Keywords

1 Introduction

To prevent accidents in petrochemical industries, safety valves (SV) are installed on process equipment, including pipelines. These are fittings designed for emergency relief of operating pressure if it exceeds the amount allowed by the technological regulations. The process of determining the SV characteristics that meet the requirements of industrial safety rules is a complex engineering task [1], the results of which depend on the chemical composition, pressure, temperature, and volume of the working medium, as well as the parameters and type of the technological process that occurs in a particular unit of equipment. According to the above, the implementation of this process can be lengthy and require not only routine operations of retrieval and processing of technological and regulatory data but also procedures for making intelligent decisions [2, 3]. It is possible to simplify and speed up the determination of SV characteristics if you create and apply special software - a problem-oriented cyber-physical system (CPS) [4,5,6,7]. However, the analysis of scientific and technical literature did not reveal models [8,9,10,11,12,13] and algorithms [14, 15] that could be used for the specified CPS development. Based on the above, the purpose of this study was to create models and algorithms that allow you to automate the process of determining the SV characteristics.

To achieve this goal, the following tasks were formulated:

  • analyze the process of determining the SV characteristics as an object of computerization;

  • develop a functional model (FM) for determining the SV characteristics as an organizational and technological process;

  • develop algorithms to automate SV selection; and

  • develop models for the representation of knowledge and data about SVs that will automate the process of determining their characteristics.

2 The Process of Determining the Safety Valves Characteristics as an Object of Computerization

The analysis of normative and technical documentation and scientific and technical literature established that the process of determining the SV characteristics consists of four main stages: calculation of the critical flow rate of the working medium, calculation of the SV effective seat area, SV brand selection, and SV quantity calculation. Moreover, the first and second stages are the most difficult in terms of computerization. This is due to the fact that the critical flow rate of the working medium has complex relationships with the parameters of a particular technological process and its hardware design, and it involves engineering calculations requiring good knowledge of chemical technology. The procedure for determining the SV effective seat area contains not only the data retrieval and processing operations, but also the procedures for making intelligent decisions, as was mentioned above. At the same time, there are dependencies between the SV and the working medium characteristics, which in most cases are discrete. Analysis of the procedures for determining the SV characteristics showed that a significant part of them can be formalized using the theory of artificial intelligence [2, 3], which allows their automation.

3 Development of a Functional Model for Determining the Safety Valves Characteristics

As a result of the analysis of knowledge about the subject of research performed using the system approach [16, 17], a logical-information model was developed that formalizes the solution to the problem of choosing the SV as an organizational and technological process. The model is described following the methodology of structural analysis and design SADT (Structured Analysis and Design Technique) (Fig. 1). The SADT methodology [18, 19] was chosen because it is often used in the development of complex systems and in many cases it is considered an integral component of CALS technologies [20, 21]. In the Russian Federation, it is also widely known as the functional modeling methodology.

Fig. 1
figure 1

Diagram A0 of the functional model for determining the safety valves characteristics: TR—technological regulations; TP—technical passport of the vessel; GCR—critical flow rate of the working medium; AS—the SV effective seat area; N—SV quantity; DB—database; KB—knowledge base

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The developed FM differs in applying a system approach and taking into account the complex relationships between the various stages of determining the SV characteristics, as well as in connection with data- and knowledge bases, which allows automating the implementation of the above steps while ensuring high-speed information exchange. As an example of FM detailing, the decomposition of block A2 (Fig. 2) of diagram A0 is presented, which shows the relationships between various functions of the procedure for calculating the SV effective seat area, as well as data- and knowledge bases.

Fig. 2
figure 2

Decomposition of block A2 of diagram A0: PS is valve setting pressure; PN is the SV nominal pressure; P2 is the highest overpressure downstream of the valve (overpressure downstream of the valve in the position of its full opening); P1 is the highest overpressure upstream of the valve (overpressure upstream of the valve equal to the pressure of full opening); ρ is the density of steam, gas or liquid upstream of the valve

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4 Development of Algorithms to Automate the Safety Valves Characterization

As a mechanism for implementing the functions indicated in the FM blocks, the corresponding heuristic-computational algorithms were developed. An example of an algorithm that automates the execution of blocks A21 and A22 is shown in Fig. 3. This algorithm formalizes the process of determining the following SV characteristics: nominal pressure PN; the highest overpressure downstream of the valve P2 and the possible nominal diameter values of the outlet pipe DNOUT. Using a given initial characteristic of the setting pressure PS and production models of knowledge representation (Table 1), the algorithm automates computational and intelligent decision-making procedures for determining SV characteristics as required by normative and technical documentation.

