Changes

[[File:BLTN13190fig1.jpg|thumb|400px|{{figure number|1}}(A) Outcrop view of delta-front clinoforms in the Ferron Sandstone Member at the Ivie Creek amphitheater, north of I-70, east-central Utah (corresponding to parasequences 1.5 and 1.6 of Deveugle et al.<ref name=Dvgl2011>Deveugle, P. E. K., M. D. Jackson, G. J. Hampson, M. E. Farrell, A. R. Sprague, J. Stewart, and C. S. Calvert, 2011, [http://archives.datapages.com/data/bulletns/2011/05may/BLTN10025/BLTN10025.HTM Characterization of stratigraphic architecture and its impact on fluid flow in a fluvial-dominated deltaic reservoir analog: Upper Cretaceous Ferron Sandstone Member, Utah]: AAPG Bulletin, v. 95, no. 5, p. 693–727, doi: 10.1306/09271010025.</ref>). Note the dipping nature of the delta-front sandstones and shales and the erosional contact with an overlying distributary channel sandstone. (B) Corresponding outcrop interpretation showing clinoforms within the delta-front deposits. (C) Corresponding line drawing highlighting approximately 25 clinoforms, shown as black lines on a white background. CP = coastal plain heteroliths; DC = distributary channel sandstone; PD = prodelta shales. Photographs and line drawings have no vertical exaggeration.]]

[[File:BLTN13190fig1.jpg|thumb|400px|{{figure number|1}}(A) Outcrop view of delta-front clinoforms in the Ferron Sandstone Member at the Ivie Creek amphitheater, north of I-70, east-central Utah (corresponding to parasequences 1.5 and 1.6 of Deveugle et al.<ref name=Dvgl2011>Deveugle, P. E. K., M. D. Jackson, G. J. Hampson, M. E. Farrell, A. R. Sprague, J. Stewart, and C. S. Calvert, 2011, [http://archives.datapages.com/data/bulletns/2011/05may/BLTN10025/BLTN10025.HTM Characterization of stratigraphic architecture and its impact on fluid flow in a fluvial-dominated deltaic reservoir analog: Upper Cretaceous Ferron Sandstone Member, Utah]: AAPG Bulletin, v. 95, no. 5, p. 693–727, doi: 10.1306/09271010025.</ref>). Note the dipping nature of the delta-front sandstones and shales and the erosional contact with an overlying distributary channel sandstone. (B) Corresponding outcrop interpretation showing clinoforms within the delta-front deposits. (C) Corresponding line drawing highlighting approximately 25 clinoforms, shown as black lines on a white background. CP = coastal plain heteroliths; DC = distributary channel sandstone; PD = prodelta shales. Photographs and line drawings have no vertical exaggeration.]]

Key factors influencing fluid flow and reservoir behavior include facies architecture and heterogeneity distribution conditioned to stratal surfaces. Within shallow-marine reservoirs, clinoforms are one such type of stratal surface. Clinoforms are dipping surfaces having geometry that preserves the depositional morphology of the delta-front or shoreface slope; and their distribution reflects the progradation history of the shoreline (Barrell, 1912; Rich, 1951; Gani and Bhattacharya, 2005; Sech et al., 2009) ([[:File:BLTN13190fig1.jpg|Figure 1]]). Clinoforms control aspects of detailed facies architecture within parasequences and can also act as low-permeability barriers or baffles to flow (Wehr and Brasher, 1996; Ainsworth et al., 1999; Dutton et al., 2000; Howell et al., 2008a, b; Jackson et al., 2009; Enge and Howell, 2010). Therefore, it is important to include clinoforms in models of shallow-marine reservoirs to properly characterize facies architecture and volumes of hydrocarbons in place (Sech et al., 2009). Under certain displacement conditions and if the clinoforms are associated with significant barriers to flow, clinoforms must be included in dynamic simulations to accurately predict likely drainage patterns and ultimate recovery of hydrocarbons (Jackson et al., 2009).

Key factors influencing fluid flow and reservoir behavior include facies architecture and heterogeneity distribution conditioned to stratal surfaces. Within shallow-marine reservoirs, clinoforms are one such type of stratal surface. Clinoforms are dipping surfaces having geometry that preserves the depositional morphology of the delta-front or shoreface slope; and their distribution reflects the progradation history of the shoreline<ref>Barrell, J., 1912, Criteria for the recognition of ancient delta deposits: Geological Society of America Bulletin, v. 23, no. 1, p. 377–446, doi: 10.1130/GSAB-23-377.</ref><ref>Rich, J. L., 1951, Three critical environments of deposition, and criteria for recognition of rocks deposited in each of them: Geological Society of America Bulletin, v. 62, no. 1, p. 1–20, doi: 10.1130/0016-7606(1951)62[1:TCEODA]2.0.CO;2.</ref><ref name=GB05>Gani, M. R., and J. P. Bhattacharya, 2005, Lithostratigraphy versus chronostratigraphy in facies correlations of Quaternary deltas: Application of bedding correlation, inL. Giosan, and J. P. Bhattacharya, eds., River deltas—Concepts, models and examples: SEPM Special Publication 83, p. 31–47.</ref><ref name=Sch09>Sech, R. P., M. D. Jackson, and G. J. Hampson, 2009, [http://archives.datapages.com/data/bulletns/2009/09sep/BLTN08144/BLTN08144.HTM Three-dimensional modeling of a shoreface-shelf parasequence reservoir analog: Part 1. Surface-based modeling to capture high resolution facies architecture]: AAPG Bulletin, v. 93, no. 9, p. 1155–1181, doi: 10.1306/05110908144.</ref> ([[:File:BLTN13190fig1.jpg|Figure 1]]). Clinoforms control aspects of detailed facies architecture within parasequences and can also act as low-permeability barriers or baffles to flow.<ref name=WB96>Wehr, F. L., and L. D. Brasher, 1996, Impact of sequence-based correlation style on reservoir model behaviour, lower Brent Group, North Cormorant field, UK North Sea, inJ. A. Howell, and J. A. Aitken, eds., High resolution sequence stratigraphy: Innovations and applications: Geological Society, London, Special Publication 104, p. 115–128.</ref><ref name=Answrth1999>Ainsworth, B. R., M. Sanlung, and S. T. C. Duivenvoorden, 1999, [http://archives.datapages.com/data/bulletns/1999/10oct/1535/1535.htm Correlation techniques, perforation strategies, and recovery factors: An integrated 3-D reservoir modeling study, Sirikit field, Thailand]: AAPG Bulletin, v. 83, p. 1535–1551.</ref><ref>Dutton, S. P., B. J. Willis, C. D. White, and J. P. Bhattacharya, 2000, Outcrop characterization of reservoir quality and interwell-scale cement distribution in a tide-influenced delta, Frontier Formation, Wyoming USA: Clay Minerals, v. 35, no. 1, p. 95–105, doi: 10.1180/000985500546756.</ref><ref name=Hwll2008a>Howell, J. A., A. Skorstad, A. MacDonald, A. Fordham, S. Flint, B. Fjellvoll, and T. Manzocchi, 2008a, Sedimentological parameterization of shallow-marine reservoirs: Petroleum Geoscience, v. 14, no. 1, p. 17–34, doi: 10.1144/1354-079307-787.</ref><ref name=Hwll2008b>Howell, J. A., Å. Vassel, and T. Aune, 2008b, Modelling of dipping clinoform barriers within deltaic outcrop analogues from the Cretaceous Western Interior Basin, U.S.A., inA. Robinson, P. Griffiths, S. Price, J. Hegre, and A. H. Muggeridge, eds., The future of geologic modelling in hydrocarbon development: Geological Society, London, Special Publication 309, p. 99–121.</ref><ref name=Jckson2009>Jackson, M. D., G. J. Hampson, and R. P. Sech, 2009, [http://archives.datapages.com/data/bulletns/2009/09sep/BLTN08145/BLTN08145.HTM Three-dimensional modeling of a shoreface-shelf parasequence reservoir analog: Part 2. Geological controls on fluid flow and hydrocarbon production]: AAPG Bulletin, v. 93, no. 9, p. 1183–1208, doi: 10.1306/05110908145.</ref> Enge and Howell, 2010) Therefore, it is important to include clinoforms in models of shallow-marine reservoirs to properly characterize facies architecture and volumes of hydrocarbons in place.<ref name=Sch09 /> Under certain displacement conditions and if the clinoforms are associated with significant barriers to flow, clinoforms must be included in dynamic simulations to accurately predict likely drainage patterns and ultimate recovery of hydrocarbons.<ref name=Jckson2009 />

