A Conductivity Model for Archie RocksNew

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SPWLA Distinguished Speaker Series.The petroleum industry’s standard porosity-resistivity model (i.e., Archie’s “law”), although it is fit for its purpose, remains poorly understood after seven decades of use. This results from the choice of the graphical display and trend formula used to analyze Archie’s seminal porosity-resistivity data, taken in the Nacatoch sandstone, a petroliferous clastic formation in the Gulf of Mexico coastal area. Archie’s model accurately predicts the conductivity – brine volume trend for this sandstone. Not all rocks follow the same porosity-resistivity trends observed in the Nacatoch sandstone, but those that do are defined as Archie rocks. Archie’s Nacatoch sandstone data set has significant irreducible “scatter”, or noise. Data with significant scatter cannot be used to uniquely define a trend. Alternative graphical analyses of Archie’s Nacatoch sandstone data indicates that Archie could have analyzed this data differently had it occurred to him to do so. A physics-based porosity-conductivity model, a “geometrical factor theory” (GFT), is preferred as an alternative to the Archie model because it has a physical interpretation. In this model the bulk conductivity of an Archie rock is the product of three factors: brine conductivity, fractional brine volume, and an explicit geometrical factor. The model is offered in the form of a theorem, proved in three steps, in order to make our arguments as explicit and transparent as possible. The model is developed through its culmination as a saturation equation to illustrate that it is a complete theory for Archie rocks. The predictive power of the Archie model and GFT are similar, but unlike the adjustable parameters of the Archie model (m, n, and a), all of the parameters of GFT have a priori physical interpretations. Through a connection to percolation theory, GFT has promise to connect porosity-conductivity interpretation in earth formation to first principles.

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Your Instructor

David Kennedy, SPWLA
David Kennedy, SPWLA

David Kennedy, in the time-honored tradition of “oil patch trash”, is a true vagabond. Having attended three universities, and receiving three degrees, David has worked in the “oil patch” since 1973 for two service companies, five oil and gas operators, one geophysical data acquisition company, not to mention brief stints at both Northrop and Lockheed, and odd jobs around the house. He did stay with Mobil and Exxon for 20 years to prove to his mother that he could hold a job, but clearly that is arguable. Beginning with training at the Schlumberger learning center in 1973, David was always confused by explanations of how rocks conduct electricity, and how induction logs responded to conducting rocks. Although he is still a bit confused, things are now much clearer, and he thinks he has contributed in a small way to the understanding of conductivity anisotropy in reservoir rocks, and how induction instruments respond to it. David has six U.S. patents covering the measurement of resistivity anisotropy in the laboratory and using tri-axial logging instruments. David has about 35 publications as author or co-author, mostly on induction logging instruments and petrophysics of conductive rocks, and maybe has a few papers still left in him. His most personally rewarding jobs (although he liked them all) have been as a Schlumberger field engineer 1973-1977, and his recent employment at Southwestern Energy where he lived the dream of finding oil and gas. David has served the SPWLA as Editor of Petrophysics, Vice President of Publications, Vice President of Technology, and President. Although in love with the oil and gas business, David is looking forward to slowing down a bit following the next few years. The slowing down schedule has recently accelerated a bit; first layoff in 43 years at age 69 – not bad, Mom. Any continuing contributions to the industry will be in the field of training. Watch for a new kind of formation evaluation learning from QED Petrophysics. Recently David joined the faculty at Texas A&M University in the Petroleum Engineering Department, so now, at least for a while, you can call him “Professor”.