Pattern Recognition in a Digital Age: A Gameboard Approach to Determining. Petrophysical Parameters

Transcription

1 Pattern Recognition in a Digital Age: Abstract Archie (942) provided a path fro qualitative log interpretation to quantitative log analysis through an equation that required paraeters which were not available fro logs, and which, in the tie before calculators and coputers, required soe effort to solve. Aware of the ability of people to recognize patterns, Hingle (959), then Pickett (973) developed graphical solutions to Archie s equation which allowed the quick deterination of water saturation by observation of the data, and without the need for nuerical calculations. As calculators and coputers becae available, the priary function of those two ethods has turned fro the quick prediction of water saturation to the prediction of calculation paraeters to be used in faster and ore detailed interpretation ethodologies. At the sae tie, the extension of Pickett plots with bulk volue water lines by Greengold (986), and the suggestion by Gael (98) and Bassiouni (994) of using Hingle and Pickett plots in concert, helped to increase the nuber of paraeters predicted, and to do so in a ore coherent and cohesive anner. A Pickett plot and Hingle plots, all with water saturation and bulk volue water lines, and Buckles plots (Buckles, 965; Morris & Biggs, 967) in linear and logarithic scales, constitute a unified pattern recognition display. This gaeboard presentation in Excel ( Microsoft) presents the data in a variety of graphical displays, and provides interactivity through sliders by which paraeter values can be odified. This allows the interpreter to not only quickly recognize possible hydrocarbon-bearing intervals, but ore iportantly, to siultaneously derive a nuber of paraeters which are required for the coputation of water saturation and porosity. Well Log Interpretation Then: Done with pencil, paper, and a slide rule on the hood of a Chevy, Bulk density or sonic traveltie plus atrix and fluid values, (slow and laborious to deterine.) in the iddle of the night, in Montana, in Deceber. Archie s Equation: Porosity, Phi Sw = Rt a Rw Phi SO: Graphical pattern recognition techniques were developed to iniize the nuber of calculations needed. Graphical solutions to Archie s Equation: Sw Pickett, 973 A Gaeboard Approach to Deterining Petrophysical Paraeters Daniel A. Krygowski, Robert M. Cluff The Discovery Group, Denver, CO, USA a Rw n Sw = Hingle, 959 = Phi Rt Phi Rt a Rw n n log ( Phi) = log( Rt) n log( Sw) +log( a Rw) Conductivity increasing Resistivity increasing Porosity increasing Schluberger, 2005 Buckles, 965; Morris & Biggs, 967 AND: Bulk volue water, BVW = Phi * Sw BVWiniu iplies Sw irreducible, which iplies little or no water production. Plotting Sw vs. Phi (linear or logarithic scales) displays BVW without having to do the calculation, and identifies the depths at BVWirreducible. Krygowski & Cluff, AAPG ACE 202: Panel

2 Well Log Interpretation Now: Calculators and coputers do the calculations, and we get paid to interpret the data, not to do arithetic SO: Use graphical pattern recognition techniques to pick the paraeters for the calculations, and let the hardware and software do the heavy lifting. Intercept at Phi = 00% is a* Rw BVW lines (Greengold, 986) The slope of the lines deterines the saturation exponent, n. The eastern edge of the data deterines BVWirreducible. The northwestern edge of the data deterines the location of the water-bearing line. Slope = -/, ceentation exponent The southwestern edge of the data deterines the location of the waterbearing line. If RHOB or Delta T are plotted, the x-intercept is the atrix value. BVW lines. The southern edge of the data deterines BVWirreducible. This iteration technique (Gael, 98; Bassiouni, 994) is the basis for the gaeboard ipleented here. AND: The final step is to include the Buckles plots (both linear and logarithic scales) as another approach to deterining BVWirreducible. Krygowski & Cluff, AAPG ACE 202: Panel 2

3 Interpretation paraeters are deterined on a gaeboard where the player odifies the paraeters and iediately sees the results of the changes, and can see the consistency of the selections. Pickett plot predicting: Foration water resistivity, Rw, Ceentation exponent,, Saturation exponent, n, Irreducible Bulk Volue Water, BVWirr. Selection of: Archie paraeters Porosity source Porosity paraeters BVW irreducible Sw and BVW lines Buckles plots: To deterine BVWirr, and To suggest fluid production. Hingle plots: Showing raw porosity easureents to deterine atrix values, and Showing calculated porosity. The data shown in the gaeboard above is ideal; that is, constructed to have zones that are at irreducible water saturation, in a transition zone, and copletely water saturated. The well ight look soething like the log at the left. Krygowski & Cluff, AAPG ACE 202: Panel 3

4 The Gaeboard Workflow Load the raw data into the spreadsheet: Deep resistivity Sonic traveltie, DeltaT, and/or Bulk density, RHOB, and/or A previously-calculated porosity. On the gaeboard: Select the porosity source: DeltaT, RHOB, or input porosity. Modify the paraeters via the sliders so that the lines in each plot coincide with the data that is displayed. In the Pickett plot: The Sw = (00%) line is at the southwest edge of the data, The BVWirr line is at the east edge of the data, The values for Rw,, n, and BVWirr are within acceptable ranges. In the Hingle plots: The Sw = (00%) line is at the northwest edge of the data, The BVWirr line is at the south edge of the data, The values for atrix paraeter and BVWirr are within acceptable ranges. In the Buckles plots: The BVWirr line is at the southwest edge of the data. Conclusions The gaeboard provides a ethod to deterine porosity and saturation paraeters in concert so that the paraeters present a ore coherent estiate of those properties than the selection of paraeters individually. While the proof of concept of the technique was executed in Microsoft Excel, developent inside a petrophysical software syste would lead to ore flexibility and functionality in the behavior of the software. References Bassiouni, Zaki, 994, Theory, Measureent, and Interpretation of Well Logs; SPE Textbook Series Vol. 4: Society of Petroleu Engineers, Richardson, Texas. Buckles, R.S., 965, Correlating and averaging connate water saturation data; Journal of Canadian Petroleu Technology, v. 9, no., pp. 42 to 52. Gael, T.B.,98, Estiation of petrophysical paraeters by crossplot analysis of well log data; MS Thesis; Louisiana State University, Baton Rouge, Louisiana, May. Greengold, Gerald E., 986, The graphical representation of bulk volue water on the Pickett crossplot: The Log Analyst, v.27, n.3; Society of Petrophysicists and Well Log Analysts, Houston, Texas. Hingle, A.T., 959, The use of logs in exploration probles: paper presented at the SEG 29 th International Annual Meeting, Los Angeles, Noveber. Morris, R.L, and W.P. Biggs, 967, Using log-derived values of water saturation and porosity; Society of Professional Well Log Analysts, 8 th Annual Syposiu Transactions, Paper X. Pickett, G.R., 966, Review of current techniques for deterination of water saturation fro logs; Journal of Petroleu Technology: SPE, Noveber, pp Pickett, G.R., 973, Pattern recognition as a eans of foration evaluation; SPWLA Fourteenth Annual Logging Syposiu, Paper A. Schluberger, 2005, Log Interpretation Charts, 2005 Edition: Schluberger, Sugar Land, Texas. Krygowski & Cluff, AAPG ACE 202: Panel 4

5 An Exaple START HERE and Rw DTatrix n and BVWirr Using density Instead So, why the differences In the paraeters? Sonic Density An enlarged and rough hole probably affected the density. Is there other inforation, in this well or one nearby, that can add light to the discrepancy here? Krygowski & Cluff, AAPG ACE 202: Panel 5