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1 SPE Lateral and Vertical Discrimination of Thin-Bed Fluvial Reservoirs: Geostatistical Inversion of a 3D Seismic Data Set Marcos Victoria, German Merletti, REPSOL-YPF, Alvaro Grijalba Cuenca,SPE, Carlos Torres Verdin,SPE, University of Texas at Austin Copyright 2001, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE Latin American and Caribbean Petroleum Engineering Conference held in Buenos Aires, Argentina, March 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 300 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 The San Jorge Basin is one of the most prolific hydrocarbon bearing zones in Argentina.The Cañadon Seco Formation is characterized by sandstones with thickness usually bellow the tuning lenght, under these conditions high uncertainty exists in sandstone prediction when seismic amplitudes are analyzed, due to interference and tuning effects. This paper presents an estimation procedure that overcomes these limitations based on the extrapolation of the well data further away from its location by Geostatistical Inversion of 3D seismic data. Although vertical sampling of the seismic data is much less dense than the one from logging, its higher lateral resolution is used to complement the high vertical resolution of the well data. Unlike conventional trace based inversion in which the source is the seismic data in Geostatistical Inversion the data source is the well, and the estimated acoustic impedance values satisfy the seismic data, in this way driving resolution to an intermediate range between the well and seismic data. With this procedure stochastic simulations of the petrophysical variables are generated, (density and lithology) that not only honour the hard data of the wells but also the seismic data, and minimize the residual error between the Synthetic model and the real 3D-Seismic trace. Each simulation (SGS- Simulated Annealing and SIS) is itself a possible solution to the problem and it is called a realization, wich is then integrated into an average to optimize the certainty of the predictions. The Acoustic Impedance, density and lithology models derived from GI have a resolution of 1ms. This allowed discriminations of lateral variations in the petrophysics of the reservoir (density porosity) and the delineation of sand packets of up to 6 meters thick. The Geostatistical Inversion turned out to be a very powerful tool for the static reservoir modelling wich can function itself as an input to the dynamic model (reservoir simulation), guide the development of the block and assists to the EOR. Introduction The Golfo San Jorge Basin is located at the southernmost region of Argentina in the heart of Patagonia, its long history of oil production began with the first discovery back in 1907, since then aproximately 160 million m3 of oil have been recovered. The area of study is located in the south-eastern flank of the basin and involves the east section of Cañadon León oil field, Fig.1 The development of the block follows the discovery of the productive well named CLORx-1, the production of this well reached levels that surpass the media of the field. The oil bearing sandstones are part of the middle cretaceous Cañadón Seco Formation, the reservoirs produce hydrocarbon generated in lower cretaceous lacustrine rocks (D-129 Formation). The oil bearing reservoirs are characterized by thin fluvial sandstones interspersed with thick shale laminations of lacustrine and flood-plain origin. The reservoirs are grouped into two main Members: Caleta Olivia member and Cañadón Seco member, both are separated by a predominantly thick shaly cicle called Mb. Pozo O-12, (Biocca et al.). The lateral continuity of the reservoirs seldom exceeds 2km, mainly the range is between 1 km to 2 km, the net pay thickness varies between 0.5m to 5m but in most of the cases is 1m to 3m. The field is being developed with a 400m well spacing pattern, due to this, much of the interwell heterogeneities just as the porosity distribution of the reservoir is laterally under sampled. The lateral heterogeneity of the sandstone bodies and their scarse areal distribution make it necessary to backup the development of the wells with data of higher lateral resolution. In this way 3D Seismic data combined with well data are integrated to find a model that allows reservoir characterization, that is, a model that predicts and delineate the distribution of heterogeneities and pay between wells.

