**2. About the problems that are due to be solved by probabilistic modeling**

Modeling demands the analysis of specificity for OGS, estimating existing uncertainties. Prominent features of objects of oil and gas manufacture, characterizing uncertainties and complexity of modeling are presented in **Table 1**.

The performed analysis has revealed prominent features of uncertainties for separate objects of oil and gas manufacture and has shown that probabilistic modeling, models for estimations and identifications, a method of Monte-Carlo, is widely and successfully applied for solving problems of technological process control. The nature of uncertainty of processes and objects of oil and gas manufacture is various; that is in many respects caused by long processes of hydrocarbon formation. Therefore, the occurrence of technology of evolutionary modeling as often named synergistic analysis (with the theory of non-linear systems and the self-organizing


processes, the determined chaos, fractal analysis, etc.) has considerably expanded possibili-

Evolutionary processes as a development basis, actively acted not only the system analysis in a control context, but also for the decision of problems at level of organizational-economic management. At this level, the nature of uncertainty is connected with many criteria. In **Figure 2**, the evolution of risk-oriented criteria is shown: from economic criteria to competitiveness.

In different areas, the heterogeneous threats for complex systems are inevitable. The uncertainties in the system's life cycle are usual. Different problems, connected with evaluations, comparisons, selections, controls, system analysis and optimization, are solved by the probabilistic modeling of processes according to system engineering standards (general–ISO/IEC/ IEEE 15288, ISO 9001, IEC 60300, 61,508, CMMI и т.д. and specific for the oil and gas industry ISO 10418, 13,702, 14,224, 15,544, ISO 15663, ISO 17776 etc.). The saved-up experience confirms the high importance of scientific system researches based on probabilistic modeling. For example, in general cases, prediction and optimization are founded on modeling different processes. Any process is a repeated sequence of consuming time and resources for outcomes' receiving in all application areas. From the probability point of view, the moments for any activity beginning and ending are random events on the timeline. In practice, a majority of timed activities is repeated during the system's life cycle (estimations, comparisons, analysis, rationale, etc.) [1–10]. See some problems that are due to be and can be solved by the mathematical modeling of processes according to ISO/IEC/IEEE 15288 "Systems and software engineering. System life cycle processes" in **Figure 3**. The applications of models allows one to manage rationally risks, raise the quality and safety of oil and gas systems and at the expense of them be successful in the market—see in **Figure 4** the example of formalized problems

ties of the researches of the natural uncertainty of oil and gas manufacture.

are developed.

**Table 1.** Distinctive uncertainties of the objects and processes in the oil and gas industry.

**Object or process Distinctive factors (uncertainty) and applicable modeling tool**

the oil and gas industry.

situations.

In the oil disperse system occur the negative phenomena, which are connected with the phase transitions in technological processes of the oil refining, hydrocarbons reservoirs development, wells drilling and other processes of

Probabilistic Modeling Processes for Oil and Gas http://dx.doi.org/10.5772/intechopen.74963 59

Physical–chemical analysis of the oil disperse systems is supposed to be the key point in development of the decisions support systems in the emergency

Combined to the experimental researches practice the computer modeling at the molecular level is carried. Based on the results the type of the catastrophe

Finally the recommendations to the management in the emergency situations

These phenomena may include: the asphaltenes, paraffins and salts

sedimentations, gas hydrates formation and others.

is evaluated and the order parameter is identified.

Management in the emergency situations and accidents

which are solved on the basis of probabilistic modeling in the life cycle [6].


**Table 1.** Distinctive uncertainties of the objects and processes in the oil and gas industry.

**Object or process Distinctive factors (uncertainty) and applicable modeling tool**

correlation measure) and other estimations.

models are applied; fractal analysis is used.

Hydrocarbons reservoirs They were formed for millions years. Recently the count of hypothesizes about

the images processing and transfer area and others [11].

The text and cartographical information symbiosis is used. The most popular tasks: correlation analysis, cluster analysis, association theory, interpolation theory. The spatial data modeling with the variograms evaluation (the spatial

Natural phenomena modeling – one of the most progressive lines of the modern science. It is based on the digital models of the geological data combined with the spatial databases. The computer modeling tasks in the practical geology are solved with help of the modeling software packages. Actual tendencies of the geostatistics are connected with the development of: spatial analogues of the Monte-Carlo methods; approaches based on the multipoint statistics; hybrid models with artificial intelligence algorithms application; with additional information of the varied type and applications in

In the oil disperse system the behavior principles and physical–chemical properties in the molecular or disperse state can be quite differ from each other, and this is the reason of the non-linear response while changing of the external input character and scale. Then the phase transitions occur, and system properties are changed in a qualitative manner. This field researches show that oil systems are structured at the nanoscale level, what creates the basics for the new technologies development in the oil and gas industry. So the phase transitions are possible with the aggregate state changing. This is the object of the synergistic analysis; also the physical–chemical analysis

the hydrocarbon reservoirs origin increased, and generally speaking the self-

Porosity, permeability are the key indexes for the estimation task solution. The deformations are typical for the reservoir rocks. In certain cases it is needed to take into account the non-Newtonian fluid and to use the rheological models.

