This article is based on
"Crain's Data Acquisition" by E.
R. (Ross) Crain, P.Eng., first published in 2010.
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The total pressure at any reservoir depth, due to the weight of
overlying fluid saturated rock column, is called the overburden
pressure, Po. The total pressure at any depth is the sum of the
overlaying fluid-column pressure Pp and the overlaying grain or
matrix column pressure Pm:
1: Po = Pp + Pm
A typical value of overburden pressure gradient is approximately one
psi per foot of depth. Overburden pressure depends on depth,
structure, consolidation of the formation, geologic age, and history
of the rock.
The weight of the overburden applies a compressive force to the
reservoir. The pressure in the rock pore spaces does not normally
approach the overburden pressure. A typical pore pressure gradient,
commonly referred to as the reservoir pressure, is approximately 0.45 psi per foot of depth, assuming that the reservoir is sufficiently
consolidated so the overburden pressure is not transmitted to the
fluids in the pore spaces. Some reservoirs are overpressured, with
gradients as high as 1.0 psi/ft, and some are underpressured due to
production of fluids.
Effects of compression on rocks
Normal sedimentary processes of
compaction compress the rocks, reducing porosity and sometimes
changing the shape and size of rock grains, as shown in the
The pressure difference between
overburden and internal pore pressure is referred to as the
effective overburden pressure. During pressure depletion (oil or gas
the internal pore pressure decreases and, therefore, the effective
overburden pressure increases. This increase causes the bulk volume of the reservoir rock
to reduce, and the rock grains to expand, reducing porosity.
Compressibility is the relative
volume change of matter per unit pressure change under conditions of
constant temperature. Usually, petroleum reservoirs can be
considered isothermal (an exception: thermal stimulation such as
steam assisted gravity drainage, SAGD, or fire floods).
Increasing pressure causes volume of material to decrease
(compression). Decreasing pressure causes volume expansion.
The coefficient of isothermal compressibility, C is always a positive
value, which accounts for the negative sign in the following
2: Cm = - (1 / Vm) * (dVm / dP)
3: Cp = - (1 / Vp) * (dVp / dP)
4: Cb = - (1 / Vb) * (dVb / dP)
Cm, Cp, Cb = rock matrix, pore space, and bulk compressibility (psi-1)
Vm, Vp, Vb = rock matrix, pore space, and bulk volume (cu.ft)
Pp = pore pressure (psi)
P = effective pressure (psi)
For some oilfield purposes, Cm and Cb are small, and the
composite formation compressibility Ct is assumed to be equal to Cp. Typical
values for Ct are 3 to 25 * 10^-6 psi-1. Ct varies inversely with
porosity and pressure, and numerous authors have published
correlations applicable to specific rock types.
The inverse of a compressibility is a bulk modulus, for example
Kc = 1 / Ct is the composite bulk modulus of the porous rock.
Descriptive terms and abbreviations used in the literature
vary widely, for example Cr is sometimes used to represent the rock
matrix compressibility Cm, and the rock matrix is sometimes referred
to as the "empty rock frame".
In reservoirs, overburden pressure is constant and the pressure of
fluid in pores changes, resulting in pore volume change. In the
laboratory, we change the confining pressure on the core plug
(overburden) while holding the pore pressure constant. The net compaction pressure on the matrix is the difference between
the overburden and pore pressures, so the net effect is the same in
both cases. This allows us to obtain useful results in the
The laboratory procedure: Core plug is 100% saturated with
brine. Core plug is placed in rubber or soft copper sleeve. As
pressure outside sleeve is increased, pore volume decreases and the
volume of expelled brine is measured.
Laboratory apparatus for measuring rock compressibility
ELASTIC PROPERTIES FROM MICRO CT SCANS
of micro CT scans to determine
elastic moduli is done by by simulating a static deformation
experiment on a 3D digital rock sample. These tests are
nondestructive and can be run on small samples such as drill
The application of stresses
to the faces of the sample generates strains in the rock frame that
are computed locally using the finite element method (FEM). The
resulting effective deformations of the sample are related to the
stresses applied at the boundaries to calculate the effective
elastic moduli. This application assumes linear elasticity laws are
valid within the sample. Therefore, the elastic moduli can be
converted into the elastic-wave velocities.
loading configurations are applied to
the same digital sample to obtain the
effective elastic moduli (e.g., the bulk
and shear). Source: