Pattern recognition in a digital age: A gameboard approach to determining petrophysical parameters

Transcription

1 Pattern recognition in a digital age: A gameboard approach to determining petrophysical parameters Daniel A. Krygowski Robert M. Cluff The Discovery Group

2 Outline Definition and history of pattern recognition techniques. Review of specific techniques: Buckles plots: to determine bulk volume water, BVW Pickett plots: to determine water saturation, Sw Hingle plots: to determine water saturation, Sw Combining the plots in a gameboard An example Conclusions 2

3 Pattern recognition techniques Definition: A graphical solution of an equation that provides results based on the location of the data points in the display (and without calculations). Value: In the age before computers, to provide results quickly with only pencil, chartbook, and slide rule, on the hood of a Chevy, in the middle of the night, in Montana, in December 3

4 Pattern recognition evolution Then (pre-intel): Quick, accurate numeric answers from the display. Prediction of parameters for possible later calculations. Now: Prediction of parameters for immediate detailed computer-based calculations. Quick, qualitative evaluation of the data. Now, we get paid to interpret the data, not to do arithmetic George Asquith, ca

5 Specifics: Buckles plots Prediction of Swaverage Buckles, 1965 Morris & Biggs, 1967 Bulk volume water: BVW = Phi * Sw and BVWirr = Phi * Swirr Lines of equal BVW are hyperbolas. Hyperbolas become straight lines. Points in the transition zone. Bateman, 1984; others Points are at irreducible BVW; therefore at Swirr, and should produce water-free. Wet points (Sw = 100%) 5

6 Specifics: Pickett plots Sw Pickett, 1973 arw Rt Phi m Archie, n Intercept at Phi = 100% is a*rw The slope of the line determines cementation exponent, m. 1 log( Phi) log( Rt) m n m log( Sw) 1 log( arw) m The southwestern edge of the data determines the location of the water-bearing line (Sw = 100%) 6

7 Pickett plots, enhanced The slope of the line determines saturation exponent, n Increasing BVW Intercept at Phi = 100% is a*rw The slope of the line = -1/m. BVW lines added. The eastern edge of the data determines BVWirreducible. The southwestern edge of the data determines the location of the waterbearing line (Sw = 100%) 7

8 Increasing conductivity The Discovery Group Specifics, Hingle plots Schlumberger, 2005 Intercept at Phi = 100% is a*rw Sw Hingle, 1959 arw Rt Phi m 1 n Archie, 1942 The northwestern edge of the data determines the location of the waterbearing line (Sw = 100%) Increasing resistivity 1 Rt 1 m n Sw arw 1 m Phi 0 porosity 100 If traveltime or bulk density is plotted, the intercept is the matrix value. Increasing sonic traveltime Increasing bulk density 8

9 Increasing conductivity The Discovery Group Hingle plots, enhanced The northwestern edge of the data determines the location of the water-bearing line (Sw = 100%) Increasing resistivity porosity Increasing porosity If traveltime or bulk density is plotted, the intercept is the matrix value. y-axis scale is linear x-axis scale is RHOB BVW lines added to the plot. The southern edge of the data determines BVWirreducible. 9

10 Question: Which plot to use? Answer: YES!! Remember, we re trying to get calculation parameters: Hingle: Matrix values Pickett: m, n, Rw, BVWirr Buckles: BVWirr The idea: from Bassiouni (1994), Gael (1981) assume m RHOma m Iterate until convergence m RHOma 10

11 The gameboard approach Put all displays (Pickett, Hingle, Buckles) in a single view. Create controls for each parameter: a, m, n, Rw, BVWirr, matrix values, fluid values (both to calculate porosity from bulk density or traveltime) Add controls for Sw and BVW lines on the plots. Create in Microsoft Excel so any parameter changes are immediately reflected in the displays. Like playing a board game 11

12 Create some ideal data for a proof of concept. At irreducible water saturation Transition zone Wet zone 12

13 The gameboard, with the ideal data Parameter controls Sw and BVW line controls 13

14 A closer look at the controls Archie parameters Porosity parameters BVW Display parameters 14

15 With the ideal data irreducible transition wet 15

16 A real example Raw data: A low porosity, shaly, West Coast (USA) sand And putting the data in the gameboard 16

17 Starting with default parameter values 17

18 Modifying values to fit the data 18

19 Arriving at a solution 19

20 Results: probably not unique But perhaps more self-consistent by determining the parameters simultaneously with the gameboard, rather than determining the parameters sequentially in a workflow. Other data (cores, ) can be used to constrain some of the parameters. Parameters: a = 1.0 m = 1.63 n = 1.70 Rw = RHOma = 2.68 BVWirr = The Discovery Group Parameters: a = 1.0 m = 1.72 n = 1.67 Rw = RHOma = 2.67 BVWirr =

21 Conclusions The gameboard, using Pickett, Hingle, and Buckles plots, provides a method to determine porosity and saturation parameters in concert. Visualizing the parameters simultaneously provides a more coherent selection than determining them individually. Very similar results (in porosity, saturation) can be achieved with different parameter sets; solutions are not unique. While Excel provided a proof of concept, the gameboard would be better implemented in petrophysical analysis software. And even if you re not interested in the numbers, the plots may be a quick way to estimate wet and irreducible zones in a reconnaissance review of an area or a formation. 21

22 Thank you! Questions? On the hood of which car would you prefer to do log analysis? $136K Original ~$2K $90K-$100K 22

23 Coming to a location near you AAPG Basic Well Log Analysis George Asquith, Dan Krygowski, Rick Lewis July 13 to 17, 2015 Ben Parker Student Center Colorado School of Mines Presenting basic openhole log interpretation since the late Cretaceous ask Dan or Bob about other options 23