Influence of computational grid space in constructing belongingress functions of relationships between petrophysical parameters

Kozhevnikova Polina Valeryevna, Kuntsev Vitaly Evgenievich, Chuvashov Artur Alexandrovich

The task of assessing the reliability of petrophysical models in the calculation of hydrocarbon reserves is one of the tasks solved under conditions of uncertainty. In conditions of uncertainty, fuzzy modeling technology can be used. The first stage of this technology is the construction of the membership function, which is based on the computational grid. The tasks that require consideration include the problem of selecting the optimal step of the computational grid. The article presents the results of the calculated membership functions of the relationships between the well logging and core parameters, built using different grid step frequencies, and the convolution of these relationships. During the experiments, the exponential model of the membership function was used. The effective parameter increased in proportion to the size of the computational grid. The results obtained in the course of the experiments make it possible to determine the reliability with greater accuracy, which reflects such a characteristic as the maximum value of the membership function of the predicted value, which was the ratio “porosity according to logging - water saturation” in this article. The maximum value of the reliability of this ratio increased from 0.741 to 0.754 with an increase in the grid size from 25×25 to 300×300, which in turn amounted to 1.7%. The article also concluded that the use of a grid of 1000 × 1000 or more is inappropriate, since it does not lead to significant changes, but increases the time spent on calculations.

Keywords:membership function, fuzzy relations, petrophysical parameters, computational grid, improving the quality of reliability assessment.