MODELING AND SIMULATION OF TRANSPORTATION TIME IN A REAL-WORLD PIPELINE NETWORK

MODELING AND SIMULATION OF TRANSPORTATION TIME IN A REAL-WORLD PIPELINE NETWORK

Deisi Spricigo

Universidade Tecnológica Federal do Paraná

Av. Sete de Setembro, 3165, CEP: 80230-901, Curitiba - PR [email protected]

Camila Baldissera de Borba Universidade Tecnológica Federal do Paraná

Av. Sete de Setembro, 3165, CEP: 80230-901, Curitiba - PR [email protected]

Ricardo Lüders

Universidade Tecnológica Federal do Paraná

Av. Sete de Setembro, 3165, CEP: 80230-901, Curitiba - PR [email protected]

ABSTRACT

The logistic chain stands out currently as a strong candidate to obtain the highest profits in the oil industry, which is due to recent studies that point to a cost reduction by using better policies for distribution of oil derivatives. Although there are flow dynamic complex models to represent transfers of oil derivatives in pipelines, there is interest on models that provide information about operational decisions in a pipeline network. In this paper, a discrete event simulation model is proposed in ARENA that allows simulating a pipeline network based on average historical data.

Time delays for transferring products can be evaluated through different routes by comparing different operational scenarios of product transportation. The developed model can be used by programmers as a tool for the operational decision making in pipeline networks.

KEYWORDS. Discrete event simulation. Pipeline network. Oil industry. AL – Application to Logistics and Transportation.

RESUMO

A cadeia logística destaca-se atualmente como forte candidata a obter os maiores lucros na indústria do petróleo, o que se deve aos recentes estudos que apontam para a redução de custo na adoção de melhores políticas de distribuição de derivados de petróleo. Apesar de existirem modelos fluido dinâmicos complexos para representar a transferência de derivados de petróleo em dutos, há interesse em modelos que forneçam informações para as decisões operacionais de uma rede de dutos. Neste trabalho, é proposto um modelo de simulação a eventos discretos em ARENA, que permite simular uma rede de dutos baseado em dados históricos. Os tempos de transporte na transferência de produtos são analisados em diferentes rotas, permitindo comparar diferentes cenários operacionais de transferência de produtos. O modelo desenvolvido pode ser usado como ferramenta de apoio a decisão dos programadores das operações nas redes de dutos.

PALAVRAS CHAVE. Simulação a eventos discretos. Rede de dutos. Indústria do petróleo. AL – Aplicação a Logística e Transportes.

1. Introduction

The logistic chain currently stands out as a strong candidate to obtain maximal profit in the oil industry, which is due to recent studies that point to a cost reduction by using better policies for distribution of oil derivatives, particularly those where pipelines are used to transport products (REKLAITIS, 1992; RELVAS, 2006; CAFARO, 2008).

Pipeline systems transport a lot of different types of crude oil and derivatives with lower cost than other transportation modes. Pipelines connect oil production fields, ports, refineries, distribution centers and customer markets (KENJI, 2007). An increasing efficiency in pipeline transportation means lower dependence regarding other transportation modes, cost reduction and profit increasing.

There are several studies in the literature about the operational scheduling for transfer and storage of products using a pipeline system (MAS and PINTO, 2003). Most of them present optimization models to obtain better performance considering total transfer time, resource utilization, energy costs and inventories. Others are dedicated to obtain the optimal scheduling of transfers in single pipelines (MAGATÃO, 2004). There are still ones that combine optimization and simulation techniques for planning of transfer operations in oil industry (CHENG &

DURAN, 2004). Although there are complex models to represent transfer of oil derivatives in pipelines, which considerer its fluid dynamics, we are interested on models for the operational decision making. These models represent main events in a product transfer: pumping start, transport delay and product reception.

Differently to other transportation modes, a precise estimation of transport delays in a pipeline network is a difficult task. Batches of products are pumped into the network in a specified flow rate, but they are received in an unexpected manner since they should be completely or partially pushed by other products being pumped into the network. This scenario can be properly captured by a discrete event simulation model (LIMA, 2002). Discrete event simulation is a technique which allows reproduction and understanding of conditions used to take decisions, allowing qualitatively and quantitatively evaluation of its consequences.

In this paper, a statistical study of transport delays imposed by a pipeline network through different routes is presented by using historical data. A discrete event simulation model in ARENA is then proposed to simulate transfer operations in the network. The results obtained by simulation are then compared to real data.

The paper is organized as follows. Section 2 presents some issues of pipeline transportation. Section 3 presents details of the proposed simulation model and Section 4 shows the obtained results. Conclusions are presented in Section 5.

