes that the earth’s surface is a principal plane. In
rock fractures systems with which hydraulic fractures this case, the stresses are termed SHmax, Shmin, and Sv for
interact. One application of passive seismic data is deter­ the maximum horizontal stress, the minimum horizontal
mining the stress state within an oil or gas reservoir. Stress stress, and the vertical stress, respectively. Note that Sv is
controls both induced fracture propagation and reactivation computed easily from log data because it is equal to the
of natural fractures. The discussion given here is general and weight of the overburden. Sv is computed at any depth by
elementary. Students needing a deeper understanding of determining the average rock density from the depth of
geomechanics are referred to Engelder (1993), Jaeger et al. interest to the surface (e.g., from a density log run to the sur­
(2007), and Zoback (2010). Readers who already have a face), then multiplying by the true vertical depth and
sound understanding of geomechanics and brittle structural acceleration of gravity.
geology should at least skim this section to ensure that they If we choose a plane that is not a principal plane, that is,
understand the terminology used in subsequent sections. a plane at some angle to the principal planes, then we can
Unconventional oil and gas development concerns both determine the normal and shear stresses on the element by
the reservoir geology which developed over geologic time making vector sums of the principal stresses parallel and
and engineering activities that are taking place today. perpendicular to the element.
Consequently, it is essential to distinguish paleostress from Effective stress is the stress in the solid skeleton of the rock
neostress. Paleostress refers to one or more ancient stress minus the stress due to fluid pressure. The contribution of
states that prevailed in the reservoir over geologic time. pore pressure to stress in the solid skeleton of a rock is pro­
Neostress is the present‐day stresses in the reservoir (also portional to Biot’s constant, α. Biot’s constant (also called the
termed the in-situ stress). poroelastic constant) is always between zero and one and is
Stress is defined as the force per unit area across a planar always <1 for any consolidated material. Biot’s constant can
element. For example, if we push or pull on a rod parallel to vary from 0.98 for unlithified clay to <0.1 or nearly zero for
the rod’s length, then the stress in the rod is given by the lithified rocks with little porosity. Since pore pressure acts
force applied to the end of the rod divided by the cross‐ outward in all directions, the effective stress in a given
sectional area of the rod. In this case, we are defining our planar direction (S ) in a porous rock with pore fluid is given by
E
reference element as perpendicular to the rod’s length. In a
fluid at rest the stress (pressure) across any element is the S E S – P ,
p
T
same regardless of the element’s orientation. In fluid that is
being deformed viscous stresses resist the shape change. We where S is the remote tectonic stress and P is the pore pressure
p
T
will consider only the stresses in solids at rest. In solids, like in the rock. The walls of a hydraulic fracture move under the
rock, the stress on a planar element depends on its orienta­ influence of the outward‐acting frac fluid pressure and the
tion. There are two kinds of stress: normal and shear. Normal inward‐acting effective stress. Leakoff from a hydraulic frac­
stress is the stress directed perpendicular to the reference ture into the matrix therefore changes the effective stresses in
element. Shear stress is the stress directed parallel to the the rock volume around the fracture. Depending on the problem
element. Consider three mutually perpendicular planar ele­ at hand, we can ignore pore pressure and consider effective
ments centered on a point. In a solid, we can rotate these stress in a fracture‐centered reference frame so that the effective
elements in 3D until we find an orientation where the shear stress on the fracture wall is the fluid pressure acting outward
stresses on each element are zero. The three planes in these minus the stress acting inward. Engelder and Lacazette (1990)
special orientations are termed the principal planes and the first discussed natural extensional rock fracture involving pore
normal stresses on these planes (i.e., the stress acting per­ pressure and fluid‐filled fractures that is equally applicable to
pendicular to the planes) are termed the principal stresses. extensional artificial hydraulic fracturing and extensional
Earth stress measurements show that in the earth’s deep sub­ natural fracturing (see Engelder,1993 and Zoback, 2010 for
surface, such as in oil and gas reservoirs, all three stresses detailed discussion of artificial hydraulic fracturing).
are always compressive. True tension is only observed near Strain is defined as the ratio of the change in length, area,
the earth’s surface, around subterranean openings like mines or volume of an element divided by the initial length, area, or
and caves, and perhaps in rare special cases such as breccia volume (respectively). Consequently, strain is dimensionless