| Between 1950 and 2002 the total volume of reserves discovered has run to over 1500 Bbbl.
for oil and 7.5 Tcf. for gas. Over half of these resources has already been produced, and has
driven the global economy for the last fifty years. All of the assessments of the volume of
hydrocarbon reserves were made using Archie‘s relationships (1942). It would be
difficult, therefore, to overestimate the impact of either the petrophysical techniques or
Archie‘s relationships on the worldwide economy. Archie‘s laws link the electrical
resistivity of a rock to its porosity, to the resistivity of the water that saturates its pores,
and to the fractional saturation of the pore space with the water, and are used to
calculate the hydrocarbon saturation of the reservoir rock from which the reserves
are then calculated. Archie’s laws contain two exponents, m and n, which Archie
called the cementation exponent and the saturation exponent, respectively. The
conductivity of the hydrocarbon saturated rock is highly sensitive to changes in
either exponent. However, despite the importance of the cementation exponent, few
petrophysicists, commercial or academic, are able to describe its real physical meaning. The
purpose of this contribution is to investigate the elusive physical meaning of the
cementation exponent. We review the traditional interpretation of the cementation
exponent and consider the extension of Archie’s first law to two conducting phases.
Consequently, we develop a new differential interpretation of the cementation exponent that
is based on a new definition for the connectedness of the conducting phases in a
porous medium. In this interpretation the connectedness of a porous medium is
defined as the availability of pathways for transport, where the connectedness is the
inverse of the formation resistivity factor, G = σo σw = 1 F (and may also
be called the conductivity formation factor). Porosity is defined as the fractional
amount of pore space in the usual manner. Connectivity is defined as the measure of
how the pore space is arranged, is given by χ = φm-1, and depends upon the
porosity and the cementation exponent m. The connectedness is then given by
G = φχ, and depends upon the amount of pore space (porosity) and the arrangement of
the pore space (connectivity). The rate of change of connectedness with porosity
dGdφ = mχ depends upon the connectivity χ and the cementation exponent m.
Hence, the cementation exponent can be interpreted differentially as the rate of
change of the connectedness with porosity and connectivity, m = d2G dχdφ. |