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1 SPE Using Artificial Intelligence to Corellate Multiple Seismic Attributes to Reservoir Properties R. S. Balch, SPE, New Mexico Petroleum Recovery Research Center, and B. S. Stubbs, SPE, Pecos Petroleum Engineering, and W. W. Weiss, SPE, and S. Wo, SPE, New Mexico Petroleum Recovery Research Center Copyright 999, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the 999 SPE Annual Technical Conference and Exhibition held in Houston, Texas, 3 6 October 999. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 3 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box , Richardson, TX , U.S.A., fax Abstract Well data gives precise information on reservoir properties at specific field locations with high vertical resolution. 3D seismic surveys cover large areas of the field but reservoir properties are not directly observable due to poor vertical resolution. For this paper, a new methodology has been developed and tested for relating reservoir properties at the well-bore to sets of seismic attributes, in order to predict reservoir properties in two zones of the Nash Draw field in SE New Mexico. Over 35 seismic attributes can be used in regression analyses of reservoir properties. Since using all attributes is computationally unfeasible and labor intensive, fuzzy logic is used to select the most statistically significant attributes for developing regression equations for individual reservoir properties. Non-linear regressions were used, as individual attributes had low correlation coefficients when cross-plotted with reservoir properties, and neural network architectures were developed to relate the selected attributes to each property. In each case the output data used for training was a reservoir property, porosity (φ), water saturation( Sw), or net pay, from 9 wells in the field. Each property was estimated using a neural network trained to CC=.8 or higher using the highest ranking seismic attributes as inputs. The validity of the solutions were tested by removing three wells from the training data, re-computing the weights, and predicting the three absent points. These tests were applied three times for each reservoir property, with different points removed. Each network accurately predicted these nine test points and the solutions are considered robust. φ, Sw, and net pay maps were generated using the regression relationships and the seismic attributes at each seismic bin location. Pore volume (φh) and hydrocarbon pore volume (hφso) maps were derived from those reservoir property maps. These new techniques maximize both the well control and seismic data and generated useful maps for targeted drilling programs in the field. Introduction The Nash Draw field in SE New Mexico produces oil and water from two sandstones of the Delaware Mountain group. The field is currently being developed, and overlying Playa lakes and Potash mining concerns require the use of horizontal drilling to target un-drained areas of the reservoir beneath these surface features. Since long horizontal wells are expensive it was decided to pursue advanced reservoir characterization prior to drilling. In 996 a high quality 3D seismic survey was shot over the field covering an area of about eight square miles. Initially, amplitude alone was used as an indicator of reservoir grade porosity 2, however, a well drilled on the basis of amplitude data alone was not an economic success. Geostatistics can provide good interpreted estimates of interwell reservoir properties, but existing Nash Draw wells primarily cover the center part of the available seismic survey, so a new technique to extrapolate reservoir properties beyond the area directly constrained by wells was developed. The new technique utilizes non-linear multivariable regression (artificial neural networks) using seismic attributes as inputs and porosity, water saturation, and net pay as outputs. The regression equations allow the prediction of these three reservoir properties in areas without direct well control, using the laterally extensive seismic attribute data, and the computation of related maps such as φh and hφso. Seismic Attribute Selection The two primary sources of data required for this method are well and seismic attribute data. The well data used in this study is tabulated in Table. Over 8 seismic attributes were extracted from the Nash Draw seismic data for the two horizons of interest. Extracted attributes were averaged across the entire interval for each of the horizons of interest (the Brushy Canyon K and L Sands), and the well data from each

