Application of multipoint geostatistics to honor multiple attribute constraints applied to a deepwater outcrop analog, Tanqua Karoo Basin, South Africa Daniel Tetzlaff, Roy Davies, David McCormick, Claude Signer*, Piotr Mirowski, and Nneka Williams, Schlumberger-Doll Research, David Hodgson, Liverpool University, James Brady, Schlumberger Information Solutions Summary We have used a multipoint geostatistics algorithm called Snesim (Strebelle, 2000) to evaluate its applicability to reservoir modeling. To test the algorithm, we used a data from a deepwater reservoir analog from outcrops in the Tanqua Karoo Basin, South Africa. Our implementation demonstrated the ability of the algorithm to efficiently and faithfully reproduce the texture of geological facies while honoring a large number (127) hard data locations plus rotation and scaling fields and soft probability fields. We have used hand-drawn stationary training images with 3-5 facies to model the proximal to distal facies relationships seen in outcrop. The results show the ability to honor hard data, soft constraints, and complex geological relationships that vary over the reservoir grid. One of the virtues of the Snesim algorithm is its ability to honor multiple soft probability fields when probability distributions overlap; there is no requirement for exclusive categorical membership with sharp cut-offs. This promises to allow better use of seismically derived attribute data for modeling of complex reservoirs. Introduction Two-point geostatistical methods (Journel and Huijbregts, 1978; Deutsch and Journel, 1997) have been widely adopted in the petroleum industry for the estimation and simulation of geophysical, geological, and reservoir property fields. However, these methods have significant limitations in their ability to reproduce complex geological shapes and textures commonly encountered in outcrop and reservoirs. Boolean or object modeling techniques were developed to produce plausible simulations of geological objects (Damsleth et al., 1992). However, object modeling techniques have limited ability to honor hard data constraints (e.g., the occurrence of the same object in multiple wells). Multipoint geostatistical methods, first proposed by Guardiano and Srivastava (1993), held the promise of being able to to model the complex geological textures seen in real outcrops and reservoirs more faithfully than with extant two-point geostatistical methods. In addition, multipoint methods have the advantage of being able to

honor many “hard” (e.g., well) data constraints that hinder object-modeling methods. Furthermore, multipoint methods allow one to condition the simulations on multiple soft probability fields, potentially with overlapping probability distributions. Strebelle (2000) created the first computationally feasible multipoint geostatistical algorithm, Snesim, for simulating categorical variables. Here we implement and test the Snesim method.

Figure 1. Perspective view of the NOMAD outcrop area and reservoir model. The reservoir model is superimposed on the digital terrain model draped with a satellite image of the Tanqua Karoo Basin. The model area is approximately 31 by 37 km in areal extent. White sticks represent the six cored and logged behind-the-outcrop wells. There are 350 locations where stratigraphic logs were measured; 121 of those stratigraphic logs are used in the reservoir model. The north-south direction is along the top border of the model; north is to the right. Deepwater geological analog dataset To test the efficacy and utility of the Snesim algorithm for reservoir-scale problems with real data, we used a dataset from the European Union funded industry–academic NOMAD (Novel Modelled Analogue Data for more efficient exploitation of deepwater hydrocarbon reservoirs) project (Hodgetts et al., 2004; Hodgson et al., in press). The central aim of the NOMAD project was to produce a series of very high resolution geological models using data

