Implementation aspects of sequential Gaussian simulation on irregular points

Abstract

The increasing use of unstructured grids for reservoir modeling motivates the development of geostatistical techniques to populate them with properties such as facies proportions, porosity and permeability. Unstructured grids are often populated by upscaling high-resolution regular grid models, but the size of the regular grid becomes unreasonably large to ensure that there is sufficient resolution for small unstructured grid elements. The properties could be modeled directly on the unstructured grid, which leads to an irregular configuration of points in the three-dimensional reservoir volume. Current implementations of Gaussian simulation for geostatistics are for regular grids. This paper addresses important implementation details involved in adapting sequential Gaussian simulation to populate irregular point configurations including general storage and computation issues, generating random paths for improved long range variogram reproduction, and search strategies including the superblock search and the k-dimensional tree. An efficient algorithm for computing the variogram of very large irregular point sets is developed for model checking.

Geostatistical Simulation of Medical Images for Data Augmentation in Deep Learning

“…Certain advantages of the SGS that help improve the classification results are that 1) it can provide numerous equiprobable realizations of texture of a medical image through the use of a spatial variance function and the simple kriging estimator, 2) the use of the semi-variogram functions can capture different types of image texture [35], [36] for more relevant data augmentation, 3) depending on the nature of texture of the images, the application of conditional or unconditional simulation can provide a feasible way for generating useful augmented data for training deep networks either from scratch or pre-trained models with limited data, and 4) the SGS applied to the grid structure of an image can avoid certain problems in adapting the simulation to populate irregular point configurations [37]. In fact, geostatistical simulation is well accepted as a method for characterizing heterogeneous properties in spatial domains and preferred to traditional interpolation approaches [14].…”

Formation mechanical mechanism of low-angle fractures in pre-salt carbonate reservoirs: a case study from Carboniferous KT-I formation of the NT oilfield in the eastern margin of the Precaspian Basin, Kazakhstan

“…Based on the calculation results of single-well rock mechanical parameters, 3D attribute models of different rock mechanical parameters were established by using sequential Gaussian simulation. The idea of sequential Gaussian simulation is to generate a simulation path randomly, and then estimate the cumulative conditional distribution function of each point, and finally give the simulation value of this point according to the distribution function (Jika et al 2020;Manchuk and Deutsch 2012). Note that the data used to calculate the cumulative conditional distribution function include both original data and simulated unconditional data.…”

Utilization of Discrete Fracture Network (DFN) in Modelling and Simulation of a Horizontal Well-Doublet Enhanced Geothermal System (EGS) with Sensitivity Analysis of Key Production Parameters

“…The algorithm allows for estimating the distributions for a collection of points using the factorization of major probability of the data points and then data kriging for conditional distribution. It was chosen as it has proven to be efficient especially for irregular grids that include Local Grid Refinement [24]. As a result, a target simulation model containing 38,400 grid blocks, with the dimensions of 48 × 40 × 20 grid blocks in x, y and z directions, was received [2].…”