Static connectivity of stacked deep-water channel elements constrained by high-resolution digital outcrop models

ABSTRACT

High-resolution digital outcrop models of stacked deep-water channel elements are constructed from the Laguna Figueroa section of the well-exposed Upper Cretaceous Tres Pasos Formation in Chilean Patagonia. The models are based on greater than 1600 m (>5250 ft) of centimeter-scale measured sections, greater than 100 paleoflow measurements, and thousands of differential global positioning system points (10-cm [4-in.] accuracy) from an outcrop belt that is approximately 2.5 km (∼1.5 mi) long and 130 m (425 ft) thick. The models elucidate the effects bed-to-geobody–scale architecture has on static sandstone connectivity among a series of stacked deep-water channel elements and how that connectivity is altered by grid cell size.

Static connectivity analyses show that channel element base drapes can strongly influence sandstone connectivity and that smaller channel element widths are more likely to produce disconnected sandstone geobodies. Net-to-gross (NTG) is not directly correlated with connectivity because of the presence of thin channel element base drapes, which do not significantly contribute to NTG. Upscaling the models consistently increases channel element contact (up to 10%) but decreases sandstone connectivity (up to 2%–3%). Channel element stacking patterns strongly impact connectivity. For example, connectivity is reduced in cases of high lateral channel element offsets. Increasing drape coverage markedly decreases connectivity. Evaluating connectivity in a vertical, along-system profile is critical to understanding flow units and reservoir piping. Ultimately, this work constrains uncertainty related to the impact of subseismic-scale stratigraphic architecture on reservoir connectivity by providing concrete knowledge that can be used to guide the model building process.

INTRODUCTION

Deep-water slope channel systems are widely recognized as important conduits for sediment transfer from slope to basin and as locations for sediment storage on slopes. As such, slope channel deposits constitute globally significant petroleum reservoirs (e.g., Stow and Mayall, 2000; Sullivan et al., 2000; Abreu et al., 2003; Samuel et al., 2003; De Ruig and Hubbard, 2006; Labourdette et al., 2006; Mayall et al. 2006; Deptuck et al., 2007; Weimer and Slatt, 2007; Cross et al., 2009; Alpak et al., 2013; Fowler and Novakovic, 2018). Advances in understanding channelized deep-water depositional systems are, in part, driven by advances in subsurface imaging (e.g., Deptuck et al., 2003; Posamentier and Kolla, 2003; McHargue et al., 2011; Sylvester et al., 2011). High-resolution three-dimensional (3-D) seismic reflection surveys, with vertical resolution commonly 10–20 m (35–65 ft), have provided substantial insight into these systems (Figure 1; Posamentier and Kolla, 2003; Mayall et al., 2013). Interpretations from high-resolution seismic reflection profiles are further improved when coupled with conventional core and well-log data and chronostratigraphic information (Posamentier and Kolla, 2003; McHargue et al., 2011; Bernhardt et al., 2012; Sharman et al., 2018). However, despite technological advances and an increased focus on deep-water slope systems, the subseismic-scale architecture that controls fluid flow and connectivity in a reservoir remains challenging to predict because of significant lithologic variability over short-length scales (Bryant and Flint, 1992; McHargue et al., 2011; Fowler and Novakovic, 2018).

Figure 1. (A) Seismic reflection image of deep-water channel system stratigraphic hierarchy from the Dalia field, West Africa (modified from Zhang et al., 2017). Channel elements are readily characterized in outcrops but are generally below the resolution of seismic reflection data. Despite this, their internal architecture as well as their stacking patterns impart an important influence on deep-water channel reservoirs. Stacked channel elements compose a channel complex (examples defined by blue dashed lines), whereas stacked channel complexes compose a channel complex set, which is most readily interpretable in subsurface data (Abreu et al., 2003; Sprague et al., 2005; McHargue et al., 2011). Well path (yellow) is associated with a gamma-ray log at left (green) and a density log at right (orange). (B) Seismic cross section of a channel system beneath the Niger Delta slope sea floor, West Africa (modified from Jobe et al., 2015). (C) Simplified line drawing interpretation of an aggradational channel complex in the deep-water channel stratigraphy (from area defined by rectangle in [B]), with channel elements similar to those modeled in this study highlighted. The sandy elements are bound by largely fine-grained levee, internal levee, or mass transport deposits, resulting in a vertically aligned succession of high-amplitude reflections 100–150 m (330–500 ft) thick. (D) Thalweg deposits in the Niger Delta data set are considered to correspond closely in terms of scale and internal architecture to channel elements preserved in the Tres Pasos Formation (modified from Jobe et al., 2017). (E) Outcrop of channel element in the Tres Pasos Formation linked to area highlighted in (D) (modified from Macauley and Hubbard, 2013 and Covault et al., 2016).

Data limitations and the financial risk associated with drilling for hydrocarbons in deep-water settings makes adequate quantification of uncertainty of utmost importance for both developing new prospects and for reservoir management (Hovadik and Larue, 2007; McHargue et al., 2011). Investigating how lateral and vertical bed-scale relationships impact reservoir performance provides a framework for more informed reservoir-scale predictions. Outcrop analog studies aid the interpreter by providing possible reservoir architectures not resolvable from conventional subsurface data to inform better reservoir management decisions and quantify economic risk, ultimately increasing reservoir performance (Campion et al., 2000; Larue and Friedmann, 2005; Bakke et al., 2008; Donselaar and Overeem, 2008; Stright et al., 2014; Hofstra et al., 2017). A better understanding of production performance comes from understanding the role internal sedimentary architecture and facies geometries of channel systems play in reservoir connectivity (Larue and Hovadik, 2006; Hovadik and Larue, 2007; Barton et al., 2010; DiCelma et al., 2011; Funk et al., 2012).

In this study, 18 slope channel elements of the Cretaceous Tres Pasos Formation are characterized from an outcrop exposure in southern Chile that is 2.5 km (1.5 mi) long and 130 m (430 ft) thick. Outcrop data and observations are used to build a 3-D outcrop-based model that is a deterministic reconstruction of the Cretaceous deep-water channel system. The exceptionally exposed deposits are ideal for study of the impact that bed-scale architecture has on 3-D connectivity because they have been the focus of ongoing research aimed at constraining internal channel element architecture, channel element geometry, and channel element stacking patterns (Macauley and Hubbard, 2013; Pemberton et al., 2018). Furthermore, the bed-scale sedimentology, stratigraphic architecture, and interpreted external controls on deep-water sedimentary processes from the bed-to-basin scale have been widely shown to share analogous attributes with slope channel stratigraphy on continental margins globally (Fildani et al., 2013; Macauley and Hubbard, 2013; Stevenson et al., 2015; Covault et al., 2016; Reimchen et al., 2016; Daniels et al., 2018). This outcrop analog data set and derivative deterministic outcrop models provide examples of how subseismic-scale architecture impacts connectivity in these types of reservoirs and how the connectivity is altered by decisions associated with modeling grid cell size.

SUBMARINE CHANNEL ELEMENTS

A globally important class of submarine channel deposit stratigraphy is composed of variably stacked architectural elements, or channel elements (Figure 1; McHargue et al., 2011). Although channel element character can vary as a result of numerous parameters, such as relative position on a paleoslope (Beaubouef et al., 1999; Gardner et al., 2003; van der Merve et al., 2014), a particularly common channel element pattern consists of a central core of amalgamated sandstone (axis) that transitions laterally into thick- to thin-bedded, nonamalgamated turbidites at the edges of the channel element (margin) (Mutti and Normark, 1987; Sullivan et al., 2000; Sprague et al., 2002; Gardner et al., 2003; Campion et al., 2005; Mayall et al., 2006; Pyles et al., 2010; Alpak et al., 2013; Gamberi et al., 2013; Macauley and Hubbard, 2013; Hubbard et al., 2014; Covault et al., 2016; Li et al., 2016). Whereas coarse-scale architecture (e.g., channel complex stacking patterns, composed of two or more stacked channel elements) can be interpreted from seismic reflection data (Abreu et al., 2003; McHargue et al., 2011), seismic resolution is generally too low to image individual channel elements, much less intraelement architecture (Prather et al., 2000; Pyles et al., 2010; Fildani et al., 2013; Hubbard et al., 2014). Delineation of internal channel element architecture is also challenging in the subsurface because of a lack of cored boreholes and high-resolution seismic data (Wynn et al., 2007).

Of particular importance to delineating internal channel element architecture are channel element base drapes. Channel element base drapes are fine-grained deposits that conformably overlie the basal composite surface of channel elements (Mutti and Normark, 1987; Mayall et al., 2006; Alpak et al., 2013; Macauley and Hubbard, 2013). They are commonly attributed to phases of sediment bypass through channels, wherein the bulk of the formative turbidity currents pass downslope, and sedimentation is primarily from the low-velocity, dilute tail of the flow (Mutti and Normark, 1987; Stevenson et al., 2015). They can also result from aggradation of turbidite caps (Bouma Td–Te) in instances where the sandy parts of flows only deposit in limited regions within a channel (e.g., thalweg) (Li et al., 2016). Drape deposits are dominantly mudstone and siltstone, can be up to a few meters thick, and can record evidence of multiple incision and sediment bypass events (Barton et al., 2010; Hubbard et al., 2014; Li et al., 2016).

Understanding the distribution and characteristics of channel element base drapes is critical for predicting reservoir performance because they exhibit a key control on reservoir compartmentalization and can act as barriers or baffles to flow (Stright, 2006; Stewart et al., 2008; Barton et al., 2010; Alpak et al., 2011, 2013). The degree to which (1) coarse-grained flows are bypassed, (2) mud can accumulate between major sediment transfer events, and (3) successive flows erode previously deposited drape facies all control the ultimate prevalence of drape deposits at channel element bases (Hubbard et al., 2014). Because the 3-D distribution of drape deposits is highly uncertain and difficult to predict, they represent a significant uncertainty for reservoir development

(Stright, 2006; Alpak et al., 2013). A better understanding of the impact that drape deposits can have on connectivity is useful when modeling reservoirs characterized by pervasive drapes (>60% coverage; Stright, 2006) that are expected to affect reservoir performance.

GEOLOGIC BACKGROUND AND STUDY AREA

The Magallanes retroarc foreland basin of southern Chile (50°30′–52°S) formed in the Late Cretaceous because of loading of the Andean fold-thrust belt (Dalziel et al., 1974; Fosdick et al., 2011). The elongate basin was infilled axially from north to south by sediment sourced predominantly from the Andean orogenic belt (Katz, 1963; Romans et al., 2010) over a period of approximately 20 m.y. during the Late Cretaceous, resulting in a 4000–5000-m (13,000–16,500-ft)-thick basin fill (Romans et al., 2011).

Figure 2. (A) Upper Cretaceous stratigraphic context for the Tres Pasos Formation, Magallanes Basin. (B) The study area location, just north of the town of Puerto Natales in southernmost Chile (see inset map). Fm = Formation; L. = Lago; U. = Upper.

The Campanian Tres Pasos Formation is part of a largely conformable marine sequence in the basin. This sequence includes the deep-water Punta Barrosa, Cerro Toro, and Tres Pasos Formations (Fildani et al., 2003; Romans et al., 2011; Daniels et al., 2018) as well as the genetically related shallow marine and deltaic deposits of the overlying Dorotea Formation (Figure 2A; Covault et al., 2009; Hubbard et al., 2010; Schwartz and Graham, 2015). This study focuses on outcropping units near Laguna Figueroa, approximately 40 km (∼25 mi) north of Puerto Natales, just west of the Chile–Argentina border (Figure 2B). Stratigraphic measurements indicate that the channel element deposits of interest were deposited in at least 900–1000 m (2900–3300 ft) of water, approximately 35–40 km (∼22–25 mi) downslope from the paleoshelf edge (Daniels et al., 2018).

Figure 3. Outcrop model showing perspective image of slope channel element strata above Laguna Figueroa, with locations of measured sections (subvertical lines) and mapped stratigraphic surfaces (subhorizontal lines) surveyed with differential global positioning system (dGPS) shown. Line colors denote date of acquisition. Paleoflow was generally from left to right (north to south), and therefore the outcrop exposes an overall depositional dip-oriented perspective. However, local gullies offer strike perspectives, which enable three-dimensional projection of deep-water channel elements.

