Changes

==Conceptual framework for clinoform modeling==

==Conceptual framework for clinoform modeling==

Clinoforms occur at a wide range of spatial scales, from large, basinward-dipping surfaces at the shelf-slope margin, to smaller surfaces associated with progradation of deltaic and shoreface systems across the shelf (e.g., Helland-Hansen and Hampson, 2009). This study focuses on developing a surface-based approach to represent clinoforms at any lengthscale in reservoir models, with emphasis on clinoforms produced by the progradation of deltaic, barrier-island, and strandplain shorelines, which are typically up to a few tens of meters in height. The 3-D geometry and spatial arrangement of shoreline-scale clinoforms reflect in large part the process regime under which they were deposited (e.g., Galloway, 1975). Fluvial-dominated deltas exhibit a hierarchy of point-sourced, teardrop-shaped sediment bodies that are fed via a downstream branching network of distributary channels. From small to large lengthscales, this hierarchy consists of mouth bars, mouth-bar assemblages, and delta lobes (Bhattacharya, 2006; equivalent to the jet-plume deposits, jet-plume-complex deposits, and delta lobes of Wellner et al., 2005). Sediment-body geometry is modified by the action of waves and tides, which respectively tend to result in shoreline-parallel and shoreline-perpendicular sediment transport that suppresses branching and switching of distributary channels (e.g., Galloway, 1975; Willis, 2005; Bhattacharya, 2006; Plink-Björklund, 2012). Clinoforms exist as a preserved record of sediment-body morphologies at each of these hierarchical lengthscales (e.g., Gani and Bhattacharya, 2007) but are most commonly described at the scale of delta lobes in outcrop and high-resolution, shallow seismic data. For example, in Pleistocene fluvial-dominated delta deposits imaged in shallow-seismic data, Roberts et al. (2004, p. 185) comment that “each clinoform set represents rather continuous deposition from a distributary or related set of distributaries, resulting in the formation of a delta lobe.” Shale drapes and cemented concretionary layers occur along depositional surfaces at each hierarchical level but generally have greater continuity and extent at larger lengthscales of the hierarchy (e.g., Gani and Bhattacharya, 2007; Lee et al., 2007; Ahmed et al., 2014). Thus, delta lobes tend to be overlain across flooding surfaces by prodelta shales and distal-delta-front heteroliths, which may cause them to behave as distinct reservoir zones that can be correlated between wells, whereas clinoforms are associated with heterogeneity between wells and within reservoir zones (e.g., Ainsworth et al., 1999; Hampson et al., 2008).

Clinoforms occur at a wide range of spatial scales, from large, basinward-dipping surfaces at the shelf-slope margin, to smaller surfaces associated with progradation of deltaic and shoreface systems across the shelf (e.g., Helland-Hansen and Hampson, 2009). This study focuses on developing a surface-based approach to represent clinoforms at any lengthscale in reservoir models, with emphasis on clinoforms produced by the progradation of deltaic, barrier-island, and strandplain shorelines, which are typically up to a few tens of meters in height. The 3-D geometry and spatial arrangement of shoreline-scale clinoforms reflect in large part the process regime under which they were deposited (e.g., Galloway, 1975). Fluvial-dominated deltas exhibit a hierarchy of point-sourced, teardrop-shaped sediment bodies that are fed via a downstream branching network of distributary channels. From small to large lengthscales, this hierarchy consists of mouth bars, mouth-bar assemblages, and delta lobes (Bhattacharya, 2006; equivalent to the jet-plume deposits, jet-plume-complex deposits, and delta lobes of Wellner et al., 2005). Sediment-body geometry is modified by the action of waves and tides, which respectively tend to result in shoreline-parallel and shoreline-perpendicular sediment transport that suppresses branching and switching of distributary channels (e.g., Galloway, 1975; Willis, 2005; Bhattacharya, 2006; Plink-Björklund, 2012). Clinoforms exist as a preserved record of sediment-body morphologies at each of these hierarchical lengthscales (e.g., Gani and Bhattacharya, 2007) but are most commonly described at the scale of delta lobes in outcrop and high-resolution, shallow seismic data. For example, in Pleistocene fluvial-dominated delta deposits imaged in shallow-seismic data, Roberts et al. (2004, p. 185) comment that “each clinoform set represents rather continuous deposition from a distributary or related set of distributaries, resulting in the formation of a delta lobe.” Shale drapes and cemented concretionary layers occur along depositional surfaces at each hierarchical level but generally have greater continuity and extent at larger lengthscales of the hierarchy (e.g., Gani and Bhattacharya, 2007; Lee et al., 2007; Ahmed et al., 2014). Thus, delta lobes tend to be overlain across flooding surfaces by prodelta shales and distal-delta-front heteroliths, which may cause them to behave as distinct reservoir zones that can be correlated between wells, whereas clinoforms are associated with heterogeneity between wells and within reservoir zones (e.g., Ainsworth et al., 1999; Hampson et al., 2008).

===Bounding Surfaces That Define Rock Volume===

===Bounding Surfaces That Define Rock Volume===

Each set of shoreline clinoforms is contained within a distinct, upward-shallowing, regressive succession, or parasequence (sensu Van Wagoner et al., 1990; Hampson et al., 2008), that is bounded at its base and top by flooding surfaces. Multiple clinoforms exist within each parasequence. Because the algorithm is generic, any top and base bounding surfaces can be used; the only requirement is that the top bounding surface is entirely above, or coincident with, the base bounding surface across the model volume ([[:File:BLTN13190fig1.jpg|Figure 1A–C]]). By using the flooding surfaces at the top and/or base of a parasequence as reference surfaces, the algorithm can produce clinoforms that are modified by postdepositional folding and faulting (Figure 2A), truncation by overlying erosion surfaces (Figure 2B), and/or progradation over irregular sea-floor topography (Figure 2C). The parasequence-bounding flooding surfaces are first read into the clinoform-modeling algorithm, using a standard gridded format exported from a reservoir modeling software package. Clinoforms created by the algorithm adapt to the morphology of either (or both) bounding surfaces, using a height function, BLTN13190eq1 (Figure 2D), that calculates the height of the clinoform relative to the length along the clinoform surface and the height difference between the top and base bounding surfaces (see Table 1 for nomenclature):  

Each set of shoreline clinoforms is contained within a distinct, upward-shallowing, regressive succession, or parasequence (sensu Van Wagoner et al., 1990; Hampson et al., 2008), that is bounded at its base and top by flooding surfaces. Multiple clinoforms exist within each parasequence. Because the algorithm is generic, any top and base bounding surfaces can be used; the only requirement is that the top bounding surface is entirely above, or coincident with, the base bounding surface across the model volume ([[:File:BLTN13190fig1.jpg|Figure 1A–C]]). By using the flooding surfaces at the top and/or base of a parasequence as reference surfaces, the algorithm can produce clinoforms that are modified by postdepositional folding and faulting ([[:File:BLTN13190fig2.jpg|Figure 2A]]), truncation by overlying erosion surfaces ([[:File:BLTN13190fig2.jpg|Figure 2B]]), and/or progradation over irregular sea-floor topography ([[:File:BLTN13190fig2.jpg|Figure 2C]]). The parasequence-bounding flooding surfaces are first read into the clinoform-modeling algorithm, using a standard gridded format exported from a reservoir modeling software package. Clinoforms created by the algorithm adapt to the morphology of either (or both) bounding surfaces, using a height function, BLTN13190eq1 ([[:File:BLTN13190fig2.jpg|Figure 2D]]), that calculates the height of the clinoform relative to the length along the clinoform surface and the height difference between the top and base bounding surfaces (see Table 1 for nomenclature):  

:<math>EQUATIONS/BLTN13190eqd1</math>

:<math>EQUATIONS/BLTN13190eqd1</math>

[[File:BLTN13190fig2.jpg|thumb|300px|{{figure number|2}}Examples of clinoforms produced by the clinoform-modeling algorithm conditioned to different bounding surfaces and clinoform geometries. (A) Bounding surfaces represent postdepositional compaction and folding of the original (depositional) geometries of the clinoform and the top and base bounding surfaces. (B) Bounding surfaces represent a clinoform within a volume truncated at its top, for example, by a channel ([[:File:BLTN13190fig1.jpg|Figure 1]]). (C) Bounding surfaces represent a clinoform downlapping onto irregular sea-floor topography. (D) Height function, BLTN13190eq2 (equation 1; see Table 1 for nomenclature). (E) Shape function, BLTN13190eq3 (equation 7; Table 1), demonstrating that increasing the exponent, BLTN13190eq4, increases the dip angle of clinoforms.]]

