Petrol Ve Gaz Yatırımlarının Monte Carlo Simülasyonu İle Değerlendirilmesi

Abstract

Yatırım kararının verilmesi, önemli ölçüde riskin göze alınmasını gerektirmektedir. Risk, rezervuar ve ekonomik parametrelerin gelecekte alacakları değerlerdeki belirsizliğin sonucudur. Bu durumda deterministik bir yaklaşım ile parametrelerin sabit bir değer alacağı varsayımı doğru olmayacaktır. Bu nedenle, çalışmada parametreler stokastik olarak değerlendirilmekte ve stokastik bir model oluşturulmaktadır. Stokastik modelde parametreler istatistiksel dağılımlar şeklinde tanımlanmaktadır. İstatistiksel dağılımların birbirleri ile etkileşimleri Monte Carlo Simülasyonu ile sağlanmaktadır. Çalışmada Stokastik Modelleme ile geliştirilen simulator, üç temel model içermektedir. Bunlar; Havza Analizi Modeli, Petrol ve Gaz Sahalarının Ekonomik Analiz Modeli ve Kuyu Loğları Modeli' dir. Havza Analizi Modeli, bir havzada anomali gösteren sahaların alan, kalınlık ve üretim faktörlerini kullanarak havzanın rezerv potansiyelini ve karlılığını belirlemektedir. Petrol ve Gaz Sahalarının Ekonomik Analiz Modeli, homojen veya çatlaklı rezervuarlara sahip petrol ve gaz sahalarında karlılık analizi yapmaktadır. Bu model üç bölümden oluşmaktadır. İlk bölümde üretilebilir rezerv hesaplanmaktadır, ikinci bölümde sahanın geliştirme programı, açılacak kuyu sayısı, kuyuların üretim performansları hesaplanmaktadır. Üçüncü bölümde sahanın kar dağılımı belirlenmektedir. Kuyu Loğları Modeli, sahada açılmış kuyuların loğlarını kullanarak Monte Carlo Simülasyonu ile gözeneklilik ve su doymuşluğu dağılımlarını elde etmektedir. Saha için rezerv dağılımı belirlenirken bu değerler kullanılmaktadır. Bu çalışmada geliştirilen simulator, istenen sonuca göre kullanım esnekliğine sahiptir. Sahada henüz kuyu açılmamış ise birinci ve ikinci model kullanılarak rezerv ve kar dağılımı elde edilebilir. Sahaya ait kuyu loğları mevcut ise üçüncü modelden elde edilen gözeneklilik ve su doymuşluğu değerleri ikinci modelde sahanın rezerv tahmini yapılırken kulanılabilir.

The environment within which decision making takes place can be divided into three parts: certainty, risk and uncertainty. Certainty exists when one can specify exactly what will happen during the period for which the decision is being made. Risk refers to a situation when one can specify a probability distribution over the possible outcomes. Uncertainty refers to the condition when one cannot specify the relative likelihood of the outcome. People generally are more comfortable when dealing with uncertainly. But most decisions in the petroleum and natural gas industry involve elements of risk and uncertainty. Decision analysis methods provide more comprehensive ways to evaluate and compare the degree of risk and uncertainty associated with each choice. The net result is that of the decision maker is given a clearer insight of potential profitability and the likelihoods of achieving various levels of profitability than older, less formal methods of investment analysis. Because of risking drilling costs, the need to search for petroleum and natural gas in deeper horizons or in remote areas of the world, increasing government control, etc., most petroleum and natural gas exploration decision makers are no longer satisfied to base decisions on experience, intuition, rules of thumb or similiar approaches. Instead, they recognize that better ways to evaluate and compare drilling investment strategies are needed. In considering the merits of decision analysis it is important to note several distinct advantages that the new approach has over the less formal procedures used in the past. 1. Decision analysis forces a more explicit look at the possible outcomes that could occur if the decision maker accepts a given prospect. 2.Certain tehniques of decision analysis provide excellent ways to evaluate the sensitivity of various factors relating to overall worth. 3. Decision analysis provides a means to compare the relative desirability of drilling prospects having varying degrees of risk and uncertainty. However, decision analysis will not eliminate risk in decision making. It's main utility is to give a better understanding of risk and uncertainty. XI Risk and uncertainties in petroleum and natural gas explorations are caused because: 1. Geologist and engineers are not be able to measure or define specific values of factors contributing to overall profit or loss at the time of decision. 2.Uncertainties about future events that could affect timing and/or size of projected cash flows from the prospects. Quantitative statements about risk and uncertainty are given as numerical probabilities, or likelihoods of occurrence. Probabilities are decimal fractions in the interval zero to 1.0. An even or outcome which is certain to occur has a probability of occurrence of 1.0. As the probability approaches zero, the event becomes increasingly less likely to occur. An event that cannot occur has a probability of occurrence of zero. Some types of risk that are needed to quantify or assess: 1. Risk of an exploratory or development dry hole, 2. Political risk, 3. Economic risk, 4. Risk relating to future oil and gas prices, 5. Risk of storm damage to offshore installations, 6. Risk that a discovery will not be large enough to recover initial exploratory costs. 