The Laguna Figueroa outcrop belt is characterized by turbiditic sandstones and mudstones exposed in a long outcrop transect that is 100–130 m (330–425 ft) thick and greater than 2 km (>1.25 mi) long (Figure 1). Macauley and Hubbard (2013) characterized the Laguna Figueroa outcrops with 1600 m (5200 ft) of section measured at centimeter scale, greater than 100 paleoflow measurements from 53 locations, and thousands of high-resolution (<10 cm [<0.5 in.] accuracy) differential global positioning system (dGPS) measurements (Figure 3). They combined these data with extensive field observations, photomosaic interpretations, and high-resolution satellite images to interpret 3-D channel element stratigraphic architecture (Figure 4). They deduced that the outcrop features a largely depositional dip-oriented perspective of channelized strata, featuring channel element fills that flowed southward, approximately parallel to the outcrop face.

Figure 4. Mapped channel elements (18) and complexes (3) extracted from the outcrop (modified from Macauley and Hubbard, 2013; Pemberton et al., 2018). (A) Planform maps of successive channel elements overlying topographic contours (north is to the top of each diagram). Through analysis of facies trends and paleoflow measurements (shown with rose diagrams), channel elements are projected behind and in front of the outcrop. (B) Dip-oriented (north-south) cross section of the channel strata, highlighting the three channel complexes and internal channel elements, numbered 1–18 (numbers correspond to maps) in (A). V.E. = vertical exaggeration.

The strata are primarily composed of deposits derived from turbidity current depositional processes (Figure 5; Bouma, 1962; Lowe, 1982; Talling et al., 2012). Three facies associations (FAs) were identified based on component sedimentation units, which are considered the fundamental architectural unit deposited from a single gravity flow event (Macauley and Hubbard, 2013). Facies association FA1 consists of massive, thick-bedded (0.2–5-m [0.5–15-ft]-thick) amalgamated sandstone (Bouma Ta division) with rare planar laminations (Tb) and ripple cross-laminations (Tc). The sandstone percentage in FA1 ranges from 71% to 100% (mean of 95%). Facies association FA2 is composed of thick- to thin-bedded, semiamalgamated sandstone. Sedimentation units are 0.05–2 m (0.15–7 ft) thick and variably include the entire Bouma sequence (Ta–Te). Sandstone makes up 29%–100% (mean of 81%) of FA2. Facies association FA3 is composed of thin-bedded (0.01–0.2-m [0.05–0.5-ft]-thick), fine- to very fine-grained sandstone interbedded with siltstone and mudstone. Amalgamation of sandstone beds is very uncommon, and sandstone percentage ranges from 0% to 80% (mean of 39%).

Figure 5. (A) Photograph of a single channel element from margin (left) toward the axis (right), with line drawing of outcrop photo in (B). This is channel element 3, and the photo is located just to the left of the central element 3 label in Figure 3B. (C) Channel element cross-sectional template used in this study to represent outcrop observations of internal channel element architecture. FA = facies association; Ta, Tb, Tc, Td and Te refer to the divisions of the Bouma (1962) sequence.

The three FAs compose the fill of mappable channelform bodies (i.e., channel elements), which represent the dominant architectural element present (Figure 5A, B). Following the methods of Sprague et al. (2005) and McHargue et al. (2011), successive channel elements that exhibit a consistent stacking pattern constitute a channel complex; two or more channel complexes constitute a channel complex set. At the Laguna Figueroa outcrop, Macauley and Hubbard (2013) described 18 channel elements and interpreted 3 channel complexes (Figure 4). Directly measuring the width of these channel elements is difficult because opposing channel element edges are typically observed hundreds of meters downdip of one another as a result of the oblique dip-oriented outcrop exposure. Channel element edges were projected based on detailed field mapping, including delineation of key surfaces and stratal terminations with dGPS (10–50-cm [5–20-in.] resolution), augmented with paleoflow data. Channel element widths were estimated to be 300 m (985 ft), whereas measured maximum thicknesses, which can be accurately measured in an outcrop, range from 12 to 16 m (40 to 50 ft) (Figures 4, 5B). Resultant channelform aspect ratios are consistent with dimensional data compiled from various data sources and basin settings around the globe (e.g., McHargue et al., 2011). Channel elements in the Laguna Figueroa section are characterized by low sinuosity (1.01–1.05) and, correspondingly, a relatively symmetric cross-sectional shape and fill pattern (Figure 5C).

At Laguna Figueroa, channel elements are observed to laterally change facies from more sandstone-rich zones in their axes (commonly where elements are the thickest) into finer-grained facies toward their edges (Figure 5A). In each element, the distribution of the three FAs therefore corresponds to three distinct zones within the channel element fill Figure 5B, C). The highest-energy amalgamated sandstone deposits of FA1 are present in channelform axes or interpreted thalweg positions. The association FA3 persists at the margins of channel elements, and FA2 is present intermediately between FA1 and FA3, in an off-axis position. In general, axis deposits contain the thickest, most amalgamated, and sandiest units; off-axis and margin deposits are defined by decreasing amounts of sandstone, bed amalgamation, and bed thickness. Importantly, particularly siltstone-rich FA3 deposits variably overlie channelform bases locally; these deposits can be up to 1 m (3.2 ft) thick at channel element margins to absent in channel element axes. We consider these as channel element base drape deposits (cf. Mutti and Normark, 1987; Hubbard et al., 2014).

METHODS

Architectural Model

We define an architectural model as a geocellular model constrained to outcrop observations, measurements, and interpretations that illustrates the distribution of channel elements. The model was constructed based on the mapping results of Macauley and Hubbard (2013), featuring stratigraphic surfaces and terminations, and measured section localities surveyed using a dGPS. Stratigraphic correlations and paleocurrent analyses were the basis for delineation of channelforms along the outcrop belt (Macauley and Hubbard, 2013); these channelforms were digitized and combined with outcrop dGPS points to generate 3-D channelform surfaces. A symmetrical thalweg position was constructed for the channel elements based on outcrop observations. The channel element surfaces were used as the framework to generate a 3-D model of channel element geobodies.

Grid Size

The model resolution is sufficient to capture the effects of static connectivity associated with bed-scale internal channel element architecture as well as juxtaposition of facies across stacked channel element boundaries. Vertical and horizontal cell sizes capture fine-scale facies, such as the channel element base drape, as well as axis (FA1) to margin (FA3) facies transitions. Areal cell size dimensions of 2 m (6.5 ft) by 2 m (6.5 ft) and 0.25 m (0.8 ft) vertically are chosen to capture thin beds and rapid lateral facies changes. This cell size is a fraction of that in a typical reservoir simulation model and produces models in excess of 600 M cells; for this study, this resolution is necessary to sufficiently quantify the impact of fine-scale heterogeneity on connectivity.

Facies Template and Facies Model

A single deterministic and interpretive cross section for a channel element is generated that represents a template of observed outcrop facies relationships (Figure 5C). Rather than modeling facies using traditional geostatistical methods, this single facies template is held constant and used to fill individual channel element surfaces at all locations along the length of the outcrop model. This simplified approach is consistent with the observations made by Macauley and Hubbard (2013) of low-sinuosity, symmetric channel elements for the Tres Pasos Formation at this location. Within the template, three model facies are distributed to capture the FAs defined by Macauley and Hubbard (2013). Facies association FA1 is composed largely of facies 1 (thick-bedded sandstone) and subordinate facies 3 (thin-bedded siltstone and sandstone) (Figure 5C). Facies association FA2 comprises facies 1 as well as facies 3 and facies 2 (thin- to thick-bedded sandstone and siltstone). Facies association FA3 is composed of facies 2 and facies 3. Facies 3 represents channel element base drape facies across the template (Figure 5C).

sserqvcfuxazrrzxbxvxwfcztvcwx Figure 6. (A) Modeled channel element. (B) Zoom in of (A) to demonstrate that conformable gridding on the edges of elements creates cells that are orthogonal to margins. (C) This approach allows control of facies template insertion, preventing distortion caused by cell orientation. (D) Each individual channel element grid is cross-scaled into a square Cartesian grid. The lowest three channel elements of channel complex 1 are shown. Vertical gridding is orthogonal in both the individual channel element model and the cross-scaled model. (E) Representative cross section through two channel elements in the model showing model grid cells.

Symmetric channel elements with constant widths are created by inserting the facies fill template at 2-m (6.5-ft) downdip increments, oriented orthogonal to the western margin of mapped channel elements (Figure 6). Individual channel elements are gridded such that grid cells are conformable to channel element edges (Figure 6B); as such, channel element cross section cells are orthogonal to margins, preventing facies template distortion caused by cell orientation (Figure 6C). Western margins are chosen as the seeding point since the lower Laguna Figueroa outcrop exposes more western margins than eastern margins or element center lines. Individual channel elements were cross-scaled into a single square Cartesian grid model, honoring the stacking patterns and scour depths measured from the outcrop (Figure 6D). Where an overlying element overlaps a stratigraphically lower element, the higher element is preserved at the expense of the scoured underlying element.

Channel Element Base Drape

Accurately capturing channel element base drape distribution is critical because these deposits are known to negatively impact connectivity in slope channel reservoirs (e.g., Alpak et al., 2013). Their distribution is typically poorly constrained in 3-D given that these features are well below the detection limit in seismic reflection data sets. Although possible to interpret in well data (e.g., Barton et al., 2010), limited penetrations provide only a hint of their distribution. Perspectives from numerous channel elements at Laguna Figueroa provide insight into drape distribution. Based on 1600 m (5250 ft) of measured section through 18 channel elements, the presence of basal drape facies is recorded for axis, off-axis, and margin deposits (Figure 5C). From this analysis, channel element base drapes occupy 42%, 69%, and 84% of channel element axis, off-axis, and margin successions, respectively (Figure 7). The channel element base drapes range in thickness from 0 to 1m (0–3.3 ft). The template explicitly represents these drapes from zero cells (no drape present) to four cells (∼1-m-[3.3-ft]-thick drape present) (facies 3 in Figure 5C).

Figure 7. Constructed cases for high and low drape coverage used in this study. The high case has a higher proportion of draping (no-flow) facies in the axis and off-axis areas and lower proportions in the margins; the low case has a higher proportion of drape coverage in the margin areas. These two cases were run for channel widths of 200, 250, and 300 m (650, 820, and 985 ft).

Locations within a channel that experience preferential erosion at their base can be gleaned from physical and numerical modeling experiments as well as from observations of the modern sea floor (e.g., Snedden, 2013). This information guides predictions of basal drape deposit distribution. Amos et al. (2010) tested low-sinuosity and high-sinuosity open channel flow in a flume to address the influence of sinuosity on flow processes and sedimentation. They found that for symmetric channels with sinuosities in the range of 1.14 to 1.94, erosion or nondeposition generally occurs toward outer bends, whereas deposition or nonerosion occurs along the inner bends of channel. As sinuosity increases, the asymmetry of erosional and depositional zones increases. Studies of active channels off the coast of British Columbia, Canada, by Conway et al. (2012) used repeat swath multibeam bathymetric data collected from surveys in 2005, 2008, and 2010 that show similar results via time-lapse perspectives of channel base aggradation or erosion. Modeling work of Sylvester et al. (2011) also found that channel deposition preferentially occurs along inner bends and erosion occurs at outer bends. All of these studies support the notion of increased preservation potential for drape deposits at the inner bends of channel elements.

Recent analysis of channel element base drapes shows that their distribution is not entirely linked to erosion and bypass. A key contributor of drape deposits is turbidity currents that are underfit relative to the full channel element width and depth (Hubbard et al., 2014; Li et al., 2016). These flows result in sand deposition in channel element axes, with capping siltstone derived from the tops of highly stratified flows deposited toward the channel element edges, contributing to thick drapes in these settings. These observations are consistent with outcrop-derived statistics, which show decreased prevalence (and proportion) of drape deposits in channel element axis zones (Macauley, 2011).

To assess the impact of channel element base drapes on reservoir connectivity, two drape coverage configurations are considered for this study (Figure 7). Both configurations honor the same channel element planform geometry but have different degrees of drape coverage. A high drape coverage scenario is guided by outcrop statistics (Figure 7), which show that axis, off-axis, and margin positions in each channel element carry probabilities of 42%, 69%, and 84% (total coverage = 72%), respectively, of being underlain by a drape. The low drape coverage scenario has 6%, 52%, and 91% (total coverage = 58%) likelihoods of axis, off-axis, and margin FAs being underlain by a channel element base drape.

