Page 47 - Petrophysics

DEVELOPMENT AND USE OF PETROPHYSICS 21

experimentally determined permeability within 10%. She was then able
to show the relative amount of fluid flowing through pores of selected
pore sizes. Thus the Hagen-Poiseuille equation, with modification to
account for the tortuous flow path in a rock, may be used for non-rigorous
analysis of fluid flow characteristics.
The general expression for fluid flow in porous media was developed
by Darcy in 1856 from investigations of the flow of water through sand
filter beds [26]. Darcy developed this expression from interpretation of
the various parameters involved in the flow of water through sand filters
to yield the expression known as Darcy’s law.
Although Darcy’s law was developed for the single-phase flow of
a fluid through a porous medium, it applied also to multiphase flow.
In 1936, Hassler et al. [27] discussed procedures and apparatus for
the determination of multiphase flow properties in rocks. Morse et al.
[28] introduced a dynamic steady-state method for simultaneous flow
of fluids in rocks, using a small piece of rock at the face of the core
to evenly distribute the fluids entering the test sample. They showed
that consistent values of the relative permeabilities of two flowing fluids
could be obtained as a function of the wetting phase saturation. In
1952 Welge [29] developed a method for calculating the ratio of the
relative permeabilities as a function of the wetting phase saturation for
unsteady-state displacement of oil from rocks, using either gas or water as
the displacing phase. Then in 1959 Johnson et al. [30] extended Welge’s
work, enabling the calculation of individual relative permeabilities for
unsteady-state displacements. This method is the most consistently used
method because it can be run in a short time and the results are consistent
with other methods that require several days for complete analysis.
In 1978, Jones and Roszelle [31] presented a graphical method for the
evaluation of relative permeabilities by the unsteady-state method.
Applications of the concept of relative permeability to analysis of
reservoir performance and prediction of recovery were introduced by
Buckley and Leveret [ 321 , who developed two equations that are known
as the fractional flow equation and the frontal advance equation. These
two equations enabled the calculation of oil recovery resulting from
displacement by an immiscible fluid (gas or water).
Research in petrophysics reached a plateau in the 1960s but received
increased emphasis in the following decades with the advent of efforts to
improve ultimate recovery by new chemical and thermal methods; this
has generally been recognized as enhanced oil recovery [33]. Enhanced
oil recovery techniques are new and developing technologies and only
a few processes (thermal and miscible phase displacement) have been
proven on a large scale. Research on the displacement mechanisms of
chemical solutions, trapping of residual oil, measurement of residual oil