Standard modeling techniques are not well suited to capturing clinoforms, particularly if they are numerous, below seismic resolution, and/or difficult to correlate between wells. Few studies have attempted to identify and correlate clinoforms in the subsurface (Livera and Caline, 1990; Jennette and Riley, 1996; Løseth and Ryseth, 2003; Matthews et al., 2005; Hampson et al., 2008) or have built two-dimensional (2-D) (Wehr and Brasher, 1996; Forster et al., 2004) or three-dimensional (3-D) (Howell et al., 2008a, b; Jackson et al., 2009; Sech et al., 2009; Enge and Howell, 2010) flow simulation models that incorporate clinoforms. Previous studies of the Ferron Sandstone Member have incorporated simple clinoform geometries into reservoir models by using either object-based (Howell et al., 2008b) or deterministic (Howell et al., 2008a) approaches. Enge and Howell (2010) used data collected by light detection and ranging (LIDAR) equipment to precisely recreate 3-D clinoform geometries from part of the Ferron Sandstone Member outcrops; the resulting flow-simulation model contained deterministically modeled clinoforms but in a volume smaller than most reservoirs (500 × 500 × 25 m [1640 × 1640 × 82 ft]). Sech et al. (2009) used a surface-based modeling approach to produce a deterministic, 3-D model of a wave-dominated shoreface–shelf parasequence from a rich, high-resolution outcrop data set (Cretaceous Kenilworth Member, Utah), and Jackson et al. (2009) used this model to investigate the impact of clinoforms on fluid flow. Jackson et al. (2009) and Enge and Howell (2010) both showed that capturing numerous clinoforms in fluid-flow simulations is feasible. Process-based forward numerical models are capable of generating geologically realistic, 3-D stratigraphic architectures containing clinoforms in shallow-marine strata (e.g., Edmonds and Slingerland, 2010; Geleynse et al., 2011), but it can be difficult to replicate geometries observed in outcrop data, or condition models to subsurface data (e.g., Charvin et al., 2009); consequently, process-based approaches have yet to be developed for routine use in reservoir modeling.

Standard modeling techniques are not well suited to capturing clinoforms, particularly if they are numerous, below seismic resolution, and/or difficult to correlate between wells. Few studies have attempted to identify and correlate clinoforms in the subsurface (Livera and Caline, 1990; Jennette and Riley, 1996; Løseth and Ryseth, 2003; Matthews et al., 2005; Hampson et al., 2008) or have built two-dimensional (2-D)<ref name=WB96 /> Forster et al., 2004) or three-dimensional (3-D)<ref name=Hwll2008a /><ref name=Hwll2008b /><ref name=Jckson2009 /><ref name=Sch09 /> Enge and Howell, 2010) flow simulation models that incorporate clinoforms. Previous studies of the Ferron Sandstone Member have incorporated simple clinoform geometries into reservoir models by using either object-based<ref name=Hwll2008b /> or deterministic<ref name=Hwll2008a /> approaches. Enge and Howell (2010) used data collected by light detection and ranging (LIDAR) equipment to precisely recreate 3-D clinoform geometries from part of the Ferron Sandstone Member outcrops; the resulting flow-simulation model contained deterministically modeled clinoforms but in a volume smaller than most reservoirs (500 × 500 × 25 m [1640 × 1640 × 82 ft]). Sech et al.<ref name=Sch09 /> used a surface-based modeling approach to produce a deterministic, 3-D model of a wave-dominated shoreface–shelf parasequence from a rich, high-resolution outcrop data set (Cretaceous Kenilworth Member, Utah), and Jackson et al.<ref name=Jckson2009 /> used this model to investigate the impact of clinoforms on fluid flow. Jackson et al.<ref name=Jckson2009 /> and Enge and Howell (2010) both showed that capturing numerous clinoforms in fluid-flow simulations is feasible. Process-based forward numerical models are capable of generating geologically realistic, 3-D stratigraphic architectures containing clinoforms in shallow-marine strata (e.g., Edmonds and Slingerland, 2010; Geleynse et al., 2011), but it can be difficult to replicate geometries observed in outcrop data, or condition models to subsurface data (e.g., Charvin et al., 2009); consequently, process-based approaches have yet to be developed for routine use in reservoir modeling.

Deterministic approaches are appropriate for modeling clinoforms that are tightly constrained by outcrop data, but they are time consuming to implement. Moreover, they do not allow flexibility in conditioning clinoform geometry and distribution to sparser data sets with a larger degree of uncertainty, such as those that are typically available for subsurface reservoirs. Incorporating hundreds of deterministic clinoform surfaces within a field-scale reservoir model would be a dauntingly time-consuming task, particularly if multiple scenarios and realizations that capture uncertainty in clinoform geometry and distribution are to be modeled. A stochastic, 3-D, surface-based modeling approach is required to address these issues. Similar approaches have been demonstrated for other depositional environments (e.g., Xie et al., 2001; Pyrcz et al., 2005; Zhang et al., 2009) and to create models of generic, dipping barriers to flow (e.g., Jackson and Muggeridge, 2000), but at present, there are no tools available to automate the generation of multiple 3-D clinoforms using a small number of parameters. The aims of this paper are to develop an efficient, quick, and practical method for incorporating clinoforms into models of shallow-marine reservoirs and to validate its application through building both geologic and fluid-flow simulation models.

Deterministic approaches are appropriate for modeling clinoforms that are tightly constrained by outcrop data, but they are time consuming to implement. Moreover, they do not allow flexibility in conditioning clinoform geometry and distribution to sparser data sets with a larger degree of uncertainty, such as those that are typically available for subsurface reservoirs. Incorporating hundreds of deterministic clinoform surfaces within a field-scale reservoir model would be a dauntingly time-consuming task, particularly if multiple scenarios and realizations that capture uncertainty in clinoform geometry and distribution are to be modeled. A stochastic, 3-D, surface-based modeling approach is required to address these issues. Similar approaches have been demonstrated for other depositional environments (e.g., Xie et al., 2001; Pyrcz et al., 2005; Zhang et al., 2009) and to create models of generic, dipping barriers to flow (e.g., Jackson and Muggeridge, 2000), but at present, there are no tools available to automate the generation of multiple 3-D clinoforms using a small number of parameters. The aims of this paper are to develop an efficient, quick, and practical method for incorporating clinoforms into models of shallow-marine reservoirs and to validate its application through building both geologic and fluid-flow simulation models.

