# 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.

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

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 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.

## Explore other courses under this discipline:

New Tools and Approaches in Reservoir Quality Prediction

Instructor: Dr Dave L. Cantrell (Cantrell GeoLogic and Stanford University, USA)

Reservoir quality prediction has long been the ultimate goal of industry geologists, yet few have achieved this in a truly quantitative fashion. This workshop presents a new approach to reservoir quality prediction that involves the integration of a variety of modeling techniques to understand, quantify and predict the geological processes that control reservoir quality. Since initial reservoir quality is established at the time of deposition, numerical process models are used to predict initial reservoir quality; diagenetic process models are then used to modify these initial results and ultimately produce a quantitative and geologically-based prediction of present-day subsurface reservoir quality.

Non-Linear Geostatistics for Reservoir Modelling

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

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.

Petroleum Exploration Strategy

Instructor: Mr Jean-Jacques Biteau (Total Professor Associate, France)

This course on 'Petroleum Exploration Strategy' focuses on aspects like the evaluation of exploration projects (working sequence, costs, economic criteria etc), partnerships, contracts and mining acreage, but also on the missions and role of a geoscience/exploration manager.
Case studies from various regions are an important part of this course.

Volumes and Risks Assessment for Conventional and Unconventional Plays and Prospects

Instructor: Prof. Dr Alexei Milkov (Colorado School of Mines, USA)

The course enables participants to transform qualitative geological descriptions of plays and prospects into technically robust quantitative success-case and risked volumetric models. Obtained learnings will help participants evaluate probabilities of success (PoS) for exploration plays, segments, prospects, wells and portfolios and to assess the range of petroleum volumes in exploration projects. Examples and case studies come from both conventional and unconventional plays, prospects and wells around the world. The learning objectives are achieved through well-illustrated lectures, numerous hands-on exercises and active class discussions. We will cover:

- Play-based exploration;
- Assessment of success-case volumes;
- Assessment of exploration risks/PoS;
- Biases;
- Post-mortem analysis.

Basin and Petroleum Systems Modelling: Applications for Petroleum Exploration Risk and Resource Assessments

Instructor: Dr Bjorn Wygrala (Schlumberger)

The term “Petroleum Systems” and the technology “Basin and Petroleum Systems Modelling” will be introduced by showing applications in areas with critical exploration challenges, including salt basins and thrustbelts. Technical breakthroughs in the last 10-15 years have been the extension of the technology from 2D to 3D, and the ability to perform multi-phase petroleum migration modelling using different methods in high resolution geological models. This enables temperature, pressure and petroleum property predictions to be made with higher levels of accuracy and in the most complex geological environments such as in the sub-salt or in thrustbelts. Case studies will be used with live software presentations to illustrate key points. Applications of the technology will range from frontier exploration in which large areas with only sparse data are screened, to detailed assessments of exploration risks in structurally complex areas, to petroleum resource assessments of yet-to-find oil and gas.

Well Logs and Borehole Image

Instructor: Prof. Dr Michael Poppelreiter (University Technology Petronas)

The most universal, comprehensive and concise descriptive documents on oil and gas wells are well logs. They impact the work of almost every oil field group from geologists to roustabouts to bankers. Familiarity with the applications of well logs is therefore essential for people forging their careers in the oil business. The instructor uses a core-based approach to help participants develop a good grounding in understanding and applying well logging techniques. General principles of physics are presented to explain the functioning of modern logging tools. Wherever possible, the physics of logging measurements is related to everyday tools and applications. Cross-plotting and reconnaissance techniques quickly and efficiently discriminate between water, oil and gas. Error minimization techniques, applicable only to computerized log analysis, produce optimal results. Participants benefit from realistic experience by working in teams on a comprehensive log interpretation exercise.

Best Practice in Pore Fluid Pressure and Fracture Pressure Prediction

Instructor: Prof. Dr Richard Swarbrick (Swarbrick GeoPressure Consultancy)

All wells drilled require a pre-drill prediction of pore fluid and fracture pressures which defines the drilling window. This course explains the objectives, methods and uncertainties of prediction, based on extensive global experience. The necessary understanding of the geological/geophysical context of abnormal pressures leading to standard algorithms will be provided. Part of the challenge is terminology and contrasting display methods of geoscience and operations/drilling groups. Both approaches are necessary and investigated in the interactive exercises which will form an essential component of the course.

Natural Fracture Systems and Fractured Hydrocarbon Accumulations, Mechanics and Management

Instructor: Dr Dirk Nieuwland (NewTec International)

Unconventional hydrocarbon systems require unconventional approaches to decide on drilling locations and development techniques. The information contained in natural fracture systems can be used to support the drilling and well stimulation technique for the development of unconventional hydrocarbon systems such as shale gas. This short course is based on geomechanics as a technique that can be used to understand and to develop unconventional hydrocarbon systems such as shale gas systems, and fractured crystalline basement, where conventional logging and seismic systems are inadequate.

3D Modelling of Naturally Fractured Reservoirs

Instructor: Dr Tim Wynn (TRACS International Ltd)

Reservoir modelling for field development planning is a well-accepted process but its application to fractured reservoirs requires specific considerations which are less commonly known. This course briefly describes a practical methodology for building 3D static ('geocellular') reservoir models for naturally fractured reservoirs using standard modelling software, covering such considerations.

The issues addressed include the integration of log, core and seismic data, the process of defining and building the static reservoir model itself, and the creation of output in a form appropriate for dynamic modelling using dual porosity reservoir simulators where appropriate.

More complex workflows using discrete fracture networks will also be summarised, as will general issues of fracture description, uncertainty-handling and developing and managing fractured reservoirs.

Deepwater Reservoirs: Exploration and Production Concepts

Instructor: Prof. Dorrik Stow (Heriot-Watt University)

Sandstones deposited in deep marine environments form important hydrocarbon reservoirs in many basins around the world. Interbedded mudstones can be important as source rocks, as well as acting as barriers, baffles and seals. Deepwater reservoirs are currently the principal target for oil and gas exploration, with over 1600 existing turbidite fields and plays.

Reservoir Model Design: How to Build Good Reservoir Models

Instructors: Dr Mark Bentley (AGR TRACS International) and Prof. Philip Ringrose (Equinor)

This short course will provide an introduction to reservoir model design, covering the following main design elements:

• Model purpose;
• The rock model;
• The property model;
• Model scaling;
• Handling uncertainty.