This allows the clinoforms to adapt to the morphology of the bounding surfaces ([[:File:BLTN13190fig2.jpg|Figure 2A]]). For cases in which an overlying erosional bounding surface is interpreted to truncate clinoforms ([[:File:BLTN13190fig2.jpg|Figure 2B]]) and/or clinoforms are interpreted to downlap onto a bounding surface that reflects irregular sea-floor topography ([[:File:BLTN13190fig2.jpg|Figure 2C]]), a planar and horizontal dummy surface is used either above the erosional bounding surface or below the bounding surface, reflecting irregular sea-floor topography. The height function BLTN13190eq30 (equation 1), is applied to the planar dummy surfaces to insert clinoforms; and, in a final step, the bounding surface geometries are used to remove the upper and/or lower portions of the clinoforms, where appropriate, to match interpreted truncation ([[:File:BLTN13190fig2.jpg|Figure 2B]]) and/or down lap ([[:File:BLTN13190fig2.jpg|Figure 2C]]).

 

This allows the clinoforms to adapt to the morphology of the bounding surfaces (Figure 2A). For cases in which an overlying erosional bounding surface is interpreted to truncate clinoforms (Figure 2B) and/or clinoforms are interpreted to downlap onto a bounding surface that reflects irregular sea-floor topography (Figure 2C), a planar and horizontal dummy surface is used either above the erosional bounding surface or below the bounding surface, reflecting irregular sea-floor topography. The height function BLTN13190eq30 (equation 1), is applied to the planar dummy surfaces to insert clinoforms; and, in a final step, the bounding surface geometries are used to remove the upper and/or lower portions of the clinoforms, where appropriate, to match interpreted truncation (Figure 2B) and/or downlap (Figure 2C).

===Plan-View Clinoform Geometry===

===Plan-View Clinoform Geometry===

The depositional processes acting at the shoreline control the plan-view shape and abundance of clinoforms and their associated heterogeneity (Howell et al., 2008a). Maps, satellite images, and aerial photographs of modern systems are used to make a first-order approximation of the distinct plan-view shape of clinoforms in different depositional environments (Figure 3), as described in the subsequent text, because there is a paucity of reliable data of this type from subsurface reservoirs and ancient analogs. This approximation assumes that the modern-day shape of a shoreline represents a snap-shot in time that mimics the geometry of clinoforms and associated depositional elements preserved in the stratigraphic record (Howell et al., 2008a). Mattson and Chan (2004) assumed a simple radial geometry in plan view for fluvial-dominated deltaic clinoforms in the Ferron Sandstone Member outcrop analog, but this geometry is not universally applicable even as a first-order approximation. For example, wave-dominated strandplains are nearly linear in plan view (Figure 3A), wave-dominated deltas have broad arcuate forms (Figure 3B), and fluvial-dominated deltaic shorelines form distinct, lobate protuberances (Figure 3C) (e.g., Galloway, 1975).

BLTN13190fig3.jpg|{{figure number|3}}Generalized, first-order approximations of the plan-view geometry of clinoforms in different depositional environments: (A) Nayarit Coast, Mexico, representative of a wave-dominated strandplain (image modified after Google Earth and DigitalGlobe, 2013); (B) Nile Delta, Egypt, representative of a wave-dominated delta (image modified after Google Earth, 2013); and (C) Wax Lake Delta, Louisiana, representative of a fluvial-dominated delta (image modified after Google Earth and TerraMetrics, 2013). Solid white lines represent a first-order approximation of the shoreline at the clinoform top, whereas the dashed white lines represent first-order approximations of the likely maximum extent of the clinoform surface and its downlap termination on the underlying sea floor.

BLTN13190fig4.jpg|{{figure number|4}}(A) A user specifies the length of the top (solid line) and base (dashed line) ellipses in depositional dip and strike directions (BLTN13190eq36, BLTN13190eq37, BLTN13190eq38, BLTN13190eq39; Table 1) relative to the clinoform origin. The surface representing the clinoform is created in the volume between the top and base ellipses. (B) At a point on the clinoform, the radius relative to the clinoform origin (black arrow, BLTN13190eq40, the radius of the base ellipse (black arrow, BLTN13190eq41 and the radius of the top ellipse (black arrow, BLTN13190eq42 are calculated. (C) Plan view of four adjacent clinoforms. The user specifies the overall progradation direction of the clinoforms relative to north, as well as the coordinates of the initial insertion point BLTN13190eq43. (D) Conceptual depositional-dip-oriented cross-section view of clinoforms. Clinoform spacing, BLTN13190eq44, is defined as the distance between the top truncation points of two adjacent clinoforms. Clinoform length, L, is defined as the distance between the top and base truncations by the user-specified bounding surfaces along a single clinoform.

[[File:BLTN13190fig3.jpg|thumb|300px|{{figure number|3}}Generalized, first-order approximations of the plan-view geometry of clinoforms in different depositional environments: (A) Nayarit Coast, Mexico, representative of a wave-dominated strandplain (image modified after Google Earth and DigitalGlobe, 2013); (B) Nile Delta, Egypt, representative of a wave-dominated delta (image modified after Google Earth, 2013); and (C) Wax Lake Delta, Louisiana, representative of a fluvial-dominated delta (image modified after Google Earth and TerraMetrics, 2013). Solid white lines represent a first-order approximation of the shoreline at the clinoform top, whereas the dashed white lines represent first-order approximations of the likely maximum extent of the clinoform surface and its downlap termination on the underlying sea floor.]]

The depositional processes acting at the shoreline control the plan-view shape and abundance of clinoforms and their associated heterogeneity (Howell et al., 2008a). Maps, satellite images, and aerial photographs of modern systems are used to make a first-order approximation of the distinct plan-view shape of clinoforms in different depositional environments ([[:File:BLTN13190fig3.jpg|Figure 3]]), as described in the subsequent text, because there is a paucity of reliable data of this type from subsurface reservoirs and ancient analogs. This approximation assumes that the modern-day shape of a shoreline represents a snap-shot in time that mimics the geometry of clinoforms and associated depositional elements preserved in the stratigraphic record (Howell et al., 2008a). Mattson and Chan (2004) assumed a simple radial geometry in plan view for fluvial-dominated deltaic clinoforms in the Ferron Sandstone Member outcrop analog, but this geometry is not universally applicable even as a first-order approximation. For example, wave-dominated strandplains are nearly linear in plan view ([[:File:BLTN13190fig3.jpg|Figure 3A]]), wave-dominated deltas have broad arcuate forms ([[:File:BLTN13190fig3.jpg|Figure 3B]]), and fluvial-dominated deltaic shorelines form distinct, lobate protuberances ([[:File:BLTN13190fig3.jpg|Figure 3C]]) (e.g., Galloway, 1975).