2 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 2 of the 9 wells used in the study were also averaged across the respective intervals. Thus the output maps presented later in this paper represent interval-averaged values for the respective reservoir properties. It is both statistically dangerous and not computationally feasable to use all 8 attributes to form regression relationships, therefore we have developed software based on a fuzzy-ranking algorithm 3 to select attributes best suited for predicting individual reservoir properties. The algorithm statistically determines how well a particular input (seismic attribute) could resolve a particular output (reservoir property at the well bore) with respect to any number of other inputs using fuzzy curve analysis. To illustrate the technique a simple example is given. Consider a set of random numbers in the range {,} using x={x i }, i=,2,,99, and x i =.*i, and plot each value (y I = Random(x i )) (Figure a). Next add a simple trend to the random data (y i =(x i )^.5+Random(x i )) and plot those values (Figureb). For each data (x i, y i ) a fuzzy membership function is defined using the following relationship F ( x) i x x b i 2 = exp( ( ) ) y Sample fuzzy membership functions are shown in Figures a-b. Here, b=., since b is typically taken as about % of the length of the input interval of x i. A fuzzy curve is built up using a summation of all individual fuzzy membership functions in (x i, y i ), and this final curve can be interpreted for the utility of given inputs for linear or non-linear regressions. The fuzzy curve function is defined below: FC( x) i= N i= = N F ( x) Where N is the size of the data set or the total number of fuzzy membership functions. Figure 2 shows the curves for the data sets shown in Figures a-b. This simple example illustrates the ability of the fuzzy ranking approach to screen apparently random data for obscure trends such as the correlation between seismic attributes and reservoir properties. Based on the deviation from a flat curve, each attribute is assigned a rank, which allows a direct estimation of which attributes would contribute the most to a particular regression. The fuzzy ranking algorithm was applied to select the optimal inputs (attributes) for six output cases: K porosity, K net pay, K water saturation, L porosity, L net pay, and L water saturation. Having selected the most statistically significant attributes, an important question remains. How physically significant are the attributes? A thorough literature review shows some direct relationships between attributes and i i F ( x) / y i i properties in lab-scale experiments. 4 But, in general relationships are very complex and vary from field to field, and even between formations within a single field so the exact relationship between frequency and porosity, for example, may be ill defined. Ideally, the rigorous use of rock physics could demonstrate fundamental quantitative relationships between seismic attributes and reservoir properties using forward modeling. However, though it seems obvious that all features of seismic signals are a result of changes in rock properties through which the seismic energy is transmitted, these relationships are not straightforward, even for relatively easily computed attributes such as instantaneous frequency. However, individual attributes have been used for a number of years in diverse reservoirs around the world to indicate variations in stratigraphy, porosity and other reservoir properties, and as such are generally accepted as meaningful. 5 At present, any study which uses seismic attributes needs to evaluate individual attributes for statistical significance and thoroughly test results. Multivariable Non-Linear Regression Linear regression for reservoir properties was not feasible for this study, as the relationships between input and outputs were poorly defined by individual attributes (Figure 3). It was decided to use non-linear regressions using software we developed based on the fast-converging, feed-forward, backpropagation conjugate gradient algorithm 6 (neural network). Input attributes were selected using the fuzzy ranking algorithm (Figure 4). Figure 5 shows a sample neural network architecture, circles represent neurons, or locations of non-linear functions, while each line represents a coefficient applied to these neurons. A back-propagation feed-forward algorithm such as the conjugate gradient algorithm used here is trained using known inputs and outputs in an iteritive fashion, with weights being sequentially adjusted until the desired fit (if possible) is achieved. The sample architecture displayed in Figure 5 is a 2-2- architecture, since there are two neurons in the input layer, 2 neurons in the hidden layer, and one output neuron. The regression equation (inverse model) for this network is as follows: Out=f(v f(w in+w 2 in2)+v 2 f(w 2 in+w 4 in2)) Two neural network architectures were utilized in the study, a 3-2-, and a 4-2- (Figure 6), both of which were minimized in order to maintain a satisfactory ratio of training data to weights (coefficients of the regression equation). For this study, reservoir properties are well known at the locations of the well-bore intersections with the K and L intervals. Seismic data that covers a much larger area is also available, and has data at the locations of the well-bore intersections as well. Seismic attribute data from the same seismic bin that contains the well is correlated to well-bore values of porosity, net pay or water saturation in an iterative process using either a 3-2-,

