STOCHASTIC MODELING OF PERMEABILITY IN DOUBLE POROSITY CARBONATES APPLYING A MONTE-CARLO SIMULATION METHOD WITH t-COPULAS

摘要

Copulas are a new way of modeling the correlation structure between variables. Over the past forty years copulas have played an important role in several areas of statistics. But, only recently copulas have become popular in simulation models. Copulas are functions that describe dependencies among variables, and provide a way to create distributions to model correlated multivariate data. Using a copula, a data analyst can construct a multivariate distribution by specifying marginal univariate distributions, and choosing a particular copula to provide a correlation structure between variables. In the present work, we explore how to use copulas for the modeling of permeability values associated with the secondary porosity in carbonate formations. This can be made using the Monte-Carlo method with a copula which reproduces the observed dependence patterns of the permeability-secondary porosity bivariate distribution. In particular, we apply a bivariate t - copula and the empirical model for the marginal distributions of secondary porosity and permeability in conjunction with different association measures such as Kendall’s τK and Spearman's ρS. The method presented does not need the assumption of linear dependence and has the ability to reproduce extreme values and the variability of the data samples. A brief discussion on how to produce dependent joint geostatistical simulations of permeability-secondary porosity using NMR permeability and conventional logs associated with secondary porosity is presented.