7. Risk of at least a given number of discoveries in a multi-well drilling program. 8. Environmental risk. In this study, a simulator created for risk analysis in petroleum and natural gas exploration investments, describing risk and uncertainty in the form of distributions of possible values which the uncertain parameters such as net pay thickness, recoveries, drilling costs, oil and gas prices, etc. could have. Risk such as political, environmental and storm damage to offshore installations are not considered in this study. These distributions are then combined to yield a distribution of the possible values of profitability which could be expected from the prospect. From such a distribution it is only a small, final step to compute an expected value parameter for use in the decision making process. This is the parameter that management can use to determine the feasibility of the drilling prospect. In addition to being able to compute the expected value directly, having the distribution of profit offers numerous graphical options for presenting information to the decision maker about the range and likelihoods of occurrence of possible levels of profit and loss. The shape of the final profit distribution is influenced by the shapes of the random variable distributions, the magnitude of the numerical values of the distribution A picture such as a probability distribution is sometimes worth a thousand words. The method is a continuous outcome model of risk and uncertainty. Xll Simulation as a means of risk anaysis in decisions under uncertainty has several synonyms, including random simulation, Monte Carlo simulation, and the Monte Carlo method. A series of repetitive calculations of possible values of profit are made. Each value is computed using random variables selected from within their respective distribution ranges. Each value of profit computed in this manner represents one possible state of nature, or possible combination of several random variables. This approach is also called stochastic modelling. Each of these repetitive computations of values of the dependent variable is called a simulation pass. The value of the independent variable used in for each pass is obtained by sampling from its original distribution in a manner which honors the shape and range of the distribution. These repetitive computations, or passes, are continued until a sufficient number of values of the dependent variable are available to define its distribution. In this study, there are two techniques for determining number of optimum simulation passes. These are Variance Reduction Technique and Determination of Mean and Shape of Distribution Technique. Exploration risk analysis has several important advantages given in the following. 1. It allows the explorationist to describe risk and uncertainty as a range and distribution of possible values for each unknown factor, rather than a single, discrete or most likely value. 2. It can be applied to any type of calculation involving random variables. It can be applied NPV profit of drilling prospects, description of a distribution of recoverable reserves, distribution of water saturation from well log data, the bottomhole position of a directionally drilled well, etc. 3. There is no limit to the number of variables which can be considered. 4. The distributions used to define the possible values for each random variable do not have to be of a specific form such as lognormal, normal, etc. 5. The expertise of the firm can be used more effectively because the judgements about the distribution of possible values of each variable can be made by the person most knowledgeable about the parameter. The geologist can define the net thickness and productive area distributions, the engineer can define the distribution of recovery factors and production schedules, and the drilling engineer can specify the probable drilling cost distribution. 6. The method lends itself to sensitivity analyses. Indeed one of the important aspects of making a simulation analysis is to be able to define the one or two or three factors which have the most significant effect on the resulting values of profit. For analyzing a drilling prospect and quantifying the degree of risk and uncertainty using a simulation analysis it is needed to follow six general steps: Step 1: Define all variables XUl Step 2: Define the relationship which ties all the variables together. Step 3: Sort the variables affecting value into two groups. Step 4: Define distributions for all the unknown, or random variables. Step 5: Perform the repetitive simulation passes so as to describe the resulting distribution value. Step 6: Compute Expected Value of the profitability distribution and prepare graphical displays of analysis procedure and results. The simulator developed in this study has three main models, and these are: 1. Basin Analysis Model.The first part of the simulator is an example of the use of a simulation analysis trying to