A Compositional Gas Flow Model For Predicting Pressure And Heating Value Distribution In Complex Pipeline Network

System

IPA07-E-07731st IPA Convention: 14 – 16 May 2007

Mucharam, L., Sidarto, K.A., Riza, L.S., Mubassiran, Sophian, S.

Background

• Gas operator companies have a responsibility to provide gas to consumers with certain rate, pressure, heating value described in the sales contract.

• In a complex gas pipelines network system where several gas sources and outlets are encountered, different gas compositions and heating values may vary across the system.

• Since the gas price is commonly determined by its heating value, therefore prediction of gas heating values distribution in pipeline network is very important.

Objectives

• Predicting/determining gas pressure distribution, flow direction, and flow rate on each segment .

• Determining gas composition and heating value on each outlet.

Work Flow

User Input :• Gas Properties• Flow Equation• Genetic Properties• Network Model• Node Properties• Pipe Properties• Inlet Composition

Output Display :• Pressure Dist.• Flow Direction• Flow rate on each segment• Composition on each node• Heating Value on each Outlet

Genetic Algorithm

Newton Raphson

Pressure Dist.

Composition Determination

Gas Rate in each Segment

Flow Direction

Mole Rates

Heating Value

MethodologyUser Input

Output Display

Assumptions

• Dry gas (no condensation)

• Steady state condition

• The fluid composition across the whole segment is uniform (i.e. non-reactive system, no leak and no chemical reaction).

Methodology

1. Model development to determine pressure distribution

– Problem representation using Kirchoff’s Law (mass balance).

– Solving using combination of Genetic Algorithm and Newton’s Method.

2. Model development to determine composition and heating value.

– Problem representation using linear equation system.

– Solving using inverse matrix.

1. Model Development To Determine Pressure Distribution

• Gas flow correlation using Panhandle A

• To represent a pipeline network system using Kirchoff’s Law (mass balance).

• Thus non linear equation system is obtained.

0.53942.6182 2 2

0.5394

ij i j

ij ijij

K D p pQ S

L

4with / 1 and 8.2634*10ij i j i jS p p p p K

1 1_ 2 1 0f Q QN

2 1_ 2 2 _ 3 2 _ 6 2 0f Q Q Q QN

3 2 _ 3 3_ 4 3 0f Q Q QN

4 3_ 4 4 _ 6 4 _ 5 4 0f Q Q Q QN

5 4 _ 5 5_ 6 5 0f Q Q QN

6 2 _ 6 4 _ 6 5_ 6 6 0f Q Q Q QN

An Example: Non Linear Equation System of pipeline network system based on Kirchoff’s Law

3

2 1

45

6

Pipeline Network

Solving of Non Linear Equation System

• Genetic Algorithm to obtain the initial value

• Newton’s Method to refine the initial value obtained from genetic algorithm as a solution of non linear equation system (final result of pressure distribution).

2. Model Development To Determine Composition and Heating Value

• To determine composition of each node: Using linear equation system

• Converting flow rate to mole rate on each segment :

PV = znRT• Heating value :

where

yi : Composition of each component

Lci : Heating value of component i (BTU/scf)Lc ideal : Heating Value (BTU/scf)

idealc i ciL y L

An Example of Model to Determine Composition on Each Node

Linear equation system:

0

0)(

0)(

0

556656

41514545114

22523525323

112212

jj

jjj

jjj

jj

xmxm

xmmxmxm

xmmxmxm

xmxm

where

is concentration of the component j at node i.

is amount of mole at segment from node i to j

jix

ijm

P = 523.69Q = - 50

P = 505.12Q = - 80

P = 643.14

P = 650 P = 650

P = 643.28

1

2

3

4

5

6

OutletJunctionInlet

Study CaseGas Distribution Network of OFF TAKE SRPG and BTG

Consist of– 2 nodes of supply – 36 nodes of delivery– 59 nodes of junction– 89 pipelines

Input Data (in the paper)– Pressure at each inlet.– Pipe specifications.– Flow rate at each outlet.– Gas composition at each inlet.– Gas properties.– Network model.

Study Case: Schematic of Network

Result: Study Case Pressure Distribution, Flow direction and Flow rate on each segments

Result Comparison OPPINET – TGNet

Comparision of OPPINET - TGNet

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

10.5

O_4

O_6

O_7

O_8

O_9

O_1

1O

_12

O_1

3O

_16

O_1

7O

_18

O_1

9O

_20

O_2

1O

_22

O_2

3O

_24

O_2

7O

_29

O_3

0O

_31

O_3

2O

_33

O_3

7O

_38

O_3

9O

_41

O_4

2O

_43

O_4

4O

_45

O_4

7O

_48

O_4

9O

_52

O_5

0_53

_34_

51

SERPONG

ST_BIT

UNG

Node Name

Pre

ss

. (b

arg

)

Oppinet Press.

TGNet Press

Differentiation (%) < 6%

Comparison of Pressure Distribution on each outlet

Result: Study Case Heating Value

P = 358.24 psiaQ = 27.36 MMscfdHeating Value = 1067.3 Btu/scf

P = 356.65 psiaQ = 18.52 MMscfdHeating Value = 910.51 Btu/scf

967.2 Btu/scf

1010.5 Btu/scf

1067.3 Btu/scf

1010.5 Btu/scf

967.2 Btu/scf

Conclusion

• Genetic Algorithm and Newton’s is robustness method in solving non linear equation system for determining gas pressure distribution.

• To calculate composition on each node, the system model could be built from system of linear simultaneous equation.

• Based on the previous results, calculating the heating value has been performed

• The model developed is viable to predict pressure distribution, flow rate, gas composition and heating value on each outlet.

Thank You