2. The problem of product transportation in pipelines

The use of pipelines to transfer oil or derivatives is done by linking two (through a single pipeline) or more areas (through a pipeline network). These areas can be ports, refineries, terminals or final customers. Given the efficiency of using pipelines as mean of transportation for oil or derivatives, there is a great concern to improve its operation by minimizing losses such as operating costs and transfer time (BOSCHETTO, 2006).

In a pipeline network, each pipe may be part of one or more routes, and each route may be composed of one or more pipes. Due to this sharing, it is necessary a good scheduling for using each pipeline to supply a specified demand within a desired time.

The total transfer time in a pipeline network includes the beginning of product pumping until the end of its receipt. It also includes time intervals in which a product does not move in the network until a new batch arrives to push it. Note that transport times depend on the product to be transferred and route to be used. Transportation is done through batches of products with specified volumes and routes to be followed. Many batches may be present in a single pipeline.

The interest of this work is to statistically evaluate the total holding time of a product in the network according to different routes that batches can follow. Although the time depends on the product to be transferred, this paper considers only the transported volume, which, in some way, indirectly represents the product dependence, because different products have different

typical batch volumes. Then, the existence of different products along the route at a given time can be characterized by an average behavior.

In Figure 1, a graph for the network studied in this work is presented. It contains 14 areas (suppliers and customers) and 23 pipelines, which comprise 17 different routes.

A

K J

I D F

B

H

E

M

C

G

L

Area ^Pipeline

1

2

3

4 5

6 7

8

9

10

11

12

13

14

15

16

17 18

19 20

21 N

22 23

Figure 1 - Pipeline network representation.

The routes definition, including origin, destination and sequence of pipelines, is shown in Table 1.

Table 1 - Routes definition.

Route Origin Destination Pipelines

1 B E 5

2 K J 17,16

3 K M 19

4 K M 18

5 K N 18, 22

6 K N 20,21

7 K L 17, 16, 13, 12

8 J I 14

9 A D 4

10 A B 1

11 C B 2

12 C E 3, 6, 8

13 C H 2, 5, 10, 11

14 C G 2, 7

15 M D 15, 9

16 N L 23, 16, 13, 12

17 I D 9

The next section describes the pipeline network model proposed to simulate transfer operations. This model is based on probability distributions for time delays in each route.

3. Modeling and simulation with Arena

Discrete event simulation is concerned with modeling of a system in which state variables change according to the occurrence of events.

For the generation and assignment of compatible values to the random variables in this models, simulation programs, such as ARENA, operationalize the use of the Monte Carlo method. In applying this technique, the data are artificially generated by using a random number generator and a frequency distribution of the interest variable (FREITAS FILHO, 2008).

In the proposed model, the transportation time in the pipeline network is a stochastic variable which is characterized by historical data as below.

3.1. Historical data

The first stage of the model construction is acquisition of sufficient and suitable historical data. For each batch transported by the network, the following information was obtained:

ƒ Volume;

ƒ Initial pumping time;

ƒ Final receiving time.

From these data, it was calculated the processing time per unit volume for each batch and these values were separated by routes. This was evaluated for 4 different scenarios, and the average time delays for each one are presented in Table 2. A scenario is an operational period of time in which batches should be transferred; in this case, it corresponds to one month. Also are shown the average time delays, calculated between the 4 scenarios, for each route.

Table 2 – Average time delays to transport 1000m³ by different routes.

Average T for the scenario (h/1000m³) Route

I II III IV Average T (h/1000m³)

Standard Deviation

Average Flow Rate (m³/h) 1 3.70 4.21 3.19 4.75 3.96 0.85 252.33 2 26.19 26.41 26.91 22.75 25.56 1.66 39.12 3 5.74 5.31 5.00 5.78 5.46 0.40 183.25 4 0.81 1.56 1.86 2.73 1.74 0.69 574.44 5 6.24 5.33 5.48 5.13 5.55 0.52 180.34 6 17.25 16.10 18.64 13.27 16.32 2.03 61.29 7 22.19 15.46 15.57 16.37 17.40 3.37 57.48 8 7.91 8.75 10.13 7.36 8.54 1.05 117.14 9 16.96 11.46 25.55 26.75 20.18 8.13 49.55 10 18.29 22.10 10.68 9.02 15.02 6.38 66.56 11 2.30 1.99 2.43 1.83 2.14 0.27 467.99 12 5.74 5.96 5.88 6.34 5.98 0.23 167.25 13 6.47 7.41 7.29 9.83 7.75 1.31 129.03 14 10.60 4.59 4.77 6.49 6.61 2.56 151.21 15 4.37 2.73 8.03 7.66 5.70 2.36 175.49 16 49.70 59.35 23.84 22.74 38.91 17.59 25.70 17 14.24 19.82 14.93 8.57 14.39 3.99 69.48 In these scenarios, historical data was used to adjust probability distributions for the processing time of each route, which is presented in Table 3. This adjustment was done through Input Analyzer tool.

