Changes

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.<ref name=Wllnr2005 />); (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.;<ref name=Wllnr2005 /> Ahmed et al.<ref name=Ahmd2014 />); and (3) clinoform geometries are locally modified by basinal processes such as waves and tides (e.g., Gani and Bhattacharya<ref name=GB07 />).

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.;<ref>Olariu, C., J. P. Bhattacharya, X. Xu, C. L. Aiken, X. Zeng, and G. A. McMechan, 2005, Integrated study of ancient delta-front deposits, using outcrop ground-penetrating radar, and three-dimensional photorealistic data: Cretaceous Panther Tongue Sandstone, Utah, U.S.A., inL. Giosan, and J. P. Bhattacharya, eds., River deltas—Concepts, models and examples: Tulsa, Oklahoma, SEPM Special Publication 83, p. 155–177.</ref> Wellner et al.<ref name=Wllnr2005 />); (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.;<ref name=Wllnr2005 /> Ahmed et al.<ref name=Ahmd2014 />); 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.

==Example 1: Ferron sandstone reservoir analog==

==Example 1: Ferron sandstone reservoir analog==

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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;<ref name=AndrsnRyr2004>Anderson, P. B., and T. A. Ryer, 2004, [http://archives.datapages.com/data/specpubs/study50/sg50ch08/sg50ch08.htm Regional stratigraphy of the Ferron Sandstone], 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. 211–224.</ref> 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;<ref name=GvdB2004>Garrison, J. R., and T. C. V. Van den Bergh, 2004, [http://archives.datapages.com/data/specpubs/study50/sg50ch06/sg50ch06.htm High resolution depositional sequence stratigraphy of the Upper Ferron Sandstone Last Chance Delta: An application of coal-zone stratigraphy], in T. C. Chidsey, Jr., R. D. Adams, and T. H. Morris, eds., Regional to wellbore analog for fluvial-deltaic reservoir modelling: The Ferron Sandstone of Utah: [http://store.aapg.org/detail.aspx?id=655 AAPG Studies in Geology 50], p. 125–192.</ref> 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 ([[:File:BLTN13190fig7.jpg|Figures 7]], [[:File:BLTN13190fig8.jpg|8]], [[:File:BLTN13190fig9.jpg|9]] & [[:File:BLTN13190fig10.jpg|10]]) lies within the dashed lines.

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;<ref name=cttr>Cotter, E., 1976, The role of deltas in the evolution of the Ferron Sandstone and its coals: Brigham Young University Studies in Geology, v. 22, p. 15–41.</ref> 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;<ref name=AndrsnRyr2004>Anderson, P. B., and T. A. Ryer, 2004, [http://archives.datapages.com/data/specpubs/study50/sg50ch08/sg50ch08.htm Regional stratigraphy of the Ferron Sandstone], 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. 211–224.</ref> 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;<ref name=GvdB2004>Garrison, J. R., and T. C. V. Van den Bergh, 2004, [http://archives.datapages.com/data/specpubs/study50/sg50ch06/sg50ch06.htm High resolution depositional sequence stratigraphy of the Upper Ferron Sandstone Last Chance Delta: An application of coal-zone stratigraphy], in T. C. Chidsey, Jr., R. D. Adams, and T. H. Morris, eds., Regional to wellbore analog for fluvial-deltaic reservoir modelling: The Ferron Sandstone of Utah: [http://store.aapg.org/detail.aspx?id=655 AAPG Studies in Geology 50], p. 125–192.</ref> 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 ([[:File:BLTN13190fig7.jpg|Figures 7]], [[:File:BLTN13190fig8.jpg|8]], [[:File:BLTN13190fig9.jpg|9]] & [[:File:BLTN13190fig10.jpg|10]]) lies within the dashed lines.

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).

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).

</gallery>

</gallery>

===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.;<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.

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.;<ref>Ciammetti, G., P. S. Ringrose, T. R. Good, J. M. L. Lewis, and K. S. Sorbie, 1995, Waterflood recovery and fluid flow upscaling in a shallow marine and fluvial sandstone sequence: SPE Paper 30783, 14 p.</ref> White and Barton;<ref name=WB1999>White, C. D., and M. D. Barton, 1999, Translating outcrop data to flow models, with applications to the Ferron Sandstone: SPE Reservoir Evaluation and Engineering, v. 2, no. 4, p. 341–350, doi: 10.2118/57482-PA.</ref> White et al.;<ref>White, C. D., B. J. Willis, S. P. Dutton, J. P. Bhattacharya, and K. Narayanan, 2004, [http://archives.datapages.com/data/specpubs/memoir80/CHAPTER7/CHAPTER7.HTM Sedimentology, statistics, and flow behaviour for a tide-influenced deltaic sandstone, Frontier Formation, Wyoming, United States], in G. M. Grammer, P. M. Harris, and G. P. Eberli, eds., Integration of outcrop and modern analogs in reservoir modeling: [http://store.aapg.org/detail.aspx?id=658 AAPG Memoir 80], p. 129–152.</ref> 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.