As the algorithm is generic, the user can specify the shape of an ellipse that approximates the plan-view geometry of clinoforms (Figure 4A). Using an ellipse, rather than a radial geometry, allows the user to specify a wide range of plan-view clinoform geometries using a simple function, depending on the interpreted environment of deposition and scale of shoreline curvature. Two ellipses are used: the top ellipse represents the shoreline at the clinoform top, and the base ellipse represents the maximum extent of the clinoform at its downlap termination on the underlying sea floor. The user defines the length of the top and base ellipses in depositional dip and strike directions (BLTN13190eq31, BLTN13190eq32, BLTN13190eq33, BLTN13190eq34; Figure 4B, Table 1) relative to the origin of the clinoform. The difference between the user-defined maximum extents of the top and base ellipses yields the clinoform length BLTN13190eq35 (Figure 4D). The maximum extent of the top and base ellipses can then be defined as  

As the algorithm is generic, the user can specify the shape of an ellipse that approximates the plan-view geometry of clinoforms ([[:File:BLTN13190fig4.jpg|Figure 4A]]). Using an ellipse, rather than a radial geometry, allows the user to specify a wide range of plan-view clinoform geometries using a simple function, depending on the interpreted environment of deposition and scale of shoreline curvature. Two ellipses are used: the top ellipse represents the shoreline at the clinoform top, and the base ellipse represents the maximum extent of the clinoform at its downlap termination on the underlying sea floor. The user defines the length of the top and base ellipses in depositional dip and strike directions (BLTN13190eq31, BLTN13190eq32, BLTN13190eq33, BLTN13190eq34; [[:File:BLTN13190fig4.jpg|Figure 4B]], Table 1) relative to the origin of the clinoform. The difference between the user-defined maximum extents of the top and base ellipses yields the clinoform length BLTN13190eq35 ([[:File:BLTN13190fig4.jpg|Figure 4D]]). The maximum extent of the top and base ellipses can then be defined as  

:<math>EQUATIONS/BLTN13190eqd2</math>

:<math>EQUATIONS/BLTN13190eqd2</math>

and  

and  

:<math>EQUATIONS/BLTN13190eqd3</math>

:<math>EQUATIONS/BLTN13190eqd3</math>

[[File:BLTN13190fig4.jpg|thumb|300px|{{figure number|4}}(A) A user specifies the length of the top (solid line) and base (dashed line) ellipses in depositional dip and strike directions (BLTN13190eq36, BLTN13190eq37, BLTN13190eq38, BLTN13190eq39; Table 1) relative to the clinoform origin. The surface representing the clinoform is created in the volume between the top and base ellipses. (B) At a point on the clinoform, the radius relative to the clinoform origin (black arrow, BLTN13190eq40, the radius of the base ellipse (black arrow, BLTN13190eq41 and the radius of the top ellipse (black arrow, BLTN13190eq42 are calculated. (C) Plan view of four adjacent clinoforms. The user specifies the overall progradation direction of the clinoforms relative to north, as well as the coordinates of the initial insertion point BLTN13190eq43. (D) Conceptual depositional-dip-oriented cross-section view of clinoforms. Clinoform spacing, BLTN13190eq44, is defined as the distance between the top truncation points of two adjacent clinoforms. Clinoform length, L, is defined as the distance between the top and base truncations by the user-specified bounding surfaces along a single clinoform.]]

The clinoform is generated in the volume between the top and base ellipses ([[:File:BLTN13190fig4.jpg|Figure 4A, B]]). In this volume, the radius of each point on the clinoform, BLTN13190eq45 (Table 1), is calculated relative to the clinoform origin (BLTN13190eq46), using  

 

The clinoform is generated in the volume between the top and base ellipses (Figure 4A, B). In this volume, the radius of each point on the clinoform, BLTN13190eq45 (Table 1), is calculated relative to the clinoform origin (BLTN13190eq46), using  

:<math>EQUATIONS/BLTN13190eqd4</math>

:<math>EQUATIONS/BLTN13190eqd4</math>

At each point on the clinoform, the radius of the top ellipse relative to the clinoform origin is calculated using  

At each point on the clinoform, the radius of the top ellipse relative to the clinoform origin is calculated using  

:<math>EQUATIONS/BLTN13190eqd6</math>

:<math>EQUATIONS/BLTN13190eqd6</math>

To specify highly lobate plan-view clinoform geometry, characteristic of a fluvial-dominated delta (Figure 3C), the user specifies a larger value for the clinoform in the depositional dip direction, BLTN13190eq47, than for the clinoform in the strike direction, BLTN13190eq48. For a highly elongate or near-linear plan-view clinoform geometry, characteristic of a wave-dominated shoreline (Figure 3A, B), the user specifies a much larger value for the clinoform in the depositional strike direction, BLTN13190eq49, than for the clinoform in the dip direction, BLTN13190eq50. Data describing clinoform extent in depositional dip and strike directions can be extracted from published data on the dimensions of ancient shorelines or by analysis of their modern counterparts (e.g., tables 1, 2 in Howell et al., 2008a).

To specify highly lobate plan-view clinoform geometry, characteristic of a fluvial-dominated delta ([[:File:BLTN13190fig3.jpg|Figure 3C]]), the user specifies a larger value for the clinoform in the depositional dip direction, BLTN13190eq47, than for the clinoform in the strike direction, BLTN13190eq48. For a highly elongate or near-linear plan-view clinoform geometry, characteristic of a wave-dominated shoreline ([[:File:BLTN13190fig3.jpg|Figure 3A, B]]), the user specifies a much larger value for the clinoform in the depositional strike direction, BLTN13190eq49, than for the clinoform in the dip direction, BLTN13190eq50. Data describing clinoform extent in depositional dip and strike directions can be extracted from published data on the dimensions of ancient shorelines or by analysis of their modern counterparts (e.g., tables 1, 2 in Howell et al., 2008a).

===Cross-Sectional Clinoform Geometry===

===Cross-Sectional Clinoform Geometry===

The shape and dip angle of a deltaic or shoreface clinoform in cross section is a function of modal grain size, proportion of mud, and the depositional process regime at the shoreline. In sandy, fluvial-dominated deltas, clinoforms have simple concave-upward geometries and steep dip angles (up to 15°) (Gani and Bhattacharya, 2005) (e.g., [[:File:BLTN13190fig1.jpg|Figure 1]]). Similar geometries have been documented in sandy, tide-influenced deltas (dip angles up to 5°–15°) (Willis et al., 1999). Concave-upward clinoform geometry is also typical of sandy, wave-dominated deltas and strandplains, although the clinoforms have smaller dip angles (typically up to 1°–2°) (Hampson and Storms, 2003; Gani and Bhattacharya, 2005). Clinoforms are consistently inclined paleobasinward down depositional dip; and, along depositional strike, they exhibit bidirectional, concave-upward dips if the delta-front was lobate in plan view (e.g., Willis et al., 1999; Kolla et al., 2000; Roberts et al., 2004) or appear horizontal if the shoreline was approximately linear (e.g., Hampson, 2000). Clinoforms are usually truncated at their tops by a variety of channelized erosion surfaces formed during shoreline advance (e.g., distributary channels, incised valleys) and by channelized and/or planar transgressive erosion surfaces (tide and wave ravinement surfaces sensu Swift, 1968) associated with shoreline retreat. Consequently, most sandy shoreline clinoforms lack a decrease in depositional dip (rollover) near their tops, although this geometry is ubiquitous in larger, shelf-slope margin clinoforms (e.g., Steckler et al., 1999) and in the outer, muddy portion of compound deltaic clinoforms with a broad subaqueous topset that lies seaward of the shoreline (e.g., Pirmez et al., 1998).

The shape and dip angle of a deltaic or shoreface clinoform in cross section is a function of modal grain size, proportion of mud, and the depositional process regime at the shoreline. In sandy, fluvial-dominated deltas, clinoforms have simple concave-upward geometries and steep dip angles (up to 15°) (Gani and Bhattacharya, 2005) (e.g., [[:File:BLTN13190fig1.jpg|Figure 1]]). Similar geometries have been documented in sandy, tide-influenced deltas (dip angles up to 5°–15°) (Willis et al., 1999). Concave-upward clinoform geometry is also typical of sandy, wave-dominated deltas and strandplains, although the clinoforms have smaller dip angles (typically up to 1°–2°) (Hampson and Storms, 2003; Gani and Bhattacharya, 2005). Clinoforms are consistently inclined paleobasinward down depositional dip; and, along depositional strike, they exhibit bidirectional, concave-upward dips if the delta-front was lobate in plan view (e.g., Willis et al., 1999; Kolla et al., 2000; Roberts et al., 2004) or appear horizontal if the shoreline was approximately linear (e.g., Hampson, 2000). Clinoforms are usually truncated at their tops by a variety of channelized erosion surfaces formed during shoreline advance (e.g., distributary channels, incised valleys) and by channelized and/or planar transgressive erosion surfaces (tide and wave ravinement surfaces sensu Swift, 1968) associated with shoreline retreat. Consequently, most sandy shoreline clinoforms lack a decrease in depositional dip (rollover) near their tops, although this geometry is ubiquitous in larger, shelf-slope margin clinoforms (e.g., Steckler et al., 1999) and in the outer, muddy portion of compound deltaic clinoforms with a broad subaqueous topset that lies seaward of the shoreline (e.g., Pirmez et al., 1998).

