Oil Export Tanker Problem- Demurrage and the Flaw of Averages

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1 ENERGY EXPLORATION & EXPLOITATION Volume 26 Number pp Oil Export Tanker Problem- Demurrage and the Flaw of Averages Mansoor Hamood Al-Harthy 1 1 Petroleum and Chemical Engineering Department, Sultan Qaboos University, Oman P.O. Box 33, Al-Khod, P.C. 123, Muscat, Sultanate of Oman. mansoor@squ.edu.om Tele: , Fax: ABSTRACT Current practice in the oil and gas industry uses average monthly production forecasting estimates to represent daily production in the scheduling of export tankers. This practice ignores the extreme lows and highs of the daily production estimates. This paper introduces a model that can be practically used and applied in the scheduling of export tankers. A stochastic approach to capture uncertainty in production forecasting is suggested, which is more realistic than using average estimates. An export tanker problem is investigated to show the impact of using average estimates. In this example, results show that there is a 45% chance that demurrage, penalty fees, will occur compared to zero chance when average estimates are used. The added value of this paper is that it shows realistic demurrage can be forecasted and anticipated by the use of uncertainty and stochastic approach than on using average estimates. Key Words: Oil and Gas, Decision Making under Uncertainty, Production Forecasting, Risk Analysis, Export tanker, Flaw of Averages. 1. INTRODUCTION Current decision making practices in the oil and gas industry put more emphasis on deterministic rather than uncertainty models. The modeling of uncertainty is generally restricted to certain areas like reserves. Many upstream oil and gas projects fail to meet their expectations and result in loss of revenue for their companies. Merrow (2003) analyzed 1000 projects in exploration and production; two thirds were offshore projects. These projects ranged in size from $1 million to more than $1 billion. Merrow found that one in eight of all major offshore developments fell into the "disaster" category. He defined disaster as those projects, which carried at least two of the following three attributes: cost growth of 30% over budget, a schedule slip up to 35% or more and operability index of less than 50% of the plan in the first year. One of the reasons of the poor performance in these projects has to deal with the lack of credible planning that incorporate uncertainty. In other words, it is the failure to predict future scenarios by relying on deterministic estimates. Some companies do

2 144 Oil Export Tanker Problem- Demurrage and the Flaw of Averages capture uncertainty only in some part of oil and gas operations and leave the rest as deterministic. Simpson et al (2000) conducted a survey of UK companies and concluded that most of the companies (82.5% -16 companies) use Monte Carlo Simulation (MCS) for reserves calculation recognizing uncertainties in input variables but only 7.5% (three companies) used MCS in economic evaluations. In general, companies assumed production, cost and economic parameters to be known deterministically. This paper focuses on the use of deterministic values such as average values to forecast production. The aim is to show the danger or the flaw of using average values and the value added by modeling and capturing uncertainty in oil production forecasting in the context of an export tanker problem. 2. THE PROBLEM: THE USE OF AVERAGES The export tanker process in the oil and gas industry starts with oil being produced from different fields which are scattered at different places in the country. Oil produced is transported through pipelines to production station where oil, gas and water are separated. Oil is then pumped into a main pipeline which transports oil to the port where storage facilities are located. Oil stored in these facilities is ready to be loaded to tankers which will export oil to different destinations around the world. The operator will schedule these tankers based on the average monthly production estimate. However, production estimates from all the fields vary on a daily as well as on a monthly and yearly basis. The first and most important point is the danger or the flaw of average estimate. The operator uses an average monthly production estimate to schedule daily shipping of export tankers. This is a potentially dangerous assumption because it ignores the extreme lows and highs of the daily production estimates. The average monthly estimate ignores the variations in daily production. This phenomenon is known as the danger or the flaw of average (Savage, 2002). This happens when an average number is used to present an uncertain event with significant variability. Savage (2002) shows this with a simple example which is the story of a man who drawn because he crossed the river estimating and calculating that the average depth of the whole river is 3 ft as shown in Figure 1. Figure 1. Flaw of average (Savage, 2002)

