Generalized Net Model of the Processes in a Petroleum Refinery—Part I: Theoretical Study

Abstract

Oil refining is a branch of industry that delivers energy to move our vehicles. The transportation of people and goods by airplanes, ships, trains, trucks, buses, and cars is unthinkable for modern mankind without the use of refined petroleum automotive fuels. Thus, the optimal functioning of this industrial branch is vital to contemporary human society. The modeling of processes that take place during refined oil products’ manufacturing, which are parallel in their essence, by generalized nets enables their activity optimization and better management. The generalized nets, which are in principle extensions of Petri nets, are applied in this research as a toolkit to model all processes from crude oil selection and delivery to a high complex refinery (Nelson index of 10.6) to the production of a great diversity of fuels, propylene, and polypropylene. The proposed article is a continuation and extension of the articles, published in Mathematics Journal in 2021 and 2023. It is the first (theoretical part) of our comprehensive study of modeling petroleum products’ production processes in a refinery, and the second part will discuss the results of the software implementation of the model.

1. Introduction

Carl Adam Petri proposed the concept of a place/transition net to model parallel processes in 1962 [1], which were later coined Petri nets (PNs). PNs have been employed to model the dynamic and not the static system behavior, and detect synchronization anomalies. They have found wide application thanks to the rich set of theoretical results that allow the analysis and the development of the supporting tools [2]. PNs have found applications in the field of risk assessment in chemical industry [3,4], in modeling the potential accident process at hydrogen refueling stations [5], in energy management and economic optimization scheduling [6], in modeling energy state and behavior [7], in modeling safety critical systems of nuclear power plants [8], in the calculation of compositional covalent bonds encoded in suitable Petri nets [9], in the assessment of domino effects during accidents occurring in chemical industry [10], in process modeling [11], in web modeling [12], in cloud systems [13], in reversible computation [14], in Internet of Things technologies [15], in modeling and simulation of the human cardiovascular system [16], in modeling and simulation of the multi-activity scheduling and allocation in the medical process [17], in modeling the collaborative process of COVID-19 prevention and the control emergency response [18], in modeling of the operation of a public bicycle sharing system with a redistribution vehicle [19], in the development of an improved method for the state estimation of a labeled time Petri net system with unobservable transitions [20], in the development of a security framework for the smart cities’ sustainability edge computing vulnerabilities using Petri Net and Genetic Algorithm-Based Reinforcement Learning [21], in the development of a method addressing the optimal allocation of emergency response forces, specifically considering front-line departments [22], and in the employment of a product line-based approach for the compact definition of variants of a given Petri net [23].

During the last 50 years, PNs have been the object of a lot of modifications and extensions, such as time PNs [20,24,25], e-nets [26,27], colored PNs [28,29], stochastic PNs [30,31], self-modified PNs [32], super nets [33], predicative/transition nets [34], and others.

In the present paper, we will use one of the PN extensions, called Generalized Nets (GNs) to model all petroleum refinery processes in their completeness and discuss the obtained results at a theoretical level, and in the second part of this research, we will discuss the results of the GN program’s realization.

2. Materials and Methods

2.1. Short Remarks on Generalized Nets

In [35], the concept of a GN was introduced and in the 1980s it was proved that the functioning and the results of the work of each type of PN can be described by a GN. Thus, GNs are actually extensions of PNs. Like the other modifications of PNs, GNs have a fixed structure (transitions and places), but for each transition, an index matrix (IM, see [36]) is associated. The elements of each such IM are predicates representing the transitions’ conditions, i.e., determining the direction of tokens’ transfer. In addition, each token enters the GN with an initial characteristic, and during its transfer in the net, it obtains new characteristics.

Formally, each transition in a GN is described by a seven-tuple:

$$Z=\langle L^{\prime },L^{″},t_1,t_2,r,M,\square \rangle ,$$

where:

(a)

The first two elements ($L^{\prime }=\{l_1^{\prime },\dots ,l_m^{\prime }\}$ and $L^{″}=\{l_1^{″},\dots ,l_n^{″}\}$) are the sets of input and output places, respectively (see Figure 1);

(b)

The processes are situated in time, and each event can occur at a specific moment and has a certain duration. In the GN’s transition Z, $t_1$ is the current time moment of the transition’s firing, and $t_2$ is the current value of the duration of its active state;

(c)

The conditions under which one can move from a given input state to a given output state are denoted in the formal definition by r. The IM r is the transition’s condition that determines which tokens will pass (or transfer) from the transition’s input to its output places;

(d)

For some processes, there are constraints on the movement between input and output states. M is an IM of the capacities $m_{i,j}$ of the transition’s arcs, where $m_{i,j}\ge 0$ is a natural number and determines how many elements (tokens) can move in one step of execution;

(e)

□ is a Boolean expression that determines in which input positions there should be tokens to activate the given event (transition). It is called transition type, and it is used to ensure that all input data, which may come from other parallel processes, will be available before executing a given phase of the process.

The parallel execution of all transitions and the events described by them in the process are determined by the GN.

Formally, each GN transition is described by a four-tuple:

$$E=\langle \langle A,{\pi }_A,{\pi }_L,c,f,{\theta }_1,{\theta }_2\rangle ,\langle K,{\pi }_K,{\theta }_K\rangle ,\langle T,t^0,t^{\ast }\rangle ,\langle X,\Phi ,b\rangle \rangle .$$

The first tuple corresponds to the description of the set of all transitions (A) in the GN—including the functions that determine their and the places’ priorities (${\pi }_A,{\pi }_L$), the place capacities (c), the activation time (${\theta }_1$), the duration of their active state (${\theta }_2$), and the evaluation of IM predicates (f).

The second tuple corresponds to the description of all tokens entering the simulation (K), their priorities (${\pi }_K$), and the time at which they enter the simulation (${\theta }_K$).

The third tuple corresponds to the description of the time component in one simulation. At least three items are needed to describe one simulation—the time moment when the GN starts functioning (T), an elementary time-step, related to the global time scale ($t^0$), and the duration of the GN’s functioning ($t^{\ast }$).

The last tuple corresponds to the description of the data for the simulation, including the initial characteristics that the tokens can receive (X), the function that assigns new characteristics ($\Phi$) of the tokens, and their maximum number for each token (b).

Figure 1. A GN transition.

Figure 1. A GN transition.

As can be seen above, the GN definition is essentially more complex than the definitions of the other types of PNs. On the other hand, it is valid that the functioning and the result of the work of the ordinary PNs, E-nets, time PNs, colored PNs, self-modifying nets, predicate/transition nets, stochastic PNs, super nets, and others can be represented by GNs (see [35]). For this reason, in the present paper, we use only GNs.

From the definition of GNs, it is evident that the GN tokens obtain characteristics that can be used in the transition condition predicates for decisions about the directions of the movement of tokens from the input to the output transition places on the one hand, and to gather information about the object represented by the corresponding token on the other. The presence of these features and the predicates associated with the transitions enable a much more detailed model compared to models using other types of Petri nets, in particular, of refinery processes. Consequently, GN models provide much more detailed information than the others.

Currently, GNs have found applications in different areas, but in practice, each PN model can be re-written and represented in a GN form. Thus, the existing current PN models related to petroleum engineering, as a part of overall engineering, such as those of Zhang et al. [37], An et al. [38], Al-Hajri and Rossiter [39], Wu, et al. [40,41], and Kaid [42], can be represented by GNs and this could be a topic of future research.

It is worth mentioning that both PNs and GNs are means for the modeling and simulation of complex parallel systems working in various fields. They can be used as follows:

*

For optimization: simulations can be used to optimize processes or systems by identifying inefficiencies and testing potential improvements.

*

To predict outcomes: simulations can help predict the outcomes of certain events or processes by analyzing the behavior of the model under different conditions.

*

For test scenarios: they allow researchers or engineers to test various scenarios without the need for real-world experimentation, which can be costly, time-consuming, or even dangerous.

*

For training: simulations are often used for training purposes, allowing individuals to practice and gain experience in a controlled environment before facing real-world situations.

*

For understanding complex systems: they provide insights into complex systems by allowing researchers to observe how different components interact and influence each other.

Overall, simulations offer a powerful tool for understanding, predicting, and optimizing real-world systems and processes. Each simulation involves creating a model that represents the key aspects, behaviors, and relationships of the system under study and then running experiments or scenarios to observe how the system behaves in different conditions. There are various mechanisms and tools for constructing simulation models and visualizing them. GNs are a universal tool for describing structured and reusable models of complex systems usually involved in parallel, simultaneous activities. To implement such a model by GN, each part of the simulation needs to be described by GN transitions and places. The modeled process is separated into particular events (parts) by an expert who is well acquainted with it. This description requires input data—information known before a given event occurs, the different states it can reach during the event, and the output result after reaching that state—how the data and information have changed and in what state our process or system is currently in.

GNs have been employed in petroleum engineering to model the production of different automotive gasoline grades [43], various grades of diesel fuel [44], fuel gas, LPG, propylene and polypropylene [45], and diverse heavy oil products [46] in a petroleum refinery. However, to the best of our knowledge, none of the oil refinery processes involved in the production of the aforementioned petroleum products have been modeled by PNs or GNs. This was the reason for us to investigate the crude oil refining processes in their completeness that take place in an oil refinery and model them using GNs. The aim of this study is to discuss the obtained results at a theoretical level, and in the second part of this research, we will discuss the results of the GN program’s realization.

When we omit some of the components from the definition of GNs, we obtain a reduced GN. For brevity, in the present paper, we will use a reduced GN that will have only sets of transition and tokens. Each transition will contain input and output places and IMs with predicates. Each token will enter the GN with an initial characteristic, and after its transfer from an input to an output place, it can obtain a new characteristic.

2.2. Petroleum Refining Processing Scheme Description

The petroleum refinery that is the subject of the current study is the “LUKOIL Neftohim Burgas” (LNB) refinery, which is one of the most complex refineries worldwide according to the Solomon Associates fuels study. More than 85% of the world’s refining capacity relies on Solomon’s fuel study. The processing scheme of the LNB refinery is depicted in Figure 2. The refinery consists of two Crude Distillation Units (CDUs)—CDU-1 and CDU-4, which fractionates the crude oil feed into dry gas, Liquified Petroleum Gas (LPG), light naphtha (fraction 30–100 °C), heavy naphtha (fraction 100–180 °C), kerosene (fraction 180–240 °C), diesel (fraction 240–360 °C), atmospheric gas oil (fraction 360–480 °C), and atmospheric residue (fraction > 360 °C). The vacuum unit of CDU-1 fractionates the atmospheric residue into light vacuum gas oil (fraction 240–360 °C), heavy vacuum gas oil (fraction 360–540 °C), and vacuum residue (fraction > 540 °C). The Vacuum Distillation Unit (VDU)-2 fractionates the atmospheric residue obtained from CDU-4 into the same fractions as explained above for the vacuum unit of CDU-1. All the above-mentioned fractions obtained during the crude oil distillation process are concurrently processed in the other refining units as follows:

-

The dry gas is processed in the Absorption Gas Fractionation Unit (AGFU);

-

The LPG is processed in the Central Gas Fractionation Unit (CGFU). A detailed processing scheme of both dry gas and LPG of the LNB refinery is given in our recent study [46];

-

The light naphtha is upgraded in HydroDeSulphurization unit1-3,5 (HDS1-3,5), while the heavy naphtha is upgraded in the Catalytic Reformer;

-

The kerosene is upgraded in the HDS-2 unit;

-

The diesel is upgraded in both units HDS-3 and HDS-5;

-

The atmospheric gas oil is upgraded in the Fluid Catalytic Cracking (FCC) feed 160 Pretreater (FCC-PT);

-

The vacuum gas oil is first upgraded in the FCC-PT unit, and then it is converted to dry gas, propane–propylene fraction, butane–butylene fraction, gasoline, Light Cycle Oil (LCO), Heavy Cycle Oil (HCO), and SLurry Oil (SLO) in the FCCU;

-

The vacuum residue is split into feed for the ebullated bed (H-Oil) hydrocracking unit and feed for the bitumen unit. The H-Oil unit hydrocracks the vacuum residue to fuel gas, wild naphtha, diesel, heavy atmospheric gas oil, light vacuum gas oil, heavy vacuum gas oil, and unconverted hydrocracked vacuum residue (VTB). The vacuum residue that feeds the bitumen unit is oxidized to produce road pavement bitumen. The processing scheme for heavy oils (boiling above 360°C) is discussed in detail in our earlier study [46].

The secondary oil product naphtha from the H-Oil hydrocracker is hydrotreated in the HDS-1 unit along with the straight run light naphtha from both CDU-1, and CDU-2. The diesel fractions from the H-Oil hydrocracker, and from the FCC-PT, are hydrotreated in the HDS-5 unit along with the straight run diesel fractions coming from CDU-1, CDU-2, and VDU-2, while the LCO from the FCC is hydrotreated along with the straight run diesel fractions coming from CDU-1 and CDU-2. The quality of the crude oils used as feed streams for the LNB refinery in this study is summarized in

Table 1. Characteristics of the crude oils processed in a blend in a ratio of 74 wt.% Urals/26 wt.% Light Siberian in the LNB refinery during the study.

Processed Crude Oils		Urals	Light Siberian
Density at 15 °C, g/m3	ASTM D 5002 [47]	0.871	0.8493
Sulphur, wt.%	ASTM D 4294 [48]	1.68	0.56
Chloride content	ASTM D3230 [49]	26.7	27.6
Total acid number, mg KOH/g	ASTM D 664 [50]	0.11	0.07
Water content, vol.%		0.132	0.144
Pour point, °C	ASTM D 5853 [51]	−9	−12
TBP distillation fraction yields. wt.%	ASTM D 2892 & D 5236 [52,53]
IBP-110 °C		8.1	11.2
110–180 °C		9.5	11.3
180–240 °C		8.9	9.9
240–360 °C		22.0	23.6
360–540 °C		27.8	26.6
>540 °C	[54]	22.8	16.5
Na, mg/kg		3.6	10.8
Ni, mg/kg		18.0	5
V, mg/kg		51.3	20.1
Fe, mg/kg		10.7	8.4
As, mg/kg		73.3	70
Ca, mg/kg		24.2	23.8

, where “ASTM” is an abbreviation of “American Standard of Testing Materials”.

