EROSION IN SURFACE-BASED MODELING USING TANK EXPERIMENT AS ANALOG

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1 EROSION IN SURFACE-BASED MODELING USING TANK EXPERIMENT AS ANALOG Siyao Xu Earth Energy and Environmental Sciences Tapan Mukerji and Jef Caers Energy Resource Engineering Abstract Characterizing deepwater reservoirs, their stratigraphy and structure can be highly uncertain due to the extremely limited data. The existence of subseismic scale fine-grained layers can significantly affect oil production of a reservoir, which requires explicitly modelling the uncertainty of these fine-grained fluid barriers. Conventional modeling techniques, such as twopoints statistics, multipoint statistics, object-based modeling, and process-based model, are incapable of providing a satisfying solution due to their inherent shortages and the lack of data. This work focuses on surface-based modeling of the deepwater system. The contribution of this work is the use of a tank experiment of delta basin to extract relevant statistics of erosion that can be used as analogs for modeling deepwater fans. The advantage of tank experiment data is the availability of the intermediate dynamic topographies of a depositional process, which is a rich source of understanding not only the deposition geometries but also the processes. Proper statistics can be inferred from these dynamic data, and will be applied in the surface-based framework to construct geologically realistic models. The benefits from this research will be a workflow of applying tank experiment data as a data source of modeling deepwater system. A highly geologically realistic model is constructed with information inferred from the data and geological knowledge. 1. Introduction 1.1 Erosion in Deepwater System Shale drapes, in terms of the depositional process in a deepwater lobate reservoir environment, occur between lobes or lobe elements (Figure 1.1). The impermeability and great lateral continuity of subseismic interbed shale layers determines that the shale drape coverage is one of the most important model parameters in the perspective of reservoir characterization. The shale drape coverage in a deepwater lobate reservoir environment is determined by erosion of

2 following depositional events (channel-lobes) (Figure 1.2). Therefore modeling erosion is a key problem for correct modeling of a deepwater reservoir. Challenges of modeling erosion in deepwater reservoirs are the extremely limited data and complex processes of deepwater environment. In the early appraisal stage of a deepwater reservoir, only a handful of wells and low quality seismic data are obtained. Thus, further understanding of the complex stratigraphy and structure of the depositional basin are impeded. Furthermore, erosion process, which is a function of particle sizes and turbidity flow condition, is extremely complex. The documented workflow honors the novel surface-based modeling technique to model the lower part of the submarine fan. For gathering more information about the processes, we use laboratory experiments and numerical simulation results as the analogue. The objective is to infer meaningful statistical information about channel-lobe geometry and deposition-erosion processes of a distributary delta and build a surface-based model with the inferred statistics. Figure 1.1: Outcrop photograph and sedimentary log corresponding to a lobe. A lobe is bounded above and below by fine-grained units. A lobe comprises several lobe elements. After Prelat et. al Figure 1.2: Outcrop example of eroded shale drapes. After Alpak et. al

3 1.2 Geological Background Deepwater turbidite systems transport sediments from the edge of shelf down to the ocean basin (Figure 1.3). A turbidite system is commonly divided into three parts: the upper, middle and lower fans. The upper fan features with submarine canyons, where canyons send sediments down from the shelf edge. Deposits are accelerated due to the work of gravity and erosion is the dominant process in this part. The middle fan part starts from the toe of slope, where topography starts flattening, the acceleration weakens and sediments start to deposit. The middle fan includes well developed channels filled with coarse-grained sediments. In the lower fan part, the turbidity flow gets more weakened till its death. Primary feature of the lower fan part are lobes and distributary channels. Lobes and channels form deepwater reservoirs (Mutti and Tinterri, 1991; Chapin et al., 1994). Generally, lobate deposits are characterized by large extent and lateral continuity (McLean, 1981). Porosity in lobes ranges from 20 to 35%, and permeability from 100 to 2000 md. The average net-to-gross varies from 40% to 60% (Fugitt et al., 2000; Saller et al., 2008). Lobe systems are therefore important hydrocarbon reserves. The purpose of deepwater reservoir characterization is to reproduce the complex heterogeneity of reservoir permeability. Therefore, channel-lobe geometry must be modeled as realistically as possible. The other important element of deepwater reservoir is the interbed subseismic scale shale layers, which behave as flow barriers in dynamic simulation. These shale layers and erosion on them by following channel-lobes need to be modeled explicitly.