3 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 3 or a 4-2- neural network. Table 2 shows which of the 8 attributes and two networks were used in regressions for each reservoir property in the K and L intervals Training and Testing It is desireable to test how robust a regression relationship is by holding some data out for testing. Since there were 9 control points (wells) it was decided to test by removing sets of three wells, training the network with 6 control points, and then using that network to predict the three withheld points. This exercise was applied three times for each property and interval, withholding differing sets of three points for each test. Figure 7a-d shows the final results of training with all 9 points, and the three test sets for the L interval porosity regression. It is evident from these cross-plots that the network has resolved porosity in a robust fashion, and that the resulting regression equation may be used to predict porosity in other areas of the field. Figure 8a-e shows the 9 point networks for the other reservoir properties of the L and the K intervals. These regressions were also tested in the same manner, and had similar results. Results The regression relationships (architecture and weights) were used to compute maps of field wide porosity, net pay, and water saturation for the K and L intervals. Additional diagnostic φ*h and h*φ*so maps were also computed to aid design of a development program. In general these maps fit the expectations from earlier geostatistical studies, and the reservoir understanding of the operator. Figure 9a-b shows L and K interval porosity maps predicted using the computed regression relationships. Both K and L horizons show patterns of distinct, or isolated porosity, and the L porosity map compares favorably with compartment maps produced independently. Figure a-b shows L and K interval net pay maps. The K horizon shows much more variation in net pay thickness than the L, which is reasonable considering that the K is considered discontinuous and thins and thickens in the field, while the L thickness is considered to be continuous across the study area. Figure a-b shows L and K interval water saturation maps. In general the K appears wet, except in distinct pods, which may represent possible drilling targets. The L zone water saturation is uniform, at about 45% across the field except in the northwest and southeast. The increased saturation in the northwest corner, which is up-dip, may be due to compartmentalization as indicated in Figure 8a. Figure 2a-b and Figure 3a-b show φh and hφso maps for the L and K horizons. The φh maps in Figure 2a-b are useful as an indicator of where sufficient pore volume exists within the field. The K horizon shows a good deal of variability, with relatively lower φh in areas where the K is interpreted to pinch out. The L interval φh shows a more uniform distribution of pore volume, though some thinner and thicker areas do exist. Fine detail across the map may assist in determining compartmentalization of porosity, as net pay is relatively uniform across the study area. The hydrocarbon pore volume maps in Figure 3a and Figure 3b for the L and K intervals, respectively, include information on oil saturation (-Sw) and essentially illustrates where the oil was in the field at the time the seismic survey was collected. Pressure variations are yet to be mapped. The wet K interval shows only isolated pods of good producing potential, while the less wet L interval shows strong undrilled potential production in the SE corner of section, the SW and NW corners of section 7, and the west half of section 4. Areas to avoid drilling for the L interval might include the east half of sections 7 and 8, the SW corner of section 3, the SE corner of section 4 and the northern half of section. Conclusion Non-linear regression for reservoir properties using multiple seismic attributes as inputs was found to be useful for extrapolating φ, Sw, and net pay across the Nash Draw field, even though wells were predominantly located only in the center of the study area. These three reservoir properties, along with associated maps (φh and hφso) allowed the operator to make more informed decisions on the drilling locations of planned expensive horizontal wells as they continue field development. Acknowledgements We would like to thank Mark Murphy of Strata Production Company for allowing us to present these results. Mr. Murphy gave valuable insights for interpreting and validating our predictions. New Mexico Tech has a generous software grant from Landmark which has greatly enhanced our research capabilities. This work was part of DOE Cooperative agreement DE-FC95BC494 with Strata Production Co. References. Final Technical, Phase I Report: Advanced Oil Recovery Technologies for Improved Recovery From Slope Basin Clastic reservoirs, Nash Draw Brushy Canyon Pool, Eddy County, NM. Department of Energy. PRRC Report (98-47). 2. Hardage, B. A., Simmons, J. L., Pendleton, V. M., Stubbs, B. A., and Uszynski, B. J.: 3D Seismic Imaging and interpretation of Brushy Canyon Slope and Basin Thin Bed Reservoirs, Northwest Delaware Basin, Geophysics (v63, no 5, 998), Lin, Y., and Cunninham, G. A.: A new approach to Fuzzy-Neural System Modeling, IEEE Transactions on Fuzzy Systems, (v3 no 2, 995), Rafipour, B.J.: Seismic Response for Reservoir Fluid Evaluation, SPE Formation. Eval. (Mar 989), Schultz, P.S., Ronen, S., Hattori, M. and Corbett, C.: Seismic-guided estimation of log properties, The Leading Edge, (may 994), Moller, M. F.: A Scaled Conjugate Gradient Method for Fast Supervised Learning, Neural Networks, (v6 993),

4 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 4 Table Well Data for K and L intervals Well K Net Pay K Porosity K Sw L Net Pay L Porosity L Sw U U U U U U U U U U U U U U U U U T-FEE T-FED Table 2 Average interval attributes used for the non-linear regressions Reservoir Property Architecture CC Attributes Max peak frequency K Porosity Avg absolute frequency Network.89 Isochron Max peak frequency Avg absolute frequency K Net-Pay Network 2.86 Avg absolute amplitude Isochron K Water Saturation Network.83 Avg reflection strength Avg peak frequency Isochron L Porosity Network.88 Isochron Avg instantaneous frequency Energy half-time L Net Pay Network.8 Avg max peak amplitude Avg RMS amplitude Avg Peak amplitude L Water Saturation Network.84 Avg instantaneous phase Avg trough amplitude Energy half-time

5 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 5 y=random(x) y=random(x)+(x)^.5 Y X Y X Fig. a One Hundred random points between and, two sample fuzzy membership functions are illustrated. Fig. b Same one hundred random points with a simple trend added, two sample fuzzy membership functions are shown. Fuzzy Curves and Their Trends Y X FC of (x)^.5 + random data in [,] trend of (x)^.5+.5 FC of random data in [,] trend of.5 Fig. 2 Fuzzy curves for the two data distributions in figure. Curves are the summation Of the fuzzy membership functions for each point. Value is given to trends with monotonic Vertical variations.

