Transcript Slide 1

Computing Oil Reserves Using
Statistical Distribution of Porosities
Author: Jon Kleppe
Assistant producer: Per Jørgen Dahl Svendsen, Ole Johan Storli
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Computing Oil Reserves Using Statistical Distribution of Porosities
Introduction
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
Fortran elements in this module
•Use of nag library
•Input & Output
•Loops
Learning goals
•
Review of methods for numerical
integration
•
Develop problem solution skills using
computers and numerical methods
•
Develop programming skills using
FORTRAN
SUMMARY
Reservoar
description
Assign porosity
Tasks
Reservoar
simulation
Water saturation
HCPV
Links and tips
Program exercise
Summary
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Computing Oil Reserves Using Statistical Distribution of Porosities
Description of reservoir
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
An oil reservoir extends over an area of 2 km x 2 km and has a thickness of 100
m. The reservoir has an initial water saturation which depends on the porosity,
and the remaining of the pores are filled with oil.
The porosities are different in each block, and will make the water saturation
(and more important, the oil saturation) differ from block to block
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Computing Oil Reserves Using Statistical Distribution of Porosities
Reservoar simulation
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
Based on well logs and core tests in the lab, it has been found that the
porosity distribution is log-normal, and that the water saturation varies
according to the following equation:
S w  0,415  1,37  1,481 2
So  1  S w
LINKS AND TIPS
SUMMARY
All reservoir simulators uses a similar procedure when assigning porosity
and permeability to different blocks. You take all the data you have (logs,
welltesting, core testing etc) in a field, and try to match it with a
distribution function.
Ironically, since the amount of information accumulates with time, the
simulator will be as close to the reality as possible when the field is shut
down
Here is an example of a water
saturation map taken from a reservoir
simulator
(Source : Reservoir Characterization
Research and Consulting, Inc. )
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Computing Oil Reserves Using Statistical Distribution of Porosities
Tasks
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
The assignment in this module is to compute the Hydro
Carbon Pore Volume (HCPV) for the imaginary reservoir
described earlier.
TASKS
Assign porosity
The following tasks should be executed:
Water saturation
HCPV
PROGRAM EXERCISE
Step1
Divide the reservoir into a number of
blocks
LINKS AND TIPS
SUMMARY
Step2
Assign a porosity to each block in
accordance with the log-normal
distribution function.
Sw Φ
HCPV
Step3
Compute water saturation for each
block by the equation presented
earlier.
Step4
Compute hydrocarbon pore volume (HCPV).
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Φ
Sw
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Computing Oil Reserves Using Statistical Distribution of Porosities
Tasks
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
TASKS
Assign porosity
The dividing of the reservoir:
Water saturation:
The dividing of the reservoar should not be a big
problem, just write a DO-loop that divides the reservoir
into blocks.
The water saturation will determine how much
hydrocarbons we can expect from a given reservoir.
In this problem we do not separate oil and gas, we
use the term hydrocarbons to include both.
Water saturation
HCPV
PROGRAM EXERCISE
LINKS AND TIPS
SUMMARY
The water saturation for each block can then be
computed based on the randomized porosities.
Assign porosity:
The porosity is to be distributed to each block by a
random number generator. To distribute porosities
randomly, we will call a NAG routine called G05DEF.
To see how this NAG routine works and which input
data you need, simply type naghelp G05DEF in the
terminal window. Upper and lower limit is to be set to
0.5 and 0.05 respectively.
For each block, Sw should be computed with:
2
w
Because the porositites are assigned by a random
number generator, the HCPV will be different each
time. By repeating the procedure many times, we may
obtain a measure of the uncertainty in the reserves of
the reservoir.
To compute the hydro carbon pore volume for a
given reservoir with known boundaries, we simply
multiply the volume, the porosity and the fraction that
contains hydrocarbons (1-Sw).
S  0,4151,37  1,481
HCPV
To compute the HCPV for a number of blocks we just
sum all of the blocks and use:
i NxN
In particular, it is interesting to see how the reserves
are affected by the number of blocks that the reservoir
is divided into (i.e. the number of realizations).
HCPV 
(1 S
) ixyh
w i
i1

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Computing Oil Reserves Using Statistical Distribution of Porosities
Program exercise
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
Make a FORTRAN program that divides the reservoir into N x N
blocks. The program should then distribute porosities to N x N blocks in
accordance with a log-normal distribution function by calling the NAGroutine G05DEF (see naghelp for description). Then, the program
should compute water saturation for each block, and finally calculate
the hydrocarbon pore volume (HCPV) .
SUMMARY
For each set of N x N blocks, the calculations are to be repeated 200
times, i.e. 200 realizations, and the average HCPV should be plotted
vs. number of realizations. Also, plot the frequency distribution curves
for porosity and HCPV.
Use the following parameters for the porosity distribution curve:
mean=0,2
=0,1 (standard deviation)
max =0,5
min=0,05
Run the program for N=1, N=2, N=5, and N=10
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Computing Oil Reserves Using Statistical Distribution of Porosities
Links and tips for the exercise
INTRODUCTION
RESERVOAR DESCRIPTION
Tips
RESERVOAR SIMULATION
-The nag routine demands that input is declared with double presicion,
i.e. REAL*8
TASKS
PROGRAM EXERCISE
-Remember to check the limits for the porosities, use an if structure to
verify that   [0.05, 0,5]
LINKS AND TIPS
SUMMARY
-The NAG routine returns the values (porosities) exponentially, use
DLOG to return the values to normal numbers
Links:
Introduction to fortran:
The whole exercise in printable fromat:
Websites:
•Professional Programmer's Guide to Fortran77
•Programming in Fortran77
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Computing Oil Reserves Using Statistical Distribution of Porosities
Summary
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
Subsequent to this module you should:
TASKS
PROGRAM EXERCISE
•Be able to translate a problem to Fortran code
LINKS AND TIPS
SUMMARY
•Write and handle DO-loops
•Know how to use NAG routines
•Know the conditional statements and use the IF structures
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Computing Oil Reserves Using Statistical Distribution of Porosities
References
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
W. H. Preuss, et al., “Numerical Recipes in Fortran”,
2nd edition, Cambridge University Press (1992)
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SUMMARY
References to the textbook :
Distribution function:
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page 604
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Computing Oil Reserves Using Statistical Distribution of Porosities
About this module
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
Title:
Computing Oil Reserves Using Statistical Distribution of Porosities
Teacher(s):
Professor Jon Kleppe
Assistant(s):
Per Jørgen Dahl Svendsen, Ole Johan Storli
Abstract:
Provide a good background for solving problems within petroleum related topics |
using numerical methods
4 keywords:
Nag Routines, Statistical Distribution, Fortran
SUMMARY
Topic discipline:
Level:
2
Prerequisites:
None
Learning goals:
Develop problem solution skills using computers and numerical methods
Size in megabytes:
0.9 MB
Software requirements:
MS Power Point 2002 or later, Flash Player 6.0
Estimated time to complete:
Copyright information:
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The author has copyright to the module and use of the content must be in
agreement with the responsible author or in agreement with
http://www.learningjournals.net.
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Computing Oil Reserves Using Statistical Distribution of Porosities
INTRODUCTION
RESERVOAR DESCRIPTION
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TASKS
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