3 ENERGY EXPLORATION & EXPLOITATION Volume 26 Number This individual made the assumption that if the whole river has an average depth of 3 ft that it was safe to cross while actually the depth in some places was far deeper than the average. This is similar to the assumption of a daily production of 700,000 barrels for the whole month based on a monthly average of 700,000 barrels per day. While in a given day, production could be 500,000 or 900,000 barrels. To demonstrate this flaw in the oil and gas industry an analysis on actual production data for a small field shows running monthly average fails to capture the actual daily production variations. The variation for this specific month ranges between 3% upside to 8% downside to the running average as shown in Figure 2. Figure 2. Running average production and actual daily production 3. THE SOLUTION: THE USE OF UNCERTAINTY There are many definitions of risk and uncertainty in the literature. Murtha definition is more appropriate and accurate and therefore it is the definition that will be adopted for this study. Murtha sees risk as "Potential gain or losses associated with each particular outcomes" and uncertainty as "the range of possible outcomes" (Murtha, 2000). In other words, risk is part of uncertainty, if there is no uncertainty, there is no risk. The importance of capturing uncertainty in planning is essential in decision making. Tobin (1993) reported examples where decision were made without considering uncertainty, but once the uncertainty was taken into account then the decision has to be changed. One of his examples is the case where an E&P firm obtained a multi-million dollar loan to pursue a major acquisition based on a single cash flow. The goal or decision was made to pay the loan in five years. After running the same case with considering uncertainty, the management realize that there is only 15% chance of meeting the goal, so the firm decided to reconsider their decision and have further discussion with the bank.

4 146 Oil Export Tanker Problem- Demurrage and the Flaw of Averages Furthermore, Tobin indicated that the lack of credible planning is due to the lack of recognition of uncertainty. He pointed out that there is a gap between theory and practice and a gap between practice and users. The gap between theory and practice is that practice does not recognize uncertainties and include them in their analysis. The other gap is that the users or decision makers do not use analytical tools to capture uncertainties such decision trees, scenarios, sensitivity analysis and Monte Carlo Simulation. The export tanker problem is no different from other problems in terms implementing plans that capture uncertainty. The use of risk and uncertainty in the tanker export problem is more realistic than the current practice of using deterministic single values. By capturing and applying uncertainty, decision makers are able to make sound decisions that are more realistic. The message is that good decisionmaking is based on good process and good process is based on the process that is able to capture risk and uncertainties in their evaluation. The next obvious question is once uncertainties and risk are identified, then how to capture and quantify them. 3.1 Quantification of risk and uncertainties Capen (1987) in his famous survey showed remarkably that we have not learned how to quantify risk and uncertainty due to our experiential biases. He proposes a simple method to quantify risk. His method is based upon quantifying risk mathematically by using statistical measures of mean and variance. He suggests that we might select two values of our perceived risk and outcome for a specified risk factor. For example: we might select an expected outcome with a 30% risk and another outcome with a 70% risk. Draw an X-Y diagram with perceived risk (%) on your horizontal axis and the expected values on vertical axis. By connecting the two points we have a big picture of perceived risk and uncertainty at the 5% and 95%. What Capen is suggesting is the use of probability distribution to describe the uncertainty about a certain variable rather then using a single estimate. Probabilistic models are better tools than deterministic ones. The probabilistic or stochastic method such as Monte Carlo Simulation (MCS) is designed to capture and quantify uncertainties through different types of distribution. In addition, it provides a way to measure the riskiness of the project. 4. EXPORT TANKER PROBLEM: FIELD CASE The problem with tanker scheduling is representative of the ultimate end point of the problems surrounding production forecasting, combined with the added complexity of arranging for the physical export of that production. Tankers are scheduled with future production estimates, which are, obviously, uncertain. If tankers arrive and have to wait for their delivery of crude, company must pay significant penalties known as Demurrage. Conversely, if tankers are not available on time due to delays, and if actual production is greater than planned, there is obviously a physically limited capacity to store production, and eventually production may need to be reduced to accommodate this limited storage with resulting production and revenue loss.