4 Figure 1.3: a) Demonstration of a deepwater depositional system. After Funk et. al b) Geological settings of the model. After Prelat et. al Surface-based Modeling for Deepwater System Surface-based modeling is a novel technique based on statistics of geometry but attempts to place geobodies with rules mimicking deposition-erosion processes to obtain highly realistic models (Pyrcz et al., 2004; Pyrcz and Strebelle, 2006; Miller et al., 2008; Biver et al., 2008; Zhang et al., 2009; Michael et al., 2010). The existing models are based on a surface stacking workflow. First the model starts by specifying the geometry of the geobody being deposited. Then, its location of sedimentation is selected according to certain geological rules. The rules aim at mimicking the sedimentary processes that occur in the environment of deposition. The new geobody is stacked on top of the current depositional surface, which can be locally eroded in the process. The geobody top surface is merged with this topography. This new surface then becomes the current depositional surface. The stacking is repeated until a stopping criterion is reached. Such models are stochastic because the parameters values used to perform a forward simulation (size of the geobodies, location of the source, etc.) are uncertain and therefore randomly drawn from probability distributions. With surface-based technique, complex geometries can be accurately generated at low computational costs. The disadvantage of surface-based technique is the complexity, which

5 comes from making proper rules for different depositional environments and model conditioning. As a forward modeling technique, surface-based model is conditioned by optimization-based method (Bertoncello et. al. 2011). 2. Methodology 2.1 Motivation As stated in above, the first challenge of this research is that reasonable modeling of erosion requires explicitly model the deposition-erosion processes, even if in an approximate manner. The reason is that erosion on shale drapes are correlated to subsequent channel-lobes, and the subsequent lobe geometry and placement are correlated to topography after previous events (channel-lobe). To explicit model the complex deposition-erosion processes leads to a forward model and will significantly increase the complexity of model conditioning. Obviously, two-point statistics and multiple-point statistics are improper for this purpose. The scarcity of data limits the use of two-point geostatistics, because the algorithm cannot obtain statistical significant spatial correlations from the sparse data. Multiple-point statistics are not ideal either. First, multiple-point statistics requires a training image to represent enough pattern variability in order to generate realistic realizations. However, a depositional basin is usually few in number of lobes. In other word, a training image for a lobate reservoir usually does not provide enough information of lobe geometry. Second, multiple-point statistics places constraints of spatial correlations of patterns implicitly through the training image, however, it still does not consider the process information. Object-based methods exceed two-point geostatistics and multiple-point statistics, in better representing nonlinear complex geometries of channel and lobes. However, since object-based methods randomly place objects into the model domain, the intermediate surface information are not used, therefore, the depositionerosion processes are still not explicitly modeled. Process-based methods are very limited in reservoir modeling for their computational costs and the methods are very difficult to be conditioned due to the inherent rigorousness of fluid dynamic equations. In summary, twopoint geostatistics, multiple-point statistics, object-based and process-based methods all face challenges to build models representing realistic deepwater reservoirs in the perspective of stratigraphy. Surface-based method is proper for modeling deepwater reservoirs because it generates complex geometries, explicitly mimicking the deposition-erosion processes with geological rules. The method can place geobodies into reasonable places with reasonable geometries. Because no equation is solved, the computational costs of surface-based method are just a fraction of

6 process-based method, but the realizations represent highly realistic stratigraphic information. Another great challenge inherent to deepwater reservoir modeling is limited data. Usually, the only available data are a handful of sparse wells and a seismic survey. Detailed reservoir stratigraphic information cannot be inferred from the sparse well data. The seismic data can definitely be used to infer the overall geometry information of the whole depositional basin. However, the reservoir, in most conditions, is a small part of the depositional basin. The reservoir top and bottom information can be inferred from the data, but the stratigraphy is subseismic and remains uncertain. Second, as a forward method, surface-based modeling requires the information of intermediate surface elevation evolution, which is lost in all stratigraphy data because of erosion. Because we lack enough dynamic data from any natural system, we propose to use tank experiment data as a new source of the deposition-erosion processes, from which the dynamic information of the process can be inferred. However, other sources of information, such as numeric simulation results, outcrop data, and satellite images, may also be used in case the tank experiment data are insufficient. The objective of documented method is to build a surface-based forward model for the lower fan part of deepwater depositional system using statistics extracted from the dynamic tank experiment data. 2.2 Concept of Surface-based Modeling The workflow used in this study follows works of Michael et. al and Bertoncello et. al (Figure 2.1). Starting from an initial topography, a new geobody is generated with key geometric parameters such as length, width, height drawn from probability distributions based on a geometry template. The geobody placement is selected according to depositional rules that partially affected by the topography. A new geobody is stacked on top of and merged with the current topography to generate a new topography. This procedure is repeated until a volume obtained from a seismic surface is filled. In the terminology of surface-based modeling, the geobody in a surface is called an event, which should be distinguished from the concept of event in sedimentology. An event in sedimentology is a single gravity flow from the top of a shelf, while an event in surface-based modeling is a geometry that includes multiple gravity flows.