[[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, ''h(r_c)'' (equation 1; see Table 1 for nomenclature). (E) Shape function, ''s(r_c)'' (equation 7; Table 1), demonstrating that increasing the exponent, ''P'', increases the dip angle of clinoforms.]]

[[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, ''h(r_c)'' (equation 1; see Table 1 for nomenclature). (E) Shape function, ''s(r_c)'' (equation 7; Table 1), demonstrating that increasing the exponent, ''P'', increases the dip angle of clinoforms.]]

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<ref name=GB07>Gani, M. R., and J. P. Bhattacharya, 2007, Basic building blocks and process variability of a Cretaceous delta: Internal facies architecture reveals a more dynamic interaction of river, wave, and tidal processes than is indicated by external shape: Journal of Sedimentary Research, v. 77, no. 4, p. 284–302, doi: 10.2110/jsr.2007.023.</ref>) 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;<ref name=GB07 /> 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.,;<ref name=Answrth1999 /> Hampson et al., 2008).

The clinoform-modeling algorithm developed here is simple to use, requiring specification of only a few input parameters: (1) the upper and lower surfaces that define the rock volume within which the clinoforms are to be modeled; (2) the plan-view geometry of clinoforms; (3) clinoform geometry in depositional-dip-oriented cross section; and (4) spacing and progradation direction of the clinoforms. The user can also use a stochastic component of the clinoform-modeling algorithm if there are uncertainties in the parameter values to be used.

The clinoform-modeling algorithm developed here is simple to use, requiring specification of only a few input parameters: (1) the upper and lower surfaces that define the rock volume within which the clinoforms are to be modeled; (2) the plan-view geometry of clinoforms; (3) clinoform geometry in depositional-dip-oriented cross section; and (4) spacing and progradation direction of the clinoforms. The user can also use a stochastic component of the clinoform-modeling algorithm if there are uncertainties in the parameter values to be used.

</gallery>

</gallery>

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).

The depositional processes acting at the shoreline control the plan-view shape and abundance of clinoforms and their associated heterogeneity.<ref name=Hwll2008a /> 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.<ref name=Hwll2008a /> 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 ([[: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 (t_s, t_D, b_s, b_D; [[: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 L ([[:File:BLTN13190fig4.jpg|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 (t_s, t_D, b_s, b_D; [[: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 L ([[:File:BLTN13190fig4.jpg|Figure 4D]]). The maximum extent of the top and base ellipses can then be defined as  

:<math>r_{\text{max}}(x, y) = \frac{(b_s b_D)}{\sqrt{\frac{(b_s^2(x_{\text{origin}} - x)^2) + (b_D^2(y_{\text{origin}} - y)^2)}{(x_{\text{origin}} - x)^2 + (y_{\text{origin}} - y)^2}}}</math>

:<math>r_{\text{max}}(x, y) = \frac{(b_s b_D)}{\sqrt{\frac{(b_s^2(x_{\text{origin}} - x)^2) + (b_D^2(y_{\text{origin}} - y)^2)}{(x_{\text{origin}} - x)^2 + (y_{\text{origin}} - y)^2}}}</math>

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, ''t_D'', than for the clinoform in the strike direction, ''t_S.'' 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, ''t_S'', than for the clinoform in the dip direction, ''t_D''. 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, ''t_D'', than for the clinoform in the strike direction, ''t_S.'' 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, ''t_S'', than for the clinoform in the dip direction, ''t_D''. 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.<ref name=Hwll2008a />).

{| class=wikitable

{| class=wikitable

===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°)<ref name=GB05 /> (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; <ref name=GB05 />). 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, ''s(r_c)'' ([[:File:BLTN13190fig2.jpg|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, ''s(r_c)'' ([[:File:BLTN13190fig2.jpg|Figure 2E]]), such as a power law for concave-upward, sandy, shoreline clinoforms:  

Each of the input parameters described for the clinoform-modeling algorithm can be applied deterministically; however, many can also be applied stochastically (Table 1). If a reservoir model is created using an outcrop data set, it may be appropriate for the user to specify the parameter values for each clinoform. If a subsurface reservoir model is being created in which the parameter values are uncertain, the user can constrain a continuous probability distribution, such as a normal distribution, to assign values to each parameter. The user specifies the mean, standard deviation, and maximum and minimum values for the distribution. Values are then drawn at random from the distribution to assign values to the parameters.

Each of the input parameters described for the clinoform-modeling algorithm can be applied deterministically; however, many can also be applied stochastically (Table 1). If a reservoir model is created using an outcrop data set, it may be appropriate for the user to specify the parameter values for each clinoform. If a subsurface reservoir model is being created in which the parameter values are uncertain, the user can constrain a continuous probability distribution, such as a normal distribution, to assign values to each parameter. The user specifies the mean, standard deviation, and maximum and minimum values for the distribution. Values are then drawn at random from the distribution to assign values to the parameters.

Because many of the input parameters can be defined stochastically, one of the consequences of this aspect of the clinoform-modeling algorithm is that it is possible to generate complex geometries, such as cases in which clinoforms are observed to onlap against older clinoforms in the same parasequence. A combination of three factors is postulated to cause subtle changes in clinoform geometry and position, which combine to produce onlap in depositional-dip-oriented cross sections: (1) in fluvial-dominated deltas, distributary mouth bars and bar complexes have complex 3-D geometries that can shift along depositional strike as well as down depositional dip (e.g., Olariu et al., 2005; Wellner et al., 2005); (2) riverine sediment supply to delta-front clinoforms exhibits temporal and spatial variability that is related, at least in part, to downstream branching and switching of distributary channels as deltas advance (e.g., Wellner et al., 2005; Ahmed et al., 2014); and (3) clinoform geometries are locally modified by basinal processes such as waves and tides (e.g., Gani and Bhattacharya, 2007).

Because many of the input parameters can be defined stochastically, one of the consequences of this aspect of the clinoform-modeling algorithm is that it is possible to generate complex geometries, such as cases in which clinoforms are observed to onlap against older clinoforms in the same parasequence. A combination of three factors is postulated to cause subtle changes in clinoform geometry and position, which combine to produce onlap in depositional-dip-oriented cross sections: (1) in fluvial-dominated deltas, distributary mouth bars and bar complexes have complex 3-D geometries that can shift along depositional strike as well as down depositional dip (e.g., Olariu et al., 2005; Wellner et al., 2005); (2) riverine sediment supply to delta-front clinoforms exhibits temporal and spatial variability that is related, at least in part, to downstream branching and switching of distributary channels as deltas advance (e.g., Wellner et al., 2005; Ahmed et al., 2014); and (3) clinoform geometries are locally modified by basinal processes such as waves and tides (e.g., Gani and Bhattacharya<ref name=GB07 />).

To produce onlap and other subtle geometric features between successive clinoforms, the user can use the stochastic component of the clinoform-modeling algorithm to generate small variations in the parameter values of either or all of the following: progradation direction, ''θ''; clinoform spacing, ''S''; and clinoform length, ''L''. If the parameters that define a clinoform cause it to be present below an earlier surface, it is truncated by the earlier surface to produce onlap. Application of the algorithm to (1) a rich, outcrop data set and (2) a sparse, subsurface data set is described in the examples in the following two sections.

