Rethinking Shaly-Sand Beliefs: Reconciling Paul Worthington’s Model with Waxman-Smits and Dual Water
Westside Houston
Speaker:
Seminar Date: Mar 20 2025
Registration Opens: Feb 17 2025 - Mar 20 2025
Time: 11:30 AM - 01:00 PM (US CDT)
Admission/Registration Link: None
Donation Link: None
Meeting/Webinar Link: None
Contact: QinShan “Shan” Yang (VP Westside, SPWLA Houston Chapter)
Corresponding: vpwestside@spwla-houston.org
Fees: FREENOTES:
Speaker : David Kennedy
Date : Thursday, March 20th , 2025
Time : 11:30 am – 1:00 pm (US CDT)
Venue : SLB, 6350 West Sam Houston Parkway North, Houston, TX 77041
Admission : This activity will include a boxed lunch.
The seminar is sponsored by SLB so there
is no charge for registration.
However, you still need to register using
the applicable links below.
Parking Info : Guest parking is available free of charge. Upon arrival, please proceed to the front desk to check in
Please register one day before the event to reserve lunch using the above provided link.
Contact : QinShan (Shan) Yang (SPWLA Houston VP Westside)
Corresponding : vpwestside@spwla-houston.org
ABSTRACT:
In 1985 Paul Worthington published his Evolution of Shaly-Sand Concepts in Reservoir Evaluation paper. The paper has been cited 137 times to date, 40 times in the past five years, and 4 times in 2024. Figure 2 in Paul’s paper has been used as a generic model to explain the effect of clay on bulk reservoir rock conductivity. Note the ‘clean’ sand trend line is straight and intercepts the origin since bulk rock conductivity must vanish as Cw 0. According to the figure if the quartz grains comprising a clean sand are replaced grain-by-grain with an equal volume of conductive clay mineral, then the bulk rock would become more conductive, the trend would shift up in the plot parallel to itself, except on the left side of the plot where the increase in conductivity is non-linear. Seems reasonable, right? Indeed, considering the slope of the line is 1/F = j m this plot embodies the Waxman-Smits ‘shaly-sand’ model, C0 = j m( Ce + Cw ) where Ce = BQv. A C0 Cw plot is an experiment performed on a single core and is therefore at constant porosity. The slope of the line is j m; if this model is to be accurate, not only is the porosity constant, m must also be constant. Now, m is correlated with pore geometry. The question is: can clay mineral crystals replace quartz without a concomitant change in pore geometry and therefore m? The data supplied in the Waxman-Smits paper (using their 115 core plug specimens) seem to answer this question with a “No!” Figure 3 in the Waxman-Smits paper provides the clue. Core 2 and core 26 have approximately the same porosity (0.212 vs. 0.229); core 2 is ‘almost clean’ (Qv = 0.052) whereas core 26 is ‘clay rich’ (Qv = 1.47). If Worthington’s model were accurate then the expectation would be that the core 26 trend would shift up in the plot parallel to the core 2 data. Conversely, if the clay in core 26 were replaced with quartz, the expectation would be the trend would shift down until it intercepted the origin. The observations belie these expectations. So, what’s wrong? The clue is in the slope of the trends. Since the slope is given by j m and j is constant, we must conclude that the mineral replacement must be accompanied by an increase in pore geometry complexity and a concomitant increase in m. Examining the entire W-S data set I discovered this behavior in every porosity bin, and no example to support Worthington’s model. What are the implications for the W-S and dual water models? It turns out the W-S model can accommodate this behavior if m is a function of Qv. The dual water model automatically produces a rotation of the trend as quartz is replaced with clay, but not enough to reproduce the observations, which also requires that m increase with clay content. I introduce a model that brings model predictions into line with observations and leads to new insights into the relationship between clean and clay-bearing sands.
BIOGRAPHY:
W. David Kennedy (you can call me ‘Dave’) has been a member of the SPWLA since 1975. He’s served the Society as Vice President of Publications (and first editor of Petrophphysics), Vice President of Technology, and President. Dave began adult life as an infantry platoon leader, serving in Vietnam. Upon return to civilian life, he finished his physics degree at Georgia Tech in 1972 and shortly thereafter was discovered by Schlumberger, who introduced him to formation evaluation at their Ventura learning center. He was skeptical of much of what was being taught, and thought petrophysics and formation evaluation might be a field where contributions could be made. His career included stints at Schlumberger, Arco, Sohio. Lockheed, Mobil, Exxon, Baker-Hughes, Pathfinder, and Southwestern Energy. Dave seems to have had issues with employers, but he did stay with Mobil and Exxon-Mobil for 20 years to prove to his Mom that he could hold a job. Along the way Dave acquired six patents as inventor or coinventor, and about sixty papers as author or coauthor on topics covering induction instrument responses and forward modeling, conductivity anisotropy, the theoretical petrophysics of conductivity in reservoir rocks, and most recently shaly sand models.