MATHEMATICAL MODELING AND SIMULATION OF LEAK DETECTION SYSTEM IN PIPELINE

BYWASIU OSENI YUSSUF(MATRIC NO:109041122)SUPERVISOR: Dr. KINGSLEY ABHULIMENAPRIL 2014

OUTLINE Introduction What is pipeline leak detection system? Causes of pipeline leaks Effect of pipeline leaks Managing pipeline leak Project objectives and scope of study Literature on leak detection in pipeline Model development and numerical

simulation Results Conclusions Recommendations

INTRODUCTION • Pipeline leak detection system is a

device that provides continuous monitoring and automated analysis of pressure, temperature, fluid properties and flow at points along the pipeline.

CAUSES OF PIPELINE LEAKS

Pipeline failure begins with leaks at poor construction points, corrosion points and small structural material cracks.

Other causes of leaks in pipelines includes bad maintenance , sudden pressure change , sabotage ,accidents ,terror ,theft , etc.

EFFECTS OF PIPELINE LEAKSPipeline leaks can leads to events with

considerable economic impact, environmental damage, injuries and fatalities.

MANAGING PIPELINE LEAKTo manage the risk of pipeline leak,

installation of a pipeline leak detection system is required which must have a high sensitivity ,reliability and speed of detection.

OBJECTIVES OF STUDYTo develop a mathematical model

describing flow behavior of a pipeline leak detection system.

Effects of variation of leak factors on velocity and pressure profiles along pipeline segments

Effects of variation of leak factors on pipeline leak-hole diameters and volumetric flow rates.

Determination of the effects of Eigen pressures and velocities with time at various leak factors along the pipeline.

SCOPE OF STUDYThis research captures correctly

the actual amount of leaks in pipeline networks.

Also effects of variation of leak factors on pressure and velocity profiles along pipelines, and the diameters of pipeline leak-hole have been adequately accounted for.

LITERATURE REVIEWS/N

AUTHOR SUMMARY OF RESEARCH APPROACH

1 Mears ,1993 The Real World Application of Pipeline Leak Detection

2 Parry etal,1992.

Compensated Volume Balance Leak Detection on a batch LPG Pipeline

3 Zhang,1993 Statistical Leak Detection in Gas and Liquid Pipelines.

4 Fuchs, 1991 Leak Detection By Acoustic Signal Analysis

5 API RP 1130,2007

Computational Pipeline Monitoring for Liquids

6 Berger,1985 Statistical Decision Theory and Bayesian Analysis

7 Timur,2005 Modern Pipeline Monitoring Techniques8 Jackson

etal,1998Leak Testing Methods

9 RELI ,1997 Review of Pipeline Leak Detection Methods for Shell International Exploration and Production Company

MODEL DEVELOPMENTModel formulation for describing flow behavior of oil and gas pipeline leak detection system

The pipeline is modelled as a cylindrical coordinate

The pipeline flow behavior is described by continuity equation and Navier Stokes equation in a cylindrical coordinate in axial direction with the introduction of leak factor KL

Flow regime considered is highly turbulent so energy is produced and dissipated.

Consider an elemental strip of pipeline segment shown below

Elemental strip of pipeline Vo V2

Po P2

T0 T2

The continuity equation derived for the elemental strip of pipeline is given as

Model for the leak detection system derived is given as

Transport equation for the rate of production of turbulent kinetic energy is given as

The rate of dissipation of turbulent kinetic energy is given as

The derived model for leak detection, the transport equation for rate of production of turbulent kinetic energy and the rate of dissipation of turbulent kinetic energy were solved using finite element method of numerical solution implemented by Comsol multi physics software using the following data and the following initial and boundary conditions.

Node

Identi

ty

Location Flow

10^3 b/d

Water

Cut

Oil

S.G

Oil

Visc

Vel

m/s

Flow

Regime

Liquid

Hold

Up

Nod

e

Pres

Bar

(0,0,0

)

M1 189.36 0.578 0.8753 5.225 1.19 0.17Emul 1.000 3.5

(0,0,1

)

M1 189.36 0.578 0.8753 5.233 1.19 0.17Emul 1.00 13.5

(0,0,2

)

M2 168.36 0.588 0.8759 4.970 1.06 0.13Emul 1.00 13.5

(0,0,3

)

M3 127.91 0.643 0.3937 7.423 1.16 Oil in

water

1.00 15.1

(0,0,4

)

M4 52.85 0.545 0.829 7.564 0.48 Water

inOil

1.00 18.5

(0,0,5

)

M5 52.85 0.5450 0.829 7.579 0.75 0.02Emul 1.00 18.5

(0,0,6

)

M5 0.000 0.000 0.000 0.000 0.00

0

0.000 0.000 20.8

(0,0,7

)

M6 0.000 0.000 0.00 0.000 0.00

0

0.000 0.000 0.0

(0,1,0

)

M8 0.000 0.000 0.000 0.000 0.00

0

No Flow 0.000 13.5

(0,1,1

)

M9 0.000 0.000 0.900 3.5 0.00

0

No Source 0.000 0.0

(0,2,0

)

M10 21.0 0.50 0.870

4

7.3 1.19 0.2Emul 1.00 13.5

Pipeline Network Flow Data

Node

Identity

Location Elev Length Pipeline

ID (in)

