Geostatistical Methods for Reservoir Geophysics

159 Pages·2017·9.59 MB·English

by  Leonardo Azevedo

Advances in Oil and Gas Exploration & Production
Leonardo Azevedo
Amílcar Soares
Geostatistical
Methods for
Reservoir
Geophysics
Advances in Oil and Gas Exploration &
Production
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Leonardo Azevedo Amílcar Soares
(cid:129)
Geostatistical Methods
for Reservoir Geophysics
123
Leonardo Azevedo Amílcar Soares
Instituto Superior Tecnico Instituto Superior Tecnico
CERENA CERENA
Lisboa Lisboa
Portugal Portugal
ISSN 2509-372X ISSN 2509-3738 (electronic)
Advances in Oil andGasExploration & Production
ISBN978-3-319-53200-4 ISBN978-3-319-53201-1 (eBook)
DOI 10.1007/978-3-319-53201-1
LibraryofCongressControlNumber:2017930189
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Leonardo Azevedo dedicates the book to his family,
friends and all professors who inspired him.
Amílcar Soares dedicates the book to his students.
Preface
The main motivation for writing this book is to report on an existing
repertoire of geostatistical methods for handling the integration of geo-
physicalinformation inreservoir modelingandfor presenting the successful
case studies that validate them.
Geostatistical methods were introduced in the 1960s (Matheron 1965) as
tools for coping with large amount of similar data and to characterize, for
example, grades dispersion in mineral deposits (David 1977; Journel and
Huijbreghts 1978). When geostatistical methods become popular for oil
reservoir characterization in the 1980s (Deutsch and Journel 1992), the lack
of well data made it necessary for another type of data integration in
geostatistical methods. Hence, a new paradigm—one based on data inte-
gration—developed in geostatistical methods though joint simulations and
stochastic sequential simulations with soft data.
Since the beginning of this century, oil and gas discoveries have been
mainly in deep and ultra-deep waters. Getting to these reservoirs involves
ever-higher costs for drilling and well data sampling; it also involves
increasedinvestmentinresearchanddevelopment(R&D)tosuccessfullyuse
cheaperandmoreefficientgeophysicalexplorationmethods.Therecenthigh
qualityofgeophysicaldata,particularlyreflectionseismicdata,representeda
breakthroughinreservoirmodelingandcharacterization.However,theuseof
3D and 4D seismic data has been a real challenge for geostatistical data
integration methods.
Using seismic reflection data, stochastic seismic inversion methods are
playing an important role in the characterization of oil and gas reservoirs,
which can basically be divided into two groups: the first based on the lin-
earized Bayesian approach to seismic inversion (Buland and Omre 2003;
Tarantola 2005); the second based on geostatistical inversion methods that
are essentially stochastic sequential simulations and optimization processes
like genetic algorithms and simulated annealing (Bortolli et al. 1993; Haas
and Dubrule 1994; Soares et al. 2007).
This book focuses on the geostatistical inversion methods, with Chap. 2
providing an overview of elementary geostatistics. Stochastic simulations
and joint simulations are presented in Chap. 3, with the different versions
used in the inversion approaches: joint simulation with joint distributions to
deal with multivariate inversion and direct inversion and simulation with
point distributions to access the data uncertainty.
vii
viii Preface
In Chap. 4 we develop seismic inversion methods—acoustic, elastic and
amplitude versus angle (AVA)—within the geostatistical framework.
Chapter 5 encompasses the direct inversion of porosity, facies and rock
physics models (RPM). Chapter 6 focuses on other methods of geophysical
integration, such as joint electromagnetic and seismic inversion and the
integrationofseismicinhistorymatchingprocesses:thatis,theintegrationof
seismic and dynamic production data in numerical reservoir models.
Thisbookisanatural extensionand asummary oftheLisbon University
Technical Institute’s (IST—Instituto Superior Técnico) Master of Science
programinPetroleumEngineeringnotesonreservoircharacterizationaswell
asthoseoftheshortcoursesgivenatotherschoolsandoilcompanies.Weare
indebted to all the students whose critiques enriched this book.
The seismic inversion methods presented here were developed and
implemented at the Centre for Modeling Petroleum Reservoirs research
Centre, which is now the Petroleum Group of the Centre for Natural
Resources and Environmental Research (CERENA—Centro de Recursos
NaturaiseAmbiente).WewouldliketoexpressourthankstoJeanPaulDiet,
who introduced us to the concept of geostatistical inversion and helped
securefundingfromCGG.WewouldalsoliketothankThierryColleau,who
helped steer us in the right direction at the outset, and António Costa Silva,
Luís Guerreiro and Carlos Maciel of Partex Oil and Gas, for their encour-
agement and support and for helping us find real applications for it in the
Middle East.
PetrobrasgeophysicistsGuentherNeto,LuciaDillonandEvaldoMundim
brought new insights and theirsubstantial experiencetothese methods.Last
butnotleast,wewouldliketoexpressourgratitudetothemanyresearchers
attheCentreforModelingPetroleumReservoir(CMRP)andourcolleagues
and friends, especially Maria João Pereira, Ana Horta, Rúben Nunes, Pedro
CorreiaandHugoCaetano,whohavehelpeddevelopthesemethodsoverthe
past15yearswithideasdevelopedinthecourseofmanyprojects,thesesand
