Global Net-to-Gross Uncertainty Assessment at Reservoir Appraisal Stage

162 Pages·2007·2.99 MB·English

by  Amisha Maharaja

GLOBAL NET-TO-GROSS UNCERTAINTY ASSESSMENT
AT RESERVOIR APPRAISAL STAGE
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF ENERGY
RESOURCES ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Amisha Maharaja
June 2007
(cid:13)c Copyright by Amisha Maharaja 2007
All Rights Reserved
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I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
(Andre Journel) Principal Adviser
I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
(Jef Caers)
I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
(Tapan Mukerji)
Approved for the University Committee on Graduate Studies.
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Abstract
Net-to-gross (NTG) is the fraction of reservoir volume occupied by hydrocarbon-
bearing rocks. It is a global attribute and as such no replicate of it can be found over
the reservoir. An estimate of global NTG is obtained from wells, but this estimate
depends heavily on the location of the few wells available. If these wells were located
elsewhere the NTG estimate would have been different. Wells at reservoir appraisal
stage are few because they are expensive, and they tend to be preferentially located
in high pay zones. Consequently, any naive estimate of NTG from these wells is likely
to over-estimate the global NTG.
Since new wells cannot be drilled from the real reservoir to assess uncertainty,
synthetic wells are re-sampled from stochastic realizations of reservoir facies which
are conditioned to all available data. Stochastic realizations, however, require a prior
knowledge of the structural model and of a global NTG, which are both highly uncer-
tain at appraisal stage. Hence, we propose to consider alternative structural models,
and to randomize the global NTG value corresponding to each structural model. The
structural model is randomized by considering alternate geological interpretations
that fit all existing data. The global NTG associated with each particular geolog-
ical interpretation is randomized by considering a probability distribution of global
NTG value, which represents both the possible range of NTG values and the prior
probability of those NTG values. Such a distribution can be obtained by pooling
together NTG values of previously discovered reservoirs that are deemed analogous
to the newly discovered reservoir. This prior probability distribution is then updated
into a posterior probability distribution given the NTG estimate observed from the
actual reservoir data.
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To perform this update, the prior NTG distribution is first discretized into M
classes. For each class a representative facies realization is simulated from each geo-
logical scenario. All such realizations must honor all available data. Synthetic data
sets are re-sampled from this realization by following the initial drilling strategy. The
NTG estimates computed from these synthetic data sets provide the likelihood of ob-
serving the initial NTG estimate in a simulated reservoir with that global NTG. Then
using Bayes rule, the prior probability of the global reservoir NTG being in any given
class m is updated given the observed NTG estimate. Repeating this procedure for
all prior global NTG classes provides the posterior probability distribution of global
NTG. This posterior global NTG distribution is a model of uncertainty specific to the
reservoir under study and to a particular geological scenario. Posterior distributions
correspondingtodifferentgeologicalscenarioscanbecombinedintoasingleposterior,
but this calls for a prior probability of occurence of each scenario.
Tests on a synthetic reservoir reveal that both initial NTG estimate and prior
NTG distribution have a large impact on the posterior NTG distribution. A biased
NTG estimate would result in non-representative posterior uncertainty intervals. Due
to its exhaustive coverage, incorporating seismic data helps correct the bias due to
preferential well location. In addition, using a prior NTG distribution based on
relevant historical information helps obtaining more representative posterior NTG
uncertainty models. Posterior statistics also depend on the discretization of the prior
NTG distribution. An early sensitivity analysis should be performed to determine
the appropriate level of discretization.
Application of the workflow to an actual deep-water reservoir showed that the
impact of the geological scenario on the posterior NTG distribution is larger when
the facies geometries are very different. The range of the posterior distribution is
always smaller than that of the prior distribution. The shape of the prior distribution
impacts the posterior probability. With each additional well the posterior uncertainty
intervals shrink, indicating that more data reduces uncertainty. The case study also
revealed challenges encountered in practice, such as re-sampling from domains of
varying thickness and deducing facies proportions from a global NTG value in the
multiple facies case.
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The proposed workflow is demanding because it requires more decisions and mod-
eling effort than any of the existing approaches. But in return it provides more