Here, a geometric approach is used to represent the depositional dip cross-section shape of a clinoform with a dimensionless shape function, BLTN13190eq62 (Figure 2E), such as a power law for concave-upward, sandy, shoreline clinoforms:  

Here, a geometric approach is used to represent the depositional dip cross-section shape of a clinoform with a dimensionless shape function, BLTN13190eq62 ([[:File:BLTN13190fig2.jpg|Figure 2E]]), such as a power law for concave-upward, sandy, shoreline clinoforms:  

:<math>EQUATIONS/BLTN13190eqd7</math>

:<math>EQUATIONS/BLTN13190eqd7</math>

:<math>EQUATIONS/BLTN13190eqd8</math>

:<math>EQUATIONS/BLTN13190eqd8</math>

By varying the exponent in the clinoform shape function, BLTN13190eq64, the user can increase or decrease the dip angle and change the shape of the clinoform (Figure 2E, Table 1). If a similar geometry is interpreted for each clinoform within a parasequence, because they are inferred to have formed under the influence of similar hydrodynamic and sedimentologic processes, then the same value of BLTN13190eq65 (equation 7) can be applied to each clinoform modeled in the parasequence. Different values of BLTN13190eq66 can be applied to distinct geographic regions of a parasequence in which clinoforms are interpreted to have different geometries (e.g., on different flanks of an asymmetric wave-dominated delta; Bhattacharya and Giosan, 2003; Charvin et al., 2010), provided that the bounding surfaces of these geographic regions have been defined (in the initial step of the method).

By varying the exponent in the clinoform shape function, BLTN13190eq64, the user can increase or decrease the dip angle and change the shape of the clinoform ([[:File:BLTN13190fig2.jpg|Figure 2E]], Table 1). If a similar geometry is interpreted for each clinoform within a parasequence, because they are inferred to have formed under the influence of similar hydrodynamic and sedimentologic processes, then the same value of BLTN13190eq65 (equation 7) can be applied to each clinoform modeled in the parasequence. Different values of BLTN13190eq66 can be applied to distinct geographic regions of a parasequence in which clinoforms are interpreted to have different geometries (e.g., on different flanks of an asymmetric wave-dominated delta; Bhattacharya and Giosan, 2003; Charvin et al., 2010), provided that the bounding surfaces of these geographic regions have been defined (in the initial step of the method).

===Spacing and Progradation Direction of Clinoforms===

===Spacing and Progradation Direction of Clinoforms===

The clinoform-modeling algorithm allows the user to specify the main progradation direction of the clinoforms and to define the intervals along the progradation path at which clinoforms are generated (i.e., the clinoform spacing). The user specifies a progradation direction relative to north, BLTN13190eq67 (Figure 4C, Table 1), along which successive clinoforms are generated, which corresponds to the progradation path of the shoreline during clinoform deposition (plan-view shoreline trajectory of Helland-Hansen and Hampson, 2009). The user also specifies the initial insertion point for the clinoforms, BLTN13190eq68 (Figure 4C). This provides flexibility in determining where to place the initial clinoform relative to the proximal model boundary. The spacing between each clinoform surface, BLTN13190eq69 (Table 1), is also designated by the user. Clinoform spacing is defined as the distance between the top-truncation points of two successive clinoforms, and it determines the origin position, BLTN13190eq70, of successive clinoforms (Figure 4D).

The clinoform-modeling algorithm allows the user to specify the main progradation direction of the clinoforms and to define the intervals along the progradation path at which clinoforms are generated (i.e., the clinoform spacing). The user specifies a progradation direction relative to north, BLTN13190eq67 ([[:File:BLTN13190fig4.jpg|Figure 4C]], Table 1), along which successive clinoforms are generated, which corresponds to the progradation path of the shoreline during clinoform deposition (plan-view shoreline trajectory of Helland-Hansen and Hampson, 2009). The user also specifies the initial insertion point for the clinoforms, BLTN13190eq68 ([[:File:BLTN13190fig4.jpg|Figure 4C]]). This provides flexibility in determining where to place the initial clinoform relative to the proximal model boundary. The spacing between each clinoform surface, BLTN13190eq69 (Table 1), is also designated by the user. Clinoform spacing is defined as the distance between the top-truncation points of two successive clinoforms, and it determines the origin position, BLTN13190eq70, of successive clinoforms ([[:File:BLTN13190fig4.jpg|Figure 4D]]).

===Stochastic Modeling of Clinoforms===

===Stochastic Modeling of Clinoforms===

[[File:BLTN13190fig5.jpg|thumb|300px|{{figure number|5}}(A) Paleogeographic reconstruction of the Late Cretaceous Last Chance and Vernal delta systems of the Ferron Sandstone Member of the Mancos Shale in present-day Utah (after Cotter, 1976; used with permission of Brigham Young University). The location of the Deveugle et al. (2011) model (Figure 5D) and a regional cross section (Figure 5B) are highlighted. (B) Schematic regional cross section through the Last Chance delta system of the Ferron Sandstone Member and its eight-component shallow-marine tongues (termed “pararasequence sets,” using the nomenclature of Deveugle et al., 2011, and numbered PSS1 to PSS8), from southwest (paleolandward) to northeast (paleoseaward) (after Anderson and Ryer, 2004; used with permission of AAPG). (C) Detailed cross section through the lowermost shallow-marine tongues (termed “parasequences,” using the nomenclature of Deveugle et al., 2011, and forming PSS1 in Figure 5B) and associated coastal-plain strata (after Garrison and Van den Bergh, 2004; used with permission of AAPG). The tongue is subdivided into constituent parasequences (after Deveugle et al., 2011). Parasequence 1.6 is modeled in this study. (D) Distribution of facies-association belts at the top of parasequence 1.6, in the Deveugle et al. (2011) model area in the Ivie Creek amphitheater. The area of the model constructed in this study (Figures 7–10) lies within the dashed lines.]]

[[File:BLTN13190fig5.jpg|thumb|300px|{{figure number|5}}(A) Paleogeographic reconstruction of the Late Cretaceous Last Chance and Vernal delta systems of the Ferron Sandstone Member of the Mancos Shale in present-day Utah (after Cotter, 1976; used with permission of Brigham Young University). The location of the Deveugle et al. (2011) model (Figure 5D) and a regional cross section (Figure 5B) are highlighted. (B) Schematic regional cross section through the Last Chance delta system of the Ferron Sandstone Member and its eight-component shallow-marine tongues (termed “pararasequence sets,” using the nomenclature of Deveugle et al., 2011, and numbered PSS1 to PSS8), from southwest (paleolandward) to northeast (paleoseaward) (after Anderson and Ryer, 2004; used with permission of AAPG). (C) Detailed cross section through the lowermost shallow-marine tongues (termed “parasequences,” using the nomenclature of Deveugle et al., 2011, and forming PSS1 in Figure 5B) and associated coastal-plain strata (after Garrison and Van den Bergh, 2004; used with permission of AAPG). The tongue is subdivided into constituent parasequences (after Deveugle et al., 2011). Parasequence 1.6 is modeled in this study. (D) Distribution of facies-association belts at the top of parasequence 1.6, in the Deveugle et al. (2011) model area in the Ivie Creek amphitheater. The area of the model constructed in this study (Figures 7–10) lies within the dashed lines.]]

