Parameter Estimation and Sensitivity Analysis in Clastic Sedimentation Modeling A. Acevedo 1, A. Khramtsov 2, H. A. Madhoo 3, L. Noomee 4, and D. Tetzlaff 5 1 Schlumberger Information Solutions,Gatwick, West Sussex, RH6 0NZ, U.K., jacevedo2@slb.com 2 Schlumberger Information Solutions,Gatwick, West Sussex, RH6 0NZ, U.K., akhramtsov@slb.com 3 Schlumberger Information Solutions,Gatwick, West Sussex, RH6 0NZ, U.K., hmadhoo@slb.com 4 Schlumberger Information Solutions,Gatwick, West Sussex, RH6 0NZ, U.K., lnoomee@slb.com 5 Schlumberger Information Solutions,5599 San Felipe Ave., Houston, TX, 77056, U.S.A., dtetzlaff@slb.com Abstract. During numeric modeling of clastic sedimentation, the modeler is faced with assigning values to several parameters that are difficult to estimate. However, proper handling of uncertainties translates to valuable uncertainty information in the output. To illustrate this process, we used a model called GPM (Geologic Process Modeler) to model a deepwater turbidite system from the Campos Basin, offshore Brazil, for which good-quality 3D seismic was available. In the first stage we used a paleo-basin floor surface reconstructed from seismic and placed sediment sources at locations indicated by the inferred paleogeography. In the second stage, we varied several input parameters within a range of reasonable values while comparing results to observed data. The results of all plausible models, considered jointly, provide a picture of the uncertainty of the occurrence of observed features and sediment properties. Keywords: Stratigraphic forward modeling, geologic process modeling, sensitivity analysis, uncertainty. 1 Introduction In recent years geology has become increasingly quantitative. Mathematical methods and software for structural reconstruction, sediment compaction, organic matter maturation, and hydrocarbon migration are commonplace in hydrocarbon exploration, while geostatistics, reservoir flow modeling, and history matching have become essential in production. A recent addition to the geologist s set of quantitative tools has been geologic process modeling [1] [2]. This technique models the processes of erosion, transport and deposition of clastic sediments, as well as carbonate growth and redistribution on the basis of deterministic physical principles. This type of modeling requires several parameters, which may not be readily available from present-day data (sediment input, sediment diffusion and transport coefficients, and primary sediment properties). These parameters must be adjusted in an iterative process giving rise to more than one plausible model. The set of plausible results is used for statistical inference of model results, providing a measure of uncertainty in reservoir geometry and petrophysical parameters.
2 Model description For the work described here, an experimental package called GPM was used. It is implemented as a plugin within a major geologic modeling package. It is based on modeling principles that have been originally used in research models in the 1980 s [3]. Initially the user must specify the general basin setting by providing an approximate, location of sources, sediment types, and sea-level curve (Fig. 1). Figure 1: GPM basic input. The user may then select a number of processes to model, which may be run concurrently. Each modeled process may require a several parameters. The simplest of these processes is diffusion, which is used to represent processes that occur at a sub-cell scale, such as minor slumps, soil creep, and biological activity. A more complex mechanism to model is free-surface water flow and the corresponding sediment transport. The GPM model provides for simulating both steady flow (as in rivers at normal stage) and unsteady flow (as in turbidity currents or river floods), as well as erosion, transport and deposition of sediment by flowing water. Carbonate growth is modeled using growth rates that are dependent on light, temperature and the energy of the environment, while modeling the destruction and redistribution of carbonates using the modules for flow and sediment transport. This approach enables modeling in full 3D much of the complexity that is inherent in carbonate systems, even when modeling in a single vertical dimension [4]. Tectonics can be represented as a vertical movement of the basement which raises or lowers the overlying sediments. Compaction is modeled by an algorithm based on a simple load assumption. GPM is often used in conjunction with other quantitative tools for modeling post depositional processes such as diagenesis and dissolution, complex structural deformation, and heat flow and hydrocarbon migration and maturation. GPM provides a detailed description of the primary depositional geometries and properties that these packages require.