informed models of NTG uncertainty reflecting a company’s geological expertise and
historical information. These valuable sources of information must be incorporated
whenassessingNTGuncertainty,especiallyatappraisalstagewhenwelldataissparse
and the stakes are high. There is no such thing as an objective or true model of un-
certainty since each model is necessarily a result of multiple subjective decisions that
go into building that model.
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Acknowledgements
First and foremost, my deepest gratitude goes to Prof. Andr´e Journel, who has been
my advisor throughout my graduate studies. I was trained as a geologist, but had
a penchant for numbers. His article on stochastic modeling and geostatistics in an
AAPG publication inspired me to pursue a degree in geostatistics at Stanford. It has
been an honor to have him as my advisor. I greatly appreciate his research guidance
and mentorship.
Second, I would like to thank Prof. Jef Caers, who has had a strong influence
on me since the very beginning. He is one of the best teachers I have ever had. His
comments and suggestions for improving my Ph.D. research were greatly appreciated.
This research would not have been possible without the financial support of
Chevron Energy Technology Corporation. I am also thankful to Chevron for pro-
viding the data set for my thesis. Special thanks goes to Dr. Sebastien Strebelle for
his advise, constant support, and enthusiam.
I would like to acknowledge the pivotal role that Dr. Guillaume Caumon played
in this research, while he was a post-doc at Stanford. His advise and tutoring with
Gocad during my two month stay in Nancy has been essential for the completion of
this thesis.
I would like to thank all my professors at Stanford, especially Steve Graham and
the ERE professors - Margot Gerritsen, Roland Horne, Lou Durlofsky, Tony Kovscek,
and Khalid Aziz. I am honored to have learnt petroleum engineering from such a
world class faculty. I am also thankful to Ginni Savalli and Thuy Nguyen of the ERE
department; their hard work and dedication has ensured a smooth stay at Stanford.
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The SCRF research group has been my home for the past five years. It has pro-
vided a thriving environment for research and passionate discussions. I have met
many wonderful and talented people here during these years, and it has been a priv-
ilege to have been a part of this group. Melton Hows, Sunderrajan Krishnan, Joe
Voelker, Burch Arpat, Tuanfeng Zhang, Jenya Polyakova have all enriched my Stan-
ford experience. Special thanks goes to Jianbing Wu and Nicolas Remy for their help
and guidance with SGeMS.
I would especially like to thank my friends Scarlet Castro, Lisa Stright, and Whit-
ney Trainor for their friendships. Each one of you are amazing individuals and I have
been fortunate to have met you.
Special thanks goes to my dear friend and mentor, Minoo Mehta, who has encour-
aged me to fly higher and push my boundaries. I would not have been at Stanford
without his encouragement and support.
My love and gratitude goes to my family, especially to my parents, Chetna and
Dipak Maharaja. I owe my academic achievement to their love and efforts towards
my education and development since my first day at school. I thank my brother Arpit
for his love and support. I have been lucky to have four loving grandparents, who
often have had more faith in me than I did myself. I will especially miss Sudha ba
and Shanti dada (daddu), both of whom I lost during the last year of my Ph.D. To
my parents and grandparents, I dedicate this thesis.
I would also like to thank the Boucher family for their love and companionship.
We have had some really great times while hiking, biking, skiing, snowshoeing and
camping together. I am fortunate to have such a wonderful new family and I look
forward to many more good times ahead.
Last, but not the least, my deepest love goes to Alexandre Boucher, who has been
my partner for most of my time at Stanford, and luckily for me, will be my partner
for life. He has been there for me, during the ups and the downs, and I thank him
for his steady love, support and encouragement.
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Contents
Abstract v
Acknowledgements viii
1 Global uncertainty assessment 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Workflow for NTG Uncertainty Assessment . . . . . . . . . . . . . . . 7
1.3.1 Net-to-gross estimation . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Building geological scenarios . . . . . . . . . . . . . . . . . . . 12
1.3.3 Prior net-to-gross distribution . . . . . . . . . . . . . . . . . . 13
1.3.4 Spatial bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.5 Update prior NTG distribution . . . . . . . . . . . . . . . . . 15
2 Workflow testing on a synthetic data set 18
2.1 The Stanford VI reservoir runs . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.1 Impact of the initial NTG estimate . . . . . . . . . . . . . . . 22
2.2.2 Impact of the prior NTG distribution . . . . . . . . . . . . . . 23
2.2.3 Impact of the re-sampling strategy . . . . . . . . . . . . . . . 24
2.2.4 Impact of seismic data . . . . . . . . . . . . . . . . . . . . . . 25
2.2.5 Impact of discretization on posterior statistics . . . . . . . . . 26
2.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
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