Table 2. Yields of products manufactured by the LNB refinery during processing of the crude oil blend 74 wt% Urals/26 wt.% Light Siberian.

Products	Yields, wt.%
Naphtha	7.6
Automotive gasoline	24.8
Aviation jet fuel	2.8
Automotive diesel	44.0
Fuel oil	8.8
LPG	1.1
Sulphur	1.3
Propylene	0.3
Polypropylene	1.0
Fuel to satisfy refinery energy needs	7.7
Losses	0.5

presents the structured product yields manufactured by the LNB refinery during the study.

3. Description of the Petroleum Refinery GN Model, Results, and Discussion

The GN contains 23 transitions and 90 places (see Figure 3). The meanings of some of the transitions are related to separate installations as follows:

$Z_1$

The organization activities in the petroleum refinery

$Z_2$

Absorption and Gas Fractionation Unit (AGFU)

$Z_3$

Catalytic Reformer (CatRef)

$Z_4$

VDU-2

$Z_7$

LPG Storage

$Z_9$

LPG HydroDeSulphurization(LPG HDS)

$Z_{10}$

FCC-PT

$Z_{11}$

H-Oil

$Z_{12}$

CGFU

$Z_{13}$

Bitumen

$Z_{14}$

HDS1-3,5

$Z_{15}$

FCC

$Z_{16}$

Iso-C4

$Z_{17}$

MTBE

$Z_{18}$

Claus unit-4

$Z_{19}$

Fuel gas (FG) Storage

$Z_{20}$

Alkylation

$Z_{21}$

Prime G

$Z_{22}$

Polypropylene Unit

$Z_{23}$

Production of finished products and expedition

The remaining transitions play an auxiliary role related to the GN notation and this will be discussed in the text below.

The meanings of some of the places are as follows:

$l_1$

crude oil, quantity and quality

$l_2$

an order for buying a final petroleum product, quantity, customer

$l_3$

information for the final petroleum products in the world market, quantity, producer

$l_4$

dry gas for AGFU, quantity

$l_5$

LPG, quantity

$l_6$

heavy naphtha (HN) for CatRef, quantity

$l_7$

light naphtha (LN), quantity

$l_8$

kerosene, quantity

$l_9$

diesel, quantity

$l_{10}$

vacuum gas oil (VGO), quantity

$l_{11}$

vacuum residue feed for H-Oil (VR), quantity

$l_{12}$

straight run vacuum residue feed for bitumen unit, quantity

$l_{13}$

(positive or negative) answer of the current order

$l_{14}$

announce what kind of products with a specific quality are available for selling in the world market

$l_{15}$

information for existing types of naphtha in the plant and a list of the types of naphtha that the dealers buy

$l_{16}$

solution for buying the most suitable naphtha, financial evaluation

$l_{17}$

archive of the full process and the Decision Maker

$l_{18}$

atmospheric residue, quantity

$l_{19}$

fuel gas for final product, quantity

$l_{20}$

fuel gas for CGFU, quantity

$l_{21}$

reformate for final product, quantity

$l_{22}$

VGO, quantity

$l_{23}$

VR, quantity

$l_{24}$

results of ICA over the data for existing and potential crude oil

$l_{25}$

financial activities for buying of the determined crude oils

$l_{26}$

LPG for sale, quantity

$l_{27}$

LPG for LPG HDS, quantity

$l_{28}$

current status of the LPG Storage (including the quantity in it)

$l_{29}$

result of ICA and other correlation analyses and selection of the most suitable petroleum

$l_{30}$

LPG for CGFU, quantity

$l_{31}$

diesel for HDS1-3,5, quantity

$l_{32}$

$H_2$S for Claus Unit, quantity

$l_{33}$

HTVGO for FCC, quantity

$l_{34}$

current status of the FCC-PT

$l_{35}$

naphtha for HDS1-3,5, quantity

$l_{36}$

diesel for HDS1-3,5, quantity

$l_{37}$

VTB for bitumen, quantity

$l_{38}$

HCKVGO for FCC, quantity

$l_{39}$

$H_2$S for Claus Unit, quantity

$l_{40}$

PBFO for sale, quantity

$l_{41}$

current status of the H-Oil

$l_{42}$

LPG for sale, quantity

$l_{43}$

Fuel gas for FG storage, quantity

$l_{44}$

N-butane for Isometrization C4, quantity

$l_{45}$

current status of the CGFU

$l_{46}$

Bitumen for sale, quantity

$l_{47}$

current status of the bitumen

$l_{48}$

HTN for sale, quantity

$l_{49}$

HTK for sale, quantity

$l_{50}$

HTD for sale, quantity

$l_{51}$

$H_2$S for Claus Unit, quantity

$l_{52}$

current status of the HDS1-3,5

$l_{53}$

LCO for HDS1-3,5, quantity

$l_{54}$

Dry gas for FG Storage, quantity

$l_{55}$

HCO for sale, quantity

$l_{56}$

CN for blending, quantity

$l_{57}$

$C_4$ for MTBE, quantity

$l_{58}$

$C_3$ for polypropylene, quantity

$l_{59}$

FCCSLO for H-Oil, quantity

$l_{60}$

current status of the FCC

$l_{61}$

Iso-butane for blending, quantity

$l_{62}$

Iso-butane for Alkylation, quantity

$l_{63}$

current status of the Isometrization

$l_{64}$

$C_4$ olefins for Alkylation, quantity

$l_{65}$

MTBE for sale, quantity

$l_{66}$

Sulphur for sale, quantity

$l_{67}$

current status of the Claus Unit

$l_{68}$

Fuel gas for burning, quantity

$l_{69}$

current status of the FG Storage

$l_{70}$

Alkylate for blending, quantity

$l_{71}$

current status of the Alkylation

$l_{72}$

Hydrotreated cracked naphtha for blending, quantity

$l_{73}$

Propylene for sale, quantity

$l_{74}$

Polypropylene for sale, quantity

$l_{75}$

current status of the propylene unit

$l_{76}$

Fuel gas, quantity

$l_{77}$

LPG, quantity

$l_{78}$

Naphtha, quantity

$l_{79}$

Sulphur, quantity

$l_{80}$

JetA-1, quantity

$l_{81}$

Euro-Diesel, quantity

$l_{82}$

A-95 (mineral/bio), quantity

$l_{83}$

A-98H, quantity

$l_{84}$

A-100H (bio), quantity

$l_{85}$

Propylene, quantity

$l_{86}$

Polypropylene, quantity

$l_{87}$

Fuel oil, quantity

$l_{88}$

RMF 0.5% sulphur, quantity

$l_{89}$

Bitumen, quantity

$l_{90}$

information for the archieve

All tokens related to the petroleum oils will be noted as $\pi$-tokens, for brevity, those without indices; the tokens related to outside or outgoing information as $\iota$-tokens; the tokens related to decision-making processesas $\delta$-tokens; and the $\alpha$-token that permanently stays in place $l_{17}$ represents the archive of the full process and the Decision Maker. Of course, in a more detailed process, this token can be changed with a whole sub-net in which the archive will have its own transition, places, and tokens and the activities of the Decision Maker can be described in essentially more detail. In some moments after the arrival of some $\iota$-token, token $\alpha$ splits into two tokens—the same token $\alpha$ and a $\delta$-token.

