IMPROVED GAS-LIFT OPTIMIZATION BY USING PORTFOLIO THEORY

by

Piyawat Tungtakul

A thesis submitted in partial fulfilment of the requirement for the degree of Master of Engineering in

Offshore Technology and Management

Examination Committee: Dr. Gregory L.F. Chiu (Chairperson) Dr. Thitisak Boonpramote (Co-Chairperson) Dr. Suwat Artichanagorn (Member)

Nationality: Thai Previous Degree: Bachelor of Engineering in Production Engineering King Mongkut's University of Technology North Bangkok, Thailand Scholarship Donor: RTG Fellowship

Asian Institute of Technology School of Engineering and Technology

Thailand May 2010

ii

ACKNOWLEDGEMENTS

First of all, the author was overwhelmed with gratitude and appreciation to Dr. Thitisak Boonpramote, the thesis advisor, for his generosity and valuable guidance to conduct this research study. His constant encouragement throughout the development of this thesis has being a point of inspiration to the author. In addition, much thanks to Dr. Gregory L.F. Chiu and Dr. Suwat Artichanagorn for their kind attention, and worthful suggestions and comments. Moreover, the author is very grateful to RTG for providing excellent scholarship for studying master engineering program in Offshore Technology and Management field at Asian Institute of Technology. The author would like to thank Sirikit oil field (S1)’s staff or PTTEP’s staff; Kitisak Nualchanchai, Chansin Kaewetchawong, Ekasok Kong-im, Natmana Piyawaranon, Kiattisak Malikhow, Perapon Sirijitt, Pongsak Metheethara, Niwat Boonyad, Tongthip Namwong, Naiyana Suaysod, and other staff for providing insight, direction and technical guidance during thesis. Finally, although this thesis touches some parts of the oil and gas business, he hopes that it can be the starting point to understand the real issues involve in the operation part of artificial gas-lift and in aspect of gas-lift allocation optimization. This thesis will not be a success if he was not tutored, advised, and supported by his advisors, S1’s staff, his colleagues and his family.

Piyawat Tungtakul

iii

ABSTRACT

This thesis studies the implementation of improving traditional method by using portfolio selection theory that generates several combination of gas lift injection rate. The objective is to consider each portfolio result with uncertainty that can make better decision than traditional method. The combination is estimated by considering more than one dimension such as the result uncertainty of each combination. The traditional method shows only optimizes production volume whether it can have consistent target or not after selecting the combination and it does not consider in term of the world economic such as oil price, gas cost, etc. If the traditional method (data given by WINGLUE simulation software) is applied by related staff, it is difficult to find the new optimal point by using the existing method, and it cannot tell the different confident level of each combination. As the results from case studies, the use of portfolio theory can guide related person to be aware of the uncertainties involved along with enhancing their efficiency in making good decision in order to gain better optimization of gas lift available than the existing method also the expected target is near the actual value or more consistent. In addition, the fast searching for new optimal point is achieved and can use for economic analysis.

iv

TABLE OF CONTENTS CHAPTER TITLE PAGE

Title Page i Acknowledgements ii Abstract iii Table of Contents iv List of Abbreviations v List of Symbols vi List of Figures vii List of Tables viii List of Appendices ix 1 Introduction 1

1.1 General and problem statement 1 1.2 Objectives 2 1.3 Scopes of work 2

2 Literature Review 3 2.1 Portfolio theory 3 2.2 Gas lift optimization 25

3 Methodology 37 3.1 Data collection, analysis, and preparation 37 3.2 Create the inflow and outflow performance relationship 38 3.3 Generate relationship graph between gas rate and oil rate 39 3.4 Rank and cut method of traditional method based on S1 39 3.5 Construct the traditional method based on S1 40 3.6 Construct the improved traditional method based on S1 42 3.7 Construct the portfolio theory method model 44 3.8 Discussions and conclusions 47

4 Results and discussions 48 4.1 Optimization with traditional method based on S1 52 4.2 Optimization with improved traditional method based on S1 56 4.3 Optimization with portfolio theory method 60

5 Conclusions and Recommendations 68 5.1 Conclusions 68 5.2 Recommendations 71

References 73 Appendixes 75

v

LISTS OF ABBREVIATIONS CAPEX Capital Expenditure NPV Net Present Value OPEX Operated Expenditure IRR Internal Rate of Return DCF Discounted Cash Flow EIA Energy Information Administration EMV Expected Monetary Value FCF Free Cash Flow GA Genetic Algorithm IPE International Petroleum Exchange in London SIMEX Singapore International Monetary Exchange NYMEX New York Mercantile Exchange PV Present Value RO Real Options ROI Return On Investment ROV Real Options Analysis MM Million BBL Barrel STB Stock Tank Barrel USD ($) U.S. Dollar GLPC Gas-Lift Performance Curve SCF Standard cubic feet STD DEV Standard deviation GUF Gas Utility Factor IGUF Incremental Gas Utility Factor WinGLUE Window Gas Lift User Environment EF Efficient Frontier ESP Electric Submersible Pump PCP Progressive Cavity Pump GL Gas-Lift MCS Monte Carlo Simulation CAO Computer-Aided Operation DCS Distributed Control System SCADA Supervisory Control and Data Acquisition RT Risk Tolerance EU Expected Utility CE Certainty equivalent DTA Decision Tree Analysis S1 Sirikit Oil field

vi

LISTS OF SYMBOLS Ei Expected value of well i Xi Weight of well i Cov ij Covariance well i and j Vi Variance of well i Si , σi Standard deviation of well i Qo Net oil production rate, BBL Qg Gas injection rate, MSCF Qw Produced water, BBL Epi Expected value of portfolio i Vpi Variance of portfolio i Pi Probability to occur value i ρij Correlation coefficient between well I and j

vii

LISTS OF FIGURES FIGURE TITLE PAGE

Figure 2.1 Bar chart shows probability distributions of table 2.1 4Figure 2.2 Graph is originated from a great many outcomes 4Figure 2.3 Graph shows the position of portfolio 6Figure 2.4 The distributions of rate of return for four portfolios 7Figure 2.5 The indifference curve 7Figure 2.6 Mr.Nofear is always accept risk whileas Mr.Riskcon does not

like risk 8

Figure 2.7 The more common case but different level of accepted risk 8Figure 2.8 The three indifference curves 8Figure 2.9 The better portfolio is located on efficient frontier 9Figure 2.10 The different value of correlation is between -1 to +1 11Figure 2.11 Many efficient portfolios generate Efficient frontier 13Figure 2.12 The difference selected portfolio, the different risk preference 13Figure 2.13 A decision tree representing all of the permutations of outcomes

for projects A and B 15

Figure 2.14 A plot of Risk vs Reward 16Figure 2.15 Components of Integrated Portfolio Management Approach 17Figure 2.16 The effect of combination of both constraints 19Figure 2.17 The improvement of adding new opportunities 20Figure 2.18 The bar chart shows before and after adding new projects 20Figure 2.19 The same expected NPV but different standard deviation 21Figure 2.20 Sensitivity analysis (Spider chart) 23Figure 2.21 Sensitivity analysis (Tornado chart) 24Figure 2.22 The cumulative probability plot 24Figure 2.23 Day to day optimization cycle 25Figure 2.24 Artificial gas lift are needed for low performance well 27Figure 2.25 Process flow diagram of artificial gas lift 27Figure 2.26 Gaslift performance curve 28Figure 2.27 WinGlue modeling panel 28Figure 2.28 Gas lift performance by WinGlue 28Figure 2.29 Real-Time Gas Lift Control Systems 29Figure 2.30 GLUE table creating by WINGLUE 29Figure 2.31 GLPC in form of production 33Figure 2.32 GLPC in term of economic 33Figure 2.33 Example of gas lift system model 34Figure 2.34 A typical gas lift performance curve 35Figure 2.35 Comparison of the optimum gas injection rates and estimated

gas injection 35

Figure 2.36 Progress of the computation 36Figure 2.37 Sketch of single-well installation 36Figure 3.1 Inflow and Outflow performance curve of gas lift wells 38Figure 3.2 Gas lift performance curve from individual well and the

combination of wells 39

vii

FIGURE TITLE PAGE

Figure 3.3 Flowchart of using traditional method model 41Figure 3.4 Flowchart of using solver option in traditional method 42Figure 3.5 Example of well selection 43Figure 3.6 The difference risk between production and exploration phase 44Figure 3.7 Flowchart of applying portfolio theory model 45Figure 3.8 Efficient frontier are generated from many portfolio 46Figure 4.1 Historical production data from well test results 49Figure 4.2 Rate of Net oil production generated by WinGLUE software 49Figure 4.3 Rate of Produced water generated by WinGLUE software 49Figure 4.4 Graph of oil production generated by WinGLUE software 50Figure 4.5 Graph of Produced water generated by WinGLUE software 50Figure 4.6 Estimated equations for oil production at given gas lift rate 51Figure 4.7 Estimated equations for produced water at given gas lift rate 51Figure 4.8 The estimated gas injection rate each well and estimated total oil

production 54

Figure 4.9 Profit oil and cost gas are used to calculate total return and profit oil

54

Figure 4.10 All the results of maximum production at given different conditions

54

Figure 4.11 All the results of maximum production at given different conditions

55

Figure 4.12 Example of well selection 56Figure 4.13 Illustrates the different optimal point when oil price change Figure 4.14 Low oil price or low case 59Figure 4.15 Normal oil price or base case 59Figure 4.16 High oil price or high case 59Figure 4.17 Two choices of consideration when oil price changes 59Figure 4.18 Gas lift range at minimum significant interval in unit of MSCF 62Figure 4.19 Gas lift range at minimum significant interval in unit of 0 to 1 62Figure 4.20 Results of 20 portfolios after simulating program in MATLAB 62Figure 4.21 Results of 20 portfolios on excel spreadsheet (0-500 MSCF) 63Figure 4.22 Results of 20 portfolios on excel spreadsheet (0-1) 63Figure 4.23 Example of average returns preparation 64Figure 4.24 Example of portfolio variance preparation 64Figure 4.25 No consideration of standard deviation of traditional method 65Figure 4.26 Basic of efficient frontier construction 66Figure 4.27 The results of all portfolios in standard deviation and net oil 66Figure 4.28 The results of all portfolios in standard deviation and average

return 67

viii

LISTS OF TABLES TABLE TITLE PAGE

Table 2.1 Set of predictions between rate of return and likelihood 3Table 2.2 The general information of project A and B 15Table 2.3 All possible cases from diversification of investment 15Table 2.4 List of close-in wells for K-3150 gas-lift compressor preventive

maintenance 31

Table 3.1 Comparison between project investment and gas lift well injection

37

Table 3.2 The important parameters for analysis 38Table 3.3 Data and information of each well 40Table 3.4 Glue Table by WinGLUE software program 40Table 3.5 Portfolios by using MATLAB at given the same objective 46Table 3.6 The comparison between traditional method and new

methodology 47

Table 4.1 The general information of gas lift injection system 48Table 4.2 Constant gas lift available and vary in capacities of water

disposal system 52

Table 4.3 Constant capacities in water disposal system and vary gas lift available

52

Table 5.1 Example of well test schedule 68

ix

LISTS OF APPENDICES

APPENDIX TITLE PAGE

Appendix 1 Flowchart of methodology 75Appendix 2 Five wells test data of 25 latest test 76Appendix 3 Method to construct the traditional method model 81Appendix 4 Method to construct the improved traditional method model 83Appendix 5 Method to construct the portfolio theory method model 86Appendix 6 Program development for weighting gas lift injection rate 89Appendix 7 Comparison between MATLAB and Excel generated model 93Appendix 8 Monte Carlo Simulation 94Appendix 9 To improve the existing procedure 101Appendix 10 Table conclusion of all methods 102Appendix 11 Operating cost 103Appendix 12 Risk preference 104

1

CHAPTER 1

INTRODUCTION

1.1. General and problem statement Normally, when hydrocarbon is produced continuously, reservoir properties changes from initial state such as reduction in pressure, change in fluid properties etc. Eventually, all production wells will become low in performance cannot be produced by primary recovery or natural flow therefore artificial lift which is the method to fill external energy into the well is needed for the well. There are many kinds of artificial lift available to enhance the performance of fluid such as sucker rod pump, hydraulic pump, progressive cavity pump, electrical submersible pump and artificial gas-lift. Some areas, the gas field can produce a lot of gases but small amount of oil. Due to low performance of oil well, artificial gas-lift is the main method that can recover additional amount of oil at high production flow rate. Frequently, many oil companies use produced gas to produce artificial gas-lift by compressing at high pressure in order to lift the oil out from well. Many oil companies have used artificial gas-lift system for a very long time and they have also developed gas-lift system to become real time gas-lift optimization which is the day-to-day optimization process which consists of monitoring, analyzing, predicting, and execution process. In S1 onshore oil field (S1), gas-lift well can produce oil up to around 60-70 %. With limited amount of gas-lift, injecting gas to each well will make different results therefore suitable wells are selected to inject the gas. Injecting too much gas to one well will not make a good result for the whole system. Hence, there is the need to look at the whole system rather than focusing on some wells. Traditional gas lift allocation system in S1 is not considered in terms of economic or gas lift optimization in order to obtain the maximum profit. For example, when oil price, gas cost, and other changes occur, they still produce at constant rate. Moreover, to estimate production from injecting gas into selected well, WinGLUE gas lift software is used to calculate and provide the important value to the related person or staff operating and controlling the gas lift system. As traditional gas lift system focuses on single value at a given maximum net oil, it lacks uncertainty consideration. Due to one value from the estimated result, the staff will not aware of uncertainty in each combination. Estimated result from WinGLUE is a single value and does not give accurate result when the real value is obtained, so an the additional activity is necessary to prepare for solving everyday uncertainty event that have not been considered and reduced in the beginning. Many activities will also be carried out if the obtained result from the given value from WinGLUE is not close to the target value. The more uncertainty the project has, the more the activities for the staffs to do. This thesis applied portfolio theory which is a new tool for oil and gas operation field to allocate gas lift system when enhancing the performance of traditional system that emphasizes in single value of maximum net oil only. For instance, the proposed method can provide more reliable output from estimation in many alternatives or wells combinations based on uncertainty consideration and can provide good guidance of well combination for a decision maker. This analytical technique is based on modern portfolio theory that provides a conceptual framework for selecting projects in order to create portfolios that offer the best combination of risk and return. Within this framework, Harry Markowitz first proposed a mathematical model that utilizes quantifiable risk/return parameters to create efficient and optimal portfolio designed to achieve the goals and risk

2

preferences of the large private or institutional investor. There are many similarities between investment project and gas-lift injection into well therefore portfolio frequency used for project investment can as well be applied to work with gas-lift injection into oil wells in order to optimize resources, help operation, reduce activities supporting uncertainty, obtain more consistency of expected target, and guide related person to be aware uncertainties involved. In addition, the new modernize additional method is proposed to improve the traditional method to be able to maximize profit based on considering gas cost and oil price when economic changes occur and can help staff in finding the new optimal point faster and correctly by using the model when the system or some constraint changes without running the whole software.

1.2. Objectives

1. To optimize gas lift available at existing gas-lift facilities 2. To create the systematic well selection process 3. To improve the existing procedure by incorporating new processes 4. To quantify uncertainty of options

1.3. Scopes of works

1. Study the previous optimization processes in gas lift system 2. Create the traditional method model 3. Improve the traditional method model 4. Apply the portfolio theory to traditional gas lift system in order to enhance

the consistency of estimated target 5. Provide Case studies to enhance understanding

• Collect the data and information of well • Implement production portfolio • Generate Efficient Frontier • Conclude result

6. Provide the improved procedure

3

CHAPTER 2

LITERATURE REVIEW

2.1. Portfolio theory

2.1.1 Main portfolio theory

2.1.1.1 State of prediction State of prediction is able to be classified is intuitive approach and scientific approach.

1. An intuitive approach

Generally, single number is always provided and used for many answer or results. For example, suppose that Mr.A is asked to analyze the rate of return of some project. As results, single value (10 percent) is easily value to describe his answer about project’s prospects, but the predicted value is probably different from actual value. It may feel uncomfortable to rely on a single value. In order to more confident, the actual amount could easily be anything such as from 5 percent to 15 percent (confident level). Therefore, it can conclude that if Mr.A is quite certain that his prediction is correct, he might rate at 1 percent, so the actual value is most likely to lie between 9 and 11 percent (given narrow range). If he is rather uncertain, he might rate it at 5 percent, so the outcome is most likely between 5 and 15 percent (given wide range).

2. A scientific approach

In order to predict precisely, scientific approach is another method to help prediction efficiency. Normally, the likelihood of an outcome is usually stated as a fraction. For example, 5 chances out of 20 are 0.25 which is called probability. Scientific approach can be explained starting from table 2.1.

Table 2.1 Set of predictions between rate of return and likelihood (Source: William Sharpe, 1970)

Figure 2.1 illustrates data in table 2.1 and it is called a probability distribution. The probability should be sum to 1, as it is sure that one of the outcomes will occur.

Rate of return,% Likelihood

6%

7%

8%

9%

10%

11%

12%

13%

14%

1 chance out of 20

2chance out of 20

4 chance out of 20

5 chance out of 20

3 chance out of 20

2 chance out of 20

1 chance out of 20

1 chance out of 20

1 chance out of 20

4

Figure 2.1 Bar chart shows probability distributions of table 2.1 (Source: William Sharpe, 1970)

If there are a few possible outcomes (6, 7, 8 . . . 14%), probability distribution will be bar charge in figure 2.1. The larger the number of outcomes, the smoother the distribution looks like in figure 2.2 that shows in case of many outcomes.

Figure 2.2 Graph is originated from a great many outcomes (Source: William Sharpe, 1970) How many numbers of outcomes should be used to describe information such as example in figure 2.2? The larger the numbers of outcomes, the better the results are. At least two values are needed if uncertainty is taken into account. There are only two numbers or two variables are used in Portfolio theory are expected value and standard deviation or variance in order to identify the probability distribution of a portfolio’s rate of return. First, the central tendency or middle of the distribution is measured by its expected value. It is very simply the weight average of the possible outcomes, using its likelihood weights each outcome. Expected value

E=∑PiOi

Equation 2.1

5

Denoted: Oi is outcome number i Pi is the probability of actual outcome that will be Oi Second, the variance and the standard deviation of outcome are used to measure the spread of distribution. The expected value is located at the middle of the distribution. Most possible outcomes surround expected value. The deviation of an outcome from the expected value is the difference in equation 2.2.