3 Application The case history described here involves a deepwater turbidite system from the Campos Basin, offshore Brazil, for which good quality 3D seismic was available. In this province, turbidite systems have been proven to be major reservoirs. In the first modeling stage, a paleo-basin floor surface was reconstructed from seismic and sediment sources were placed at locations indicated by the inferred paleo-bathymetry (Fig. 2). After adjusting the amount and type of sediment carried by turbidity currents, a reasonable match with observed seismic was obtained in terms of sequence architecture. This was assumed to represent a base case : Figure 2: Initial basin floor surface and base-case scenario of basin fill. Sands in the deep part of the basin represent basin floor fans deposited by turbidity currents originating in the upper end of the basin (upper left of the figure). In the second stage, sea level, transport coefficient (which determines the ease of sediment transport by water) and diffusion coefficient (which affects sediment transport due to slumps, creep, and wave action) were varied within geological ranges of uncertainty. As long as the resulting model was compatible with observed data, the varied values were considered plausible. The result of each plausible model was individually converted to a Chance of Adequacy (COA) map to qualitatively estimate the merit of each output. For example a sand prone area is associated with better reservoir quality, and hence is assigned a high COA (yellow to green Figure 3). Although the detailed features of each realization are not certain, the joint set of all plausible models provided an estimate of the COA for
reservoir presence and inferred quality in this case. Furthermore, similar estimates can provide insight into possible occurrence of source and seal facies. Adequacy in this case was defined as a reservoir thickness and quality exceeding a defined industry average minimum. The workflow is briefly outlined in Figure 3. Figure 3: Schematic view of workflow in which input parameters that have been varied within their ranges of uncertainty and final results combined in a probabilistic chance-ofadequacy map showing probability of success as a percentage. I. paleo-basin floor map from seismic plus base case result of GPM simulation, II. Examples of uncertainty ranges by Sea Level, Transport and Diffusion Coefficients, III. Respective Chance of Adequacy (COA) maps for each parameter, and IV. Combination of individual COA maps producing an overall COA for reservoir facies. Note: I. & II. Refer to sediment color bar; III. & IV. Refer to COA color bar. 4 Conclusions GPM and similar stratigraphic forward modeling tools are only a part of a growing cluster of quantitative applications used in hydrocarbon exploration and production. The
results of the examples mentioned in this paper (as well as other case histories not detailed here) show that modeling of sedimentary processes is ripe for quantitative treatment. This technology provides a quantitative framework that may help either confirm or discard preexisting conceptual models. It also provides a means to quantify uncertainty in situations that were heretofore left largely to intuition, such as the chances of success under varying sea-level change conditions. GPM does require some a priori knowledge or assumptions about paleogeographic conditions and thus is most useful if some knowledge of the basin is already available. The technology is readily applicable in exploration and early production situations, in which alternative hypotheses may have to be selected, or existing conceptual models may need quantitative refinement. At the reservoir scale, GPM can predict the general architecture, geometry and connectivity of permeable beds. Its results may be useful as training images for geostatistical methods in areas where detailed analogs may not be available. Acknowledgments. The authors would like to thank Schlumberger for permission to publish this paper and to Western Geco for providing the seismic data. We thank also Lars Sonneland and Per Salomonsen of Schlumberger Information Solutions, Stavanger, Norway, for their support in developing the technology described herein. References 1. MERRIAM, D.F. & DAVIS, J.C., 2001, Geologic modeling and simulation, sedimentary systems, Kluwer Academic/Plenum Publishers, New York, 352 p. 2. TETZLAFF, D.M. & PRIDDY, G., 2001, Sedimentary Process Modeling: From Academia to Industry. In: Geologic Modeling and Simulation, Sedimentary Systems (Ed. by D.F. Merriam & J.C. Davis), Kluwer Academic/Plenum Publishers, New York, 352 pp. 3. TETZLAFF, D.M. & HARBAUGH, J.W., 1989: Computer Simulation of Clastic Sedimentary Processes, van Nostrand Reinhold series in Mathematical Geology, Plenum Publishing Co., 297 pp. 4. BURGESS, P.M. & POLLITT, D.A., 2012. The origins of shallow-water carbonate lithofacies thickness distributions: one-dimensional forward modelling of relative sea-level and production rate control. Sedimentology 59, 57-80.