Changes

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

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

Clinoforms occur at a wide range of spatial scales, from large, basinward-dipping surfaces at the shelf-slope margin, to smaller surfaces associated with progradation of deltaic and shoreface systems across the shelf (e.g., Helland-Hansen and Hampson<ref name=HHH>Helland-Hansen, W., and G. J. Hampson, 2009, Trajectory analysis: Concepts and applications: Basin Research, v. 21, no. 5, p. 454–483, doi: 10.1111/j.1365-2117.2009.00425.x.</ref>). This study focuses on developing a surface-based approach to represent clinoforms at any lengthscale in reservoir models, with emphasis on clinoforms produced by the progradation of deltaic, barrier-island, and strandplain shorelines, which are typically up to a few tens of meters in height. The 3-D geometry and spatial arrangement of shoreline-scale clinoforms reflect in large part the process regime under which they were deposited (e.g., Galloway<ref name=Glwy>Galloway, W. E., 1975, Process framework for describing the morphological and stratigraphic evolution of deltaic depositional systems, in M. L. Broussard, ed., Deltas, models for exploration: Houston, Texas, Houston Geological Society, p. 87–98.</ref>). Fluvial-dominated deltas exhibit a hierarchy of point-sourced, teardrop-shaped sediment bodies that are fed via a downstream branching network of distributary channels. From small to large lengthscales, this hierarchy consists of mouth bars, mouth-bar assemblages, and delta lobes<ref name=Bhttchry2006>Bhattacharya, J. P., 2006, Deltas, inH. W. Posamentier, and R. Walker, eds., Facies models revisited: SEPM Special Publication 84, p. 237–292.</ref> (equivalent to the jet-plume deposits, jet-plume-complex deposits, and delta lobes of Wellner et al., 2005). Sediment-body geometry is modified by the action of waves and tides, which respectively tend to result in shoreline-parallel and shoreline-perpendicular sediment transport that suppresses branching and switching of distributary channels (e.g., Galloway;<ref name=Glwy /> Willis, 2005; Bhattacharya;<ref name=Bhttchry2006 /> Plink-Björklund, 2012). Clinoforms exist as a preserved record of sediment-body morphologies at each of these hierarchical lengthscales (e.g., Gani and Bhattacharya<ref name=GB07>Gani, M. R., and J. P. Bhattacharya, 2007, Basic building blocks and process variability of a Cretaceous delta: Internal facies architecture reveals a more dynamic interaction of river, wave, and tidal processes than is indicated by external shape: Journal of Sedimentary Research, v. 77, no. 4, p. 284–302, doi: 10.2110/jsr.2007.023.</ref>) but are most commonly described at the scale of delta lobes in outcrop and high-resolution, shallow seismic data. For example, in Pleistocene fluvial-dominated delta deposits imaged in shallow-seismic data, Roberts et al. (2004, p. 185) comment that “each clinoform set represents rather continuous deposition from a distributary or related set of distributaries, resulting in the formation of a delta lobe.” Shale drapes and cemented concretionary layers occur along depositional surfaces at each hierarchical level but generally have greater continuity and extent at larger lengthscales of the hierarchy (e.g., Gani and Bhattacharya;<ref name=GB07 /> Lee et al., 2007; Ahmed et al., 2014). Thus, delta lobes tend to be overlain across flooding surfaces by prodelta shales and distal-delta-front heteroliths, which may cause them to behave as distinct reservoir zones that can be correlated between wells, whereas clinoforms are associated with heterogeneity between wells and within reservoir zones (e.g., Ainsworth et al.,;<ref name=Answrth1999 /> Hampson et al.<ref name=Hmpsn2008 />).