Oi-E

The variance is the weighted average of the squared deviations, with each weighted by its likelihood as shown in equation 2.3 below. Variance

V=∑Pi [(Oi-E) 2]

The standard deviation is the square root of variance as illustrated in equation 2.4 below. Standard deviation

σ = V Generally, the standard deviation measures the “spread” of a probability distribution is especially clear if it is normal distribution or looks like bell-shaped curve. Normally, it is popular to use 3 standards of possible outcomes as follows. Firstly, the chances are approximately 67 out of 100 or 1 sigma that the actual outcome will be between (E- σ) and (E+ σ). Secondly, the chances are roughly 95 out of 100 or 2 sigma that the actual outcome will be between (E-2σ) and (E+2σ). Lastly, the chances of the actual outcome will be between (E-3σ) and (E+2σ) about 99 out of 100 or 3 sigma or most likely. 2.1.1.2 Investors’ preferences Ep and σp are used to express portfolio desirability. Portfolio theory assumes that investor would consider such a portfolio equivalent. Portfolio can be represented by small point or dot in figure 2 that expected and standard deviation of return are plotted in. Expected of return is shown in y-axis and standard deviation of return is represented on x-axis. How does an investor select among alternative portfolios? Simply rules are assumed applying to any investor as follows.

1. If comparison between two portfolios that have the same standard deviation of return but different in expected of return, which one give larger expected of return will be preferred.

2. If comparison between two portfolios that have the same expected of return but different in standard deviation of return, which one give lower standard deviation of return will be preferred.

3. If any portfolios have both a larger expected of return and a smaller standard deviation of return than another, it is strongly preferred.

Equation 2.2

Equation 2.3

Equation 2.4

6

Figure 2.3 Graph shows the position of portfolio (Source: William Sharpe, 1970) The rules may be summarized succinctly:

4. Ep indicates good way: any investor prefers this parameter equal, more than less others.

5. σp indicates bad way: other things are equal, less are preferred to more.

William Sharpe, (1970) reported that the number of evidence indicates that almost all investors are a risk averter such an assumption number 5 when making a significant decision. In this case, portfolio 1 is less interested from investor because it is not only less expected of return and it also has more standard deviation of return. It can be concludes briefly about investor preferences imply that:

Portfolio 2 is preferred to portfolio 1 (rule 1, 4) Portfolio 3 is preferred to portfolio 1 (rule 2, 5) Portfolio 4 is preferred to portfolio 1, 2 and 3 (rule 1,2,3,4 and 5)

A better portfolio is points that lie to the northwest because it means that portfolio will have more expected of return and also less standard deviation of return. Or it means that investors like Ep and dislike σp. It comes up with following question as. How strong is their dislike? How much uncertainty are they willing to accept to enhance their prospects for a likely return? It can say that the more risk, the more return. The distribution of return for 4 portfolios that are plotted in figure 2.3 is shown in figure 2.4.

5 10

5

10

0 σp

Ep

Standard deviation of return

Expected of return

1

24

3

7

Figure 2.4 The distributions of rate of return for four portfolios (Source: William Sharpe, 1970) It is able to represent the feeling of a particular investor by using indifference curve as figure 2.5. The curve upper area or lightly shaded area contains all possible point representing portfolios which investor prefers to portfolio 1. All the points on curve that divides region will be considered that all portfolios on curve will be equivalent to portfolio 1. Figure 2.5 The indifference curve (Source: William Sharpe, 1970) For instance, the indifference curve in figure 2.5 is Mr. A’s feelings. Many more curves are needed if he would make alternatives in a lot variety of circumstances. In figure 2.6 and 2.7, every point on I3 has to be preferred to every point on I2. An indifference curves give a summary of the preferences of a given individual. There are two extreme cases in figure 2.6 that show the behavior of Mr. Nofear and Mr. Riskcon respectively. Mr. Nofear is lacking conscious awareness of risk (lacks of risk consideration) but Mr. Riskcon is oblivious to everything except risk (Risk aversion). Figure 2.7 illustrates more likely cases. Both Mr. Bean and Mr. Fly are conservative to increase in expected of return (Ep) to lead him to accept greater uncertainty (σp). It can be concluded that no one like uncertainty, but especially Mr. Bean dislikes it more.

8

Figure 2.6 Mr.Nofear is always accept risk whileas Mr.Riskcon does not like risk (Source: William Sharpe, 1970) Figure 2.7 The more common case but different level of accepted risk (Source: William Sharpe, 1970) 2.1.1.3 Portfolio Selection In Figure 2.8, Mr.D’s preferences are illustrated by several indifference curves. There are many points are fully filled as shade area. The question will be that which point will Mr. D prefer? The answer is point B. Figure 2.8 The three indifference curves (Source: William Sharpe, 1970)

Figure 2-9

σp Mr.Nofear

I1

I2I3

Ep

Mr.Riskcon

Ep

σp

I3 I2 I1

Mr.Bean

Ep

σp Mr.Fly

Ep

σp

9

It can be broken into three separate phases that consist of security analysis, portfolio analysis, and portfolio selection. It can be applied to this thesis from considering security in stock market to focusing well in oil and gas field production. Security analysis is an art. Prediction is required about the future prospects of securities (stocks, bonds, jobs, wives, etc.). Both uncertainty and interrelationship must be taken into account for these predictions. In particular, they should be properly prepared in order to use in next step or next phase. Portfolio analysis provides portfolio prediction. In form of Ep and σp estimates, the results are entirely derived from the predictions about securities produced in previously step. Portfolio selection is the final phase. Available Ep, σp combinations are already given, the investors or someone’s preference are known or prepared in order to select a good portfolio or good decision making. 2.1.1.4 Portfolio Analysis In the first place, portfolio analysts provided predictions about securities. What the the Ep, σp combinations of portfolio looks like? There will be a large number of points fully filling area or shaded area in figure 2.8. Even if analyst also can create portfolio, it is not easy to select the single best portfolio for a given investor. However he can reject certain amount number of possibilities of portfolio. Especially, any portfolio are not represented on the upper line that it is created after already having a large number of portfolio. This is shown in figure 2.9. Moreover in figure 2.9, for example, portfolio i is dominated by portfolio e Because portfolio e has larger expected of return at given the same standard deviation of return, therefore any portfolio at the line or upper border such a portfolio e is called efficient portfolio but the other portfolio is called inefficient portfolio such a portfolio i. So, upper line or upper border of region is called the efficient frontier. Normally, portfolio analysis’s task is to find the set of efficient portfolios and the associated efficient frontier.

Figure 2.9 The better portfolio is located on efficient frontier (Source: William Sharpe, 1970) In practice, only some of all the possibilities are focused. It is not simple task to proper selection of a group of potential candidates. The number considered of alternatives may be small or large depend on many consideration such as advantages and disadvantages of limited versus a more complete selection.

10

By portfolio theory, portfolio is able to be described by the proportion invested in each security. For example of parameter definition, it can be denoted that X1 is the proportion for security 1. Finally, sum of all proportion must be equal to 1 as equation 2.5.

∑ Xi = 1 (i=1,2,… N)

The actual return of each portfolio is calculated following the equation 2.6, it is the weighted average of return of its component securities by using the proportions invested as weights. Rp represents the actual return on portfolio and Ri is actual return of security i.

Rp = ∑XiRi (i=1,2,… N) 2.1.1.5 Interrelationships Interrelationships is one of the major attributes of portfolio theory is taken into account. The relationships between each pair of securities return may be described in terms of correlation coefficients, coefficients of determination, or covariance. It is one big problem to estimate relationship from many securities. How related are the return on the pair of securities such as between security 1 and 2? between security 1 and 3? between security 2 and 3? All the relationships of return between each pair securities are obtained from among securities. Then separate value for each pair will be calculated and provided as portfolio theory.

1. Correlation In figure 2.10, there are some basic relationship between two securities can occur. How related are the returns on one security to another security? How likely are various pairs of actual values? What does the obtained value mean? For more understanding, it will be explained one by one from figure 2.10a to figure 2.10d as follows. Figure 2.10 (a) illustrates an extreme case and less likely to occur. The returns are perfectly correlated. Related pair data plotting on straight line are only considered possible. Figure 2.10 (b) illustrates a more likely case. Related pair data plotting within the highlight area is only considered possible. Wide range values of return of security one (R1) are likely to be associated with wide value of return of security two (R2), but the association is not exact the same as in figure 2.10 (a). But it can suggest that the relationship of each returns are correlated. Figure 2.10 (c) shows a case in which the returns are uncorrelated. It means that if return of security one increase, it cannot suggest anything for the return of security two. Figure 2.10 (d) and (e) show situations in which a high return on one is likely to be associated with a low return on the other. Figure 2.10 (e) is perfectly correlated in opposite way but figure 2.10 (d) is not perfectly correlated in opposite way.

Equation 2.5

Equation 2.6

11

Figure 2.10 The different value of correlation is between -1 to +1 (Source: William Sharpe, 1970) The relationship between two securities’ return can be explained by using correlation coefficient. Figure 2.10 (a) shows perfect positive correlation is value of +1. A value of 0 indicates no correlation as shown in Figure 2.10 (c). A value of -1 indicates perfect negative correlation as given in Figure 2.10 (e). For figure 2.10 (b), the correlation value is between 0 and +1and in a case such as that shown in Figure 2.10 (d), the correlation value is between 0 and -1.

2. Correlation coefficient The correlation coefficient is represented by rho (ρ). Subscripts are used to indicate the securities: ρj,k is the correlation coefficient for return of security j (Rj) and the return of security k (Rk). Therefore, correlation coefficients of security j and security k are calculated following equation 2.7. ρjk = ∑Pr(Rj, Rk) [(Rj-Ei)/σj][(Rk-Ek)/σk] Where Pr(Rj, Rk) = probability of the pair Rj, Rk

3. Covariance

The covariance between two security’s return is the weighted average of the product of the unnormalized deviations: It also can calculate covariance between two returns of securities as equation 2.8 below. Cjk = ∑Pr(Rj, Rk) [(Rj-Ei)(Rk-Ek)] Or covariance (Cjk) can be calculated from the equation 2.9 that it is easy after correlation coefficient (ρjk) and the standard deviation of each security are known. Cjk = ρjk σj σk

Figure 3-1

Equation 2.7

Equation 2.8

Equation 2.9

12

4. Portfolio expected return

A portfolio’s expected return can be obtained straight forward because it is the summation of each security’s return by each proportions invested security which is called weights. Equation 2.10 shows formula finding a portfolio’s expected return.

Ep = ∑XiEi

All securities (X’s) will be included in system, even if any security is not preferred to choose or include in portfolio but it would be instead by setting to be 0. Portfolio’s actual return is the weighted average of the actual returns on its component securities. Weights are the invested proportions to each security.

5. Portfolio variance

Portfolio variance depends on each security’s weight, each pair correlation coefficient and each security’s standard deviation. All the mentioned parameter is can be used to calculate with equation 2.11below. σp

2 = ∑i ∑j Xi Xj ρij σi σj

The formula “works” for all securities since Xi= 0 if security i is not included in the portfolio. There are N2 numbers to be included together because equation 2.11 is composed of double summation. Suppose that N=2 (1, 2), each of the numbers is obtained by substituting one of the possible pairs of values for i and j into the expression as shown in equation 2.12. σp

2= X1X1 ρ1,1 σ1 σ1+ X1X2 ρ1,2 σ1σ2+ X2X1 ρ2,1σ2σ1+ X2X2 ρ2,2 σ2 σ2 It can be simplified because of the first term and the last term. Clearly, it is perfectly correlated by compare the security by itself, therefore, ρ1, 1 = 1, as does ρ2, 2. The second and third terms can be combined, since ρ2, 1 = ρ1, 2. The result will be as equation 2.13. σp

2= X12 σ1

2 + X2

2σ22+ 2X1X2 ρ1,2 σ1σ2

The product (ρijσiσj) is Cij –the covariance between i and j. The general formula can be written as shown in equation 2.14. σp

2 = ∑i∑jXiXj Cij 2.1.1.6 Efficient portfolio Securities combination A portfolio or securities combination consists of many proper securities. Understanding portfolios, it must understand the outcomes or effects of securities combination. The numbers of efficient portfolios are on efficient frontier or indifference curve are mean that any given level of risk obtain the maximum respected return as shown in figure 2.11. A selected portfolio can be selected differently on the efficient frontier depends on decision maker or risk preference as shown in Figure 2.12.

Equation 2.10

Equation 2.14

Equation 2.11

Equation 2.12

Equation 2.13

13

Figure 2.11 Many efficient portfolios generate Efficient frontier (Source: William Sharpe, 1970) Figure 2.12 The difference selected portfolio, the different risk preference (Source: William Sharpe, 1970)

14

2.1.2 Supportive portfolio theory and optimization in oil and gas industry To cover all portfolio theory and optimization in oil and gas industry, there are many parts that are not mentioned in the beginning. From the past up to present, many authors who reported and shared a lot of interesting journal both re-introduce theory, propose the application, propose additional theory, etc. Without lesson learn from the past, it is easy to do mistake, take time, no development, etc. To increase the basic background, some of the papers are very interesting which will be raised to re-explain and use it continuously developing in this thesis. 2.1.2.1 Diversification Traditionally, most of project investment lack of considering about risk or uncertainty or negative side, so outcomes will be high risk or high uncertainty because project selection does not have good method to control the uncertainty. For example, some time is very high profit, and some time is very high loss. That means that is not fun to play with uncertainty event. It is better to have target prediction that has more consistency or small deviation. To obtain more consistency, many choices or alternatives of projects are necessary to be available. Basically, decision maker will not consider only each project but he also focuses on proportion of each project. This method is called diversification that is proved that it works for many industries. To understand how diversification works according to M.L. Hightower and A. David 1991, it should have to understand the meaning of covariance. The covariance is the return correlation between two projects. If one project tends to have higher returns while a second project has higher returns, for whatever reason, these mean that two projects are positively correlated. The covariance value in this case is positive. Likewise, if one project tends to have lower returns when the second project has higher returns, their returns are negatively correlated. The covariance value in this case is negative. If one project’s return varies independently to another project’s return, the calculated covariance value indicates that no correlation exists between the two projects. This independent between project returns explains diversification. If two projects are perfectly positively correlated, it means no diversification. However, if two projects are perfectly negatively correlated, it means complete diversification. With oil and gas investments, projects are positively correlated because of their common dependence on oil and gas prices. As reported of Don Merritt 2000, Portfolio Optimization using Efficient Frontier Theory, he shows how diversification works in oil and gas company investment by considering two project that have different both returns and probability of success. Decision tree analysis, which is a intelligent tool based on considering such as expected monetary value, is used to calculate about many options that most likely occur after providing the expected return with probability value. As the results, it helps decision maker to make good decision based on selecting higher expected monetary value. In addition, he illustrated the specific point or main propose about how to manage or reduce the risk or uncertainty with method of share or more combination. It can say that the choicer you have, the less uncertainty you are. Oil and gas company exploration and production that consists of expected value and level of risk. The following investment example by Don Merritt 2000, is shown about value of diversification in table 2.2 below.

15

Table 2.2 The general information of project A and B (Source: Don Merritt, 2000)

Project Investment $US 1,000

NPV$US 1,000

POS *ENPV $US 1,000

A 2,000 9,000 40% 2,400 B 2,000 20,000 20% 2,400

ENPV = NPV*POS - Investment*(1-POS)

Some time considering expected monetary return method (ENPV) is not enough for making decision such a result of project A and B in table 2.2 that are equal. If risk of each project is another consideration for investment, defined in this case by the probability of success (POS), Project A will be preferred to invest entirely more than project B because project A has a lower risk than B. There is where intuition might fail us. There are another way to consider a case where it is decided to invest 50% in A and 50% in B.

It is summarizes of all the possible outcomes in table 2.3 below. It shows about the probabilities and the total ENPV of all case. In figure 2.13, decision tree is used with this example to find the value of project. Table 2.3 all possible cases from diversification of investment (Source: Don Merritt, 2000)

Figure 2.13 A decision tree representing all of the permutations of outcomes for projects A and B. (Source: Don Merritt, 2000) It is a combination projects between A and B at 50% equity in each has been assumed, so the probability of success will be changed that it derives from a product of individual probabilities of event. For instance, POSAB, ENPVAB, and Total ENPVAB are calculated as equation 2.16, 2.17, 2.18 respectively.

Equation 2.15

16

POSAB = POSA *POSB

ENPVAB = POSA *NPVA + POSB*NPVB

Total ENPVAB = POSAB*ENPVAB

After separating investment from single project at 100%, the results of diversification of two projects is still $2.4 million, but the risk of diversification effect is lower. Only in fail-fail case in number 4 can show worse case at probability of a loss about 52%. However, the worst case of diversification is 52% that is lower than the probability of project A only loss at 60%. It can be concluded that the diversification is not only maintained expected value, but it also reduce the risk. In figure 2.14, it is a graph plotting between expected value and risk.

Figure 2.14 A plot of Risk vs Reward (Source: Don Merritt, 2000) 2.1.2.2 Rank and cut analysis Traditionally, A few indicators will be selected to be representative to measure the project characteristics or project performance; many of projects are candidate to be measured based on some indicator before selecting or investing project. Then after referring to some indicator, the range of project at given any indicator will be considered from the best to the lower one until running out of resource or facing other constraints. For example, in project selection, NPV is one indicator to measure how interesting project is by considering the higher the NPV, the better the project is. It is not only NPV indicator, but also there are a lot of indicators that are created such as IRR, PI, ENPV, etc. they are selected different way and depended on decision maker. Rank and cut analysis is the most popular usage since the past up to the present because it is very close to real operation that means easily to apply and require a few indicator or small amount of data. With these reasons, each asset was put into the portfolio based on its NPV and other parameters. The maximum value of NPV becomes the first priority consideration to invest or make a decision, but it was not true after a few companies were not succeed because it does not address the issue of risk. 2.1.2.3 Portfolio management approach Framework is the underlying structure that supporting work and containing many important data and information. Framework is one part of portfolio management approach because it helps relevant person to understand the overall system and it is the system that guide everyone follow the same method that already proved. Integrated portfolio

Equation 2.17

Equation 2.16

Equation 2.18

17

management approach is reported by M. Erdogan , 2005 , Going Beyond the Efficient Frontier Analysis Using an Integrated Portfolio Management Approach. He concluded many interesting parts into one framework or one system as illustrated in figure 2.15 which composited of economic evaluation, Multi-Dimensional Portfolio Data Cube, and portfolio optimization.

Figure 2.15 Components of Integrated Portfolio Management Approach (Source: M. Erdogan , 2005) Three steps in the integrated portfolio management approach are explained shortly as the following below:

• Creating and constructing economic evaluations model and storing these models and the results from model into centralized database;

• Constructing a multi-dimensional corporate data cube to collect or roll up the results for portfolio analysis;

• Using portfolio optimization framework tests different strategies for portfolio constructing based on minimizing risk and maximizing returns within the practical envelope of opportunities.

