Geostatistical Prediction of Reservoir Petrophysical Properties by Copula-Based Dependence Models Between Seismic Attributes and Petrophysical Properties

Abstract

Abstract

In the context of geological and petrophysical reservoir modeling proper prediction of petrophysical property spatial distributions is a crucial task because the correct estimation of reserves and the development and optimal exploitation of the reservoir heavily depend on it.

Only in recent years, it has imposed on the oil industry a comprehensive and multidisciplinary approach that combines all available information sources such as: core data, geological models, seismic surveys and well logs, by the application of geostatistical models in a systematic way.

One of the most common ways to combine seismic data with well logs, is to establish correlations between seismic attributes and petrophysical properties. These models are quite restrictive because in most cases they assume that variables follow a Gaussian distribution and a strong linear dependence exists between them. Moreover, also the classical multivariate geostatistical models as Cokriging and Sequential Gaussian simulation method (Parra and Emery, 2013) also consider these assumptions.

A non-parametric (distribution-free) method is proposed, which does not assume linear dependence, but rather seeks to represent, reproduce and exploit the underlying dependency between attributes and petrophysical properties: a Bernstein copula dependence model, that was successfully applied for petrophysical simulation at well log scale (Hernandez-Maldonado, et al., 2012).

The methodology basically consists of two steps: firstly, a dependence model between seismic attributes and petrophysical properties at well log scale is established and then this model is used to estimate (median regression approach) or to simulate (stochastic approach using simulated annealing) petrophysical properties to seismic scale.

The application of the methodology is illustrated in a case study where the results are compared with sequential Gaussian method.

References

1.- Hernández-Maldonado, V., Díaz-Viera, M., Erdely, A. (2012) A joint stochastic simulation method using the Bernstein copula as a flexible tool for modeling nonlinear dependence structures between petrophysical properties. Journal of Petroleum Science and Engineering 90-91:112-123.

1.- Parra J., Emery X. (2013) Geostatistics applied to cross-well reflection seismic for imaging carbonate aquifers. Journal of Applied Geophysics 92:68–75.

AAPG Datapages/Search and Discovery Article #90260 © 2016 AAPG/SEG International Conference & Exhibition, Cancun, Mexico, September 6-9, 2016