7 Figure 2.1: Workflow of surface-based modeling. After Bertoncello et. al Surface Generation Geobody Template Generation Centerline Controlled Geometry Boundary Observing channel-lobe geometry from laboratory experiment data (Figure 2.2) that will be introduced in Chapter 2.4, several features of the channel-lobe morphology can be characterized:

8 1) The channel parts are smooth constant-width belts with mild sinuosity corresponding to topography; 2) The lobe geometry shows projecting oval shape with slight variance in response to the topography; Figure 2.2: Geometry examples obtained from tank experiment photos For the purpose of realistically representing the geometric features, we propose to use a centerline controlled boundary. The overall geometry are controlled by key parameters such as lobe width/length ratio, however, the shape variance corresponding to topography can be represented by rule-based shifting control points on the centerline (Figure 2.3). The sample in Figure 2.3 marked out five types of centerline control points, all of which are with geological interpretation. 1) Channel mouth: the starting point of a channel-lobe object; 2) Channel toe (lobe source): marking the end of channel and the start of a lobe; 3) Channel intermediate points: control points between 1) and 2), controlling the shape variance of distributary channel; 4) Depocenter: the thickest point of a lobe; 5) Lobe End: the end of a lobe; 6) Boundary Control: a boundary control point is calculated from a centerline point by Equation 2.1.

9 Given a set of centerline control points, the centerline can be interpolated by a spline function. The Channel width is set to be constant relative to the lobe width, which is interpreted from tank experiment geomorphology (Figure 2.2). The advantage of using centerline control points is that statistics of key points with geological meaning are easier to be interpreted in case that the analog data are imperfect. The lobe geometry (Figure 2.4) is defined by an oval shape equation. Given a point P on the lobe part centerline, the half distance from P to its W corresponding boundary control point,, is calculated by Equation (1). P 2 (1) where L is the given lobe length, f W L max w = is the lobe width/length ratio; is the normalized distance from point Pto the channel toe; c c are built-in constants correlated to oval geometry. 1, 2 Figure 2.3 A sample centerline controlled channel-lobe boundary

10 Figure 2.4: Lobe Geometry Calculation, refer to Equation 2.1. Distance Maps Given the centerline and the boundary of object, the channel and lobe distance map is generated to represent the general trend of channel and lobe geometry. The channel geometry shows a trend from centerline to boundary, therefore the trend map is generated by calculating the normalized distance map from centerline to channel boundary (Figure 2.5 a, b). Figure 2.5: a) Normalized distance from channel boundary to channel centerline; b) Channel Trend Map; The lobe geometry shows a trend from lobe boundary to channel toe, thus the lobe trend map is generated by calculating the normalized distance map from lobe boundary to channel toe (Figure 2.6).

11 a) b) Normalized Boundary-Channel Toe Distance 1 0 Figure 2.6: a) Normalized Boundary-Channel Toe Distance; b) Lobe Trend Map The Concept of Positive and Negative Surface for Erosion For modeling erosion, here we introduce the concept of positive and negative surface (Figure 2.7). In surface-based modeling, deposition is represented by geometry with thickness information. However, the increased elevation of the topography is not equal to lobe thickness because of the erosion process. In other words, a portion of the new geobody will be below the previous topography. In this study, we call this portion of the lobe the Negative Surface and the remained portion the Positive Surface. Therefore, the sum of absolute value of negative surface and the positive surface is the lobe thickness. Our problem of modeling erosion is converted into determining the negative surface given a new geobody, honoring statistics from the tank experiment data.

