PATTERN RECOGNITION IN A DIGITAL AGE: A GAMEBOARD APPROACH TO DETERMINING PETROPHYSICAL PARAMETERS

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1 SPWLA 56 th Annual Logging Symposium, July 8-22, 205 PATTERN RECOGNITION IN A DIGITAL AGE: A GAMEBOARD APPROACH TO DETERMINING PETROPHYSICAL PARAMETERS Daniel A. Krygowski, Robert M. Cluff: The Discovery Group Copyright 205, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors. This paper was prepared for presentation at the SPWLA 56th Annual Logging Symposium held in Long Beach, California, USA, July 8-22, 205. ABSTRACT Graphical pattern recognition interpretive techniques have been part of petrophysics since quantitative interpretation began, as a way to quickly determine properties of interest with a minimum of calculations. When calculators and computers were introduced to petrophysics, the focus of the techniques changed from determining the quantities themselves to determining the parameters needed to calculate those quantities. As an example, Hingle plots (959) and Pickett plots (966, 973), first used to quickly determine water saturation for a few points in a reservoir, can now instead be used to determine the parameters needed in Archie s (942) water saturation equation, so that the parameters and associated well log data can be used to calculate water saturation in much more detail and with more precision than before. An extension of those graphical techniques is shown here, where Hingle, Pickett, and Buckles (965) plots (Morris and Biggs, 967) are displayed simultaneously. In this gameboard display in Excel ( Microsoft), data is displayed on all the plots. The selection and modification of computational parameters is immediately reflected in all plots, leading to a more coherent prediction of those parameters than from the same plots used independently. Pickett plots, with bulk volume water lines added as shown by Greengold (986), Hingle plots, with bulk volume water lines added as shown by Krygowski and Cluff (202), and Buckles plots (using both linear and logarithmic scales) can predict in a common environment the following parameters: Matrix parameters to derive porosity from bulk density or sonic slowness, Archie porosity (cementation) exponent (m), saturation exponent (n), and water resistivity (Rw), and irreducible bulk volume water (BVWirr). The display uses those three plots not commonly displayed simultaneously, and has the plots linked so that changes made to the parameters determined from one plot are reflected in the other plots and the computations derived from those plots. By being able to change the values of any of the parameters while seeing how those changes impact the other parameters and the calculated porosity, water saturation, and bulk volume water, the user can quickly try different interpretive scenarios and determine which results best honor all the data at hand. Other information, such as from core measurements, can limit or set the values of some of the parameters while still allowing the values of other parameters to be determined in the context of that other data. INTRODUCTION From its beginnings, petrophysics has used graphical ( pattern recognition ) displays to identify zones of interest, to initially speed the determination of reservoir properties of interest, and currently to determine parameters needed in the calculation of those properties. Such displays range from depth displays of raw log data ( QuickLook methods) to x-y plots ( crossplots ) of acquired data. In the era before calculators and computers, calculations were tedious and time-consuming, compounded by urgency when drilling activities were suspended waiting for interpreted results. While slide rules and nomographs helped speed the calculation process, development of pattern recognition techniques provided the means for interpreters to quickly assess a well and focus on intervals of critical interest. With the advent of machine-assisted calculations, individuals could concentrate on interpretation instead of arithmetic, and the focus of pattern recognition techniques turned from determining reservoir properties of interest (like porosity and water saturation) to predicting the parameters needed to calculate those properties in a more detailed and robust manner. This paper shows a proof-of-concept in the combination of three pattern recognition techniques; Buckles, Hingle, and Pickett plots, which are used to simultaneously determine three Archie saturation equation parameters (m, n, Rw), matrix parameters for

