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Clinoform surfaces control aspects of facies architecture within shallow-marine parasequences and can also act as barriers or baffles to flow where they are lined by low-permeability lithologies, such as cements or mudstones. Current reservoir modeling techniques are not well suited to capturing clinoforms, particularly if they are numerous, below seismic resolution, and/or difficult to correlate between wells. At present, there are no modeling tools available to automate the generation of multiple three-dimensional clinoform surfaces using a small number of input parameters. Consequently, clinoforms are rarely incorporated in models of shallow-marine reservoirs, even when their potential impact on fluid flow is recognized.

Clinoform surfaces control aspects of facies architecture within shallow-marine parasequences and can also act as barriers or baffles to flow where they are lined by low-permeability lithologies, such as cements or [[mudstones]]. Current reservoir modeling techniques are not well suited to capturing clinoforms, particularly if they are numerous, below seismic resolution, and/or difficult to correlate between wells. At present, there are no modeling tools available to automate the generation of multiple three-dimensional clinoform surfaces using a small number of input parameters. Consequently, clinoforms are rarely incorporated in models of shallow-marine reservoirs, even when their potential impact on fluid flow is recognized.

A numerical algorithm that generates multiple clinoforms within a volume defined by two bounding surfaces, such as a delta-lobe deposit or shoreface parasequence, is developed. A geometric approach is taken to construct the shape of a clinoform, combining its height relative to the bounding surfaces with a mathematical function that describes clinoform geometry. The method is flexible, allowing the user to define the progradation direction and the parameters that control the geometry and distribution of individual clinoforms. The algorithm is validated via construction of surface-based three-dimensional reservoir models of (1) fluvial-dominated delta-lobe deposits exposed at the outcrop (Cretaceous Ferron Sandstone Member, Utah), and (2) a sparse subsurface data set from a deltaic reservoir (Jurassic Sognefjord Formation, Troll Field, Norwegian North Sea). Resulting flow simulation results demonstrate the value of including algorithm-generated clinoforms in reservoir models, because they may significantly impact hydrocarbon recovery when associated with areally extensive barriers to flow.

A numerical algorithm that generates multiple clinoforms within a volume defined by two bounding surfaces, such as a delta-lobe deposit or shoreface parasequence, is developed. A geometric approach is taken to construct the shape of a clinoform, combining its height relative to the bounding surfaces with a mathematical function that describes clinoform geometry. The method is flexible, allowing the user to define the progradation direction and the parameters that control the geometry and distribution of individual clinoforms. The algorithm is validated via construction of surface-based three-dimensional reservoir models of (1) fluvial-dominated delta-lobe deposits exposed at the outcrop (Cretaceous Ferron Sandstone Member, Utah), and (2) a sparse subsurface data set from a deltaic reservoir (Jurassic Sognefjord Formation, Troll Field, Norwegian North Sea). Resulting flow simulation results demonstrate the value of including algorithm-generated clinoforms in reservoir models, because they may significantly impact hydrocarbon recovery when associated with areally extensive barriers to flow.

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The top and base flooding surfaces of parasequence 1.6 were extracted from the model of Deveugle et al.<ref name=Dvgl2011 /> and served as the bounding surfaces used in the clinoform algorithm ([[:File:BLTN13190fig2.jpg|Figure 2]]). The surfaces were cropped to cover a model area of 750 × 3000 m (2461 × 9843 ft) in the Ivie Creek amphitheater ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Additional surfaces representing the boundaries between facies associations from the model of Deveugle et al.<ref name=Dvgl2011 /> were also extracted and similarly cropped; these define the distribution of facies associations present in each rock volume bounded by two clinoforms (i.e., clinothem) (cf. table 1 in Deveugle et al.<ref name=Dvgl2011 />). From distal to proximal, the modeled facies associations are prodelta mudstone (PD), distal delta-front heteroliths (dDF), proximal delta-front sandstones (pDF), and stream-mouth-bar sandstones (SMB) ([[:File:BLTN13190fig5.jpg|Figure 5D]]). Where facies associations pinch out, the facies association boundary surfaces were adjusted to coincide throughout the remainder of the model volume with either the top or base parasequence bounding surface. This ensures that the surface is defined across the entire model volume and is suitable for gridding.<ref name=Jckson2009 /> There are no faults within the model volume of 750 × 3000 × 6 m (2461 × 9843 × 20 ft). In a final step, isochore maps were generated between the top and base flooding surfaces and between facies association boundary surfaces and the base flooding surface. The base bounding surface was flattened, to mimic clinoform progradation over a flat, horizontal sea floor, and isochore maps were used to modify the geometries of the top bounding surface and facies association boundary surfaces above this horizontal base surface. As a result of flattening on the base bounding surface, the bounding surfaces from the existing model of Deveugle et al.<ref name=Dvgl2011 /> have been modified.

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.,<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]]).

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]]).