For more detail of three main steps, it can be found in SPE journal of M. Erdogan , 2005 , Going Beyond the Efficient Frontier Analysis Using an Integrated Portfolio Management Approach. Moreover, the study of Sholarin Ebenezer (2006) also related with portfolio management approach by applying the strategic project management principles (Project Management Institute or PMI’s Guide to project management body of knowledge (PMBOK)). In addition, he demonstrates how modern risk techniques can make easier the decision making process in E&P operation. It shows how decision maker can manage the strategic value of projects, risk and return to choose an optimal portfolio before making decision or investing funds. For more detail of his journal, it was written by Sholarin Ebenezer (2006) in SPE journal in title of Applying Integrated Project Management Methodology to Hydrocarbon Portfolio Analysis and Optimization.

18

2.1.2.4 Portfolio optimization (Objective and constraint) Normally, optimization is composed of objective function and constraint function that it can possibly be constructed both easy and difficult depended on many aspects such as both quantity and quality of information, data, mathematic algorithm, related person, etc. In this case, it combines between portfolio and optimization, so the results are better than individual consideration. Researchers and relevant person pay the attention to Portfolio optimization in order to enhance the existing system to more optimization. There are many interesting parts to be able to reanalyze or redevelop, therefore the results is also better than the past. The study of Don Merritt, (2000) provided a guideline the portfolio optimization process in financial assets as follows. This process is one of the integrated economic modeling that generate the risk and reward of each portfolio with optimization.

1. Create economic models for each asset 2. Create probability distributions for all economic input parameters 3. Run Monte Carlo simulation for all assets and the raw distribution of cash

flow and store results in a database. 4. Find the portfolios that satisfy with company objectives and constraint 5. These objective and constraint are run thru a mathematical algorithm for

optimization. 6. The raw Monte Carlo results are accessed and consolidated to recalculate the

statistics such as mean and standard deviation for selected portfolios. 7. These statistical results are plotted for each portfolio in order to analyze the

efficient frontier.

The study of M.Erdogan (2005) also related with portfolio optimization that it was reported about portfolio optimization framework. To find the optimal allocation and test a different strategy for constructing the portfolio that maximizes return and also minimizes risk. He defined the downside exposure or loss is used as risk and NPV is used as return with optimization problem. Typically, upstream projects (exploration and production project) have greatly skewed or lognormal values distributions with high probabilities of achieving low-value outcomes. Normally, if project objective is minimization of the portfolio standard deviation, also it will affect to upside as well as downside potential. It is a problem as upside also is associated with minimization of portfolio standard deviation, therefore it can overcome this problem by selecting statistics like semi-standard deviation, mean-loss, certainty and coefficient of variability when defining an optimization problem. Because of the involvement of complexity and uncertainty, simulation often becomes a basis for solving complex decisions such as E&P portfolio optimization problem. Typically, objective and constraint function are defined in equation 2.19 below: Objective function

Max or Min F(x) Constraints

Ax≤ b Constraints gl ≤ G(x) ≤ gu Requirements l ≤ x ≤ u Bounds Where x could be continuous or discrete probability.

F(x) is represented objective. Constraints set has to be linear and the coefficient matrix “A” and value b is right-hand-side must be known. “gl” and “gu” values are the bounds must

Equation 2.19

19

be known and constants. Each evaluation of F(x) and G(x) requires a Monte Carlo simulation of the portfolio. Portfolio optimizations can provide the different results depended on the objective function and constraint such as given case below in order to define the entire feasible envelop and to determine the impact of different scenarios and evaluate a variety of decision alternatives. For more detail of three cases, M.Erdogan (2005) provided in SPE journal in title of Applying Integrated Project Management Methodology to Hydrocarbon Portfolio Analysis and Optimization.

• Case1 – Rank PI and use limited capital • Case2 – Use constraint and compare with case1 (Rank PI) • Case3– Increase condition and there are 2 scenarios (Exploration and

Develop)

L.C. Faya is one who interested in portfolio optimization as he proposed the new approach in 2006 to show the concrete portfolio management application. Traditional way to rank project as one or several economic indicator results such as expected net present value (ENPV), profitability index (PI), return on expenditures (ROE) , etc. It has been proved that this allocation method is inefficient (Brashear, 2000; Faya, 2006). L.C. Faya 2006 described three portfolio applications that point out corporate decision makers. He suggested that the most efficient approach to allocate the available funds is to use the portfolio optimization. The first application relates to the effect of production and capital constraints that it will close to realistic goals. The second application shows how acquisition can be estimated in the portfolio context, and the effect that those projects have on the company objectives. The last application explains the use of portfolio optimization to move the company strategy. After our project portfolios are estimated or evaluated, decision makers have to decide which projects to exercise. The use of Portfolio optimization is focused as managing tool. Three sections are provided as example and the following questions are added in each section below:

• How do the constraints imposed on the optimization affect the solutions? • How can we use the portfolio to manage acquisitions and divestures? • How can we use the portfolio as a tool to manage and drive the company

strategy? Production and capital constraints It is possibly to have several constraints acting at the same time. In this case, the production and capital expenditures constraints are combined. It is clear when compare the solution with and without constraint. Figure 2.16 shows how the effects from both constraints are combined in a single efficient frontier. On the lower NPV values, it is limited the possible portfolios by setting up a minimum production. On the upper NPV, it is constrained the possible solutions by enforcing limits on the available funds.

20

Figure 2.16 The effect of combination of both constraints (Source: L.C. Faya 2006, Beyond Portfolio Optimization) It is possible to generate many constraints to be only one feasible portfolio, or very narrow efficient frontier obtained. It is more convenient to start without any constraint analyzing the effect from each constraint. And then the constraints could be gradually added to analyze the effect of each constraint having on the portfolio optimization. Therefore, it can be estimated which projects are always selected, which ones are always neglected, and if it is possible, which type of projects should be added, or discarded to the existing portfolio. Project selection (with and without new project) In this section, we will illustrate how to perform the analysis of a project acquisition using the portfolio optimization as the selection tool. Project selection schematic is shown in appendix 6. To build this example, a portfolio consists of five projects. Production and capital expenditure constraint are applied and analyze the results from including both constraints. Afterwards, new project is added in a portfolio without varying the initial set of constraints. Hence, it can be analyze the effect of adding a new project on the efficient frontier and also can compare with the existing portfolio. The improvement of efficient frontier by adding of new project is shown in figure 2.17.

Figure 2.17 The improvement of adding new opportunities (Source: L.C. Faya 2006, Beyond Portfolio Optimization) From study in this case, it means that the same level of risk but more value is obtained from adding new project. As the available budget was not changed, if the new project is selected affecting to a reduction on the participation of the existing. For instance, in this case, two projects previously funded were excluded from the portfolio (projects D and E), project A participation was reduced to 20%, and the new project was completely funded, Figure 2.18.

Figure 2.18 The bar chart shows before and after adding new projects (Source: L.C. Faya 2006, Beyond Portfolio Optimization)

21

Figure 2.19 shows how the addition of the new project shifts the distribution to the right; therefore, reducing the portfolio risks.

Figure 2.19 The same expected NPV but different standard deviation (Source: L.C. Faya 2006, Beyond Portfolio Optimization) 2.1.2.5 Portfolio modeling After understanding the portfolio theory, it is necessary to model the real system or interested system. Next, the portfolio model is designed and constructed on excel spreadsheet for many parameters, formula, information, data and others. At least, created portfolio model is based on the fundamental of portfolio theory such as including average return, standard deviation, correlation, coefficient, expected return, variance, etc. There are many advantages for constructing portfolio model by user that it can develop out of scope or create for doing many things as well as understand whole portfolio model. However, it also takes time to construct and develop the model and it is not suitable for large system. A example was reported by Zvi B., Alex K., and Alan J. (1999), Investments, shows how to construct portfolio model in excel spreadsheet which that model was used in financial asset. Using Excel is quite far from the best program and is limited in the number of assets it can handle. Due to portfolio selection starting from financial asset, therefore a few documents are developed or applied to oil and gas industry. M.L. Hightower,and A. David, 1991, Portfolio Modeling: A Technique for Sophisticated Oil and Gas Investor, demonstrated how a modified model can be effectively applied to the selection process of petroleum ventures. Their modeling technique was applied to an investment decision involving the construction of an exploratory drilling program. Their example can predict how efficient and optimal portfolio can be constructed given an opportunity set of investments and the goals of the oil and gas investor. In addition, he reported the use of semi-variance instead of normal variance due to variance reflects both upsides potential as well as downside. In case of minimize risk or variance, the model eliminates both upside (not prefer) and downside (prefer). Therefore, the semi-variance parameter is created and thought that it may be better measure of risk. Unlike the variance parameter, the semi-variance parameter quantifies only the dispersion below a defined level of return. The semi-variance of the return distribution SV(R) is mathematically defined as: SV(R) = ∑ (Ri-B)2/T if (Ri < B) B = an acceptable level of return below which is considered risky T = the total number of returns in a distribution Ri =the return

Equation 2.20

22

Semi-covariance between projects must be determined, like the covariance, and this parameter are derived from using the simulation. He also claimed that due to more intensive of mathematically, the semi-variance model chooses more optimal combinations by minimizing only the return below an acceptable level. So, he highly recommended using the semi-variance. 2.1.2.6 Uncertainty analysis (Monte Carlo Simulation + Sensitivity Analysis) What is the relationship between Uncertainty and Monte Carlo simulation? Typically, uncertainty is the value that it does not know exactly value because it is the future value. If one attempts to predict some value in the future, it is sure that it consists of many the uncertainty parameter. It is easy to compare or know the trend that which project have more uncertainty but it is difficult to show the exactly number of that uncertainty. It is hard to input the qualitative of uncertainty (large, a little) into the model because the model never relates to the qualitative of uncertainty. It can communicate and relate in term of quantitative number (10, 20, and 30%) in number with the probability. Many models are associated with the uncertainty parameter. Monte Carlo simulation is based on random variation is used for the uncertainty analysis such as use in economic evaluation. For example, a numerical distribution is used for each key variable that affect the economic result of a project. Monte Carlo simulation was explained by Don Merritt, 2000 that with the input forecast in place, simulation were run on all of the assets. Each asset was run 500 modest simulation. For each simulation, a number of results were stored until reach 500 iterations. The more iteration the more accuracy. After running full simulation, we retain the ability to statistically utilize these results in our analysis, such as the probabilistic assessment of reserves. What is the sensitivity analysis? It is study about changing of outcome when input variable is varied since single variable at given assigned range. If a tiny change occurs in input parameter and output variable change more, it means that that input variable is sensitive to the outcome, on the other hand, if output variable change a little bit, it means that that input variable is not sensitive to the outcomes. Basic steps are provided as follows:

1. Define interested parameter that parameter change usually may be obtained from estimated value

2. Define space (range) and class (incremental rate) of change for each parameter 3. Define measurement method for economic worth 4. Calculate the result of economic worth for a given interested parameter 5. Draw graph result in order to clear understand 6. Interpret and conclude from graph

There are 2 main considering parts of sensitivity analysis

1. Sensitivity analysis of single variable It is easy to calculate by using excel and plotting graph to show the sensitivity of that input parameter whether it is sensitive to outcome or not.

2. Sensitivity analysis of multi-variables Normally, it is not have only one input, but also it consists of many input variable. In addition, specific software such as top rank in excel add-in are

23

required to run the sensitivity analysis of many input parameter as the same time. There will be two kind of sensitivity analysis available to show are tornado chart and spider chart. Therefore, it is convenient to know that which input parameter is sensitive to outcome and should aware and consider. Tornado chart are shown in figure 2.20 below.

Figure 2.20 Sensitivity analysis (Spider chart) (Source: http://www.scribd.com/doc/18129241/Slide-14-Sensitivity-Analysis) Using Monte Carlo Simulation in valuating oil and gas projects is one title of Sholarin Ebenezer 2006, Applying Integrated Project Management Methodology to Hydrocarbon Portfolio Analysis and Optimization, the example project using Monte Carlo simulation technique to generate the results. Before using Monte Carlo simulation in this case, economic model should be prepared and constructed. This model is used for estimation the quantity of oil and gas which be obtained from the projects under review on a yearly basis and the lifecycle costs associated with producing these volumes. The example calculating the expected value (NPV) according to the formula below: Legend: NPV = net present value ($) i =discount rate (fraction) m =periods of the year Q0 =initial flow rate (bbl/day) Dr= decline rate (fraction) D =days per period (days) n =total number of periods P r= productivity ratio N b = net back ($/bbl) K 0 =Capex funds p = inflation rate

Equation 2.21

% Change in individual parameter

Rat

e of

ret

urn

on c

apita

l

24

For sensitivities analysis, each parameter was varied one time with holding other parameters is constant at their initial values, while sensitivity analysis is created from Monte-Carlo simulation during which all variable inputs vary at the same time as each other. The sensitivity analysis gave the results illustrated in figure 2.21 that is interactions and correlation between inputs.

Figure 2.21 Sensitivity analysis (Tornado chart) (Source: Sholarin Ebenezer 2006, Applying Integrated Project Management Methodology to Hydrocarbon Portfolio Analysis and Optimization) In figure 2.21, it can be seen that results are most impacted by oil revenue and followed by operating expenses (OPEX). The main significance of a sensitivity chart is that it provides visual representations of the effect of individual variables are expected to have on a given economic indicator. For Monte Carlo Simulation, all parameters were varied at the same time; with individual values generated randomly from probability distributions over many trials. Figure 2.22 shows a cumulative probability function (CDF) plot of the NPV generated from the aggregation of the individual input variables. From this plot, the P10, P50, and P90 NPVs can be calculated graphically.

Figure 2.22 The cumulative probability plot (Source: Sholarin Ebenezer 2006, Applying Integrated Project Management Methodology to Hydrocarbon Portfolio Analysis and Optimization)

25

2.2. Gas-Lift Optimization

2.2.1 Real Time Gas-Lift Optimization

Thanks to Queen Sirikit 1 that is PTTEP’s asset, there are many important parts which is importance knowledge in oil and gas operation field including this operation procedure document that it is very useful document and related to this thesis in part of gas lift optimization as follows.

2.2.1.1 Day-to-Day Optimization Normally, almost all the process will be considered about optimization because it will help to enhance the productivity. In oil and gas production field, optimization is one major continuous close-loop process and it is related through all departments. It happens within one day or it is considered very short period of time; therefore, it is called day-to-day optimization. Figure 2.23 Day to day optimization cycle (Source: PTTEP OJT center, 2007) It is very rudimentary process that consists of monitoring, analysis, prediction, and execution. There are totally 4 steps which will be explained step by step as follows: Monitoring Monitoring is data gathering process. The data are obtained through the following parts:

• Real–time systems i.e. CAO (computerized assisted operation and PI system (supplementary system) and DCS (Distributed Control System)

• Well test activity • Data recorded by operator • Data analyzed by Lab • Well services activity (FGS, SGS, BHP,MPLT survey) • Reservoir Engineer (Well proposal, Well logging, Perforation proposal)

CAO is the powerful system that help operator such as monitor abnormality of wells and take action as appropriate to remove or mitigate the problems. In addition, Programming engineer will supervise the operator and give for further advice. All important well data will be transferred via both wire line and wireless and recorded into performance system that called PIS (production information system). Normally before recording data into the

26

system, it is required approve or validate from production programming engineer. Microsoft query is used to retrieve the data for analysis. Analysis Production Programming Engineer is responsible to important role in performing day-to-day optimization associated with PIS (production information system) which is very powerful tool used for managing data. For instance, its data can be retrieved to plot as required. Moreover, there are many software supporting analysis part such as WINGLUE, PIPESIM, PROSPER and GAP software are also used for the analysis to check the gathered data whether it is in line with its well, pipeline and equipment performance. Prediction To optimize production process, high performance software and system such as WINGLUE, PIPESIM, PROSPER and GAP software is used to predict or estimate what will happen and give the important information to related person to take action up-front or in time. Generally, programming engineer will usually update software in order to up to date. For example, updating WINGLUE model generates the important individual well gas-lift performance curve, Glue table or prepared gas lift plan. This table will be downloaded to CAO and CAO Will use that table to adjust gas lift real time or called real-time gas lift optimization in order to maximize oil. Execution Production Programmer will provide advice and program to CAO operator and relevant parties who will optimize wells and related system through CAO and DCS and manual system i.e. bean-up/down by wellsite operator, zone change and gas-lift valve change-out by Well service operator, etc. Many activities are listed below are performed in order to achieve day to day optimization:

• Gas lift conversion and gas lift valve change-out • Optimize amount of gas lift via individual well • Conversion to intermittent well • Bean up or bean back the well • Close in low performance wells and re-open up the shut-in wells • Zone change • Zone commingle/de-commingle • Conversion to fluid lifted well (internal gas lifting) • Stage perforation • Optimization of artificial lift such as PCP, ESP and Beam pump

2.2.1.2 Gas-lift conversion and gas-lift valve change-out The same history in oil field or oil well around the world, Well performance would meet reduction or declination of oil rate production while the water-cut will increase due to becoming low performance well after oil well is started production continuously. Typical well history is able to show as figure 2.24 below:

27

Figure 2.24 Artificial gas lift are needed for low performance well (Source: PTTEP OJT center, 2007) At the time t1, artificial lift is required to restore or increase its production. Gas lift is a primary artificial used in S1 field due to huge gas production before changing to others artificial such as progressive cavity pump (PCP), electrical submersible pump (ESP), beam pump, hydraulic pump, etc. Normally, gas lift system comprises of piping system, two-phase separator, gas compressor, glycol system and gas lift valves installed in the side pocket mandrels of the production tubing of the well. It can be shown in figure 2.25 below. Figure 2.25 Process flow diagram of artificial gas lift (Source: PTTEP OJT center, 2007) When gas lift valves are designed, three important things that production programming engineer would like to achieve as lists below in order to obtain the optimum condition resulting to maximize net oil.

1. Well flow stable 2. Inject a right amount of lift gas 3. Inject lift gas as deep as possible

Whether the wishes as mentioned above are achieved or not it is dependent of reservoir pressure, water-cut, formation gas, gas lift mandrel spacing, gas lift pressure, etc. As these parameters change over period of time, production engineer must collect them and monitor individual well performance, “A” annulus pressure trend regularly to change via gas lift valve in order to keep the well at optimum condition.