Clinoforms occur at a wide range of spatial scales, from large, basinward-dipping surfaces at the shelf-slope margin, to smaller surfaces associated with progradation of deltaic and shoreface systems across the shelf (e.g., Helland-Hansen and Hampson<ref name=HHH>Helland-Hansen, W., and G. J. Hampson, 2009, Trajectory analysis: Concepts and applications: Basin Research, v. 21, no. 5, p. 454–483, doi: 10.1111/j.1365-2117.2009.00425.x.</ref>). This study focuses on developing a surface-based approach to represent clinoforms at any lengthscale in reservoir models, with emphasis on clinoforms produced by the progradation of deltaic, barrier-island, and strandplain shorelines, which are typically up to a few tens of meters in height. The 3-D geometry and spatial arrangement of shoreline-scale clinoforms reflect in large part the process regime under which they were deposited (e.g., Galloway<ref name=Glwy>Galloway, W. E., 1975, Process framework for describing the morphological and stratigraphic evolution of deltaic depositional systems, in M. L. Broussard, ed., Deltas, models for exploration: Houston, Texas, Houston Geological Society, p. 87–98.</ref>). Fluvial-dominated deltas exhibit a hierarchy of point-sourced, teardrop-shaped sediment bodies that are fed via a downstream branching network of distributary channels. From small to large lengthscales, this hierarchy consists of mouth bars, mouth-bar assemblages, and delta lobes<ref name=Bhttchry2006>Bhattacharya, J. P., 2006, Deltas, inH. W. Posamentier, and R. Walker, eds., Facies models revisited: SEPM Special Publication 84, p. 237–292.</ref> (equivalent to the jet-plume deposits, jet-plume-complex deposits, and delta lobes of Wellner et al.<ref name=Wllnr2005>Wellner, R., R. Beaubouef, J. C. Van Wagoner, H. H. Roberts, and T. Sun, 2005, Jet-plume depositional bodies—The primary building blocks of Wax Lake delta: Transactions of the Gulf Coast Association of Geological Societies, v. 55, p. 867–909.</ref>). Sediment-body geometry is modified by the action of waves and tides, which respectively tend to result in shoreline-parallel and shoreline-perpendicular sediment transport that suppresses branching and switching of distributary channels (e.g., Galloway;<ref name=Glwy /> Willis;<ref >Willis, B. J., 2005, Deposits of tide-influenced river deltas, in L. Giosan, and J. P. Bhattacharya, eds., River deltas—Concepts, models, and examples: SEPM Special Publication 83, p. 87–129.</ref> Bhattacharya;<ref name=Bhttchry2006 /> Plink-Björklund<ref>Plink-Björklund, P., 2012, Effects of tides on deltaic deposition: Causes and responses: Sedimentary Geology, v. 279, p. 107–133, doi: 10.1016/j.sedgeo.2011.07.006.</ref>). Clinoforms exist as a preserved record of sediment-body morphologies at each of these hierarchical lengthscales (e.g., Gani and Bhattacharya<ref name=GB07>Gani, M. R., and J. P. Bhattacharya, 2007, Basic building blocks and process variability of a Cretaceous delta: Internal facies architecture reveals a more dynamic interaction of river, wave, and tidal processes than is indicated by external shape: Journal of Sedimentary Research, v. 77, no. 4, p. 284–302, doi: 10.2110/jsr.2007.023.</ref>) but are most commonly described at the scale of delta lobes in outcrop and high-resolution, shallow seismic data. For example, in Pleistocene fluvial-dominated delta deposits imaged in shallow-seismic data, Roberts et al.<ref name=Rbrts2004>Roberts, H. H., R. H. Fillon, B. Kohl, J. M. Robalin, and J. C. Sydow, 2004, Depositional architecture of the Lagniappe delta; sediment characteristics, timing of depositional events, and temporal relationship with adjacent shelf-edge deltas, inJ. B. Anderson, and R. H. Fillon, eds., Late Quaternary stratigraphic evolution of the northern Gulf of Mexico margin: Tulsa, Oklahoma, SEPM Special Publication 79, p. 143–188.</ref> comment that “each clinoform set represents rather continuous deposition from a distributary or related set of distributaries, resulting in the formation of a delta lobe.” Shale drapes and cemented concretionary layers occur along depositional surfaces at each hierarchical level but generally have greater continuity and extent at larger lengthscales of the hierarchy (e.g., Gani and Bhattacharya;<ref name=GB07 /> Lee et al.;<ref>Lee, K., M. D. Gani, G. A. McMechan, J. P. Bhattacharya, S. Nyman, and X. Zeng, 2007, [http://archives.datapages.com/data/bulletns/2007/02feb/BLTN05114/BLTN05114.HTM Three-dimensional facies architecture and three-dimensional calcite concretion distributions in a tide-influenced delta front, Wall Creek Member, Frontier Formation, Wyoming]: AAPG Bulletin, v. 91, no. 2, p. 191–214, doi: 10.1306/08310605114.</ref> Ahmed et al.<ref name=Ahmd2014>Ahmed, S., J. P. Bhattacharya, D. Garza, and L. Giosan, 2014, Facies architecture and stratigraphic evolution of a river-dominated delta front, Turonian Ferron Sandstone, Utah, USA: Journal of Sedimentary Research, v. 84, no. 2, p. 97–121, doi: 10.2110/jsr.2014.6.</ref>). Thus, delta lobes tend to be overlain across flooding surfaces by prodelta shales and distal-delta-front heteroliths, which may cause them to behave as distinct reservoir zones that can be correlated between wells, whereas clinoforms are associated with heterogeneity between wells and within reservoir zones (e.g., Ainsworth et al.,;<ref name=Answrth1999 /> Hampson et al.<ref name=Hmpsn2008 />).