In some steps of GN functioning, an $\iota$-token enters place $l_2$ with the initial characteristic

$$“\mathrm{an} \mathrm{order} \mathrm{for} \mathrm{buying} \mathrm{of} \mathrm{a} \mathrm{final} \mathrm{petroleum} \mathrm{product}, \mathrm{quantity}, \mathrm{customer}”,$$

or place $l_3$ with the initial characteristic

$$“\mathrm{information} \mathrm{for} \mathrm{the} \mathrm{final} \mathrm{petroleum} \mathrm{products} \mathrm{in} \mathrm{the} \mathrm{world} \mathrm{market}, \mathrm{quantity}, \mathrm{producer}”.$$

The structure of the model corresponds to the actual processes taking place in an oil refinery. As an example, the LUKOIL Neftohim Burgas refinery is given. Therefore, no constraints are imposed in the model. The petroleum’s feedstock properties presented in Table 1 for this particular case are set as the initial characteristics of the $\pi$-tokens.

$$Z_1=\langle \{l_1,l_2,l_3,l_{17},l_{25},l_{41},l_{84}\},\{l_4,l_5,l_6,l_7,l_8,l_9,l_{10},l_{11},l_{12},l_{13},l_{14},l_{15},l_{16},l_{17}\},$$

$$\begin{array}{ccccccccccccccc}& l_4& l_5& l_6& l_7& l_8& l_9& l_{10}& l_{11}& l_{12}& l_{13}& l_{14}& l_{15}& l_{16}& l_{17}\\ l_1& W_{1,4}& W_{1,5}& W_{1,6}& W_{1,7}& W_{1,8}& W_{1,9}& W_{1,10}& W_{1,11}& W_{1,12}& F& F& F& F& F\\ l_2& F& F& F& F& F& F& F& F& F& F& F& F& F& T\\ l_3& F& F& F& F& F& F& F& F& F& F& F& F& F& T\\ l_{17}& F& F& F& F& F& F& F& F& F& W_{17,13}& W_{17,14}& W_{17,15}& W_{17,16}& T\\ l_{25}& F& F& F& F& F& F& F& F& F& F& F& F& F& T\\ l_{41}& F& F& F& F& F& F& F& F& F& F& F& F& F& T\\ l_{90}& F& F& F& F& F& F& F& F& F& F& F& F& F& T\end{array}\rangle ,$$

where

$W_{1,4}=$ “there is a necessity of dry gas for AFGU”,

$W_{1,5}=$ “there is a necessity of LPG for LPG Storage”,

$W_{1,6}=$ “there is a necessity of Heavy Naphta (HN) for CatRef”,

$W_{1,7}=$ “there is a necessity of Light Naphtha (LN) for HDS1-3,5”,

$W_{1,8}=$ “there is a necessity of kerosene for HDS1-3,5 ”,

$W_{1,9}=$ “there is a necessity of diesel for HDS1-3,5 ”,

$W_{1,10}=$ “there is a necessity of Vacuum Gas Oil (VGO) for FCC-PT”,

$W_{1,11}=$ “there is a necessity of Vacuum Residue (VR) for Bitumen)”,

$W_{1,12}=$ “there is a necessity of VR for H-Oil”,

$W_{17,13}=$ “there is a solution for the current order”,

$W_{17,14}=$ “there is a possibility to announce of what kind of products with specific quality are available for selling”,

$W_{17,15}=$ “there are data for new types of petroleum that the dealers can buy”,

$W_{17,16}=$ “the most suitable petroleum for buying is determined”.

In respect of the truth values of the predicates $W_{1,4},W_{1,5},W_{1,6},W_{1,7},$$W_{1,8},W_{1,9},W_{1,10},$$W_{1,11},W_{1,12}$, token $\pi$ from place $l_1$ splits to one, two, …, or eight $\pi$-tokens that enter places $l_4,l_5,\dots ,l_{12}$ with characteristics

$$“\mathrm{d}\mathrm{r}\mathrm{y} \mathrm{g}\mathrm{a}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{A}\mathrm{G}\mathrm{F}\mathrm{U},\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{L}\mathrm{P}\mathrm{G}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{H}\mathrm{N} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{C}\mathrm{a}\mathrm{t}\mathrm{R}\mathrm{e}\mathrm{f}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{L}\mathrm{N}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{k}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{D}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{l}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{V}\mathrm{G}\mathrm{O}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{V}\mathrm{R}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{V}\mathrm{R}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

respectively.

In respect of the truth values of the predicates $W_{17,13},W_{17,14},W_{17,15},$$W_{17,16}$, token $\alpha$ from place $l_{17}$ splits into two tokens: the same token $\alpha$ that continues to stay in place $l_{17}$ and a token $\delta$ that enters place $l_{13}$ with the characteristic

$$“(\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{o}\mathrm{r} \mathrm{n}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}) \mathrm{a}\mathrm{n}\mathrm{s}\mathrm{w}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{o}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{r}”,$$

or place $l_{14}$ with the characteristic

$$\begin{gathered} “\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{w}\mathrm{h}\mathrm{a}\mathrm{t} \mathrm{k}\mathrm{i}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{f} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{s} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{c} \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{a}\mathrm{v}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \\ \mathrm{i}\mathrm{n} \mathrm{w}\mathrm{o}\mathrm{r}\mathrm{l}\mathrm{d} \mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{e}\mathrm{t}”, \end{gathered}$$

or place $l_{15}$ with the characteristic

$$\begin{gathered} “\mathrm{i}\mathrm{n}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{e}\mathrm{x}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{y}\mathrm{p}\mathrm{e}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{a}\mathrm{p}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{a} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{t} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{a} \mathrm{l}\mathrm{i}\mathrm{s}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{y}\mathrm{p}\mathrm{e}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{a}\mathrm{p}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{a} \\ \mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{c}\mathrm{a}\mathrm{n} \mathrm{b}\mathrm{u}\mathrm{y}”, \end{gathered}$$

or place $l_{16}$ with the characteristic

$$“\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{b}\mathrm{u}\mathrm{y}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{o}\mathrm{s}\mathrm{t} \mathrm{s}\mathrm{u}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{p}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{a}, \mathrm{f}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{e}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}”.$$

When one of the tokens $\delta$ from place $l_{25}$, $l_{29}$, or $l_{90}$ enters place $l_{17}$, it unites with token $\alpha$, and the latest token obtains the characteristic

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{i}\mathrm{n}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{s} \mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{h}\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{t}”.$$

$$Z_2=\langle \left\{l_4\right\},\{l_{19},l_{20}\},\begin{array}{ccc}& l_{19}& l_{20}\\ l_4& W_{4,19}& W_{4,20}\end{array}\rangle ,$$

where

$W_{4,19}=$ “there is a necessity of fuel gas for final product”,

$W_{4,20}=$ “there is a necessity of fuel gas for CGFU”.