28

2.2.1.3 Optimize amount of gas-lift via individual well It is necessary to consider that prior to inject lift gas to a well; Firstly, its gas lift performance has to be known by using WINGLUE or PROSPER software. Secondly, it also recognizes that the right amount of injected gaslift to each well depends on available gas lift and well condition and other constraints as such stated in figure 2.26. Figure 2.26 Gaslift performance curve (Source: PTTEP OJT center, 2007) As reported of S1 training center, most of production in S1 about 60-70% is obtained from gas lift wells. Due to limitation of available gas lift, gas lift is very important resource that should be used properly because if they inject too much gas lift into one well, the additional return may increase but not much. It is better idea to inject the right amount of available gas lift into each well, as the result, it is certainty to obtain the return more than inject too much in one well. Therefore, it needs to be looked at the whole system rather than concentrating on some wells. Because of a lot of gas lift wells, operators cannot efficiently adjust gas lift via all wells by themselves, therefore SGAS software is used to help operator in doing reallocation gas lift via CAO to all wells at optimum points in real-time to maximize total field production. Normally, production programming engineer has to generate gas lift performance curve by WINGLUE to all gaslift wells, namely, GLUE table and regularly update the table downloading to SGAS. All the gas lift system are shown in figure 2.27, 2.28, 2.29, and 2.30.

Figure 2.27 WinGlue modeling panel Figure 2.28 Gas lift performance by WinGlue (Source: PTTEP OJT center, 2007) (Source: PTTEP OJT center, 2007)

1. Unlimited Gas or maximum flowrate is desired

2. Limited Gas or the most economical rate is desired

3. Production is fixed -Water/gas coning -Sand production -Government regulations

29

Figure 2.29 Real-Time Gas Lift Control Systems (Source: PTTEP OJT center, 2007)

Figure 2.30 GLUE table creating by WINGLUE (Source: PTTEP OJT center, 2007)

30

2.2.1.4 Conversion to intermittent well When Productivity index (PI) of well is low or its reservoir pressure decreases below the efficiency while using continuous gas lift method. To sustain its production before converting to other artificial lift methods, the well should be converted to intermittent gas lift well. The concept of the intermittent gas lift is to push the accumulated liquid inside the tubing to surface by injecting a large amount of lift gas at the predetermined cycle time. Normally, before converting to intermittent gas lift well, the liquid accumulated inside production tubing over period of time must be known in order to calculate cycle time and unloading valve set point. The information between liquid accumulated and time can be obtained through the FBU survey. Generally, each cycle pushes the liquid up to the surface needs a large amount of lift gas with a few minutes. This causes an adverse affect to the whole gas lift pressure system drop and affect to the continuous gas lift wells drop as well. Based on production programming engineer’s experience, they solve problem by using the continuously injecting very small amount of lift gas at the constant rate to push the accumulated liquid. However, it is not easy to design exactly, trial and error need to be done at work site to determine a proper cycle time and the injection rate.

2.2.1.5 Bean up or bean back the well Bean up or bean back the well is the normal operation to control well. To choose the bean (or choke) on a flowing well is standard oil field practice. It is to serve many purposes. For example, it is used to avoid effect of variation in down-stream pressure (flow-line) to well performance, control GOR, control sand, control flow rate, etc. It is standard oil field practice to choose the bean (or choke) on a flowing well. This is to serve various purposes such as avoiding effect of a small variation in down-stream pressure (flow-line) to well performance, GOR control, sand control, flow rate control etc. The Gilbert’s empirical formula of bean performance is given in equation 2.22. It can be applied when the flowing tubing head pressure is at least double the flow-line pressure.

Ptf = 435R0.546q/S1.89

Ptf = flow tubing-head pressure, psig R = Gas/liquid ratio, mscf/bbl q = gross liquid rate, bbl/day S = bean size, 1/64 inch It should be opened via the small bean first if the new well, new zone, newly perforated reservoirs, acid stimulated well or other remedial work are performed. This is to control its drawdown not to screw up the well, for example, producing sand, gas cusping and water coning. Water-cut and sand production will be known from laboratory after getting liquid and formation gas flow rate from well test activity. If they need more production, bean the well up will be performed. Beaned up is in step of 4/64” to 32/64” bean before testing the well. Not all cases beaned up to 32/64, it depends on FTHP (flow tubing-head pressure), flow-line pressure, water-cut and sands content of each step of bean-up. Bean-up may end up at 24/64” bean if the surface facilities cannot handle an increase of the gas production. If well cannot flow

Equation 2.22

31

naturally, it will be beaned up to full bean and available gas lift will be injected to assist well flowing again. Beaning back the well is normally applied to:

• The well is producing sand more than 10 pptb (pound per thousand barrel) • The water-cut suddenly increases • Control gas flaring

2.2.1.6 Close in and open up wells Due to the limitation of available gas lift, only the better GUF wells (gaslift utilization factor = net oil/1000 scf of gaslift) will be selected to produce while the lower GUF wells will be closed in. GUF is the important parameter to rank the priority well performance, so each well’s GUF needs to be regularly monitored and compared with all wells. Well will be closed in or open up depended on GUF consideration. This must be done again and again over the long period of time. Apart from above, production engineer must co-operate with production planner to provide a list of wells to be closed in to minimize deferment for execution of the activities in the IOP plan. The following criteria are applied for selecting wells to be closed in.

• Due to K-3150 gaslift compressor preventive maintenance: to rank the wells by GUF and close in wells starting from lowest GUF until the amount of lift gas the same as the capacity of K-3150 gaslift compressor. List of close-in wells is shown in table 2.4.

• Due to gas compressor preventive maintenance: to rank the wells by GOR and close in wells starting from highest GOR until the amount of gas the same as the capacity of compressor.

• Water disposal pump preventive maintenance; rank the wells by % water-cut and close wells starting from highest water-cut until the amount of water the same as the capacity of the disposal pump.

Table 2.4 List of close-in wells for K-3150 gaslift compressor preventive maintenance (Source: PTTEP OJT center, 2007)

Well Str Sts Date Choke FTHP FlowType Gross Net Gas Gaslift GOR GUF Cumulative GasliftNTM-A04 T O 30-Mar-08 128 65 GL T 24 22 532 519 571 0.04 519.00LKU-B14 T O 19-Apr-08 128 121 GL T 28 25.099 410.7928 387 948 0.06 906.00LKU-Y03 T O 14-Sep-07 128 120 IL T 68 19 298 250 2553 0.08 1156.00LKU-H03 T O 14-Nov-07 128 150 IL T 22 19 256 248 411 0.08 1404.00LKU-E33 T O 2-Feb-08 128 112 GL T 349 32 390 375 476 0.09 1779.00NMM-A07 T O 10-Mar-08 128 115 GL T 241 43.38 516.5552 500 381.632 0.09 2279.00LKU-C22 T O 28-Feb-08 128 122 GL T 30 26 479 300 6765 0.09 2579.00LKU-R04 T O 13-Jul-05 128 103 GL T 231 32 467 349 3675 0.09 2928.00LKU-F20 T O 13-Jan-08 128 162 GL T 110 28 340 300 1450 0.09 3228.00LKU-CA07 T O 21-Mar-08 128 130 GL T 31 28 395 295 3627 0.09 3523.00LKU-CA06 T O 20-Mar-08 128 140 GL T 52 30 422 316 3471 0.10 3839.00LKU-W08 T O 21-Jan-08 128 190 GL T 131 29.475 383.454 300 2831.348 0.10 4139.00LKU-C18 T O 1-Mar-08 128 133 GL T 56 46.368 609.0067 465 3106 0.10 4604.00LKU-R11 T O 7-Dec-07 128 152 GL T 98 35.28 453.3312 350 2928.888 0.10 4954.00LKU-C19 T O 3-Mar-08 128 130 GL T 66 33 327 300 825 0.11 5254.00LKU-T01 T O 25-Mar-08 128 136 GL T 174 39.15 433.916 358 1939.106 0.11 5612.00LKU-L08 T O 27-Feb-08 128 114 GL T 67 39.798 362.0139 350 301.8724 0.11 5962.00NMM-A01 T O 14-Mar-08 128 150 GL T 176 48 474 400 1561 0.12 6362.00LKU-C01 T O 21-Nov-05 128 123 GL T 135 30 255 250 151 0.12 6612.00WTN-B03 T O 1-Jan-08 128 160 GL N 300 68 590 550 596 0.12 7162.00LKU-K19 T O 17-Apr-08 128 120 GL T 48 8.64 75.3056 69 729.814 0.13 7231.00Total 2437 682.5 8470.11 7231 39296.7

32

2.2.2 Gas lift optimization Many interested persons who work in petroleum field wrote relevant detail of gas lift system since past up to the present. Some explained in part of gas lift technique such as how gas lift system design should be. Other reported in specific process and management about how to allocate gas lift injection by considering many related parts. Both parts are the same target that is gas lift optimization. From historical development of gas lift allocation, they categorized gas lift allocation to be two different approaches that composed of economic optimization and production optimization. In previous development, Economic optimization was paid more attention by [1]Mayhill,[2] Radden and [5]Kanu and production optimization was focused by [3]Gomez and [4] Hong. A few last decades, many researches can be categorized to be 3 group are composed of gas lift system in the beginning of study, gas lift allocation optimization, and automatic gas lift optimization system. These three groups have more detail about their studies and are able to guide for the new interested people as bellows: 2.2.2.1 Gas lift system in the beginning of study Before studying gas lift optimization, one article wrote about overview of gas lift system was reported by Mayhill (1974) in topic of Simplified method gas-lift well identification and diagnosis. He suggested that gas lift wells depend on kinds of design and operating problems both surface and subsurface and also proposed the normal problems as follows: Surface

• Plugging in choke • Underside flowlines • High separator pressure • Underside gas distribution system • Wet gas • Excessive flowlines restriction

Subsurface

• Leaks in the flow string • Changing well condition • Improper flow valve operation • Excessive aeration • Foam condition • Improper flow valve operation • Low fluid heads or submergence heading or surging conditions • Excessive slippage of fluid or fallback

To detect and analyze abnormal gas lift wells requires many activities as follows:

• Well tests • Fluid level • Temperature survey • Pressure transverse • Surface temperature recording • Casing-tubing pressure recording

In his study, he presented a better method to analyze gas lift wells by using well test results that will collect many important data and information by using automated system. The results from welltest activity is routine work for individual well as the schedule. In addition, the data and information will be useful for planning, monitoring, controlling, designing, implementing, etc. The specific part is the identification and diagnosis of gas lift

33

wells because it will not reach the optimum point if many problems still exist in gas lift well system. There are many story which help to detect, analyze poorly performing gas lift wells, predict the operating valve, spot equipment malfunctions and calculate an efficient gas injection rate. For calculating an efficient gas injection rate, he explained about gas lift performance curve (GLPC) both in form of production volume as figure 2.31 and in term of economic as figure 2.32. Figure 2.31 GLPC in form of production Figure 2.32 GLPC in term of economic (Source: T.D. Mayhill, (1974) SPE 5151) (Source: T.D. Mayhill, (1974) SPE 5151)

GLPC in figure 2.31 is the best known method in gas lift well optimization because it can help predicted net oil production by injecting any gas lift injection. Also it can be shown in term of economic in figure 2.32 if the objective changes to optimize the profit.

Another article was proposed the same time as previous paper written by J. David Redden, T.A. Glen Sherman, and Jack R.Blann in topic of optimizing gas-lift systems. They reported analytical procedure is composed of system model, and calculating the optimum gas distribution.

1. System model or major related parts in gas lift well that can affect to gas lift optimization. The system model is composed of compressor, gas-lift manifolds, wells, and separator stations as shown in figure 2.33 below. In this paper, they considered the overall system because individual part can still optimize the total result.

2. Calculating the optimum gas distribution is main consideration in gas lift allocation system because normally available gas lift is limited by production facilities. The allocation gas lifts of each well should be operated at the suitable point. For example in figure 2.32 where the slope is equal to one. This rate assumes no limitations on gas availability or system production capacity. This process to find the optimal point needs to recalculate again and again because many relevant parts always change uncertainty.

3. A simplified outline of gas-lift optimization logic 3.1. Use well test data, well information and field producing system description 3.2. Calculate productivity index for each gas lift well.

3.3. Calculate economic optimum producing rate for each gas lift well without limitation of system.

3.4. Supply gas at high pressure gas to all the wells of gas lift by compressor plant, determine, determine if the gas available is sufficient to produce the wells at their unlimited optimum rate.

3.5. Check to see whether there are any limitations of production capacity on the gas

34

lift well at the separator station or not. 3.6. Check to see whether there are any limitations of production on the gas lift wells

because of compressor plant gas inlet capacity. Figure 2.33 Example of gas lift system model (Source: J.David Redden, T.A. Glen Sherman, and Jack R. Blann, (1974) SPE 5151) 2.2.2.2 Gas lift allocation optimization This section emphasizes in gas lift operation or gas lift allocation system that is nothing to do with operation facilities improvement or development or it focuses only the capacity of existing facilities. Many questions are asked by interested persons for example what is the best method to find the optimal point of gas lift in order to achieve the maximum net oil or profit? A lot of mathematic algorithm are used for solve the optimization problem but the results is not clear when comparing each other. For example, some researcher showed the best results from using their method and later another person proved that the results were not real or the results overestimated. A few papers reported their approach that very interesting at given the better optimal point than the past. One is economic approach oil production and gas allocation in continuous gas lift by Eni P. Kanu,(1981) that his method is considering slope and using equal slope. He presented the economic formulation of a simple slope, and using the economic slope with a simple procedure to arrange and find the optimal economic point at given in case of unlimited available gas lift, and the total gas requirement for a field. Another significant aspect of gas allocation in the real world is the limited available gas lift. A method is presented that uses a simple graphical procedure to allocate gas to wells efficiently in a field operating under such a condition. To more understanding looks at in Eni Pl Kanu, (1981), approach oil production and gas allocation in continuous gas lift. Second is an Improved Method for Gas Lift Allocation Optimization by N. Nishikiori, et al.(1989) that he provided the A new method for finding the optimal gas injection rates for a combination of gas lift wells to maximize the total oil production rate. This method uses a quasi-Newton non-linear optimization technique which is incorporated with the gradient projection method along with the results of numerical experimentation and a comparison with the equal slope allocation method. They developed and enhanced the potential ability

35

of computer program to implement the new optimization method and generate the initial value of gas lift injection rates. He claimed that this program was already successfully tested on field data both unlimited and limited available gas lift. In addition, this optimization technique shows superior performance, greater application, faster convergence than normal method “equal slope allocation” procedure. The typical gas lift performance curve, the comparison between estimated and optimum gas injection rate, and the progress of the computation are illustrate in figure 2.34, 2.35, 2.36 respectively. An additional detailed analysis of this method can be found in Nishikiori, N, Gas allocation optimization for continuous flow gas lift systems. Figure 2.34 A typical gas lift performance curve (Source: N.Nishikiori, et al. A improved method for gas lift allocation optimization) Figure 2.35 Comparison of the optimum gas injection rates and estimated gas injection rates. (Source: N.Nishikiori, et al. A improved method for gas lift allocation optimization)

36

Figure 2.36 Progress of the computation (Source: N.Nishikiori, et al. Improved methods for gas lift allocation optimization) 2.2.2.3 Real time gas lifts optimization Most oil and gas companies have developed their business by using high technology or automation in oil and gas operation field although investment cost is so high. However, there are a lot of advantages from installing this equipment such as convenient, comfortable, secure, fast, economical, and credible operation system. Also optimization in oil and gas filed is certain to enhance the efficiency of producing hydrocarbon because this automation helps transfer data and information between field and production station faster and also keeps important data into data base instantly. The distance between control room and gas lift wells is no problem because using supervisory control and data acquisition (SCADA), which is communication software unit control and monitor equipment from many parts work together, is able to solve the problem on time. Normally there are two modes available to choose are manual mode, semi auto mode, and auto mode. Especially, in auto mode, when system change, and the equipment recognizes change then automatic control system will adjust by itself, therefore the save of total accumulate of loss opportunity is also gas lift optimization. There is new automated continuous gas-lift control system improve operational efficiency reported by Terry Bergeron and Andrew Cooksey (1999), they proposed the gas lift optimization from using automatic control system in operation gas lift or called SCADA that perfectly consists of sensors both actuate and measure, or monitor and control from different area. It is faster to know the problem and solve the problem or make less opportunity loss early. The simple system is shown in figure 2.37 below: Figure 2.37 sketch of single-well installation (Source: Terry Bergeron and Andrew Cooksey (1999))

37

CHAPTER 3

METHODOLOGY Theoretical background and literature review in chapter 2 can provide more understanding of this chapter. This thesis provides new methodology to optimize resource of gas-lift and helps related parties to make decision about selecting the best performance group of gas-lift well. This methodology is based on portfolio theory and real time gas-lift optimization system. This thesis emphasizes on how to optimize the resource of gas-lift by applying the method of portfolio theory and compare it with present system. The following steps of this methodology are shown below and Appendix 1 illustrates flowchart of this methodology.

Analogy parameter between investing in project and injecting Gas-lift in well. Normally, portfolio theory is associated with money and securities or projects and it is used to select the preferred group at given risk and return. There are many similarities between project investment and Gas-lift injection. Portfolio selection method is very popular and is recognized around the world because it can help many decision makers in analyzing and selecting the group of securities or projects. Moreover, efficient portfolio or efficient frontier which is a risk and return plotted graph will be created to see the group of project that is efficient to select. Due to their similarities, it is very challenging to apply portfolio theory in projects to using gas-lift wells which can be described as follows: Table 3.1 Comparison between project investment and gas lift well injection

No. Project Investment Gas-lift well injection 1. Budget constraint (M$) Produced gas lift constraint (MM$) 2. Project available (50 projects) Well available (400 wells) 3. Which project is suitable to invest

money Which well is suitable to inject gas

4. Risk of failure Risk of failure (operational risk) 5. NPV of each project Oil of each well 6. Probability of success of each project Probability of certainty of each well 7. What is the proper faction in each

selected project What is proper fraction of gas in each selected well

8. Rarely decision making Frequently decision making

3.1. Data Collection, analysis and preparation Data and information from gas-lift wells are very rudimentary because they are able to express the difference of well performance and also they are used to analyze both in term of creating graph and generating gas-lift simulation model. More data and information needs to be collected for analysis and optimization. This methodology also needs a lot of data listed as follows.

38

Table 3.2 The important parameters for analysis

In order to obtain a lot of data, it is necessary to visit operation field and needs the cooperation of the staff. The more data we have, the better the analysis in term of precision.

