fundamentals of compressible flows in pipelines · 2018. 12. 13. · compressible flow •...

Fundamentals of Compressible

Flows in pipelines

Dr. Ahmed ElmekawyFall 2018

1

Compressible Flow• Incompressible Flow Study

Flow in a Single Pipe – Branched Pipes - Network of Pipes – Unsteady Flow

( Density is Constant W.R.T Pressure)

• Compressible Flow Study

Density is VARIABLE W.R.T Pressure or Compressibility of

the Fluid

Egyptian Liquefied Natural Gas Plant (ELNG)

Transportation of natural gas

• Pipeline

• By ship as

liquefied natural

gas (LNG)

• By ship as

compressed natural

gas (CNG)

Over v iew

Compressible Flow

• Incompressible Flow Study

(1) Mathematical Formulations

Darcy-Weisbach Equation

(2) Empirical Formulae

Hazen William Equation

Colbroack Equation

g d 5f l Q2

hl = 0.8

Compressible Flow

• Flowrate Analysis

m= Q = AV

Incompressible Flow: Density is Constant…

Thus,

m/ = Q = AVConstant Constant

Compressible Flow

• Flowrate Analysis

m= Q = AVConstant

Variable Variable Volume Flowrate

We Can NOT Use Darcy-Weisbach Equation Directly in Compressible Flow Analysis…

( Variable HEAD LOSS !!! )

Compressible Flow


1 N2

P

Assume a Pipeline 1-N is divided into sections1-2, 2-3, 3-4, …etc.

Pressure Loss or Pressure Change over any section is decreased. Thus,

Density Change is decreased Too

Density can be considered as a CONSTANT Value for each pipe

segment only.

Compressible Flow


1 N2

P

Const.

Darcy-Weisbach Equation Could Be Used Now on Every Section of The Pipe

Compressible Flow

2

1

g d 5hl1−2 = 0.8

f x (m / )

1 N2

P

Const.

x

Compressible Flow

2

1

g d 5hl1−2 = 0.8

f x (m / )

1

1

P1

R T =

P1 / 1 = R T1


Assuming Constant Density

Compressible Flow

2

1

g d 5hl1−2 = 0.8

f x (m / )

P1 − P2 = P

P1− P2= g hl1−2

P2= P1− g hl1−2


Compressible Flow

2

2

g d 5hl2−3 = 0.8

f x (m / )


Pressure Values at 1 and 2 are known

With The Same Procedure We Could get the Value of the end pressure at the pipeline outlet and overall head loss.

Compressible Flow

• Example

Compressible Flow


Values obtained from the previous procedures have some error because of a lot of criterion:

1. Ideal Gas Assumption

2. Assuming constant Density in each section.

3. Accuracy depends on Section Numbers (directly)

Compressible Flow


Compressible Flow Analysis Depends on

Supplied Pressure or Delivered Pressure

Gas Well

Industry

Storage

P1 = Known P2 = ????

Compressor Station

P1 = ???? P2 = Known

Compressible Flow

Compressible Flow

Compressible Flow

Compressibility Factor (Z)

Low or Moderate Pressure-Temperature Conditions

P = R TAt High or Very Low Pressure-Temperature Conditions

P = Z R TWhere Z is a dimensionless factor represents the fluid behavior deviation of ideal gas to account for higher pressure and temperature. At low pressures and temperatures Z is nearly equal to 1.00 whereas at higher pressures and temperatures it may range between 0.75 and 0.90

Compressible Flow

Compressibility Factor (Z)

At High Pressure-Temperature Conditions

P = Z R T

Z = Fn ( P , T )

Compressibility Factor could be obtained through Engineering Tables or Charts as follows

Compressible Flow

• Compressible Factor (Z)The critical temperature of a pure gas is that temperature above which the gas cannot be compressed into a liquid, however much the pressure. The critical pressure is the minimum pressure required at the critical temperature of the gas to compress it into a liquid.As an example, consider pure methane gas with a critical temperature of 343 R and critical pressure of 666 psia.The reduced temperature of a gas is defined as the ratio of the gas temperature to its critical temperature, both being expressed in absolute units (R or K). It is therefore a dimensionless number.Similarly, the reduced pressure is a dimensionless number defined as the ratio of the absolute pressure of gas to its critical pressure.Therefore we can state the following:

Compressible Flow

• Compressible Factor (Z)Using the preceding equations, the reduced temperature and reduced pressure of a sample of methane gas at 70 F and 1200 psia pressure can be calculated as follows

The Standing-Katz chart, Fig. can be used to determine the compressibility factor of a gas at any temperature and pressure, once the reduced pressure and temperature are calculated knowing the critical properties

Compressible Flow

Compressible Flow

• Compressible Factor (Z)Another analytical method of calculating the compressibility factor of a gas is using the CNGA equation as follows:

The CNGA equation for compressibility factor is valid when the average gas pressure Pavg is greater than 100 psig. For pressures less than 100 psig, compressibility factor is taken as 1.00. It must be noted that the pressure used in the CNGA equation is the gauge pressure, not the absolute pressure.