2 SPWLA 56 th Annual Logging Symposium, July 8-22, 205 conversion of bulk density or acoustic slowness to porosity, and irreducible bulk volume water to help predict water production from hydrocarbon-bearing zones. By predicting the parameters simultaneously, the interpretation process can be shortened through the immediate iteration process, and the interpretation parameters are more coherent, having been determined together. The spreadsheet is referred to as a gameboard because as with a board game, changes are made directly on the board and other parts (like game pieces) respond immediately. THE PLOTS: HISTORY AND CURRENT USAGE Buckles Plot Buckles (965), in creating a method to determine average water saturation, found that in intervals at irreducible water saturation, the product of water saturation and porosity would be a constant related to pore surface area. When porosity was plotted against water saturation for those points, the resulting curve was a hyperbola while points in a transition zone plotted at values above the points at irreducible saturation. Morris and Biggs (965) extended the use of the constant (often referred to as the Buckles number ) to not only identify transition zones from zones at irreducible saturation, but also to estimate permeability. They also noted that the porosity-water saturation product was the bulk volume water fraction of the porosity, or bulk volume water, BVW. Bulk Volume Water, BVW Sw [] Figure shows Buckles plots in two forms; the linear plot shown by Buckles, and Morris and Biggs, and the plot with logarithmic scales, as shown by Bateman (984) and others. In the linear plot, the equal BVW values are hyperbolas, while in the full logarithmic plot, the iso-bvw lines are linear. The displays provide the same information; the choice of which to use is up to the interpreter, as the one easiest to personally interpret. For intervals at irreducible water saturation, Swirr, and with a range of porosities, the bulk volume water is irreducible, BVWirr. Pickett Plot Pickett (966, 973) proposed a graphical solution to Archie s equation. Equation 2shows the solution in terms of resistivity, and Equation 3 shows the equation solved for porosity, adapted to the graph paper available at the time (and the usual form of the crossplot). 2 log( Rt) m log( ) n log( Sw) log( a Rw) log( ) log( Rt) n *log( Sw) log( a Rw) m m m [2] [3] As shown in Figure 2, the plot is full logarithmic; that is, both scales are logarithmic, with resistivity on the x- axis and porosity on the y-axis. In use, data points are plotted by porosity and resistivity. From the location of the points, a water-bearing line can be drawn at the southwest edge of the data. From that line, and an assumption of a value for the saturation exponent, n, a family of lines of decreasing water saturation can be drawn, which are parallel to the water-bearing line. As originally designed, the water saturation, Sw, of each plotted point can be read directly from the plot. The use of Archie s equation is bypassed, as is the knowledge of formation water resistivity, Rw. In addition, two parameters in Archie s equation are predicted by the plot: the porosity exponent, m, from the negative inverse of the slope of the water-bearing line, and formation water resistivity, Rw, from the intercept of the water-bearing line at porosity equal to (00%), with a user estimate of tortuosity factor, a. To use Pickett s plot, the interpreter plotted points on full logarithmic paper, placed the water-bearing line based on the location of the data points, and placed the lines of decreasing water saturation based on the location of the water-bearing line and an assumed value for the saturation exponent, n. The saturation value at each point could then be read directly from the plot. With the advent of machine-aided computations, the Pickett plot can still be used to quickly determine from the pattern of data points if there are any intervals with promising water saturations, but it is not necessary to actually read Sw values from the crossplot. The crossplot does provide an estimate of the porosity exponent from the slope of the Sw lines, and an estimate of Rw from the intercept of the Sw = line at porosity =. Greengold (986) added bulk volume water lines to the Pickett plot. Rearranging equation []: BVW Sw And substituting for Sw, equation [2] becomes: log( Rt) ( n m) log( ) n log( BVW ) log( a Rw) [4] [5] As shown in Figure 3, zones at the lowest value of BVW, on the eastern edge of the data, are at