3.2. Create the inflow and outflow performance relationship All parameters need to be sorted or classified before used in the analysis. Some parameters are constant while others always change during production so historical data is required to predict future performance. Inflow performance curve and outflow performance curve are created by some parameters of well such as pressure, gas-lift injection rate, oil flow rate etc. The production rate is calculated from the IPR as follows: Figure 3.1 Inflow and Outflow performance curve of gas lift wells

q = production flow rate, bbl/d J = productivity index

RP = average reservoir pressure, psia Pwf = wellbore flowing pressure, psia IPR = Inflow performance relationship OPR = Outflow performance relationship

Well1

Well2

Well3

)( wfR PPJq −=

39

3.3. Generate relationship graph between gas rate and oil rate The gas-lift performance need to be known before injecting gas in order to know the relationship between gas-lift injection and produced net oil. The gas-lift performance will be created from WinGLUE (that is the software available in S1). The gas-lift performance will be created not only from individual well but also group of selected wells using WinGLUE as shown below: Figure 3.2 Gas lift performance curve from individual well and the combination of wells

3.4. Rank and cut method of traditional method based on S1 Rank method is a popular method useful for gas-lift system. GUF stands for gas utilization factor and it is used to rank performance of each well. Only better GUF wells are produced while the lower GUF wells are closed in. GUF is calculated from the following equation below. Data and information of all wells is filled into WINGLUE in order to ranks the well from higher performance of GUF to lower performance of GUF until resource of gas-lift is exhausted. Table 3.3 shows the range of GUF and table 3.4 is schedule to inject gas into gas-lift well at different available gas lift resources.

Well3

Well2

Well1 Well1 & Well2

Well1 & Well3

GUF = Net Oil / MSCF of gas

40

Table 3.3 Data and information of each well Inject gas-lift rate weights starting from high GUF to low GUF until run out of available gas lift resource. Table 3.4 Glue Table by WinGLUE software program

41

3.5. Construct the traditional method based on S1

To imitate the real system, it is basically the steps to create the traditional method model in excel spreadsheet by considering every related part in real time gas lift system. This thesis will start from obtaining gas lift performance curve data that was formulated by WINGLUE software. Optimization problem model of gas-lift will be created to be flexible to change or develop data in order to study the whole from the allocation of gas-lift system. Many case studies are provided to give better understanding and the following steps taken to construct the model are shown in figure 3.3. Flowchart of traditional method

Figure 3.3 Flowchart of using traditional method model Moreover, excel solver is used to find the optimal point from the programme that is already developed tool build in Microsoft excel. In order to optimize the problem, that is normally in form of mathematical equation, it is better to use the solver in excel which save time from developing another program and it is more convenient and comfortable to use. The

Start

Enter input and output in model

Run simulation by using excel solver under constraint and objective function

The optimum outcome

Finish

Fit curve finding estimated equation of each well

Input and output preparation

GLPC data generated by WinGLUE

42

following steps are used for creating the traditional method which is related to the use of solver option in Excel as illustrated in figure 3.4 below: Flowchart of creating traditional method model by using Excel solver

Figure 3.4 Flowchart of using solver option in traditional method

3.6. Construct the improved traditional method based on S1 After constructing the traditional method for the model, the overviews of all gas lift system are obtained. Enhance gas lift allocation process is proposed in this part by considering the economic aspect of oil price and gas cost. In addition, the method used to improve the traditional method in order to have more optimization is to use the increase of gas utility factor (ΔGUF) and also it is suitable for the interrupted system (some system parameter is adjusted parameter that is not the same as given by program and the user do not want to run the whole system again). The basic principle is provided as follows.

Start

Create Model both objective function and constraint function in Excel spreadsheet

Open solver in excel spread sheet and set parameters and options before solving

Input parameter depended on the objective and constraint of case study in excel spreadsheet

Run simulation by pressing solve button

The results show Max or Min value from objective function and changed value of selected parameter in excel spreadsheet

Finish

Record the results of objective function and changed value

43

3.6.1 To find new optimal points supporting system change (new net oil optimization)

This part proposes the methodology to find the optimal point when some constraint in the system changes or traditional software is interrupted from user. To prefer the new optimal point is not related to rerunning the whole system and do not waste too much time. The step to construct this method is proposed as follows:

• Propose methodology framework on Appendix 8 • Develop program on MATLAB software to be able to find better optimal

point • Input the change of parameter such as change in gas lift resource. • Run developed program to find new optimal point • Obtain new optimal point based on focusing slope

For example, when available gas lift rate is more than the estimated gas or present gas usage, this process will find the highest performance well to inject the exceeded gas lift rate in order to achieve the maximum output. In this example, which well should be selected to inject more gas lift available (X2 –X1)? The answer is obtained from calculating the incremental slope or GUF. Figure 3.5 Example of well selection 3.6.2 To add in profit and cost part (profit maximization) For this part, when the oil price has fluctuated, the optimal point of profit will change. Therefore, the method to consider the economical part that is more reasonable to use for setting the optimal point or controlling and producing net oil in order to obtain the best profit of each situation. There are few steps here as shown below:

• Create Traditional method model • Improve model to support cost gas and price oil by raising three case of oil

price such as low case, base case, and high case. • Input additional parameter of gas lift cost and oil price into model • Obtain the best profit of each scenario • Calculate the additional gain after using this model

Y1

Y2 Y3 Y4

Well A

Well B

Gas Rate

Net Oil

X1 X2

P1

P2 P3

P4

44

3.7. Construct the portfolio theory method model

Using portfolio theory by involving uncertainty of expected return and expected return of each well

Most of investors are risk averse that is they do not like high probability of risk at given high return. All projects consist of risk and uncertainty so they need tool to help decision making. Portfolio is associated with considering risk and return. Not only risk involves in the projects investment but also risk involves in gas-lift rate injection. Uncertainty of expected return from injecting gas lift into produced well is shown in the following example below:

1. Each well has difference of water cut level 2. Each well has difference of changing of water cut (some well may be constant

water cut and some well may change water cut very fast. 3. Updating properties of well (well test result) is not properly or too late, so

data base may be low accurately to predict the target. 4. Condition within well change (such as formation damage, wax accumulation,

sand production, etc.)

Although real time gas-lift system is in production phase, risk is still involved. Uncertainty of estimated target between in exploration phase and production phase are very different are shown as figure 3.6. Figure 3.6 The difference risk between production and exploration phase We need to find out causes of uncertainty that can affect decision making such as opportunity loss to obtain more, less consistency of expected target, etc. There are some major factors as listed below:

• Wax • Water cut • Facility fail • Formation damage • Political • and other

45

There are simple processes of building portfolio model that gives the better estimated target nearby target or more consistency target that are illustrated as shown in the figure 3.7 below: Flowchart of Portfolio theory method

Figure 3.7 Flowchart of applying portfolio theory model

Start

Run developed program in MATLAB with constraints to find the different combination n cases

The different results from n cases in term of portfolio mean and portfolio variance

Finish

Fit curve of each well and know the equation

The results from WINGLUE

Provide assumption such as oil price, gas cost, input, and output

Select range in net oil historical data to represent of each well

Link each combination of each portfolio to excel spreadsheet

The model includes STD DEV, Average return of each well, Covariance, Correlation between each other

Create Efficient Frontier

Select the preferred portfolio

46

Using MATLAB generates portfolio optimization at a given objective. To select the best combination, this portfolio with the developed program in MATLAB and Excel are able to perform several cases such as based on random, GUF ranking, incremental slope ranking, combination of several measurement parameters, etc. The example of combination of available wells is shown as in table 3.5. Table 3.5 Portfolios by using MATLAB at given the same objective Efficient frontier is created from many portfolios. Efficient frontier is more useful to the decision maker because it guides with better way that is most likely the highest return (expected net oil) at given any level of risk (standard deviation). The example of efficient frontier as shown below: Figure 3.8 Efficient frontier are generated from many portfolio

47

3.8. Discussion and conclusion Consider comparing the differences between traditional method that is old method using GUF and new method which consist of improved traditional and portfolio methods using the best point of wells combination are subjected to different scenario. Table 3.6 The comparison between traditional method and new methodology Comparison lists Old system New system

Alternative of Expected return

or net oil

Single value and less confident

Continuous value with confident level

Method to find optimal point

Rank and cut off by considering GUF of each well

Rank by GUF, ∆GUF, best point and involved risk

Operation Difficult to find better well when constraint change

Faster convergence, easier, and more consistency.

Decision making Easy to making decision due to single value

More consistency of expected target, and many options with uncertainty

Actual value less consistency of expected target

More consistency of expected target, optimum gas and maximum profit

Operation cost No cost Development program *Deferment oil The same Reduce

*Deferment is the difference between actual and estimated return Finally, the old method and the new method are concluded briefly as shown in appendix and more explanation will be discussed and concluded in chapter 4 and 5.

48

CHAPTER 4

RESULTS AND DISCUSSIONS This chapter focuses on the results of the optimization analysis carried out and discuss on the results from traditional method, improved traditional and portfolio method.

Oil field Development Overview F1 is the biggest onshore oil field, located in the northern part of Thailand, totally consisting of 92.879 sq.km of proposed production area. This oil field produces mostly gas and some oil. As oil is more valuable than gas, most of produced gas is used for helping oil production therefore many of wells are produced from artificial gas lift method. There are about 250 wells from 450 wells that are produced by artificial gas lift. There are many activities or facilities related to gas-lift and there are many gas-lift wells. It is therefore a better way to understand both the traditional and proposed a new approach by starting from 5 wells consideration including many case studies and different conditions. Well A10, B24, C18, D19, and E17 are representative of all gas-lift wells which are located in different areas also having different fluid properties. Therefore, we need to know the relationship between them. Appendix 2 shows the latest 25 wells test data of five wells. Each well and combination of wells has different behaviors. This case study is provided as follows:

1. The capacity of gas lift compressor is about 2,000 MSCF (Gas-lift compressor) but maximum produced gas is about 2,500 MSCF.

2. Available water disposal system is about 2,000 BBL (Water disposal pump) but maximum water system is about 2,500 BBL.

3. The limitations of minimum and maximum gas lift injection rate in each well ranges from 0 to 500 MSCF/D respectively.

4. The limitations of gas lift pressure are available at wellhead. 5. The other information are provided as table 4.1 below:

Table 4.1 The general information of gas lift injection system

Oil density

35 ̊API

Profit oil (PO) before deducing TGC

$80.00/BBL

Total gas handling cost (TGC)

$2/MSCF

For the value of oil, refers to http://www.oil-price.net/index.php?lang=en on March 1, 2010 and for the cost of gas-lift, refers to Queen Sirikit 1’s operating cost on March 1, 2010. In Appendix 11, operating cost income or OCI and other information are explained in detail such as PO and TGC. Crude oil properties in Thailand, refers to Dubai benchmark to be the standard due to the fact that most likely, the same components and refined oil price uses the reference from SIMEX exchange market (Singapore International Monetary Exchange) because Singapore is a big trade off market around this region, and its location is very close to Thailand.

49

6. The historical well test results of 5 wells example are given at the figure below.

Figure 4.1 Historical production data from well test results

7. Important data of gas-lift performance curve (GLPC) is given by WinGLUE software. Net oil and produced water are provided through varying gas injection rate and are transferred into this model in order to reanalyze again in figure 4.2 and 4.3 respectively.

Figure 4.2 Rate of Net oil production generated by WinGLUE software

Figure 4.3 Rate of Produced water generated by WinGLUE software

50

Figure 4.4 Graph of oil production generated by WinGLUE software

Figure 4.5 Graph of Produced water generated by WinGLUE software WinGLUE software is specific commercial software in gas lift system, designed for gas lift analysis, surveillance, troubleshooting, and optimization. As some part are out of the scope, therefore GLPC data are required from WinGLUE. Net oil production and produced water are the big part which needs to be considered, planned, monitored, controlled and decided. Traditionally, GLPC is created by considering inflow performance relationship (IPR) and outflow performance relationship (OPR). Figure 4.4 and 4.5 are plotted to show the summary of each well performance and GLPC which is convenient to convert from any gas lift injection rate to oil production rate. There are many parts of GLPC that need to be considered such as slope of each well, production value in y-axis at given the same gas lift rate in x-axis . After the relationship between gas lift injection rate and oil production rate of each well are created by WinGLUE, the data is transferred and fitted into a curve which is used for estimating the equation of each well as figure 4.6 and 4.7.

51

Figure 4.6 Estimated equations for oil production at given gas lift rate

Figure 4.7 Estimated equations for produced water at given gas lift rate 8. Assumption

8.1 25 latest test results are used to calculate STD (Net oil will be assumed to

find STD DEV each well) 8.2 Average return of each well comes from using 100% gas injection rate 8.3 Supposing that the same rate of gas lift is used while testing of each well

(ignore for the different gas-lift rate). For example about (300-400), well A10 used 300 Mscf, well B24 used 400 Mscf.

8.4 While testing, well test result from all wells come from the same gas lift injection rate are 500 Mscf

8.5 GLPC is generated by WINGLUE software program (Curve fitting method) 8.6 Cost of gas-lift ($/MSCF) and profit of net oil ($/BBL) are referred to Dubai

benchmark crude oil property (in order to compare in economic term)

52

4.1. Optimization with traditional method based on S1 This method is basically the method that provides fundamental information to understand all the process. Further, it focuses on the optimization problem that is composed in the objective function and constraint function under many constraints such as the limitation in gas lift compressor system, water disposal system and fluid properties and well performance. In addition, the estimated gas lift equation after carrying out curve fitting from WINGLUE will be used to indicate the relationship between gas lift injection rate and oil production rate. The oil and gas wells are not applicable to linear programming problem because well behavior and curve fitting is shown in polynomial 2nd order. In order to understand the overall process of gas lift system, there are many case studies raised to show why the main propose, limitation and others factors need to be considered before making decision. Problem may occur with water disposal system. Table 4.2 Constant gas lift available and vary in capacities of water disposal system

Limited gas 2000 limited water 1000 Limited gas 2000 limited water 1500 Limited gas 2000 limited water 2000

Problem may occur with gas lift compressor system Table 4.3 Constant capacities in water disposal system and vary gas lift available

Limited gas 1000 limited water 2000 Limited gas 1500 limited water 2000 Limited gas 2000 limited water 2000

This part will talk about the constraint in many cases, especially in total gas injection rate available and total capacity of water disposal system of plant. If the system has a lot of limitation, it will cause to less production as well. Therefore, the staff in charge need to know the plant potential and well performance before making decision about selecting the possible well and injecting the proper rate of gas. 4.1.1 Objective and constraint function

In this case, the basic principle of oil production is specifically gas lift system. Gas lift optimization problem will be provided as follow.

Where;

Qot = the quantity of total oil production per day Qoi = the quantity of oil production in well i per day Qgt = the quantity of total gas-lift injection rate per day Qgi = the quantity of gas-injection rate in well i per day Qwt = the quantity of total capacity of water disposal system per day Qwi = the quantity of produced water in well i per day i = Well number 1,2,3,4,5

53

Objective Function (Maximization net oil production) Max Qot =Qo1 + Qo2 + Qo3 + Qo4 + Qo5 oil production

; Qoi = (A)(Qgi)2+(B)(Qgi)+C i=1,2,3,4,5

Constraint Function Qg1+Qg2+Qg3+Qg4+Qg5 <= Qgt gas-lift resource

Qw1+Qw2+Qw3+Qw4+Qw5 <= Qwt water disposal system Qgi <= Qgmax i=1,2,3,4,5 well restriction Qgi >= Qgmin i=1,2,3,4,5 well restriction Qwi >= 0 i=1,2,3,4,5 water production

All variable >= 0

4.1.2 Case study of traditional method 4.1.2.1 Optimization with unlimited gas lift usage or/and unlimited water disposal

system (Under limitation of gas lift injection per well 0-500) Using solver with available maximum gas 2500 MSCF and available maximum water disposal system 2500 BBL (There is no combination using more than unlimited resource)

Define, Unlimited gas = 2500 MSCF, Unlimited water = 2500 BBL

1. Unlimited gas (2500 MSCF) and unlimited water (2500 BBL) ----rarely 2. Unlimited gas (2500 MSCF) and limited water 1000 BBL------rarely 3. Unlimited gas (2500 MSCF) and limited water 1500 BBL------rarely 4. Unlimited gas (2500 MSCF) and limited water 2000 BBL------rarely 5. Limited gas 1000 MSCF and unlimited water (2500 BBL) ------rarely 6. Limited gas 1500 MSCF and unlimited water (2500 BBL) ------rarely 7. Limited gas 2000 MSCF and unlimited water (2500 BBL) ------rarely

4.1.2.2 Optimization with limited gas lift usage and limited water disposal system (Under limitation of gas lift injection per well 0-500) Using solver with available maximum gas 2000 and available water 2000

8. Limited gas 1000 MSCF and limited water 1000 BBL -----Normally 9. Limited gas 1000 MSCF and limited water 1500 BBL -----Normally 10. Limited gas 1000 MSCF and limited water 2000 BBL -----Normally 11. Limited gas 1500 MSCF and limited water 1000 BBL -----Normally 12. Limited gas 1500 MSCF and limited water 1500 BBL -----Normally 13. Limited gas 1500 MSCF and limited water 2000 BBL -----Normally 14. Limited gas 2000 MSCF and limited water 1000 BBL -----Normally 15. Limited gas 2000 MSCF and limited water 1500 BBL -----Normally 16. Limited gas 2000 MSCF and limited water 2000 BBL -----Normally

54

The Flowchart to construct the traditional method by using excel solver is illustrated in chapter 3 and the method to calculate the optimal solution by using excel solver is shown in Appendix 3 step by step. After that, we obtain the estimated gas injection rate of each well and the estimated oil production from all the production wells in figure 4.8 in case of unlimited gas lift and water disposal system. In well C18, only 392.5 MSCF/D is optimal rate giving the best net oil although gas-lift available can be injected more than 392.5 MSCF/D. Figure 4.8 The estimated gas injection rate each well and estimated total oil production The results can be shown in term of total return and profit oil by using referred data in figure 4.9 below. In term of monetary, given assumption of cost gas and profit oil is constant.