Fig. 3
figure 3

Block diagram of a heuristic-computational algorithm for determining the SV characteristics: nominal pressure PN; the highest overpressure downstream of the valve P2; possible nominal pressure values of the outlet pipe DNOUT

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Table 1 Production model for representing valve performance knowledge
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An example of the heuristic-computational algorithm that automates the execution of block A24 is shown in Fig. 4.

Fig. 4
figure 4

Block diagram of a heuristic-computational algorithm for determining the effective seat area of a safety valve

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The following designations are used in the algorithm (Fig. 4): β is pressure ratio; βCR is a critical pressure ratio; B1, B2, B3 are coefficients for determining the effective seat area for gases and water vapor; k is the adiabatic index; RSP is gas constant.

The developed algorithm formalizes the process of determining the effective seat area of a spring safety valve. Using the specified initial characteristics of the working medium (P2, GCR, ρ) and production models for the knowledge representation, the algorithm automates computational and intelligent decision-making procedures for determining the SV effective seat area as required by regulatory and technical documentation.

An example of the algorithm that automates the execution of block A3 is shown in Fig. 5.

Fig. 5
figure 5

The block diagram of the SV brand selection algorithm

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With the help of the specified initial parameters (PN, DNOUT, AS) and the database, the algorithm (Fig. 5) allows you to automate computational and intelligent decision-making procedures for selecting SVs as required by regulatory and technical documentation.

5 Development of Models for the Representation of Knowledge and Data on the Rules for Determining SV

To ensure the automated operation of the algorithm for determining the effective seat area, production models for representing knowledge used in the methods of the theory of artificial intelligence were created [5, 7]: of valve characteristics, of B2 coefficient, and gas characteristics.

An example of a production model for the valve’s characteristics is given in Table 1. This model formalizes the regulatory relationship between the setting pressure (of the safety valve) PS on the one hand and the SV characteristics (PN, P2, DNOUT—the SV outlet pipe nominal diameter) on the other hand.

An example of a production model for the coefficient B2 is shown in Table 2. This model takes into account the correlation between the B2 coefficient on the one hand and the adiabatic index k as well as the pressure ratio β (the ratio of the highest overpressure downstream of the valve to the highest overpressure upstream of the valve) on the other.

Table 2 Production model for B2 coefficient knowledge representation
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An example of a production model for the characteristics of gases is presented in Table 3. The model establishes a mutual relationship between the type of gas on the one hand and its gas constant RSP, as well as the adiabatic exponent k on the other. The adiabatic index k is necessary for calculating the critical ratio of pressures (βCR), coefficients B1 and B3 as well as for determining the B2 coefficient.

Table 3 Production model for gas characteristics knowledge representation
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6 Conclusion

Thus, as a result of this study, using the analysis of regulatory and technical documentation and scientific and technical literature, as well as a system approach to the process of determining the SVs characteristics, the following were developed:

  • A functional model for the selection of safety valves as an organizational and technological process, characterized by applying a system approach and taking into account the complex relationships between the various stages of determining the SV characteristics, as well as by connecting to databases and knowledge, which allows automating the procedure for selecting the SV and providing high speed of information exchange.

  • Heuristic-computational algorithms, which, with the help of predetermined initial process characteristics and production models of knowledge representation, enable automated computational and intelligent decision-making procedures for determining SV characteristics as required by regulatory and technical documentation.

  • Production models for representing knowledge of the valves and gases characteristics, ensuring the operation of algorithms for calculating and selecting SV characteristics, which formalize regulatory relationships between process parameters on the one hand and SV characteristics on the other.

The developed models and algorithms will make it possible to create a CPS, the use of which will reduce the duration of the data retrieval and processing procedures, as well as the number of subjective errors, which will increase the quality of determining the structural and technological characteristics of SVs, and, consequently, the industrial safety and economic efficiency of petrochemical plants in general.