Multipoint geostatistical modeling of a deepwater outcrop analog

collected from an outcrop of a deepwater fan system from the Karoo Basin of South Africa’s Western Cape Province. A combination of GIS and GPS technologies were used to accurately locate data from over 350 outcrop logs and six cored- and wireline-logged boreholes in 3D space. These data were imported into a commercial reservoir modeling package and used to construct a series of very high-resolution geological models (ca. 50 million 3D cells per model) for three different submarine fans from the Karoo basin (Figure 1). The case study presented here uses data from one of these fan models to demonstrate the power of the Snesim multi-point geostatistical algorithm for producing highly detailed realizations of complex geological relationships. Snesim Multipoint Modeling Method The Snesim algorithm has been implemented as a plugin in Schlumberger’s Petrel reservoir modeling software. The method has one required input: a template or training image, which imprints the geological texture and facies relationships. Optional inputs include hard well data; grids which specify the rotation and affinity of features in the training images; simulation region boundaries; and soft probability grids for each facies or category to be modeled. A key element of multipoint geostatistics is the use of training images, which impart geological texture to the realizations. Training images for multipoint geostatistical methods must satisfy stationarity and ergodicity constraints (Caers and Zhang, 2004). These training images are not the same as natural images from aerial images or actual reservoirs. As such they commonly have to be hand-drawn, transformed from natural images, or generated by forward geological modeling. The user has significant ability to control the model results. The use of affinity regions allows one to control the 3D aspect ratios of features in different areas of the model. This enables one to model the proximal-to-distal changes in facies location and geometry. The relative proportion of different facies can be honored directly from the hard well data, or the user can honor the proportions in the training image, or set global facies probabilities, or honor vertical proportion of facies by layer. This even allows the user to specify the existence and proportion of facies that are absent in well data. All of these capabilities were used in our tests with the Tanqua Karoo dataset. Modeling the deepwater analog with Snesim The particular NOMAD fan model we have used is 319 by 368 by 429 cells. We have used Snesim to model two zones: a silt-prone and a sand-prone zone. These two zones

have, respectively, 3 and 5 facies present and have 30-50 layers. The training images used in the simulation were essentially single layer maps resampled to to200 by 191 by 1 cell grids (Figure 2). They were drawn by hand to mimic facies relationships seen in outcrop and to satisfy the stationarity constraints required by the Snesim algorithm.

Figure 2. A three-facies training image used to model silt-prone zone of the fan model. Yellow represents structureless, channelized sands; orange represents structured sand sheets adjacent to channels; green represents interbedded lobate silts and sands. Training image is 200 by 191 by 1 cells. The training images were approximately half the size of the reservoir model (Figure 3).

Figure 3. Example of the relationship between the model grid and the training image used in the conditional simulation of the silt-prone zone. The training image is approximately half the size of the output model. The outcrop and well data show significant proximal-to-distal changes in the proportion of facies. These changes were mapped and transformed into facies proportion soft probability grids (Figure 4), one for each facies. The rotation

Multipoint geostatistical modeling of a deepwater outcrop analog

grid was produced by mapping and extrapolating paleocurrent data collected in the outcrops. The affinity grid was produced by comparing, for example, outcrop measurements of the widths of channelized facies (yellow); boundaries were mapped to creating regions separating areas with different facies geometries (aspect ratios).

Figure 4. Map view of sandy facies proportion grid used in simulation of the silt-prone zone. Red is high proportion and purple is low proportion. The fingering shapes of the color contours are derived from mapping facies proportions derived from outcrop measurements across the study area. We experimented with and were able to exert considerable control over the realizations by exercising all of the constraints: rotation, affinity, and facies proportions (Figure 5). This allowed us to mimic the fanning pattern of channelized facies and their rotation as the fan system turned from NE-directed to NNW-directed. Global facies probability constraints allowed us to match better the proportions of facies in wells compared to those in our training images. Affinity categories allowed channelized facies to become more elongate and continue to the outer margins of the model. The modeling process was computationally efficient and was capable of honoring the 127 hard well constraints, the rotation and affinity constraints, and all the soft probability grids in zones that contained several million cells. The resulting realizations were good matches to the geological outcrop data and significant proximal-to-distal trends in the fan system. Facies Probabilities “Soft” facies data (i.e., data that may bias but not strictly determine the facies at each point in a model) are often given in the form of one probability map for each facies. They provide a powerful means of incorporating uncertain information into a model. Such maps can be derived, for example from seismic impedances using a Bayesian

approach (Figure 6). Traditional non-geostatistical techniques for modeling facies have difficulty in using probability maps to model facies. The theoretically reasonable approach of assigning to each point the facies that is locally the most likely fails on a number of counts, most importantly: (1) a facies with a broad statistical distribution (poorly correlated to impedance) may be assigned only at point with impedances at the tails of the distribution (Figure 6) where it is more likely than the other facies, but still highly unlikely (far from the mode of its distribution), and (2) the facies maps would have very low resolution, much lower than the original impedance maps. The Snesim method uses all the facies-probability fields, but integrates them in its estimation mechanism (Strebelle, 2000) to produce high resolution realizations. The use of AVO data, in addition to impedance data, can lead to even better probability estimation because the facies-probability graphs (Figure 6), would have at least one more variable besides impedance in the domain, and facies probability distributions would separate better in two dimensions than they do in one.