Model Scenarios

Fine Scale

Six deterministic model scenarios were generated as a basis to elucidate channel element stacking pattern influence on static connectivity; three different element widths of 200, 250, and 300 m (650, 820, and 985 ft) were considered, each with the high and low channel element base drape scenario (250-m [820-ft]-wide channel element model shown in Figure 8). These widths are within the range of those most commonly observed in subsurface data sets (100–300 m [330–985 ft]) (McHargue et al., 2011). The model with a channel element width of 250 m (820 ft) and low base drape configuration is considered the “base case,” which was the basis for comparison with the other five models. Variable channel element body widths were constructed to test the sensitivity of this measure on connectivity. Furthermore, holding the channel element widths constant for each model is consistent with observations that downdip variation in element size is small for a single channel system, especially along only 2–3 km (1.25–2.0 mi) of down-paleoslope (longitudinal) distance (McHargue et al., 2011; Sylvester et al., 2011; Janocko et al., 2013). Thickness for all elements was fixed at 14 m (45 ft), which is the typical maximum element thickness in the study area (Macauley and Hubbard, 2013).

Figure 8. (A) Outcrop model that is the foundation of the connectivity analysis in this study, featuring 18 channel elements. Note the downdip division of the model into 10 segments. (B) Net sandstone map, featuring sandstone-rich channel belt from north to south, incorporating the entire stratigraphic succession. (C) A series of cross sections featuring the varied channel element stacking arrangement along the length of the outcrop belt. High-net sandstone trends are apparent where channel elements are vertically aligned.

Channel element base drape coverage has also been shown to vary among slope channel systems; models with differing drape coverage specifically test the impact of these features on connectivity.

Coarse Scale

Because of computational efficiency inherent in grid-based modeling (e.g., software limitations, restrictions on grid size, and finite time), modeling on a coarse scale grid is necessary before flow-simulating reservoir models. Maintaining key facies and geobody characteristics throughout the upscaling process is especially important (Larue and Legarre, 2004; Larue and Friedmann, 2005; Larue and Hovadik, 2006). Furthermore, it is important to understand how gridding decisions impact the overall sandstone connectivity in a model. Channel base drapes (facies 3 in Figure 5C) are assumed to block connectivity regardless of their thickness. As long as a single cell is preserved in the upscaling to capture the drape, and it is represented along the length of the base of the channel where the drape exists in the fine-scale model, the flow barrier will be adequately characterized.

To better understand the effect that different cell sizes have on connectivity, a gridding analysis was performed. This analysis was designed to (1) test what cell sizes are necessary to capture the observed channel element architecture and (2) explore differences in connectivity results from models that were upscaled to different cell dimensions. To accomplish this, the base case model (i.e., 250-m [820-ft] element width, low drape scenario) was upscaled from 2 × 2 × 0.25 m (6.5 × 6.5 × 0.8 ft) cell size to three new grids: (1) 10 × 10 × 0.25 m (33 × 33 × 0.8 ft) (areal upscale only); (2) 2 × 2 × 1 m (6.5 × 6.5 × 3 ft) (vertical upscale only); and (3) 10 × 10 × 1 m (33 × 33 × 3 ft) (upscaled in all three dimensions). Although even the coarsest grid size is still fine relative to industry practice, the analysis successfully tests the impact of cell size variation on static connectivity.

Static Connectivity Analysis

Static connectivity analyses were performed in two ways for each of the six models to evaluate facies connectivity: (1) through the models, stratigraphically, and (2) by using 10 proximal to distal segment models that are equally sized (∼250 m [∼820 ft] wide × ∼1000 m [∼3300 ft] long × 120 m [390 ft] thick) along the length of the channel system (Figure 8A). The static connectivity statistic used was modified from Funk et al. (2012). They proposed two measures of static connectivity, called margin connectivity and sand-on-sand connectivity, to assess the impact of variable facies between stacked channel elements on a cross section interface, essentially characterizing connectivity along a line. In this study, we leverage the three-dimensionality of our models to expand these statistics to connectivity across surfaces shared between intersecting channel elements; in this manner, true flow potential (flux) between elements is computable. By quantifying facies relationships across these shared surfaces, we were able to categorize all element contact surface area available for (1) high-quality fluid flux (nondraped sandstone–sandstone facies juxtapositions [SAsand]; (2) medium-quality fluid flux (nondraped sandstone–interbedded sandstone or shale juxtapositions [SAsand–interbedded]); (3) no flux (draped channel element base [SAdraped]); and (4) potential flux–background facies (channel element–levee or background mudstone [SAbackground]; Figure 9A). Each surface area is normalized by the total surface area (SAtotal) at the base of a channel element to convert it to a proportion of total surface area available for fluid flux, and there are four resulting equations (Figure 9B). First, a calculation of the highest-quality surface area connection is the proportion of channel element surface area available for fluid flux through nondraped sandstone–sandstone connections (Cnd_ss):

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Second, incorporating lower-quality facies connections into the calculation, the proportion of surface area available for fluid flux through nondraped sandstone–interbedded (thick and thin) sandstone or sandstone–sandstone connections (Cnd_all) can be determined with the following equation:

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Third is the gross channel element surface area connection, including the draped part of the channel element (Cg). This is the proportion of channel element surfaces that are in connection with another channel element, regardless of the facies juxtaposition:

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Finally, the remaining part of channel element surface area available for fluid flow to background, out-of-channel stratigraphy (Cbg) can be determined with the following equation:

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The normalization of these surface areas was modified from the original Funk et al. (2012) formulation to be the entire base of a channel element rather than the area of geobody intersection. Furthermore, Cg and Cbg are introduced to capture all potential surfaces for fluid flux. The motivation for changing the normalization was that a small overlap between channelforms that are characterized by complete sandstone–sandstone juxtaposition produced a high connectivity statistic similar to that of a scenario with a large overlap between channelforms with a small sandstone–sandstone connection. In both cases, the surface area available to fluid flow is relatively small, but the arrangement of channel elements is very different (Figure 9C). Finally, the original statistic was intended to be performed pairwise between geobodies (i.e., channel elements). In this work, we acknowledge that connectivity can occur between multiple amalgamated channel elements and the statistics herein reflect all channel element juxtapositions, not just those associated with sequentially formed channel element pairs (e.g., the connectivity was assessed between element pairs 1 and 2, 2 and 3, and 1 and 3 if they were in contact).

Figure 9. Cross-sectional illustration of modified static connectivity statistics from Funk et al. (2012), including (1) sandstone–sandstone connectivity (Cnd_ss); (2) channel element surface area connections that are not draped (Cnd_all); (3) global channel element surface area connectivity (Cg); and (4) proportion of the channel surface area connected to background (out-of-channel) facies (Cbg) statistics, defined in this study. Metrics presented hereafter are calculated in three dimensions as surface areas, rather than lines in two dimensions as shown here. (A) Channel element pair interface, with inset showing the facies relationship definitions at this location. (B) Depiction of how statistics are shown in the study and the equations used to calculate them. Cs = sandstone–sandstone surface area connectivity (as defined by Funk et al., 2012, shown for comparison to our definition herein as SAsand); SAdraped = draped surface area; SAsand = sandstone–sandstone surface area; SAsand–interbedded = sandstone–interbedded facies surface area (including interbedded–interbedded facies surface area); SAtotal = total basal channel element surface area.

Pairwise Statistics: Normalized Scour Volumes and Lateral Offset

Scour volumes represent the volume of sediment removed as one channel incises into a previously deposited channel element. The two elements involved in this scenario are described herein as a “channel element pair.” In this study, we consider a normalized scour volume, which is the volume of sediment removed via erosion divided by the total volume of sediment in the original two channel elements. Intuitively, the deeper the upper channel element is scoured into the lower channel element, the greater the likelihood of connectivity between the channel element pair.

Furthermore, the proportion of the FA that was scoured was also calculated. As the three FAs correspond to axis, off-axis, and margin zones within an element, the FA proportions indicate how much and which part of each successive channel element was removed by incision. The range of lateral offset between successive channel element center lines was tracked in the models because this exerts a key control on normalized scour volumes and facies juxtapositions.

RESULTS

Surface area connectivities (Cnd_ss, Cnd_all, Cg, and Cbg) are presented and compared with channel element amalgamation, net-to-gross (NTG), the range of lateral offset from channel element–element, and a normalized scour volume shaded by proportion of the FA removed because of scour (Figures 10, 11). The lateral offset and scour behavior are tracked only between two successive channel elements and do not account for multielement amalgamation (i.e., a single element incising into more than one previously deposited channel element is not considered).

Figure 10. Base case model showing connectivity statistics stratigraphically for the entire length of the channel system outcrop. (A) Representative strike-oriented cross section of the model. (B) Channel element pair surface area proportion statistics, which represent sandstone–sandstone connectivity (yellow), channel element surface area connections that are not draped (brown), overall physical connection by channel element pair (gray), and proportion of the channel surface area connected to background (out-of-channel) facies (cross-hatched). Refer to Figure 9 for color key. (C) Number of amalgamated channel elements is calculated element by element by counting the number of overlying channels touching that element. For example, channel element 1 is only contacting channel element 2, so there is only one channel amalgamated to channel 1. However, channel element 10 is being contacted by two overlying channel elements (numbers 11–12), so the amalgamation number for channel 10 is 2. Note, the contacts are tracked along the length of the model and show changes not seen in the single cross section in (A). (D) Net-to-gross (NTG) calculated within a moving window (10 m [33 ft]) to create a vertical profile that captures multiple channel elements in a single perspective. (E) Distance of lateral offset (migration) between channel element pairs, upward through the stratigraphic succession. (F) Normalized scour volume is defined by the volume of rock removed during channel incision divided by the total volume of two channel elements; the proportion of facies that were removed during erosion is shown as a proportion of the normalized scour volume. Throughout the stratigraphic section, approximately 50% of what was scoured was associated with channel element axis sandstone (facies association [FA] 1), approximately 35% was associated with off-axis deposits (FA2), and approximately 15% was associated with thin-bedded margin deposits (FA3).

Stratigraphic Channel Element Connectivity

A representative cross section from the base case model (i.e., 250-m [820-ft] width, low drape scenario) is shown in Figure 10A and used to illustrate channel element stacking patterns and channel complex boundaries. Stratigraphic channel element connectivity results are displayed graphically, with the vertical axis representing the location of channel element pairs where the data point is positioned at the bottom of the second, or upper, element in the pair (Figure 10B–F). In the surface area proportion plot (Figure 10B), note the physical break in connection between the lowest channel complex 1 and the overlying channel complex 2. This break coincides with limited amalgamation between element 4 at the top of channel complex 1 and element 5 at the base of channel complex 2. This boundary also displays the largest range of lateral offset between successive channel elements observed in the model (Figure 10C, E). In general, higher channel element amalgamation correlates visually with sandstone connectivity (Figure 10B, C). As a moving average up through the model, NTG shows limited visual correlation to sandstone connectivity (Figure 10B, D).

sserqvcfuxazrrzxbxvxwfcztvcwx Figure 11. Base case model showing connectivity statistics of proximal (north) to distal (south) segments within the channel system (see Figure 8A for segment delineation). (A) Net sandstone thickness map, with black arrows highlighting areas of particularly high values. (B) Channel element pair surface area proportion statistics. Refer to Figure 9 for color key. (C) Amalgamation ratio and number of amalgamated channels in italics. The number of amalgamated channels is the sum of all channel element surface contacts within a segment. When all stratigraphic channel element amalgamations are summed vertically in Figure 10C, the total number of elemental surface amalgamations for the entire system is 33 amalgamation surfaces. Because of changes in lateral offset, within a segment the number of amalgamated channels is less than 33. The amalgamation ratio is the number of amalgamated channels within a segment divided by 33 (the element surface connections in the model). (D) Average net-to-gross (NTG) by segment. (E) Distance of lateral offset (migration) for all channel element pairs by segment. (F) Normalized scour volume is defined by the volume of rock removed during channel incision divided by the total volume of two channel elements; the proportion of facies that were removed during erosion is shown as a proportion of the normalized scour volume. Throughout the stratigraphic section, approximately 40% of what was scoured was associated with channel element axis sandstone (facies association [FA] 1), approximately 45% was associated with off-axis deposits (FA2), and approximately 5% was associated with thin-bedded margin deposits (FA3).

The normalized scour volume is consistently small in channel complex 1 (Figure 10F). Channel complex 2 is characterized by the largest normalized scour volumes, which taper off into channel complex 3. Throughout the stratigraphic section, approximately 50% of what was scoured was associated with channel element axis sandstone (FA1), 35% was associated with off-axis deposits (FA2), and 15% was associated with thin-bedded margin deposits (FA3). These percentages remain consistent from base to top of the channel system. The exception to this occurs at the contact between channel complex 1 and channel complex 2, where there is a dramatic increase in off-axis and margin facies scour and decrease in axis facies scour.

The Cg value shows that channel complex 1 has the least amount of contact area among channel elements but that physical connections increase up through the stratigraphy (gray shaded area in Figure 10B). The complex 1–complex 2 boundary is also marked with low Cg values, which is consistent with a system shift where a marked reduction in channel element pair contact surface area is noted. Both the normalized scour volume and the Cg are minimized at the complex 1–complex 2 transition and clearly record this boundary.

