THE PRINCIPLES OF MONTE CARLO SIMULATION
Lecture One:
Overview
•Numerical Modeling
•Uncertainty
•Language of Probability
•Transfer of Uncertainty
•Decision Making
•Plan for the Course
Course Preparation
• The course was prepared by the Centre for Computational Geostatistics
(CCG), a research group at the University of Alberta
• CCG directed by Prof. Clayton V. Deutsch
• Course preparation by C. Deutsch team of graduate students:
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Oy Leuangthong
Hanh Nguyen
Karl Norrena
Julian Ortiz
Bora Oz
Michael Pyrcz
Stefan Zanon
• Excellent first attempt at course on Monte Carlo Simulation (MCS)
• Key concepts are explained with a focus on ultimate practical application
and a minimum of unnecessary mathematical development
Background
• Course is for anyone interested in Monte Carlo Simulation
• The focus is on fundamental principles of:
– Monte Carlo simulation,
– Uncertainty assessment, and
– Decision-making
• The domain of application is nominally upstream oil and gas industry
• Participants should leave the course with
– Appreciation for the place of Monte Carlo Simulation (MCS) in support of
optimal decision-making,
– Knowledge of the implicit limitations of MCS, and
– Background knowledge necessary to put MCS to practice with latest
software tools.
• This course effectively conveys selected concepts from the large area
of Monte Carlo analysis
• Basic courses in statistics and mathematics would make this class
easier, but stay awake and we will cover everything
Numerical Modeling
• There has been a major revolution in science and reasoning over the last 100
years that has largely gone unnoticed
• Historically, science involved (1) extensive data collection and physical
experimentation, then (2) deduction of laws and relationships consistent
with the data
• Now, science is much more concerned with (1) understanding and
quantifying physical laws, and (2) numerical modeling for inference
• We now accept that uncertainty cannot be removed (account of E. Teller’s
statement of how science has changed)
• In general:
– Numerical modeling has become more important than physical experimentation,
– Inductive reasoning has become more popular than deductive reasoning,
– Uncertainty is quantified and managed rather than ignored.
• Numerical modeling is ubiquitous in modern
science and engineering (virtually all design
is on the computer…)
Stochastic Reservoir Modeling
A comparison between reality and a numerical model
Reality
Distribution of Rock/Fluid Properties
single true distribution
Recovery Process
actual process implemented
Field Response
Single true response
Model
Distribution of the Rock/Fluid Properties
multiple stochastic models
Recovery Process
numerical model of process
Field Response
Distribution of
possible responses
Some Comments on Uncertainty
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Uncertainty exists because of incomplete data:
– Cannot be avoided,
– Can be reduced by consideration of all relevant data, and
– Can be managed
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The main steps we will propose are:
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Conceptualize a model for the process
Quantify the uncertainty in each of the inputs
Transfer the input uncertainty through to output uncertainty
Make optimal decision in presence of uncertainty
Let’s look at a nice little example (see pre-course reading
material)
An Application to Miscible
Flood Design
Srivastava, 1990
The decision to be optimized:
How much solvent should be injected?
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The answer depends on the connected pore volume.
The uncertainty in the connected pore volume can be quantified with geostatistical
simulation.
The loss function is a function of the cost of solvent and the oil price.
Continuity of the Sand
• Assessment of the connected pore volume requires
numerical models of the reservoir
• The most important input for construction of numerical
reservoir models is a variogram assessment of spatial
continuity:
Numerical Reservoir Models
• Geostatistical procedures are
used to build reservoir
models:
– 3-D models
– Honor all available data
– Reflect appropriate pattern of
continuity
• Most important input source
of uncertainty for this little
problem
Transfer Function
• Full transfer function would be flow simulation to evaluate connected
reservoir accessible to miscible flood
• A simple transfer function, that is, a random walk simulator to
determine connected reservoir was considered
What is Connected?
• Cannot inject a stochastic amount of solvent
• Decision requires a single value to be decided upon
• What value should be retained?
Loss Function
• Consequences of injecting too much (cost of wasted solvent)
• Consequences of not injecting enough (cost of lost revenue)
• Determine optimal amount that generates the maximum expected
revenue or minimum expected loss
The Answer
• Depends on the relative cost of solvent and price of oil
• Makes intuitive sense
• Provides a quantitative approach to balance factors that have
historically been addressed by “feel”
Plan for the Course
• Series of Seven Lectures:
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Probability Distributions
Statistical Models and Stationarity
Monte Carlo Simulation
Dependence and Multivariate Distributions
Problem Formulation, Implementation Details, and Validation
Transfer of Uncertainty
Decision Making
• Followed by more details on geostatistics
Review of Main Points
• Numerical modeling has largely replaced physical
experimentation
• Inference has largely replaced deduction
• Uncertainty exists because of our incomplete knowledge
• Monte Carlo Simulation (MCS) is the key technology to
quantify uncertainty
• Must also quantify consequences of making a mistake for
optimal decision making