In respect of the truth values of the predicates $W_{4,19}$ and $W_{4,20}$, the $\pi$-token from place $l_4$ enters the respective output place or splits into two tokens that enter place $l_{19}$ with the characteristic

$$“\mathrm{f}\mathrm{u}\mathrm{e}\mathrm{l} \mathrm{g}\mathrm{a}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{f}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”$$

or place $l_{20}$ with the characteristic

$$“\mathrm{f}\mathrm{u}\mathrm{e}\mathrm{l} \mathrm{g}\mathrm{a}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{C}\mathrm{G}\mathrm{F}\mathrm{U}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”.$$

$$Z_3=\langle \left\{l_4\right\},\left\{l_{21}\right\},\begin{array}{cc}& l_{21}\\ l_4& T\end{array}\rangle .$$

The token from place $l_6$ enters place $l_{21}$ with the characteristic

$$“\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{f}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”.$$

$\pi$-tokens with the initial characteristic

$$“\mathrm{A}\mathrm{t}\mathrm{m}\mathrm{o}\mathrm{s}\mathrm{p}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{c} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{u}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”$$

enter the net through place $l_{18}$.

$$Z_4=\langle \left\{l_{18}\right\},\{l_{22},l_{23}\},\begin{array}{ccc}& l_{22}& l_{23}\\ l_6& W_{6,22}& W_{6,23}\end{array}\rangle ,$$

where

$W_{6,22}=$ “there is a necessity of VGO for FCC-PT”,

$W_{6,23}=$ “there is a necessity of VGO for H-Oil”.

In respect of the truth values of the predicates $W_{6,22}$ and $W_{6,23}$, the token from place $l_6$ enters the respective output place or splits into two tokens that enter place $l_{22}$ with the characteristic

$$“\mathrm{V}\mathrm{G}\mathrm{O}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”$$

or place $l_{23}$ with the characteristic

$$“\mathrm{V}\mathrm{R}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”.$$

$$Z_5=\langle \left\{l_{15}\right\},\left\{l_{24}\right\},\begin{array}{cc}& l_{24}\\ l_{15}& T\end{array}\rangle .$$

Token $\delta$ from place $l_{15}$ enters place $l_{24}$ with the characteristic “results of Intercriteria Analysis (ICA, see [55]) over the data for existing and potential crude oil”.

$$Z_6=\langle \left\{l_{16}\right\},\left\{l_{25}\right\},\begin{array}{cc}& l_{25}\\ l_{16}& T\end{array}\rangle .$$

Token $\delta$ from place $l_{16}$ enters place $l_{25}$ with the characteristic

$$“\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{b}\mathrm{u}\mathrm{y}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{c}\mathrm{r}\mathrm{u}\mathrm{d}\mathrm{e} \mathrm{o}\mathrm{i}\mathrm{l}\mathrm{s}”.$$

$$Z_7=\langle \{l_5,l_{20},l_{28}\},\{l_{26},l_{27},l_{28}\},\begin{array}{cccc}& l_{26}& l_{27}& l_{28}\\ l_5& F& F& T\\ l_{20}& F& F& T\\ l_{28}& W_{28,26}& W_{28,27}& T\end{array}\rangle ,$$

where

$W_{28,26}=$ “there is a necessity of LPG for sale”,

$W_{28,27}=$ “there is a necessity of LPG for LPG HDS”.

In respect of the truth values of the predicates $W_{20,26}$ and $W_{20,27}$, the token from place $l_{28}$ splits into two or three tokens that enter place $l_{26}$ or place $l_{27}$ and (obligatory) place $l_{28}$, where they obtain the characteristic

$$“\mathrm{L}\mathrm{P}\mathrm{G} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

or

$$“\mathrm{L}\mathrm{P}\mathrm{G} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{L}\mathrm{P}\mathrm{G} \mathrm{H}\mathrm{D}\mathrm{S}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

or

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{L}\mathrm{P}\mathrm{G} \mathrm{S}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e} (\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{i}\mathrm{n} \mathrm{i}\mathrm{t})”,$$

respectively.

$$Z_8=\langle \left\{l_{24}\right\},\left\{l_{29}\right\},\begin{array}{cc}& l_{29}\\ l_{24}& T\end{array}\rangle .$$

Token $\delta$ from place $l_{24}$ enters place $l_{29}$ with the characteristic

$$“\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{u}\mathrm{l}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{I}\mathrm{C}\mathrm{A} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{a}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{y}\mathrm{s}\mathrm{e}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{s}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{o}\mathrm{s}\mathrm{t} \mathrm{s}\mathrm{u}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{p}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{u}\mathrm{m}”.$$

$$Z_9=\langle \left\{l_{27}\right\},\left\{l_{30}\right\},\begin{array}{cc}& l_{30}\\ l_{27}& T\end{array}\rangle .$$

The token from place $l_{27}$ enters place $l_{30}$ with the characteristic

$$“\mathrm{L}\mathrm{P}\mathrm{G} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{C}\mathrm{G}\mathrm{F}\mathrm{U}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”.$$

$$Z_{10}=\langle \{l_{10},l_{22},l_{34}\},\{l_{31},l_{32},l_{33},l_{34}\},\begin{array}{ccccc}& l_{31}& l_{32}& l_{33}& l_{34}\\ l_{10}& F& F& F& T\\ l_{22}& F& F& F& T\\ l_{34}& W_{34,31}& W_{34,32}& W_{34,33}& T\end{array}\rangle ,$$

where

$W_{34,31}=$ “there is a necessity of FCC-PT diesel for HDS1-3,5”,

$W_{34,32}=$ “there is a necessity of Hydrogen Sulphide (H₂S) for Claus Unit”,

$W_{28,34}=$ “there is a necessity of HydroTreated Vacuum Gas Oil (HTVGO) for FCC”.

In respect of the truth values of the predicates $W_{34,31},W_{34,32}$, and $W_{34,33}$, the token from place $l_{34}$ splits into two, three, or four tokens that enter place $l_{31}$ and/or $l_{32}$ and/or place $l_{33}$, and place $l_{34}$ where they obtain the characteristic

$$“\mathrm{D}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{l} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{H}\mathrm{D}\mathrm{S}1\text{-}3,5, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“{\mathrm{H}}_2\mathrm{S} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{C}\mathrm{l}\mathrm{a}\mathrm{u}\mathrm{s} \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{t}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{H}\mathrm{T}\mathrm{V}\mathrm{G}\mathrm{O} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{F}\mathrm{C}\mathrm{C}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{F}\mathrm{C}\mathrm{C}\text{-}\mathrm{P}\mathrm{T}”,$$

respectively.

$$Z_{11}=\langle \{l_{11},l_{23},l_{41},l_{59}\},\{l_{35},l_{36},l_{37},l_{38},l_{39},l_{40},l_{41}\},$$

$$\begin{array}{cccccccc}& l_{35}& l_{36}& l_{37}& l_{38}& l_{39}& l_{40}& l_{41}\\ l_{11}& F& F& F& F& F& F& T\\ l_{23}& F& F& F& F& F& F& T\\ l_{41}& W_{41,35}& W_{41,36}& W_{41,37}& W_{41,38}& W_{41,39}& W_{41,40}& T\\ l_{59}& F& F& F& F& F& F& T\end{array}\rangle ,$$

where

$W_{41,35}=$ “there is a necessity of naphtha for HDS1-3,5”,

$W_{41,36}=$ “there is a necessity of diesel for HDS1-3,5”,

$W_{41,37}=$ “there is a necessity of hydrocracked Vacuum Residue (VTB) for Bitumen”,

$W_{41,38}=$ “there is a necessity of hydrocracked VGO (HCKVGO) for FCC”,

$W_{41,39}=$ “there is a necessity of H₂S for Claus Unit”,

$W_{41,40}=$ “there is a necessity of Partially Blended Fuel Oil (PBFO) for sale”.

