INTRINSIC RANDOM FUNCTIONS OF HIGH ORDER AND THEIR APPLICATION TO THE MODELING OF NON-STATIONARY GEOTHERMAL PARAMETERS

Abstract

Geothermal reservoirs are typical examples of natural systems having incomplete and discontinuous information. Data obtained show heterogeneity, frequently, at a high degree. Any geothermal reservoir manifests the following paradox: it is a natural phenomenon whose existence is uniquely determined in time and in space, but that can only
be known or measured in an incomplete and fractional manner. Advanced simulators used to study and predict the behavior of such systems require petrophysical and thermodynamical continuous parameters, even at places
where they have never been measured.

Traditional statistics used to calculate average values of those parameters, becomes evidently insufficient because the geothermal processes involved, are non-stationary. For example, temperature and pressure increase with depth, while porosity and permeability decrease. In this document we introduce practical applications of a numerical technique based on the theory of Intrinsic Random Functions of order k (k > l), for the optimum spatial interpolation of geothermal parameters. This method
allows the construction of geo-statistical generalized estimators composed by two functions: one portion can be totally random, while the second portion is deterministic, containing the spatial trend of the non-stationary
parameter. This methodology has great potential usefulness in the risk analysis of any geothermal project.