REVIEW AND IMPROVEMENT OF RESISTIVITY-TEMPERATURE-CONCENTRATION MODELS
Date: November 16th 2016
Location: Auditorium at 1500 Louisiana Street (Chevron building)
Time: 11:30 am -1:00 pm
Limited parking on the street side using Park&Pay (Cash only)
Room Capacity: 200
Lunch provided on 3x - 6ft Catering Tables
Officer Contact: Rohollah A. Pour, 512-965-7248
Speaker: David Kennedy
|Formation brine resistivity is one of the essential input parameters to models estimating hydrocarbon saturations from resistivity and porosity logs. Accurate estimation of brine resistivity is therefore essential for accurate reserve predictions based upon resistivity and porosity logs. Brine resistivity varies with both salt concentration and temperature. The resistivity of a brine of constant concentration depends upon temperature. The resistivity of a brine at constant temperature depends upon its concentration.
|It is, perhaps, unappreciated that there is no analytical function, derivable from theory, which describes this relationship except for “infinitely dilute” solutions. Any functions that are used for concentrated solutions typical of reservoir brines are empirical, customarily modeled graphically, rather than by equations. The source of the seminal data for the definition of such functions is published as tables in two volumes of the seven-volume International Critical Tables of Numerical Data, Physics, Chemistry and Technology published between 1926 and 1930. These data comprise just 81 data points, for seven temperatures ranging from 32 degrees F to 312.8 degrees F, and ten concentrations ranging from 60 ppm to 200,000 ppm NaCl (by mass), with the data becoming sparse at high concentrations and temperatures, but forming the entire basis of resistivity-temperature-concentration transforms used in formation evaluation. Values of concentration, temperature, and resistivity between the 81 data points in the ICT tables are estimated by interpolating between the data points in the table.
|The first interpolating formula to come into common use was invented by J. J. Arps in 1953. The first resistivity-temperature-concentration chart based upon the Arps formula was published in 1955. This chart plotted iso-concentration lines on a log-log plot of temperature (50-to-400 degrees F) versus resistivity (0.01-to-10.0 ohm meters). Although the Arps approximation loses accuracy at both low and high temperatures, this was not publicized. Except for minor extensions at the high-concentration end (above 200,000 ppm NaCl), the chart remained unchanged until 1996.
|In 1996, the iso-concentration lines on the commonly used service company chart labeled GEN-6 changed, becoming subtly curved. The new chart was based not only on the ICT data, but also upon new data, observed by Carl Scala at Schlumberger-Doll Research, for temperatures up to 400 degrees F, and concentrations from 6,000 ppm up to approximately 200,000 ppm. Plotting the data points on chart GEN-6 reveals that the curved iso-concentration lines approximate the observations much better than earlier versions of the chart which were based upon the Arps approximation. The approximating function has not been published to date.
|The subject of this paper is not only to review the history of, and science supporting, resistivity-temperature-concentration approximation, but also explain how to design even better approximations, and to publish an improved approximation both as a traditional chart and also the analytical approximation used to construct the chart. Designers of log-interpretation software should find the formula useful.
Affiliation: QED Petrophysics
Bio: 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.
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