1. Computing Oil Reserves Using Statistical Distribution of Porosities
Author: Jon Kleppe
Assistant producer: Per Jørgen Dahl Svendsen, Ole Johan Storli

2. Reservoar description
Introduction
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
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
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
SUMMARY
Reservoar description
Assign porosity
Reservoar simulation
Tasks
Water saturation
HCPV
Links and tips
Program exercise
Summary

3. Description of reservoir
INTRODUCTION
RESERVOAR DESCRIPTION
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
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
SUMMARY

4. (Source : Reservoir Characterization Research and Consulting, Inc. )
Reservoar simulation
INTRODUCTION
RESERVOAR DESCRIPTION
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:
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
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
SUMMARY
Here is an example of a water saturation map taken from a reservoir simulator
(Source : Reservoir Characterization Research and Consulting, Inc. )

5. HCPV Φ Sw Tasks Step1 Step2 Step3 Step4
INTRODUCTION
RESERVOAR DESCRIPTION
The assignment in this module is to compute the Hydro Carbon Pore Volume (HCPV) for the imaginary reservoir described earlier.
The following tasks should be executed:
RESERVOAR SIMULATION
Assign porosity
TASKS
Water saturation
HCPV
Step1
PROGRAM EXERCISE
LINKS AND TIPS
Divide the reservoir into a number of blocks
SUMMARY
Step2
Assign a porosity to each block in
accordance with the log-normal
distribution function.
HCPV Sw Φ
Step3
Compute water saturation for each
block by the equation presented
earlier.
Step4
Compute hydrocarbon pore volume (HCPV).

6. Tasks Water saturation: The dividing of the reservoir:
INTRODUCTION
RESERVOAR DESCRIPTION
The dividing of the reservoir:
The dividing of the reservoar should not be a big problem, just write a DO-loop that divides the reservoir into blocks.
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.
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.
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).
Water saturation:
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.
The water saturation for each block can then be computed based on the randomized porosities.
For each block, Sw should be computed with:
HCPV
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).
To compute the HCPV for a number of blocks we just sum all of the blocks and use:
RESERVOAR SIMULATION
Assign porosity
TASKS
Water saturation
HCPV
PROGRAM EXERCISE
LINKS AND TIPS
SUMMARY

7. mean=0,2 =0,1 (standard deviation) max =0,5 min=0,05
Program exercise
INTRODUCTION
RESERVOAR DESCRIPTION
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 NAG-routine G05DEF (see naghelp for description). Then, the program should compute water saturation for each block, and finally calculate the hydrocarbon pore volume (HCPV) .
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:
Run the program for N=1, N=2, N=5, and N=10
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
SUMMARY
mean=0,2 =0,1 (standard deviation)
max =0,5 min=0,05

8. Links and tips for the exercise
INTRODUCTION
RESERVOAR DESCRIPTION
Tips
-The nag routine demands that input is declared with double presicion, i.e. REAL*8
-Remember to check the limits for the porosities, use an if structure to verify that   [0.05, 0,5]
-The NAG routine returns the values (porosities) exponentially, use DLOG to return the values to normal numbers
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
SUMMARY
Links:
Websites:
Professional Programmer's Guide to Fortran77
Programming in Fortran77
Introduction to fortran:
The whole exercise in printable fromat:

9. Summary Be able to translate a problem to Fortran code
Subsequent to this module you should:
INTRODUCTION
Summary
RESERVOAR DESCRIPTION
Be able to translate a problem to Fortran code
Write and handle DO-loops
Know how to use NAG routines
Know the conditional statements and use the IF structures
RESERVOAR SIMULATION
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
SUMMARY

10. References INTRODUCTION RESERVOAR DESCRIPTION
W. H. Preuss, et al., “Numerical Recipes in Fortran”,
2nd edition, Cambridge University Press (1992)
References
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
References to the textbook :
Distribution function: page 604
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
SUMMARY

11. About this module
INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
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
Topic discipline:
Level: 2
Prerequisites: None
Learning goals: Develop problem solution skills using computers and numerical methods
Size in megabytes: 0.9 MB
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Copyright information: The author has copyright to the module and use of the content must be in agreement with the responsible author or in agreement with
TASKS
PROGRAM EXERCISE
LINKS AND TIPS
SUMMARY

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INTRODUCTION
RESERVOAR DESCRIPTION
RESERVOAR SIMULATION
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