12 Figure 2.7: A new lobe is generated and placed onto previous surface a); Because of the erosion process, a portion of the new lobe is placed below the previous topography b); In this study, the portion below previous topography is called negative surface, representing erosion caused by the new lobe; the portion above previous topography is called positive surface, representing deposition caused by the new lobe c). Therefore, the erosion problem in surface-based modeling is converted into generating a negative surface given a positive surface, honoring statistics from tank experiment data. Currently, we assume that the negative surface is geometrically analogous and translated to the positive surface. Figure 2.8 demonstrates some examples of the positive/negative surface geometries. Figure 2.8: Examples of positive surfaces and negative surfaces. 0.3 Thickness of the positive surface and depth of the negative surface is calculated by two sets of geometrical functions. Figure 2.9 demonstrates the calculations. For the channel positive surface, the thickness is calculated with Equation (2). a?? (2) where hpis the thickness at point P; dpis the normalized distance generated in the channel trend map (Figure 2.5); h1max is the maximum thickness of the channel positive surfaces; cis a

13 built-in geometric constant. Equation (2) can be directly applied for obtaining depth of the negative surface by replacing h1max with?? where f pn is a given parameter of the ratio of channel positive thickness vs. channel negative depth. Figure 2.9: Computation of Surface Thickness, refer to Equation (2) (4). The lobe surfaces are calculated with Equation (3) and (4). a?? (3)?? (4) where hpis the thickness at point P; dpis the normalized distance generated in the lobe trend map (Figure 2.5); h1max is the maximum thickness of the lobe positive surfaces; cis a built-in geometric constant; hchannel is the channel thickness; d1depois the distance from channel toe to the thickest point of the lobe positive surface. Equation (3) and (4) can also be directly applied to obtain the depth of the negative lobe surface Geobody Placement In the documented model, the channel-lobe placement is determined by the combined

14 depositional model. In the framework of surface-based modeling, a depositional model is a probability map conceptualized from geological understanding about the depositional processes. A depositional model has several components, based on geological rules. In the documented model, the depositional model has three components: 1) the distance to sources; 2) the distance to previous lobe; 3) the deposition thickness. The depositional model and its components at an intermediate simulation step are demonstrated in Figure For the distance-to-source and distance-to-previous-channel-end components, areas closer to those points are assigned higher probabilities; for the total-deposition-thickness component, the thinner deposition areas are given higher probabilities. All of the probabilities are linearly converted from distance and thickness. Finally, the intermediate deposition model is combined from three components by Tau model, from which the next channel-end point is picked up. Figure 2.10 a) Intermediate total deposited elevation surface (topography), the model source and previous channel end point are plotted out; b) the distance-to-source component; c) the distance-to-previous-channel-end component; e) the total-deposition-thickness map; d) the combined deposition model; 2.3 Tank Experiment Data Tank experiment data are studied and characterized for the surface-based model. In cooperation with Chris Paola, St. Anthony National Laboratory, an experiment for turbidite environment is in preparation. Currently, we start with a dataset from a distributary delta experiment. The data includes three sets of 1D intermediate dynamic topography, respectively measured from proximal, medial, distal part of a distributary delta experiment.

15 2.3.1 Experiment Setting The experiment discussed here (DB-03) was performed and originally documented by Sheets et al. (2007). The main focus of the work of Sheets et al. was documenting the creation and preservation of channel-form sand bodies in alluvial systems. Since this initial publication, data from the DB-03 experiment have been used in studies on compensational stacking of sedimentary deposits (Straub et al., 2009) and clustering of sand bodies in fluvial stratigraphy (Hajek et al., 2010). In this section we provide a short description of the experimental setup. For a more detailed description see Sheets et al. (2007). The motivation for the DB-03 experiment was to obtain detailed records of fluvial processes, topographic evolution and stratigraphy, with sufficient spatial and temporal resolution to observe and quantify the formation of channel sand bodies. The experiment was performed in the Delta Basin at St. Anthony Falls Laboratory at the University of Minnesota. This basin is 5 m by 5 m and 0.61 m deep (Figure 2.11). Accommodation is created in the Delta Basin by slowly increasing base level by way of a siphon-based ocean controller. This system allows for the control of base level with mm-scale precision (Sheets et al., 2007). Figure 2.11: a) Schematic of the experimental arrangement. b) A photograph of the DB-03 experiment at a run time of approximately 11h. After Genti et. al