Figure 5. Map view of a Snesim realization in the silt-prone zone. All hard and soft constraints have been applied to create this realization. The change in orientation of channelized yellow facies is controlled by a rotation grid. The change in width and length of channelized yellow facies is controlled by the affinity regions and scales. The outward decrease in proportion of yellow and orange facies, and increase in proportion of green facies is controlled by soft facies proportion grids. Global facies probability constraints were used to provide a better match those seen in outcrop. Conclusions The resulting multipoint geostatistics conditional simulations with Snesim applied to a deepwater fan analog model honor multiple data: hard data at wells, rotational and affinity fields, and multiple soft probability fields with overlapping distributions. The method has worked efficiently with three and five facies. This ability to honor

Multipoint geostatistical modeling of a deepwater outcrop analog

multiple attributes in a Bayesian sense promises to allow better use of seismically derived estimations of facies, lithology, or other reservoir property distributions.

Figure 6. Typical statistical distributions of three facies as a function of seismic impedance. While the probability of each facies can be estimated by Bayes rule from a given impedance, using the highest probability as the facies to assign in a model is undesirable. Facies A, for example would be assigned only at very high or very low impedances, though it is more likely at intermediate values. References Caers, J., and Zhang, T. (2004). Multiple-point geostatistics: a quantitative vehicle for intergration geologic analogs into multiple reservoir models, in, M. Grammer, P. M. Harris and G. P. Eberli. (eds.), Integration of Outcrop and Modern Analogs in Reservoir Modeling. Tulsa, OK, AAPG Memoir 80. Damsleth, E., Tjolsen, C. B., Omre, H., and Haldorsen, H. H. (1992). A Two-Stage Stochastic Model Applied to a North Sea Reservoir. Journal of Petroleum Technology: 402-501. Deutsch, C. V., and Journel, A. G. (1997). GSLIB: Geostatistical Software Library and User's Guide, Oxford University Press. Guardiano, F. and Srivastava, R.M., 1993. Multivariate geostatistics: beyond bivariate moments. In: A. Soares (Editor), Geostatistics-Troia. Kluwer Academic Publications, Dordrecht, Netherlands, pp. 133-144. Hodgetts, D., Drinkwater, N.J., Hodgson, D.M., Kavanagh, J., Flint, S.S., Keogh, K.J. & Howell, J.A. 2004. Three-dimensional geological models from outcrop data using digital data collection techniques: an example from the Tanqua Karoo depocentre, South Africa In: Curtis, A. and Wood, R. (eds) Geological Prior Information: informing science and engineering. Geological Society, London, Special Publications, 239, 57-75

Hodgson, D. M., Flint, S. S., Hodgetts, D., Drinkwater, N. J., Johannesson, E., and Luthi, S., in press. Stratigraphic and palaeogeographic evolution of Permian submarine fan systems in the Tanqua depocentre, South Africa. Journal of Sedimentary Research. Journel, A. G., and Huijbregts, C. J. (1978). Mining geostatistics. London, Academic Press. Strebelle, S. (2000). Sequential simulation drawing structure from training images. Ph.D Dissertation, Stanford University, Stanford, CA, USA, Acknowledgements We would like to thank the NOMAD Consortium (www.nomadproject.org) for permission to use and publish results using the Tanqua Karoo outcrop dataset. NOMAD consists of the following companies and institutions: Schlumberger; Statoil; Liverpool University; Technical University of Delft, and Stellenbosch University. NOMAD was sponsored by the European Union’s 5th Framework Programme under the Energy, Environment and Sustainable Development thematic programme.