Segment

Roughness

(0,0,0) M1 0 45870 24.00 0.0499

(0,0,1) M2 0 0 24.00 0.0499

(0,0,2) M3 0 9450 24.0 0.0499

(0,0,3) M4 0 18970 20.0 0.0499

(0,0,4) M5 0 0 16.0 0.0499

(0,0,5) M6 0 16640 16.0 0.0499

(0,0,6) M7 0 17050 16.0 0.0499

(0,0,7) M8 0 30310 16.0 0.04998

(0,0,8) M9 0 0 16.0 0.0498

Pipeline Node Segment Roughness Data

Initial and boundary conditions1. at the inlet

U o= 0 V o=0 W o=1192. Outlet P o=03. at the wall Logarithmic wall function

RESULTS RESULTS FOR PIPELINE SEGMENT 1

Velocity profile along pipeline segment 1 with length

Pressure profile along pipeline segment 1 with length

1.565 1.57 1.575 1.58 1.585 1.59 1.595

-80

-70

-60

-50

-40

-30

-20

-10

0

10

Time (min)

Eige

n Ve

loci

ty

Eigen velocity against time for pipeline segment 1

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

4

Time (min)Ei

gen

Pres

sure

Eigen pressure against time for pipeline segment 1

RESULTS FOR PIPELINE SEGMENT 2

Velocity profile along pipeline segment 2 with length

Pressure profile along pipeline segment 2 with length

6.24 6.26 6.28 6.3 6.32 6.34 6.36 6.38 6.4 6.42

-160

-140

-120

-100

-80

-60

-40

-20

0

20

Seri...

Time (min)

Eige

n Ve

loci

ty

Eigen velocity against time for pipeline segment 2

0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

3

Time (min)

Eige

n Pr

essu

re

Eigen pressure against time for pipeline segment 2

RESULTS FOR PIPELINE SEGMENT 7

Velocity profile along pipeline segment 7 with length

Pressure profile along pipeline segment 7 with length

7 7.05 7.1 7.15 7.2 7.25

-40

-35

-30

-25

-20

-15

-10

-5

0

5

Time (min)

Eige

n Ve

loci

ty

Eigen velocity against time for pipeline segment 7

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

Time (min)Ei

gen

Pres

sure

Eigen pressure against time for pipeline segment 7

Diameter of leak hole for pipeline segment 1&2

Leak factor(K L )

Pipe diameter (D)in inches

Leak volumetric flow rate(QL) in barrels/day

Pipeline Leak hole diameter(DL) in inches

Outlet crude oil volumetric flow rate(Q2)in barrels/day

Inlet crude oil volumetric flow rate(Q1)in barrels/day

Velocity of crude(v) in feet/second

0.018644 16 3530.428 3.295885 185829.6 189360 3.90.108687 16 20580.97 7.957767 168779 189360 3.90.113258 16 21446.53 8.123382 167913.5 189360 3.90.268018 16 50751.89 12.49639 138608.1 189360 3.90.335629 16 63554.71 13.98402 125805.3 189360 3.90.392866 16 74393.11 15.1295 114966.9 189360 3.90.430052 16 81434.65 15.82934 107925.4 189360 3.90.509448 16 96469.07 17.22869 92890.93 189360 3.90.527864 16 99956.33 17.53733 89403.67 189360 3.9

0.655057 16 124041.6 19.53629 65318.41 189360 3.9

Pipeline Segment 1,2(same flow properties)

Diameter of leak hole for pipeline segment 4

Leak factor(K L )

Pipe diameter (D)in inches

Leak volumetric flow rate(QL) in barrels/day

Pipeline Leak hole diameter(DL) in inches

Outlet crude volumetric flow rate(Q2)in barrels/day

Inlet crude oil volumetric flow rate(Q1)in barrels/day

Velocity of crude(v) in feet/second

0.018644 12 985.3354 2.744308 51864.66 52850 1.570.108687 12 5744.108 6.62601 47105.89 52850 1.570.113258 12 5985.685 6.763909 46864.31 52850 1.570.268018 12 14164.75 10.40508 38685.25 52850 1.570.335629 12 17737.99 11.64375 35112.01 52850 1.570.392866 12 20762.97 12.59753 32087.03 52850 1.570.430052 12 22728.25 13.18025 30121.75 52850 1.570.509448 12 26924.33 14.34542 25925.67 52850 1.570.527864 12 27897.61 14.6024 24952.39 52850 1.570.655057 12 34619.76 16.26683 18230.24 52850 1.57

Pipeline segment 5,6(same flow properties)

NOTE: Pipeline segment 7 was not considered for sizing because the crude oil volumetric flow rate at the inlet condition is zero and the diameter of leak depends on this.

CONCLUSIONSThe pressure profile decreases sharply as leak factor

increases along the pipeline distanceThe velocity profile increases as leak factor

increases along the pipeline distanceLeak and surge locations were being captured by

the model as the case of pipeline segment 2 and pipeline segment 7 respectively.

Pipeline leak hole diameter and volumetric flow rate of crude oil increase with increase in leak factor

Sinusoidal waveform characterizes leak and surge behaviours for velocity measurements whereas decay curves characterize surge behavior for pressure measurements

Due to sharp drop in the pressure profiles, pressure measurements are more sensitive parameters for leak detection than velocity measurements

RECOMMENDATIONSThere are other fluids that may be

transported by pipeline system other than crude oil. It is therefore recommended that the effect of leak factor on the velocity and pressure profiles of these fluids can be study by other researchers. Although finite element is all encompassing in terms of its accuracy in solving this kind of problems other numerical methods could however be used for the same study

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