The Archie Equations and the Search for Water Saturation.

A Workshop on their History and Geological Significance

A Shell geologist, Gus Archie, published a paper in 1942 that demonstrated a link between laboratory resistivity and porosity measurements with independently measured water saturation values. The obvious conclusion to this paper was to apply these equations to the recently developed wireline resistivity tool, which when used alone could identify hydrocarbon-bearing zones, and with the soon-to-be introduction of downhole porosity tools would be used to quantify in-situ water saturations. The concept that Archie worked from was based on a simple model of electrical conduction in a porous rock, that he transformed into a resistivity-based model with the inputs being the measured resistivity of the saturated rock, the resistivity of the conducting brine and an estimate of the pathway of the conducting brine. State-of-Art data analysis at that time was to plot resistivity, permeability and porosity values from a small data set of high-porosity, high-permeability “clean” formations on different scales. The log-log plot produced straightforward trends that were characterized by power-law functions whose slopes defined certain equation parameters. These equations became the Archie Equations. These “simple” equations were the basis of log interpretation efforts for the next several generations, despite their apparent failings, most notably being based on a very small and select set of clean sandstones that was not representative of the oil-bearing rocks found throughout the world. While the absence of a true physics underpinning bothered some, numerous modified forms of the equations were developed over the years to account for the presence of “shale” and the contribution of surface conduction associated with electric double layers. These modifications became more substantial by the 1960s-70s, with the “shale” conductivity component being linked to clay mineral surface properties. Even these modifications were highly empirical with the model inputs being extracted from log-derived data, and not first principles. Which is where we stand today, imperfect models for water saturation that work reasonably well under a wide variety of circumstances. The workshop is divided into two sections; the first being a historical review of  the contributions of Archie and subsequent researchers on the solutions to solving for water saturation with wireline logs, with some insights on how geological knowledge can aid in estimating various parameters. The second section is a walk-through of some of the methods used by Petrophysicists to analyze log data to extract critical parameters and to optimize water saturation calculations. 

Bios:

James Howard is the current President of the Tulsa Chapter of the SPWLA. His career included stints at Schlumberger-Doll Research where he was introduced to Archie’s equations, and met Henri Doll, and a longer stay at the Phillips Petroleum / ConocoPhillips laboratories in Bartlesville. His research over the years focused on the impact of clay minerals on petrophysical properties and the characterization of pore geometry through a variety of techniques, including NMR and high-resolution imaging. He has B.S. and Ph.D. degrees from long ago, both in geology. 

Patrick J Ryan is the Treasure of the Tulsa Chapter of SPWLA and the Oklahoma Well Log Library, Inc.  He has a Bachelors and Master in Geology and an MBA.  He started his career in Houston where he worked at Shell Oil and Conoco before moving to Tulsa where he spent the majority of his 49 year career working as an Independent Geologist and for large Independents such as Newfield Exploration.  Most of his exploration and development efforts were divided among the Arkoma Basin, the Golden Trend and the Anadarko Basin.  During this time, he gained considerable experience and expertise in the Petrophysical Analysis of the various hydrocarbon producing formations of these areas.