To produce onlap and other subtle geometric features between successive clinoforms, the user can use the stochastic component of the clinoform-modeling algorithm to generate small variations in the parameter values of either or all of the following: progradation direction, ''θ''; clinoform spacing, ''S''; and clinoform length, ''L''. If the parameters that define a clinoform cause it to be present below an earlier surface, it is truncated by the earlier surface to produce onlap. Application of the algorithm to (1) a rich, outcrop data set and (2) a sparse, subsurface data set is described in the examples in the following two sections.

===Geological Setting===

===Geological Setting===

Construction and fluid-flow simulation of models based on outcrop analogs is an established method for investigating geologic controls on subsurface reservoir performance (e.g., Ciammetti et al., 1995; White and Barton, 1999; White et al., 2004; Jackson et al., 2009; Sech et al., 2009; Enge and Howell, 2010). Here, the clinoform-modeling algorithm is used to build a reservoir model utilizing a high-resolution outcrop data set from the Ferron Sandstone Member, Utah, at a scale that is comparable to the interwell spacing (750 × 3000 m [2461 × 9843 ft] areally) in a typical hydrocarbon reservoir and captures several tens of clinoforms and their associated heterogeneities. Previously, Forster et al. (2004) constructed 2-D flow-simulation models of the same outcrop analog via data-intensive, deterministic mapping of clinoforms and facies boundaries in cliff-face exposures. In contrast, our aim is to verify that the clinoform-modeling algorithm can produce realistic 3-D stratigraphic architectures that mimic rich outcrop data sets when conditioned to sparse input data that are typical in the subsurface. The scale of the model fills the gap between detailed but sparse 2-D core and well-log data and low-resolution but extensive 3-D seismic data.

Construction and fluid-flow simulation of models based on outcrop analogs is an established method for investigating geologic controls on subsurface reservoir performance (e.g., Ciammetti et al., 1995; White and Barton, 1999; White et al., 2004; Jackson et al.;<ref name=Jckson2009 /> Sech et al.;<ref name=Sch09 /> Enge and Howell, 2010). Here, the clinoform-modeling algorithm is used to build a reservoir model utilizing a high-resolution outcrop data set from the Ferron Sandstone Member, Utah, at a scale that is comparable to the interwell spacing (750 × 3000 m [2461 × 9843 ft] areally) in a typical hydrocarbon reservoir and captures several tens of clinoforms and their associated heterogeneities. Previously, Forster et al. (2004) constructed 2-D flow-simulation models of the same outcrop analog via data-intensive, deterministic mapping of clinoforms and facies boundaries in cliff-face exposures. In contrast, our aim is to verify that the clinoform-modeling algorithm can produce realistic 3-D stratigraphic architectures that mimic rich outcrop data sets when conditioned to sparse input data that are typical in the subsurface. The scale of the model fills the gap between detailed but sparse 2-D core and well-log data and low-resolution but extensive 3-D seismic data.

The Ferron Sandstone Member of the Mancos Shale is located in east-central Utah. The unit was deposited during the Late Cretaceous (Turonian–Coniacian) on the western margin of the Western Interior Seaway and, in the study area, records the progradation of the Last Chance delta system from southwest (paleolandward) to northeast (paleoseaward) (Cotter, 1976) ([[:File:BLTN13190fig5.jpg|Figure 5A]]). These deltaic deposits form a basinward-thinning wedge that passes eastward into the offshore deposits of the Mancos Shale. The wedge contains either seven (Ryer, 1991; Gardner, 1993; Barton et al., 2004) or eight sandstone tongues (Anderson and Ryer, 2004; Garrison and Van den Bergh, 2004), such that one tongue is equivalent to a parasequence set of Deveugle et al.<ref name=Dvgl2011 /> ([[:File:BLTN13190fig5.jpg|Figure 5B]]). A single delta-lobe deposit within the lowermost sandstone tongue is the focus of the study (bedset Kf-1-Iv[a] of Anderson et al., 2004; parasequence 1h of Garrison and Van den Bergh, 2004; parasequence 1.6 of Deveugle et al.<ref name=Dvgl2011 />) ([[:File:BLTN13190fig5.jpg|Figure 5C, D]]). The delta-lobe deposit is fluvial dominated with low-to-moderate wave influence (Gardner, 1993; Garrison and Van den Bergh, 2004; Ryer and Anderson, 2004) and contains numerous, well-documented clinoforms in the exposures of the Ivie Creek amphitheater (Anderson et al., 2002, 2003, 2004; Forster et al., 2004; Enge and Howell, 2010) ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Clinoform-related bedding geometries and facies distributions imply that clinoforms mapped by previous workers, and used as input data for the models presented below ([[:File:BLTN13190fig6.jpg|Figure 6A]], after Forster et al., 2004), bound clinothems equivalent to mouth bars (sensu Bhattacharya, 2006). Subtle, apparently cyclic variations in clinoform spacing and dip angle probably define mouth-bar assemblages (sensu Bhattacharya, 2006; “bedsets” sensu Enge et al., 2010). Smaller-scale lithologic variation at the scale of individual beds occurs between the mapped clinoforms and records incremental growth of a mouth bar because of varying water and sediment discharge through the feeder distributary channel. Deveugle et al.<ref name=Dvgl2011 /> used a high-resolution outcrop data set to build a reservoir-scale (7200 × 3800 × 50 m [23622 × 12467 × 164 ft]), surface-based model of the lower two tongues (parasequence sets) of the Ferron Sandstone Member. Clinoforms were not represented in the delta-lobe deposits (cf. parasequences) of the Deveugle et al.<ref name=Dvgl2011 /> model, and their surface-based model is used here as the context in which the clinoform-modeling algorithm should be applied.

The Ferron Sandstone Member of the Mancos Shale is located in east-central Utah. The unit was deposited during the Late Cretaceous (Turonian–Coniacian) on the western margin of the Western Interior Seaway and, in the study area, records the progradation of the Last Chance delta system from southwest (paleolandward) to northeast (paleoseaward) (Cotter, 1976) ([[:File:BLTN13190fig5.jpg|Figure 5A]]). These deltaic deposits form a basinward-thinning wedge that passes eastward into the offshore deposits of the Mancos Shale. The wedge contains either seven (Ryer, 1991; Gardner, 1993; Barton et al., 2004) or eight sandstone tongues (Anderson and Ryer, 2004; Garrison and Van den Bergh, 2004), such that one tongue is equivalent to a parasequence set of Deveugle et al.<ref name=Dvgl2011 /> ([[:File:BLTN13190fig5.jpg|Figure 5B]]). A single delta-lobe deposit within the lowermost sandstone tongue is the focus of the study (bedset Kf-1-Iv[a] of Anderson et al., 2004; parasequence 1h of Garrison and Van den Bergh, 2004; parasequence 1.6 of Deveugle et al.<ref name=Dvgl2011 />) ([[:File:BLTN13190fig5.jpg|Figure 5C, D]]). The delta-lobe deposit is fluvial dominated with low-to-moderate wave influence (Gardner, 1993; Garrison and Van den Bergh, 2004; Ryer and Anderson, 2004) and contains numerous, well-documented clinoforms in the exposures of the Ivie Creek amphitheater (Anderson et al., 2002, 2003, 2004; Forster et al., 2004; Enge and Howell, 2010) ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Clinoform-related bedding geometries and facies distributions imply that clinoforms mapped by previous workers, and used as input data for the models presented below ([[:File:BLTN13190fig6.jpg|Figure 6A]], after Forster et al., 2004), bound clinothems equivalent to mouth bars (sensu Bhattacharya, 2006). Subtle, apparently cyclic variations in clinoform spacing and dip angle probably define mouth-bar assemblages (sensu Bhattacharya, 2006; “bedsets” sensu Enge et al., 2010). Smaller-scale lithologic variation at the scale of individual beds occurs between the mapped clinoforms and records incremental growth of a mouth bar because of varying water and sediment discharge through the feeder distributary channel. Deveugle et al.<ref name=Dvgl2011 /> used a high-resolution outcrop data set to build a reservoir-scale (7200 × 3800 × 50 m [23622 × 12467 × 164 ft]), surface-based model of the lower two tongues (parasequence sets) of the Ferron Sandstone Member. Clinoforms were not represented in the delta-lobe deposits (cf. parasequences) of the Deveugle et al.<ref name=Dvgl2011 /> model, and their surface-based model is used here as the context in which the clinoform-modeling algorithm should be applied.