Segment Connectivity

Connectivity statistics along 10 equally sized segments, numbered 1 to 10 from proximal (north) to distal (south) (Figure 11), are compared with NTG values calculated for each segment (cumulative facies 1 sandstone thickness divided by the entire model thickness; Figure 11A, D). The NTG signature shows two distinct peaks, which correspond to high (≥75 m [≥250 ft]) net sandstone areas, centered at segments 2–3 and 7–8 (Figure 11D).

The net sandstone map (Figure 11A) shows two areas of particularly thick net sandstone, which generally do not correlate with the (1) elevated channel element bounding surface area connections in all segments (Figure 11B); (2) number of channel element amalgamations in a segment (Figure 11C); (3) lateral channel element offset (Figure 11E); and (4) normalized scour volumes (Figure 11F). In general, there is a strong visual correlation between overall physical channel element connection (Cg; color-shaded area in Figure 11B) and amalgamation ratio (Figure 11C) as well as normalized scour volume (Figure 11F). Additionally, an inverse relationship is visually observed between Cg and lateral channel element offset; this observation is consistent with a north-south decrease in connectivity and an increase in lateral offset, as reflected by the elements splaying outward in the southern part of the model (Figure 8). Despite these changes in lateral channel element offset and connectivity downdip, it is interesting to note that the average ratio between surface area characterized by sandstone and gross surface area remains constant at approximately 0.23 for all channel element configurations in each model segment (Figure 11B).

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ABSTRACT

High-resolution digital outcrop models of stacked deep-water channel elements are constructed from the Laguna Figueroa section of the well-exposed Upper Cretaceous Tres Pasos Formation in Chilean Patagonia. The models are based on greater than 1600 m (>5250 ft) of centimeter-scale measured sections, greater than 100 paleoflow measurements, and thousands of differential global positioning system points (10-cm [4-in.] accuracy) from an outcrop belt that is approximately 2.5 km (∼1.5 mi) long and 130 m (425 ft) thick. The models elucidate the effects bed-to-geobody–scale architecture has on static sandstone connectivity among a series of stacked deep-water channel elements and how that connectivity is altered by grid cell size.

Static connectivity analyses show that channel element base drapes can strongly influence sandstone connectivity and that smaller channel element widths are more likely to produce disconnected sandstone geobodies. Net-to-gross (NTG) is not directly correlated with connectivity because of the presence of thin channel element base drapes, which do not significantly contribute to NTG. Upscaling the models consistently increases channel element contact (up to 10%) but decreases sandstone connectivity (up to 2%–3%). Channel element stacking patterns strongly impact connectivity. For example, connectivity is reduced in cases of high lateral channel element offsets. Increasing drape coverage markedly decreases connectivity. Evaluating connectivity in a vertical, along-system profile is critical to understanding flow units and reservoir piping. Ultimately, this work constrains uncertainty related to the impact of subseismic-scale stratigraphic architecture on reservoir connectivity by providing concrete knowledge that can be used to guide the model building process.

INTRODUCTION

Deep-water slope channel systems are widely recognized as important conduits for sediment transfer from slope to basin and as locations for sediment storage on slopes. As such, slope channel deposits constitute globally significant petroleum reservoirs (e.g., Stow and Mayall, 2000; Sullivan et al., 2000; Abreu et al., 2003; Samuel et al., 2003; De Ruig and Hubbard, 2006; Labourdette et al., 2006; Mayall et al. 2006; Deptuck et al., 2007; Weimer and Slatt, 2007; Cross et al., 2009; Alpak et al., 2013; Fowler and Novakovic, 2018). Advances in understanding channelized deep-water depositional systems are, in part, driven by advances in subsurface imaging (e.g., Deptuck et al., 2003; Posamentier and Kolla, 2003; McHargue et al., 2011; Sylvester et al., 2011). High-resolution three-dimensional (3-D) seismic reflection surveys, with vertical resolution commonly 10–20 m (35–65 ft), have provided substantial insight into these systems (Figure 1; Posamentier and Kolla, 2003; Mayall et al., 2013). Interpretations from high-resolution seismic reflection profiles are further improved when coupled with conventional core and well-log data and chronostratigraphic information (Posamentier and Kolla, 2003; McHargue et al., 2011; Bernhardt et al., 2012; Sharman et al., 2018). However, despite technological advances and an increased focus on deep-water slope systems, the subseismic-scale architecture that controls fluid flow and connectivity in a reservoir remains challenging to predict because of significant lithologic variability over short-length scales (Bryant and Flint, 1992; McHargue et al., 2011; Fowler and Novakovic, 2018).

Figure 1. (A) Seismic reflection image of deep-water channel system stratigraphic hierarchy from the Dalia field, West Africa (modified from Zhang et al., 2017). Channel elements are readily characterized in outcrops but are generally below the resolution of seismic reflection data. Despite this, their internal architecture as well as their stacking patterns impart an important influence on deep-water channel reservoirs. Stacked channel elements compose a channel complex (examples defined by blue dashed lines), whereas stacked channel complexes compose a channel complex set, which is most readily interpretable in subsurface data (Abreu et al., 2003; Sprague et al., 2005; McHargue et al., 2011). Well path (yellow) is associated with a gamma-ray log at left (green) and a density log at right (orange). (B) Seismic cross section of a channel system beneath the Niger Delta slope sea floor, West Africa (modified from Jobe et al., 2015). (C) Simplified line drawing interpretation of an aggradational channel complex in the deep-water channel stratigraphy (from area defined by rectangle in [B]), with channel elements similar to those modeled in this study highlighted. The sandy elements are bound by largely fine-grained levee, internal levee, or mass transport deposits, resulting in a vertically aligned succession of high-amplitude reflections 100–150 m (330–500 ft) thick. (D) Thalweg deposits in the Niger Delta data set are considered to correspond closely in terms of scale and internal architecture to channel elements preserved in the Tres Pasos Formation (modified from Jobe et al., 2017). (E) Outcrop of channel element in the Tres Pasos Formation linked to area highlighted in (D) (modified from Macauley and Hubbard, 2013 and Covault et al., 2016).

Data limitations and the financial risk associated with drilling for hydrocarbons in deep-water settings makes adequate quantification of uncertainty of utmost importance for both developing new prospects and for reservoir management (Hovadik and Larue, 2007; McHargue et al., 2011). Investigating how lateral and vertical bed-scale relationships impact reservoir performance provides a framework for more informed reservoir-scale predictions. Outcrop analog studies aid the interpreter by providing possible reservoir architectures not resolvable from conventional subsurface data to inform better reservoir management decisions and quantify economic risk, ultimately increasing reservoir performance (Campion et al., 2000; Larue and Friedmann, 2005; Bakke et al., 2008; Donselaar and Overeem, 2008; Stright et al., 2014; Hofstra et al., 2017). A better understanding of production performance comes from understanding the role internal sedimentary architecture and facies geometries of channel systems play in reservoir connectivity (Larue and Hovadik, 2006; Hovadik and Larue, 2007; Barton et al., 2010; DiCelma et al., 2011; Funk et al., 2012).

In this study, 18 slope channel elements of the Cretaceous Tres Pasos Formation are characterized from an outcrop exposure in southern Chile that is 2.5 km (1.5 mi) long and 130 m (430 ft) thick. Outcrop data and observations are used to build a 3-D outcrop-based model that is a deterministic reconstruction of the Cretaceous deep-water channel system. The exceptionally exposed deposits are ideal for study of the impact that bed-scale architecture has on 3-D connectivity because they have been the focus of ongoing research aimed at constraining internal channel element architecture, channel element geometry, and channel element stacking patterns (Macauley and Hubbard, 2013; Pemberton et al., 2018). Furthermore, the bed-scale sedimentology, stratigraphic architecture, and interpreted external controls on deep-water sedimentary processes from the bed-to-basin scale have been widely shown to share analogous attributes with slope channel stratigraphy on continental margins globally (Fildani et al., 2013; Macauley and Hubbard, 2013; Stevenson et al., 2015; Covault et al., 2016; Reimchen et al., 2016; Daniels et al., 2018). This outcrop analog data set and derivative deterministic outcrop models provide examples of how subseismic-scale architecture impacts connectivity in these types of reservoirs and how the connectivity is altered by decisions associated with modeling grid cell size.

SUBMARINE CHANNEL ELEMENTS

A globally important class of submarine channel deposit stratigraphy is composed of variably stacked architectural elements, or channel elements (Figure 1; McHargue et al., 2011). Although channel element character can vary as a result of numerous parameters, such as relative position on a paleoslope (Beaubouef et al., 1999; Gardner et al., 2003; van der Merve et al., 2014), a particularly common channel element pattern consists of a central core of amalgamated sandstone (axis) that transitions laterally into thick- to thin-bedded, nonamalgamated turbidites at the edges of the channel element (margin) (Mutti and Normark, 1987; Sullivan et al., 2000; Sprague et al., 2002; Gardner et al., 2003; Campion et al., 2005; Mayall et al., 2006; Pyles et al., 2010; Alpak et al., 2013; Gamberi et al., 2013; Macauley and Hubbard, 2013; Hubbard et al., 2014; Covault et al., 2016; Li et al., 2016). Whereas coarse-scale architecture (e.g., channel complex stacking patterns, composed of two or more stacked channel elements) can be interpreted from seismic reflection data (Abreu et al., 2003; McHargue et al., 2011), seismic resolution is generally too low to image individual channel elements, much less intraelement architecture (Prather et al., 2000; Pyles et al., 2010; Fildani et al., 2013; Hubbard et al., 2014). Delineation of internal channel element architecture is also challenging in the subsurface because of a lack of cored boreholes and high-resolution seismic data (Wynn et al., 2007).

Of particular importance to delineating internal channel element architecture are channel element base drapes. Channel element base drapes are fine-grained deposits that conformably overlie the basal composite surface of channel elements (Mutti and Normark, 1987; Mayall et al., 2006; Alpak et al., 2013; Macauley and Hubbard, 2013). They are commonly attributed to phases of sediment bypass through channels, wherein the bulk of the formative turbidity currents pass downslope, and sedimentation is primarily from the low-velocity, dilute tail of the flow (Mutti and Normark, 1987; Stevenson et al., 2015). They can also result from aggradation of turbidite caps (Bouma Td–Te) in instances where the sandy parts of flows only deposit in limited regions within a channel (e.g., thalweg) (Li et al., 2016). Drape deposits are dominantly mudstone and siltstone, can be up to a few meters thick, and can record evidence of multiple incision and sediment bypass events (Barton et al., 2010; Hubbard et al., 2014; Li et al., 2016).

Understanding the distribution and characteristics of channel element base drapes is critical for predicting reservoir performance because they exhibit a key control on reservoir compartmentalization and can act as barriers or baffles to flow (Stright, 2006; Stewart et al., 2008; Barton et al., 2010; Alpak et al., 2011, 2013). The degree to which (1) coarse-grained flows are bypassed, (2) mud can accumulate between major sediment transfer events, and (3) successive flows erode previously deposited drape facies all control the ultimate prevalence of drape deposits at channel element bases (Hubbard et al., 2014). Because the 3-D distribution of drape deposits is highly uncertain and difficult to predict, they represent a significant uncertainty for reservoir development (Stright, 2006; Alpak et al., 2013). A better understanding of the impact that drape deposits can have on connectivity is useful when modeling reservoirs characterized by pervasive drapes (>60% coverage; Stright, 2006) that are expected to affect reservoir performance.

GEOLOGIC BACKGROUND AND STUDY AREA

The Magallanes retroarc foreland basin of southern Chile (50°30′–52°S) formed in the Late Cretaceous because of loading of the Andean fold-thrust belt (Dalziel et al., 1974; Fosdick et al., 2011). The elongate basin was infilled axially from north to south by sediment sourced predominantly from the Andean orogenic belt (Katz, 1963; Romans et al., 2010) over a period of approximately 20 m.y. during the Late Cretaceous, resulting in a 4000–5000-m (13,000–16,500-ft)-thick basin fill (Romans et al., 2011).

Figure 2. (A) Upper Cretaceous stratigraphic context for the Tres Pasos Formation, Magallanes Basin. (B) The study area location, just north of the town of Puerto Natales in southernmost Chile (see inset map). Fm = Formation; L. = Lago; U. = Upper.

