Changes

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.

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)<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.

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.<ref name=Eng2010>Enge, H. D., J. A. Howell, and S. Buckley, 2010, The geometry and internal architecture of stream mouth bars in the Panther Tongue and the Ferron Sandstone Members, Utah, U.S.A.: Journal of Sedimentary Research, v. 80, no. 11, p. 1018–1031, doi: 10.2110/jsr.2010.088.</ref>). 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 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 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.;<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.,<ref name=Eng2010 /> 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.<ref name=Eng2010 /> 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.<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.

A cornerpoint gridding scheme in which variations in facies architecture are represented by variations in grid architecture was used.<ref name=WB1999 /><ref>Jackson, M. D., S. Yosida, A. H. Muggeridge, and H. D. Johnson, 2005, [http://archives.datapages.com/data/bulletns/2005/04apr/0507/0507.HTM Three-dimensional reservoir characterisation and flow simulation of heterolithic tidal sandstones]: AAPG Bulletin, v. 89, no. 4, p. 507–528, doi: 10.1306/11230404036.</ref><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 />

We begin by investigating the ability of the clinoform-modeling algorithm to generate realistic stratal geometries from the Ferron Sandstone Member outcrops. Visual inspection of the algorithm-generated model against outcrop photo pans ([[:File:BLTN13190fig1.jpg|Figure 1]]) and bedding diagram interpretations ([[:File:BLTN13190fig6.jpg|Figure 6A]]) reveals a close correspondence between key geometric aspects of the observed data and concepts reproduced in the model, as outlined below.

We begin by investigating the ability of the clinoform-modeling algorithm to generate realistic stratal geometries from the Ferron Sandstone Member outcrops. Visual inspection of the algorithm-generated model against outcrop photo pans ([[:File:BLTN13190fig1.jpg|Figure 1]]) and bedding diagram interpretations ([[:File:BLTN13190fig6.jpg|Figure 6A]]) reveals a close correspondence between key geometric aspects of the observed data and concepts reproduced in the model, as outlined below.

A single delta lobe is present in the model and extends beyond the model volume (Figures 5D, 8A). As a result, clinoforms are larger in their depositional dip and strike extent (''t_D'' and ''t_s'', respectively; Table 2) than the model area, and they form arcs in plan view in the model ([[:File:BLTN13190fig8.jpg|Figure 8B]]). This plan-view geometry is consistent with the approximately lobate plan-view geometries of clinoforms in fluvial-dominated deltas ([[:File:BLTN13190fig3.jpg|Figure 3C]]). The clinoform-modeling algorithm generates the concave-upward clinoform geometry observed at the outcrop (Figures 7B, 8C), while honoring the topography of the parasequence bounding surfaces. The variation in topographic elevation of the modeled parasequence (Figures 7, 8) is attributed to postdepositional compaction. In a depositional strike cross section of the clinoform-bearing model, the algorithm produces bidirectional concave-upward dips (Figures 7C, 8D) that are consistent with delta-front bodies that are lobate in plan view (e.g., Willis et al.;<ref name=Wllsetal1999 /> Kolla et al.;<ref name=Kll /> Roberts et al.<ref name=Rbrts2004 />). Additionally, the model contains stratal geometries observed at the outcrop, such as onlap and downlap of younger clinoforms on to older clinoforms (Figures 7B, 8C). The clinoform-modeling algorithm also produces clinoforms that are consistently distributed in the same orientation as those in the observed delta-lobe deposits and its interpreted plan-view progradation direction (Figures 5A, 8B). Facies proportions in the model are 8% SMB sandstones, 50% pDF sandstones, 31% dDF heteroliths, and 11% PD mudstone. Using porosity values that are characteristic of these facies associations in analogous reservoirs (Table 3), the volume of oil in place in the model is 7.1 million bbl. The clinoform-bearing model is now used to investigate the impact of heterogeneities associated with clinoforms on fluid flow during waterflooding within this fluvial-dominated deltaic parasequence.

A single delta lobe is present in the model and extends beyond the model volume ([[:File:BLTN13190fig5.jpg|Figures 5D]], [[:File:BLTN13190fig8.jpg|8A]]). As a result, clinoforms are larger in their depositional dip and strike extent (''t_D'' and ''t_s'', respectively; Table 2) than the model area, and they form arcs in plan view in the model ([[:File:BLTN13190fig8.jpg|Figure 8B]]). This plan-view geometry is consistent with the approximately lobate plan-view geometries of clinoforms in fluvial-dominated deltas ([[:File:BLTN13190fig3.jpg|Figure 3C]]). The clinoform-modeling algorithm generates the concave-upward clinoform geometry observed at the outcrop ([[:File:BLTN13190fig7.jpg|Figures 7B]], [[:File:BLTN13190fig8.jpg|8C]]), while honoring the topography of the parasequence bounding surfaces. The variation in topographic elevation of the modeled parasequence ([[:File:BLTN13190fig7.jpg|Figures 7]], [[:File:BLTN13190fig8.jpg|8]]) is attributed to postdepositional compaction. In a depositional strike cross section of the clinoform-bearing model, the algorithm produces bidirectional concave-upward dips (Figures 7C, 8D) that are consistent with delta-front bodies that are lobate in plan view (e.g., Willis et al.;<ref name=Wllsetal1999 /> Kolla et al.;<ref name=Kll /> Roberts et al.<ref name=Rbrts2004 />). Additionally, the model contains stratal geometries observed at the outcrop, such as onlap and downlap of younger clinoforms on to older clinoforms ([[:File:BLTN13190fig7.jpg|Figures 7B]], [[:File:BLTN13190fig8.jpg|8C]]). The clinoform-modeling algorithm also produces clinoforms that are consistently distributed in the same orientation as those in the observed delta-lobe deposits and its interpreted plan-view progradation direction ([[:File:BLTN13190fig5.jpg|Figures 5A]], [[:File:BLTN13190fig8.jpg|8B]]). Facies proportions in the model are 8% SMB sandstones, 50% pDF sandstones, 31% dDF heteroliths, and 11% PD mudstone. Using porosity values that are characteristic of these facies associations in analogous reservoirs (Table 3), the volume of oil in place in the model is 7.1 million bbl. The clinoform-bearing model is now used to investigate the impact of heterogeneities associated with clinoforms on fluid flow during waterflooding within this fluvial-dominated deltaic parasequence.

{| class = wikitable

{| class = wikitable

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<ref name=Hwll2008b /> or deterministic methods to map clinoforms.<ref name=Hwll2008a /><ref name=EH2010 /> 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 /><ref name=EH2010 /> 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 /><ref name=EH2010 /> 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 /><ref name=EH2010 /><ref>Jackson, M. D., G. J. Hampson, J. H. Saunders, A. El Sheikh, G. H. Graham, and B. Y. G. Massart, 2014, Surface-based reservoir modelling for flow simulation, in A. W. Martinius, J. A. Howell, and T. R. Good, eds., Sediment-body geometry and heterogeneity: Analogue studies for modelling the subsurface: Geological Society, London, Special Publication 387, p. 271–292, doi: 10.1144/SP387.2.</ref> 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.,<ref name=Grhm2015 /> 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.,<ref name=Grhm2015 /> 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.

# 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.

# 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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# 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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# Holgate, N. E., G. J. Hampson, C. A.-L. Jackson, and S. A. Petersen, 2014, Constraining uncertainty in interpretation of seismically imaged clinoforms in deltaic reservoirs, Troll Field, Norwegian North Sea: Insights from forward seismic models of outcrop analogs: AAPG Bulletin, v. 98, no. 12, p. 2629–2663, doi: 10.1306/05281413152.

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