[[File:BLTN13190fig6.jpg|thumb|300px|{{figure number|6}}(A) Interpreted line drawing of clinoforms in parasequence 1.6 at the Junction Point section of Ivie Creek amphitheater (Figure 5D) (modified after Forster et al., 2004). Each clinoform bounds a mouth bar and equivalent delta-front deposits. Data from 104 clinoforms were collected to condition the clinoform-modeling algorithm. Frequency distributions of values measured from outcrop data for (B) clinoform length (Figure 4D), and (C) clinoform spacing (Figure 4D), which are used as input parameters in the clinoform-modeling algorithm (Table 2).]]

[[File:BLTN13190fig6.jpg|thumb|300px|{{figure number|6}}(A) Interpreted line drawing of clinoforms in parasequence 1.6 at the Junction Point section of Ivie Creek amphitheater (Figure 5D) (modified after Forster et al., 2004). Each clinoform bounds a mouth bar and equivalent delta-front deposits. Data from 104 clinoforms were collected to condition the clinoform-modeling algorithm. Frequency distributions of values measured from outcrop data for (B) clinoform length ([[:File:BLTN13190fig4.jpg|Figure 4D]]), and (C) clinoform spacing ([[:File:BLTN13190fig4.jpg|Figure 4D]]), which are used as input parameters in the clinoform-modeling algorithm (Table 2).]]

===Model Construction===

===Model Construction===

The top and base flooding surfaces of parasequence 1.6 were extracted from the model of Deveugle et al. (2011) and served as the bounding surfaces used in the clinoform algorithm (Figure 2). The surfaces were cropped to cover a model area of 750 × 3000 m (2461 × 9843 ft) in the Ivie Creek amphitheater (Figure 5D). Additional surfaces representing the boundaries between facies associations from the model of Deveugle et al. (2011) were also extracted and similarly cropped; these define the distribution of facies associations present in each rock volume bounded by two clinoforms (i.e., clinothem) (cf. table 1 in Deveugle et al., 2011). From distal to proximal, the modeled facies associations are prodelta mudstone (PD), distal delta-front heteroliths (dDF), proximal delta-front sandstones (pDF), and stream-mouth-bar sandstones (SMB) (Figure 5D). Where facies associations pinch out, the facies association boundary surfaces were adjusted to coincide throughout the remainder of the model volume with either the top or base parasequence bounding surface. This ensures that the surface is defined across the entire model volume and is suitable for gridding (Jackson et al., 2009). There are no faults within the model volume of 750 × 3000 × 6 m (2461 × 9843 × 20 ft). In a final step, isochore maps were generated between the top and base flooding surfaces and between facies association boundary surfaces and the base flooding surface. The base bounding surface was flattened, to mimic clinoform progradation over a flat, horizontal sea floor, and isochore maps were used to modify the geometries of the top bounding surface and facies association boundary surfaces above this horizontal base surface. As a result of flattening on the base bounding surface, the bounding surfaces from the existing model of Deveugle et al. (2011) have been modified.

The top and base flooding surfaces of parasequence 1.6 were extracted from the model of Deveugle et al. (2011) and served as the bounding surfaces used in the clinoform algorithm ([[:File:BLTN13190fig2.jpg|Figure 2]]). The surfaces were cropped to cover a model area of 750 × 3000 m (2461 × 9843 ft) in the Ivie Creek amphitheater (Figure 5D). Additional surfaces representing the boundaries between facies associations from the model of Deveugle et al. (2011) were also extracted and similarly cropped; these define the distribution of facies associations present in each rock volume bounded by two clinoforms (i.e., clinothem) (cf. table 1 in Deveugle et al., 2011). From distal to proximal, the modeled facies associations are prodelta mudstone (PD), distal delta-front heteroliths (dDF), proximal delta-front sandstones (pDF), and stream-mouth-bar sandstones (SMB) (Figure 5D). Where facies associations pinch out, the facies association boundary surfaces were adjusted to coincide throughout the remainder of the model volume with either the top or base parasequence bounding surface. This ensures that the surface is defined across the entire model volume and is suitable for gridding (Jackson et al., 2009). There are no faults within the model volume of 750 × 3000 × 6 m (2461 × 9843 × 20 ft). In a final step, isochore maps were generated between the top and base flooding surfaces and between facies association boundary surfaces and the base flooding surface. The base bounding surface was flattened, to mimic clinoform progradation over a flat, horizontal sea floor, and isochore maps were used to modify the geometries of the top bounding surface and facies association boundary surfaces above this horizontal base surface. As a result of flattening on the base bounding surface, the bounding surfaces from the existing model of Deveugle et al. (2011) have been modified.

The parameters used to insert clinoforms into the model volume are summarized in Table 2. The delta lobe in parasequence 1.6 is approximately 8.1 km (5.03 mi) wide and 12.2 km (7.58 mi) long, giving a plan-view aspect ratio of 0.7 (Deveugle et al., 2011), comparable to values for lobes of the Pleistocene Lagniappe delta (after data in Kolla et al., 2000; Roberts et al., 2004) and the modern Wax Lake Delta lobe (after data in Wellner et al., 2005) (Figure 3C). These dimensions were likely smaller during the growth of the delta lobe, and it is assumed here that the lobe initiated with dimensions (BLTN13190eq73, BLTN13190eq74) that were a third of those of the final preserved delta lobe, consistent in areal proportions to a single mouth-bar assemblage or jet-plume complex in the modern Wax Lake Delta lobe (after data in Wellner et al., 2005). The length, BLTN13190eq75, and spacing, BLTN13190eq76, of clinoforms in depositional dip cross section were extracted from the bedding-diagram interpretations of Forster et al. (2004) (Figure 6A), clinoform length and dip statistics of Enge et al. (2010), and the LIDAR data used to create the model of Enge and Howell (2010). A database of clinoform lengths, dips, and spacings was compiled from these data sources, yielding frequency distributions from which the geometry or spatial arrangement of clinoforms that bound mouth-bar clinothems (sensu Bhattacharya, 2006), or a trend in these parameters, can be extracted (Figure 6B, C). The clinoform-modeling algorithm was used to build 31 clinoforms in the modeled volume of parasequence 1.6 (Figure 7). For simplicity, clinoform spacing is fixed at 25 m (82 ft), which is the average value observed at outcrop (Figure 6C). Heterogeneity at bed scale is recognized to be present but is not explicitly captured by surfaces in the model; rather, the effective petrophysical properties assigned to the facies associations (particularly the ratio of vertical-to-horizontal permeability) are modified to account for these (e.g., Jackson et al., 2009; Deveugle et al., 2011; Graham et al., 2015, this volume). A constant value of 2 was assigned to the clinoform shape-function exponent, P (Figure 2E), to ensure that the clinoform dip angle is always in the range extracted from the data of Enge et al. (2010). The initial clinoform insertion point, BLTN13190eq77 (Figure 4C), was qualitatively matched with a plan-view map of facies association belts at the top of parasequence 1.6 (Figure 5D). The overall progradation direction for the clinoforms BLTN13190eq78 was assigned an azimuth of 274° relative to north, which corresponds to the interpreted progradation direction of the delta lobe in parasequence 1.6 (Deveugle et al., 2011). In a subsequent step, the facies association boundary surfaces extracted from the model of Deveugle et al. (2011) were used to create facies association zones within each clinothem. Application of the clinoform-modeling algorithm yields a surface-based model measuring 750 × 3000 × 6 m (2461 × 9843 × 20 ft), which contains 95 surfaces: the top- and base-parasequence bounding surfaces, 31 clinoforms, and 62 facies-association boundary surfaces (Figure 8).