Figure 4.9 Profit oil and cost gas are used to calculate total return and profit oil Therefore the total return is 12.59% Or profit oil after deducting cost of gas = 60,243.97-4,785 = 55,459 USD Record of the results of net oil production, gas lift usage, produced water, return and profit oil of all the case studies that are mentioned in the beginning are shown below. After running the simulation by changing some parameter as the condition of each case study, the total results of sixteen case studies are illustrated in figure 4.10

Figure 4.10 All the results of maximum production at given different conditions

55

As shown in the results, the results from the sixteen case studies are different because the limitation of facility is varied especially in gas lift resource and the capacity of water disposal system. In this case study, the capacity of water disposal system is more useful than available gas lift. For example, case 3 with more gas injection rate (gas = 2,000 MSCF and water=1,500BBL) can produce 647 BBL of oil is less than case 13 with more capacity for water production (gas=1,500 MSCF and water=2,000 BBL) can produce 686 BBL of oil. Therefore, it means that the capacity of water disposal system is more important than gas lift available. The maximum oil production will obtain from the unlimited water and unlimited gas lift in case 1, but it does not mean that this is the best selection because the additional gas lift rate and the capacity of water disposal system causes increase in operating cost as shown in term of low return (13%) . Generally, gas lift rate and the capacity of water disposal system is less than 2,500 MSCF (unlimited gas) and 2,500 BBL (unlimited capacity of produced water) respectively. In my view, the performance of each well and the combination of wells are mainly considered because they are able to change the best outcome. In case of unlimited water disposal system (2,500 BBL) but varies rate of gas lift from 1,000 to 2,500 MSCF as shown in figure 4.11, the numbers of many values are plotted in the graph and then it will be able to create the estimated curve in order to predict any rate of gas lift injection and provide the results of net oil quite real. Finally, the curve is called gas lift performance curve which is use to predict the net oil production at given the gas injection rate. Not only the numbers of many points are created but also proper mathematical algorithms to fit and represent these points are very important because it can indicate the accuracy of the prediction by using estimated equation.

Figure 4.11 All the results of maximum production at given different conditions As the result shows, this graph will be able to estimate the target net oil in y-axis by using different rate of gas lift in x-axis with the same condition such as objective and constraint.

Total gas lift rate (MSCF)

Total net oil (BBL)

56

The best result is both unlimited gas and unlimited water in order to achieve the maximum net oil or profit but normally gas usage and capacity of water disposal are limited such as limited facilities, investment cost. Besides, if they need to increase the available gas lift or capacity of water disposal, they need to calculate the additional cost from investment, additional profit by using the model to simulate the most likely results before making decision.

4.2. Optimization with improved traditional method based on S1 An additional method is the improvement of traditional method which its essential process to enhance the performance of gas lift operation system because there are many problems neglected and it was not practically corrected. Nowadays, the problem is always solved by relevant persons with more experience. Traditional method uses commercial software (WinGLUE) which is not able to do everything and some of its parts should be modified or developed by relevant person in each field. There are two parts which are not quite big issue problem but it is interesting to take into account as follows:

1. To find new optimal points supporting system change (new allocation gas-lift optimization)

2. To add consideration of profit and cost aspects (profit maximization)

4.2.1 To find new optimal points supporting system change (new allocation gas-lift optimization)

It is a process which recalculate from the most recent solution after changing some parts of system. Due to the changes in constraints such as available gas to lift, it is useful to recalculate and find new optimize points by considering some parts but not to rerun or start from the beginning. The proposed additional method performs when some parts in the system change after the whole system have been run already. It takes more time for the traditional method if there is change of constraint such as supply of gas lift, water disposal system, and other factors, gas lift system has to rerun the whole system. The additional process is a small process that considers and begins from the most recent optimal point to find new optimal point by using another indicator that is ∆GUF or slope consideration for each well, and then they will know which well is suitable to change or improve to reach the optimal point again. For example, when available gas lift rate is more than the estimated gas or present gas usage, this process will find the highest performing well to inject the exceeded gas lift rate in order to achieve the maximum output. Figure 4.12 Example of well selection

Y1

Y2 Y3 Y4

Well A

Well B

Gas Rate

Net Oil

X1 X2

P1

P2P3P4

57

Let us take a look at the simple case in figure 4.12 which shows the same incremental gas lift rate but different additional net oil in y-axis or different increment of GUF. Supposing that, there is 50 MSCF gas lift rate available that needs to be injected to some well in order to have more net oil. Where, X1=100, X2=150 Y1=50, Y2=80, Y3=90, Y4=100 ∆x1-x2=50, ∆y1-y2=30, ∆y3-y4=10 4.2.1.1 Traditional method Normally, it will be considered for only one point or one rate of each well and compare it with the highest value which will be preferred more than others. Let us take a look at the example below:

GUF of well A = Y1/X1=50/100= 0.5 GUF of well B = Y3/X1=90/100=0.9

From the result of traditional method above, well B is preferred and selected to inject additional 50 MSCF of gas into well B (10 more net oil), but actually the correct well to be selected is well A because well A gives additional net oil more than well B (30 more net oil). 4.2.1.2 Improved traditional method There is a better way to find the optimal well to improve or change the gas lift rate, which is by considering the incremental GUF or slope consideration as shown below:

∆GUF of well A = (∆y1-y2)/ (∆x1-x2) = 30/50 =0.6 ∆GUF of well B = (∆y3-y4)/ (∆x1-x2) =10/50 =0.2

As the result of improved method shown above, well A is preferred and selected to inject more 50 MSCF of gas into well A and the correct answer is also well A because it gives additional net oil more than well B. The program development process for this method is explained in details in Appendix 4. 4.2.1.3 Conclusion Initially the first, well selection method to inject gas lift uses GUF to be the indicator. Secondly, after the optimal well and optimal point are provided, the way to change the rate of gas lift in each well uses ∆GUF to be the indicator in order to help in making decision. For small system, there is no problem because it is easy to calculate all the parameter and relevant parts are not complicated, therefore it is recommended to rerun the whole system. For the big system, the improved traditional method has not only gain its usefulness for the huge system due to additional time saving, but also it is suitable for modified system which optimal solution from commercial software does not at times fit the real system, so the programmer need to adjust it again. Due to the inability to rerun of the whole system when system constraint changes by relevant person or staff, the improved traditional method is therefore very useful in finding the new optimal point to achieve the maximum net oil by continuing from the present operation or the latest optimal point.

58

4.2.2 To add consideration of profit and cost parts (profit maximization) Normally, in production field, operators only focus on the quantity of net oil production, so oil price and gas cost are not considered. Even if oil price is very high, they will try to do everything in order to increase the productivity as much as possible. It means that they think about the more net oil, the higher profitability, but actually it may not be the highest profitability because average of return may decrease lower and lower against increasing net oil. It is a good idea if they have additional method to monitor and control both the profit part and cost part. In this case, it focuses on total profit and then shows the different results from considering net oil only. There are three cases of oil price which consist of low, base, and high oil price case.

• Gas cost is equal to 10 $/MSCF at every cases. Normally, gas price have tendency similar to oil price. (Assume: use constant gas sales agreement)

• Oil price low case is equal to 40 $/BBL • Oil price base case is equal to 80 $/BBL • Oil price high case is equal to 120 $/BBL

Figure 4.13 Illustrates the different optimal point when oil price change After using traditional method which provides the first step of allocating gas lift to achieve the maximum net oil at varied gas lift rate at the same constraint such as maximum of water disposal system capacity and available gas lift, the GLPC of all good wells combination is created in figure 4.11 and will be used to create new model as shown in figure 4.13 by including the cost of gas lift and oil price. Figure 4.13 shows the change of optimal point when oil price change. When oil price is too low about 40 $/BBL, the highest profit (15,625$) using 1,000 MSCF gas lift injection rate. If they inject gas at a rate more than 1,000 MSCF (>1,000) at the same given oil price (40$/BBL), incremental net oil will be obtained but the total profit will decrease because average return (profit/cost) decreases as shown in figure 4.14. Figure 4.14 shows that if rate of gas lift is increased more than 1,000 MSCF or 10,000 $ in x-axis, total profit tends to decrease. Figure 4.15 and figure 4.16 are oil price at base case and high case respectively. In addition, oil price increases or decreases affects and change the graph as well. Therefore, it is better to reallocate gas lift injection rate to touch new optimal point or maximum total profit.

Low case

Base caseHigh case

Available

Define;

59

Figure 4.14 Low oil price or low case Figure 4.15 Normal oil price or base case

Figure 4.16 High oil price or high case

The purpose of creating the model is to help in making decision when the system constraint (oil price and cost gas) changes and the model will be able to suggest the right way to follow, otherwise the operator do not know when to change or reinvest in order to reduce the usage or increase usage resources such as gas lift injection rate, how much gas lift injection rate is suitable for several events? If we know the exact point, we can reallocate gas lift rate in order to have better profit or outcome. Generally, cost in operation will not be considered seriously only less than estimated budget, therefore average return is low and tend to reduce as they do in many activities in order to attain high net oil or high revenue or look at only positive part (revenue). Figure 4.17 Two choices of consideration when oil price changes

1st choice

2nd choice

***

Total profit ($)

Total cost ($)

Total profit ($)

Total cost ($)

Total profit ($)

Total cost ($)

60

For example, Now, oil price is about 40 $/BBL, gas lift usage of about 1,000 MSCF is able to give the profitability about 15,625 $. Take a look at this example, there are 2 choices to exercise or make decision when oil price change which are do nothing (not change) and reallocate gas lift injection to new optimal point. Suppose that at base case or 80 $/BBL, if we try to increase gas lift rate to be 1,400 MSCF from 1,000 MSCF and suppose that at high case or 120 $/BBL, if we try to increase gas lift rate to be 1,500 MSCF from 1,000 MSCF, we will obtain more than other cases. Let us take a look at the following choices below: Let; When oil price change from 40 to 80 or 120 $/BBL respectively, the operator has to make decision between the first and second choice. First choice is to do nothing by using the same rate that is used previously therefore the profit will be increase depending on oil price only. Presently, oil price will increase or decrease when gas lift usage is the same around 1,000 MSCF, operators recognize increase in production but they do not know about which rate of gas lift should be? Second choice changes gas lift rate from the initial rate to the optimal rate at different oil price, consequently the profit will increase from oil price about 40 $/BBL by increasing gas lift rate to be the optimal rate. For example, profit is 15,625 at 40 $/BLL it will be increased to 41,249 and 66,874 $ at 80, 120 $/BBL respectively without changing gas lift rate about 1,000 MSCF constantly. It is a good idea if you change the rate from the beginning to be the new optimal rate because oil price already change. In this case, there will be additional profit when you increase rate of gas lift and also increase profit at the end. For instance, If oil price changes to 80 $/BBL, and gas lift usage will be increased to 1,400 MSCF in order to have additional profit about 43,264-41,249 = 2,015 $. Therefore, we need to consider the significant factor such as oil price, gas cost, etc. In the future, if there are many wells are available, the total gas lift requirement may not be enough, so we need to consider finding another way of enhancing the capacity of gas lift compressor because the existing system can give the maximum gas lift production of about 2,000 MSCF, new investment need to be estimate by using model to help in order to weight between cost investment and additional profit for additional more 500 MSCF (new rate = 2,000+500 = 2,500).

4.3. Optimization with portfolio theory method

Nowadays, many calculation methods always provide the end result in form of deterministic or one value. It is very easy to use it in next process and to be understood by everyone but it is not quite good because it never faces that value and makes everyone lacks awareness. It is better way to provide the end results by including the range of uncertainty of the results (stochastic or continuous value) under confident interval percentage. Moreover, it can help train users of this method to have more awareness in order to make good decision. In part of production field, portfolio theory is never applied to gas lift optimization problem. However, portfolio theory was able to be applied to everything that includes uncertainty part. In this case, the process of gas lift system was selected based on applying portfolio theory because many parts are similar to the traditional portfolio in the economic aspect. Fluid properties and other relevant information of each well are not frequently used but this tool requires many data to be analyze and can provide the most likely well and the relationship between wells. The end results of portfolio theory are to provide several wells

61

combination, and also several results in form of stochastic or continuous value. Then, the decision maker will make a good decision with all information and know the exact value within possible range and have more awareness of uncertainty under confident percentage. In this part, we need to prepare the important parameters as follows:

1. Average return ------ > Using 1 latest well test result and price assumption 2. Standard deviation----------- > Using 25 latest historical data from well test 3. Covariance-------------------- > the relationship between wells 4. Correlation coefficient---- - > the relationship between wells 5. Weight of gas lift injection-- > There are many ways or objectives to create it 6. Portfolio Return ------------- > Return of well combination 7. Portfolio variance------------ > Variance of well combination

4.3.1 Average return Average return shows that each well performance depended on oil price and cost. The more average return a well has, the more valuable well is. For instance, if well has good average return it means that the well’s revenue is more than its cost. There are many steps to generate average return in Appendix 5. 4.3.2 Standard deviation (STD DEV) σi Standard deviation is parameter which measures well characteristic by looking at spreading of data group. A high standard deviation means that the well has more fluctuated net oil production which is not quite constant and is difficult to estimate the result. To find the standard deviation, is by using equation in chapter 2. In this case, the net oil of each well is selected to be the representative in order to calculate individual standard deviation. Historical data is prepared and calculated by mathematic function in excel which is also shown in Appendix 5. 4.3.3 Correlation coefficient (ρij) Correlation Coefficient is very necessary because it can tell the relationship between each pair of well combination. Normally, the value of correlation coefficient is between minus one and plus one. Positive value means that the relationship between two wells tends to be the same way but negative value means otherwise. It is very good if correlation coefficient is right. Correlation coefficient was calculated using the formula in chapter 2 and the steps to calculate it is shown in Appendix 5. 4.3.4 Covariance or coefficient of variation, CV Covariance is measurement of return between two wells and it can be negative, positive or zero. High positive value means high return between two well combinations and the steps also are as shown in Appendix 5. 4.3.5 Gas Lift Weight It is very important rudimentary parameter because this part will be used to generate many wells combination of gas lift system by weighting gas lift injection rate with limited constraint. In this part, it was focused on by using MATLAB to generate the different well

62

combinations around 20 portfolios. Normally, there are two ways to generate the well combination or weighting different gas lift injection rate into wells.

1. Using MATLAB software (program developed by myself) to find the well combination with constraint by ranking from highest to lowest net oil and in this case, the program was already prepared for 20 combinations or 20 portfolios. In MATLAB software, many combination of gas lift rate can be created in it depending on the program that was developed at any constraints. Moreover, advantages and disadvantages of using MATLAB are shown in Appendix 7.

2. Using excel solver or complete program (without writing program) generates in other cases such as equal weight (1st port), highest net oil (2nd port), lowest variance (3rd port), etc. For this case, they are out of consideration.

Figure 4.18 shows the possible value in MATLAB program and figure 4.33 show the possible values in portfolio theory. These possible values can be changed by programmer. Figure 4.18 Gas lift range at minimum significant interval in unit of MSCF Before using it in the last step of the calculation of portfolio return and portfolio variance is used, real unit from 0 to 500 MSCF will be converted to range of 0 to 1 as figure 4.19.

Figure 4.19 Gas lift range at minimum significant interval in unit of 0 to 1

After MATLAB is run with all constraints included, the possible results will be shown in the example below and then rank from the highest net oil down to 20 values in figure 4.20. Moreover, the sequence of the program in MATLAB software is created and explained in details in Appendix 6. Figure 4.20 Results of 20 portfolios after simulating program in MATLAB

63

In figure 4.20, Using gas lift at 2,000 MSCF consists of 871 cases based on random method. Besides, each portfolio will provide the quantity of gas lift in each well along with the total estimated net oil and produced water. Furthermore, it is very flexible to generate possible portfolio in MATLAB software because it is able to change the objective and constraints function directly. After weight of each well is provided in accordance with objective and constraints requirement, they will be linked to calculate in excel spreadsheet in figure 4.21. Suppose available gas lift is 2,000 MSCF Figure 4.21 Results of 20 portfolios on excel spreadsheet (0-500 MSCF) Suppose available gas lift is 1.00 Figure 4.22 Results of 20 portfolios on excel spreadsheet (0-1)

64

After all portfolios are created by quantity and then they will be linked to the next process to calculate portfolio return and portfolio variance. For example, portfolio number 1 will be raised to explain step by step. 4.3.6 Portfolio Return (Rp) Portfolio return is straightforward to be calculated because return of every well will be summed up. Average return will be prepared and calculated with oil price and cost gas in figure 4.23 by taking an example using portfolio 1. The portfolio return of port 1 is about 85.81%.

Figure 4.23 Example of average returns preparation 4.3.7 Portfolio variance (σp) Portfolio variance is calculated using the formula in Chapter 2. Portfolio variance is used to check the deviation of each combination or each portfolio this is a very important parameter because it shows different results in term of percentage of the standard deviation. Moreover, it helps decision maker make good decision and knows which port has more confident or more consistency estimated target. Example of calculations and preparations are shown in figure 4.24 Figure 4.24 Example of portfolio variance preparation Finally, portfolio variance is summation of the lowest line 541.02+95.57+169.45+ (-28.06) +19.16 = 797.14 And portfolio standard deviation is 28.23 % In summary,

Portfolio return = 85.81% Portfolio standard deviation = 28.23%

65

4.3.8 All portfolios results and Efficient Frontier construction 4.3.8.1 The results of portfolios without standard deviation consideration. If no standard deviation of each well (σ = 0) it mean that every time you estimate the net oil target is the same as actual net oil and also portfolio variance is zero. (The result is the same as traditional method as shown in figure 4.25) Figure 4.25 No consideration of standard deviation of traditional method Therefore, traditional method is shown in figure4.25, it is straightforward to decide that the best selected portfolio is portfolio number 1 because it provides highest net oil production. Although it is very easy method of selecting portfolio, it never meets the estimated value and makes users lack awareness. Besides, they do not know that is the possible range should be? Finally, they always have one answer that is the highest return only and they do not know anything else. What is the efficient frontier and what is the benefit of construction of efficient frontier? The results of portfolios can be illustrated and considered in term of net oil and average return. Efficient frontier (EF) is the line which each standard deviation at given highest return (look at vertical axis first and then horizontal axis later); therefore if any portfolio is near or on efficient frontier, it will be the good candidate portfolio. For example, there are 3 portfolios which are composed of portfolio 1, 2, and 3 as figure 4.26.

66

Figure 4.26 Basic of efficient frontier construction

In comparison between port 1 and port 2, answer is port 2 In comparison between port 2 and port 3, answer is port 3 In comparison between port 1 and port 3, answer is port 3

Therefore, efficient frontier will be created pass portfolio 3 4.3.8.2 Results of all portfolios are shown between standard deviation and net oil and after that efficient frontier will be created in order to make a good decision. Figure 4.27 The results of all portfolios in standard deviation and net oil They should be separated in different level or group in order to analyze it before making good decision by following the steps. First, this case will be separated to 3 regions that are in different groups of return in figure 4.27. The principal of portfolio theory with efficient frontier is selection at or near efficient frontier line. For example, region 1 or high return prefers portfolio 1 (746 BBL) more than port 2(746.36 BBL) and port 3(745.16 BBL) and the same thing with region 2 and region 3 should prefer port 4(743.46 BBL), port 8(742.07 BBL), and port18 (738.26) respectively. Although net oil of portfolio1 in figure 4.27 is the highest value but standard deviation also is not good or quite high as well. However, it is absolutely to choose portfolio 1 because it does not only provides the highest value but it also have lower standard deviation than portfolio number 2 and 3.