3 irreducible bulk volume water, BVWirr, (and therefore Swirr), and should produce only hydrocarbons. If there is a sufficient range of porosity at irreducible water saturation, the slope of the BVWirr line can be determined. The slope is (m-n), so knowing m from the slope of the water-bearing line, the saturation exponent, n, can be estimated. If n = m, the BVW lines will be vertical. Those points at the southwestern edge of the data are in the water-bearing zone, and will produce only water. The points between those two edges are in the transition zone, where some combination of water and hydrocarbons will be produced. Hingle Plot Previous to Pickett s method, Hingle (959) proposed the first widely-used graphical solution to Archie s equation. To do so, he solved the equation for resistivity in this form: m Sw n m Rt a Rw [6] Hingle s work, including the form of the equation, appears to be an extension of the work of Tixier et al, 958, in determining water saturation from resistivity and sonic slowness. Tixier s method required the knowledge of formation water resistivity, Rw, but by using Hingle s method the value of Rw can be determined from the data. As shown in Figure 4 (right plot), the x-axis is porosity increasing to the right. Instead of using a calculated porosity, raw bulk density (as shown) or acoustic slowness can be used. The y-axis is a non-linear scale, shown in the figure in both resistivity and conductivity. In use, data points are plotted by porosity and resistivity. From the location of the points, a water-bearing line is drawn at the northwest edge of the data. From that line, and the assumption of a value for saturation exponent, n, a family of lines of decreasing water saturation can be drawn, which fan out from the intercept of the waterbearing line at the x-axis. As originally designed, the water saturation, Sw, of each plotted point can be read directly from the plot. The use of Archie s equation is bypassed, and the knowledge of formation water resistivity, Rw, is not needed, nor is a calculated porosity. In addition, if bulk density or acoustic slowness is plotted instead of porosity, the x-intercept of the water-bearing line predicts the matrix value. From that value, and an estimate of fluid value, the porosity can be calculated, with the data having predicted the matrix value, instead of the interpreter estimating the value. The value of formation water resistivity, Rw, can be predicted from the intercept of the water-bearing line at 3 porosity equal to (00%), with a user estimate of tortuosity factor, a. This prediction, however, was rarely done using the chart, as the porosity scale that was usually used, spread the points in the expected porosity range over the available space, and the resistivity scale of the plot was often insufficient to both plot data points accurately and visually determine Rw. The plot at the top left of Figure 4 shows in the y-axis the calculated value of (/Rt)^(/m), and is displayed on a linear scale. The value is calculated and displayed in Microsoft Excel, and its interpretation is the same as with the right-hand plot, but resistivity values cannot be read directly from the plot. This plot also has the porosity scale extended to 00% porosity ( =.0). The intercept of the water-bearing line at 00% porosity is a*rw. The plot at the bottom left shows the same data, but with scales that spread the data over the plot space in a manner most usually seen in use. To use Hingle s plot, the interpreter needed to use specially-constructed graph paper (usually available in logging company chartbooks), and had to assume a value for porosity exponent, m, as the y-axis changes with that value. The interpreter then placed the waterbearing line based on the location of the data points, and placed the lines of decreasing water saturation based on the location of the water-bearing line and an assumed value for saturation exponent, n. The saturation value at each point could then be read directly from the plot. With the advent of machineaided computations, the Hingle plot can still be used to quickly determine if there are intervals with promising water saturations, but it is not necessary to actually read Sw values directly from the crossplot. The crossplot does provide an estimate of matrix density or matrix slowness; a parameter needed in determining porosity. Analogous to the work of Greengold (986) on Pickett plots, Krygowski and Cluff (202) added bulk volume water lines to Hingle plots. This is shown in Figure 5. The points at the lowest value of BVW, on the southern edge of the data, are at irreducible bulk volume water, BVWirr, (and therefore Swirr), and should produce only hydrocarbons. Those at the northwestern edge of the data are in the water-bearing zone, and will produce only water. The points between those two edges are in the transition zone, where some combination of water and hydrocarbons will be produced.

4 SPWLA 56 th Annual Logging Symposium, July 8-22, 205 BEHAVIOR OF THE GAMEBOARD Figure 6 (left illustration) shows the concept of the behavior of the gameboard. This iterative process, from Gael (98) and Bassiouni (994) shows an iteration between Hingle and Pickett plots to converge on cementation exponent and matrix density. The implication, from the figure, is that the iteration takes place one step at a time, with the interpreter picking a value for one variable from one plot and using it in another to determine the value of a second variable. By using a spreadsheet with a simultaneous display of the plots, changes made in one plot can be immediately reflected in other plots, thereby decreasing the time needed for the iteration. Figure 6 (right illustration) shows the gameboard control area in detail. The user can change the Archie parameter values, matrix and fluid parameter values, and irreducible bulk volume water values by the slider bars and arrows. The porosity calculation (input calculated porosity, density porosity, or sonic porosity) can be selected, which activates the appropriate matrix and fluid values. The user can also change the water saturation and BVW lines that are displayed. Figure 7 shows the entire spreadsheet with data plotted, but modification of the parameters not yet begun. The spreadsheet consists of a control area (upper left), two Buckles plots (linear and logarithmic), three Hingle plots (one for calculated porosity, one with bulk density, and one with sonic traveltime (slowness)), and a Pickett plot. The Pickett and Hingle plots all have both water saturation lines and bulk volume water lines. Porosity, water saturation, and bulk volume water are calculated each time a parameter value is changed. The data in Figure 7, shown in log format in Figure 8, are constructed to have a range of porosity, with a water zone, a transition zone, and a zone of irreducible bulk volume water. The value of Swirr varies with porosity so that BVWirr is a constant. The gameboard in Figure 7 has parameters defaulted to common values; m = n = 2.0, a =.0, RHOma = 2.7 (limestone), and Rw = 0.0 as an arbitrary value. The Hingle bulk density plot shows the choice of RHOma to be incorrect (not aligning with the plotted points), as does the Pickett plot, where the southwestern points show a curved line instead of a straight line (Pickett, 966). The misalignment of the suspected waterbearing points on the Pickett and Hingle plots is similar to points at the east side of the Buckles plots as well. 4 The user could start the iteration of the data by changing any of the variables, but probably the variables having the most effect would be RHOma and Rw. As the Sw lines and data points begin to converge, the user would see from the Pickett plot that a change in m would be of benefit. Once the data was aligned with the Sw lines, n and BVWirr could be modified to bring the BVW lines in alignment with the appropriate sides of the data cloud. The results of the modification of the parameters are shown in Figure 9, where the points in all the plots show an alignment with the Sw and BVW lines, and with the intercepts which specify RHOma and Rw. Again, the order in which the parameters are changed is up to the individual interpreter, and interpreters may find one sequence of change to be especially efficient. When actual data is used, and depending on the range of porosities and saturations, there may be some ambiguity in the results, with different sets of parameters delivering the same fit of the lines and intercepts to the data. As always, any other available appropriate data should be used to arrive at a solution which honors all the data at hand. CONCLUSIONS By using a number of pattern recognition techniques; namely Pickett, Hingle, and Buckles plots, one can determine parameters for the calculation of porosity and water saturation in an interactive mode, which makes that determination faster and more coherent than using the same techniques individually. The methods, used individually or in concert, provide a method to quickly identify zones of interest in what are often long intervals with no production potential. The identification of zones can be quantitative, through the determination of specific values for calculation parameters, or can be qualitative, through observation of the pattern of points on the plots with respect to water saturation and bulk volume water lines. While Microsoft Excel was used to implement this method as a proof of concept, the methodology would be better suited for implementation in an existing petrophysical or geological software program, either as a user program (given the appropriate software functionality), or as an enhancement to existing functionality.

