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Three-dimensional modeling of clinoforms in shallow-marine reservoirs (view source)

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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><ref name=EH2010>Enge, H. D., and J. A. Howell, 2010, [http://archives.datapages.com/data/bulletns/2010/02feb/BLTN08112/BLTN08112.HTM Impact of deltaic clinothems on reservoir performance: Dynamic studies of reservoir analogs from the Ferron Sandstone Member and Panther Tongue, Utah]: AAPG Bulletin, v. 94, no. 2, p. 139–161, doi: 10.1306/07060908112.</ref> 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 />

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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<ref>Livera, S. E., and B. Caline, 1990, The sedimentology of the Brent Group in the Cormorant Block IV oil field: Journal of Petroleum Geology, v. 13, no. 4, p. 367–396, doi: 10.1111/j.1747-5457.1990.tb00855.x.</ref><ref>Jennette, D. C., and C. O. Riley, 1996, Influence of relative sea level on facies and reservoir geometry of the Middle Jurassic Lower Brent Group, UK North Viking Graben, inJ. A. Howell, and J. F. Aitken, eds., High-resolution sequence stratigraphy: Innovations and applications: Geological Society, London, Special Publication 104, p. 87–113.</ref><ref>Løseth, T. M., and A. Ryseth, 2003, A depositional model and sequence stratigraphic model for the Rannoch and Etive formations, Oseberg field, northern North Sea: Norwegian Journal of Geology, v. 83, p. 87–106.</ref><ref>Matthews, S., A. D. Thurlow, F. J. Aitken, S. Gowland, P. D. Jones, G. J. Colville, C. I. Robinson, and A. M. Taylor, 2005, A late life opportunity: Using a multidisciplinary approach to unlock reserves in the Rannoch Formation, Ninian field, inA. G. Doré, and B. A. Vining, eds., Petroleum geology: Northwest Europe and global perspective: Proceedings of the 6th Conference of the Geological Society (London), p. 496–510.</ref><ref name=Hmpsn2008>Hampson, G. J., A. B. Rodriguez, J. E. A. Storms, H. D. Johnson, and C. T. Meyer, 2008, Geomorphology and high-resolution stratigraphy of progradational wave-dominated shoreline deposits: Impact on reservoir-scale facies architecture, inG. J. Hampson, R. J. Steel, P. M. Burgess, and R. W. Dalrymple, eds., Recent advances in models of siliclastic shallow-marine stratigraphy: SEPM Special Publication 90, p. 117–142.</ref> 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 /><ref name=EH2010 /> 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<ref name=EH2010 /> 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<ref name=EH2010 /> 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.

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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<ref>Livera, S. E., and B. Caline, 1990, The sedimentology of the Brent Group in the Cormorant Block IV oil field: Journal of Petroleum Geology, v. 13, no. 4, p. 367–396, doi: 10.1111/j.1747-5457.1990.tb00855.x.</ref><ref>Jennette, D. C., and C. O. Riley, 1996, Influence of relative sea level on facies and reservoir geometry of the Middle Jurassic Lower Brent Group, UK North Viking Graben, inJ. A. Howell, and J. F. Aitken, eds., High-resolution sequence stratigraphy: Innovations and applications: Geological Society, London, Special Publication 104, p. 87–113.</ref><ref>Løseth, T. M., and A. Ryseth, 2003, A depositional model and sequence stratigraphic model for the Rannoch and Etive formations, Oseberg field, northern North Sea: Norwegian Journal of Geology, v. 83, p. 87–106.</ref><ref>Matthews, S., A. D. Thurlow, F. J. Aitken, S. Gowland, P. D. Jones, G. J. Colville, C. I. Robinson, and A. M. Taylor, 2005, A late life opportunity: Using a multidisciplinary approach to unlock reserves in the Rannoch Formation, Ninian field, inA. G. Doré, and B. A. Vining, eds., Petroleum geology: Northwest Europe and global perspective: Proceedings of the 6th Conference of the Geological Society (London), p. 496–510.</ref><ref name=Hmpsn2008>Hampson, G. J., A. B. Rodriguez, J. E. A. Storms, H. D. Johnson, and C. T. Meyer, 2008, Geomorphology and high-resolution stratigraphy of progradational wave-dominated shoreline deposits: Impact on reservoir-scale facies architecture, inG. J. Hampson, R. J. Steel, P. M. Burgess, and R. W. Dalrymple, eds., Recent advances in models of siliclastic shallow-marine stratigraphy: SEPM Special Publication 90, p. 117–142.</ref> or have built two-dimensional (2-D)<ref name=WB96 /><ref name=Frstr2004>Forster, C. B., S. H. Snelgrove, and J. V. Koebbe, 2004, [http://archives.datapages.com/data/specpubs/study50/sg50ch14/sg50ch14.htm Modelling permeability structure and simulating fluid flow in a reservoir analog: Ferron Sandstone, Ivie Creek area, east-central Utah], in T. C. Chidsey, Jr., R. D. Adams, and T. H. Morris, eds., Regional to wellbore analog for fluvial-deltaic reservoir modeling: The Ferron Sandstone of Utah: [http://store.aapg.org/detail.aspx?id=655 AAPG Studies in Geology 50], p. 359–382.</ref> or three-dimensional (3-D)<ref name=Hwll2008a /><ref name=Hwll2008b /><ref name=Jckson2009 /><ref name=Sch09 /><ref name=EH2010 /> 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<ref name=EH2010 /> 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<ref name=EH2010 /> 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.