</gallery>

</gallery>

The top and base flooding surfaces of parasequence 1.6 were extracted from the model of Deveugle et al.<ref name=Dvgl2011 /> 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 ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Additional surfaces representing the boundaries between facies associations from the model of Deveugle et al.<ref name=Dvgl2011 /> 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.<ref name=Dvgl2011 />). 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) ([[:File:BLTN13190fig5.jpg|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.<ref name=Dvgl2011 /> have been modified.

The top and base flooding surfaces of parasequence 1.6 were extracted from the model of Deveugle et al.<ref name=Dvgl2011 /> 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 ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Additional surfaces representing the boundaries between facies associations from the model of Deveugle et al.<ref name=Dvgl2011 /> 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.<ref name=Dvgl2011 />). 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) ([[:File:BLTN13190fig5.jpg|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.<ref name=Jckson2009 /> 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.<ref name=Dvgl2011 /> 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,<ref name=Dvgl2011 /> 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 (''t_D'', ''t_s'') 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, ''L'', and spacing, ''S'', of clinoforms in depositional dip cross section were extracted from the bedding-diagram interpretations of Forster et al. (2004) ([[:File:BLTN13190fig6.jpg|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 ([[:File:BLTN13190fig6.jpg|Figure 6B, C]]). The clinoform-modeling algorithm was used to build 31 clinoforms in the modeled volume of parasequence 1.6 ([[:File:BLTN13190fig7.jpg|Figure 7]]). For simplicity, clinoform spacing is fixed at 25 m (82 ft), which is the average value observed at outcrop ([[:File:BLTN13190fig6.jpg|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; <ref name=Dvgl2011 /> 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, ''P_o'' ([[:File:BLTN13190fig4.jpg|Figure 4C]]), was qualitatively matched with a plan-view map of facies association belts at the top of parasequence 1.6 ([[:File:BLTN13190fig5.jpg|Figure 5D]]). The overall progradation direction for the clinoforms (''θ'') was assigned an azimuth of 274° relative to north, which corresponds to the interpreted progradation direction of the delta lobe in parasequence 1.6.<ref name=Dvgl2011 /> In a subsequent step, the facies association boundary surfaces extracted from the model of Deveugle et al.<ref name=Dvgl2011 /> 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 ([[:File:BLTN13190fig8.jpg|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,<ref name=Dvgl2011 /> 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 (''t_D'', ''t_s'') 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, ''L'', and spacing, ''S'', of clinoforms in depositional dip cross section were extracted from the bedding-diagram interpretations of Forster et al. (2004) ([[:File:BLTN13190fig6.jpg|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 ([[:File:BLTN13190fig6.jpg|Figure 6B, C]]). The clinoform-modeling algorithm was used to build 31 clinoforms in the modeled volume of parasequence 1.6 ([[:File:BLTN13190fig7.jpg|Figure 7]]). For simplicity, clinoform spacing is fixed at 25 m (82 ft), which is the average value observed at outcrop ([[:File:BLTN13190fig6.jpg|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.<ref name=Jckson2009 /><ref name=Dvgl2011 /> 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, ''P_o'' ([[:File:BLTN13190fig4.jpg|Figure 4C]]), was qualitatively matched with a plan-view map of facies association belts at the top of parasequence 1.6 ([[:File:BLTN13190fig5.jpg|Figure 5D]]). The overall progradation direction for the clinoforms (''θ'') was assigned an azimuth of 274° relative to north, which corresponds to the interpreted progradation direction of the delta lobe in parasequence 1.6.<ref name=Dvgl2011 /> In a subsequent step, the facies association boundary surfaces extracted from the model of Deveugle et al.<ref name=Dvgl2011 /> 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 ([[:File:BLTN13190fig8.jpg|Figure 8]]).

A cornerpoint gridding scheme in which variations in facies architecture are represented by variations in grid architecture was used (White and Barton, 1999; Jackson et al., 2005; Sech et al., 2009). The grid has vertical pillars with a constant spacing of 20 m (66 ft) in x and y (horizontal) directions. Grid layering in the z (vertical) direction within each facies-association zone conforms to the underlying clinoform surface, so layers are parallel to, and build up from, the underlying clinoform. Grid layers have a constant thickness of 0.2 m (0.66 ft); however, each facies-association zone is gridded separately, and the grid layers pinch out against facies-association boundaries and parasequence-bounding flooding surfaces. This gridding approach was used by Sech et al. (2009); it ensures that the grid layering conforms to the architecture of the clinoform surfaces, preserving their dip and geometry, and captures facies association boundaries ([[:File:BLTN13190fig9.jpg|Figure 9]]). Where a grid layer pinches out, the grid cells have zero thickness and are set to be inactive in flow simulations. These zero-thickness cells are bridged using nonneighbor connections so that they do not act as barriers to flow. The chosen cell size of 20 × 20 × 0.2 m (66 × 66 × 0.66 ft) yields a total of approximately 5 million cells, of which 140,000 (2.6%) are active. Because the number of active grid cells is small, fluid-flow simulations can be performed on the grid without upscaling.

A cornerpoint gridding scheme in which variations in facies architecture are represented by variations in grid architecture was used (White and Barton, 1999; Jackson et al., 2005; <ref name=Sch09 />). The grid has vertical pillars with a constant spacing of 20 m (66 ft) in x and y (horizontal) directions. Grid layering in the z (vertical) direction within each facies-association zone conforms to the underlying clinoform surface, so layers are parallel to, and build up from, the underlying clinoform. Grid layers have a constant thickness of 0.2 m (0.66 ft); however, each facies-association zone is gridded separately, and the grid layers pinch out against facies-association boundaries and parasequence-bounding flooding surfaces. This gridding approach was used by Sech et al.;<ref name=Sch09 /> it ensures that the grid layering conforms to the architecture of the clinoform surfaces, preserving their dip and geometry, and captures facies association boundaries ([[:File:BLTN13190fig9.jpg|Figure 9]]). Where a grid layer pinches out, the grid cells have zero thickness and are set to be inactive in flow simulations. These zero-thickness cells are bridged using nonneighbor connections so that they do not act as barriers to flow. The chosen cell size of 20 × 20 × 0.2 m (66 × 66 × 0.66 ft) yields a total of approximately 5 million cells, of which 140,000 (2.6%) are active. Because the number of active grid cells is small, fluid-flow simulations can be performed on the grid without upscaling.

