Mathematical Geosciences

, Volume 44, Issue 3, pp 327–341

An Approach for the Reliable Evaluation of the Uncertainties Associated to Petrophysical Properties


DOI: 10.1007/s11004-011-9358-1

Cite this article as:
Viberti, D. & Verga, F. Math Geosci (2012) 44: 327. doi:10.1007/s11004-011-9358-1


The new frontiers of the oil industry are deep offshore reservoirs, fields located in harsh environments with unconventional hydrocarbon accumulations. Extraction of oil or gas from these environments share technical challenges and high development costs. Consequently, an evaluation of the risks associated with exploiting these resources is needed before any investment decisions are made. Potential risks can be properly assessed only by considering all the possible sources of uncertainty affecting the reservoir characterization. Porosity, fluid saturations and net to gross are strategic information used to both calculate hydrocarbon originally in place and define proper field development plans. These quantities are obtained through the log interpretation process, which is an inverse problem where the main petrophysical characteristics are calculated as the acceptable minimum of a cost function describing the discrepancy between measured and simulated logs, the latter being reproduced on the basis of an assumed formation model. The results of the calculation process can be affected by several uncertainties related to the physics and calibration of the measuring tools, the identification of the proper formation model, and the quantification of the model coefficients. An effective methodology able to provide a reliable evaluation of the hydrocarbon volume and the assessment of the associated uncertainties is presented and discussed in this paper. The log interpretation process was approached as a linearly constrained optimization problem, solved by coupling a Lagrange-Newton method with a primal active set algorithm. The evaluation of the uncertainties was obtained by coupling the optimization algorithm with the Monte Carlo approach. The results obtained by the application of the methodology to a real case are shown.


Log interpretationInversion problemLinear constraintsLagrangian relaxationMonte Carlo

Copyright information

© International Association for Mathematical Geosciences 2011

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria dell’Ambiente, del Territorio e delle GeotecnologiePolitecnico di TorinoTorinoItaly