International Journal of Computer Science Research and Application 2012, Vol. 02, Issue. 01(Special Issue), pp. 56-62 ISSN 2012-9564 (Print) ISSN 2012-9572 (Online) © Tudorica Daniela. Authors retain all rights. IJCSRA has been granted the right to publish and share, Creative Commons 3.0

INTERNATIONAL JOURNAL OF COMPUTER SCIENCE RESEARCH AND APPLICATION www.ijcsra.org

A software application for modelling the pipeline transportation process Daniela Tudorica1 1

Petroleum-Gas University of Ploiesti,Romania, Department of Information Technology, Mathematics and Physics Author Correspondence: no. 39 Bd. Bucuresti, 100680, Ploiesti, ROMANIA [email protected]

Abstract Pipeline transportation can benefit from a large suite of automation techniques, which can help to monitoring, controlling or optimizing the process. This paper deals with the modelling of the fluid flow in pipelines and presents the results obtained from the model. The software application developed from the model allows designing a pipeline system, computing the properties of a fluid in any point of the pipeline and producing the reports needed for interpreting the results. The model is using the transfer function to convey the dependencies between the process parameters (temperature, pressure, flow) using the computation based on momentum conservation, energy conservation and flow equations from the fluid mechanics and hydraulics.

Keywords: Pipeline, Transportation process, Modelling, Automated system

1. Introduction Although liquids or gases are transported also in other ways (rail train, cars, ships), the transportation through pipelines is the method most used and most profitable. Obviously an important issue is to ensure continuously the safety of pipelines against damage. DOT-OPS (U.S. Department of Transportation Office of Pipeline Safety) recent research indicate that, despite technological advances and more stringent rules, the rate of occurrence of incidents in the pipeline system (cracks, leaks, etc.). Not changed significantly in recent decades. Statistics show that in the case of the small (short) pipes is reported at least one incident during the lifetime (20 years), and for pipelines (1,200 km) is expected every year to see a significant incident. (API, 2000) Studies indicate that the best ways to reduce the number of cases of cracking and leakage prevention are such as better training of service personnel or perform monitoring and control systems more efficient.

2. The Transportation Process – a Systemic Approach The concept of system has a very wide use, in all areas. The system is defined as a set of elements which interact with the outside towards a goal. Automated controlling systems, automated systems in short, are a particular type of system, whose purpose is to operate without human intervention.

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The automated system consists of two subsystems: the system technology or the automated process (P) and the automation device (AD) which sets out the law governing the process or algorithm, according to a schedule. In Figure 1 is presented an automated system’s architecture. The elements involved are: r – reference or system prescribed program; u – control or management of the process; y – output; yr – the main reaction; pi – disturbance.

pi r

AD

u

PROCESS

y

yr Figure 1: An automated system’s Architecture Pipeline transportation can benefit from a large suite of automation techniques. The concepts presented below refer to the process of transport, as a subsystem of an automated system. Process parameters are physical quantities related to the process. These are of three types: input parameters, state (intermediate) parameters and output parameters. The main parameters of the transportation process through pipeline are pressure, flow and temperature. The transfer function is an expression of dependencies between process parameters. It models in analytical terms the behaviour of the process and it is also called mathematical model of the process. For the pipeline transport process, it is used advanced modelling of fluid mechanics and hydraulics (calculations based on momentum conservation, the energy conservation and numerous equations of flow). Given the classification of automated systems (Cirtoaje, 2003), the one for transportation process has the following characteristics: - Sampling system (discretized system) - continuous signals are sampled (discretized), resulting in digital signals; - Dynamic (with memory) system - characterized by transients, as a consequence of its structure that includes elements able to accumulate and transfer significant amounts mass and energy; - System with distributed parameters - associated physical quantities (pressure, temperature etc.) have different values along the pipeline route; often given the complexity of mathematical formalism, distributed parameter systems are treated in the manner of the concentrated parameters, choosing as input-output variables local physical quantities associated with points (usually extreme) of the physical object (in this case, the ends of a pipe segment); - Non-stationary system (with variables) - at least one variable parameter over time; - Multivariable system - at least two inputs and two outputs; - System with dead time - between the size of the output and input quantities can be highlighted a pure delay of "dead time" during which the effect is imperceptible to the exit; - Deterministic system - with no parameters to vary randomly; - Open system if we are talking of monitoring the process (by measuring and signalling) or a closed system if it includes controlling also.

