A composite solution method for physical equations and its application in the Nea Kessani geothermal field (Greece)

Abstract

We propose a method for solving physical equations under conditions of uncertainty and we use it to study the Nea Kessani (Greece) geophysical system formed by a thermal reservoir of arcosic sandstones. The method is based on the Bayesian maximum entropy theory and generates temperature solutions that are (1) composite, in the sense that apart from being consistent with the physical model, they also account for the multisourced uncertainty of the model parameters and the site‐specific information at a set of vertical drill holes indicating that hot fluids rising from depth enter the reservoir in a restricted area and flow toward local thermal springs; and (2) complete, in the sense that the whole temperature probability density is generated at each spatial location. From these densities, different temperature maps can be derived (most probable, error minimizing, etc., maps), depending on the study objectives. The proposed composite solution is distinguished from the standard (direct) physical model solution in a formal mathematical sense. By means of comparative analysis, it is shown that the numerical composite solution is more informative than the direct temperature solution as well as the analytical solution obtained using simplified boundary conditions (the composite solution offers a more realistic representation of the real‐world phenomenon, and unlike the previous methods, it is in agreement with empirical quartz geothermometry analyses). The composite method can be a valuable contribution for scientists and engineers working on incorporating secondary information for improving the quality of the solutions obtained from a physical model in general.