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

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

===Cross-Sectional Clinoform Geometry===

===Cross-Sectional Clinoform Geometry===

The shape and dip angle of a deltaic or shoreface clinoform in cross section is a function of modal grain size, proportion of mud, and the depositional process regime at the shoreline. In sandy, fluvial-dominated deltas, clinoforms have simple concave-upward geometries and steep dip angles (up to 15°)<ref name=GB05 /> (e.g., [[:File:BLTN13190fig1.jpg|Figure 1]]). Similar geometries have been documented in sandy, tide-influenced deltas (dip angles up to 5°–15°) (Willis et al., 1999). Concave-upward clinoform geometry is also typical of sandy, wave-dominated deltas and strandplains, although the clinoforms have smaller dip angles (typically up to 1°–2°) (Hampson and Storms, 2003; <ref name=GB05 />). Clinoforms are consistently inclined paleobasinward down depositional dip; and, along depositional strike, they exhibit bidirectional, concave-upward dips if the delta-front was lobate in plan view (e.g., Willis et al., 1999; Kolla et al., 2000; Roberts et al., 2004) or appear horizontal if the shoreline was approximately linear (e.g., Hampson, 2000). Clinoforms are usually truncated at their tops by a variety of channelized erosion surfaces formed during shoreline advance (e.g., distributary channels, incised valleys) and by channelized and/or planar transgressive erosion surfaces (tide and wave ravinement surfaces sensu Swift, 1968) associated with shoreline retreat. Consequently, most sandy shoreline clinoforms lack a decrease in depositional dip (rollover) near their tops, although this geometry is ubiquitous in larger, shelf-slope margin clinoforms (e.g., Steckler et al., 1999) and in the outer, muddy portion of compound deltaic clinoforms with a broad subaqueous topset that lies seaward of the shoreline (e.g., Pirmez et al., 1998).

The shape and dip angle of a deltaic or shoreface clinoform in cross section is a function of modal grain size, proportion of mud, and the depositional process regime at the shoreline. In sandy, fluvial-dominated deltas, clinoforms have simple concave-upward geometries and steep dip angles (up to 15°)<ref name=GB05 /> (e.g., [[:File:BLTN13190fig1.jpg|Figure 1]]). Similar geometries have been documented in sandy, tide-influenced deltas (dip angles up to 5°–15°) (Willis et al., 1999). Concave-upward clinoform geometry is also typical of sandy, wave-dominated deltas and strandplains, although the clinoforms have smaller dip angles (typically up to 1°–2°) (Hampson and Storms, 2003; <ref name=GB05 />). Clinoforms are consistently inclined paleobasinward down depositional dip; and, along depositional strike, they exhibit bidirectional, concave-upward dips if the delta-front was lobate in plan view (e.g., Willis et al., 1999; Kolla et al., 2000; Roberts et al.<ref name=Rbrts2004 />) or appear horizontal if the shoreline was approximately linear (e.g., Hampson, 2000). Clinoforms are usually truncated at their tops by a variety of channelized erosion surfaces formed during shoreline advance (e.g., distributary channels, incised valleys) and by channelized and/or planar transgressive erosion surfaces (tide and wave ravinement surfaces sensu Swift, 1968) associated with shoreline retreat. Consequently, most sandy shoreline clinoforms lack a decrease in depositional dip (rollover) near their tops, although this geometry is ubiquitous in larger, shelf-slope margin clinoforms (e.g., Steckler et al., 1999) and in the outer, muddy portion of compound deltaic clinoforms with a broad subaqueous topset that lies seaward of the shoreline (e.g., Pirmez et al., 1998).

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

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

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

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

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

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.

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., 2000; Roberts et al., 2004) and the modern Wax Lake Delta lobe (after data in Wellner et al., 2005) ([[:File:BLTN13190fig3.jpg|Figure 3C]]). These dimensions were likely smaller during the growth of the delta lobe, and it is assumed here that the lobe initiated with dimensions (''t_D'', ''t_s'') that were a third of those of the final preserved delta lobe, consistent in areal proportions to a single mouth-bar assemblage or jet-plume complex in the modern Wax Lake Delta lobe (after data in Wellner et al., 2005). The length, ''L'', and spacing, ''S'', of clinoforms in depositional dip cross section were extracted from the bedding-diagram interpretations of Forster et al. <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., 2000; 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 (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.