3. Modelling the Transportation Process 3.1 Non-stationary (unsteady) motion of liquids through pipelines Usually, flows in pipelines are in an unsteady state. Modifying the rate of flow can cause large pressure fluctuations, called pressure transients. The state of flow in which they occur is called transient flow. In the unsteady motion modelling are two basic equations: the equation of continuity and equation of motion. Since flow and pressure depend on both time and distance, these equations are partial differential equations. The next chapters use the following notations: p – pressure; x – distance;

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λ - hydraulic resistance coefficient proportional to the length d – internal diameter of pipe; ρ - density; v – flow velocity; q – mass flow; β - isothermal compressibility coefficient; t – time; L – length of pipe; A – area of pipe; g – gravitational constant.

3.2 Equation of motion To study the transfer function of the transport process (i.e. developing the mathematical model) starts from the equation of motion:

∂p λ v 2 − = ρ ∂x d 2

(1)

q = ρv

(2)

By introducing the mass flow: the equation (1) becomes:

−

q λ ∂p = ∂x 2 ρ d

(3)

Considering the equation of state (pressure below 500 bar) relative to reference conditions:

ρ = ρ 0 [1 + β ( p − p 0 )] and notating

P = 1 + β ( p − p0 )

(4)

, the equation (3) becomes:

∂p βq 2 λ − = ∂x 2 ρ 0 P d

(5)

∂p ∂ ( ρv) = ∂t ∂x

(6)

3.3 Equation of continuity Equation of continuity is:

−

To obtain the model it is used also the definition of sound speed:

c2 =

1

ρβ

(7)

Using (2) and (4), equation (6) becomes:

−

∂p ∂q = βc 2 ∂t ∂x

(8)

3.4 The Mathematical Model Eliminating the mass flow in relationships (5) and (8) is achieved a partial differential equation of second order. Equation (9) is called the fundamental equation of pressure in unsteady motion:

ρ 0 βd ∂ 2 P 2 ∂P 2 = c2 ∂t λ ∂x 2

P2 ∂P 2 ∂x

(9)

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The mathematical model adds the following conditions: - initial condition - the distribution of pressure along the pipeline in steady

p ( x,0) = p1 − ( p1 − p 2 )

x L

(10)

where p1 and p2 are the pressures at the ends of the pipe. - boundary conditions At the head of the pipe pressure remains constant:

p(0, t ) = p1 2

(11) 2 1

P (0, t ) = P

(12)

( ρq)1 < ( ρq) 2 . For x=L results: At the end of the pipe the mass flow decreases to the value ∂2 p = − β ( ρq )12 2 ∂x

(13) Equation (9), together with the conditions (10), (12) and (13) is the mathematical model of (unsteady) nonstationary motion of liquids through pipes.

3.5 Solving the mathematical model As stated above, the mathematical model of unsteady motion through pipeline consists of quasi-linear equations, hyperbolically, partial differential equations. It is not available a closed-form solution for these equations. By neglecting or with linearization of the nonlinear terms, several methods have been used for numerically integrating nonlinear, hyperbolic partial differential equations, such as method of characteristics, finite-difference method, finite element method, and linear element method. Many studies show that the advantageous method in this case is the method of characteristics. (Tullis, J.P., 1989; Scott A., 2003). This transforms the two partial differential equations in four total differential equations in first order. These total differential equations will then be integrated to yield finite difference equations, and furthermore algebraic equations, which can be conveniently handled. For the analysis of systems having complex boundary conditions, this method has proven to be superior to other methods in several aspects, such as its stability, accuracy, easy of programming, and efficiency of computations. (Tianhe Wen, 2001) Model equations are rewritten as:

∂q ∂p β q 2 + gA + =0 ∂t ∂x 2dA ∂q ∂p L2 = c 2 + gA =0 ∂x ∂t

L1 =

(14) (15)

It is considered a linear combination of equations (14) and (15), where k is an unknown multiplier:

L = L1 + kL2

(16)

It comes in two pairs of characteristic equations in unknown t, grouped under the name C+ si C-.

 gA dp dq β q 2 + + =0  +  c dt dt 2 dA C :  dx = a  dt  gA dp dq β q + + =0 − −  c dt dt 2 dA C :  dx = − a  dt

(17)

2

(18) The C+ and C- characteristic equations may be transformed into other forms in which time is a subscript, and in which the characteristic lines extend to more than one reach, generally the full pipe length. The equations are called Algebraic Equations.