2 2 MARCOS VICTORIA, et al SPE The present study describes the use of Geostatistical Inversion to optimize the reservoir characterization of the block, taking advantage of the high vertical resolution from the log data and the high lateral sampling given by 3D seismic data. In this way Geostatistical Inversion analysis provides a variety of models wich are consistent with well data and honors the 3D seismic information. All models depicts plausible solutions, and have a finer vertical sampling than the standard 3D seismic analysis. Volumes of total acoustic p-impedance, density (porosity) and lithology are yielded by the simulation process, afterwards, those different but possible solutions, are averaged into one final volume (for each physical property) that best describes the fine scale distribution of lithology and porosity and improves the development of the block. Further studies will include the results of Geostatistical Inversion in dynamic reservoir simulations. Input Data The subsurface of Cañadon León prospect, was highlighted by a 240km 2 3D seismic volume (20km x 12km with a 25 m bin size), the dominant frecuency is 35 Hz and considering the velocity of the studied interval it yields a tuning thicknes of 18m, far above the resolution needed to discriminate the sand bodies individually. Four key wells guided the Geostatistal analysis Fig.1, c, all of them were edited in order to remove the bad borehole effect due to washouts and invasion and tied properly to the seismic, using a time-depth relation and information from a VSP acquired in CLORx-1 well. Computed petrophysical logs (such as effective porosity, shale volume an water saturation) were available for many of them. A structural framework was carefully interpreted prior to the process of inversion and then refined using reflectivity data derived from the process of trace based inversion, the key horizons are shown Fig.2 Description of the Problem Only two seismic data set had been inverted in the basin before performing this study, the two prospects were located far enough from each other, and the analysis of both acoustic impedance data set had yielded similar results, sand packets were seen as intermediate to high values of acoustic impedance, Fig. 3 With this assumption in hand we began to analize the new log and seismic data set. One important step to do before transforming the seismic data into acoustic impedances is to know how is the acoustic response of the reservoirs, this knowledge allows us to estimate if the inversion process will succeed or not in predicting the vertical and lateral distribution of sand packets in a priori basis. Full log resolution analysis shows that sands in the interval of interest are low acoustic impedances, and that the embedding shales are high acoustic impedances. When the same log is transformed to the seismic bandwith domain, by means of a high cut filter, the response of the reservoirs changes and must be carefully analyzed, Fig. 4 Not only we can not assume that all reservoirs are highs, but also a thickness-porosity vs acoustic impedance relation must be considered. Thick porous sand packets ( 15m up) are relative lows, the higher the porosity the lower the impedance, but for equivalent stratigraphyc units, thick tight sands (low porosity) are highs. Thin sands independently from porosity are highs, mostly due to a problem of resolution and interference caused by the embedding shales, Fig 5 A, B An schematic like cartoon describing the behaviour of P-impedance as a function of thickness and petrophysics for sand packets, is shown in Fig. 6 All these conclusions lead us to interpretet this particular acoustic impedance volume in a different way from previous studies, and let us conclude that the relative position of the oil field within the Golfo San Jorge Basin, plays an important role when analyzing the seismic response of the reservoirs, and should also be considered. Constrained Sparse Spike Inversion The transformation of the seismic trace into a pseudo acoustic p-impedance log is called trace based inversion, in such process the wavelet effect is removed from the seismic in order to find the best reflectivity model, which is itself a bandlimited (seimic frequency domain) aproximation to the reflectivity of the subsurface. As we deal with bandlimited data, (it lacks the low frequencies), the solution to the problem is non-unique, it means, several combinations of acoustic impedances can yield the same reflectivity model, which once convolved with the seismic wavelet reproduces properly the input seismic trace, Fig. 7 In this way the agreement between the modeled seismic trace (synthetic) and the real seismic trace is necessary but is not the condition that narrows the solution space, therefore other conditions must be taken into account. As several mathematical solutions geologically feasible can meet the criteria, it is necessary to impose some restrictions, since we can know from key wells how is the lateral variability of impedances, a track of allowed impedances can be built to be used in the inversion process, thus rejecting all the possible mathematical solutions with no geologic sense, Fig. 8 Again, the result of the inversion lacks the compaction trend because of the bandlimited character of the seismic wavelet, but it is possible to build a geologic model by interpolating