The Campanian Tres Pasos Formation is part of a largely conformable marine sequence in the basin. This sequence includes the deep-water Punta Barrosa, Cerro Toro, and Tres Pasos Formations (Fildani et al., 2003; Romans et al., 2011; Daniels et al., 2018) as well as the genetically related shallow marine and deltaic deposits of the overlying Dorotea Formation (Figure 2A; Covault et al., 2009; Hubbard et al., 2010; Schwartz and Graham, 2015). This study focuses on outcropping units near Laguna Figueroa, approximately 40 km (∼25 mi) north of Puerto Natales, just west of the Chile–Argentina border (Figure 2B). Stratigraphic measurements indicate that the channel element deposits of interest were deposited in at least 900–1000 m (2900–3300 ft) of water, approximately 35–40 km (∼22–25 mi) downslope from the paleoshelf edge (Daniels et al., 2018).

Figure 3. Outcrop model showing perspective image of slope channel element strata above Laguna Figueroa, with locations of measured sections (subvertical lines) and mapped stratigraphic surfaces (subhorizontal lines) surveyed with differential global positioning system (dGPS) shown. Line colors denote date of acquisition. Paleoflow was generally from left to right (north to south), and therefore the outcrop exposes an overall depositional dip-oriented perspective. However, local gullies offer strike perspectives, which enable three-dimensional projection of deep-water channel elements.

The Laguna Figueroa outcrop belt is characterized by turbiditic sandstones and mudstones exposed in a long outcrop transect that is 100–130 m (330–425 ft) thick and greater than 2 km (>1.25 mi) long (Figure 1). Macauley and Hubbard (2013) characterized the Laguna Figueroa outcrops with 1600 m (5200 ft) of section measured at centimeter scale, greater than 100 paleoflow measurements from 53 locations, and thousands of high-resolution (<10 cm [<0.5 in.] accuracy) differential global positioning system (dGPS) measurements (Figure 3). They combined these data with extensive field observations, photomosaic interpretations, and high-resolution satellite images to interpret 3-D channel element stratigraphic architecture (Figure 4). They deduced that the outcrop features a largely depositional dip-oriented perspective of channelized strata, featuring channel element fills that flowed southward, approximately parallel to the outcrop face.

Figure 4. Mapped channel elements (18) and complexes (3) extracted from the outcrop (modified from Macauley and Hubbard, 2013; Pemberton et al., 2018). (A) Planform maps of successive channel elements overlying topographic contours (north is to the top of each diagram). Through analysis of facies trends and paleoflow measurements (shown with rose diagrams), channel elements are projected behind and in front of the outcrop. (B) Dip-oriented (north-south) cross section of the channel strata, highlighting the three channel complexes and internal channel elements, numbered 1–18 (numbers correspond to maps) in (A). V.E. = vertical exaggeration.

The strata are primarily composed of deposits derived from turbidity current depositional processes (Figure 5; Bouma, 1962; Lowe, 1982; Talling et al., 2012). Three facies associations (FAs) were identified based on component sedimentation units, which are considered the fundamental architectural unit deposited from a single gravity flow event (Macauley and Hubbard, 2013). Facies association FA1 consists of massive, thick-bedded (0.2–5-m [0.5–15-ft]-thick) amalgamated sandstone (Bouma Ta division) with rare planar laminations (Tb) and ripple cross-laminations (Tc). The sandstone percentage in FA1 ranges from 71% to 100% (mean of 95%). Facies association FA2 is composed of thick- to thin-bedded, semiamalgamated sandstone. Sedimentation units are 0.05–2 m (0.15–7 ft) thick and variably include the entire Bouma sequence (Ta–Te). Sandstone makes up 29%–100% (mean of 81%) of FA2. Facies association FA3 is composed of thin-bedded (0.01–0.2-m [0.05–0.5-ft]-thick), fine- to very fine-grained sandstone interbedded with siltstone and mudstone. Amalgamation of sandstone beds is very uncommon, and sandstone percentage ranges from 0% to 80% (mean of 39%).

Figure 5. (A) Photograph of a single channel element from margin (left) toward the axis (right), with line drawing of outcrop photo in (B). This is channel element 3, and the photo is located just to the left of the central element 3 label in Figure 3B. (C) Channel element cross-sectional template used in this study to represent outcrop observations of internal channel element architecture. FA = facies association; Ta, Tb, Tc, Td and Te refer to the divisions of the Bouma (1962) sequence.

The three FAs compose the fill of mappable channelform bodies (i.e., channel elements), which represent the dominant architectural element present (Figure 5A, B). Following the methods of Sprague et al. (2005) and McHargue et al. (2011), successive channel elements that exhibit a consistent stacking pattern constitute a channel complex; two or more channel complexes constitute a channel complex set. At the Laguna Figueroa outcrop, Macauley and Hubbard (2013) described 18 channel elements and interpreted 3 channel complexes (Figure 4). Directly measuring the width of these channel elements is difficult because opposing channel element edges are typically observed hundreds of meters downdip of one another as a result of the oblique dip-oriented outcrop exposure. Channel element edges were projected based on detailed field mapping, including delineation of key surfaces and stratal terminations with dGPS (10–50-cm [5–20-in.] resolution), augmented with paleoflow data. Channel element widths were estimated to be 300 m (985 ft), whereas measured maximum thicknesses, which can be accurately measured in an outcrop, range from 12 to 16 m (40 to 50 ft) (Figures 4, 5B). Resultant channelform aspect ratios are consistent with dimensional data compiled from various data sources and basin settings around the globe (e.g., McHargue et al., 2011). Channel elements in the Laguna Figueroa section are characterized by low sinuosity (1.01–1.05) and, correspondingly, a relatively symmetric cross-sectional shape and fill pattern (Figure 5C).

At Laguna Figueroa, channel elements are observed to laterally change facies from more sandstone-rich zones in their axes (commonly where elements are the thickest) into finer-grained facies toward their edges (Figure 5A). In each element, the distribution of the three FAs therefore corresponds to three distinct zones within the channel element fill Figure 5B, C). The highest-energy amalgamated sandstone deposits of FA1 are present in channelform axes or interpreted thalweg positions. The association FA3 persists at the margins of channel elements, and FA2 is present intermediately between FA1 and FA3, in an off-axis position. In general, axis deposits contain the thickest, most amalgamated, and sandiest units; off-axis and margin deposits are defined by decreasing amounts of sandstone, bed amalgamation, and bed thickness. Importantly, particularly siltstone-rich FA3 deposits variably overlie channelform bases locally; these deposits can be up to 1 m (3.2 ft) thick at channel element margins to absent in channel element axes. We consider these as channel element base drape deposits (cf. Mutti and Normark, 1987; Hubbard et al., 2014).

METHODS

Architectural Model

We define an architectural model as a geocellular model constrained to outcrop observations, measurements, and interpretations that illustrates the distribution of channel elements. The model was constructed based on the mapping results of Macauley and Hubbard (2013), featuring stratigraphic surfaces and terminations, and measured section localities surveyed using a dGPS. Stratigraphic correlations and paleocurrent analyses were the basis for delineation of channelforms along the outcrop belt (Macauley and Hubbard, 2013); these channelforms were digitized and combined with outcrop dGPS points to generate 3-D channelform surfaces. A symmetrical thalweg position was constructed for the channel elements based on outcrop observations. The channel element surfaces were used as the framework to generate a 3-D model of channel element geobodies.

Grid Size

The model resolution is sufficient to capture the effects of static connectivity associated with bed-scale internal channel element architecture as well as juxtaposition of facies across stacked channel element boundaries. Vertical and horizontal cell sizes capture fine-scale facies, such as the channel element base drape, as well as axis (FA1) to margin (FA3) facies transitions. Areal cell size dimensions of 2 m (6.5 ft) by 2 m (6.5 ft) and 0.25 m (0.8 ft) vertically are chosen to capture thin beds and rapid lateral facies changes. This cell size is a fraction of that in a typical reservoir simulation model and produces models in excess of 600 M cells; for this study, this resolution is necessary to sufficiently quantify the impact of fine-scale heterogeneity on connectivity.

Facies Template and Facies Model

A single deterministic and interpretive cross section for a channel element is generated that represents a template of observed outcrop facies relationships (Figure 5C). Rather than modeling facies using traditional geostatistical methods, this single facies template is held constant and used to fill individual channel element surfaces at all locations along the length of the outcrop model. This simplified approach is consistent with the observations made by Macauley and Hubbard (2013) of low-sinuosity, symmetric channel elements for the Tres Pasos Formation at this location. Within the template, three model facies are distributed to capture the FAs defined by Macauley and Hubbard (2013). Facies association FA1 is composed largely of facies 1 (thick-bedded sandstone) and subordinate facies 3 (thin-bedded siltstone and sandstone) (Figure 5C). Facies association FA2 comprises facies 1 as well as facies 3 and facies 2 (thin- to thick-bedded sandstone and siltstone). Facies association FA3 is composed of facies 2 and facies 3. Facies 3 represents channel element base drape facies across the template (Figure 5C).

Figure 6. (A) Modeled channel element. (B) Zoom in of (A) to demonstrate that conformable gridding on the edges of elements creates cells that are orthogonal to margins. (C) This approach allows control of facies template insertion, preventing distortion caused by cell orientation. (D) Each individual channel element grid is cross-scaled into a square Cartesian grid. The lowest three channel elements of channel complex 1 are shown. Vertical gridding is orthogonal in both the individual channel element model and the cross-scaled model. (E) Representative cross section through two channel elements in the model showing model grid cells.

Symmetric channel elements with constant widths are created by inserting the facies fill template at 2-m (6.5-ft) downdip increments, oriented orthogonal to the western margin of mapped channel elements (Figure 6). Individual channel elements are gridded such that grid cells are conformable to channel element edges (Figure 6B); as such, channel element cross section cells are orthogonal to margins, preventing facies template distortion caused by cell orientation (Figure 6C). Western margins are chosen as the seeding point since the lower Laguna Figueroa outcrop exposes more western margins than eastern margins or element center lines. Individual channel elements were cross-scaled into a single square Cartesian grid model, honoring the stacking patterns and scour depths measured from the outcrop (Figure 6D). Where an overlying element overlaps a stratigraphically lower element, the higher element is preserved at the expense of the scoured underlying element.

Channel Element Base Drape

Accurately capturing channel element base drape distribution is critical because these deposits are known to negatively impact connectivity in slope channel reservoirs (e.g., Alpak et al., 2013). Their distribution is typically poorly constrained in 3-D given that these features are well below the detection limit in seismic reflection data sets. Although possible to interpret in well data (e.g., Barton et al., 2010), limited penetrations provide only a hint of their distribution. Perspectives from numerous channel elements at Laguna Figueroa provide insight into drape distribution. Based on 1600 m (5250 ft) of measured section through 18 channel elements, the presence of basal drape facies is recorded for axis, off-axis, and margin deposits (Figure 5C). From this analysis, channel element base drapes occupy 42%, 69%, and 84% of channel element axis, off-axis, and margin successions, respectively (Figure 7). The channel element base drapes range in thickness from 0 to 1m (0–3.3 ft). The template explicitly represents these drapes from zero cells (no drape present) to four cells (∼1-m-[3.3-ft]-thick drape present) (facies 3 in Figure 5C).

sserqvcfuxazrrzxbxvxwfcztvcwx Figure 7. Constructed cases for high and low drape coverage used in this study. The high case has a higher proportion of draping (no-flow) facies in the axis and off-axis areas and lower proportions in the margins; the low case has a higher proportion of drape coverage in the margin areas. These two cases were run for channel widths of 200, 250, and 300 m (650, 820, and 985 ft).

Locations within a channel that experience preferential erosion at their base can be gleaned from physical and numerical modeling experiments as well as from observations of the modern sea floor (e.g., Snedden, 2013). This information guides predictions of basal drape deposit distribution. Amos et al. (2010) tested low-sinuosity and high-sinuosity open channel flow in a flume to address the influence of sinuosity on flow processes and sedimentation. They found that for symmetric channels with sinuosities in the range of 1.14 to 1.94, erosion or nondeposition generally occurs toward outer bends, whereas deposition or nonerosion occurs along the inner bends of channel. As sinuosity increases, the asymmetry of erosional and depositional zones increases. Studies of active channels off the coast of British Columbia, Canada, by Conway et al. (2012) used repeat swath multibeam bathymetric data collected from surveys in 2005, 2008, and 2010 that show similar results via time-lapse perspectives of channel base aggradation or erosion. Modeling work of Sylvester et al. (2011) also found that channel deposition preferentially occurs along inner bends and erosion occurs at outer bends. All of these studies support the notion of increased preservation potential for drape deposits at the inner bends of channel elements.