In the final step before fluid-flow simulation, the grid cells were populated with petrophysical properties from a mature subsurface reservoir analog (table 1 of Deveugle et al.<ref name=Dvgl2011 />). Petrophysical properties were assigned to each facies association, which typically have permeabilities that differ by approximately one order of magnitude from their overlying or underlying neighbor. In a separate step, transmissibility multipliers are assigned along the base of the grid cells in the layer directly above each clinoform surface to represent baffles and barriers to fluid flow along clinoforms in a geometrically accurate and efficient way. The transmissibility multipliers were assigned using a stochastic technique that decreases the probability of barriers being present along the upper part of the clinoform. This aspect of modeling is discussed in greater detail in a companion article (Graham et al., 2015, this volume).

In the final step before fluid-flow simulation, the grid cells were populated with petrophysical properties from a mature subsurface reservoir analog (table 1 of Deveugle et al.<ref name=Dvgl2011 />). Petrophysical properties were assigned to each facies association, which typically have permeabilities that differ by approximately one order of magnitude from their overlying or underlying neighbor. In a separate step, transmissibility multipliers are assigned along the base of the grid cells in the layer directly above each clinoform surface to represent baffles and barriers to fluid flow along clinoforms in a geometrically accurate and efficient way. The transmissibility multipliers were assigned using a stochastic technique that decreases the probability of barriers being present along the upper part of the clinoform. This aspect of modeling is discussed in greater detail in a companion article (Graham et al., 2015, this volume).

[[File:BLTN13190fig11.jpg|thumb|400px|{{figure number|11}}(A) Recovery factor and water cut as function of time in the simulation model of part of parasequence 1.6 of the Ferron Sandstone Member. Note the significant decrease in recovery factor for the model with 90% barrier coverage along clinoforms. (B) Oil and water production rate as a function of time. In the models with 90% barrier coverage along clinoforms, the target production rate was not met and water breakthrough occurred earlier than in models where barriers were not present along clinoforms.]]

[[File:BLTN13190fig11.jpg|thumb|400px|{{figure number|11}}(A) Recovery factor and water cut as function of time in the simulation model of part of parasequence 1.6 of the Ferron Sandstone Member. Note the significant decrease in recovery factor for the model with 90% barrier coverage along clinoforms. (B) Oil and water production rate as a function of time. In the models with 90% barrier coverage along clinoforms, the target production rate was not met and water breakthrough occurred earlier than in models where barriers were not present along clinoforms.]]

When clinoforms are not associated with barriers to flow, they have little impact on production ([[:File:BLTN13190fig10.jpg|Figure 10C]]); however, if barriers occupy 90% of the clinoform surfaces, then their impact on recovery is significant. Models that omit barriers to flow along clinoforms can overestimate recovery by up to 36% (cf. [[:File:BLTN13190fig10.jpg|Figures 10C, D]]; [[:File:BLTN13190fig11.jpg|11A]]), consistent with previous simulation studies of the Ferron Sandstone Member that found barrier-lined clinoforms reduced hydrocarbon recovery by several tens of percent (Howell et al., 2008b; Enge and Howell 2010). Reduced recovery is caused by decreased sweep efficiency as each clinothem becomes hydraulically separated from its neighbors. Consequently, significant oil is bypassed in the reservoir, particularly beneath barriers along clinoforms and at the toe of each clinothem ([[:File:BLTN13190fig10.jpg|Figure 10D]]). Increased reservoir compartmentalization also means that the target oil production rate cannot be met; and, as a result, models that include barriers along clinoforms produce significantly lower volumes of oil per day ([[:File:BLTN13190fig11.jpg|Figure 11B]]). Enge and Howell (2010) also found that including barriers along clinoforms in reservoir models of the Ferron Sandstone Member increased reservoir compartmentalization.

When clinoforms are not associated with barriers to flow, they have little impact on production ([[:File:BLTN13190fig10.jpg|Figure 10C]]); however, if barriers occupy 90% of the clinoform surfaces, then their impact on recovery is significant. Models that omit barriers to flow along clinoforms can overestimate recovery by up to 36% (cf. [[:File:BLTN13190fig10.jpg|Figures 10C, D]]; [[:File:BLTN13190fig11.jpg|11A]]), consistent with previous simulation studies of the Ferron Sandstone Member that found barrier-lined clinoforms reduced hydrocarbon recovery by several tens of percent.<ref name=Hwll2008b />; Enge and Howell 2010). Reduced recovery is caused by decreased sweep efficiency as each clinothem becomes hydraulically separated from its neighbors. Consequently, significant oil is bypassed in the reservoir, particularly beneath barriers along clinoforms and at the toe of each clinothem ([[:File:BLTN13190fig10.jpg|Figure 10D]]). Increased reservoir compartmentalization also means that the target oil production rate cannot be met; and, as a result, models that include barriers along clinoforms produce significantly lower volumes of oil per day ([[:File:BLTN13190fig11.jpg|Figure 11B]]). Enge and Howell (2010) also found that including barriers along clinoforms in reservoir models of the Ferron Sandstone Member increased reservoir compartmentalization.

Finally, models that include barriers along clinoforms have earlier water breakthrough than models that lack barriers along clinoforms ([[:File:BLTN13190fig11.jpg|Figure 11]]). Including barrier-lined clinoforms increases the tortuosity of flow pathways because the fluids can only move between clinothems by exploiting the gap in the barriers at the top of each clinoform. However, as the number of potential flow pathways is decreased by including barriers to flow along clinoforms, the injected water exploits the pathways between the injectors and producers faster, which leads to earlier water breakthrough. Similar results were obtained in clinoform-bearing models of a wave-dominated shoreface system (Jackson et al., 2009).

Finally, models that include barriers along clinoforms have earlier water breakthrough than models that lack barriers along clinoforms ([[:File:BLTN13190fig11.jpg|Figure 11]]). Including barrier-lined clinoforms increases the tortuosity of flow pathways because the fluids can only move between clinothems by exploiting the gap in the barriers at the top of each clinoform. However, as the number of potential flow pathways is decreased by including barriers to flow along clinoforms, the injected water exploits the pathways between the injectors and producers faster, which leads to earlier water breakthrough. Similar results were obtained in clinoform-bearing models of a wave-dominated shoreface system .<ref name=Jckson2009 />

Although barriers to flow along clinoforms are thin (<20 cm [<8 in.]) and constitute only a small proportion of the overall model volume, they significantly affect permeability architecture, sweep pattern and simulated oil recovery. Therefore, under certain displacement conditions, it is important to include barriers associated with clinoforms in simulation models of analogous shallow-marine reservoirs. The clinoform-modeling algorithm supports the results of previous studies of the Ferron Sandstone Member and demonstrates an efficient new method to incorporate multiple, geometrically realistic clinoforms into simulation models.

Although barriers to flow along clinoforms are thin (<20 cm [<8 in.]) and constitute only a small proportion of the overall model volume, they significantly affect permeability architecture, sweep pattern and simulated oil recovery. Therefore, under certain displacement conditions, it is important to include barriers associated with clinoforms in simulation models of analogous shallow-marine reservoirs. The clinoform-modeling algorithm supports the results of previous studies of the Ferron Sandstone Member and demonstrates an efficient new method to incorporate multiple, geometrically realistic clinoforms into simulation models.

[[File:BLTN13190fig13.jpg|thumb|400px|{{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.]]

[[File:BLTN13190fig13.jpg|thumb|400px|{{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.]]