3 LATERAL AND VERTICAL DISCRIMINATION OF THIN-BED FLUVIAL RESERVOIRS: GEOSTATISTICAL SPE INVERSION OF A 3D SEISMIC DATA SET 3 the acoustic impedance data from the wells and then high cut filter it to 4Hz / 6Hz. The merging of both data yields a new class generally called total or absolute acoustic impedance, in wich every trace is a pseudo acoustic impedance log (this data is no more interface dependent as it is the seismic, but property lithology dependent), Fig. 9, 10 Interpretation work has been done in both volumes, Bandlimited acoustic impedance and Total acoustic impedance, in a back and forth quality control basis, since the low frequency geologic model can be affected by the interpolation process, this may lead us to misinterpret the data. The reflectivity data having a higher resolution than 3D Seismic presents an optimum scenario to delimit top and base of acoustic impedance events that best describe the vertical and lateral sand distribution, in a standard interpretation basis, Fig.11 More sophysticated 3D visualization techniques can be foccussed directly to impedance data, in order to get 3D bodies consistent with lithology and connectivity criteria. The model of lithology properties, which is acoustic impedances, works well when it comes to characterize sand packets response, but it fails when a finer heterogeneity model is needed. Geostatistical Inversion Quick look to the methodology Each one of the steps involved in the geostatistical inversion process has been described carefully by several authors (see for instance Haas and Dubrule (1994), Pendrel and van Riel (1997), Torres Verdin et al., (1999), etc.), it is not the scope of this paper make an strict description of the whole process, but presents results showing the power of geostatistical inversion in resolving sand bodies distributions not seen by the conventional inversion process in the area of study. Geostatistical modeling honors the data at the well location (hard data) and simulates the values where they are unknown, 3D seismic guides the process in the sense that each simulated model of acoustic impedance is a plausible geologic solution and satisfies the 3D seismic data. A solid geologic model is the framework in wich histograms and variograms are estimated and respect the structure and the stratigraphy of the model. Stationarity is assumed for each layer within the solid model. In the vertical direction, variograms are estimated from well data, whereas in the horizontal direction the estimation comes from the inverted acoustic impedance model. The knowledge of the 3D spatial continuity (vertical and horizontal variograms) is crucial in finding property values in locations in wich they are unknowns. Histograms, variograms and neighbouring data values are used (Kriging) to estimate the local probability density function at random located grid points. The unknowns are generated (Sequential Gaussian Simulation) by multiple random draws, however, although volumes encountered are consistent with histograms and variograms we are not completly sure these sets of simulated values satisfy the 3D seismic volume. This problem is solved by applying a technique based on a random-walk sthochastic simulation of acoustic impedances with an acceptance-rejection criteria based on fit to the seismic data, thus the outcome of the process is less dependent on variogram than standard geostatistical techniques. The volumes of acoustic impedances are broad band, and have higher frequencies than input seismic Fig.12 In addition to inverting for acoustic impedance values, a stochastic co-simulation process yielded independent simulations for both density and lithology. Results Geostatistical Inversión of Acoustic Impedance Histograms and three dimensional variograms were computed corresponding to both inputs, wireline data (in this case p-impedance and bulk density) and p-impedance from a priori trace based inversion, and were used to drive the geostatistical simulations constrained by 3D seismic data, Fig.13 and Fig.14. Once the statistics were computed, and the spatial continuity model was known, 10 full independant simulations of acoustic impedance were done, the geostatistical inversions were performed with a vertical resolution better than 2ms, in this case 1ms, all of the geostatistical analysis supporting the simulations were made consistent with this sampling intervals, thus driving the vertical resolution to an intermediate point between well data and 3D seismic data. This new model of p- impedance with higher lateral and vertical resolution is considered to refine the horizontal model of lateral variability (horizontal variograms), then, thirty geostatistical simulations of p-impedance were done, each one of the these multiple realizations was in agreement with the input seismic data. Fig. 15 shows plan views of the correlation between the measured and simulated seismic data sets for 3 independent simulations, the correlation is acceptably high, we see that an almost 99.8% agreement is reached for each one of them. By applying statistics we can summarize the information in our results, in the same cell we are able to generate for instance the mean and standard deviation for the p-impedance values for that cell, it is clear that the standard deviation decrease to cero in the vicinity of key wells, it reminds us that well data drives the simulation process. The accuracy of the prediction decrease away from wells, in this particular case we feel very confident up to 1 well-spacing.