16 The experiment included an initial build-out phase in which sediment and water were mixed in a funnel and fed into one corner of the basin while base-level remained constant. The delta was allowed to prograde into the basin and produced an approximately radially symmetrical fluvial system. After the system prograded 2.5 m from source to shoreline a base-level rise was initiated. Subsidence in the Delta Basin was simulated via a gradual rise in base level, at a rate equal to the total sediment discharge divided by the desired fluvial system area. This sediment feed rate allowed the shoreline to be maintained at an approximately constant location through the course of the experiment. A photograph of the experimental set-up, including the topographic measurement line, is shown in Figure (Sheets et al. 2007) used a sediment mixture of 70% 120??m silica sand and 30% bimodal (190??m and 460??m) anthracite coal. Topographic measurements were taken in a manner modeled on the Experimental Earthscape Basin (XES) subaerial laser topography scanning system (Sheets et al., 2002). Unlike the XES system, however, where the topography of the entire fluvial surface is mapped periodically, topography was monitored at 2 minute intervals along a flow-perpendicular transect located 1.75 m from the infeed point. A time series of deposition along this transect is shown in Figure This system provided measurements with a data-sampling interval of 0.8 mm in the horizontal and with a measurement precision of 0.9 mm in the vertical. The experiment lasted 30 hours and produced an average of 0.2m of stratigraphy. Upon completion of the experiment, the deposit was sectioned and imaged at the topographic strike transect. This allows direct comparison of the preserved stratigraphy to the elevation fluctuations that generated the stratigraphy. No attempt was made to formally scale the results from this experiment to field scale, nor were the experimental parameters set to produce an analog to any particular field case. Rather, the goal of the experiment was to create a self-organized, distributary depositional system in which many of the processes characteristic of larger depositional channel systems could be monitored in detail over spatial and temporal scales which are impossible to obtain in the field. The rationale for such experiments is discussed in detail in (Paola et al 2009). The point here is that our focus is on identifying the general class of distributions (i.e. heavy vs. thin tail) that characterize the kinematics of topography in the DB-03 experiment and their relationship to the architecture of the preserved stratigraphy Data Exploration For each section, we have 1180 dynamic intermediate surfaces. The finalized surfaces of the distal cross line are demonstrated in Figure Figure 2.13 demonstrates the surface evolution with a subset of the distal section. The first problem for data exploration is to

17 determine regions in the tank sediments that are equivalent to reservoirs in a real deepwater system and visualize geometry information of positive surfaces and negative surfaces. Depending on visualized geometry patterns, statistics will be characterized, however, since the tank experiment is not scaled to any real environment, only dimensionless geometric ratios will be extracted but not the absolute length, width etc. Terminology For the ease of quantifying geology and formulating the problem, several geological concepts are formulated as follows and will be used through this study. Topography intermediate top surfaces at every t Symbol: Z t (x,i), x is the location vector; surface index is a scalar i = 1,2,3,,t Stratigraphy all previous surfaces at every t Symbol: S t (x,i), x is the location vector; surface index is a vector i = [1,2,3,,t] Erosion E t+dt (x,i) Where Z t+dt (x,i) < Z t (x,i) Deposition D t+dt (x,i) Where Z t+dt (x,i) > Z t (x,i)

18 Figure 2.12: Finalized surfaces of the distal cross section.

19 Figure 2.13: Surface evolution in the deposition process at the distal section. Numbers represent the sequence of charts.

20 Geobody Definition in Surfaces Because we are looking for geometry information of channel-lobe objects, the first step is to identify these objects in the tank data. The deposition/erosion geometries (Figure 2.14) are plotted to visualize patterns of deposition/erosion. In Figure 2.14, a), b) are the deposition and erosion maps for the distal section.the vertical axis represents time and horizontal axis represents section line vertical to flow direction (refer to Figure 2.11 a). All maps are thresholded to clean up minor deposition/erosion and to emphasize the primary patterns. The plots reveal several interesting features of the patterns: 1) Deposition and erosion processes demonstrate spatial and temporal clustering. Discontinuity appears both spatially and temporally between clusters; 2) Depositional process is usually correlated to erosion processes. However, the erosion is not as laterally continuous as correlated deposition. Feature 1) can be interpreted as several deposition events that occurs in similar region, which can be defined as one geobody. The spatial and temporal gap between one cluster and the other is the interruption of two sets of deposition events and therefore distinguish two geobodies formed by them. Feature 2) provides some hints of geobody geometry. Deposition is represented by the positive surface, which are generated by given geobody template. Erosion is represented by the negative surface, however, erosion pattern in the data are laterally less continuous than deposition pattern, which indicates that the negative surfaces can be discontinous patterns and modifications should be made on our current geobody design.