In respect of the truth values of the predicates $W_{41,35},W_{41,36},\dots ,W_{41,40}$, the token from place $l_{41}$ splits into two, three, or …, or seven tokens that enter place $l_{35}$ and/or place $l_{36}$ and/or …, and/or place $l_{40}$, and (obligatory) place $l_{41}$, where they obtain the characteristic

$$“\mathrm{n}\mathrm{a}\mathrm{p}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{a} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{H}\mathrm{D}\mathrm{S}1\text{-}3,5, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{d}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{l} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{H}\mathrm{D}\mathrm{S}1\text{-}3,5, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{V}\mathrm{T}\mathrm{B} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{B}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{n}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{H}\mathrm{C}\mathrm{K}\mathrm{V}\mathrm{G}\mathrm{O} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{F}\mathrm{C}\mathrm{C}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“{\mathrm{H}}_2\mathrm{S} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{C}\mathrm{l}\mathrm{a}\mathrm{u}\mathrm{s} \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{t}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

or

$$“\mathrm{P}\mathrm{B}\mathrm{F}\mathrm{O} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

and

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{H}\text{-}\mathrm{O}\mathrm{i}\mathrm{l}”,$$

respectively.

$$Z_{12}=\langle \{l_{30},l_{45}\},\{l_{42},l_{43},l_{44},l_{45}\},\begin{array}{ccccc}& l_{42}& l_{43},& l_{44}& l_{45}\\ l_{30}& F& F& F& T\\ l_{45}& W_{45,42}& W_{45,43}& l_{45,44}& T\end{array}\rangle ,$$

where

$W_{45,42}=$ “there is a necessity of LPG for sale”,

$W_{45,43}=$ “there is a necessity of fuel gas for FG Storage”,

$W_{45,44}=$ “there is a necessity of n-butane for Isometrization C₄”,

In respect of the truth values of the predicates $W_{45,42},W_{45,43}$, and $W_{45,44}$, the token from place $l_{45}$ splits into two, three, or four tokens that enter place $l_{42}$ and/or place $l_{43}$ and/or place $l_{44}$, and (obligatory) place $l_{45}$ where they obtain the characteristic

$$“\mathrm{L}\mathrm{P}\mathrm{G} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{F}\mathrm{u}\mathrm{e}\mathrm{l} \mathrm{g}\mathrm{a}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{F}\mathrm{G} \mathrm{S}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

or

$$“\mathrm{N}\text{-}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{e} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{I}\mathrm{s}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{z}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} {\mathrm{C}}_4, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

and

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{C}\mathrm{G}\mathrm{F}\mathrm{U}”,$$

respectively.

$$Z_{13}=\langle \{l_{12},l_{37},l_{47}\},\{l_{46},l_{47}\},\begin{array}{ccc}& l_{46}& l_{47}\\ l_{12}& F& T\\ l_{37}& F& T\\ l_{47}& W_{47,46}& T\end{array}\rangle ,$$

where

$W_{47,46}=$ “there is a necessity of Bitumen for sale”.

When the predicate $W_{47,46}$ is true, the token from place $l_{47}$ splits into two tokens that enter place $l_{46}$ and (obligatory) place $l_{47}$ where they obtain the characteristic

$$“\mathrm{B}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{n} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”$$

and

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{B}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{n}”,$$

respectively.

$$Z_{14}=\langle \{l_7,l_8,l_9,l_{31},l_{35},l_{36},l_{52}\},\{l_{48},l_{49},l_{50},l_{51},l_{52}\},$$

$$\begin{array}{cccccc}& l_{48}& l_{49}& l_{50}& l_{51}& l_{52}\\ l_7& F& F& F& F& T\\ l_8& F& F& F& F& T\\ l_9& F& F& F& F& T\\ l_{31}& F& F& F& F& T\\ l_{35}& F& F& F& F& T\\ l_{36}& F& F& F& F& T\\ l_{52}& W_{52,48}& W_{52,49}& W_{52,50}& W_{52,51}& T\end{array}\rangle ,$$

where

$W_{52,48}=$ “there is a necessity of Hydrotreated Naphtha (HTN) for sale”,

$W_{52,49}=$ “there is a necessity of Hydrotreated Kerosene (HTK) for sale”,

$W_{52,50}=$ “there is a necessity of Hydrotreated Diesel (HTD) for sale”,

$W_{52,51}=$ “there is a necessity of H₂S for Claus Unit”.

In respect of the truth values of the predicates $W_{52,48},\dots ,W_{52,51}$, the token from place $l_{52}$ splits into two, three, or …, of five tokens that enter place $l_{48}$ and/or place $l_{49}$ and/or …, and/or place $l_{51}$, and (obligatory) place $l_{52}$ where they obtain the characteristic

$$“\mathrm{H}\mathrm{T}\mathrm{N} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{H}\mathrm{T}\mathrm{K} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{H}\mathrm{T}\mathrm{D} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“{\mathrm{H}}_2\mathrm{S} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{C}\mathrm{l}\mathrm{a}\mathrm{u}\mathrm{s} \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{t}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

and

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{H}\mathrm{D}\mathrm{S}1\text{-}3,5”,$$

respectively.

$$Z_{15}=\langle \{l_{33},l_{38},l_{60}\},\{l_{53},l_{54},l_{55},l_{56},l_{57},l_{58},l_{59},l_{60}\},$$

$$\begin{array}{ccccccccc}& l_{53}& l_{54}& l_{55}& l_{56}& l_{57}& l_{58}& l_{59}& l_{60}\\ l_{33}& F& F& F& F& F& F& F& T\\ l_{38}& F& F& F& F& F& F& F& T\\ l_{60}& W_{60,53}& W_{60,54}& W_{60,55}& W_{60,56}& W_{60,57}& W_{60,58}& W_{60,59}& T\\ l_{59}& F& F& F& F& F& F& F& T\end{array}\rangle ,$$

where

$W_{60,53}=$ “there is a necessity of LGO for HDS1-3,5”,

$W_{60,54}=$ “there is a necessity of Dry gas for FG Storage”,

$W_{60,55}=$ “there is a necessity of HCO for blending in fuel oil and sale”,

$W_{60,56}=$ “there is a necessity of Cracked Naphtha (CN) for Prime G”,

$W_{60,57}=$ “there is a necessity of C₄ (Butane–Butylene Fraction) for MTBE”,

$W_{60,58}=$ “there is a necessity of C3 fraction for Polypropylene”,

$W_{60,59}=$ “there is a necessity of Fluid Catalytic Cracking Slurry Oil (FCCSLO) for H-Oil”.