Recent analysis of channel element base drapes shows that their distribution is not entirely linked to erosion and bypass. A key contributor of drape deposits is turbidity currents that are underfit relative to the full channel element width and depth (Hubbard et al., 2014; Li et al., 2016). These flows result in sand deposition in channel element axes, with capping siltstone derived from the tops of highly stratified flows deposited toward the channel element edges, contributing to thick drapes in these settings. These observations are consistent with outcrop-derived statistics, which show decreased prevalence (and proportion) of drape deposits in channel element axis zones (Macauley, 2011).

To assess the impact of channel element base drapes on reservoir connectivity, two drape coverage configurations are considered for this study (Figure 7). Both configurations honor the same channel element planform geometry but have different degrees of drape coverage. A high drape coverage scenario is guided by outcrop statistics (Figure 7), which show that axis, off-axis, and margin positions in each channel element carry probabilities of 42%, 69%, and 84% (total coverage = 72%), respectively, of being underlain by a drape. The low drape coverage scenario has 6%, 52%, and 91% (total coverage = 58%) likelihoods of axis, off-axis, and margin FAs being underlain by a channel element base drape.

Model Scenarios

Fine Scale

Six deterministic model scenarios were generated as a basis to elucidate channel element stacking pattern influence on static connectivity; three different element widths of 200, 250, and 300 m (650, 820, and 985 ft) were considered, each with the high and low channel element base drape scenario (250-m [820-ft]-wide channel element model shown in Figure 8). These widths are within the range of those most commonly observed in subsurface data sets (100–300 m [330–985 ft]) (McHargue et al., 2011). The model with a channel element width of 250 m (820 ft) and low base drape configuration is considered the “base case,” which was the basis for comparison with the other five models. Variable channel element body widths were constructed to test the sensitivity of this measure on connectivity. Furthermore, holding the channel element widths constant for each model is consistent with observations that downdip variation in element size is small for a single channel system, especially along only 2–3 km (1.25–2.0 mi) of down-paleoslope (longitudinal) distance (McHargue et al., 2011; Sylvester et al., 2011; Janocko et al., 2013). Thickness for all elements was fixed at 14 m (45 ft), which is the typical maximum element thickness in the study area (Macauley and Hubbard, 2013).

Figure 8. (A) Outcrop model that is the foundation of the connectivity analysis in this study, featuring 18 channel elements. Note the downdip division of the model into 10 segments. (B) Net sandstone map, featuring sandstone-rich channel belt from north to south, incorporating the entire stratigraphic succession. (C) A series of cross sections featuring the varied channel element stacking arrangement along the length of the outcrop belt. High-net sandstone trends are apparent where channel elements are vertically aligned.

Channel element base drape coverage has also been shown to vary among slope channel systems; models with differing drape coverage specifically test the impact of these features on connectivity.

Coarse Scale

Because of computational efficiency inherent in grid-based modeling (e.g., software limitations, restrictions on grid size, and finite time), modeling on a coarse scale grid is necessary before flow-simulating reservoir models. Maintaining key facies and geobody characteristics throughout the upscaling process is especially important (Larue and Legarre, 2004; Larue and Friedmann, 2005; Larue and Hovadik, 2006). Furthermore, it is important to understand how gridding decisions impact the overall sandstone connectivity in a model. Channel base drapes (facies 3 in Figure 5C) are assumed to block connectivity regardless of their thickness. As long as a single cell is preserved in the upscaling to capture the drape, and it is represented along the length of the base of the channel where the drape exists in the fine-scale model, the flow barrier will be adequately characterized.

To better understand the effect that different cell sizes have on connectivity, a gridding analysis was performed. This analysis was designed to (1) test what cell sizes are necessary to capture the observed channel element architecture and (2) explore differences in connectivity results from models that were upscaled to different cell dimensions. To accomplish this, the base case model (i.e., 250-m [820-ft] element width, low drape scenario) was upscaled from 2 × 2 × 0.25 m (6.5 × 6.5 × 0.8 ft) cell size to three new grids: (1) 10 × 10 × 0.25 m (33 × 33 × 0.8 ft) (areal upscale only); (2) 2 × 2 × 1 m (6.5 × 6.5 × 3 ft) (vertical upscale only); and (3) 10 × 10 × 1 m (33 × 33 × 3 ft) (upscaled in all three dimensions). Although even the coarsest grid size is still fine relative to industry practice, the analysis successfully tests the impact of cell size variation on static connectivity.

Static Connectivity Analysis

Static connectivity analyses were performed in two ways for each of the six models to evaluate facies connectivity: (1) through the models, stratigraphically, and (2) by using 10 proximal to distal segment models that are equally sized (∼250 m [∼820 ft] wide × ∼1000 m [∼3300 ft] long × 120 m [390 ft] thick) along the length of the channel system (Figure 8A). The static connectivity statistic used was modified from Funk et al. (2012). They proposed two measures of static connectivity, called margin connectivity and sand-on-sand connectivity, to assess the impact of variable facies between stacked channel elements on a cross section interface, essentially characterizing connectivity along a line. In this study, we leverage the three-dimensionality of our models to expand these statistics to connectivity across surfaces shared between intersecting channel elements; in this manner, true flow potential (flux) between elements is computable. By quantifying facies relationships across these shared surfaces, we were able to categorize all element contact surface area available for (1) high-quality fluid flux (nondraped sandstone–sandstone facies juxtapositions [SAsand]; (2) medium-quality fluid flux (nondraped sandstone–interbedded sandstone or shale juxtapositions [SAsand–interbedded]); (3) no flux (draped channel element base [SAdraped]); and (4) potential flux–background facies (channel element–levee or background mudstone [SAbackground]; Figure 9A). Each surface area is normalized by the total surface area (SAtotal) at the base of a channel element to convert it to a proportion of total surface area available for fluid flux, and there are four resulting equations (Figure 9B). First, a calculation of the highest-quality surface area connection is the proportion of channel element surface area available for fluid flux through nondraped sandstone–sandstone connections (Cnd_ss):

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Second, incorporating lower-quality facies connections into the calculation, the proportion of surface area available for fluid flux through nondraped sandstone–interbedded (thick and thin) sandstone or sandstone–sandstone connections (Cnd_all) can be determined with the following equation:

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Third is the gross channel element surface area connection, including the draped part of the channel element (Cg). This is the proportion of channel element surfaces that are in connection with another channel element, regardless of the facies juxtaposition:

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Finally, the remaining part of channel element surface area available for fluid flow to background, out-of-channel stratigraphy (Cbg) can be determined with the following equation:

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The normalization of these surface areas was modified from the original Funk et al. (2012) formulation to be the entire base of a channel element rather than the area of geobody intersection. Furthermore, Cg and Cbg are introduced to capture all potential surfaces for fluid flux. The motivation for changing the normalization was that a small overlap between channelforms that are characterized by complete sandstone–sandstone juxtaposition produced a high connectivity statistic similar to that of a scenario with a large overlap between channelforms with a small sandstone–sandstone connection. In both cases, the surface area available to fluid flow is relatively small, but the arrangement of channel elements is very different (Figure 9C). Finally, the original statistic was intended to be performed pairwise between geobodies (i.e., channel elements). In this work, we acknowledge that connectivity can occur between multiple amalgamated channel elements and the statistics herein reflect all channel element juxtapositions, not just those associated with sequentially formed channel element pairs (e.g., the connectivity was assessed between element pairs 1 and 2, 2 and 3, and 1 and 3 if they were in contact).

Figure 9. Cross-sectional illustration of modified static connectivity statistics from Funk et al. (2012), including (1) sandstone–sandstone connectivity (Cnd_ss); (2) channel element surface area connections that are not draped (Cnd_all); (3) global channel element surface area connectivity (Cg); and (4) proportion of the channel surface area connected to background (out-of-channel) facies (Cbg) statistics, defined in this study. Metrics presented hereafter are calculated in three dimensions as surface areas, rather than lines in two dimensions as shown here. (A) Channel element pair interface, with inset showing the facies relationship definitions at this location. (B) Depiction of how statistics are shown in the study and the equations used to calculate them. Cs = sandstone–sandstone surface area connectivity (as defined by Funk et al., 2012, shown for comparison to our definition herein as SAsand); SAdraped = draped surface area; SAsand = sandstone–sandstone surface area; SAsand–interbedded = sandstone–interbedded facies surface area (including interbedded–interbedded facies surface area); SAtotal = total basal channel element surface area.

Pairwise Statistics: Normalized Scour Volumes and Lateral Offset

Scour volumes represent the volume of sediment removed as one channel incises into a previously deposited channel element. The two elements involved in this scenario are described herein as a “channel element pair.” In this study, we consider a normalized scour volume, which is the volume of sediment removed via erosion divided by the total volume of sediment in the original two channel elements. Intuitively, the deeper the upper channel element is scoured into the lower channel element, the greater the likelihood of connectivity between the channel element pair.

Furthermore, the proportion of the FA that was scoured was also calculated. As the three FAs correspond to axis, off-axis, and margin zones within an element, the FA proportions indicate how much and which part of each successive channel element was removed by incision. The range of lateral offset between successive channel element center lines was tracked in the models because this exerts a key control on normalized scour volumes and facies juxtapositions.

RESULTS

Surface area connectivities (Cnd_ss, Cnd_all, Cg, and Cbg) are presented and compared with channel element amalgamation, net-to-gross (NTG), the range of lateral offset from channel element–element, and a normalized scour volume shaded by proportion of the FA removed because of scour (Figures 10, 11). The lateral offset and scour behavior are tracked only between two successive channel elements and do not account for multielement amalgamation (i.e., a single element incising into more than one previously deposited channel element is not considered).

Figure 10. Base case model showing connectivity statistics stratigraphically for the entire length of the channel system outcrop. (A) Representative strike-oriented cross section of the model. (B) Channel element pair surface area proportion statistics, which represent sandstone–sandstone connectivity (yellow), channel element surface area connections that are not draped (brown), overall physical connection by channel element pair (gray), and proportion of the channel surface area connected to background (out-of-channel) facies (cross-hatched). Refer to Figure 9 for color key. (C) Number of amalgamated channel elements is calculated element by element by counting the number of overlying channels touching that element. For example, channel element 1 is only contacting channel element 2, so there is only one channel amalgamated to channel 1. However, channel element 10 is being contacted by two overlying channel elements (numbers 11–12), so the amalgamation number for channel 10 is 2. Note, the contacts are tracked along the length of the model and show changes not seen in the single cross section in (A). (D) Net-to-gross (NTG) calculated within a moving window (10 m [33 ft]) to create a vertical profile that captures multiple channel elements in a single perspective. (E) Distance of lateral offset (migration) between channel element pairs, upward through the stratigraphic succession. (F) Normalized scour volume is defined by the volume of rock removed during channel incision divided by the total volume of two channel elements; the proportion of facies that were removed during erosion is shown as a proportion of the normalized scour volume. Throughout the stratigraphic section, approximately 50% of what was scoured was associated with channel element axis sandstone (facies association [FA] 1), approximately 35% was associated with off-axis deposits (FA2), and approximately 15% was associated with thin-bedded margin deposits (FA3).

Stratigraphic Channel Element Connectivity

A representative cross section from the base case model (i.e., 250-m [820-ft] width, low drape scenario) is shown in Figure 10A and used to illustrate channel element stacking patterns and channel complex boundaries. Stratigraphic channel element connectivity results are displayed graphically, with the vertical axis representing the location of channel element pairs where the data point is positioned at the bottom of the second, or upper, element in the pair (Figure 10B–F). In the surface area proportion plot (Figure 10B), note the physical break in connection between the lowest channel complex 1 and the overlying channel complex 2. This break coincides with limited amalgamation between element 4 at the top of channel complex 1 and element 5 at the base of channel complex 2. This boundary also displays the largest range of lateral offset between successive channel elements observed in the model (Figure 10C, E). In general, higher channel element amalgamation correlates visually with sandstone connectivity (Figure 10B, C). As a moving average up through the model, NTG shows limited visual correlation to sandstone connectivity (Figure 10B, D).