6 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 6 Avg Instantaneous Phase R 2 = Sw Avg Peak Amplitude R 2 = Sw Fig. 3 Sample crossplots illustrating the best (instantaneous phase) and worst (peak ampltude) individual correllation of seismic attributes to water saturation for the L interval. This figure illustrates the need for multivariate analysis to better resolve reservoir properties. Fuzzy Curve for Insantaneous Phase vs Sw Fuzzy curve for L Ave Peak Amplitude.6.8 Fuzzy Curve Value.4.2 Fuzzy Curve Value Normalized Sw Normalized Sw Fig. 4 Fuzzy curves for the sample attribute crossplots in Figure 3. Note the continuous and semi-monotonic nature of the curve for Instantaneous phase, which indicates correlability to Sw. The curve for Peak amplitude is discontinuous and primarily flat, indicating a poor correlability with Sw.

7 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 7 Input Hidden Output in w w2 f v f out in2 w3 w4 f v2 where f represents the activation function, f ( x) = + exp( α x) Fig. 5 Schematic neural network using 2-2- architecture. Out (output) is described in the text. f, the activation function is a predefined step function designed to simulate the response of a real neuron to a stimulus. A Network A2 A3 φ, h, Sw Network 2 A A2 A3 φ, h, Sw A4 Fig. 6 Actual network architectures used in this study. Table 2 shows which network and input attributes were used to characterize each reservoir property of interest in both the K and L intervals.

8 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 8 L Porosity training - All 9 points L Porosity training - Points a 7b L Porosity training - Points -8 & 2-9 L Porosity training - Points c 7d Fig. 7-- Results of training for L interval porosity. The 7a cross-plot shows normalized values of actual well-bore porsity vs. well-bore porosity computed by the non-linear regression. Perfect results would have all points exactly on the line between, and,. Real world noise and generalization makes the coefficient of correlation, cc=.875, acceptable for predicting intra and extra well porosities. b), c), and d), show the results of exclusion testing for the L interval porosity regression, with gray points, excluded, and then predicted, by the subset neural networks.

9 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 9 L Net Pay Training- all 9 points L Saturation training- All 9 points.8.8 Actual a 8b K Porosity training- all 9 points c K Saturation training- all 9 points K Net Pay Training- All 9 points d 8e Fig. 8--Full regressions for L interval net pay and Sw, and K interval porosity, net pay, and Sw. These networks were tested in the same manner as the L interval porosity in Figure 7, with similar results.

10 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES Fig. 9a L interval predicted porosity map. Porosities are good throughout the center of the field, low in south central section of the field. An interesting, laterally extensive porosity feature (%) is located in the northwest corner, updip of higher porosities in the center of the field. Fig. 9b K interval predicted porosity map. Discrete areas can have large porosity compared to adjacent regions.

11 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES Fig. a L interval predicted net pay map. Primarily uniform across the field with 3-35 ft thickness. Fig. b K interval predicted net pay map. Note the discontinuous depositional thicknesses.

12 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 2 Fig. a L interval predicted water saturation map. Generally water saturation is less than 45%, and fairly uiform. Fig. b K interval predicted water saturation map. Water saturation is generally high (85% or more), but locally low.

13 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 3 Fig. 2a L interval pore volume map generated from predicted porosity and net pay maps. Greatest pore volume is denoted by the darkest gray s, and indicate that some good potential drill sites remain. Fig. 2b K interval pore volume map generated using predicted porosity and net pay maps. Wide variations in pay are due to thinning and thickening of the K interval in the study area as well as wide variations in porosity.

14 SPE USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 4 Fig. 3a K interval hydrocarbon pore volume map generated from predicted property maps. The far northwest and southeast appear to be non-productive (wet), but a number of good targets still exist in other areas. Fig. 3b K interval hydrocarbon pore volume map generated from predicted property maps. Only a few small targets exist.