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., 1999; Kolla et al., 2000; Roberts et al., 2004). Additionally, the model contains stratal geometries observed at the outcrop, such as onlap and downlap of younger clinoforms on to older clinoforms (Figures 7B, 8C). The clinoform-modeling algorithm also produces clinoforms that are consistently distributed in the same orientation as those in the observed delta-lobe deposits and its interpreted plan-view progradation direction (Figures 5A, 8B). Facies proportions in the model are 8% SMB sandstones, 50% pDF sandstones, 31% dDF heteroliths, and 11% PD mudstone. Using porosity values that are characteristic of these facies associations in analogous reservoirs (Table 3), the volume of oil in place in the model is 7.1 million bbl. The clinoform-bearing model is now used to investigate the impact of heterogeneities associated with clinoforms on fluid flow during waterflooding within this fluvial-dominated deltaic parasequence.

A single delta lobe is present in the model and extends beyond the model volume (Figures 5D, 8A). As a result, clinoforms are larger in their depositional dip and strike extent (''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., 1999; Kolla et al., 2000; 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.

{| class = wikitable

{| class = wikitable

 

# Anderson, P. B., T. C. Chidsey, Jr., K. McClure, A. Mattson, and S. H. Snelgrove, 2002, Ferron Sandstone stratigraphic cross-sections, Ivie Creek area, Emery County, Utah: Utah Geological Survey, Open File Report 390, CD-ROM.

# Anderson, P. B., T. C. Chidsey, Jr., K. McClure, A. Mattson, and S. H. Snelgrove, 2002, Ferron Sandstone stratigraphic cross-sections, Ivie Creek area, Emery County, Utah: Utah Geological Survey, Open File Report 390, CD-ROM.

# Anderson, P. B., T. C. Chidsey, Jr., T. A. Ryer, R. D. Adams, and K. McClure, 2004, Geological framework, facies paleogeography, and reservoir analogs of the Ferron Sandstone in the 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. 331–356.

# Anderson, P. B., T. C. Chidsey, Jr., T. A. Ryer, R. D. Adams, and K. McClure, 2004, Geological framework, facies paleogeography, and reservoir analogs of the Ferron Sandstone in the 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. 331–356.

# Kantorowicz, J. D., I. D. Bryant, and J. M. Dawans, 1987, Controls on the geometry and distribution of carbonate cements in Jurassic sandstones: Bridport Sands, southern England and Viking Group, Troll Field, Norway, inJ. D. Marshall, ed., Diagenesis of sedimentary sequences: Geological Society, London, Special Publication 36, p. 103–118.

# Kantorowicz, J. D., I. D. Bryant, and J. M. Dawans, 1987, Controls on the geometry and distribution of carbonate cements in Jurassic sandstones: Bridport Sands, southern England and Viking Group, Troll Field, Norway, inJ. D. Marshall, ed., Diagenesis of sedimentary sequences: Geological Society, London, Special Publication 36, p. 103–118.

# Kolla, V., P. Biondi, B. Long, and R. Fillon, 2000, Sequence stratigraphy and architecture of the late Pleistocene Lagniappe delta complex, northeast Gulf of Mexico, inD. Hunt, and R. L. Gawthorpe, eds., Sedimentary responses to forced regressions: Geological Society, London, Special Publication 172, p. 291–327.

# Kolla, V., P. Biondi, B. Long, and R. Fillon, 2000, Sequence stratigraphy and architecture of the late Pleistocene Lagniappe delta complex, northeast Gulf of Mexico, inD. Hunt, and R. L. Gawthorpe, eds., Sedimentary responses to forced regressions: Geological Society, London, Special Publication 172, p. 291–327.

# Lee, K., M. D. Gani, G. A. McMechan, J. P. Bhattacharya, S. Nyman, and X. Zeng, 2007, Three-dimensional facies architecture and three-dimensional calcite concretion distributions in a tide-influenced delta front, Wall Creek Member, Frontier Formation, Wyoming: AAPG Bulletin, v. 91, no. 2, p. 191–214, doi: 10.1306/08310605114.

#  

# Lien, S. C., H. H. Haldorsen, and M. Manner, 1992, Horizontal wells: Still appealing in formations with discontinuous vertical permeability barriers?: Journal of Petroleum Technology, v. 44, no. 12, p. 1364–1370, doi: 10.2118/20962-PA.