Compressible Flow

• Compressible Factor (Z)

Fundamentals of Gas Transmission

Governing Equations

Real Gas Law

P v = Z R T P:v:

Pressure

Specific VolumeR: Gas Constant

T: Temperature

ρ: Gas Density

Z: Compressibility Factor

o

m =.A .u

Continuity Equation

= Mass Flow Rate A:u:

Cross SectionalArea

Gas Velocity

α

Bernoulli’s Equation

u du

v dP

dH

(π D dY v/A) . τ

: Kinetic Energy

: Pressure Energy

: Potential Energy

: Friction Energy Loss

D

u

A

τ

v

dP

dH

: Diameter

: Gas Velocity

: Cross SectionalArea

: Shear Stress

: Specific Volume

: Pressure Differential

: Elevation Differential

The general flow EquationIt can be used instead of dividing the pipe line into segments

The general flow Equation

Widely used Steady State Flow Equations

Equation Formula*Transmission Factor

(F)Flow Description

FritzscheT (P 2 −P 2 )D 5

0.538 1

0.462

Q b = 1.72 b 1 2

Pb Tf L G 5 . 145 ( Re .D ) 0 .071

High Pressure

High Flow Rate

Large Diameter

AGA Fully

Turbulent

T P 2 − P 20.5

3.7 DQ b = 0.4696

b 1 2 log .D2.5

Pb GTf Zav K e

4 log 3.7D

K e

High Pressure

High Flow Rate

Medium to Large Diameter

Panhandle B

T 1.02 P 2 − P2

0.51

Q b = 2.431b

1 2 D2.53

Pb L Tf G 0.96 Z av

16 . 49 (R e )0 . 01961Medium to High Pressure

High Flow Rate

Large Diameter

Used when Re < 40 million

Colebrook-

White

T P 2 − P 2 0.5

K 1 .4126F Q b = 0 .4696

b 1 2 log e + D 2 .5

Pb L G Tf Zav 3.7D Re −2 L o g

k e +2 .5 F

3.7D Re

Used when the flow is near the

transition zone (border line)

IGT

Distribution

T P 2 − P 2 5 /9

D 8 / 3 Q b = 0.6643

b 1 2 4 / 9 1 / 9

Pb LTf G

4 . 619 ( Re ) 0 . 1Used in Natural Gas Distribution

Networks.

Mueller

T P 2 − P 2 0.575

D2.275 Q b = 0.4973

b 1 2 Pb LTf

G 0.425 0.15

3 . 35 ( Re ) 0 .13

Panhandle A

T 1.078 P 2 − P 2

0.539 D 2.618

Q b = 2.45b

1 2 Pb L Tf Zav

G 0.461

6 . 872 (Re )0 .073Medium to High Pressure

Moderate Flow Rate

Medium Diameter

Weymouth

T (P 2 −P 2 )D16 / 3 0.5

Q b = 1.3124 b 1 2

Pb LGTf 11 . 19 D1 /6

High Pressure

High Flow Rate

Large Diameter

Powerpoint TemplatesPage 227

Summary of Pressure Drop Equations

Equation Application

General FlowFundamental flow equation using friction or transmission factor; used

with Colebrook-White friction factor or AGA transmission factor

Colebrook-WhiteFriction factor calculated for pipe roughness and Reynolds number;

most popular equation for general gas transmission pipelines

Modified

Colebrook-White

Modified equation based on U.S. Bureau of Mines experiments; gives

higher pressure drop compared to original Colebrook equation

AGATransmission factor calculated for partially turbulent and fully

turbulent flow considering roughness, bend index, and Reynolds

number

Panhandle A

Panhandle B

Panhandle equations do not consider pipe roughness; instead, an

efficiency factor is used; less conservative than Colebrook or AGA

WeymouthDoes not consider pipe roughness; uses an efficiency factor

used for high-pressure gas gathering systems; most conservative

equation that gives highest pressure drop for given flow rate

IGTDoes not consider pipe roughness; uses an efficiency factor used on

gas distribution piping

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Determining the Flow Regime

1

1

Re

f

= 4.log − 0.6f

The Prandtl-Von Karman Equation

D

Q bGRe =45.