(BB

L)

1

2

3

3 2

1

EF Net oil (BBL)

Std DEV (%)

67

4.3.8.3 The results of all portfolios illustrate between standard deviation and Average return

Figure 4.28 The results of all portfolios in standard deviation and average return The results show that between the standard deviation and the average return in figure 4.28 which have different answers to the results in figure 4.27. If the main objective is considered to be average return that is associated with profit and cost, so it will consider profit per unit of cost. Although the total gas lifts usage is the same but the return per unit is different. Region 1 at high standard deviation and high return should prefer port folio 3 (107.9 % average return) because it is very close to EF or lower standard deviation than portfolio 16 (106.43). Region 2 with wide range of distribution should prefer port 8 (89.09 % average return) because of its lowest standard deviation which is more consistent compared to others and average return are almost highest in this region. However, it is still difficult to select one portfolio to gas lift allocation system, risk preference of decision maker that is out of the scope of this thesis that is able to solve this problem or find one optimal portfolio which is also explained in Appendix 12.

1

2

68

CHAPTER 5

CONCLUSIONS AND RECOMMENDATIONS

5.1. Conclusions This thesis analyzes about oil output of a set of wells combination to obtain estimated net oil and associate it with uncertainty. It started by studying and constructing the basic model of the present method of S1 or traditional method which is high powerful, efficient and simple tool to apply in oil and gas field. The traditional method definitely lacks flexibilities and consideration for uncertainties, therefore this project or this thesis will further be generated by taking advantages of individual and combination of well. After that, I introduced the new approach for well selection, portfolio theory method, and reviewed what the portfolio theory method is, how it can be applied and how the oil field operation in Thailand can gain more value through the use of portfolio theory method. Traditional method model is basically created model to provide the basic learning process of gas lift system because this part did not only provide more understanding of the overall technique of gas lift system but it also describe how to optimize originally allocation gas lift system. After traditional method model is created and used to model the real system by raising case study of 5 wells with different objective and constraints, it provides different results to the study and familiarity given the different consideration such as available gas lift, consequently it produces many interesting outcomes. Therefore, it can be concluded that this model tries to imitate the real traditional method, the results of this model shows the regular operation system, normal gas-lift optimization and operation of gas lift facilities. For improved traditional method model, it is additional method of traditional method which help in making it a flexible model suppose something change and we need to find the optimal condition considering oil price and cost. This model is developed on excel spreadsheet and MATLAB because it provides the flexibility when developing the method. From the results, it supports both cases that usually changes in constraint or situation that saves time from rerunning the whole system. In addition, it provides the additional profit consideration when fluctuation occurs in world economic such as changes in oil price. The traditional method and improved traditional method do not only give the overall basic gas lift optimization system, portfolio theory method also guides the additional process in order to make good decision. Also, it generates from excel spreadsheet and MATLAB that is powerful tool which helps in the model construction. To get the results, this method will provide one more dimension to be considered, however many information and data are required in order to complete the model. As in these results, the model gives the different optimal selection or more consideration about identifying the uncertainty of each combination. The end result does not give one value or one well combination, but it can provide many choices before making decision and provide more consistency of each group estimated target. This method provides many combinations and more consistency of each group expected targets (recommended portfolio is high expected target or net oil when given more consistency or less uncertainty of expected target). It is better to provide the end result more than one value at each combination and it is also going to give the range of the result with percentage confident or confident level that it is

69

closely real value because it is difficult to meet exact value by giving one value. In this thesis, the model shows what should the estimated target be with how much percentage confident (Using Monte Carlo Simulation in Appendix 8). Table of conclusion of all method are illustrated in Appendix 10. 5.1.1 The difference between traditional method and portfolio theory Traditional method

1. Traditional method only provides the result that is composed of which well is suitable to be open, how much gas lift rate is proper to inject, and how much net oil production is estimated to be produce (ignore uncertainty).

2. As from the result, traditional method may not be the best answer in well selection, therefore it means that the resources are not utilized and cause less profit than when the correct wells selection is carried out.

3. Traditional method uses WinGLUE software that is gas lift optimization program developed more than 15 years. The requirement of this program is less or small amount of input parameters than other programs. The WinGLUE is more powerful but it is not flexible to case that related with interruption by human factors.

4. Traditional method gives only one answer which is the highest net oil by ignoring other choices that may have quite nearly the same value of maximum net oil. For example, combination B is predicted less net oil than combination A, so the selection is A, but eventually combination B may provide better net oil more than A.

Portfolio Theory method

1. Actually, portfolio theory is the improvement of traditional method because it is not only giving the same result like the traditional method, but it also provides additional information (standard deviation of each well)

2. The requirement of portfolio theory is better than the traditional method in terms to finding the net oils standard deviation or behavior of each well and knowing the wells relationship.

3. Portfolio theory provides many choices that have many values at a given or quite nearly the same single value with the traditional method and also provides related parameter in each combination (portfolio standard deviation of each combination).

4. Portfolio Theory gives more choices for decision maker, so that they will find out which portfolio is suitable to select. The best portfolio is highest net oil at given lowest level of standard deviation. (more consistency result) For example, it is known in the beginning that combination B will provide more consistency than combination A, so combination B will be selected to get more consistency and this method will increase the accuracy of prediction.

5.1.2 Advantages of using portfolio theory to make good decision in oil and gas industries. The benefits for manager are shown as follows:

1. The more information they have, the better decision they make.

70

2. It can be used in term of cost and profit based on assumption such as oil price, gas cost, etc. (when should we invest new facilities system or what is the return of new facility?)

3. This model can be modified and easy to use for everyone. 4. This model/method can demonstrate consistency of each well result and

whether the combination between each other is good or not? 5. We can modify this model to help in making good decision in development

part that is whether to increase investment or not, how much is the breakeven point, and when will new facilities be installed given any price (Real Option).

6. In field operation, normally, they think about target oil, but they lack operation cost (OPEX) consideration only controlling cost less than available budget. (It is better if we can achieve the target and handle suitable cost) Therefore, average return should be considered. For instance, it is not good if oil production can achieve its target, but they spend more money as well and it shows low average rate of return.

7. We can be confident in target, when we use the outcome of this model. It will provide quite more consistency in target than traditional method.

8. We will know that when oil price, gas price or others change occurs, we should know how much oil production and how much gas injection will be sufficient to reach the highest of average return, not only to produce the maximum oil. Maybe gas, oil price increase or decrease, should we invest on new gas compressor or water disposal system?

9. If they use this model, gas will be extremely optimized and it will lead to maximize net oil production.

5.1.3 What are the new results? or what are the advantages of this thesis?

1. Create model for finding the optimal point of both maximum net oil and maximum profit.

2. Create model when considering changes in oil price and cost of gas as shows change in optimal point.

3. Add new indicator that is incremental range (∆GUF) using consideration from traditional method of one point consideration (GUF) without a rerun simulation of whole system (time saving  and  have  nothing  to  do  with  the operator).

4. Illustrate the importance of different well selection and gas injection  rate in term of portfolio and show many choices at different rate of return and uncertainty

5. Provide more consistency target. 6. Train the relevant user of the model to be aware of the uncertainty and be

familiar with probability range with high confident interval. 7. Suggest improved process such as in well test activities to enhance the

performance of this model and other analysis carried out.  8. Ability to develop a new model that can be use with new facilities associated

with gas lift system and can also use this model when calculating NPV,IRR, PI and so on.

71

9. Not only time is saved due to the fact that the whole system is not return but also it is sometimes used with the interrupted system that relevant person already modify to match with real situation, therefore they do not want to rerun WinGLUE again.  

5.2. Recommendation

Since the study is mainly concerned on many assumptions, some recommendations for oil field operation and future research are as follows:

5.2.1 Recommendation for process improvement

1. Every well should be recorded at least every month Suppose in 3 months.

Table 5.1 Example of well test schedule

Therefore, Well A ------------------ the total is 3 times Well B ------------------ the total is 6 times

Well C ------------------ the total is 12 times

2. They need to carry out well test at the same time as the latest test time (Such as well A in the morning) because temperature or time may affect the different results such as in the morning and afternoon.

3. It should note the description or more detail when facing the difference between present well test result and the last well test result both in Thai and English(It means that engineer should be responsible to analyze and record everything that is related to that wells).

4. They should install sensors to monitor and record interested production net oil of interested wells in order to study well behavior and other parameters.

5.2.2 Recommend for further study

1. The relationship of each well (the communication in reservoir) 2. It is very important because (for example, if well A and B have relationship

between each other, maybe produce high rate at well A can cause decrease in the production of well B. If we know we can estimate the exactly results.

3. The method to calculate standard deviation or average rate of return of each well still can be developed and improved because it is difficult to find the best method and no specific method is used now.

Well name Each week Each 2 week Each month

Well A constant

Well B less constant

Well C inconstant

72

4. It takes time because several steps are not only proceeded in excel but also are calculated in MATLAB (For now, I link most parts together but some parts need to be developed).

5. This method or model can still be developed in terms of assumption, the search method, in optimization method, or additional constraint.

6. After obtaining efficient frontier, one difficulty is to select one portfolio; however, risk preference that is the tool for calculating individual risk preferred by a decision maker can help to select a portfolio. Risk preference of decision maker is not included in this study, so it is better to continue this study by considering risk preference.

73

REFERENCES

Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, Vol. VII, No 1, pp. 77-91. Markowitz, H. (1997). Portfolio Selection. Efficient Diversification of Investments, Blackwell, Cambridge, 2nd ed. Sharpe, W. (1970). Portfolio theory and capital markets.

Hightower, M.L., David, A. (1991). Portfolio Modeling: A technique for sophisticated Oil and Gas Investors. paper SPE 22016. Palsson, B., Davies, D.R., Todd, A.C., and Somerville, J.M. (2003). Water injection optimized with statistical methods. Paper SPE 84048.

Newendorp, P.D. (1975). Decision Analysis for Petroleum Exploration. PennWell Books. Tulsa, Oklahoma. Howell, J.I., and Tyler, P.A. (2001). Using Portfolio Analysis to Develop Corporate Strategy. Paper SPE 68576. Walls, M. R. (1999). Corporate Risk Taking In the E&P industry. Oil and Gas Journal, Executive Report, Vol. 2, No 2, pp 42. Orman, M., Duggan, T.E. (1998). Applying Modern Portfolio Theory to Upstream Investment Decision Making. paper SPE 49095. Erdogan, M., Mudford, B., Chenoweth, G., Holeywell, R., Jakubson, J. (2001). Optimization of Decision Tree and Simulation Portfolios. paper SPE 68575. Edwards, R.A., Hewett, T.A. (1993). Applying Financial Portfolio Theory to the Analysis of Producing Properties. paper SPE 26392. Clark, M. (2006). Virtual Reality. Journal of Petroleum Economist, pp 8-9. Poulisse, H., et al. (2006). Continuous Well Production Flow Monitoring and Surveillance. Paper SPE 99963. Cramer, R., et al. (2006). Well Test Optimisation and Automation. paper SPE 99971. Steven, C., et al. Numerical Methods for Engineers. Fourth Edition, Mc Graw Hill. Zvi, B., Alex, K., Alan, j. (1999). Investments, McGraw-Hill, Fourth Edition, pp.217-226. PTTEP.(2007).S1 Operation. PTTEP OJT center. Merritt, D. (2000). Portfolio Optimization using Efficient Frontier Theory. Paper SPE 59457.

74

Erdogan, M. (2005). Going Beyond the Efficient Frontier Analysis Using an Integrated Portfolio Management Approach, Paper SPE 94565. Sholarin, E. (2006). Applying Integrated Project Management Methodology to Hydrocarbon Portfolio Analysis and Optimization, Paper SPE 100967. Faya, L.C. (2006).Beyond Portfolio Optimization. Paper SPE 107709. Mayhill, T.D. (1974). Simplified Method for Gas-Lift Well Problem Identification and Diagnosis. Paper SPE 5151. Radden, D., Glen Sherman, L.C., and Jack, R.B. (1974).Optimizing Gas-Lift System. Paper SPE 5150. Kanu, E.(1981). Economic approach to oil production and gas allocation in continuous gas lift. Journal of Petroleum Technology,pp. 1887-1892. Gomez, V. (1974). Optimization of continuous flow gas lift systems. M.S. Thesis, U.of Tulsa. Hong, H.T.(1975). Effect of the Variables on Optimization of continuous gas lift system. M.S. Thesis, U. of Tulsa. Clegg, J. D. (1982).Discussion of Economic approach to oil production and gas allocation in continuous gas lift, Journal of Petroleum Technology, pp. 301-302. N. Nishikiori, et al.(1989).an Improved Method for Gas Lift Allocation Optimization. Terry, B. and Andrew, C. (1999). new automated continuous gas-lift control system improve operational efficiency.

75

APPENDIX 1

Flowchart of methodology

Flowchart of thesis methodology is illustrated as figure below. There are three main method models are focused, constructed, discussed, and concluded are composed of traditional method, improved traditional method, and portfolio theory method.

76

APPENDIX 2

Five wells test data of 25 latest tests

Table 1 Well test data 25 latest of Well A10

77

Table 2 Well test data 25 latest of Well B24

78

Table 3 Well test data 25 latest of Well C18

79

Table 4 Well test data 25 latest of Well D19

80

Table 5 Well test data 25 latest of Well E17

81

APPENDIX 3

Method to construct the traditional method model

The process creating traditional method model is on the excel spreadsheet and relate to the solver excel that use for solving mathematic problem as follows. For example, using 2000 MSCF gas lift available and 2500 BBL capacity of water disposal system is the majority constraint.

1. Create Model both objective function and constraint function in Excel spreadsheet. Objective function is the main propose. For instance of this case, the objective is to find the maximum value of net oil (Qot) by varying variable of each well gas lift injection rate (Qo1, Qo2, Qo3, Qo4, and Qo5) as figure 1.

2. Input the value into the model as figure 1 depends on the objective and

constraints of case study in excel spreadsheet. Before creating the model, it is better to understand the relationship between maximum output (Qot) and input variable (Qo1,Qo2,Qo3,Qo4, and Qo5).

Figure 1 Objective function consists of the combination of each well production

Figure 2 Constraint function relates to gas lift available and produced water

82

3. Open solver in excel spreadsheet and set parameters and options such as setting target cell to minimize or maximize and selecting changing cell for variable when facing the solution and also setting the constraint in order to close the real situation as figure 3. Further, solver options window in figure 4 is used for setting algorithms matching to problem.

Figure 3 Solver Parameter window for setting the objective and constraint

Figure 4 Solver Options for setting important value before simulation

4. Run simulation by pressing solve button in solver options window as figure 3 5. The results show maximum value in total production oil and proper variable

gas injection rate each well with the selected algorithm in solver options.

Figure 5 results show the maximum value of oil production and proper gas injection rate

83

APPENDIX 4

Method to construct the improved traditional method model Example of Well selection Where

A s=Initial supply of gas lift @t0 Ad=real usage of gas lift @t0 B = Available Gas lift @t+1 ∆ =different between A and B N= How many time of adjusting J= order (=1,2,3….N)

1. In case; new available gas lift less than previous calculated available gas lift

yt = latest optimal point in BBL yt+1=new optimal point in BBL = yt+1(xt+1)=A(xt+1)+B(xt+1)^2+C xt = latest optimal point in MSCF xt+1 = latest optimal point in MSCF =(xt-50)

∆GUF = )1()()1()(

+−+−

txtxtyty =

50)1()( +− tyty

2. In case; new available gas lifts more than previous calculated available gas lift

yt = latest optimal point in BBL yt+1=new optimal point in BBL = yt+1(xt+1)=A(xt+1)+B(xt+1)^2+C xt = latest optimal point in MSCF xt+1 = latest optimal point in MSCF =(xt+50)

∆GUF = )()1()()1(

txtxtyty

−+−+ =

50)()1( tyty −+

Well A

Well B P1

P2

X (1) (2) Gas Rate

Net Oil

New Gas lift rate at (1) = available gas lift t1 less than at t0 Gas lift rate at (x) = Latest optimal point @ available gas lift

New Gas lift rate at (2) = available gas lift t1 more than at t0

84

Flowchart of improved traditional method program development

(Available Gas lift@t1=B) is less than the initial value

(B<Ad)

∆=A-B

N=ceil(∆/50) %How many iterations?

j=0; t=0

(Available Gas lift@t1=B) is less than the initial value

(B>Ad)

∆=B-A

N=ceil(∆/50) %How many iterations?

j=0; t=0

j=j+1

If j=N -----> R = [∆ - (N-1)*50] else R=50 %normal R=50 except final

∆GUF1=( y1(t)- y1(t+1))/( x1(t)- x1(t+1)) ∆GUF2=( y2(t)- y2(t+1))/( x2(t)- x2(t+1)) ∆GUF3=( y3(t)- y3(t+1))/( x3(t)- x3(t+1)) ∆GUF4=( y4(t)- y4(t+1))/( x4(t)- x4(t+1)) ∆GUF5=( y5(t)- y5(t+1))/( x5(t)- x5(t+1))

Find lowest ∆GUF

Preparation of x(t+1) and y(t+1) x1(t+1)=x1(t)-R; y1t+1(x1(t+1))=A1(x1(t+1))+B1(x1(t+1))^2+C1 x2(t+1)=x2(t)-R; y2t+1(x2(t+1))=A2(x2(t+1))+B2(x2(t+1))^2+C2 x3(t+1)=x3(t)-R; y3t+1(x3(t+1))=A3(x3(t+1))+B3(x3(t+1))^2+C3 x4(t+1)=x4(t)-R; y4t+1(x4(t+1))=A4(x4(t+1))+B4(x4(t+1))^2+C4 x5(t+1)=x5(t)-R; y5t+1(x5(t+1))=A5(x5(t+1))+5B(x5(t+1))^2+C5

j=j+1

If j=N -----> R = [∆ - (N-1)*50] else R=50 %normal R=50 except final

∆GUF1=( y1(t+1) -y1(t))/( x1(t+1) -x1(t)) ∆GUF2=( y2(t+1) -y2(t))/( x2(t+1) -x2(t)) ∆GUF3=( y3(t+1) -y3(t))/( x3(t+1) -x3(t)) ∆GUF4=( y4(t+1) -y4(t))/( x4(t+1) -x4(t)) ∆GUF5=( y5(t+1) -y5(t))/( x5(t+1) -x5(t))

Find highest ∆GUF

Preparation of x(t+1) and y(t+1) x1(t+1)=x1(t)+R; y1t+1(x1(t+1))=A1(x1(t+1))+B1(x1(t+1))^2+C1 x2(t+1)=x2(t)+R; y2t+1(x2(t+1))=A2(x2(t+1))+B2(x2(t+1))^2+C2 x3(t+1)=x3(t)+R; y3t+1(x3(t+1))=A3(x3(t+1))+B3(x3(t+1))^2+C3 x4(t+1)=x4(t)+R; y4t+1(x4(t+1))=A4(x4(t+1))+B4(x4(t+1))^2+C4 x5(t+1)=x5(t)+R; y5t+1(x5(t+1))=A5(x5(t+1))+5B(x5(t+1))^2+C5

Available gas lift change

Latest optimal point (initial value supply@t0= As), (real usage@t0 =Ad) (supposing that Ad=As);

Ad=X1+X2+X3+X4+X5

Start

85

Display (Ytot,Ad,x1,x2,x3,x4,x5)

Finish

No

If ∆GUF1= highest ∆GUF;--> y1(t)=y1(t+1) & x1(t)=x1(t+1) If ∆GUF2= highest ∆GUF; --> y2(t)=y2(t+1) & x2(t)=x2(t+1) If ∆GUF3= highest ∆GUF; --> y3(t)=y3(t+1) & x3(t)=x3(t+1) If ∆GUF4= highest ∆GUF; --> y4(t)=y4(t+1) & x4(t)=x4(t+1) If ∆GUF5= highest ∆GUF; --> y5(t)=y5(t+1) & x5(t)=x5(t+1)

Ytot=y1+Y2+y3+y4+y5 Ad=x1+x2+x3+x4+x5

Yes

J =N & Ad=B No

If ∆GUF1= lowest ∆GUF;--> y1(t)=y1(t+1) & x1(t)=x1(t+1) If ∆GUF2= lowest ∆GUF; --> y2(t)=y2(t+1) & x2(t)=x2(t+1) If ∆GUF3= lowest ∆GUF; --> y3(t)=y3(t+1) & x3(t)=x3(t+1) If ∆GUF4= lowest ∆GUF; --> y4(t)=y4(t+1) & x4(t)=x4(t+1) If ∆GUF5= lowest ∆GUF; --> y5(t)=y5(t+1) & x5(t)=x5(t+1)

Ytot=y1+Y2+y3+y4+y5 Ad=x1+x2+x3+x4+x5

Yes

J =N & Ad=B

86

APPENDIX 5

Method to construct the portfolio theory method model

Average return Average return shows each well performance depended on oil price and cost. The more average return well have, the more valuable well is. For instance, well has good average return means that well’s revenue is more than cost. There are many steps to generate average return as follows.