The parameters used to insert clinoforms into the model volume are summarized in Table 2. The delta lobe in parasequence 1.6 is approximately 8.1 km (5.03 mi) wide and 12.2 km (7.58 mi) long, giving a plan-view aspect ratio of 0.7 (Deveugle et al., 2011), comparable to values for lobes of the Pleistocene Lagniappe delta (after data in Kolla et al., 2000; Roberts et al., 2004) and the modern Wax Lake Delta lobe (after data in Wellner et al., 2005) ([[:File:BLTN13190fig3.jpg|Figure 3C]]). These dimensions were likely smaller during the growth of the delta lobe, and it is assumed here that the lobe initiated with dimensions (BLTN13190eq73, BLTN13190eq74) that were a third of those of the final preserved delta lobe, consistent in areal proportions to a single mouth-bar assemblage or jet-plume complex in the modern Wax Lake Delta lobe (after data in Wellner et al., 2005). The length, BLTN13190eq75, and spacing, BLTN13190eq76, of clinoforms in depositional dip cross section were extracted from the bedding-diagram interpretations of Forster et al. (2004) (Figure 6A), clinoform length and dip statistics of Enge et al. (2010), and the LIDAR data used to create the model of Enge and Howell (2010). A database of clinoform lengths, dips, and spacings was compiled from these data sources, yielding frequency distributions from which the geometry or spatial arrangement of clinoforms that bound mouth-bar clinothems (sensu Bhattacharya, 2006), or a trend in these parameters, can be extracted (Figure 6B, C). The clinoform-modeling algorithm was used to build 31 clinoforms in the modeled volume of parasequence 1.6 (Figure 7). For simplicity, clinoform spacing is fixed at 25 m (82 ft), which is the average value observed at outcrop (Figure 6C). Heterogeneity at bed scale is recognized to be present but is not explicitly captured by surfaces in the model; rather, the effective petrophysical properties assigned to the facies associations (particularly the ratio of vertical-to-horizontal permeability) are modified to account for these (e.g., Jackson et al., 2009; Deveugle et al., 2011; Graham et al., 2015, this volume). A constant value of 2 was assigned to the clinoform shape-function exponent, P ([[:File:BLTN13190fig2.jpg|Figure 2E]]), to ensure that the clinoform dip angle is always in the range extracted from the data of Enge et al. (2010). The initial clinoform insertion point, BLTN13190eq77 ([[:File:BLTN13190fig4.jpg|Figure 4C]]), was qualitatively matched with a plan-view map of facies association belts at the top of parasequence 1.6 (Figure 5D). The overall progradation direction for the clinoforms BLTN13190eq78 was assigned an azimuth of 274° relative to north, which corresponds to the interpreted progradation direction of the delta lobe in parasequence 1.6 (Deveugle et al., 2011). In a subsequent step, the facies association boundary surfaces extracted from the model of Deveugle et al. (2011) were used to create facies association zones within each clinothem. Application of the clinoform-modeling algorithm yields a surface-based model measuring 750 × 3000 × 6 m (2461 × 9843 × 20 ft), which contains 95 surfaces: the top- and base-parasequence bounding surfaces, 31 clinoforms, and 62 facies-association boundary surfaces (Figure 8).

[[File:BLTN13190fig7.jpg|thumb|300px|{{figure number|7}}Surfaces generated by the clinoform-modeling algorithm for the model of part of parasequence 1.6 of the Ferron Sandstone Member (Figure 5C, D). (A) Single three-dimensional (3-D) surface representing a clinoform generated by the clinoform modeling algorithm. (B) 3-D dip cross section showing the concave-upward geometry of the clinoforms. (C) 3-D strike section of the model showing surfaces that exhibit bidirectional dips. Not all surfaces used in the model of part of the Ferron Sandstone Member (Figure 8) are shown.]]

[[File:BLTN13190fig7.jpg|thumb|300px|{{figure number|7}}Surfaces generated by the clinoform-modeling algorithm for the model of part of parasequence 1.6 of the Ferron Sandstone Member (Figure 5C, D). (A) Single three-dimensional (3-D) surface representing a clinoform generated by the clinoform modeling algorithm. (B) 3-D dip cross section showing the concave-upward geometry of the clinoforms. (C) 3-D strike section of the model showing surfaces that exhibit bidirectional dips. Not all surfaces used in the model of part of the Ferron Sandstone Member (Figure 8) are shown.]]

We begin by investigating the ability of the clinoform-modeling algorithm to generate realistic stratal geometries from the Ferron Sandstone Member outcrops. Visual inspection of the algorithm-generated model against outcrop photo pans ([[:File:BLTN13190fig1.jpg|Figure 1]]) and bedding diagram interpretations (Figure 6A) reveals a close correspondence between key geometric aspects of the observed data and concepts reproduced in the model, as outlined below.

We begin by investigating the ability of the clinoform-modeling algorithm to generate realistic stratal geometries from the Ferron Sandstone Member outcrops. Visual inspection of the algorithm-generated model against outcrop photo pans ([[:File:BLTN13190fig1.jpg|Figure 1]]) and bedding diagram interpretations (Figure 6A) reveals a close correspondence between key geometric aspects of the observed data and concepts reproduced in the model, as outlined below.

A single delta lobe is present in the model and extends beyond the model volume (Figures 5D, 8A). As a result, clinoforms are larger in their depositional dip and strike extent (BLTN13190eq79 and BLTN13190eq80, respectively; Table 2) than the model area, and they form arcs in plan view in the model (Figure 8B). This plan-view geometry is consistent with the approximately lobate plan-view geometries of clinoforms in fluvial-dominated deltas (Figure 3C). The clinoform-modeling algorithm generates the concave-upward clinoform geometry observed at the outcrop (Figures 7B, 8C), while honoring the topography of the parasequence bounding surfaces. The variation in topographic elevation of the modeled parasequence (Figures 7, 8) is attributed to postdepositional compaction. In a depositional strike cross section of the clinoform-bearing model, the algorithm produces bidirectional concave-upward dips (Figures 7C, 8D) that are consistent with delta-front bodies that are lobate in plan view (e.g., Willis et al., 1999; Kolla et al., 2000; Roberts et al., 2004). Additionally, the model contains stratal geometries observed at the outcrop, such as onlap and downlap of younger clinoforms on to older clinoforms (Figures 7B, 8C). The clinoform-modeling algorithm also produces clinoforms that are consistently distributed in the same orientation as those in the observed delta-lobe deposits and its interpreted plan-view progradation direction (Figures 5A, 8B). Facies proportions in the model are 8% SMB sandstones, 50% pDF sandstones, 31% dDF heteroliths, and 11% PD mudstone. Using porosity values that are characteristic of these facies associations in analogous reservoirs (Table 3), the volume of oil in place in the model is 7.1 million bbl. The clinoform-bearing model is now used to investigate the impact of heterogeneities associated with clinoforms on fluid flow during waterflooding within this fluvial-dominated deltaic parasequence.

A single delta lobe is present in the model and extends beyond the model volume (Figures 5D, 8A). As a result, clinoforms are larger in their depositional dip and strike extent (BLTN13190eq79 and BLTN13190eq80, respectively; Table 2) than the model area, and they form arcs in plan view in the model (Figure 8B). This plan-view geometry is consistent with the approximately lobate plan-view geometries of clinoforms in fluvial-dominated deltas ([[:File:BLTN13190fig3.jpg|Figure 3C]]). The clinoform-modeling algorithm generates the concave-upward clinoform geometry observed at the outcrop (Figures 7B, 8C), while honoring the topography of the parasequence bounding surfaces. The variation in topographic elevation of the modeled parasequence (Figures 7, 8) is attributed to postdepositional compaction. In a depositional strike cross section of the clinoform-bearing model, the algorithm produces bidirectional concave-upward dips (Figures 7C, 8D) that are consistent with delta-front bodies that are lobate in plan view (e.g., Willis et al., 1999; Kolla et al., 2000; Roberts et al., 2004). Additionally, the model contains stratal geometries observed at the outcrop, such as onlap and downlap of younger clinoforms on to older clinoforms (Figures 7B, 8C). The clinoform-modeling algorithm also produces clinoforms that are consistently distributed in the same orientation as those in the observed delta-lobe deposits and its interpreted plan-view progradation direction (Figures 5A, 8B). Facies proportions in the model are 8% SMB sandstones, 50% pDF sandstones, 31% dDF heteroliths, and 11% PD mudstone. Using porosity values that are characteristic of these facies associations in analogous reservoirs (Table 3), the volume of oil in place in the model is 7.1 million bbl. The clinoform-bearing model is now used to investigate the impact of heterogeneities associated with clinoforms on fluid flow during waterflooding within this fluvial-dominated deltaic parasequence.

