Geology - Structural Geology

Non-Linear Geostatistics for Reservoir Modelling

 

Instructor

  Prof.Dr. Stephen Tyson and Dr.Ing. Sebastian Hörning (Universiti Teknologi Brunei and The University of Queensland)

Duration

  2 to 5 days

Disciplines

  Geology – Geological Modelling

Level

  Advanced

Language

  English, German

EurGeol

  10 to 25 CPD points

Keywords

 
 SPATIAL COPULA   PYTHON   RESERVOIR MODELLING   PERMEABILITY   GEOSTATISTICS   UNCERTAINTY 

 

Course description

The course will show the attendees how to test for linear spatial dependence and introduce the concepts of non-linear geostatistics. Attendees will develop an excel spreadsheet and a python notebook which can be used for spatial data analysis and non-linear stochastic simulation.

Existing geostatistics algorithms based on the kriging matrix can be shown to underestimate the connectivity of extreme values because they assume a linear spatial dependence model. Moreover, the estimation of uncertainty based on these techniques uses the kriging variance, which is not dependent on the values of the spatially distributed variable. It can also be shown that these uncertainty estimate are often implausible. This course will explain the reasons why most spatial variables in geoscience do not have a linear spatial dependence, even after monotonic transformations, and what the impact of this in the estimation of petrophysical properties.

The course will show the attendees how to test for linear spatial dependence and introduce the concepts of non-linear geostatistics. Attendees will develop an Excel spreadsheet and a python notebook which can be used for spatial data analysis and non-linear stochastic simulation.

 

Course objectives

Upon completion of the course participants will be able to;

1. Assess whether spatial dataset has a linear spatial dependence
2. Determine the dependence structure between two or more variables (i.e. go way beyond linear correlation)
3. Understand what different correlation measurements mean
4. Understand the importance of asymmetry in spatial modeling
5. Run spatial interpolation and simulation using copulas.

 

Course outline

Theoretical part

1. Demonstration of the shortcomings of traditional geostatistics based on simple and clear examples (Assumptions, Symmetry, Uncertainty…)
2. Brief repetition of basic statistics, multivariate statistics, and traditional geostatistics
3. Introduction to rank-order geostatistics and copulas
4. Different copula models and spatial copulas
5. Copula-based measures of dependence (Rank correlation, different types of asymmetry functions)
6. Spatial interpolation using copulas
7. Spatial simulation using copulas

Practical part (Exercise based on Excel and IPython)

1. Empirical data analysis
2. Variogram and Covariance functions (just to repeat the basics)
3. Empirical copula densities
4. Rank-correlation function
5. Different asymmetry functions
6. Spatial interpolation/simulation using copulas

 

Participants' profile

This course is designed for petrophysicists, geomodellers, geologists, anyone with an interest in spatial modelling, volume estimation, preparation of simulation models and uncertainty analysis.

 

Prerequisites

Some knowledge of Excel and some basic statistics.

 

Recommended reading

Bárdossy, A.: Copula Based Geostatistical Models for Groundwater Quality Parameters. Water Resources Research 42 (2006). W11416, doi:10.1029/2005WR004754

Bárdossy, A. und J. Li: Geostatistical Interpolation using Copulas. Water Resources Research 44 (2008) W07412. doi: 10.1029/2007WR006115

P. Guthke ; Non-multi-Gaussian spatial structures: process-driven natural genesis, manifestation, modeling approaches, and influences on dependent processes
http://elib.uni-stuttgart.de/opus/volltexte/2013/8652/

C. Haslauer ; Analysis of real-world spatial dependence of subsurface hydraulic properties using copulas with a focus on solute transport behaviour
http://elib.uni-stuttgart.de/opus/volltexte/2012/6832/

S. Hörning ; Process-oriented modeling of spatial random fields using copulas
http://elib.uni-stuttgart.de/bitstream/11682/8888/5/SHDiss.pdf

 

About the instructors

Stephen Tyson

Steve Tyson is the Chair Professor of Petroleum Engineering at the Universiti Teknolig Brunei. Previously he was Chair of Subsurface Modeling at the Centre for Coal Seam Gas and Director of the Centre for Geoscience Computing in the School of Earth Sciences. He has worked in reservoir characterization and modeling in the oil industry for more than 30 years in both conventional and unconventional reservoirs. His current research interests are in model validation, verification and acceptance criteria for both static and dynamic models, upscaling, uncertainty modeling and non-linear geostatistics and spatio-temporal reservoir analytics

 

Sebastian Horning

Sebastian Hörning heads the Spatio-Temporal Reservoir Analytics group in the Centre for Geoscience Computing at the University of Queensland. His research covers spatial statistics problems over a range of scales; he has worked on basin scale spatial dependence and on the spatial models from micro CT images. In all cases he has found compelling evidence indicating that linear spatial dependence is rare. Tests for linear dependence are simple, even with conventional geostatistical software. However new techniques had to be developed to estimate spatial variables with more complex spatial dependence structures. Dr Hörning joined the University of Queensland in 2016 from the University of Stuttgart where he worked with Professor Andras Bardossy on the development of non-linear geostatistics.

 

 

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