21 Figure 2.14: a) Deposition geometry of the highlighted region in Figure 2.12; b) Erosion geometry of the highlighted region in Figure 2.12; c) the overlapped geometries of 2.14 a) and 2.14 b); d) the zoomed in geometry of highlighted region in 2.14 c); Further studying the geometries in Figure 2.14 d), the geometries can be grouped into three categories, which correlate to different channel-lobe types (Table 2.1). According to the relative width of a pair of deposition-erosion geometry, the geometries are interpreted to be 1) channels; 2) lobes with erosion; 3) lobes without erosion. Three statistics are characterized from Figure 2.14 d) for each of the groups: 1) ratio of lobes with erosion over lobes without erosion; 2) the probability distribution of dimensionless ratio of maximum lobe erosion depth de L over maximum lobe deposition thickness dd L ; 3) the probability distribution of dimensionless ratio of maximum channel erosion de C over the maximum channel deposition thickness dd C.

22 Deposition Width <= Erosion Width Interpreted as channels Deposition Width > Erosion Width Interpreted as Lobes with erosion No Erosion Interpreted as Lobes without erosion Table 2.1: Groups of different Geometries The ratio of lobes with erosion over lobes with erosion is 30%. The pdfs and cdfs of statistics 2) and 3) are demonstrated in Table 2.2. These three statistics are used to control the simulation using the simple surface-based model documented in the above sections. PDF CDF Lobe with erosion Channel Table 2.2: Statistics of dimensionless ratios of maximum erosion depth and deposition thickness from Figure 2.14 d). 3. Simulation Results The objective of this test simulation aims at verifying that the statistics from a simulated cross

23 section reproduces the statistics in Section 2.3.3, therefore the model is not correlated to any real length scale but just the model unit representing relative sizes and locations of the geometries. The geometry scales are given by lobe length L, other parameters such as lobe width, lobe thickness etc. are set correlated to the lobe length by a ratio. Primary parameters are listed in Table 3.1. Some intermediate steps of the simulation are demonstrated in Figure 3.1. Grid Dimension 300 x 250 dx 1 Lobe Length [50dx, 130dx] uniformly distributed Lobe Width [0.3L, 0.7L] uniformly distributed Lobe Thickness [0.002L,0.008L] uniformly distributed Number of Surfaces 1180 Initial Surface Flat Table 3.1: Primary simulation Parameters a) b) c) d) Figure 3.1: Intermediate depositional thickness of one simulation. a) Depositional thickness at T = 20; b) Depositional thickness at T = 40; c) Depositional thickness at T = 200; d) Depositional thickness at T = 1180, a cross section at the line is taken out for comparison of statistics;

24 Figure 3.2: a) Distal cross section of the simulated realization b) Deposition-erosion geometries of a subregion of the simulated realization circled out in Figure 3.2 a). The same statistics in Table 2.2 is characterized from this Figure 3.2 (Table 3.2).

25 Lobe with Erosion Channel Table 3.2: Statistics of dimensionless ratios of maximum erosion depth and deposition thickness from Figure 3.2. Figure 3.3 a) QQ-plot comparing Lobe Erosion/Deposition Ratio Distribution and Simulated Lobe Erosion/Deposition Ratio Distribution; b) QQ-plot comparing Channel Erosion/Deposition Ratio Distribution and Simulated Lobe Erosion/Deposition Ratio Distribution;