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,<ref name=AndrsnRyr2004 /><ref name=GvdB2004 /> 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;<ref name=GvdB2004 /> 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; <ref name=GvdB2004 /> 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<ref name=Bhttchry2006 />). Subtle, apparently cyclic variations in clinoform spacing and dip angle probably define mouth-bar assemblages (sensu Bhattacharya;<ref name=Bhttchry2006 /> “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)<ref name=cttr /> ([[: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<ref>Ryer, T. A., 1991, Stratigraphy, facies and depositional history of the Ferron Sandstone in the Canyon of Muddy Creek, east-central Utah, inT. C. Chidsey, Jr., ed., Geology of east-central Utah: Utah Geological Association Publication 19, p. 45–54.</ref><ref name=Grdnr>Gardner, M. H., 1993, Sequence stratigraphy and facies architecture of the Upper Cretaceous Ferron Sandstone Member of the Mancos Shale, east-central Utah: Ph.D. dissertation, Colorado School of Mines, Golden, Colorado, 528 p.</ref><ref>Barton, M. D., E. S. Angle, and N. Tyler, 2004, [http://archives.datapages.com/data/specpubs/study50/sg50ch07/sg50ch07.htm Stratigraphic architecture of fluvial-deltaic sandstones from the Ferron Sandstone outcrop, 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. 193–210.</ref> or eight sandstone tongues,<ref name=AndrsnRyr2004 /><ref name=GvdB2004 /> 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;<ref name=GvdB2004 /> 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<ref name=Grdnr /><ref name=GvdB2004 /> 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<ref name=Bhttchry2006 />). Subtle, apparently cyclic variations in clinoform spacing and dip angle probably define mouth-bar assemblages (sensu Bhattacharya;<ref name=Bhttchry2006 /> “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===

===Model Construction===

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.;<ref name=Kll /> Roberts et al.<ref name=Rbrts2004 />) and the modern Wax Lake Delta lobe (after data in Wellner et al.<ref name=Wllnr2005 />) ([[: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.<ref name=Wllnr2005 />). 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<ref name=Bhttchry2006 />), 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 /><ref name=Grhm2015 /> 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.;<ref name=Kll /> Roberts et al.<ref name=Rbrts2004 />) and the modern Wax Lake Delta lobe (after data in Wellner et al.<ref name=Wllnr2005 />) ([[: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.<ref name=Wllnr2005 />). 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<ref name=Bhttchry2006 />), 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 /><ref name=Grhm2015 /> 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; <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.

A cornerpoint gridding scheme in which variations in facies architecture are represented by variations in grid architecture was used.<ref name=WB1999 /> 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.<ref name=Grhm2015 />

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.<ref name=Grhm2015 />

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# Bakke, N. E., E. T. Ertresvåg, A. Næss, A. C. MacDonald, and L. M. Fält, 1996, Application of seismic data and sequence stratigraphy for constraining a stochastic model of calcite cementation: SPE Paper 35487, 13 p.

# Dilib, F. A., M. D. Jackson, A. Mojaddam Zadeh, R. Aasheim, K. Årland, A. J. Gyllensten, and S. M. Erlandsen, 2015, Closed-loop feedback control in intelligent wells: Application to a heterogeneous, thin oil-rim reservoir in the North Sea: SPE Reservoir Evaluation and Engineering, v. 18, no. 1, 15 p., doi: 10.2118/159550-PA.

# Dilib, F. A., M. D. Jackson, A. Mojaddam Zadeh, R. Aasheim, K. Årland, A. J. Gyllensten, and S. M. Erlandsen, 2015, Closed-loop feedback control in intelligent wells: Application to a heterogeneous, thin oil-rim reservoir in the North Sea: SPE Reservoir Evaluation and Engineering, v. 18, no. 1, 15 p., doi: 10.2118/159550-PA.

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# Dreyer, T., M. Whitaker, J. Dexter, H. Flesche, and E. Larsen, 2005, From spit system to tide-dominated delta: Integrated reservoir model of the Upper Jurassic Sognefjord Formation on the Troll West field, inA. G. Doré, and B. A. Vining, eds., Petroleum geology: From mature basins to new frontiers—Proceedings of the 6th Petroleum Geology Conference: Petroleum Geology Conference Series 6: London, Geological Society, p. 423–448.

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