In respect of the truth values of the predicates $W_{60,53},\dots ,W_{60,59}$, the token from place $l_{60}$ splits into two, three, or …, or eight tokens that enter place $l_{53}$ and/or place $l_{54}$ and/or …, and/or place $l_{59}$, and (obligatory) place $l_{60}$ where they obtain the characteristic

$$“\mathrm{L}\mathrm{C}\mathrm{O} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{H}\mathrm{D}\mathrm{S}1\text{-}3,5, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{D}\mathrm{r}\mathrm{y} \mathrm{g}\mathrm{a}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{F}\mathrm{G} \mathrm{S}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{H}\mathrm{C}\mathrm{O} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“\mathrm{C}\mathrm{N} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{b}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“C_4 \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{M}\mathrm{T}\mathrm{B}\mathrm{E}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

$$“C_3 \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{P}\mathrm{o}\mathrm{l}\mathrm{y}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

or

$$“\mathrm{F}\mathrm{C}\mathrm{C}\mathrm{S}\mathrm{L}\mathrm{O} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{H}\text{-}\mathrm{O}\mathrm{i}\mathrm{l}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

and

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{F}\mathrm{C}\mathrm{C}”,$$

respectively.

$$Z_{16}=\langle \{l_{44},l_{63}\},\{l_{61},l_{62},l_{63}\},\begin{array}{cccc}& l_{61}& l_{62}& l_{63}\\ l_{44}& F& F& T\\ l_{63}& W_{63,61}& W_{63,62}& T\end{array}\rangle ,$$

where

$W_{63,61}=$ “there is a necessity of Iso-butane for blending”,

$W_{63,62}=$ “there is a necessity of Iso-butane for Alkylation”.

In respect of the truth values of the predicates $W_{63,61}$ and $W_{63,62}$, the token from place $l_{63}$ splits into two or three tokens that enter place $l_{61}$ or place $l_{62}$ and (obligatory) place $l_{63}$ where they unite with the characteristic

$$“\mathrm{I}\mathrm{s}\mathrm{o}\text{-}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{e} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{b}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

or

$$“\mathrm{I}\mathrm{s}\mathrm{o}\text{-}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{e} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{A}\mathrm{l}\mathrm{k}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

and

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{I}\mathrm{s}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{z}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}”,$$

respectively.

$$Z_{17}=\langle \left\{l_{57}\right\},\{l_{64},l_{65}\},\begin{array}{ccc}& l_{64}& l_{65}\\ l_{57}& W_{57,64}& W_{57,65}\end{array}\rangle ,$$

where

$W_{57,64}=$ “there is a necessity of C4 olefinsfor Alkylation”,

$W_{57,65}=$ “there is a necessity of MTBE for sale”,

In respect of the truth values of predicates $W_{57,64}$ and $W_{57,65}$, the token from place $l_{57}$ enters place $l_{64}$ with the characteristic

$$“\mathrm{C}4 \mathrm{o}\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{A}\mathrm{l}\mathrm{k}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”$$

and place $l_{65}$ with the characteristic

$$“\mathrm{M}\mathrm{T}\mathrm{B}\mathrm{E} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”.$$

$$Z_{18}=\langle \{l_{32},l_{39},l_{51},l_{67}\},\{l_{66},l_{67}\},\begin{array}{ccc}& l_{66}& l_{67}\\ l_{32}& F& T\\ l_{39}& F& T\\ l_{51}& F& T\\ l_{67}& W_{67,66}& T\end{array}\rangle ,$$

where

$W_{67,66}=$ “there is a necessity of Sulphur for sale”.

When the predicate $W_{67,66}$ is true, the token from place $l_{67}$ splits into two tokens that enter place $l_{66}$ and (obligatory) place $l_{67}$ where they obtain the characteristic

$$“\mathrm{S}\mathrm{u}\mathrm{l}\mathrm{p}\mathrm{h}\mathrm{u}\mathrm{r} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”$$

and

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{C}\mathrm{l}\mathrm{a}\mathrm{u}\mathrm{s} \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{t}”,$$

respectively.

$$Z_{19}=\langle \{l_{19},l_{43},l_{54},l_{69}\},\{l_{68},l_{69}\},\begin{array}{ccc}& l_{68}& l_{69}\\ l_{19}& F& T\\ l_{43}& F& T\\ l_{54}& F& T\\ l_{69}& W_{69,68}& T\end{array}\rangle ,$$

where

$W_{69,68}=$ “there is a necessity of Fuel Gas for burning”.

When the predicate $W_{69,68}$ is true, the token from place $l_{69}$ splits into two tokens that enter place $l_{68}$ and (obligatory) place $l_{69}$ where they obtain the characteristic

$$“\mathrm{F}\mathrm{u}\mathrm{e}\mathrm{l} \mathrm{G}\mathrm{a}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{b}\mathrm{u}\mathrm{r}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”$$

and

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{F}\mathrm{G} \mathrm{S}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}”,$$

respectively.

$$Z_{20}=\langle \{l_{62},l_{64},l_{71}\},\{l_{70},l_{71}\},\begin{array}{ccc}& l_{70}& l_{71}\\ l_{19}& F& T\\ l_{43}& F& T\\ l_{54}& F& T\\ l_{71}& W_{71,70}& T\end{array}\rangle ,$$

where

$W_{71,70}=$ “there is a necessity of Alkylate for blending”.

When the predicate $W_{71,70}$ is true, the token from place $l_{71}$ splits into two tokens that enter place $l_{70}$ and (obligatory) place $l_{71}$ where they obtain the characteristic

$$“\mathrm{A}\mathrm{l}\mathrm{k}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{b}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”$$

and

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{A}\mathrm{l}\mathrm{k}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}”,$$

respectively.

$$Z_{21}=\langle \left\{l_{56}\right\},\left\{l_{72}\right\},\begin{array}{cc}& l_{72}\\ l_{56}& T\end{array}\rangle .$$

The token from place $l_{56}$ enters place $l_{72}$ with the characteristic

$$“\mathrm{H}\mathrm{y}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{c}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{k}\mathrm{e}\mathrm{d} \mathrm{n}\mathrm{a}\mathrm{p}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{a} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{b}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”.$$

$$Z_{22}=\langle \{l_{58},l_{75}\},\{l_{73},l_{74},l_{75}\},\begin{array}{cccc}& l_{73}& l_{74}& l_{75}\\ l_{58}& F& F& T\\ l_{75}& W_{75,73}& W_{75,74}& T\end{array}\rangle ,$$

where

$W_{75,73}=$ “there is a necessity of Propylene for sale”,

$W_{75,74}=$ “there is a necessity of Polypropylene for sale”.