5 ENERGY EXPLORATION & EXPLOITATION Volume 26 Number THE EXPORT TANKER MODEL The actual design of the export tanker problem is complex and time consuming. Here an overview is given of the main components of the export tanker problem and the important equations used. This model is built in Excel spreadsheet. The export tanker problem is composed of four components, production, storage facility, scheduling and demurrage. PRODUCTION Oil produced from all the fields is transported to a pipe line to be exported to tankers. Oil production is estimated based on a monthly average estimate. This monthly estimate is then used as an average of daily production. Because of local refinery demands portion of the oil produced is used to meet local demands by refineries and the rest is transported to international markets. The following equations are used to construct the model: Net Production per day (P N ) = Production forecasted per day (P F ) Refinery demands per day (P R ) (1) Net Pr oduction per day Net Production barrels per time (P NT ) = (2) Time ( hours per day) Equation (2) is needed to analyze net production in discrete times in order to estimate its impact on demurrage as it is measured in hour basis. Net Production per time (P NT ) is defined as production in barrels every three hours. The whole production per day is divided by 8 hours to get production every three hours. This is to simplify calculations and scheduling of tankers for modeling purposes. In this model, production is treated as the only changing variable or to be more specific as uncertain and the rest of the variables will be treated as deterministic. Production forecasting will be modeled using three case scenarios as it will be shown later in the experiment section. The model also assumes that a local refinery demand is estimated to be 100,000 barrels per day. STORAGE TANKS Once oil is produced, then it is loaded into storage tanks. There are more than one storage tanks, for simplification, we assume that all small storage tanks are represented by one large storage tank. This storage tank has some constraints. The maximum capacity it can hold is 4.5 million barrels, this is due to it capacity limitation and the minimum level of oil is 1 million barrels. This acts as a lower bound. This is reserved for other reasons by the company policy such as satisfying local market demands. To model storage level activities the following equations are used: Tank Storage level at any time (barrels per time) (TS t ) = Previous Tank Storage level (barrels per time) (TS t-1 ) - Total loading of all ships at that time (barrels per time) (TL t ) + Net Production barrels per time (P NT ) (3) n t = 1 Total loading of all ships at that time (barrels per time) (TL t ) = SL (4) t

6 148 Oil Export Tanker Problem- Demurrage and the Flaw of Averages Where SL t is a tanker loading at a given time. The initial storage tank for any day is the closing storage tanks for the previous day and so on. In this model we will assume that the initial storage capacity is 2 million barrels, this is the available crude at the storage tanks when export of tankers started, and the operator has to maintain a safe storage level between 1 and 4.5 million barrels. SCHEDULING The scheduling of ships is done two or three months in advance, thus why the scheduling is done on average estimates because the production in the future is uncertain. The size of tanker to export oil to international markets varies. In this model we consider three type of ship sizes; a ship with a capacity of 500,000 barrels, 1 million barrels and 1.5 million barrels. These capacities are the actual nomination for each one of these ships. This model assumes it takes 3 hours to hook the ship to the terminal to be loaded and 2 hours to unhook. Also, the model assumes two terminals to load oil to tankers. At any time, two ships can be loaded at the same time; each one of the two terminals has a loading rate that range between 10,000 to 60,000 barrels per hour. This loading rate is a variable that is controlled by the operator. The loading process is modeled through the following equations: Actual Nomin ation of a ship ( N) Tanker loading at a given time (SL t ) = (5) Adjusted Time ( AT ) Adjusted Time (AT) = Hours to load a ship (HR) + Unhook/Hook hours (6) Actual Nomin ation of a ship ( N) Hours to load a ship (HR) = (7) Loading rate ( LR) In each terminal, once the ship is fully loaded then it is unhook, and then if the second ship is available then it is hooked and the loading process starts again. This model assumes the operator schedules 9 tankers starting from March 8 th to March 18 th as it shows in Figure 3. This Figure shows the name of the ship, the actual schedule of each ship based on two terminals with each being apply to load up to 60,000 barrels per hour. This schedule shows that if two tankers are assigned to one terminal, then one ship has to load first and then followed by another as the case between tanker 1 and tanker 3. Any delays in tanker 1 will cause tanker 3 to be delayed as well. Table 1 lists the ship name, the actual nomination which is the amount of crude to be loaded, starting date of the month the ship should commence loading and starting hours during that day. This scheduling has been prepared with purpose of not encountering demurrage based on a monthly average production forecasting of 650,000 barrel per day.