The stratigraphic framework of the reservoir model is defined by flooding surfaces that bound seven parasequences. The bounding surfaces are offset by two postdepositional faults that are oriented northwest–southeast across the model volume. The faulted parasequence-bounding flooding surfaces were extracted from the existing reservoir model (Dilib et al., 2015). The faulted parasequence boundaries were used to construct the final Troll West sector model but, as a quality control step for applying the clinoform-modeling algorithm, these boundaries were adjusted so that they were horizontal. Each parasequence also contains a surface that represents the facies-association boundary between m sands below and c sands above; these surfaces were extracted from the model of Dilib et al. (2015) and are laterally continuous across the clinoforms modeled here, because they were extracted from a model that omits clinoforms. Consequently, facies interfingering across clinoforms is not captured here, and this may further increase the impact of modeling clinoforms on flow (Jackson et al., 2009). The facies-association boundary surfaces were adjusted to remove the effects of faulting in the same way as the flooding surfaces. Additionally, where facies associations pinch out, the facies association boundary surfaces are adjusted to coincide throughout the remainder of the model volume with the top parasequence bounding surface. This procedure created flooding surfaces and facies-association boundaries in the model that mimic their depositional geometries, which were used as a reference framework to validate that the clinoform geometries and distributions applied later using the faulted parasequence-bounding surfaces are consistent with geologic concepts.

The stratigraphic framework of the reservoir model is defined by flooding surfaces that bound seven parasequences. The bounding surfaces are offset by two postdepositional faults that are oriented northwest–southeast across the model volume. The faulted parasequence-bounding flooding surfaces were extracted from the existing reservoir model (Dilib et al., 2015). The faulted parasequence boundaries were used to construct the final Troll West sector model but, as a quality control step for applying the clinoform-modeling algorithm, these boundaries were adjusted so that they were horizontal. Each parasequence also contains a surface that represents the facies-association boundary between m sands below and c sands above; these surfaces were extracted from the model of Dilib et al. (2015) and are laterally continuous across the clinoforms modeled here, because they were extracted from a model that omits clinoforms. Consequently, facies interfingering across clinoforms is not captured here, and this may further increase the impact of modeling clinoforms on flow.<ref name=Jckson2009 /> The facies-association boundary surfaces were adjusted to remove the effects of faulting in the same way as the flooding surfaces. Additionally, where facies associations pinch out, the facies association boundary surfaces are adjusted to coincide throughout the remainder of the model volume with the top parasequence bounding surface. This procedure created flooding surfaces and facies-association boundaries in the model that mimic their depositional geometries, which were used as a reference framework to validate that the clinoform geometries and distributions applied later using the faulted parasequence-bounding surfaces are consistent with geologic concepts.

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 (''t_s'') 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 ''t_D'' is half of ''t_s'', 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 (''L'') 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 ([[:File:BLTN13190fig13.jpg|Figure 13A]]), and values were then drawn at random from this distribution to populate the model volume ([[:File:BLTN13190fig13.jpg|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 ([[:File:BLTN13190fig13.jpg|Figure 13B]]), and values were drawn at random from this distribution to populate the model volume ([[:File:BLTN13190fig13.jpg|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) ([[:File:BLTN13190fig13.jpg|Figure 13]]). A value of 2 was used for the exponent in the clinoform shape function (defined by ''P'' 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, ''P'' has the same value as used in the Ferron Sandstone Member example, ''L'' values in the Troll Field sector model are larger ([[:File:BLTN13190fig13.jpg|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 (''P_o'') 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 ''θ'' 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 (''t_s'') 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 ''t_D'' is half of ''t_s'', to give a plan-view aspect ratio of 2 (cf. wave-dominated shoreface systems in Howell et al.<ref name=Hwll2008a />). 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 (''L'') 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 ([[:File:BLTN13190fig13.jpg|Figure 13A]]), and values were then drawn at random from this distribution to populate the model volume ([[:File:BLTN13190fig13.jpg|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 ([[:File:BLTN13190fig13.jpg|Figure 13B]]), and values were drawn at random from this distribution to populate the model volume ([[:File:BLTN13190fig13.jpg|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.<ref name=Sch09 />) ([[:File:BLTN13190fig13.jpg|Figure 13]]). A value of 2 was used for the exponent in the clinoform shape function (defined by ''P'' 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, ''P'' has the same value as used in the Ferron Sandstone Member example, ''L'' values in the Troll Field sector model are larger ([[:File:BLTN13190fig13.jpg|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 (''P_o'') 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 ''θ'' 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.

{| class = wikitable

{| class = wikitable

</gallery>

</gallery>

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 ([[:File:BLTN13190fig14.jpg|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 (θ = 320°), 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) ([[:File:BLTN13190fig15.jpg|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) ([[:File:BLTN13190fig13.jpg|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 ([[:File:BLTN13190fig14.jpg|Figures 14A]], [[:File:BLTN13190fig15.jpg|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. [[:File:BLTN13190fig2.jpg|Figures 2A]], [[:File:BLTN13190fig15.jpg|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 ([[:File:BLTN13190fig14.jpg|Figure 14B]]), consistent with the interpreted plan-view geometries of wave-dominated shoreface systems ([[:File:BLTN13190fig3.jpg|Figure 3A]]),<ref name=Hwll2008a /> consistently prograde west-northwestward (θ = 320°), 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) ([[:File:BLTN13190fig15.jpg|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; <ref name=Sch09 />) ([[:File:BLTN13190fig13.jpg|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 ([[:File:BLTN13190fig14.jpg|Figures 14A]], [[:File:BLTN13190fig15.jpg|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. [[:File:BLTN13190fig2.jpg|Figures 2A]], [[:File:BLTN13190fig15.jpg|15C]]).

===Production Strategy===

===Production Strategy===

[[File:BLTN13190fig17.jpg|thumb|400px|{{figure number|17}}(A) Oil, (B) water, (C) gas production rates, and (D) cumulative oil production as a function of time in the simulation model of the Sognefjord Formation in a fault-bounded sector of the Troll Field ([[:File:BLTN13190fig12.jpg|Figure 12B]]) for production from a single horizontal well through gas cap expansion and aquifer influx ([[:File:BLTN13190fig16.jpg|Figure 16]]). In the models with 90% barrier coverage along clinoforms, free gas breakthrough is delayed ([[:File:BLTN13190fig17.jpg|Figure 17C]]) and liquid production is decreased ([[:File:BLTN13190fig17.jpg|Figure 17A, B, D]]) relative to the models lacking barriers along clinoforms.]]

[[File:BLTN13190fig17.jpg|thumb|400px|{{figure number|17}}(A) Oil, (B) water, (C) gas production rates, and (D) cumulative oil production as a function of time in the simulation model of the Sognefjord Formation in a fault-bounded sector of the Troll Field ([[:File:BLTN13190fig12.jpg|Figure 12B]]) for production from a single horizontal well through gas cap expansion and aquifer influx ([[:File:BLTN13190fig16.jpg|Figure 16]]). In the models with 90% barrier coverage along clinoforms, free gas breakthrough is delayed ([[:File:BLTN13190fig17.jpg|Figure 17C]]) and liquid production is decreased ([[:File:BLTN13190fig17.jpg|Figure 17A, B, D]]) relative to the models lacking barriers along clinoforms.]]