During the analysis of input data, some outliers were excluded due to very small volumes compared to the rest of population. The estimated probabilities distributions for each route were verified against Chi-square and Kolmogorov-Smirnoff tests.

Table 3 - Average processing time for each route and theoretical probability distributions adjusted, according to each route, for historical data.

Route Number of data

Average T (min/m³)

Standard

deviation Probabilities distribution

1 24 0.302 0.294 Lognormal LOGN(0.291, 0.217)

2 36 1.433 0.766 Beta

3.31*BETA(1.58, 2.07)

3 48 0.334 0.136 Normal NORM(0.334, 0.135)

4 23 0.140 0.145 Beta

BETA(0.561, 2.35904)

5 31 0.331 0.254 Erlang ERLA(0.165, 2)

6 23 0.876 0.367 Weibull

0.15 + WEIB(0.82, 2.13)

7 24 1.061 0.503 Normal NORM(1.06, 0.492)

8 40 0.556 0.568 Lognormal LOGN(0.549, 0.634)

9 32 1.110 0.842 Exponential EXPO(1.11)

10 33 1.026 0.611 Beta

0.07 + 2.88*BETA(1.3, 2.63)

11 18 0.122 0.039 Triangular TRIA(0.06, 0.0646, 0.24)

12 44 0.347 0.108 Lognormal

0.11 + LOGN(0.242, 0.105)

13 28 0.444 0.177 Normal NORM(0.444, 0.174)

14 100 0.449 0.317 Lognormal LOGN(0.451, 0.34)

15 7 0.399 0.341 Lognormal 0.06 + LOGN(0.33, 0.325)

16 10 1.772 0.912 Beta

0.53 + 3.31*BETA(0.784, 1.3)

17 25 0.814 0.601 Exponential EXPO(0.814)

3.2. Simulation

Arena is a computational tool to implement a discrete event simulation model. This model is basically built by connecting blocks that perform different functions over entities flowing through them. Each block performs a specific function, which may be reading, writing,

decision and recording, among others. The developed model has a very simple structure in which its main block is a process block. A sketch of the model is shown in Figure 2.

The entities that come into the network are batches of products to be pumped. By passing through the block “Read data”, the following information are set as attributes of an entity:

ƒ Code;

ƒ Product;

ƒ Volume;

ƒ Route;

ƒ Initial pumping time.

Figure 2 – Sketch of the pipeline network model.

Thus, each entity is processed according to the information it presents to the system, being the volume, initial time of pumping and route. The other attributes, code and product, were defined for the report and presentation, but, however, have no influence on the model implementation.

The block "Process entities" is composed by several other blocks, whose representation can be seen in Figure 3.

In the “Process entities” submodel, the batches follow for each particular route. Each route has its probability distribution of the processing time, which is implemented in the model as a delay action.

Finally, the block “Record data”, shown in Figure 2, is used to record the attributes of each batch, which are those listed above, in the entities arrivals, but now there is the final time of receipt, which is the simulation time at the point that each batch leaves the route, it means when it arrives at its destination.

To test the model, the batches were chosen from a particular operation, which will be called “Test Scenario”. This data were not included in the historical data, used to adjust the probability distributions. The simulation was done with 10 replications, all of them with the same batches portfolio, from the Test Scenario.

Figure 3 – Submodel of the block "Process entities", referring to the choice of route.

4. Results

After performing the simulation in Arena, it is possible to compare the final receiving time of products at destination, resulting from the simulation, with the real times of the Test Scenario. Each new scenario must be simulated and compared with real data to verify that the historical data used as base are representative of this new scenario.

The simulation results are presented in Table 4 where they can be compared to real data from the Test Scenario.

Table 4 – Comparison between simulation and Test Scenario.

Simulation Real Test Scenario Route

Number of batches

Average T (min/m³)

Standard deviation

Average T (min/m³)

Standard deviation 1 6 0.314 0.070 0.321 0.252 2 9 1.452 0.284 1.502 0.936 3 14 0.339 0.045 0.276 0.067 4 8 0.217 0.043 0.094 0.0003 5 7 0.316 0.088 0.374 0.340 6 4 0.806 0.085 1.041 0.236 7 7 1.184 0.141 0.790 0.277 8 12 0.545 0.117 0.529 0.683 9 9 1.302 0.475 1.480 2.214 10 6 1.017 0.262 0.441 0.263 11 4 0.136 0.021 0.112 0.027 12 12 0.362 0.031 0.321 0.045 13 6 0.464 0.047 0.416 0.169 14 23 0.428 0.112 0.236 0.120 15 3 0.434 0.171 0.447 0.486 16 4 1.817 0.259 1.352 0.290 17 8 1.005 0.357 0.879 1.010 As can be seen in Table 4, the simulation results are very similar to the test data obtained by a real network operation. To better compare the average times obtained, a hypothesis test was done and will be presented below.