4 4 MARCOS VICTORIA, et al SPE When comparing the previous acoustic impedance model (derived from trace based inversion) with the mean of multiple simulations derived from geostatistical inversion we can clearly observe an improvement in the lateral and vertical resolution of the latter, not only this allows us to vertically discriminate sand bodies of up to 5-7m thick, but also lateraly map thiner acoustic impedance events that corresponds to sandstone, Fig. 16. Geostatistical Inversión of Density and Lithology Three lithology categories were recognized based on statistics and cross-plots analysis in this project : shales, tight sands and porous sands. Full statistics analysis were computed for each particular lithology group separately, see Fig.17. The relationship between density and acoustic impedance, depicted in Fig.18, is lithology dependent, in this way, it is possible to simulate a lithology type (using a lithology PDF), then we can randomly draw a sample of density for that particular lithotype which is finally used to draw a random sample of acoustic impedance via the joint PDF that relates density with acoustic p-impedance. Again these simulated values of p-impedance once convolved with the seismic wavelet must generate a synthetic trace that satisfy the input 3D seismic. The stochastic simulations results yields prediction of lithology type, acoustic p-impedance and density (porosity), Fig. 19 Standard interpretation and 3D visualization techniques were applied to the high-resolution cubes in order to laterally map the distribution of lithology and porosity within the CLORx-1 block. a lithology model that perfectly satisfy the input 3D seismic data and wireline data. We have shown that Geostatistical Inversion by integrating all the available data can be used to improve the imaging and interpretability of sand packets in Mb. Caleta Olivia. Also to discriminate its lateral and vertical distribution, as well as to build a finer model of heterogeneity in the interwell spacing, which finally can be used in reservoir flow simulators to support the water flooding proyect of the block. Acknowledgments We thank Division Regional Sur (REPSOL-YPF) for permission to publish this paper and those people from the Department of Petroleoum Engineering University of Texas at Austin who helped us in performing this study. References 1. A.Grijalva Cuenca, C.Torres Verdin, H. Debeye Geostatistical Inversión of 3D Seismic Data to Extrapolate Wire Line Petrophysical Variables Laterally Hawai From the Well. SPE Annual Technical Conference, Dallas R.Lattimer, S Bahret, C Sullivan, R. Horine, W Mills, V. Sturrock Reservoir characterization using Geostatistical inversion for the Amberjack Field, offshore Gulf of Mexico. SEG, Annual meeting, technical program. Houston, J. Pendrel, P. van Riel, Using Seismic Inversion and Geostatistics to Estimate Porosity: A Western Canadian Reef Example. CSEG Fig.20 shows an arbitrary line across the CLORx-1 well, 6 time dependent intervals were analyzed, the lithology volume (this is the result of the count of the number of ocurrencies of a given lithotype, referred as to lithology mode) presents an optimum scenario to directly extract lithology attributes from those windows such as Net sands and Gross sands. Extra works must be done to refine the framework, in order to generate a higher number of time windows that encompass individual sand units. The resulting volumes containing a higher lateral and vertical variability and a finer sampling time interval (1ms) will be converted to depth to be imported into a reservoir flow simulator. Conclusions For sand packets corresponding to Caleta Olivia Mb. the acoustic response can be a high or a low in the p-impedance values depending on the petrophysics (porosity). By applying Geostatistical Inversion we can reduce the uncertainty in the prediction of a particular lithology group (sands), by building

5 LATERAL AND VERTICAL DISCRIMINATION OF THIN-BED FLUVIAL RESERVOIRS: GEOSTATISTICAL SPE INVERSION OF A 3D SEISMIC DATA SET 5 Fig.1- A- Location of Golfo San Jorge Basin and Cañadon Leon prospect. B- Structural map showing wells distribution and position of study area. C- Close-up view of key wells that guided the Geostatistical Inversion of the block.

6 6 MARCOS VICTORIA, et al SPE Fig.2- Arbitrary line through some wells from the block, color density logs shows effective porosity, wigle Type logs are spontanous potential and seismic is shown as background. The key structural framework is in red. Postack seismic traces in this particular case fails to do direct lithology predictions. Fig.3- Acoustic Impedance response of sand packets from different prospects in the Golgo San Jorge basin. High values of AI, are represented by warm colors, lithology log is SP (wigle trace).

7 LATERAL AND VERTICAL DISCRIMINATION OF THIN-BED FLUVIAL RESERVOIRS: GEOSTATISTICAL SPE INVERSION OF A 3D SEISMIC DATA SET 7 Fig.4- Stratigraphyc setting and compaction compartments for one of the studied wells. Hydrocarbon producing interval is represented by fluvial sandstones from Mb. Caleta Olivia. Well P-Impedance has been high cut filtered to 65 Hz in order to see the acoustic impedance response of the reservoir in the seismic bandwidth domain. In color density (leftpanel) is shown the trend compaction of the block, the more dramatic changes occurs at the sequence boundaries or major discontinuity surfaces.