# Lien, S. C., H. H. Haldorsen, and M. Manner, 1992, Horizontal wells: Still appealing in formations with discontinuous vertical permeability barriers?: Journal of Petroleum Technology, v. 44, no. 12, p. 1364–1370, doi: 10.2118/20962-PA.

# Lien, S. C., K. Seines, S. O. Havig, and T. Kydland, 1991, The first long-term horizontal-well test in the Troll thin oil zone: Journal of Petroleum Technology, v. 43, no. 8, p. 914–973, doi: 10.2118/20715-PA.

# Lien, S. C., K. Seines, S. O. Havig, and T. Kydland, 1991, The first long-term horizontal-well test in the Troll thin oil zone: Journal of Petroleum Technology, v. 43, no. 8, p. 914–973, doi: 10.2118/20715-PA.

# Patruno, S., G. J. Hampson, C. A.-L. Jackson, and T. Dreyer, 2015, Clinoform geometry, geomorphology, facies character and stratigraphic architecture of a sand-rich subaqueous delta: Jurassic Sognefjord Formation, offshore Norway: Sedimentology, v. 62, no. 1, p. 350–388, doi: 10.1111/sed.12153.

# Patruno, S., G. J. Hampson, C. A.-L. Jackson, and T. Dreyer, 2015, Clinoform geometry, geomorphology, facies character and stratigraphic architecture of a sand-rich subaqueous delta: Jurassic Sognefjord Formation, offshore Norway: Sedimentology, v. 62, no. 1, p. 350–388, doi: 10.1111/sed.12153.

# Pirmez, C., L. F. Pratson, and M. S. Steckler, 1998, Clinoform development by advection-diffusion of suspended sediment; modeling and comparison to natural systems: Journal of Geophysical Research B: Solid Earth and Planets, v. 103, p. 24,141–24,157, doi: 10.1029/98JB01516.

# Pirmez, C., L. F. Pratson, and M. S. Steckler, 1998, Clinoform development by advection-diffusion of suspended sediment; modeling and comparison to natural systems: Journal of Geophysical Research B: Solid Earth and Planets, v. 103, p. 24,141–24,157, doi: 10.1029/98JB01516.

#  

#  

# 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.

# 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.

# Ryer, T. A., and P. B. Anderson, 2004, Facies of the Ferron Sandstone, 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. 59–78.

# Ryer, T. A., and P. B. Anderson, 2004, Facies of the Ferron Sandstone, 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. 59–78.

# Vinje, J., R. Nybø, and G. Grinestaff, 2011, A new simulation grid type is demonstrated for the giant Troll oil and gas field: SPE Paper 148023, 14 p.

# Vinje, J., R. Nybø, and G. Grinestaff, 2011, A new simulation grid type is demonstrated for the giant Troll oil and gas field: SPE Paper 148023, 14 p.

#  

#  

# 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.

# 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.

# White, C. D., B. J. Willis, S. P. Dutton, J. P. Bhattacharya, and K. Narayanan, 2004, Sedimentology, statistics, and flow behaviour for a tide-influenced deltaic sandstone, Frontier Formation, Wyoming, United States, inG. M. Grammer, P. M. Harris, and G. P. Eberli, eds., Integration of outcrop and modern analogs in reservoir modeling: AAPG Memoir 80, p. 129–152.

# White, C. D., B. J. Willis, S. P. Dutton, J. P. Bhattacharya, and K. Narayanan, 2004, Sedimentology, statistics, and flow behaviour for a tide-influenced deltaic sandstone, Frontier Formation, Wyoming, United States, inG. M. Grammer, P. M. Harris, and G. P. Eberli, eds., Integration of outcrop and modern analogs in reservoir modeling: AAPG Memoir 80, p. 129–152.

# Willis, B. J., 2005, Deposits of tide-influenced river deltas, inL. Giosan, and J. P. Bhattacharya, eds., River deltas—Concepts, models, and examples: SEPM Special Publication 83, p. 87–129.

#  

# Willis, B. J., J. P. Bhattacharya, S. L. Gabel, and C. D. White, 1999, Architecture of a tide-influenced river delta in the Frontier Formation of central Wyoming, USA: Sedimentology, v. 46, no. 4, p. 667–688, doi: 10.1046/j.1365-3091.1999.00239.x.

# Willis, B. J., J. P. Bhattacharya, S. L. Gabel, and C. D. White, 1999, Architecture of a tide-influenced river delta in the Frontier Formation of central Wyoming, USA: Sedimentology, v. 46, no. 4, p. 667–688, doi: 10.1046/j.1365-3091.1999.00239.x.