62
3 PARTICLES, PORES, AND PERMEABILITY
For all the various methods of directly determining porosity it is necessary to determine both the total volume of the rock sample and either the volume of its porosity or
of its bulk volume. Most methods rely on the measurement of the porosity by vacuum
extraction of the fluids contained within the pores. Such methods, therefore, measure
not total porosity but effective porosity. This is not terribly important because it is the
porosity of the interconnected pores that is of significance in an aquifer or hydrocarbon
reservoir.
3.2.1.2.2 Indirect methods of porosity measurement
It is often impossible to obtain large enough samples for porosity analysis from underground rocks that hold water, oil, or gas. The porosity of such host rocks must be known
in any attempt to assess their economic potential. A number of methods are now available for measuring the porosity of rocks in place when penetrated by a borehole. These
are based on measurements of various geophysical properties of the rock by a sonde, a
complex piece of electronic equipment that is lowered on a cable down the well bore.
Different sondes are designed to measure various properties of the rock. Sondes that
can measure the porosity of a rock include the sonic, neutron, and density logs. Of these
the sonic method is the least accurate. This is because the acoustic velocity of a rock varies, not only with its porosity, but also with its mineralogy (the acoustic velocity for calcite, for example, is much faster than for quartz). Nonetheless it is described here, because it is so intimately related to the seismic method discussed later. Sonic velocity is
recorded continuously by use of an acoustic device in a sonde lowered down a well bore.
The sonic velocity of the formation is recorded in microseconds per foot. Given the
sonic velocity of the pore fluid and of the pure rock mineral (the sonic velocity of calcite
is used for limestones, and of silica for sandstones, etc.) the porosity may be found from
the Wyllie equation (Wyllie et al., 1956) thus:
tlog m tm a
9
tf -- tma
where ~b is the porosity, tlog is the sonic velocity measured on the log, tma is the sonic velocity of the matrix (i.e., nonpore rock), and tf is the sonic velocity of the pore fluid. Additional discussion of indirect methods of measuring porosity will be found in Bateman
(1995) and Selley (1998). These geophysical well-logging techniques can give accurate
measurements of porosity.
The Wyllie equation can also be used to measure porosity from seismic surveys. The
interval velocity of a formation is calculated from the seismic data, and velocities for
rock and fluid taken from standard values or, better still, from values measured from real
samples of the formations taken from boreholes. The accuracy of the seismic method
is as good as the values for fluid and rock velocity. It will work well, for example, in thick
formations of uniform limestone, but will be less accurate for heterogeneous clastic formations with rapid lateral and vertical lithological variations.
Detailed discussion of this topic is beyond the scope of this book, but can be found in
standard geophysical text books such as Doyle (1995) and Sheriff and Geldert (1995).
3 PARTICLES, PORES, AND PERMEABILITY
For all the various methods of directly determining porosity it is necessary to determine both the total volume of the rock sample and either the volume of its porosity or
of its bulk volume. Most methods rely on the measurement of the porosity by vacuum
extraction of the fluids contained within the pores. Such methods, therefore, measure
not total porosity but effective porosity. This is not terribly important because it is the
porosity of the interconnected pores that is of significance in an aquifer or hydrocarbon
reservoir.
3.2.1.2.2 Indirect methods of porosity measurement
It is often impossible to obtain large enough samples for porosity analysis from underground rocks that hold water, oil, or gas. The porosity of such host rocks must be known
in any attempt to assess their economic potential. A number of methods are now available for measuring the porosity of rocks in place when penetrated by a borehole. These
are based on measurements of various geophysical properties of the rock by a sonde, a
complex piece of electronic equipment that is lowered on a cable down the well bore.
Different sondes are designed to measure various properties of the rock. Sondes that
can measure the porosity of a rock include the sonic, neutron, and density logs. Of these
the sonic method is the least accurate. This is because the acoustic velocity of a rock varies, not only with its porosity, but also with its mineralogy (the acoustic velocity for calcite, for example, is much faster than for quartz). Nonetheless it is described here, because it is so intimately related to the seismic method discussed later. Sonic velocity is
recorded continuously by use of an acoustic device in a sonde lowered down a well bore.
The sonic velocity of the formation is recorded in microseconds per foot. Given the
sonic velocity of the pore fluid and of the pure rock mineral (the sonic velocity of calcite
is used for limestones, and of silica for sandstones, etc.) the porosity may be found from
the Wyllie equation (Wyllie et al., 1956) thus:
tlog m tm a
9
tf -- tma
where ~b is the porosity, tlog is the sonic velocity measured on the log, tma is the sonic velocity of the matrix (i.e., nonpore rock), and tf is the sonic velocity of the pore fluid. Additional discussion of indirect methods of measuring porosity will be found in Bateman
(1995) and Selley (1998). These geophysical well-logging techniques can give accurate
measurements of porosity.
The Wyllie equation can also be used to measure porosity from seismic surveys. The
interval velocity of a formation is calculated from the seismic data, and velocities for
rock and fluid taken from standard values or, better still, from values measured from real
samples of the formations taken from boreholes. The accuracy of the seismic method
is as good as the values for fluid and rock velocity. It will work well, for example, in thick
formations of uniform limestone, but will be less accurate for heterogeneous clastic formations with rapid lateral and vertical lithological variations.
Detailed discussion of this topic is beyond the scope of this book, but can be found in
standard geophysical text books such as Doyle (1995) and Sheriff and Geldert (1995).