IAMG 2001--Cancún Technical Program--Session J

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All Models Are Wrong, but Some Models Are Useful: "Solving" the Simandoux Equation by John H. Doveton, Kansas Geological Survey, USA Log analysis solutions for water saturation in shaly sandstone hydrocarbon reservoirs are elaborations of the Archie equation, with extra terms that accommodate volumes of shale or bound water and their associated electrical properties. There are a large number of alternative shaly sandstone equations that are used today because no uniquely satisfactory solution has been reached. Simpler equation forms can become oversimplistic, but are robust, comprehensible, and can perform surprisingly well. More complex equations are better functional representations, but involve additional terms which are often difficult to estimate, while introducing more error interactions. With the typical situation of limited subsurface information and the variety of shaly sandstones, the comparative performance of any equation model is debateable. However, petrophysicists often select the equation that they consider to reflect the "truth" and take values for the equation shale terms from shales between the reservoir intervals, even though it is widely recognized that their clay mineralogy and morphology is likely to be different from reservoir zone clays. If models are used from the point of view of utility, then the calibration of shale effects from within the reservoir can be made as an optimization problem based on a (provisional) recognition of water zones. For example, by applying Newton’s method to the classic Simandoux shaly sandstone equation, an iterative search can be made for the best values of the terms in this quadratic that produce a minimum squared difference between computed water saturations and the ideal of total water saturation in water zones. In this search, constraints are applied, so that values occur in petrophysically reasonable ranges. By this means, a petrophysical optimum is honored rather than a purely mathematical one. Following a satisfactory analysis, the calibrated equation can then be applied to the productive interval. The use of a spreadsheet medium allows the rapid evaluation and comparison of a variety of common shaly sandstone models. The approach applies a statistical derivation of parameter values from the shaly sandstone reservoir under analysis within the framework of classic shaly sandstone equations that have been proposed from theoretical and laboratory considerations. Paper in PDF format Doveton, Acrobat PDF, 88 k.