Figure 11. Base case model showing connectivity statistics of proximal (north) to distal (south) segments within the channel system (see Figure 8A for segment delineation). (A) Net sandstone thickness map, with black arrows highlighting areas of particularly high values. (B) Channel element pair surface area proportion statistics. Refer to Figure 9 for color key. (C) Amalgamation ratio and number of amalgamated channels in italics. The number of amalgamated channels is the sum of all channel element surface contacts within a segment. When all stratigraphic channel element amalgamations are summed vertically in Figure 10C, the total number of elemental surface amalgamations for the entire system is 33 amalgamation surfaces. Because of changes in lateral offset, within a segment the number of amalgamated channels is less than 33. The amalgamation ratio is the number of amalgamated channels within a segment divided by 33 (the element surface connections in the model). (D) Average net-to-gross (NTG) by segment. (E) Distance of lateral offset (migration) for all channel element pairs by segment. (F) Normalized scour volume is defined by the volume of rock removed during channel incision divided by the total volume of two channel elements; the proportion of facies that were removed during erosion is shown as a proportion of the normalized scour volume. Throughout the stratigraphic section, approximately 40% of what was scoured was associated with channel element axis sandstone (facies association [FA] 1), approximately 45% was associated with off-axis deposits (FA2), and approximately 5% was associated with thin-bedded margin deposits (FA3).

The normalized scour volume is consistently small in channel complex 1 (Figure 10F). Channel complex 2 is characterized by the largest normalized scour volumes, which taper off into channel complex 3. Throughout the stratigraphic section, approximately 50% of what was scoured was associated with channel element axis sandstone (FA1), 35% was associated with off-axis deposits (FA2), and 15% was associated with thin-bedded margin deposits (FA3). These percentages remain consistent from base to top of the channel system. The exception to this occurs at the contact between channel complex 1 and channel complex 2, where there is a dramatic increase in off-axis and margin facies scour and decrease in axis facies scour.

The Cg value shows that channel complex 1 has the least amount of contact area among channel elements but that physical connections increase up through the stratigraphy (gray shaded area in Figure 10B). The complex 1–complex 2 boundary is also marked with low Cg values, which is consistent with a system shift where a marked reduction in channel element pair contact surface area is noted. Both the normalized scour volume and the Cg are minimized at the complex 1–complex 2 transition and clearly record this boundary.

Segment Connectivity

Connectivity statistics along 10 equally sized segments, numbered 1 to 10 from proximal (north) to distal (south) (Figure 11), are compared with NTG values calculated for each segment (cumulative facies 1 sandstone thickness divided by the entire model thickness; Figure 11A, D). The NTG signature shows two distinct peaks, which correspond to high (≥75 m [≥250 ft]) net sandstone areas, centered at segments 2–3 and 7–8 (Figure 11D).

The net sandstone map (Figure 11A) shows two areas of particularly thick net sandstone, which generally do not correlate with the (1) elevated channel element bounding surface area connections in all segments (Figure 11B); (2) number of channel element amalgamations in a segment (Figure 11C); (3) lateral channel element offset (Figure 11E); and (4) normalized scour volumes (Figure 11F). In general, there is a strong visual correlation between overall physical channel element connection (Cg; color-shaded area in Figure 11B) and amalgamation ratio (Figure 11C) as well as normalized scour volume (Figure 11F). Additionally, an inverse relationship is visually observed between Cg and lateral channel element offset; this observation is consistent with a north-south decrease in connectivity and an increase in lateral offset, as reflected by the elements splaying outward in the southern part of the model (Figure 8). Despite these changes in lateral channel element offset and connectivity downdip, it is interesting to note that the average ratio between surface area characterized by sandstone and gross surface area remains constant at approximately 0.23 for all channel element configurations in each model segment (Figure 11B).

Normalized scour volume, by segment, shows high values in the northern section of the model, which steadily decreases southward (Figure 11F). The proportion of facies that are preferentially scoured show no substantial trends down depositional dip (Figure 11F). The NTG values, similar to normalized scour volumes and Cg, also decrease in the southern third of the model. Correspondingly, the net sandstone map displays thinner sandstone accumulations across a broader east-west area (Figure 11A). This characteristic, along with the lower normalized scour volumes and decreased Cg, suggests less vertically aligned channel element stacking (i.e., increased lateral offset) was responsible for reduced connectivity in the lower part of the stratigraphic section.

Channel Element Widths

Modifying the channel element width from the base case alters the size and shape of sandstone bodies and the composite net sandstone of the entire channel system (Figure 12A). The net sandstone maps show that areas of thick net sandstone are greater with increasing element width. For example, the 200-m (650-ft) width map has two distinct areas (total area = 4.88E4 m2 [5.25E5 ft2]) of net sandstone greater than or equal to 75 m (≥250 ft). The 250-m (820-ft) width map is characterized by two large areas and two smaller potential areas (total area = 1.81E5 m2 [1.95E6 ft2]), which constitutes a 272% increase in area of net sandstone greater than or equal to 75 m (≥250 ft). The 300-m width map increases the area of net sandstone greater than or equal to 75 m (≥250 ft) by only 7% from the 250-m (820-ft) model (1.95E5 m2 [2.10E6 ft2]).

Figure 12. The impact of channel element width and net-to-gross (NTG) on channel element surface area connectivity. (A) Net sandstone maps, highlighting sandstone-rich channel belt for the three different channel element width models (200, 250 [base case], and 300 m [650, 820, and 985 ft]), with black arrows highlighting areas of particularly high values. Internal element facies were scaled in conjunction with the element width, and as such, facies proportions within elements remained constant; global proportions of channel element and out-of-channel (background) facies shifted as element widths were modified. The changes in prominent, high-net sandstone areas reflect the shift to more out-of-channel facies and lower overall sandstone proportions. (B) Comparison of the change in channel element pair surface area connectivity from the base case width (250 m [820 ft]) to 200-m (650-ft) channel element width stratigraphically through entire model, revealing a 1.5%–3% decrease in connectivity. (C) Comparison of the change in channel element pair surface area connectivity from the base case width (250 m [820 ft]) to 300-m (985-ft) channel element width, revealing a 1.5%–3% increase in connectivity. Changes in sandstone–sandstone connectivity and channel element surface area connections that are not draped for proximal (north) to distal (south) model segments from the base case width (250 m [820 ft]) to 200-m (650-ft) channel element width (D), and the base case width (250 m [820 ft]) to 300-m (985-ft) channel element width (E). These changes can loosely be related to the change in global sandstone proportions, although the correlation between NTG and connectivity is not directly related because of low-net drape facies. Cg = overall physical connection by channel element pair.

In the channel element pair assessments, the connectivity increases in magnitude with increased channel element width (Figure 12B, C). The range in values for nondraped connection (Cnd_all) and nondraped sandstone connection (Cnd_ss) for each channel element pair invariably decreases with increasing channel element width. From the base case of 250-m (820-ft) channel element width down to 200-m (650-ft) channel element width, the average decrease in Cnd_all and Cnd_ss connectivity range is 18% (Figure 11B); from the base case of 250-m (820-ft) channel element width up to 300-m (980-ft) width, the average increase in range is 10% (Figure 12C). This suggests that the increase in connectivity with increased element width is accompanied by a convergence toward the average of the Cnd_all and Cnd_ss values.

Surface area connections, specifically those associated with sandstone, increase with increased channel element width. With decreased element width there is less area of physical connection available for fluid flow, and significantly, these elements are greater than 1.5 times as likely to be stratigraphically segmented by poorer reservoir quality margin deposits (FA3) across channel element and complex boundaries.

Internal Architecture

To examine the effect of channel element base drape configurations on model connectivity, as well as differences between surface area connectivity (Cnd_ss and Cnd_all) trends, the low- and high-drape scenarios of the 250-m (820-ft) channel element base case model width were isolated and compared (Figure 13). In the pairwise assessment, Cnd_ss and Cnd_all for both drape scenarios capture the low connectivity at the complex 1–complex 2 boundary (Figure 13A, B). For every segment and every channel element pair, the low drape scenario has higher Cnd_ss, Cnd_all (Figure 13C, D), and connected volume values than the high drape scenario. The drape configuration impacts the number of channel element amalgamations in a segment by interrupting sandstone juxtaposition with draping facies.

Figure 13. The impact of channel base drape coverage on channel element connectivity. An approximately 10% difference in connectivity between high and low drape coverage models is present. (A, B) show stratigraphic variations in sandstone–sandstone connectivity (Cnd_ss) and nondraped channel element surface area connections (Cnd_all). (C) Proximal to distal variation in Cnd_ss and (D) Cnd_all. Less impact on connectivity from channel base drape coverage is present with larger lateral channel element offsets, such as in segments 8–10. Refer to Figure 11A, B for reference to segment distribution. (E) Number of amalgamated channel elements, calculated by counting the number of touching channel elements that also contain Cnd_ss across channel element boundaries. As the drape coverage increases, fewer channel elements are amalgamated. Cg = overall physical connection by channel element pair. Refer to figure 9 for color legend.

Upscaling

The base case model was upscaled from 2 × 2 × 0.25 m (6.5 × 6.5 × 0.8 ft) cell size to 10 × 10 × 0.25 m (33 × 33 × 0.8 ft) (areal upscale only), to 2 × 2 × 1 m (6.5 × 6.5 × 3 ft) (vertical upscale only), and to 10 × 10 × 1 m (33 × 33 × 3 ft) (upscaled in all three dimensions) (Figure 14). The area of connection between channel element pairs (Cg) increased the most in the vertical upscaling case (2 × 2 × 1 m [6.5 × 6.5 × 3 ft]) and the least in the areal upscaling case (10 × 10 × 0.25 m [33 × 33 × 0.8 ft]) (bottom bar in tornado charts in Figure 15A–C). Although upscaling increased the overall surface area connections, the sandstone connectivity (Cnd_ss) generally decreased in all cases in which a vertical channel element stacking arrangement is prevalent in the outcrop (Figure 15A–C; complex 2 and 3; channel elements 5–18). Vertical upscaling strongly enhanced sandstone connectivity in laterally offset channel element stacking (Figure 15A, complex 1; channel elements 1–4). Areal upscaling increased channel element margin facies connectivity and decreased sandstone connectivity (Figure 15B), whereas upscaling both vertically and horizontally decreased overall connectivity of sandstone and margin facies (Figure 15C). These data show that upscaling in the areal direction, vertical direction, or both invariably increases cell–cell connectivity but introduces more flow barriers and longer, more complex flow paths. Along the length of the model, where the channel belt is dominated by more vertically aligned elements, sandstone connections are preserved and channel margin facies connections are increased slightly (Figure 15D–F, yellow and brown curves). Where stacking is more dispersed (i.e., broader range of lateral channel offset), sandstone connectivity is decreased when models are upscaled.

Figure 14. Cross sections of model chosen to highlight different architectural and connectivity characteristics associated with different cell sizes. (A) Broad view of different connectivity styles for each grid size. (B) Insets from (A) showing that the use of 1-m (3-ft) vertical grid cells created sandstone connectivity vertically between two channel elements that is not present at finer (0.25-m [0.8-ft]) grid cell sizes. (C) Insets showing induced lateral sandstone connectivity, present only in the 10 × 10 × 0.25-m (33 × 33 × 0.8-ft) model.

DISCUSSION

The Coupled Impact of Internal Channel Element Architecture and Stacking on Connectivity

Consistent with other data sets, channel element thicknesses are typically less than 15 m (<50 ft) thick, which is well below seismic resolution in most instances (McHargue et al., 2011). It is more likely that composite channel complexes, which are generally greater than 20–40 m (>65–130 ft) thick, are resolved in seismic data (Figure 1; Abreu et al., 2003; Posamentier and Kolla, 2003; Mayall et al., 2006; Cross et al., 2009). However, channel element stacking patterns exert a significant control on overall connectivity (Clark and Pickering, 1996; McHargue et al. 2011; Labourdette et al., 2013). A general trend of channel complex evolution from initially laterally offset channel elements to vertically aligned channel elements through the evolution of a long-lived channel system has been widely demonstrated (e.g., Deptuck et al., 2003; Labourdette and Bez, 2010; Hodgson et al., 2011; McHargue et al., 2011; Bain and Hubbard, 2016; Covault et al., 2016; Jobe et al., 2016).

Figure 15. Changes in channel element pair surface area connectivity because of upscaling vertically (A, D), areally (B, E), and both areally and vertically (C, F). The top row shows statistics stratigraphically, from base of the channel system to the top, whereas the bottom row shows planform perspective from proximal (north) to distal (south) segments. Cumulative change for sandstone–sandstone connectivity (Cnd_ss), channel element surface area connections that are not draped (Cnd_all), and overall physical connection by channel element pair (Cg) in the stratigraphic case is shown in the bar plots. See Figure 9 for color legend.