26 One obvious observation from Figure 3.3 is that the pdfs from the simulated realization have close to the pdfs directly interpreted from the tank experiment data. Moreover, the ratio of lobes with erosion over lobes with erosion is from the simulated realization is 32.1%, similar to 30% that is interpreted from the tank experiment data. However, no attempt has been made to control the geobody placement, the clustering of geobody in the simulated realization (Figure 3.2 a and b) is different from the tank experiment data (Figure 2.14 d). 5. Conclusion and Future Works In summary of the documented study, with the surface-based modeling techniques, our simulation produced similar dimensionless statistics in the cross section taken at the similar location of that taken in the tank experiment. However, no real spatial patterns and statistics are achievable using information from a 1D cross section data. The further study will focus on the use of 2D overhead photos taken at the same intervals of the dynamic cross section data. More specific geometry information and spatial statistics can be interpreted from the overhead photos when the photos are matched with the topography cross section, such as the spatial correlation of the negative surface and the positive surface. More specific geometric information and rules of geobody placement are expected to be extracted from the overhead photos as well. Reference Arpart, G., Caers, J., Conditional simulation with patterns. Mathematical geology 38 2, Bertoncello, A., Conditioning surface-based models to well and thickness data. Ph.D. thesis, Stanford University. Bouma, A., Normak, R., N, B., Submarine fans and related turbidite systems. New York Springer. Chapin, M., Davies, P., Gipson, J., Pettingill, H., Reservoir achitecture of turbidite sheet sandstones in laterally extensive outcrops, ross formation, western ireland. In: Submarine fan and turbidite systems. Gulf Coast Section SEPM 15th Annual Research Conference. Deutsch, C., Wang, L., Hierachical object-based stochastic modeling of fluvial reservoirs. Mathematical Geology 28, Ganti, V., K. M. Straub, E. Foufoula-Georgiou, and C. Paola (2011), Space-time dynamics of depositional systems: Experimental evidence and theoretical modeling of heavy-tailed statistics, J. Geophys. Res., 116, F02011,

27 doi: /2010jf Garland, C., Haughton, P., King, R., T., M., Capturing resrvoir heterogeinty in a sand rich submarine fan, milel field. In: Fleet and Boldy edition. Petroleum Geology of northwestern Europe: Proceedings of the 5th Conference. Gervais, A., Mudler, T., Savoye, T., Gonthier, B., Sediment distribution and evolution of sedimentary processes in a small and sandy turbidte system: implication for various geometries based on core framework. Geo-Marine Letters 26, Groenenberg, R., Hodgson, D., Prelat, A., Luthi, S., Flint, S., Flow-deposit interaction in submarine lobes: insights from outcrop observations and realizations of a process-based numerical model. Journal of Sedimentary Research 80, Hajek, E. A., P. L. Heller, and B. A. Sheets (2010), Significance of channel-belt clustering in alluvial basins, Geology, 38, Holman, W., Robertson, S., Field development, depositional model and production performance of the turbiditic j sands at prospect bullwinkle, greencanyon 65 field, outer shelf gulf of mexico. Submarine fans and turbidite systems: Gulf Coast SectionSEPM, Hooke, R. Le B. (1968), Model geology: prototype and laboratory streams:discussion, Geol. Soc. Am. Bull., 79, Journel, A., Combining knowledge from diverse sources: an altenative to traditional data independance hypotheses. Mathematical Geology 34, Lessenger, M., Cross, T., An inverse stratigraphic simulationmodel-is stratigraphic inversion possible? Energy exporation and exploitation 14, Levy, M., Harris, P., Strebelle, S., Rankey, E., Geomorphology of carbonate systems and reservoir modeling: Carbonate training images, fdm cubes, and mps simulations. Long Beach CA. Li, H., Caers, J., Geological modelling and history matching of multiscale flow barriers in channelized reservoirs: methodology and application. Petroleum geoscience 17, Li, H., Genty, C., Sun, T., Miller, J., Modeling flow barriers and baffles in distributary systems using a numerical analog from process-based. San Antonio, TX. Madej, M. A., Development of channel organizatuib and roughness following sediment pulses in single thread, gravel bed rivers. Water Resources Research 37, Mallet, J., Space-time mathematical framework for sedimentary geology. Mathematical Geology 36, McGee, D., Bilinski, P., Gary, P., Pfeiffer, D., Sheiman, J., Models and reservoir geometries of auger field, deep-water gulf of mexico. pp McLean, H., Reservoir properties of submarine-fan facie: Great valley sequence, california. Journal of Sedimentary Petrology 51, Michael, H., Gorelick, S., Sun, T., Li, H., Caers, J., Boucher, A., Combining geologic process models and geostatistics for conditional simulation of 3-D subsurface heterogeneity. Water Resources Research. Miller, J., Sun, T., Li., H., Stewart, J., Genty, C., Li, D., Direct modeling of reservoirs through forward processbased models: Can we get there?. IPTC, Malaysia. Mutti, E., Normak, W., Comparing example of modern and ancient turbidites systems: problems and concepts. New York Springer. Mutti, E., Tinterri, R., Seismic Facies and Sedeimntary processes of Modern and Ancient Submarine Fans. Springer Verlag, New York, pp Paola, C., K. Straub, D. Mohrig, and L. Reinhardt (2009), The unreasonable effectiveness of stratigraphic and