The initial information has the statistical character, then the mathematical statistics and probabilistic modeling apparatus is actively applied. The

Non-linear processes with catalysts' application, and its activity, are varied with time. Most wide-spread modeling and engineering evaluations systems are actively used for the project design as well as the calculations providing in

While solving the problem of the hydrocarbons production on the reservoir the task of the adjusted management with Kalman filter application. In classic case the adjusted management task supposes the object model correction with control input generation. Toward to the hydrocarbons reservoir the uncertainty is increased with the changing of the object

The tasks of the estimation and identification are widely used and applied.

organizing processes are typical for the oil and gas reservoirs.

The most dependencies have the non-linear character.

characteristics while the reservoir development process.

percolation task is also has its special features.

management.

Geological structures (it is the isolated area of the earth shell, differing from the cross-border regions for the tectonic behavior, i.e. specific combination of the geological formations, its bedding and structuring conditions)

58 Probabilistic Modeling in System Engineering

The Oil (it is typified as the oil

Hydrocarbons reservoir rock (it is mine rock containing the voids, i.e. the pores, cavities and others and having the potential to store and

Processes of the petrochemical industry and oil refining

Management of the oil production

(Intelligent field, i.e. I-field)

filtrate the fluids)

process

disperse system)

processes, the determined chaos, fractal analysis, etc.) has considerably expanded possibilities of the researches of the natural uncertainty of oil and gas manufacture.

Evolutionary processes as a development basis, actively acted not only the system analysis in a control context, but also for the decision of problems at level of organizational-economic management. At this level, the nature of uncertainty is connected with many criteria. In **Figure 2**, the evolution of risk-oriented criteria is shown: from economic criteria to competitiveness.

In different areas, the heterogeneous threats for complex systems are inevitable. The uncertainties in the system's life cycle are usual. Different problems, connected with evaluations, comparisons, selections, controls, system analysis and optimization, are solved by the probabilistic modeling of processes according to system engineering standards (general–ISO/IEC/ IEEE 15288, ISO 9001, IEC 60300, 61,508, CMMI и т.д. and specific for the oil and gas industry ISO 10418, 13,702, 14,224, 15,544, ISO 15663, ISO 17776 etc.). The saved-up experience confirms the high importance of scientific system researches based on probabilistic modeling. For example, in general cases, prediction and optimization are founded on modeling different processes. Any process is a repeated sequence of consuming time and resources for outcomes' receiving in all application areas. From the probability point of view, the moments for any activity beginning and ending are random events on the timeline. In practice, a majority of timed activities is repeated during the system's life cycle (estimations, comparisons, analysis, rationale, etc.) [1–10]. See some problems that are due to be and can be solved by the mathematical modeling of processes according to ISO/IEC/IEEE 15288 "Systems and software engineering. System life cycle processes" in **Figure 3**. The applications of models allows one to manage rationally risks, raise the quality and safety of oil and gas systems and at the expense of them be successful in the market—see in **Figure 4** the example of formalized problems which are solved on the basis of probabilistic modeling in the life cycle [6].

**Figure 2.** Evolution of risk-oriented criteria.

The summary of the analysis of existing approaches is presented in the next section.

**Figure 3.** The problems that are due to be and can be solved by probabilistic modeling processes.

Probabilistic Modeling Processes for Oil and Gas http://dx.doi.org/10.5772/intechopen.74963 61

**Figure 4.** Examples of formalized problems which are solved on the base of probabilistic modeling.

An existing risk control concept tries to consider different uncertainties. But in the application for various areas, the results of information gathering and processing are not used purposefully for modeling, because as the used models of risk prediction that are used in a majority of complex systems, are specific, results and interpretations are not comparable. A universal objective scale of measurement is not established yet. Moreover, the terms "acceptable quality" and "admissible risk" should be defined on a probability scale level only in dependence with corresponding methods and precedents (considering system analogue). For heterogeneous threats, an analytical rationale of the balanced preventive measures of system integrity support at limitations on admissible risks and resources cannot be solved in many cases. The probabilistic modeling, aimed at pragmatic effects, helps to prove probability levels of" acceptable quality" and "admissible risk" for different systems in uniform interpretation, creates techniques to solve different problems for quality and helps in risk optimization. It supports making-decisions in quality and safety and/or helps to avoid wasted expenses in the system's life cycle—see the proposed purposeful way in **Figure 5**, based on dozens of probabilistic models and software tools [6]. There are proposed universal metrics for system processes: probabilities of success or failure during a given period for an element, subsystem and system. A calculation of these metrics within the limits of the offered probability space built on the basis of the theory for random processes allows one to predict quality and risks on a uniform probability scale, quantitatively proving comprehensive levels of acceptable quality and admissible risks from "precedents cases." The prediction of risks can use widely safety monitoring data and statistics. In practice, an application of the proposed model and method

#### Probabilistic Modeling Processes for Oil and Gas http://dx.doi.org/10.5772/intechopen.74963 61

**Figure 3.** The problems that are due to be and can be solved by probabilistic modeling processes.

The summary of the analysis of existing approaches is presented in the next section.

