# Fitting Deterministic Arcuate Map View/Sigmoidal Cross Section Surfaces to IHS Beds in Heavy Oil Fluvial Point Bars

## Abstract

The geocellular models most faithful to the formation architecture are those in which the cell layers are parallel to bedding. Achieving this in fluvial point bar deposits is difficult because bedding in the heterolithic upper point bar is neither parallel to the point bar's scour base nor to the overlying seal beds. In general, the upper point bar bed geometry is sigmoidal in cross section and arcuate in map view. This shape can be described with the following algorithm: (1) Ps = (SQRT( (Xc - Xs)^{2} + (Yc - Ys)^{2}) - R) / W (2) IF Ps < 0 THEN Zs = UpperZ (3) ELSE IF Ps > 1 THEN Zs = LowerZ (4) ELSE Zs = UpperZ+ (0.5 × cos( 3.14159 × Ps) - 0.5) * (UpperZ-LowerZ) where: Ps = normalized position of the sample point on the sigmoidal slope Xs = sample location X coordinate Ys = sample location Y coordinate * Xc = circular planform shape centroid X coordinate * Yc = circular planform shape centroid Y coordinate * R = circular planform shape radius to top of sigmoid slope * W = width of sigmoid from top of slope to base of slope Zs = calculated elevation of sample * UpperZ = elevation of top of sigmoid slope * LowerZ = elevation of base of sigmoid slope * = term in sigmoid shape equation The dip angle of the sigmoidal surface at any location can be determined as the first derivative of the above function. Also, the down-dip azimuth can be calculated as the angle between any sample point and the shape centroid relative to due North. The algorithm of Equations 1 through 4 is optimized to the surface elevation picks in wells and/or geophysical data using a spreadsheet that iteratively modifies the six equation parameters of the mathematically defined surface (denoted with asterisks) until an objective function of fit to the real data is minimized. The objective function is a weighted summation of elevation * estimation* error, dip angle

*error, and dip azimuth*

**estimation***error. After the best-fit equation terms are determined, the same algorithm is used to assign elevation values to the nodes of a surface elevation grid. These surfaces can then be flexed to match well data and/or geophysical interpretations and then used as zone boundaries, as layer orientation guides for the geocellular framework, or to help correlate between widely spaced wells. This method has been successfully applied to a Brazos River (Texas) modern point bar with dense borehole coverage, and to two heavy oil reservoirs in Alberta, one with 3D seismic and the other with ground penetrating radar.*

**estimation**AAPG Datapages/Search and Discovery Article #90216 ©2015 AAPG Annual Convention and Exhibition, Denver, CO., May 31 - June 3, 2015