The hypothesis are:

2

: 1

0

θ

⁾ =

θ

⁾

H and H1:

θ

⁾₁ ≠

θ

⁾₂,

where

θ

⁾₁ is the average processing time of the Real Test Scenario and

θ

⁾₂ is the average processing time from the simulation result.

If P

(

Tn1+n2 ^>

^τ )

^<

^α

, H0 should be rejected.

The statistics from Equation 1 and Equation 2 were calculated.

2 1 1

2 1

1

2 1 2

1

n n T S

n n n n

+

= −

+ +

θ θ

^{) )}

(1)

2 2 1

2 2 1

1 ^{2 2}

2

1 + −

= +

+ n n

S n S

S_{n n} n (2)

To use Equation 1 and Equation 2, the following variables are necessary:

n1 – amount of data from the Test Scenario;

n2 - amount of data from the simulation result;

S1 - variance of the data of Test Scenario;

S2 - variance of data from the simulation result.

To find the probability P, it was used the “t Student” distribution. The level of significance α used was 0.05, corresponding to a 95% level of confidence.

The calculated values are presented in Table 5.

Table 5- Hypothesis test.

Real Test Scenario Simulation Result Route

Number of batches

Average T (min/m³)

Variance

Average T (min/m³)

Variance Sn1+n2 Tn1+n2 P Valid hypothesis 1 6 0.321 0.064 0.314 0.005 0.203 0.019 0.493 H0 2 9 1.502 0.877 1.452 0.081 0.734 0.032 0.487 H0

3 14 0.276 0.005 0.339 0.002 0.059 0.405 0.344 H0

4 8 0.094 0.0000001 0.217 0.002 0.032 1.923 0.038 H1 5 7 0.374 0.116 0.316 0.008 0.269 0.115 0.455 H0 6 4 1.041 0.056 0.806 0.007 0.205 0.810 0.224 H0 7 7 0.790 0.076 1.184 0.020 0.237 0.889 0.196 H0

8 12 0.529 0.467 0.545 0.014 0.512 0.013 0.495 H0

9 9 1.480 4.903 1.302 0.226 1.699 0.049 0.481 H0

10 6 0.441 0.069 1.017 0.069 0.288 1.157 0.137 H0

11 4 0.112 0.001 0.136 0.000 0.028 0.596 0.286 H0

12 12 0.321 0.002 0.362 0.001 0.040 0.413 0.342 H0

13 6 0.416 0.029 0.464 0.002 0.136 0.207 0.420 H0

14 23 0.236 0.014 0.428 0.012 0.119 0.480 0.317 H0

15 3 0.447 0.236 0.434 0.029 0.446 0.024 0.491 H0

16 4 1.352 0.084 1.817 0.067 0.318 1.034 0.170 H0

17 8 0.879 1.019 1.005 0.128 0.810 0.077 0.470 H0

For all entries in Table 5 but entry number 4, there is no significant (statistical) difference between results obtained by simulation from ones obtained by the test scenario. This means that values obtained by simulation can be used as a good estimation for transfer time in each route.

The difference observed for entry number 4 is probably due to little variation in network processing times of Test Scenario in comparison with historical data, that is, historical data showed greater variability for this route than it really showed in this scenario, then, the probability distribution adjusted for this route was not representative of the Test Scenario data.

The low variability of Route 4 may occur because this route is composed of only one pipeline, then, do not suffer interference from other routes. This apparently also influences the route speed. Route 4 and route 11, which are composed by only one pipeline, are the fastest, while route 16, with a four pipelines sequence, is the slowest one. Obviously, the time delay for a route is related not only to the route length but also to the number of pipelines in the route.

Routes with many pipelines are quite perturbed by other product transfers, since pipelines are shared among several routes.

5. Conclusion

This paper proposed a discrete event model for the operational behavior of a pipeline network. It aimed to characterize transport time as a stochastic processing time for different routes which transfer different products. The delay time on a given route, although uncertain and dependent on the product portfolio, can be characterized by a stochastic variable. Using this characterization, the network operation can be simulated for different portfolios, obtaining the approximate time of reception of products in their destinations. Historical data and simulation results showed that the time delay for a route is related to the number of pipelines in this route, while the routes with fewer pipelines, which suffer less interference, show less variability in the

transportation times and are also faster. Future work will consider including transport time for each route in an optimization model able to provide a better operational scheduling.

6. Acknowledgements

This work received financial support from ANP – Agência Nacional do Petróleo, Gás Natural e Biocombustíveis - and FINEP – Financiadora de Estudos e Projetos, through

“Programa de Recursos Humanos para o Setor de Petróleo e Gás Natural” - UTFPR/PRH10.

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