The presence of barriers along 90% of the area of each clinoform surface significantly alters the movement of fluids in the reservoir by increasing the tortuosity of flow pathways. As a result, gas breakthrough is later when calcite-cemented barriers are present along clinoforms (30 vs. 15 days, [[:File:BLTN13190fig17.jpg|Figure 17C]]), and oil production remains at plateau for longer (30 vs. 15 days, [[:File:BLTN13190fig17.jpg|Figure 17A]]). However, after gas breakthrough, the rate of oil production rapidly falls below that for the case lacking calcite-cemented barriers ([[:File:BLTN13190fig17.jpg|Figure 17A]]). Water cut is significantly lower for the model containing calcite-cemented barriers throughout production ([[:File:BLTN13190fig17.jpg|Figure 17B]]). The calcite-cemented barriers along clinoforms prevent lateral movement of oil and the upward movement of water from the aquifer to the well ([[:File:BLTN13190fig16.jpg|Figure 16D]]) but have a less significant effect on the downward movement of more mobile gas. As a result, the gas:oil ratio increases for production in the model containing calcite-cemented barriers along clinoforms. Most importantly, the recovery of oil could be overestimated by up to 14% if calcite cements associated with clinoforms were omitted from the reservoir model ([[:File:BLTN13190fig17.jpg|Figure 17D]]; cf. [[:File:BLTN13190fig16.jpg|Figure 16C, D]]); this is consistent with the results of Jackson et al. (2009), which showed that omitting clinoforms from wave-dominated shoreface systems could lead to overprediction of hydrocarbon recovery.

The presence of barriers along 90% of the area of each clinoform surface significantly alters the movement of fluids in the reservoir by increasing the tortuosity of flow pathways. As a result, gas breakthrough is later when calcite-cemented barriers are present along clinoforms (30 vs. 15 days, [[:File:BLTN13190fig17.jpg|Figure 17C]]), and oil production remains at plateau for longer (30 vs. 15 days, [[:File:BLTN13190fig17.jpg|Figure 17A]]). However, after gas breakthrough, the rate of oil production rapidly falls below that for the case lacking calcite-cemented barriers ([[:File:BLTN13190fig17.jpg|Figure 17A]]). Water cut is significantly lower for the model containing calcite-cemented barriers throughout production ([[:File:BLTN13190fig17.jpg|Figure 17B]]). The calcite-cemented barriers along clinoforms prevent lateral movement of oil and the upward movement of water from the aquifer to the well ([[:File:BLTN13190fig16.jpg|Figure 16D]]) but have a less significant effect on the downward movement of more mobile gas. As a result, the gas:oil ratio increases for production in the model containing calcite-cemented barriers along clinoforms. Most importantly, the recovery of oil could be overestimated by up to 14% if calcite cements associated with clinoforms were omitted from the reservoir model ([[:File:BLTN13190fig17.jpg|Figure 17D]]; cf. [[:File:BLTN13190fig16.jpg|Figure 16C, D]]); this is consistent with the results of Jackson et al.,<ref name=Jckson2009 /> which showed that omitting clinoforms from wave-dominated shoreface systems could lead to overprediction of hydrocarbon recovery.

==Discussion==

==Discussion==

We have described the conceptual and mathematical basis of a modeling algorithm to generate surface-based reservoir models that include clinoforms, and demonstrated its application using (1) a deterministic approach in which a rich, high-resolution data set is available (Ferron Sandstone Member outcrop analog) and (2) a stochastic element where the data are sparse (Sognefjord Formation, Troll Field sector).

We have described the conceptual and mathematical basis of a modeling algorithm to generate surface-based reservoir models that include clinoforms, and demonstrated its application using (1) a deterministic approach in which a rich, high-resolution data set is available (Ferron Sandstone Member outcrop analog) and (2) a stochastic element where the data are sparse (Sognefjord Formation, Troll Field sector).

Several previous studies of the Ferron Sandstone Member have incorporated clinoforms in flow simulation models using a combination of object-based methods to place barriers along clinoforms (Howell et al., 2008b) or deterministic methods to map clinoforms (Howell et al., 2008a; Enge and Howell, 2010). Although these studies have demonstrated that, under certain displacement conditions, it is important to include clinoforms in models of shallow-marine reservoirs, it is not clear how these models could be applied in the subsurface or at the full-field scale. Other studies have indicated that surfaces should be used to incorporate clinoforms into reservoir models, as surfaces are much less computationally expensive to generate and manipulate than large 3-D geocellular grids (Jackson et al., 2009; Sech et al., 2009; Enge and Howell, 2010; Jackson et al., 2014). These deterministic approaches are appropriate for modeling clinoforms that are tightly constrained by outcrop data but do not allow flexibility in conditioning clinoform geometry and distribution to sparser data sets with a large degree of uncertainty.

Several previous studies of the Ferron Sandstone Member have incorporated clinoforms in flow simulation models using a combination of object-based methods to place barriers along clinoforms<ref name=Hwll2008b /> or deterministic methods to map clinoforms.<ref name=Hwll2008a /> Enge and Howell, 2010). Although these studies have demonstrated that, under certain displacement conditions, it is important to include clinoforms in models of shallow-marine reservoirs, it is not clear how these models could be applied in the subsurface or at the full-field scale. Other studies have indicated that surfaces should be used to incorporate clinoforms into reservoir models, as surfaces are much less computationally expensive to generate and manipulate than large 3-D geocellular grids.<ref name=Jckson2009 /><ref name=Sch09 /> Enge and Howell, 2010; Jackson et al., 2014). These deterministic approaches are appropriate for modeling clinoforms that are tightly constrained by outcrop data but do not allow flexibility in conditioning clinoform geometry and distribution to sparser data sets with a large degree of uncertainty.

Our results support previous work in demonstrating that it is important to include clinoforms in models of shallow-marine reservoirs to accurately predict fluid-flow patterns and hydrocarbon recovery. However, the work presented here differs from previous modeling investigations in providing a generic method of incorporating clinoforms with geologically realistic geometries and spacing into models of shallow-marine reservoirs. The algorithm can be also be applied at a variety of lengthscales, as demonstrated in Graham et al. (2015, this volume), in which a reservoir scale model that comprises multiple stacked parasequences is used to investigate the impact of clinoforms under geologic uncertainty and reservoir engineering decisions.

Our results support previous work in demonstrating that it is important to include clinoforms in models of shallow-marine reservoirs to accurately predict fluid-flow patterns and hydrocarbon recovery. However, the work presented here differs from previous modeling investigations in providing a generic method of incorporating clinoforms with geologically realistic geometries and spacing into models of shallow-marine reservoirs. The algorithm can be also be applied at a variety of lengthscales, as demonstrated in Graham et al. (2015, this volume), in which a reservoir scale model that comprises multiple stacked parasequences is used to investigate the impact of clinoforms under geologic uncertainty and reservoir engineering decisions.

{{reflist}}

{{reflist}}

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# Ahmed, S., J. P. Bhattacharya, D. Garza, and L. Giosan, 2014, Facies architecture and stratigraphic evolution of a river-dominated delta front, Turonian Ferron Sandstone, Utah, USA: Journal of Sedimentary Research, v. 84, no. 2, p. 97–121, doi: 10.2110/jsr.2014.6.

# Ainsworth, B. R., M. Sanlung, and S. T. C. Duivenvoorden, 1999, Correlation techniques, perforation strategies, and recovery factors: An integrated 3-D reservoir modeling study, Sirikit field, Thailand: AAPG Bulletin, v. 83, p. 1535–1551.

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