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BLTN13190fig5.jpg|{{figure number|5}}(A) Paleogeographic reconstruction of the Late Cretaceous Last Chance and Vernal delta systems of the Ferron Sandstone Member of the Mancos Shale in present-day Utah (after Cotter, 1976; used with permission of Brigham Young University). The location of the Deveugle et al.<ref name=Dvgl2011 /> model ([[:File:BLTN13190fig5.jpg|Figure 5D]]) and a regional cross section ([[:File:BLTN13190fig5.jpg|Figure 5B]]) are highlighted. (B) Schematic regional cross section through the Last Chance delta system of the Ferron Sandstone Member and its eight-component shallow-marine tongues (termed “pararasequence sets,” using the nomenclature of Deveugle et al.,<ref name=Dvgl2011 /> and numbered PSS1 to PSS8), from southwest (paleolandward) to northeast (paleoseaward) (after Anderson and Ryer, 2004; used with permission of AAPG). (C) Detailed cross section through the lowermost shallow-marine tongues (termed “parasequences,” using the nomenclature of Deveugle et al.,<ref name=Dvgl2011 /> and forming PSS1 in [[:File:BLTN13190fig5.jpg|Figure 5B]]) and associated coastal-plain strata (after Garrison and Van den Bergh, 2004; used with permission of AAPG). The tongue is subdivided into constituent parasequences (after Deveugle et al.<ref name=Dvgl2011 />). Parasequence 1.6 is modeled in this study. (D) Distribution of facies-association belts at the top of parasequence 1.6, in the Deveugle et al.<ref name=Dvgl2011 /> model area in the Ivie Creek amphitheater. The area of the model constructed in this study (Figures 7–10) lies within the dashed lines.

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BLTN13190fig6.jpg|{{figure number|6}}(A) Interpreted line drawing of clinoforms in parasequence 1.6 at the Junction Point section of Ivie Creek amphitheater ([[:File:BLTN13190fig5.jpg|Figure 5D]]) (modified after Forster et al.~~, 2004~~). Each clinoform bounds a mouth bar and equivalent delta-front deposits. Data from 104 clinoforms were collected to condition the clinoform-modeling algorithm. Frequency distributions of values measured from outcrop data for (B) clinoform length ([[:File:BLTN13190fig4.jpg|Figure 4D]]), and (C) clinoform spacing ([[:File:BLTN13190fig4.jpg|Figure 4D]]), which are used as input parameters in the clinoform-modeling algorithm (Table 2).

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BLTN13190fig6.jpg|{{figure number|6}}(A) Interpreted line drawing of clinoforms in parasequence 1.6 at the Junction Point section of Ivie Creek amphitheater ([[:File:BLTN13190fig5.jpg|Figure 5D]]) (modified after Forster et al.<ref name=Frstr2004 />). Each clinoform bounds a mouth bar and equivalent delta-front deposits. Data from 104 clinoforms were collected to condition the clinoform-modeling algorithm. Frequency distributions of values measured from outcrop data for (B) clinoform length ([[:File:BLTN13190fig4.jpg|Figure 4D]]), and (C) clinoform spacing ([[:File:BLTN13190fig4.jpg|Figure 4D]]), which are used as input parameters in the clinoform-modeling algorithm (Table 2).

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===Geological Setting===

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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<ref name=EH2010 />). 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.

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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<ref name=EH2010 />). 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. <ref name=Frstr2004 /> 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.

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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;~~ <ref name=EH2010 /> ([[: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.

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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; <ref name=Frstr2004 /><ref name=EH2010 /> ([[: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. <ref name=Frstr2004 />), 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.

===Model Construction===

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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.

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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 (''tD'', ''ts'') 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.<ref name=EH2010 /> 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, ''Po'' ([[: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 (''tD'', ''ts'') 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. <ref name=Frstr2004 /> ([[: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.<ref name=EH2010 /> 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, ''Po'' ([[: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; <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.

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# Evensen, J. E., M. Skaug, and P. Goodyear, 1993, Production geological challenges of characterizing the thin oil rims in the Troll Field: OTC Paper 7172, Proceedings from the Offshore Technology Conference, Houston, Texas, USA, May 3–6, 1993, 12 p.

# Farrell, M. E., and V. Abreu, 2006, Reservoir connectivity in fluvial-deltaic depositional environments: South Timbalier 26 field study (abs.): AAPG International Conference and Exhibition, Perth, Australia, November 5–8, 2006, accessed January 14, 2013, http://www.searchanddiscovery.com/-abstracts/pdf/2006/intl_perth/abstracts/ndx_farrell.pdf.

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# Forster, C. B., S. H. Snelgrove, and J. V. Koebbe, 2004, Modelling permeability structure and simulating fluid flow in a reservoir analog: Ferron Sandstone, Ivie Creek area, east-central Utah, inT. C. Chidsey, Jr., R. D. Adams, and T. H. Morris, eds., Regional to wellbore analog for fluvial-deltaic reservoir modeling: The Ferron Sandstone of Utah: AAPG Studies in Geology 50, p. 359–382.

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#

# Fraser, S. I., A. M. Robinson, H. D. Johnson, J. R. Underhill, D. G. A. Kadolsky, R. Connell, P. Johanessen, and R. Ravnås, 2003, Upper Jurassic, inD. Evans, C. Graham, A. Armour, and P. Bathurst, eds., The millennium atlas: Petroleum geology of the central and northern North Sea: London, The Geological Society, p. 158–189.

# Galloway, W. E., 1975, Process framework for describing the morphological and stratigraphic evolution of deltaic depositional systems, inM. L. Broussard, ed., Deltas, models for exploration: Houston, Texas, Houston Geological Society, p. 87–98.

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