5 DEFINITIONS a m n Archie equation tortuosity factor Archie equation porosity (cementation) exponent Archie equation saturation exponent Rw Formation connate water resistivity (ohmm) Rt Sw Swirr BVW BVWirr RHOma True or undisturbed formation resistivity (ohmm) total porosity (decimal) formation water saturation (decimal) irreducible water saturation (decimal) bulk volume water (decimal) irreducible bulk volume water (decimal) formation matrix or grain density (g/c3) REFERENCES Archie, G.E., 942, The electrical resistivity log as an aid to determining some reservoir characteristics: Petroleum Technology, January; SPE of AIME. Bassiouni, Zaki, 994, Theory, Measurement, and Interpretation of Well Logs, SPE Textbook Series Volume 4, Society of Petroleum Engineers, Richardson Texas. Bateman, R.M, 984, Watercut prediction from logs run in feldspathic sandstone with fresh formation waters; SPWLA 25th Annual Logging Symposium, New Orleans, Paper EE. Buckles, R.S., 965, Correlating and averaging connate water saturation data; Journal of Canadian Petroleum Technology, 9(), pp Gael, T.B.,98, Estimation of petrophysical parameters 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 volume water on the Pickett crossplot: The Log Analyst, 27(3); Society of Petrophysicists and Well Log Analysts, Houston, Texas. Hingle, A.T., 959, The use of logs in exploration problems: paper presented at the SEG 29th International Annual Meeting, Los Angeles, November. Krygowski, Daniel A., Robert M. Cluff, 202, Pattern recognition in a digital age: a gameboard approach to determining petrophysical parameters: Poster Session Theme, P98, AAPG Annual Conference and Exhibition, Long Beach, April. Morris, R.L, and W.P. Biggs, 967, Using log-derived values of water saturation and porosity; Society of Professional Well Log Analysts, 8th Annual Symposium Transactions, Paper X. Pickett, G.R., 966, Review of current techniques for determination of water saturation from logs; Journal of Petroleum Technology: Society of Petroleum Engineers, November, pp Pickett, G.R., 973, Pattern recognition as a means of formation evaluation; SPWLA Fourteenth Annual Logging Symposium, Paper A. Schlumberger, 2005, Log Interpretation Charts, 2005 Edition, Appendix A, p.264: Schlumberger, Sugar Land, Texas. Tixier, M.P., R.P. Alger, C.A. Doh, 958, Sonic logging: presented at 33rd Fall Meeting of the Society of Petroleum Engineers, paper T.P