1. Use the same gas-lift injection rate at 500 MSCF with every well to get oil results

2. Assume the cost gas and oil price -Oil price = 80 $/BBL (Refer to Dubai crude) -Cost gas = 2 $/MSCF (Refer to field operation in Thailand) 3. Use the equation that is given by curve fitting as figure 1 below

Figure 1 estimated equation are created from WINGLUE software’s data

4. Figure 2 shows how to calculate average return which is profit oil is divided by cost gas

Figure 2 example calculation of average return Let assume that average return of every well is calculated from injecting gas lift rate at 500 MSCF. As the results, well C18 is the highest average return and well A10 is lowest average return. It means that the same quantity of gas lift rate is injected into wells, but return per unit of injection of well C18 more than others. Standard deviation (STD DEV) σi Standard deviation is parameter which measures well characteristic by looking at spreading of data group. A high standard deviation mean that well has more fluctuate of oil production or net oil production is not quite constant and difficult to estimate the result. To find standard deviation is using equation in chapter 2. In this case, net oil of each well is

87

selected to be representative in order to calculate individual standard deviation. Historical data is prepared and calculated by mathematic function in excel as figure 3. Figure 3 Example historical data for standard deviation Then, standard deviation needs to be converted to percentage as it should be the same unit as average return which is previously mentioned. Figure 4 shows standard deviation in percentage term. Average or mean of historical data in figure 4 is not used in next steps. Figure 4 Standard deviation in term of percentage Note that: Standard deviation is depended on data selection It is noticed that average return is prepared from figure 2 but standard deviation is prepared from figure 4. After average return and standard deviation are calculated, they will be prepared in figure 5. Figure 5 Average return and standard deviation in percentage

88

Correlation coefficient (ρij)

Correlation Coefficient is very necessary because it can tell the relationship of each pair well combination. Normally, the value of correlation coefficient is between minus one and plus one. Positive value is able to tell the relationship between two wells tend to the same way but negative value is on the other hand. It is very good if correlation coefficient is right. Correlation coefficient will be calculated follow the formula in chapter 2 and the results are illustrated in figure 6. Figure 6 Correlation coefficient of each two well Covariance or coefficient of variation, CV Covariance is measurement of return between two wells and it can be negative, positive or zero. High positive value means high return between two well combinations. It is shown in figure 7 below. Figure 7 Covariance of each two well

89

APPENDIX 6

Program development for weighting gas lift injection

function RANKP1W m=500 ; % m = Maximum gas injection rate n=20 ; % n = Number of Portfolio ii=0 ; % initial value Wav=2500 ; % Wav = input('Water system available') for X1=0: 50 :m ; % Minimum gas injection rate can be 0 or .....350 Now use Yi,Y2,Y3,Y4,Y5 >= 0 control for X2=200:50:m ; % Minimum gas injection rate can be 0 or .....200 for X3= 150:50:m ; % Minimum gas injection rate can be 0 or .....150 for X4 =100:50:m ; % Minimum gas injection rate can be 0 or .....100 for X5= 0:50:m ; % Minimum gas injection rate can be 0 or .....200 Xtot=X1+X2+X3+X4+X5 ; if Xtot==2000 ; %[Xtot<=2000 & Xtot>=1950] or [Xtot==2000] but the last value or 20th order is less than range such as 1900-2000 X1; X2; X3; X4; X5; W1=-0.0003*X1^2 + 0.3572*X1 -66.76 ; %we need to update when we test again W2=-0.0043*X2^2 + 4.851*X2 + 415.46 ; %we need to update when we test again W3=-2E-05*X3^2 + 0.013*X3 +29 ; %we need to update when we test again W4=-6E-06*X4^2 + 0.0027*X4 + 1.7 ; %we need to update when we test again W5=-0.0021*X5^2 + 2.7735*X5 - 211.64 ; %we need to update when we test again Wtot=W1+W2+W3+W4+W5 ; if Wtot<=Wav & W1>=0 & W2>=0 & W3>=0 & W4>=0 & W5>=0 % All variable >= 0 Y1 = -0.0007*X1^2 + 0.7576*X1-141.73 ; %we need to update when we test again Y2 = -0.0004*X2^2 + 0.4852*X2 + 41.45 ; %we need to update when we test again Y3 = -0.0001*X3^2 + 0.0785*X3 + 219.18 ; %we need to update when we test again Y4 = -0.00003*X4^2 + 0.0389*X4 + 148.38 ; %we need to update when we test again Y5 = -0.0003*X5^2 + 0.4415*X5 - 33.736 ; %we need to update when we test again if Y1>=0 & Y2>=0 & Y3>=0 & Y4>=0 & Y5>=0 % All variable >= 0

90

Ytot=Y1+Y2+Y3+Y4+Y5 ; ii=ii+1 ; Xa1(ii)=X1; Xa2(ii)=X2; Xa3(ii)=X3; Xa4(ii)=X4; Xa5(ii)=X5; Ya1(ii)=Y1; Ya2(ii)=Y2; Ya3(ii)=Y3; Ya4(ii)=Y4; Ya5(ii)=Y5; Wa1(ii)=W1; Wa2(ii)=W2; Wa3(ii)=W3; Wa4(ii)=W4; Wa5(ii)=W5; XN(ii)= Xtot ; % Array for Xtot at ii YN(ii)= Ytot ; % Array for Ytot at ii WN(ii)= Wtot ; % Array for Wtot at ii disp(sprintf('%12.2f',ii,Xtot,Ytot,Wtot)) end end end end end end end end disp('_______________________________') disp('To create Ymax array n order') % To create Ymax array n order disp('.') disp('.') disp('.') disp('____________________________________________________________________') disp(' n Ymax Xtot X1 X2 X3 X4 X5') disp('____________________________________________________________________') for i=1:n Ym=max(YN); Table(i,7)=Ym; % test by myself Ymax(i)=max(YN); k=length(YN); for j=1:k if YN(j)==max(YN) YN(j)=0; Xmax(i)=XN(j); Xm=XN(j);

91

Table(i,6)=Xm; % test by myself X1=Xa1(j); Table(i,1)=X1; % test by myself X2=Xa2(j); Table(i,2)=X2; % test by myself X3=Xa3(j); Table(i,3)=X3; % test by myself X4=Xa4(j); Table(i,4)=X4; % test by myself X5=Xa5(j); Table(i,5)=X5; % test by myself save data.mat end end disp(sprintf('%8.2f',i,Ym,Xm,X1,X2,X3,X4,X5)) end Ymax

92

Results

The results of 20 portfolios after simulating program in MATLAB

93

APPENDIX 7

Comparison between MATLAB and Excel generated model

Advantages and Disadvantages of MATLAB generated portfolio model comparing with Excel generated traditional model Advantages Disadvantages

1. Using MATLAB in portfolio model, it provide consistency to expected target

1. It is difficult to apply with many wells because the program need to be revise it again

2. It is useful in portfolio method because MATLAB program can generate easily more than 1 value as required.

2. It is not support in event of immediately change(The program need to be rerun again)

3. It is able to be adjusted the resolution of gas lift rate as required acceptation (such as 0, 50, 100, …..)

3. The program need to be supervised by human

4. The model can be modified to be economic model in case of new facilities investment.

4. Based on Random method, output is close to the true value less than traditional method which generate by mathematical method (such as Newton search method).

5. It is not only considering in term of quantity of hydrocarbon but for this model is also able to optimize in term of profit and cost.

94

APPENDIX 8

Monte Carlo Simulation

Advantages It can provide more than single value from the results and they are most likely the real of estimated values by using simulation with many iterations. Moreover, it can show the consistent range of value at given the confident level. Recommendation From choosing the distribution, the results can mistake if the use of distribution is wrong therefore, it is necessary to follow the method that have more reliable and reasonable. Flowchart to construct model of Monte Carlo Simulation

Start

Use the raw data of each well from well test record in the past around 25 times latest.

Choose distribution that is representative of each well

Use @Risk software to fit the proper curve of each well and consequently

Formulate the relationship between input and output

Set the parameter about the simulation and set showing the required options.

Finish

Run simulation as set parameter and option

The results and conclusions

95

1. Use the raw data of each well from well test record in the past 25 times latest. Create model supporting Monte Carlo Simulation method

Each cell of defining distribution is illustrated as follows. =RiskLognorm(64.768, 51.646, RiskShift(-1.211), RiskFit(95254, 27554, "Lognorm")) =RiskLognorm(227.55, 25.724, RiskShift(-128.34), RiskFit(95254, 95380, "Lognorm")) =RiskExpon(225.26, RiskShift(22.288), RiskFit(95254, 62611, "Best Chi-Sq")) =RiskNormal(156.55, 52.381, RiskFit(95254, 17733, "Normal")) =RiskTriang(44.417, 133.64, 148.9, RiskFit(95254, 11556, "Triang"))

Net oil from well test results for 25 latest values Each well test data came from single rate of gas lift injection test as follows. Gas lift rate test of well A10 = 300 MSCF/D Gas lift rate test of well B24 = 450 MSCF/D Gas lift rate test of well C18 = 300 MSCF/D Gas lift rate test of well D19 = 300 MSCF/D Gas lift rate test of well E17 = 400 MSCF/D

96

Therefore, the total of gas lift usage was 1750 MSCF/D

2. Use @Risk software to fit the proper curve of each well and consequently After selecting cell, one should identify the probability distribution into that cell. Normally, this option allow user to input data directly or use curve fit to find the distribution to represent well. In case of finding distribution from available data, it is starting from clicking “New Fit” button as figure below. Identify name of each gas lift well data and set the range of data that require finding the probability distribution as figure below.

3. Choose the proper distribution that is representative of each well The probability distribution of each well data is essential to identify that which type of probability distribution is fit and able to represent of well. The process to identify distribution of five gas lift wells is expressed as follows.

97

3.1. Fit curve of well A10 To identify the probability distribution of well A10, as the result, it is log normal distribution from fitting curve of 25 latest well test data by using @risk software.

3.2. Fit curve of well B24, To identify the probability distribution of well B24, as the result, it is log normal distribution from fitting curve of 25 latest well test data by using @risk software.

3.3. Fit curve of well C18, To identify the probability distribution of well C18, as the result, it is exponential distribution from fitting curve of 25 latest well test data by using @risk software.

98

3.4. Fit curve of well D19, To identify the probability distribution of well D19, as the result, it is normal distribution from fitting curve of 25 latest well test data by using @risk software.

3.5. Fit curve of well E17, To identify the probability distribution of well E17, as the result, it is triangular distribution from fitting curve of 25 latest well test data by using @risk software.

4. Formulate the relationship between input (each well) and output.

Click cell output and create the formula and variable input Total output = RiskOutput() + K30+K31+K32+K33+K34

5. Set the parameter Set parameter for simulation and set showing the required options. In this case, 10,000 iterations are set in order to obtain the results more accurate because given results is based on most likely occur with distribution function. The example setting of parameter and other are shown in figure below.

99

6. Run simulation as set parameter and option above

7. The results and conclusions

As the results, mean is equal to 678.68 BBL/D and standard deviation is 238.32 BBL/D at given the total gas lift test rate about 1750 MSCF/D. The expected result from generating by using Monte Carlo simulation is quite the same as traditional method that provides about 687.28 BBL/D at the same rate of gas lift usage. From 10,000 iterations, the results are composed of mean, standard deviation of total net oil production that are more

100

accuracy , the sensitivity analysis of each input parameter, etc. In this case, Well C18 (No.3) is the highest sensitivity and Well E17 is the lowest sensitivity. It means that Well C18 is the most effect to output of this combination or the same change of each well does not affect to change in output equal to change in Well C18.

101

APPENDIX 9

To improve the existing procedure Existing procedure to operate gas lift optimization

Add new well into gas lift system

1. Input required data from well schematic into simulation software (WINGLUE)

2. Provide the gas lift performance curve (GLPC) and others of each well

Operate is routine day or frequently

1. Test the significant well as scheduled 2. Calibrate the results from latest well test and the results that given by

WINGLUE 3. Run simulation software (WINGLUE) to optimize gas lift system 4. Obtain the estimated results table at different gas lift available 5. Adjust some parameter in order to be close the real system before operating

In order to improve the existing procedure, new process is necessary to incorporate

Add new well into gas lift system

1. Input required data from well schematic into simulation software (WINGLUE)

2. Provide the gas lift performance curve (GLPC) and others of each well 2.1. Use new model to input more data such as historical well test data and gas

and oil price

Operate is routine day or frequently

1. Test the significant well as scheduled 1.1. Improve plan for well test and data record needs to be change in order to

achieve the essential data or interested data 2. Calibrate the results from latest well test and the results that given by

WINGLUE 3. Run simulation software (WINGLUE) to optimize all wells 3.1. Run new model in excel spreadsheet with MATLAB program to generate

both economic and production optimization 4. Obtain the estimated results table at different gas lift available 4.1. Obtain more estimated results of each combination 5. Adjust some parameter in order to be close the real system before operating

(consider by themselves if something changes and cannot use software to recalculate)

5.1. Use new approach to recalculate to find new optimal point starting from the latest one

5.2. Select the portfolio depended on the decision maker and recommends finding and using the risk preference of decision maker.

102

APPENDIX 10

Table Conclusion of all methods Conclusion of all method

The main different between portfolio theory and Monte Carlo simulation is: Traditional method Improved Traditional

method Operation Easy More difficult Useful Less (net oil only) More (net oil, profit, etc) Searching new optimal point Part of operator (GUF

consideration) By model (∆GUF consideration)

Time consuming Slow Fast The main different between portfolio theory and Monte Carlo simulation is: Portfolio method Monte Carlo Simulation Effect of combination Consider No Require a lot of data Less than More than Reliability of results Less than More than

Traditional method

Improved traditional method

Portfolio theory method

Monte Carlo Simulation

Operation easy easy Not quite easy difficult Consistency less less Best (consider

relationship ) More (give range)

Predicted value Not accurate Not accurate More accuracy More accuracy uncertain Awareness

No No Yes Yes

Characteristic of Result

Deterministic (Single value)

Deterministic (Single value)

Deterministic +Std dev

Probabilistic distribution

Probability Distribution

No No No Yes

Profit cost calculation

No Yes Yes Yes

production history data requirement

No No Yes Yes

Main problem When economic change, result is the same.

No confident in expected value

Reliability in Method to find STD DEV and relation value

Require a lot of data and many process operation

Main advantage easy Easy and flexible

More consistent in expected target

More consistent in expected target

103

APPENDIX 11

Operating cost

Operating cash income (OCI) is the end result from deducting the total revenue by other costs is related to many parts such as oil price, gas price, oil and gas operating cost, water disposal cost, and other costs. The main factors consideration consists of price for oil and gas, handling costs for oil and gas, severance tax rate, water disposal, overhead, fixed operating cost, and property tax and insurance factor. The following calculation will be illustrated as below. But in this case, severance tax rate, overhead, gas sale, property tax and insurance factor is omitted in order to make model easily to understand.

Given: QO= oil rate

OP= oil price

OHC= oil handling cost

WDC= water disposal cost

FOC= fixed operating cost

TGC= Total gas handling cost per MCF of gas

PO= Profit oil per bbl before deducting TGC

B= Total Fixed Operating cost per bbl of oil; water disposal cost is constant

Total fixed operating cost per bbl of oil

B= OHC+ WDC+ FOC

Profit oil per bbl before deducting TGC

PO= OP-B ; For example, let’s assume PO= 80 $/BBL

Thus, OCI is calculated by:

OCI= (PO*QO)-(TGC*QG) ; For example, let’s assume TGC= 2 $/MCF

104

APPENDIX 12

Risk preference In order to find the optimal portfolio, risk preference of each decision maker is need to be found that what kind of risk the decision maker has? Normally, there are three kinds of risk preference which consist of risk lover, risk neutral, and risk averse. For example, supposing risk preference of staff A has risk lover that likes high risk that is represent by black curve and high return around region 1. The intersection between of black curve and green circle is selected portfolio, so highest return is his preference or port 1(746.92). For region 2 and 3 is the risk neutral and risk averse respectively. The calculation for risk preference is not included in this thesis.

(BB

L)

1

2

3