7 ENERGY EXPLORATION & EXPLOITATION Volume 26 Number Figure 3. Tanker schedule Table 1. Tanker scheduling inputs Vessel Actual Terminal Lay Time Time Name Nomination Loading times Start Start (Barrels) (hours) Date (Hours) Tanker 1 1,000, Tanker 2 500, Tanker 3 500, Tanker 4 1,000, Tanker 5 1,000, Tanker 6 1,000, Tanker 7 1,500, Tanker 8 500, Tanker 9 500, DEMURRAGE Demurrage is the fee paid by a company to the ship owner whenever the ship arrived at the terminal and had to wait for crude to be loaded. If the ship waited for more hours than the lay time for the ship to be loaded, then company pays demurrage. Table 1 shows the lay times based on the size of the ship. The hours are based on the size of the ship. Charge rate is per hour based on the market charging price as agreed between company and shipowner. For simplification, we have assumed that a fixed rate (F) which is $100 per hour as a charging rate. Every hour a ship is delayed, company has to pay an hourly charge rate for that ship. Smaller ships will have lower lay times compared to larger ships as it takes them longer hours to be loaded as it can be observed from Figure 3 and Table 1. Demurrage for a ship is calculated as number of hours that a ship exceeds its lay times, added with berth awaiting time and all are multiplied by charging rate per hour through the following equation: Demurrage (D S ) = (Adjusted Time (AT) -Lay time for the ship (LT S )+ Berth Awaiting time (BW S ) )* Charging rate ($) per hour (F) (8)

8 150 Oil Export Tanker Problem- Demurrage and the Flaw of Averages Total Demurrage (TDs) = D (9) Berth waiting time is basically the number of hours a tanker has to wait while available to be loaded. The impact of demurrage magnifies when a ship is delayed and it causes other ships to delay as well especially if these ships are scheduled in times that are close to each others. Total demurrage for all ships is summed into a single value as shown in Equation (9). The export tanker problem is an interesting and challenging problem, because it combines complexity, uncertainty and optimization. It is complex, because all the four components; production, storage facility, scheduling and demurrage have many details elements and constraints that are needed to be integrated with each other. It has an uncertainty element which is in this case is the production forecasting. In addition to these two issues, it requires an optimization. The challenge and the objective function is to minimize demurrage given the uncertainty in production forecasting. The minimization problem is defined as Minimize Total Demurrage (TD S ), which is the objective function By changing n t = 1 Loading Rate (LR) Berth awaiting time (BW s ) s Subject to 1 million barrel <= Tank Storage level at any time (TS t ) <= 4.5 million barrel 10,000 barrels per hour <= Loading Rate (LR) <= 60,000 barrels per hour 0 hours <= Berth Awaiting time (BW s )<= 150 hours The logic behind this optimization is that in order to reduce demurrage, the operator can control the amount of oil to be load in a ship, meaning a ship can be loaded slower or faster as long as the operator stays within the lay time hours of the ship. In addition, the operator has to satisfy the constraint on storage tank level by not exceeding its capacity nor going beyond the minimum levels. Finally, the operator can change the starting hours a ship can be loaded as long as it will not exceed it s lay times. 6. EXPERIMENTS In order to investigate the impact of production forecasting on demurrage and to show the impact of using averages on the export tanker problem, the following three experiments were carried out: Case 1: The use of average With this case we present what the industry is currently practicing which is basically using an average monthly production estimates as a daily estimates. In this case, we will assume the average monthly production forecasting is 650,000 barrels per day. This is basically saying that the daily production is 650,000 barrels per day in all the days in our model. Case 2: Simple realistic situation In this case we assume production in all days is the same as the average which is 650,000 barrels per day. However, in the 10 th and 11 th of the month, production on these two days dropped to 400,000 barrels per day as shown in Figure 4.

9 ENERGY EXPLORATION & EXPLOITATION Volume 26 Number Case 3: Production uncertainty In this case we assume Future production is uncertain and it is represented by a distribution. In any day, production could be any value in the range of a distribution 1. This is more realistic compared to the practice of using averages because it captures all ranges that could possible exist in any day as shown in Figure 5. Production forecasting is represented with a normal distribution with a mean of 650,000 barrels, standard deviation of 150,000 barrels and truncated with a minimum of 300,000 barrels and a maximum of 900,000 barrels. A cumulative distribution function for production forecasting is illustrated as well in Figure 5. We have assumed a normal distribution for simplification, however any other type of distribution could be used. Figure 4. Production forecasting Figure 5. Production forecasting modeled with a probability distribution function and a cumulative distribution function 1 In reality production levels in adjacent time periods are related, it is not completely random.