6 SPWLA 56 th Annual Logging Symposium, July 8-22, 205 ABOUT THE AUTHORS Daniel A. (Dan) Krygowski Senior Petrophysical Advisor, The Discovery Group Dan has over 35 years of experience in the art and science of petrophysics, and in the design and development of petrophysical software. Dan earned a B.A. in Physics from the State University of New York at Geneseo. After earning M.S. and Ph.D. degrees in geophysics (with a focus on petrophysics) from the Colorado School of Mines, he joined Cities Service Company, and worked in Denver and Tulsa. After Citco, he joined Atlantic Richfield Company (ARCO). In both companies, he gained experience in a variety of geologic and geographic areas in both technical and management positions in petrophysics. After ARCO, he joined Landmark Graphics, and was a member of the PetroWorks development team, providing petrophysical expertise and was also involved in interface design, and development of documentation and training materials. When Landmark closed its Austin, Texas office, Dan joined Chevron, working in deep Gulf of Mexico and Chad, Africa projects. He also supported internal petrophysical training efforts. Dan joined The Discovery Group in late Since the late Cretaceous, Dan has taught the AAPG Basic Well Log Analysis course annually with Dr. George Asquith of Texas Tech University. Dan also teaches Basic Openhole Log Interpretation, a similar, but shorter course, and Petrophysics Elements, a longterm, low-intensity course. In 2004, the AAPG published George and Dan's book, Basic Well Log Analysis, a second edition of George's 983 similarly-named book which was one of the AAPG's all-time best selling publications. Dan is a member of the Society of Petrophysicists and Well Log Analysts (SPWLA), American Association of Petroleum Geologists (AAPG), Society of Petroleum Engineers (SPE), Society of Exploration Geophysicists (SEG), the Rocky Mountain Association of Geologists (RMAG), and the Denver Well Logging Society (DWLS). Dan is a Texas Registered Professional Geoscientist (#504). Robert M (Bob) Cluff President, The Discovery Group Bob Cluff is a geologist and petrophysicist with over 35 years experience in oil and gas exploration, development, and research. His principal areas of expertise are petrophysics, petroleum geology of carbonate and clastic reservoirs, and the integration of petrophysical data with geological data in detailed reservoir studies. He has worked and published extensively in the fields of non-conventional gas from both tight sandstones and shales, petrophysics, source rock analysis and basin modeling. He has conducted and supervised projects in most sedimentary basins of North America as well as South America, Europe, Southeast Asia, and Australia. Bob received his BS degree in Geology from the University of California at Riverside (high honors), an MS in Geology from the University of Wisconsin at Madison, and a BA in Mathematics from the Metropolitan State College of Denver. From 976 to 98 he was a geologist with the Coal and Oil and Gas Sections of the Illinois State Geological Survey, worked as an independent consulting geologist from , founded The Discovery Group in 987. Bob is active in several professional societies including the American Association of Petroleum Geologists, Society of Petroleum Engineers, the Rocky Mountain Association of Geologists (past-president 2006), the Denver Well Logging Society (past-president), and the Society of Petrophysicists and Well Log Analysts (Vice President Technology; Vice President Membership, Regional Director North America). He is a registered geologist in the states of Texas (873), Illinois ( ), and Wyoming (33), and is a DPA Certified Petroleum Geologist (368). 6

7 porosity FIGURES Figure : Buckles plots with linear scales (left) and logarithmic scales (right). BVWirr BVWirr Figure 2: Pickett plot with saturation lines placed based on the location of data points. Pickett Plot a*rw Sw = Sw = 0.8 Sw = Slope = -/cementation exponent, m Sw = 0.4 Sw = 0.2 Data Sw = Resistivity 7

8 (/Rt)^(/m) Increasing conductivity, ms Increasing resistivity, ohmm (/Rt)^(/m) SPWLA 56 th Annual Logging Symposium, July 8-22, 205 Figure 3: Pickett plot with Bulk Volume Water lines added. a*rw Increasing BVW BVWirr Slope = (m-n) Slope = -/cementation exponent, m Sw =.0 Figure 4: Hingle plots: In the original format (right) with porosity from zero to 00%, and with a calculated y-axis (left) with two different ranges of porosity and calculated Hingle value [ (/Rt)^(/m) ]. 3 Hingle (RHOB) Schlumberger, Phi = 00% Bulk density Calculation from Rt and m Sw =.0 Hingle (RHOB) Resistivity scaling reflects m = Bulk density Porosity Increasing porosity

9 Figure 5: Hingle plot with Bulk Volume Water lines added. Sw =.0 Increasing BVW BVWirr RHOma Figure 6: Gameboard concept and gameboard controls. assume m RHOma m Iterate until convergence m RHOma Gael, 98, from Bassiouni, 994 9

10 wet transition irreducible SPWLA 56 th Annual Logging Symposium, July 8-22, 205 Figure 7: Pattern recognition gameboard with ideal data and initial (default) parameter values. Figure 8: Ideal log data: a range of porosities in wet, transition, and irreducible BVW zones. 0

11 Figure 9: Pattern recognition gameboard with ideal data and final parameter values.