The units used are:

Qb

G

D

: ft³/hr

: Dimensionless

: Inches

Flow regimes experienced in gas transmission:

Partially TurbulentFlow

Fully Turbulent Flow

Reynold’s Number

If Reynold’s Number is larger that the

Prandtl-Von Karman’s Reynold’s

Number, the flow is Fully Turbulent.

Moody Chart

Hydraulic Analysis Parameters

MaG =

Mg

Gas Gravity:

The ratio of gas molecular weight to air molecular weight.

Compressibility Factor:

Two methods were used:

Van Der Waals Equation – Long iterative solution

a1, a2, a3 are function of pseudo-reduced properties.Z3 −a 1 Z2 +a 2 Z −a 3 =0 .0

CNGA Equation – Direct solution

f

avg

T3.825

344400(10)1.785G P1 +

1Z =

Where,

Pavg :

Tf :

G :

Average Gauge Gas Pressure, psig

Fluid Temperature, R

Gas Gravity

After comparing both equations, the results of the CNGA

Equation were very accurate to Van Der WaalsEquation.

The comparison was done at constant temperature and for the same gascomposition.

Mg depends on the GasComposition.

Temperature Profile

Pressure Drop decreases

Pipeline Length

Pre

ssu

reom CP

− UA

Ti+1 =(Ti −Tg ).e

Temperature has a significant effect on the pressuredrop.

As temperature decreases Gas Viscosity decreases

Temperature Profile Calculation

Where:

Ti+1TiU

A

m

Cp

Tg

: Downstream Temperature

: Upstream Temperature

: Overall Heat Transfer Coefficient

: Heat Transfer Area (Lateral)

: Mass Flow Rate

: Gas Specific Heat

: Ground/Surrounding Temperature

Temperature Profile

Pressure Drop decreases

Pipeline Length

Pre

ssu

reom CP

− UA

Ti+1 =(Ti −Tg ).e

Temperature has a significant effect on the pressuredrop.

As temperature decreases Gas Viscosity decreases

Temperature Profile Calculation

Where:

Ti+1TiU

A

m

Cp

Tg

: Downstream Temperature

: Upstream Temperature

: Overall Heat Transfer Coefficient

: Heat Transfer Area (Lateral)

: Mass Flow Rate

: Gas Specific Heat

: Ground/Surrounding Temperature

Studies have proven that a pressure drop of (15 -25

Kpa/Km) or (3.5 -5.85 psi/mile) is optimal.

Pressure drops below 15 Kpa/Km are an indication that

too many facilities have been installed)

Compressible Flow

• General Flow Equation for Compressible Flow(Empirical)

T P2 −P21 2

G Tf l z f

2.5−3Q =1.149410 b DPb

Compressible Flow

T P2 − P21 2

G Tf l z f

2.5−3Q =1.149410 b DPb

Q

L

D

G

f

P1

P2

Gas Flow rate (m3/day)

Pipe Length (m)

Diameter (mm)

Gas Gravity (Specific Gravity)

Friction Coefficient (Dimensionless)

Upstream Pressure or Supplied (kPa)

Downstream Pressure or Delivered (kPa)

Compressible Flow

T P2 − P21 2

G Tf l z f

2.5−3Q =1.149410 b DPb

- Reference Value -

- Reference Value -

Z

Pb

Tb

Tf

Compressibility Factor

Base Pressure (kPa)

Base Temperature (K0)

Flow Average Temperature (K0)

Compressible Flow

Base Parameters (P,T)

For constant flow rate (m=const.) m= 1 Q1 = 2 Q2

= P / R T

Q1(P1 /T1)= Q2(P2 /T2 )

Thus, the flowrate could be obtained W.R.T standard flowrate atstandard atmospheric pressure and temperature as a reference…

Compressible Flow


And the general flow equation could be…

b

Pb P Q = Q T T

Compressible Flow

P

Tb D

P2 −P21 2

G Tf l z f

2.5−3Qb b =1.149410


DT

P

P2 −P2

1 2

G Tf l z f

2.5−3Q =1.149410

Compressible FlowErosional Velocity of gas in pipe flow

Gas Composition

Dahshour –Assiut- Aswan Gas pipe Line

Compressible FlowExample

fundamentals of compressible flows in pipelines · 2018. 12. 13. · compressible flow •...

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