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The complete solving of the model by characteristics method is presented in (Tianhe Wen, 2001).

4. Software Implementation of the Model To implement the model was chosen CBuilder - a visual environment that allows object oriented programming and implementation of a graphical friendly user interface. It is important that the application can be used for process modelling and simulation of pipeline without the need for writing any code. Purpose of the application software is to set a pipeline system and to simulate the transportation process for a period of time. The application will determine the values of process parameters (pressure, flow) at any point on the pipeline and after the simulation will produce reports for interpreting the results. As with any problem solved using the computer, the first step consists in fixing the input and output data. Input data entry refer to the pipeline system configuration (number of pipes, the connection mode, settlement), pipeline characteristics (length, diameter, friction coefficient), product features throughput (in condition, pressure, composition and chemical reactivity) etc. Output data are of two types: file and graphics. The file refers to the parameters values into the pipeline at some point. The graphic refers to the development of graphics representing the flow vs. time and pressure vs. time. The algorithm underlying the application can be described as follows: Start Read input data Design (construct) the pipeline system Determine initial parameters While t
Figure 2: User Interface – setting the pipeline characteristics After entering all input data, from the Simulation menu is selected the Start option. At the end of the simulation is build a report containing the parameter values in different parts of the pipeline. These data are written into a text file that can be opened and read with any text editor (Notepad, Wordpad, etc.).

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In Figure 3 are presented the results obtained by simulating the transport process through a simple pipe with diameter 0.7 m, length 45 m, friction 0.55. There were considered three control points for measuring parameters and simulation time of 20 sec, with dt = 0.3.

Figure 3: The simulation results Flow vs. Time 0,900000 0,800000 0,700000 0,600000

Flow

0,500000 0,400000 0,300000 0,200000 0,100000 0,000000 0,00 -0,100000

5,00

10,00

15,00

20,00

25,00

Time

Figure 4: The graphic output In Figure 4 is presented a graphic output representing the flow vs. time. We can see how flow increases in time, with a sharp increase after the first second.

4. Conclusion The purpose of this paper was to design and implement a software application for modelling the pipeline transportation process. In the first part it is presented a systemic approach of the transportation process, useful in obtaining the mathematical model of the process. The model is based on two equations (the equation of motion and equation of continuity) and describes the dependencies between the process parameters (pressure, flow). The model was solved using the characteristics method, the most suitable in this case. The software application was developed using CBuilder and it allows designing a pipeline system, computing the properties of a fluid in any point of the pipeline and producing the reports needed for interpreting the results. The application can be integrated into a complex solution for automated monitoring of the pipeline transportation process.

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References American Petroleum Institute (API), 2001, Pipeline Variable Uncertainties and Their Effects on Leak Detectability, API Publication 1149. American Petroleum Institute, 2000, Computational Pipeline Monitoring, API Publication 1130. Cîrtoaje V., 2003, Elements of Electronics and Automation, Ed. UPG Ploiesti. Hovey D.J., Farmer E.J., 2003, DOT Stats Indicate Need to Refocus Pipeline Accident Prevention, Oil & Gas Journal. Scott A. Sarra, 2003, The Method of Characteristics & Conservation Laws, Journal of Online Mathematics and its Applications, February 2003. Soare Al., 2002, Transport and storage of fluids, Vol 1, Ed.UPG Ploiesti. Soare Al., 2002, Transport and storage of fluids, Vol 2, Ed.UPG Ploiesti. Stoianov I., Dellow D., Maksimovic C., Graham N.J.D., 2003, Field Validation of the Application of Hydraulic Transients for Leak Detection in Transmission Pipelines, Proceedings of CCWI 2003 Advances in Water Supply Management Conference, London, UK. Tiahne Wen, 2001, The Development of a Simulation Mode1 of Pipeline Network Systems with Check Valve, A Thesis in the Depamnent of Mechanical Engineering Faculty of Engineering and Computer Science, Concordia University Montreal, Quebec, Canada. Tullis J.P., 1989, Hydraulics of Pipelines – Pumps, Valves, Cavitation, Transients, John Wiley & Sons, New York.

A Brief Author Biography Daniela Tudorica – Assistant Professor at the Department of Information Technology, Mathematics and Physics of Petroleum-Gas University of Ploiesti, Romania. PhD candidate in Systems Engineering, on thesis "Contributions to automatic monitoring of pipeline transportation systems for oil products". Research interests: modelling and simulation processes, numerical analysis, statistics and data mining.

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