Axial deposits along the thalweg of a channel element generally contain the coarsest-grained sediment (i.e., greatest reservoir quality), such that vertical amalgamation of these facies from successive elements increases connectivity, whereas laterally offset stacking degrades connectivity. Lateral channel element offset distance greater than approximately one-third of a channel element width reduces sandstone–sandstone connection to below 10% (blue shaded area in Figure 16). Connectivity is reduced to 0% where offset distance is greater than approximately two-thirds of a channel element width (gray shaded area in Figure 16). Vertical channel element offset has a significantly lower impact on connectivity, such that there is little to no clear trend in sandstone–sandstone surface area connectivity versus magnitude of incision between successive channel elements (green shaded area in Figure 16). In the connected sandstone volume analysis in this study, the only significant and consistent disconnect between channel elements occurred at the boundary between the lowest and middle channel complexes (Figure 17) where the distribution of lateral offsets are all greater than two-thirds of the channel element width (Figure 10E). Connectivity generally increases upward through channel complexes (Figures 10B; 12B; 13A, B; 15A–C). Drape deposits were not widely observed at channel element axes in the Tres Pasos Formation, and their absence in our models led to significant vertical connectivity. However, if drape deposits are preserved along the base of the channel element or composite channel complex conduit across their entire width, then vertical connectivity would be severely impacted (Labourdette, 2007; Alpak et al., 2013).

Figure 16. Crossplot showing the impact of vertical channel element offset (aggradation) versus lateral channel element offset (migration) on connectivity. Lateral channel offset (normalized by channel element width) is a clear, primary control on sandstone–sandstone connectivity (Cnd_ss). A distant, secondary factor is the amount of vertical offset between successive channel elements (normalized by channel element thickness), which shows only a small control on Cnd_ss. The gray area shows that lateral offset greater than approximately 65% of a channel element width decreases Cnd_ss to 0%. The blue shaded area shows that channel offset between approximately 35% and 65% of a channel element width decreases Cnd_ss to less than 10% of available channel element surface area. The green shaded area shows that the highest Cnd_ss (10%–45% of channel surface area) is associated with channel elements that are offset less than 35% of a channel element width.

The high sandstone content and vertically aligned channel element stacking patterns observed in the Tres Pasos Formation make sandstone connection likely at most channel element contact points—however, this is not the case in complex 1, where channel elements are characterized by high lateral offset. In turbidite systems that are less sandstone rich (e.g., Porter et al., 2006), dominated by laterally offset channel elements (e.g., Mayall et al., 2006), or characterized by high channel element cross-sectional facies asymmetry (e.g., Covault et al., 2016; Reimchen et al., 2016), predictions of lateral connectivity are more important. In these systems especially, accurate characterization of lateral sandstone connectivity at both the intra- and inter-element scales is critical and requires a thoughtful approach to the benefits and issues when building reservoir models associated with cells that are areally long and vertically thin.

Impacts of Channel Element Width and Net-to-gross on Connectivity

Because channel element widths may not always be known (i.e., exact size is below the resolution of seismic data), it is important to understand the implications of different element widths on reservoir connectivity when constructing a reservoir model. As shown in the connected sandstone volume analysis, smaller channel element widths are more likely to result in numerous disconnected sandstone bodies, especially in instances where channel element base drapes are widely preserved. In this study, as the channel element widths decrease, so too does the NTG because of the scaling of the internal facies distribution. The destruction of connectivity is exacerbated by the increase in proportion of channel element margin facies. However, NTG independent of channel element width is poorly correlated with the connectivity variables shown in this study, and the prediction of connectivity from NTG alone should be used with caution. For example, surface area proportions for 10 model segments from proximal to distal is shown in Figure 11B. Very little variation in sandstone–sandstone connectivity is present between segments, resulting in poor correlation with NTG (Figure 11D). However, when the vertical profile of surface area connectivity is shown for each segment, clear flow units, or vertically segregated flow paths, appear because of the fine-scale, low-net shale barriers (Figure 17), indicating that large variations in connectivity can be prevalent across zones characterized by similar NTG. Thus, factors such as channel element stacking patterns, channel element width, and drape continuity are vital in establishing connectivity in a deep-water channel reservoir, with a lesser influence from NTG.

Figure 17. Stratigraphic connectivity for all 10 segments, from proximal to distal in the model. (A) Net sandstone map of base case model. Black line shows position of cross section in (B), oriented to encounter a high-net section of the model. (B) Cross section of model with channel complexes delineated. Note the limited channel element connections in complex 1 and the highly amalgamated channel elements in complexes 2 and 3. (C) Vertical connectivity diagrams by segment to illustrate the downdip, three-dimensional (3-D) nature of connectivity and the correlation of flow units to key stratigraphic surfaces. Flow units (defined loosely here by whether flow is able to move between layers and across segments based on the statistics) do not clearly follow channel complex boundaries; interchannel complex flow is commonly impacted by a baffle or a barrier at different parts of the channel model, showing the complexity of flow paths in 3-D controlled by bed-scale heterogeneity.

The low-net drape facies is subseismic in nature, and its presence and continuity cannot accurately be predicted from seismic attribute maps (Figure 1). Further, although the draped base of a channel element may appropriately be interpreted from core and wire-line log data, its continuity away from the well location is difficult to predict (e.g., Barton et al., 2010; Stevenson et al., 2015). This work can be extrapolated to show that in deep-water channel systems with a high prevalence of channel element base drape facies (e.g., Beaubouef et al., 1999; Gardner et al., 2003; Macauley and Hubbard, 2013), smaller element widths are more likely to disconnect the reservoir, whereas for systems in which channel element base drapes are not common, the concern of width variation is decreased.

Upscaling: Preserving the Effects of Facies on Connectivity

As models are upscaled, both increases and decreases in connectivity occur despite facies volumes remaining relatively constant (one exception: drape facies, 10 × 10 × 0.25 m [33 × 33 × 0.8 ft] model). This suggests that the simple preservation of deposit volumes and facies proportions between the fine-scale and upscaled models is not a sufficient test for whether key architecture was preserved in the upscaling process. Maintaining facies volumes between grid sizes does not ensure connectivity remains the same and likely provides a false sense of confidence in the upscaled model. The modeling community has explored petrophysical rock property algorithms (Li et al., 1995; Christie, 1996; Durlofsky et al., 1997; Farmer, 2002; Lake and Srinivasan, 2004; White et al., 2004; Durlofsky, 2005; Boschan and Nœtinger, 2012), coarse or upscaled facies models (Stright, 2006; Burns et al., 2010; Babak et al., 2013; Alpak, 2015; Lajevardi and Deutsch; 2015), and multiscale modeling approaches (Mikes and Geel, 2006; Ringrose et al., 2008) to optimize upscaling.

Many studies have noted that small cell sizes in the z-dimension are of great importance for capturing and maintaining geologically significant features (Christie, 1996; Stright, 2006; Roggero et al., 2007; Huysmans and Dassargues, 2012). Results from this upscaling analysis, although not in contrast with this, do provide an important caution. Extending areal cell size to offset a decrease in cell size vertically (to maintain computational efficiency) comes at a cost. This large areal cell size can “create” laterally extensive and thin facies bodies, which, in turn, produce high connectivity estimates associated with sandstone in channel element margins. The results of this study show that these estimates can be larger than the original connectivity values. Furthermore, the modeled influence of the drape on connectivity will break down when the vertical grid cell size increases to a point where the drape is not explicitly represented as a continuous flow barrier.

This is a known problem in instances where a fine-scale flow barrier is attempted to be explicitly represented in Cartesian grids (Deutsch, 2002; Stright, 2006; Alpak et al., 2010; Jackson et al., 2014) and is the motivation for surface-based modeling algorithms with the use of surface-associated transmissibility multipliers to represent shale drapes (Eikeland and Hansen, 2009; Alpak and van der Vlugt, 2014; Jackson et al., 2014). Although curvilinear grids generated from surface-based modeling algorithms succeed in better capturing highly complex curvilinear surfaces that act as flow barriers, they commonly introduce issues with irregularly sized grid cells that are not conducive to effective simulation in standard flow simulators (Aziz, 1993).

Capturing Three-Dimensional Connectivity in Models

Modeling efforts strive for continued improvement in capturing geologically realistic channel element shape and fill, which will facilitate increasingly accurate predictions for connectivity in 3-D (Larue and Hovadik, 2006; Labourdette, 2008; Labourdette and Bez, 2010; McHargue et al., 2011; Sylvester et al., 2011; Pyrcz et al., 2015; Hofstra et al., 2017; Kaplan et al., 2017; Marques et al., 2017; Peter et al., 2017; Rongier et al., 2017; Zhang et al., 2017). Further, these efforts continue to explore the impact of internal channel element architecture on flow in coarse-scale models (e.g., Alpak et al., 2010, 2011). Despite this progress, three gaps are still prevalent: (1) a lack of robust statistical data sets that capture internal element architectures; (2) a paucity of modeling studies that systematically test the impact of element stacking and internal architecture on connectivity, flow, and ultimately recovery; and (3) limited workflows or new algorithms that directly leverage bed and architecture statistics to capture the realistic impact of internal architecture combined with channel element stacking patterns and grid type and cell size within history-matching processes to generate more predictive models. Studies such as that of Larue and Hovadik (2006) test connectivity generated by modeling algorithms but not necessarily in the context of realistic bed-to-system–scale stratigraphic architecture. We are not suggesting that detailed, fine-scale models with a large cell count are required but rather that systematic investigation of the contributions of bed-to-system–scale stratigraphic architecture to fluid flow pathways (similar to the top-down reservoir modeling approach of Williams et al., 2004) is necessary to elucidate the link between the level of architectural detail input into models and the impact of grid types and cell sizes and their control on continuity, connectivity, and subsequent recovery predictions.

CONCLUSIONS

Slope channel strata of the Cretaceous Tres Pasos Formation at Laguna Figueroa, southern Chile, are widely considered as an analog to reservoirs on continental margins globally. A detailed bed-to-geobody–scale geocellular model of the 130-m (425-ft)-thick and 2.5-km (1.5-mi)-long outcrop is used to determine which aspects of stratigraphic architecture are particularly relevant to accurately modeling connectivity in slope channel reservoirs.

Key outcomes of the study include the following.

1. Channel element stacking patterns strongly impact connectivity. In particular, connectivity is reduced in instances where lateral offset is greater than approximately one-third of a channel element width and completely blocked when later offset is greater than approximately two-thirds of a channel element width. The amount of vertical aggradation is less important as long as the channel elements are touching and the axis of the channel element is not draped.

2. Although stacking patterns are a primary control on connectivity, the internal architecture is also an important factor. Increasing fine-grained drape coverage at channel element bases markedly decreases connectivity.

3. The width of modeled channel elements provides an important control on connectivity. Reduced element widths are more likely to produce disconnected sandstone geobodies and, thus, poorer connectivity.

4. Connectivity is not directly correlated with NTG because of the presence of thin channel element base drapes, which can severely impede connectivity but do not significantly contribute to NTG.

5. Upscaling the models consistently increases the proportion of shared channel element contact area between successively stacked elements (up to 10%) but decreases sandstone connectivity (up to 2%–3%). The upscaling analysis also demonstrates how small differences in cell geometry can have large impacts on the architecture of the model, which at times induces channel element connectivity that otherwise would not exist.

6. The bounding surfaces of flow units do not always coincide with widespread stratigraphic surfaces such as channel complex boundaries, which are commonly interpreted from seismic reflection data. Furthermore, flow unit character can change markedly downdip because of channel element stacking variability.

Our analysis demonstrates that upscaling in any dimension invariably increases static connectivity, supporting the notion that characterization of fine-scale internal channel element architecture is critical because of its strong impact on fluid flow pathways. The results of this study may inform standard industry modeling practices and decisions not by suggesting that more bed-scale detail be added to reservoir models but rather by using the knowledge of where and when bed-scale detail is going to impact field-scale flow behavior to mitigate risk. Ultimately, this work constrains uncertainty related to subseismic-scale stratigraphic architecture, as well as its impact on reservoir connectivity, by providing concrete data that can be used to build more predictive models.

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ACKNOWLEDGMENTS

The funding for this work was generously provided by the industrial sponsors of the Chile Slope Systems Joint Industry Project Phase 1 (Anadarko, BG Group, BHP Billiton, BP, Chevron, ConocoPhillips, Hess, Maersk, Marathon, Nexen, Shell, Statoil, Talisman) and Phase 2 (Anadarko, BHP Billiton, Chevron, ConocoPhillips, Equinor, Hess, Nexen CNOOC, Repsol, Shell). We are grateful to the landowner, Armando Alvarez S., as well as Jose Antonio Kusanovic and Tamara Mac-Leod for facilitating land access. We are also thankful for the thoughtful feedback from reviewers Matthew Pranter, Jean Borgomano, and Brad Prather as well as AAPG Editor Barry J. Katz, which greatly enhanced the clarity and quality of the manuscript. Finally, we are grateful for the generous donation from Schlumberger, enabling us to use Petrel for this research project.

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