8 8 MARCOS VICTORIA, et al SPE Fig.5, A- Full log resolution wireline data, density porosity (background), SP (yellow), P-Impedance (blue), P-Velocity (red), reservoirs with different thickness responds with minimum acoustic impedance (white arrows), the embedding shales shows higher acoustic impedance than sands. The net pay interval shows an almost constrast P-Velocity, therefore the decrease in the impedance value is dominated by bulk density of the sand. B- Same log data set high cut filtered to the seismic resolution domain, thin sands (1-7m) and tight sands (1-15m) responds as maximum values of P-Impedance, thick porous sands are seen as minimum of P-Impedance. Fig.6- Schematic cartoon descibing the behaviour of P-Impedance as a function of thickness and petrophysics of sand packets.

9 LATERAL AND VERTICAL DISCRIMINATION OF THIN-BED FLUVIAL RESERVOIRS: GEOSTATISTICAL SPE INVERSION OF A 3D SEISMIC DATA SET 9 Fig.7- Influence of sand thickness and porosity on acoustic impedance data derived from seismic trace-based inversion. For equivalent stratigraphic interval (blue arrow), acoustic impedance decreses due to an increase in the effective porosity of net pay. The thickness interval (>15m.) is equivalent for both wells.

10 10 MARCOS VICTORIA, et al SPE Fig.8- Compaction trend along with acoustic p-impedance filtered to seismic bandwidth, black lines represents the track of allowed impedances. Seismic wavelet, along with its amplitude and phase spectrum. Fig.9- Show a total acoustic impedance (left), and a band-limited acoustic impedance arbitrary lines (right). Fig.10- Shows a total acoustic p-impedance arbitrary line (background, left panel) with reflectivity overlaid (wigle trace). On the right panel it is clear the broader bandwidth (higher frequencies) of the reflectivity with respect to 3D Seismic (background).

11 LATERAL AND VERTICAL DISCRIMINATION OF THIN-BED FLUVIAL RESERVOIRS: GEOSTATISTICAL SPE INVERSION OF A 3D SEISMIC DATA SET 11 Fig.11- Total acoustic p-impedance, plan view of porous sand packets distribution corresponding to the time window interval encompassed by black markers (above). Fig.12- Pseudo acoustic impedance trace from standard trace-based inversion and from geostatistical inversion (blue), the high frequency is recovered from well logs, note the possibility to discriminate thin sand packets due to an improvement in resolution.

12 12 MARCOS VICTORIA, et al SPE Fig.13- Depicts histograms of the key wells (left) and inverted impedance model (right), the normal Gaussian transformation applied to be used in the process is in blue. Fig.14- Shows the variograms of p-impedance from 5 key wells, in red is the exponential function that best fit the variogram. Fig.15- Correlation maps for 3 independent realizations, the misfit between seismic and synthetic is low, an almost 99.8% of correlation is reached in each simulation.

13 LATERAL AND VERTICAL DISCRIMINATION OF THIN-BED FLUVIAL RESERVOIRS: GEOSTATISTICAL SPE INVERSION OF A 3D SEISMIC DATA SET 13 Fig.16- Arbitrary line showing acoustic impedance from trace-based inversion (a) and Geostatistical Inversion (b), a finer model is yielded and sand packets up to 5m note can be discriminated

14 14 MARCOS VICTORIA, et al SPE Fig.17- Lithology cut-offs derived from the density-impedance cross-plot, SP is color coded. Fig.18- Shows the density-impedance relationship, in red is drawn the correlation line for shales, green for tight sands and black for porous sands.

15 LATERAL AND VERTICAL DISCRIMINATION OF THIN-BED FLUVIAL RESERVOIRS: GEOSTATISTICAL SPE INVERSION OF A 3D SEISMIC DATA SET 15 Fig. 19- Shows the result of 30 stochastic reaalizations, lithology and density are simulated in order to find acoustic impedance traces that when convolved with the seismic wavelet yields a synthetic trace that satisfy the input seismic; the simulations are integrated into an average to reduce the uncertainty of the model

16 16 MARCOS VICTORIA, et al SPE Fig.20- Lithology model, shales (black), tight sands (brown), porous sand (yellow), along with time windows in which gross and net sand values has been extracted. The 2D color coded maps of net sands are vertical stacked samples of porous within the interval.