CONNEC3D: a computer program for connectivity analysis of 3D random set models

Abstract

Geostatistical simulation is used in risk analysis studies to incorporate the spatial uncertainty of experimental variables that are significantly under-sampled. For example, the values of hydraulic conductivity or porosity are critical in petroleum reservoir production modelling and prediction, in assessing underground sites as waste repositories, and in modelling the transport of contaminants in aquifers. In all these examples connectivity of the permeable phase or permeable lithofacies is a critical issue. Given an indicator map on a regular two- or three-dimensional grid, which can be obtained from continuous-valued or from categorical variables, CONNEC3D performs a connectivity analysis of the phase of interest (coded 0 or 1 by an indicator function). 3D maps of multiple indicators, categories or continuous variables can also be analysed for connectivity by suitable coding of the input map. Connectivity analysis involves the estimation of the connectivity function τ (h) for different spatial directions and a number of connectivity statistics. Included in the latter are the number of connected components (ncc), average size of a connected component (cc), mean length of a cc in the X , Y and Z directions, size of the largest cc, maximum length of a cc along X, Y and Z and the numbers of percolating components along X, Y and Z. In addition, the program provides as output a file in which each cc is identified by an integer number ranging from 1 to ncc.The implementation of the program is demonstrated on a random set model generated by the sequential indicator algorithm. This provides a means of estimating the computational time required for different grid sizes and is also used to demonstrate computationally that when the semi-variogram of the indicator function is anisotropic the connectivity function is also anisotropic. There are options within the program for 6-connectivity analysis, 18-connectivity analysis and 26-connectivity analysis. The software is provided in two formats, as a stand-alone program that can perform connectivity analysis of an indicator map and as a subroutine that can be repeatedly called in order to calculate averages of connectivity analyses of a large number of realizations of indicator maps, or to identify critical realizations generated by conditional simulations of continuous variables or categorical variables. © 2003 Elsevier Science Ltd. All rights reserved.