One of the principal contributions made by petrophysicists to an understanding of hydrocarbon distribution within the reservoir is the saturation height function. Unfortunately, the shortage of specifically designed commercial software forces many petrophysicists to transform the input data into a domain where it is quasi-linear, so that least squares linear regression techniques can be used to derive coefficients in the equations. This can impose artificial weighting and undesirable constraints on the fitting process. We present a simple, robust, non-linear formulation and optimization method, designed so that each term in the function can be related directly to a physical parameter such as irreducible water saturation, ratio of contact angle and surface tension between laboratory and reservoir conditions, threshold capillary entry pressure, and height difference between free water level and oil water contact. The transformation applied to the function by altering each term is predictable, comprehensible, and independent of the other terms. This property allows petrophysicists to make optimal use of the log, capillary pressure and other special core data at their disposal, capitalising on the relative merits of each type of data. When deriving a saturation height relationship petrophysicists need to be aware of the variation of field area with height above contact. The weighting option of the optimization process recognises this requirement, and fits the data best where each foot of vertical height represents the largest areal extent of the field. Finally, the implications of saturation-related phenomena connected with variations in rock properties observed in the wells on field-wide hydrocarbon distribution are discussed. The optimization method, backed by resistivity profile modelling, is used to distinguish artifacts arising from resolution incompatibilities from real rock property variations.

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