Dan Krygowski Denver Colorado USA

Transcription

1 Archie, Hingle, and Pickett: Determining fluid saturation for fun and profit Dan Krygowski Denver Colorado USA

2 Where Dan hopes to go today Answer the question, So, why do we care about fluid saturation, anyway? Hawking A review of Archie s equation. A look at some graphical solutions to Archie s equation (Hingle and Pickett plots) which quickly provide saturation answers, and also predict some Archie parameters that we d otherwise have to estimate. A few closing remarks (and a run for the door). 2

3 Formation fluid saturation Formation fluid saturation is an important quantity: But It is necessary to determine the volume of fluids (water and hydrocarbons) present; It may give us some indication as to what will be produced. We often have to estimate several parameters that are needed to make the saturation calculation. 3

4 A reminder of history 1927 Conrad and Marcel Schlumberger run the first log in Pechelbron field in France. Electric coring is born Gus Archie presents a paper at the AIME meeting in Dallas quantifying the relationship between fluid saturation and formation resistivity. So it took 15 years to go from a qualitative response to a quantitative, but empirical, relationship. 4

5 Archie s equation Defining the terms: tortuosity factor formation water resistivity water saturation S w = a R Rt φ w m 1 n saturation exponent cementation exponent formation resistivity porosity 5

6 Archie s equation Defining Traditional the sources: terms: tortuosity corefactor formation samples, water SP resistivity logs water saturation S w = a R Rt φ w m 1 n saturation corexponent cementation coreexponent formation electric resistivity logs, induction logs, laterologs sonic, porosity density, neutron, nuclear magnetic resonance, resistivity logs 6

7 Another history lesson: pc No, not precambrian, precomputer: When big, burly guys (usually engineers) stood over you while you looked at the log data, and said, Hey, do I run pipe or call for cement? You re costing me money here So, we needed techniques to get quantitative answers quickly. If they helped in other ways, so much the better A pattern recognition approach. 7

8 So it s not just equations two examples for illustration: 1. Last Chance High Country #1 A constructed well to illustrate the techniques. 2. Bill Barrett Last Dance 43C Mamm Creek, Piceance Basin, Colorado (a small section of the Mesaverde) A well to bring us back to reality. 8

9 Last Chance High Country #1 9

10 Barrett Last Dance 43C Mamm Creek, Piceance Basin, Colorado 10

11 Enter Tom Hingle [1959, SEG 29 th Annual Meeting] A graphical solution to Archie s equation so that plotting resistivity against porosity will produce arrangements of the data (which are recognizable as patterns): y = 1 Rt 1 m = n S w a R w m*x +b (b=0) 1 m φ Y-axis A family of lines from which information can be discerned. X-axis 11

12 Hingle plot The y-axis is built from 1 1 m but scaled in resistivity or R t conductivity so the points can be plotted directly on the graph. The y-axis becomes (very) non-linear. The x-axis is scaled so that porosity increases from left to right. Porosity, bulk density, or sonic traveltime can be plotted. Conductivity The y-axis on this plot is constructed using m=2.0 The water-bearing line is placed by the location of the data points. Zero porosity (= RHOmatrix or DTmatrix) Water-bearing line (data) Resistivity, Rt Lines of decreasing water saturation porosity 12

13 So, with the Hingle plot One can determine water saturation directly from the plot, without knowing Rw, or having to calculate porosity. In addition, the plot will predict matrix values of sonic or density, so porosity can be more confidently calculated. But, one has to assume values for a, m, n, And special paper must be used, which depends on the assumed value of m. 13

14 Looking at our ideal data Hingle Plot; m = 2.0 Sw = Rt Bulk Density Baker Atlas,

15 Looking at real data 0.25 Hingle plot Sw = 1 0 (1/Rt)^(1/m) Vshale Bulk Density 1 15

16 Enter Dick Pickett [1966, SPE (JPT) 1973, SPWLA] A graphical solution to Archie s equation so that plotting resistivity against porosity (both on logarithmic scales) will produce linear arrangements of the data: y = log(φ ) m*x + b 1 = log t w log m ( R ) n log( S ) + ( a R ) w (graph paper format) Y-intercept Y-axis X-axis A family of lines from which information can be discerned. 16

17 Pickett plot Both scales are logarithmic. To save calculations DT-DTma or RHOma-RHOB could be used on the y- axis instead of porosity. The intercept of the waterbearing line at Phi = 1 is a*rw. Porosity The water-bearing line is placed by the location of the data points. Water-bearing line. Slope = -1/cementation exponent (data) No special graph paper is needed. Lines of decreasing water saturation The plot can be done in Excel. Resistivity 17

18 So, with the Pickett plot One can determine water saturation directly from the plot, without knowing Rw, or knowing m. In addition, the plot will predict Rw and m. But, one has to assume matrix values if sonic or density is used for porosity. And the plot can be done on readily available graph paper, or more easily in MS Excel. 18

19 Looking at our ideal data Pickett Plot 1 Sw = PhiD Rt 19

20 Looking at our real data 1 Pickett plot 0 Sw = Density Porosity 0.1 Vshale Deep Resistivity

21 So, what happens now? Well, we have two graphical methods to quickly determine water saturation, and other parameters: Hingle: Porosity matrix values Pickett: Rw, and cementation exponent, m Q: Can we use them in concert? A: Well, sort of 21

22 Pickett and Hingle in concert Bassiouni (1974, SPE) shows a method to use both to resolve several parameters, BUT it is painful to do by hand. m ρ ma AND, while interactive Pickett plots are common in many software packages, few packages have Hingle plots, and only one has linked interactive Pickett and Hingle plots. SO it s possible, but tedious. m Iterate until convergence ρ ma m 22

23 In conclusion Pickett and Hingle plots are two slightly different graphical solutions of Archie s saturation equation. While fluid saturation is needed for the calculation of volumetrics, it is less useful in predicting production. And, are other quantities, like Bulk Volume Water, more helpful there? 23

24 In conclusion Pickett and Hingle plots also predict some other Archie or porosity parameters. Each can give a quick and useful view of the data, even when you have a computer to do the grunt calculation work for you. In the information age, pattern recognition is alive and well, and it may provide some insights to the subsurface that numbers won t. 24