10 152 Oil Export Tanker Problem- Demurrage and the Flaw of Averages 7. RESULTS AND DISCUSSION In order to investigate the impact of uncertainty in production forecasting on demurrage, the three cases experiments were carried out and the following results were obtained: The first case: use the average monthly production as an estimate for a daily production for the whole month. This is a deterministic approach. The results show that a zero demurrage would be obtained. This is what we would expect, because the operator has chosen this schedule based on the average production to avoid demurrage and the results support this view. This is the upper portion in Figure 6. NO DEMURRAGE Figure 6. Cumulative distribution function of demurrage The Second case: tries to explore and introduce the impact of variance in production forecasting around the mean by changing the 10 th and 11 th days of the month production to 400,000 barrels per day compared to the mean. The model output shows $3500 as a demurrage. This clearly shows the impact of capturing variance in production forecasting which gave a different result than one obtained in the first case. Figure 6 shows two sides of the cumulative distribution function of demurrage. The upper portion, greater than zero demurrage, shows that demurrage was not incurred. The lower portion shows that a company incurred demurrage and a negative sign was added to the demurrage amount to reflect the loss and hence the value is -$3500. The third case: assume uncertainty exists in production forecasting represented by a normal distribution which captures all the ranges of production. Cumulative distribution function of demurrage indicated that there is a 45% chance that demurrage will occur. In addition, better knowledge of the chances of getting demurrage, for example, results indicated that there is a 30% chance that demurrage is $7,944 and 10% chance it is $22,833 as shown in Figure 6. Furthermore, results indicated that as the production levels go above 606,711 barrels per day, demurrage did not occur. This makes sense because more oil was available for all tankers to be loaded as nominated by the operator. Below this production level demurrage was encountered.

11 ENERGY EXPLORATION & EXPLOITATION Volume 26 Number Another benefit of capturing uncertainty in production forecasting is that it shows that any uncertainty range below the average of 7% is acceptable and can not cause demurrage. This is the level of uncertainty in production forecasting that can be tolerated without incurring demurrage. The implication of this result is so powerful that it points out to the operator the need to capture uncertainty in production forecasting. Furthermore, the results show that the practice of using the average monthly production as an estimate for scheduling of tankers is a flawed one because it does not really show the potential danger of incurring demurrage which is more realistic than just simply ignoring it. This practice of using average monthly production forecast, case one, prevents the operator from seeing the complete picture. The use of average to forecast production prevents the operator to see the lower portion of Figure 6, and only see a single point on the upper portion, which shows no demurrage. Unfortunately demurrage occurs based on available crude to be provided at any given time which is a function of daily production, and not on a month average production estimate. However, with the application of using distribution to capture the uncertainty in production forecasting, the operator is able to see the complete picture, case three, which represent the actual real situation of what might happened during the ship loading periods which is both the upper and lower portion of Figure 6. If the operator knew that there is a 45% chance to incur demurrage, then he might alter his decision on the scheduling and re-run the model to find what is the best scheduling that will minimize demurrage amount. It is important to point out that that the operator deals with range of demurrage outcomes. It is difficult to achieve a target of zero demurrage due to uncertainty in production forecasting. The operator will have to manage this level of uncertainty as given to him. However, if better production forecasting methodology could be used to narrow the distribution of production forecasting then we would expect demurrage to be reduced by the reduction of uncertainty in production forecasting. One of the quick solutions that someone might suggest is to go back and reduce number of export tankers. It is important to point out that this is not a solution. An operator need to be careful about this, reducing tankers might reduce the demurrage values, if production rates are below average, however, for above average production then there is a high chance that it might lead to storage tank capacity being full and the operator ending up shutting down wells which is loss of revenue to the company. Adding to this is that the operator would not know if production would be above average or below all the times because of the uncertainty in production forecasting. Another possible solution that could be suggested would be to schedule based on the lowest production forecasting values, then take that schedule and use it expecting that it should work for all the other production forecasting, this was tried however, this schedule will have to be the same for all the other production forecasting greater than the minimum values. The results showed that again this is not practical because the operator will end up again facing a situation where storage capacity is getting full as the production forecasting values are increasing. A more practical solution is by filling tankers to an 80% not to the full level as it can be agreed between the ship owner and the operator. This will make crude available