===Production Strategy===

===Production Strategy===

Table 4 shows the parameters used in the clinoform-modeling algorithm. To honor the nearly linear plan-view geometry of clinoforms observed in seismic data (figures 3, 12 in Dreyer et al., 2005), a width for the top-clinoform ellipse (BLTN13190eq120 that is far greater than the depositional-dip extent of the bounding surfaces in the model area (3200 m [10,499 ft]) was defined; the top-clinoform ellipse length BLTN13190eq121 is half of BLTN13190eq122, to give a plan-view aspect ratio of 2 (cf. wave-dominated shoreface systems in Howell et al., 2008a). Seismically resolved clinoform dip values of 1.5°–4° (Dreyer et al., 2005; Patruno et al., 2015) were used in conjunction with the estimated parasequence thickness to calculate clinoform length (BLTN13190eq123) using simple trigonometry. As there are only a small number of seismically resolved clinoforms in a few paleogeographic locations and within a few stratigraphic levels to extract clinoform length, a normal distribution based on the extracted data was generated (Figure 13A), and values were then drawn at random from this distribution to populate the model volume (Figure 13A). Finally, the premodeling lengths were compared with the seismically resolved clinoforms (Dreyer et al., 2005) to validate that the algorithm-generated lengths are reasonable. Similarly, the horizontal spacing of seismically resolved clinoforms (figures 3, 12 in Dreyer et al., 2005) was used to generate a normal distribution of values for clinoform spacing, S (Figure 13B), and values were drawn at random from this distribution to populate the model volume (Figure 13B). The resulting values of clinoform length and spacing are consistent with those observed at the outcrop for other wave-dominated shorelines (e.g., Hampson, 2000; Sech et al., 2009) (Figure 13). A value of 2 was used for the exponent in the clinoform shape function (defined by BLTN13190eq124 in equation 8), as this gives a good match to the seismically resolved clinoforms; and, furthermore, it was assumed that a similar geometry is shared by clinoforms in all parasequences in all locations throughout the model volume, consistent with observations of seismically resolved clinoforms over similar-size volumes (Patruno et al., 2015). Although, BLTN13190eq125 has the same value as used in the Ferron Sandstone Member example, BLTN13190eq126 values in the Troll Field sector model are larger (Figure 13A, Table 4) such that clinoform dip angles are shallower, consistent with the seismically resolved clinoforms (Dreyer et al., 2005; Patruno et al., 2015). As a first step, the insertion point of the first clinoform (BLTN13190eq127) was arbitrarily selected in the center of the proximal model boundary, and consistent west-northwest progradation of clinoforms (Dreyer et al., 2005; Patruno et al., 2015) was used to define a BLTN13190eq128 of 320°. The facies-association boundary surfaces extracted from the model of Dilib et al. (2015) were then used to create zones of m sands and c sands within each clinothem. The application of the clinoform-modeling algorithm yields a model containing 100 clinoforms. A visual quality control check was then performed to ensure that the clinoforms produced by the algorithm are consistent with the geologic concepts of the model (e.g., clinoform spacing, dip, length) in the absence of postdepositional faults.

Table 4 shows the parameters used in the clinoform-modeling algorithm. To honor the nearly linear plan-view geometry of clinoforms observed in seismic data (figures 3, 12 in Dreyer et al., 2005), a width for the top-clinoform ellipse (BLTN13190eq120 that is far greater than the depositional-dip extent of the bounding surfaces in the model area (3200 m [10,499 ft]) was defined; the top-clinoform ellipse length BLTN13190eq121 is half of BLTN13190eq122, to give a plan-view aspect ratio of 2 (cf. wave-dominated shoreface systems in Howell et al., 2008a). Seismically resolved clinoform dip values of 1.5°–4° (Dreyer et al., 2005; Patruno et al., 2015) were used in conjunction with the estimated parasequence thickness to calculate clinoform length (BLTN13190eq123) using simple trigonometry. As there are only a small number of seismically resolved clinoforms in a few paleogeographic locations and within a few stratigraphic levels to extract clinoform length, a normal distribution based on the extracted data was generated (Figure 13A), and values were then drawn at random from this distribution to populate the model volume (Figure 13A). Finally, the premodeling lengths were compared with the seismically resolved clinoforms (Dreyer et al., 2005) to validate that the algorithm-generated lengths are reasonable. Similarly, the horizontal spacing of seismically resolved clinoforms (figures 3, 12 in Dreyer et al., 2005) was used to generate a normal distribution of values for clinoform spacing, S (Figure 13B), and values were drawn at random from this distribution to populate the model volume (Figure 13B). The resulting values of clinoform length and spacing are consistent with those observed at the outcrop for other wave-dominated shorelines (e.g., Hampson, 2000; Sech et al., 2009) (Figure 13). A value of 2 was used for the exponent in the clinoform shape function (defined by BLTN13190eq124 in equation 8), as this gives a good match to the seismically resolved clinoforms; and, furthermore, it was assumed that a similar geometry is shared by clinoforms in all parasequences in all locations throughout the model volume, consistent with observations of seismically resolved clinoforms over similar-size volumes (Patruno et al., 2015). Although, BLTN13190eq125 has the same value as used in the Ferron Sandstone Member example, BLTN13190eq126 values in the Troll Field sector model are larger (Figure 13A, Table 4) such that clinoform dip angles are shallower, consistent with the seismically resolved clinoforms (Dreyer et al., 2005; Patruno et al., 2015). As a first step, the insertion point of the first clinoform (BLTN13190eq127) was arbitrarily selected in the center of the proximal model boundary, and consistent west-northwest progradation of clinoforms (Dreyer et al., 2005; Patruno et al., 2015) was used to define a BLTN13190eq128 of 320°. The facies-association boundary surfaces extracted from the model of Dilib et al. (2015) were then used to create zones of m sands and c sands within each clinothem. The application of the clinoform-modeling algorithm yields a model containing 100 clinoforms. A visual quality control check was then performed to ensure that the clinoforms produced by the algorithm are consistent with the geologic concepts of the model (e.g., clinoform spacing, dip, length) in the absence of postdepositional faults.

[[File:BLTN13190fig13.jpg|thumb|300px|{{figure number|13}}Normal distributions, shown as black lines, for (A) clinoform length (Figure 4D) and (B) clinoform spacing (Figure 4D) generated from published seismic data from the Sognefjord Formation (figures 3, 12 in Dreyer et al., 2005). Gray bars represent the values for clinoform length and spacing drawn at random from the normal distribution and used to populate the Troll sector model.]]

[[File:BLTN13190fig13.jpg|thumb|300px|{{figure number|13}}Normal distributions, shown as black lines, for (A) clinoform length ([[:File:BLTN13190fig4.jpg|Figure 4D]]) and (B) clinoform spacing ([[:File:BLTN13190fig4.jpg|Figure 4D]]) generated from published seismic data from the Sognefjord Formation (figures 3, 12 in Dreyer et al., 2005). Gray bars represent the values for clinoform length and spacing drawn at random from the normal distribution and used to populate the Troll sector model.]]

