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

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

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

(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. )

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).

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

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

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:

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

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

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 Software requirements: MS Power Point 2002 or later, Flash Player 6.0 Estimated time to complete: 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 http://www.learningjournals.net. TASKS PROGRAM EXERCISE LINKS AND TIPS SUMMARY

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