12 154 Oil Export Tanker Problem- Demurrage and the Flaw of Averages for other ships to load and hence reduce demurrage. Another possible practical solution, would be to have a stand by storage capacity that is ready to load crude whenever there is no sufficient crude to be loaded to ships. An extra storage tanker with a capacity of 600,000 barrels was assumed and used whenever production was below 606,711 barrels per day. Below this level the availability of crude to load is low and hence the extra storage tank is used. The model was run again with extra storage capacity, the results show that there is 35% chances that demurrage might occur and also a10% chance that demurrage is $12,294. This extra storage tanks has reduced demurrage by 10% with a difference in the lowest values of $20,000 as shown in Figure 7. Figure 7. Cumulative distribution function of demurrage with and without extra storage tank These results show the added value of capturing uncertainty over the use of average estimates by giving a complete realistic picture of good side, no demurrage, and bad side, demurrage. In addition, it forces the operator to find other possible practical solution that might reduce demurrage compared to the initial situation of ignoring it. 8. CHALLENGING WORK AHEAD It is important to point out that this paper has used the export tanker problem as an example to illustrate the impact of uncertainty in production forecasting and the flaw of averages. However, the export tanker problem is more complicated than what this paper presents. For example, uncertainty exist not only production forecasting, but also in refinery demands. The level of scheduling also matters, if the operator schedule with few ships or more. Furthermore, the assumption that the level of storage tank started at 2,000,000 barrels, could be invoked, it could be any value greater than a million barrels. Furthermore, the focus of the paper was on production levels until 900,000 barrels as the maximum, what if production was greater than 900,000 then the above constraint of capacity limit will require production to be reduced, so the

13 ENERGY EXPLORATION & EXPLOITATION Volume 26 Number problem switched from demurrage minimization to a balance between the right level of commitment that will minimize demurrage and not to target zero demurrage. 9. CONCLUSION This paper investigates the current practice in the oil and gas industry of using averages estimates in export tanker problem. It has demonstrated that this practice is dangerous because it prevent the operator to see a complete picture of demurrage. This paper suggests a probabilistic approach to capture uncertainty in production forecasting. It concludes that using uncertainty to capture production forecasting is more realistic and gives an estimate of demurrage and the probability of incurring it, compared to the traditional approach of using average estimates which actually shows no demurrage. The added value of this paper is that it shows better demurrage can be forecasted and anticipated by the use of uncertainty and not on average estimates. 10. REFERENCES Capen, E.C. (1976). "The difficulty of assessing Uncertainty." SPE-AIME, August, pp Murtha, J.(2000). "Decisions involving Uncertainty, tutorial for the petroleum industry." Palisade Corporation. Savage, S. (2002). "Flaw of Averages." Harvard Business Review. November, p Tobin, J.C. (1993). "Credibility in Forecasting and Planning or why should Management Use an Analysis of Uncertainty in Their Investment Decision Process." SPE presented at the SPE Hydrocarbon Economics and Evaluation Symposium held in Dallas, Texas, March

14 156 Oil Export Tanker Problem- Demurrage and the Flaw of Averages 11. APPENDIX Appendix Symbol P N P NT P F P R TS t TS t-1 TL t t N S n SL t LR HR AT LT s D s TD s F BW s Description Net Production per day (barrels per day) Net Production per time (barrels per time), Production forecasted per day (barrels per day) Refinery demands per day (barrels per day) Tank Storage level at any time (barrels per time) Previous Tank Storage level (barrels per time) Total loading of all ships at that time (barrels per time) Time (hours) Nomination of the ship (barrels), a ship size of 1.5 million barrels could have a nomination of 1 million barrels or 1.5 million barrels or any other amount of nomination. Tanker Number of ships to be loaded Tanker loading at a given time (barrels per hour) Loading rate (barrels per hour) Hours to load a ship added with hook and unhook of a ship Adjusted time which is total number of hours to load a ship adjusted every three hours. Lay time which is basically number of hours the ship has to be loaded without incurring demurrage. Demurrage which is the fee paid by company to ship owner if this ship is delayed. Here it is represented by dollars. Total demurrage incurred by all tankers. Charging rate per hour, demurrage fees or penalty Berth waiting time for the ship