After this validation, the clinoform-modeling algorithm was applied with the same parameters (Table 4) but using the faulted parasequence-bounding flooding surfaces and the faulted facies-association boundary surfaces. The resulting surface-based model contains clinoforms with geometries and distributions that reflect present-day reservoir structure, measures approximately 3200 × 750 × 150 m (10,499 × 2461 × 492 ft), and contains 215 surfaces: the 8 top and base parasequence bounding surfaces, 100 clinoform surfaces, and 107 facies-association-boundary surfaces between clinoform pairs. A hybrid gridding method is used, because previous work shows that this approach better captures the movement of gas and water in the vicinity of a horizontal production well located in a thin oil rim (Vinje et al., 2011). The areal grid resolution of the model is fixed (50 × 25 m [164 × 82 ft]), but the vertical resolution varies. In the gas cap and aquifer, the vertical layering is stratigraphic, conforming to the flooding surfaces that bound the parasequences and with a single grid layer representing each facies association zone. In an interval of the reservoir that contains the oil column, from 3 m (10 ft) above the gas–oil contact (GOC) to 3 m (10 ft) below the oil–water contact (OWC), the grid is horizontal and regular, with finer layering (0.25–2 m [0.82–7 ft]) parallel to the initial GOC and OWC (Dilib et al., 2015). Very fine grid resolution is required to capture the geometry of clinoforms in this regular, orthogonal part of the grid. For the model to be suitable for flow simulation, it is not possible to have this level of grid resolution everywhere in the model. Petrophysical properties were assigned by facies association in a similar manner to the model of the Ferron Sandstone Member reservoir analog. Clinoform-related heterogeneity was incorporated in flow-simulation models by using transmissibility multipliers along clinoform surfaces, where a trend was used to enforce greater continuity and extent of heterogeneity in the m sands that lie above the lower part of each clinoform. A different approach was used to model the clinoform-controlled heterogeneity than for the Ferron Sandstone Member model, because part of the grid is horizontal and regular. Transmissibility multipliers representing the heterogeneity along clinoforms are placed in the cells adjacent to the clinoform surface in the orthogonal part of grid around the oil rim. As the orthogonal grid is very fine, this approach honors the geometry of the clinoform surfaces.

After this validation, the clinoform-modeling algorithm was applied with the same parameters (Table 4) but using the faulted parasequence-bounding flooding surfaces and the faulted facies-association boundary surfaces. The resulting surface-based model contains clinoforms with geometries and distributions that reflect present-day reservoir structure, measures approximately 3200 × 750 × 150 m (10,499 × 2461 × 492 ft), and contains 215 surfaces: the 8 top and base parasequence bounding surfaces, 100 clinoform surfaces, and 107 facies-association-boundary surfaces between clinoform pairs. A hybrid gridding method is used, because previous work shows that this approach better captures the movement of gas and water in the vicinity of a horizontal production well located in a thin oil rim (Vinje et al., 2011). The areal grid resolution of the model is fixed (50 × 25 m [164 × 82 ft]), but the vertical resolution varies. In the gas cap and aquifer, the vertical layering is stratigraphic, conforming to the flooding surfaces that bound the parasequences and with a single grid layer representing each facies association zone. In an interval of the reservoir that contains the oil column, from 3 m (10 ft) above the gas–oil contact (GOC) to 3 m (10 ft) below the oil–water contact (OWC), the grid is horizontal and regular, with finer layering (0.25–2 m [0.82–7 ft]) parallel to the initial GOC and OWC (Dilib et al., 2015). Very fine grid resolution is required to capture the geometry of clinoforms in this regular, orthogonal part of the grid. For the model to be suitable for flow simulation, it is not possible to have this level of grid resolution everywhere in the model. Petrophysical properties were assigned by facies association in a similar manner to the model of the Ferron Sandstone Member reservoir analog. Clinoform-related heterogeneity was incorporated in flow-simulation models by using transmissibility multipliers along clinoform surfaces, where a trend was used to enforce greater continuity and extent of heterogeneity in the m sands that lie above the lower part of each clinoform. A different approach was used to model the clinoform-controlled heterogeneity than for the Ferron Sandstone Member model, because part of the grid is horizontal and regular. Transmissibility multipliers representing the heterogeneity along clinoforms are placed in the cells adjacent to the clinoform surface in the orthogonal part of grid around the oil rim. As the orthogonal grid is very fine, this approach honors the geometry of the clinoform surfaces.

===Geologic Model Results===

===Geologic Model Results===

The clinoforms incorporated into the Troll sector model show similar geometries and spacing to those that are seismically resolved in the Sognefjord Formation (Dreyer et al., 2005; Patruno et al., 2015). The clinoforms are linear in plan view over the small (750 m [2461 ft]) depositional-strike extent of the model (Figure 14B), consistent with the interpreted plan-view geometries of wave-dominated shoreface systems (Figure 3A) (Howell et al., 2008a), consistently prograde west-northwestward (BLTN13190eq140), as established through 3-D seismic data (Dreyer et al., 2005; Patruno et al., 2015), and have the concave-upward geometry observed in seismic dip sections through the Sognefjord Formation (Dreyer et al., 2005; Patruno et al., 2015) (Figures 14A, 15B). In depositional strike cross section, the algorithm produces near-horizontal clinoform geometries, consistent with seismically resolved clinoforms (Dreyer et al., 2005; Patruno et al., 2015) (Figure 15C). The stochastic component of the clinoform-modeling algorithm distributes clinoforms with cross-sectional geometries and spacings (Figures 14A, 15B) that are consistent with outcrop studies of wave-dominated deltas (Hampson, 2000; Sech et al., 2009) (Figure 13) and honor the sparse subsurface data. In contrast to the Ferron Sandstone Member example, the Troll West sector model does not contain subtle clinoform geometries, such as onlap and downlap of younger clinoforms on to older clinoforms (Figures 14A, 15B). Such features are below the resolution of the seismic data used to extract the parameters that were used in the algorithm. The clinoforms are also faulted in the same way as the parasequence-bounding flooding surfaces (cf. Figures 2A, 15C).

The clinoforms incorporated into the Troll sector model show similar geometries and spacing to those that are seismically resolved in the Sognefjord Formation (Dreyer et al., 2005; Patruno et al., 2015). The clinoforms are linear in plan view over the small (750 m [2461 ft]) depositional-strike extent of the model (Figure 14B), consistent with the interpreted plan-view geometries of wave-dominated shoreface systems ([[:File:BLTN13190fig3.jpg|Figure 3A]]) (Howell et al., 2008a), consistently prograde west-northwestward (BLTN13190eq140), as established through 3-D seismic data (Dreyer et al., 2005; Patruno et al., 2015), and have the concave-upward geometry observed in seismic dip sections through the Sognefjord Formation (Dreyer et al., 2005; Patruno et al., 2015) (Figures 14A, 15B). In depositional strike cross section, the algorithm produces near-horizontal clinoform geometries, consistent with seismically resolved clinoforms (Dreyer et al., 2005; Patruno et al., 2015) (Figure 15C). The stochastic component of the clinoform-modeling algorithm distributes clinoforms with cross-sectional geometries and spacings (Figures 14A, 15B) that are consistent with outcrop studies of wave-dominated deltas (Hampson, 2000; Sech et al., 2009) (Figure 13) and honor the sparse subsurface data. In contrast to the Ferron Sandstone Member example, the Troll West sector model does not contain subtle clinoform geometries, such as onlap and downlap of younger clinoforms on to older clinoforms (Figures 14A, 15B). Such features are below the resolution of the seismic data used to extract the parameters that were used in the algorithm. The clinoforms are also faulted in the same way as the parasequence-bounding flooding surfaces (cf. Figures 2A, 15C).

[[File:BLTN13190fig14.jpg|thumb|300px|{{figure number|14}}Surfaces generated by the clinoform-modeling algorithm for the Troll sector model. (A) Three-dimensional (3-D) dip cross section of clinoforms in the model demonstrating their concave-upward geometry. (B) 3-D view of clinoforms in the model showing close to linear clinoforms in plan view within fault-bounded compartment. Not all surfaces used in the Troll sector model (Figure 15) are shown.]]

[[File:BLTN13190fig14.jpg|thumb|300px|{{figure number|14}}Surfaces generated by the clinoform-modeling algorithm for the Troll sector model. (A) Three-dimensional (3-D) dip cross section of clinoforms in the model demonstrating their concave-upward geometry. (B) 3-D view of clinoforms in the model showing close to linear clinoforms in plan view within fault-bounded compartment. Not all surfaces used in the Troll sector model (Figure 15) are shown.]]