**Figure 2.** Evolution of risk-oriented criteria.

60 Probabilistic Modeling in System Engineering

An existing risk control concept tries to consider different uncertainties. But in the application for various areas, the results of information gathering and processing are not used purposefully for modeling, because as the used models of risk prediction that are used in a majority of complex systems, are specific, results and interpretations are not comparable. A universal objective scale of measurement is not established yet. Moreover, the terms "acceptable quality" and "admissible risk" should be defined on a probability scale level only in dependence with corresponding methods and precedents (considering system analogue). For heterogeneous threats, an analytical rationale of the balanced preventive measures of system integrity support at limitations on admissible risks and resources cannot be solved in many cases. The probabilistic modeling, aimed at pragmatic effects, helps to prove probability levels of" acceptable quality" and "admissible risk" for different systems in uniform interpretation, creates techniques to solve different problems for quality and helps in risk optimization. It supports making-decisions in quality and safety and/or helps to avoid wasted expenses in the system's life cycle—see the proposed purposeful way in **Figure 5**, based on dozens of probabilistic models and software tools [6]. There are proposed universal metrics for system processes: probabilities of success or failure during a given period for an element, subsystem and system. A calculation of these metrics within the limits of the offered probability space built on the basis of the theory for random processes allows one to predict quality and risks on a uniform probability scale, quantitatively proving comprehensive levels of acceptable quality and admissible risks from "precedents cases." The prediction of risks can use widely safety monitoring data and statistics. In practice, an application of the proposed model and method

**Figure 4.** Examples of formalized problems which are solved on the base of probabilistic modeling.

item (renamed) may be estimated instead of the probability of information faultlessness during the required term (according to referenced model [6]). A soundness of the checked item means the zero of defects (or anomalies) after non-destructive testing during the given term.

Probabilistic Modeling Processes for Oil and Gas http://dx.doi.org/10.5772/intechopen.74963 63

What about the effectiveness of non-destructive testing methods for some technical items?

checked 10,000 conditional items is more than 0.90.

**Figure 6.** Examples of item content analysis.

because first-type and second-type errors seldom occur in example 1.

will exceed 0.95 at continuous work within 8 h of working hours.

The results of probabilistic modeling are reflected in **Figure 7**.

Example 1: Let an application of some instruments of non-destructive testing be planned in the applications to check 10,000 conditional items (the items can be meters of pipes, square meters of walls in storehouses and so on). The operator using instruments forms a system for non-destructive testing. Speed of testing equals 5000 items a day. Taking into account the human factor, a frequency of first-type errors (when the absence of defect [anomaly] is accepted as defect [anomaly]) equals one error a week. The mean time between second-type errors for the system (when real defect [anomaly] does not come to light) is equal once a month. The non-destructive testing is performed permanently for 10 days. It needs to estimate the maximum density of defects (anomalies) for which the probability of soundness of the

Results of probabilistic modeling have shown that the required density is about 0.02%, that is, 2 defects (anomalies) on 10,000 items. In addition it is expedient to notice that since density of defects about 1%, the probability of soundness is stabilized at level 0.88. It does not fall as less,

Example 2: Continuing example 1, it needs to prove minimum speed of non-destructive testing, the checked volume for which the probability of soundness of 10,000 conditional items

The analysis shows that the found rational speed is about 1100 items per hour. And the part of defects after the control in the checked-up volume of 10,000 items will be 0.0008% against the primary 0.02%. It can be interpreted: at the checked volume of 1,00,000 items (i.e., in 10 times more primary 10,000, when quantity of defects is 20), the average residual quantity of defects

**Figure 5.** The proposed way to support making-decisions in quality and safety.

allows a customer to formulate better justified requirements and specifications, a developer to implement them rationally without wasted expenses and a user to use the system's potential in the most effective way [1–12].

In a general case, a probabilistic space (*Ω*, *B*, *P*) for the evaluation of system operation processes should be proposed, where *Ω* is a limited space of elementary events; *B* is a class of all subspaces of the *Ω* space, satisfied to the properties of *σ* algebra; *P* is a probability measure on the space of elementary events *Ω*. Because *Ω = {ω<sup>k</sup> }* is limited, there is enough to establish a reflection *ω<sup>k</sup>* →*pk = P(ω<sup>k</sup> )* like *pk 3 0* and ∑ *pk* <sup>=</sup> 1.

The descriptions for some from the proposed probabilistic models and methods for their transformations, adaptations, applications and result interpretations are the following.

*k*