assess the range and probable distribution of total recoverable reserves in a sedimentary basin after only a limited amount of exploratory drilling. The unique feature of the model is the use of random number sampling scheme to simulate the results of drilling all the observed and/or projected prospects in the basin. Each structure is described by a distribution of area, net pay thickness and a distribution of recovery factors (barrels per acre-foot) (or MCF per acre-foot if in a gas province) to reflect the ranges of possible hydrocarbon recoveries. These are several charecteristics of this model: a. Probabilities of discovery (p) are revised after each structure has been tested to reflect a sampling without replacement process. b. On each pass the structures which have oil will vary. c. The drilling sequence on each pass will continue until all the structures have been tested or until all the structures hypothesized to be productive have been found, whichever comes first. 2. The Economic Analysis Model of Prospects of Petroleum and Gas: The second part of the simulator uses uncertainty in the form of distributions of possible values the uncertain variables: pay thickness, recoveries and drilling cost etc. Uncertain variables are also called random variables. Some of the random variables affecting profitability may be related to one another. For example, net pay thickness and well productivity are related by virtue of Darcy's equation (flow rate is directly proportional to reservoir thickness). Other examples of possible dependencies: connate water saturation (Sw) generally increases as prosity ($) decreases, field productivity is related to thickness, to the physical producing capacity of the well bore, and to storage capacity and tanker arrival schedules, pipeline costs are related to field productivities, etc. XIV If there is dependency between random variables it must be included into simulation model. This is an extremely important issue, and the results obtained from a simulation analysis can be very misleading if the analysis does not honor the dependent relationship. According to the relationship between random variables, dependency is divided into three category. These are called dependent, independent and partial dependent random variables. These distributions are then combined to yield a distribution of the possible levels of profitability which could be expected from the prospects. This model has been working both fractured and homogen oil and gas reservoirs. The model of consists of all the variables and computation steps that are used to determine the conditional distribution of an oil or gas discovery. These computational steps consist of the three main sections. These are: a. Determination of recoverable reserves, b. Determination of development well program, initial and future production schedules, c. Calculation of costs, revenues and profitability. 3. Well Logs Model: This model, using well logs, obtains the distribution of porosity and water saturation. These distributions are used estimating recoverable reserves in second model. In applications section, three field applications are done. First of all used the second and third model for an oil prospect in Southeast Region. In this application, three well development programs for prospect are used. Using these development programs, net profit distributions of field are determined. The highest net profit values are obtained by the second method. Second application is done for a gas field. Second method and different discount rates are used in this application. Choosing different discount rates enable to see the sensitivity of discount rate to net profit values. Third application is done for a case which homogeneous and fractured reservoir were assumed İn a prospect on Southeast Region. This applications are executed for different well development programs, discount rates and oil or gas prices. Profit sensitivity is also measured for above variables. In Figure 7.4 different well development programs for an oil field in Southeast Region are compared, most optimistic results are obtained from Method-2. In this method, project can compensate itself in less time. Method- 1 and Method-3 XV contain lower riskness. In Figure 7.5, the effect of different ranges of oil price on Ne t Profit Distribution is examined. In Figure 7.6, the same application is repeated for different discount rates. In Figure 7.7, Method-2 is used to calculate Net Profit Distribution for a gas field. At % 50 cumulative probability, the increase of % 2 in discount rate causes the decrease of %20 in Net Present Values. In Figure 7.8, Net Profit Values are determined both fractured and homogeneous reservoirs. The following general conclusions are obtained from this study, 1. Reserve potential of basins is determined, 2. Using seismic anomalies, profitability homogeneous and fractured oil and gas reserves is analyzed, 3. Using well logs in a field porosity and water saturation distributions are obtained and these distributions can be calculated for reserve potential of this field, 4. This model also enables to use sensitivity analysis.