In respect of the truth values of the predicates $W_{75,73}$ and $W_{75,74}$, the token from place $l_{75}$ splits into two or three tokens that enter place $l_{73}$ or place $l_{74}$ and (obligatory) place $l_{75}$ where they unite with the characteristic

$$“\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{e} \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

or

$$“\mathrm{P}\mathrm{o}\mathrm{l}\mathrm{y}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{e} \mathrm{f}\mathrm{i}\mathrm{e} \mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,$$

and

$$“\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{P}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{e} \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}”,$$

respectively.

$$Z_{23}=\langle \{l_{21},l_{26},l_{40},l_{42},l_{46},l_{48},l_{49},l_{50},l_{55},l_{61},l_{65},l_{67},l_{69},l_{71},l_{72},l_{73}\},$$

$$\{l_{75},l_{76},l_{77},l_{78},l_{79},l_{80},l_{81},l_{82},l_{83},l_{84},l_{85},l_{86},l_{87},l_{88},l_{89}\},$$

$$\begin{array}{cccccccccccccccc}& l_{76}& l_{77}& l_{78}& l_{79}& l_{80}& l_{81}& l_{82}& l_{83}& l_{84}& l_{85}& l_{86}& l_{87}& l_{88}& l_{89}& l_{90}\\ l_{21}& F& F& F& F& F& F& T& T& T& F& F& F& F& F& T\\ l_{26}& F& T& F& F& F& F& F& F& F& F& F& F& F& F& T\\ l_{40}& F& F& F& F& F& F& F& F& F& F& F& F& T& T& T\\ l_{42}& F& T& F& F& F& F& F& F& F& F& F& F& F& F& T\\ l_{46}& F& F& F& F& F& F& F& F& F& F& F& F& F& T& T\\ l_{48}& F& F& T& F& F& F& T& F& F& F& F& F& F& F& T\\ l_{49}& F& F& F& F& T& T& F& F& F& F& F& F& F& F& T\\ l_{50}& F& F& F& F& F& T& F& F& F& F& F& F& F& F& T\\ l_{55}& F& F& F& F& F& F& F& F& F& F& F& T& T& F& T\\ l_{61}& F& F& F& F& F& F& T& T& T& F& F& F& F& F& T\\ l_{65}& F& F& F& F& F& F& T& T& T& F& F& F& F& F& T\\ l_{66}& F& F& F& T& F& F& F& F& F& F& F& F& F& F& T\\ l_{68}& T& F& F& F& F& F& F& F& F& F& F& F& F& F& T\\ l_{70}& F& F& F& F& F& F& T& T& T& F& F& F& F& F& T\\ l_{72}& F& F& F& F& F& F& T& T& T& F& F& F& F& F& T\\ l_{73}& F& F& F& F& F& F& F& F& F& T& F& F& F& F& T\\ l_{74}& F& F& F& F& F& F& F& F& F& F& T& F& F& F& T\end{array}\rangle .$$

Each $\pi$-token splits into two tokens: the same $\pi$-token that enters a place, determined from the respective predicate in the IM with the characteristic, as follows:

$$\begin{array}{c}\mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{76}: “\mathrm{F}\mathrm{u}\mathrm{e}\mathrm{l} \mathrm{g}\mathrm{a}\mathrm{s}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{77}: “\mathrm{L}\mathrm{P}\mathrm{G}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{78}: “\mathrm{N}\mathrm{a}\mathrm{p}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{a}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{79}: “\mathrm{S}\mathrm{u}\mathrm{l}\mathrm{p}\mathrm{h}\mathrm{u}\mathrm{r}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \end{array}$$

$$\begin{array}{c}\mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{80}: “\mathrm{J}\mathrm{e}\mathrm{t}\mathrm{A}\text{-}1, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{81}: “\mathrm{E}\mathrm{u}\mathrm{r}\mathrm{o}\text{-}\mathrm{D}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{l}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{82}: “\mathrm{A}\text{-}95(\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}/\mathrm{b}\mathrm{i}\mathrm{o}), \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{83}: “\mathrm{A}\text{-}98\mathrm{H}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{84}: “\mathrm{A}\text{-}100\mathrm{H} \left(\mathrm{b}\mathrm{i}\mathrm{o}\right), \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{85}: “\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{86}: “\mathrm{P}\mathrm{o}\mathrm{l}\mathrm{y}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{e}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{87}: “\mathrm{F}\mathrm{u}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{i}\mathrm{l},\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{88}: “\mathrm{R}\mathrm{M}\mathrm{F} 0.5\% \mathrm{s}\mathrm{u}\mathrm{l}\mathrm{p}\mathrm{h}\mathrm{u}\mathrm{r}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \\ \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e} l_{89}: “\mathrm{B}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{n}, \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}”,\hfill \end{array}$$

and a $\delta$-token that enters place $l_{90}$ with the same characteristic (information for the archive).

This paper theoretically investigates the application of GNs to model the actual processes that take place in petroleum refining and the production of final commodity petroleum products. The question of the practical application of the model will be addressed in the second part, which will discuss the programming of the model and its application in practice to optimize processes under different scenarios, such as changes in market conditions, problems with the supply of raw materials, chemicals, and reagents, as well as the occurrence of incidents in the plants themselves and how this affects the entire refining process, etc.

Table 2 gives an example of the final characteristics of $\pi$-tokens when processing oil with the characteristics described in Table 1.

We can see that the present GN model includes as sub-nets the previous models, as follows:

• places $l_{21},l_{48},l_{61},l_{65},l_{70},l_{72},l_{78},l_{82},l_{83},l_{84}$ are places in the model from [43];
• places $l_{49},l_{50},l_{80},l_{81}$ are places in the model from [44];
• places $l_{26},l_{42},l_{77}$ are places in the model from [45];
• places $l_{40},l_{46},l_{55},l_{87},l_{88},l_{89}$ are places in the model from [46].

The processes in the petroleum refinery run in parallel. All fractions fractionated from the refinery crude oil feed in CDU-1, and CDU-2, and VDU-2 (so called straight run fractions) are further concurrently treated in upgrading and conversion processes. Besides the straight run distillate fractions, the distillate fractions obtained in the conversion processes, FCC-PT, FCC, and H-Oil, are further upgraded or converted in the hydrotreating and catalytic cracking processes. This complicated process that consists of multiple sub-processes was modeled by GN. In the second part of the research, the results from the program’s realization of the so-constructed GN model will be discussed. The GN refinery model can be used in the future for following in real time the streams of oil products for the simulation of a situation when an incident arises in any refinery units, for the simulation of a change in the processing scheme, the shut down of any refinery unit, the evaluation of changes from one production scheme to another one, etc. For example, when an injury occurs in any production line, the corresponding predicate that has the form “there is necessity of …” will obtain the truth value “false” (F), and as a result, no token will enter the corresponding position; that is, no oil products will be sent to the injured refinery unit. In the case where an unplanned shutdown occurs due to very high catalyst deactivation, for example, or an unexpected high corrosion rate, this predicate will again obtain the truth value F, and within the framework of the model, the possibility of finding an alternative route for the direction of the oil products to produce alternative refined oil products can be searched for. In the case where this is impossible, as is the case with polypropylene, in the model, an option can search for an alternative direction for the use of unutilized intermediate products to produce finished oil products.

4. Conclusions

The petroleum refining processes and the production of finished petroleum products are investigated using the toolbox of GNs. It is found that GNs, which can be considered as extensions of Petri nets and whose definition is more complex than that of Petri nets and therefore they allow the construction of a much more detailed model than any Petri net, can be used to model the parallel processes that take place in an oil refinery. The model developed in this study is theoretical in nature and can be used to evaluate refinery performance in a variety of specific situations after its program realization, which will be discussed in the second part of this study, “GN model of the processes in a petroleum refinery. Part II: Program realization and practical application” It is interesting to note that the first GN model of an oil refinery, made 31 years ago [56], is a very particular case of the present one, and it was used in the 1990s to simulate real processes, mostly related to the economic side of the process.