28 geomorphic experiments, Earth Sci. Rev., 97, Prelat, A., Hodgson, D., Flint, S., Evolution, architecture and hierarchy of distributary deep-water deposits: a high-resolution outcrop investigation of submarine lobe deposits from the permian karoo basin, south africa. Sedimentology, 56, Prelat, A.,Covault. J, Hodgeson, D., Fildani, A., Flint, S., Intrinsic controls on the range of volumes, morphologies, and dimensions of submarine lobes. Sedimentary Geology, Volume 232, Issues 1 2, Pages Pyrcz, M., Catuneanu, O., Deutsch, C., Stochastic surface-based modeling of turbidite lobes. AAPG bulletin 89, Pyrcz, M., Strebelle, S., Event-based geostatistical modeling of deepwater systems. Gulf Coast Section SEPM 26th Bob F. Perkins Research Conference. Reading, H., Richards, M., Turbidite systems in deep-water basin margins classified by grain size and feeder system. Bull. Am. Ass. Petrol. Geol. 78, R.Slatt, Weimer, P., Turbidte systems: Part 2: Subseismic-scale reservoir characteristics. The Leading Edge 18, Saller, A., Werner, K., Sugiaman, F., Cebastiant, A., R. May, D. G., Barker, C., Characteristics of pleistocene deep-water fan lobes and their application to an upper miocene reservoir model, offshore east kalimantan. Geophysics 92-7, Scheidt, C., Caers, J., A new method for uncertainty quantification using distances and kernel methods. application to a deepwater turbidite reservoir. SPE Journal 14, Shmaryan, L., Deutsch, C., Object-based modeling of fluvial-deepwater reservoirs with fast data conditioning: Methodology and case studies. Mathematical Geology 30, Steffens, G., Shipp, R., Prather, B., Nott, J., Gibson, J., Winker, C., The use of near-seafloor 3D seismic data in deep water exploration and production. The geological Society of London, pp Stow, D., King, M., Deep-water sedimentary systems: New models for the 21st century. Marine and Petroleum Geology 17, Sheets, B., C. Paola, and J. M. Kelberer (2007), Creation and preservation of channel-form sand bodies in an experimental alluvial basin, Sedimentary Processes, Environments and Basins, edited by G. Nichols, E. Williams,and C. Paola, pp , Blackwell, Oxford, U. K. Straub, K. M., C. Paola, D. Mohrig, M. A. Wolinsky, and T. George(2009), Compensational stacking of channelized sedimentary deposits, J. Sediment. Res., 79, Strebelle, S., Conditional simulation of complex geostatitical structures using multiple-point statistics. Mathematical geology 34, Strebelle, S., Payrazyan, K., Caers, J., Modeling of a deepwater turbidite reservoir conditional to seismic data using principal component analysis and multiple-point geostatistics. SPE Journal 8, Strebelle, S., Zhang, T., Non-stationary multiple-point geostatistical models. Banff Canada. Sullivan, M., Jensen, G., Goulding, F., Jennette, D., Foreman, L., Stern, D., Architectural analysis of deepwater outcrops: Implications for exploration and development of the diana sub-basin, western gulf of mexico. pp Wellner, R., Awwiller, D., Sun, T., Energy dissipation and the fundamental shape of siliciclastic sedimentary bodies. American Association of Petroleum Geologists Official Program 12. Zhang, K., Pyrcz, M., Deutsch, C., Stochastic surface based modeling for integration of geological Information in turbidite reservoir. Petroleum Geoscience and Engineering 78,