publications.
Finally, a special acknowledge to Ângela Pereira, Catarina Marques and
Pedro Pereira for the detailed revision of the manuscript and the valuable
recommendationsandRúbenNunesforalltheprogrammingrelatedwiththe
DSS algorithm.
Lisboa, Portugal Leonardo Azevedo
Amílcar Soares
Contents
1 Introduction—Geostatistical Methods for Integrating
Seismic Reflection Data into Subsurface Earth Models. . . . . 1
1.1 Spatial Resolution Gap. . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Seismic Inversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Fundamental Geostatistical Tools for Data Integration. . . . . 5
2.1 Spatial Continuity Patterns Analysis and Modeling. . . . . . 6
2.1.1 Bi-point Statistics . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Complex Morphologic Patterns:
Auxiliary and Reference Images . . . . . . . . . . . . . 8
2.1.3 Spatial Random Fields. . . . . . . . . . . . . . . . . . . . 8
2.1.4 Variograms and Spatial Covariances . . . . . . . . . . 9
2.1.5 Spatial Representativeness of the Variogram. . . . . 12
2.1.6 Spatial Continuity for Multivariate Systems . . . . . 13
2.1.7 Variogram Modeling Workflow . . . . . . . . . . . . . 15
2.1.8 Theoretical Variogram Models . . . . . . . . . . . . . . 16
2.1.9 Linear Combinations of Variogram Models:
Imbricated Structures. . . . . . . . . . . . . . . . . . . . . 18
2.1.10 Co-regionalized Models
of Multivariate Systems . . . . . . . . . . . . . . . . . . . 23
2.2 Estimation Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.1 Linear Estimation of Local Statistics . . . . . . . . . . 24
2.2.2 Probabilistic Model of the Geostatistical
Linear Estimator . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Kriging Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.1 Kriging System Resolution. . . . . . . . . . . . . . . . . 27
2.4 Linear Estimation of Non-stationary Phenomena:
Simple Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Co-kriging Estimate. . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.6 Co-estimation with a Secondary Variable in a Much
Denser Sample Grid: Collocated Co-kriging . . . . . . . . . . 31
2.7 Estimation of Local Probability Distribution Functions. . . 31
2.7.1 Gaussian Transform of the Experimental Data. . . . 32
2.8 Estimation of Categorical Variables . . . . . . . . . . . . . . . . 33
3 Simulation Models of Physical Phenomena
in Earth Sciences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1 Stochastic Simulation Models . . . . . . . . . . . . . . . . . . . . 37
3.2 Sequential Simulation Models. . . . . . . . . . . . . . . . . . . . 39
ix
x Contents
3.3 Sequential Gaussian Simulation. . . . . . . . . . . . . . . . . . . 39
3.4 Direct Sequential Simulation from Experimental
Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.1 Direct Sequential Simulation. . . . . . . . . . . . . . . . 41
3.4.2 Direct Sequential Co-simulation . . . . . . . . . . . . . 42
3.4.3 Stochastic Sequential Co-simulation
with Joint Probability Distributions . . . . . . . . . . . 44
3.4.4 Stochastic Simulation with Uncertain Data: DSS
with Point Probability Distributions. . . . . . . . . . . 46
3.5 Simulation of Categorical Variables. . . . . . . . . . . . . . . . 47
3.5.1 Indicator Simulation . . . . . . . . . . . . . . . . . . . . . 47
3.5.2 Alternative Simulation Methods
for Categorical Variables . . . . . . . . . . . . . . . . . . 49
3.5.3 High-Order Stochastic Simulation
of Categorical Variables. . . . . . . . . . . . . . . . . . . 49
4 Integration of Geophysical Data for Reservoir Modeling
and Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1 Seismic Inversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 Bayesian Framework for Integrating Seismic
Reflection Data into Subsurface Earth Models. . . . . . . . . 54
4.3 Iterative Geostatistical Seismic Inversion
Methodologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.1 Frequency Domain of Geostatistical
Seismic Inversion . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.2 Trace-by-Trace Geostatistical Seismic
Inversion Methodologies . . . . . . . . . . . . . . . . . . 57
4.3.3 Global Geostatistical Seismic
Inversion Methodologies . . . . . . . . . . . . . . . . . . 58
4.3.4 Global Geostatistical Acoustic Inversion. . . . . . . . 60
4.3.5 Global Geostatistical Elastic Inversion . . . . . . . . . 62
4.3.6 Geostatistical Seismic AVA Inversion . . . . . . . . . 65
4.3.7 Application Example with Geostatistical
Seismic AVA Inversion. . . . . . . . . . . . . . . . . . . 72
4.3.8 Seismic Inversion with Structural
Local Models . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.4 Integration of Low-Frequency Models
into Geostatistical Seismic Inverse Methodologies . . . . . . 86
5 Deriving Petrophysical Properties with Seismic Inversion. . . 91
5.1 Characterization of Petrophysical Properties
Based on Acoustic and Velocity Models. . . . . . . . . . . . . 91
5.2 Direct Inversion of Porosity Models. . . . . . . . . . . . . . . . 92
5.3 Geostatistical Seismic Inversion Directly
for Petrophysical Properties. . . . . . . . . . . . . . . . . . . . . . 95
5.3.1 Geostatistical Seismic AVA Inversion
to Facies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3.2 Application Examples with Geostatistical
Seismic AVA Inversion Directly to Facies . . . . . . 99
5.4 Integration of Rock Physics Models
into Geostatistical Seismic Inversion. . . . . . . . . . . . . . . . 106