Summary
We have studied the electrical transport properties of porous media and the
physical meaning of Archie’s parameters with 2D lattice gas automata (LGA). On
the basis of our simulations, we have developed a set of new equations to
calculate fluid saturation from electrical measurements. The calculations from
the new equations show very good agreement with laboratory measurements and
published data on sandstone samples. There are limitations for this study in
applying mesoscale modeling to the resistivity-index/ water-saturation (I/Sw)
relationship for porous rocks because only 2D models of sandstone rock were
simulated. Some important factors like wettability were not modeled. However,
current flow simulations on the 3D digital rock samples of various types
reconstructed from thin sections and high-resolution CT scans of real rocks
have been ongoing in our laboratory as the next step to address these
issues.
Introduction
Archie’s (1942) equations (F = aΦ–m and I = bSw–n, where a, b, m, and n are
constants and called Archie parameters) have been the fundamental equations
used to calculate fluid saturation of porous rocks from electrical well logs.
There have long been questions and arguments about the true physical meaning of
the Archie parameters because the micropore structure, the flow of fluid, and
the electrical current in a porous medium cannot be directly observed and
controlled in laboratory measurements. In oilfield electrical-logging-data
interpretation, non-Archie behavior of the porous rocks (i.e., the I/Sw
relationship not being linear on a log-log scale) has been increasingly
observed and reported by log analysts and petroleum engineers (Diederix
1982).
Diederix (1982), Li (1989), Worthington and Pallatt (1992), and Jing et al.
(1993), among others, have studied this so-called “non-Archie phenomenon” of
porous rocks extensively. The non-Archie phenomenon generally becomes more
evident as the water saturation decreases further. However, because of the
limitations of macroscale laboratory experiments, it is not possible to
quantify the factors that influence the I/Sw relation. Many researchers have
tried to simulate the behavior numerically at the pore scale. Schopper (1966)
used a resistor network to study the formation factor/porosity relationship.
Yale (1984) developed a 3D pore-network model to simulate the transport
properties of porous rocks. Tao et al. (1995) used Yale’s model to interpret
electrical-conductivity and elastic-wave data simultaneously measured on
fluid-saturated sandstone samples. Man and Jing (2001) further developed Yale’s
model to account for the electrical transport properties of
multiphase-fluid-saturated porous media. Jonas et al. (2000) used a statistical
network to study the physical basis of Archie’s first equation. However,
because these models do not simulate closely enough the real pore structures
and fluid distributions, the theoretical modeling has achieved only limited
success.
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
20 December 2004
- Revised manuscript received:
22 October 2005
- Manuscript approved:
1 February 2006
- Version of record:
20 June 2006
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