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
• Compressible Flow Study
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
• Compressible Flow Study
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
• Compressible Flow Study
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 Study
Compressible Flow
2
2
g d 5hl2−3 = 0.8
f x (m / )
• Compressible Flow Study
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
• Example
Compressible Flow
• Compressible Flow Study
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 Study
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)
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
http://www.powerpointstyles.com/http://www.powerpointstyles.com/
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
Base Parameters (P,T)
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
Base Parameters (P,T)
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
Compressible FlowExample
Compressible FlowExample
Compressible FlowExample
Compressible FlowExample
Compressible FlowExample
Compressible FlowExample
Compressible FlowExample
Compressible FlowExample