gas property+flow eqn+ pdrop due to friction ch1,2_2

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GAS PROPERTIES

Lecture Notes : M . Tech. Pipeline Engg.

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A gas : A homogenous fluid with low density and viscosity. Gases are Compressible. It expands to fill the vessel that contains the gas. The molecules that constitute the gas are spaced farther

apart in comparison with a liquid and, therefore, a slight change in pressure affects the density of gas more than that of a liquid.

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MASS AND WEIGHT

Mass is the quantity of matter in a substance. It is sometimes used interchangeably with weight. Mass is measured in slugs in the (USCS) of units and

kilograms (kg) in System International (SI) units. (1 slug = 14.5 kg) USCS: United States Customary Systems

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Standard Conditions

Standard conditions (also called base conditions) of temperature and pressure (60°F and 14.7 psia in USCS units),

Standard conditions in SI system are 150 C & 101.325 Kpa.

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Volume

Volume of gas is measured in ft3 in USCS units and m3 in SI units. Other units for volume include thousand ft 3 (Mft3 ) and million

ft3(MMft3) in USCS units and thousand m3 (km3 ) and million m3(Mm3) in SI units

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NOTE: In USCS units : M represents a thousand. MM refers to million In SI : k (kilo) represents a thousand)

M (Mega) refers to million. Therefore, 500 MSCFD in USCS units refers to 500

thousand standard cubic feet per day, whereas 15 Mm3/day means 15 million cubic meters per day in SI units.

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SPECIFIC GRAVITY

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VISCOSITY

Since natural gas is a mixture of gases such as methane , ethane , and small portion of other gases, following formula is used to calculate the viscosity from the viscosities of component gases:

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Average Molecular Weight of Gas mixture

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Ques

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COMPRESSIBILITY FACTOR

It is a measure of how close a real gas is to an ideal gas. The compressibility factor is defined as the ratio of

the gas volume at a given temperature and pressure to the volume the gas would occupy if it were an ideal gas at the same temperature and pressure.

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Ideal gas law PV=nRT Modified ideal gas equation / eqn of state for real gases :

PV=ZnRT

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The following methods are available to calculate the compressibility factor:

a. Standing-Katz method b. Dranchuk , Purvis, and Robinson method c. AGA method d. CNGA method (most commonly used )

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California Natural Gas Association (CNGA) Method

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This formula for the compressibility factor is valid when the average gas pressure , Pavg , is more than 100 psig.

For pressures less than 100 psig, Z is approximately equal to 1.00

where

P avg = average gas pressure, psig

T f = average gas temperature, °R (1R=0.556 K)

G = gas gravity (air = 1.00)

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Average Pressure Calculations

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Ques. The gravity of a natural gas mixture is 0.60. Calculate the compressibility factor of this gas at 1200 psig average pressure and a temperature of 70°F, using the CNGA method.

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Gas temperature Tf = 70 + 460 = 530°R

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HEATING VALUE

The heating value of a gas is defined as the thermal energy per unit volume of the gas.

It is expressed in Btu / ft3

(1 BTU = 1055 Joules) For a gas mixture , the term gross heating value is used. It is calculated based upon the heating values of the component

gases and their mole fractions using the following equation:

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where

Hm = gross heating value of mixture, Btu/ft3

yi = mole fraction or percent of gas component i

Hi = heating value of gas component, Btu/ft3

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Super Compressibility Factor

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(Gas Flow Equations )

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FLOW EQUATIONS Several equations are available that relate the gas flow rate with gas

properties, pipe diameter and length, and upstream and downstream pressures.

These equations are listed as follows:

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1. General Flow equation2. Colebrook-White equation

3. Modified Colebrook-White equation

4. AGA equation

5. Weymouth equation6. Panhandle A equation7. Panhandle B equation8. IGT equation

9. Spitz glass equation

10. Mueller equation

11. Fritzsche equation

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GENERAL FLOW EQUATION

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Transmission Factor

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Effect of pipe elevations Case -1 (Single slope )

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In SI units, the elevation adjustment parameter s is defined as follows:

whereH1 = upstream elevation, mH2 = downstream elevation, m

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Case -2 (Multiple slopes ) In the calculation of Le it has been assumed that there is a single

slope between the upstream point 1 and the downstream point 2. If, however, the pipe segment of length L has a series of slopes, then

we introduce a parameter j as follows for each individual pipe sub segment that constitutes the pipe length from point 1 to point 2.

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The parameter j is calculated for each slope of each pipe sub segment of length L1 , L2 , etc. that make up the total length L. The equivalent length term Le in is calculated by summing the individual slopes as defined below.

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The terms j1, j2 , etc. for each rise or fall in the elevations of individual pipe sub segments are calculated for the parameters s1, s2, etc. for each segment ,from the pipeline inlet to the end of each segment.

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VELOCITY OF GAS IN A PIPELINE

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EROSIONAL VELOCITY It is always tried to keep the flow rate of gas and hence the velocity as

high as possible in a pipeline. But a high velocity in pipeline leads to vibration and noise . In addition, higher velocities will cause erosion of the pipe interior

over a long period of time. The upper limit of the gas velocity is usually calculated approximately

from the following equation:

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Since the gas density may be expressed in terms of pressure and temperature, using the gas law , the maximum velocity can be rewritten as

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where Z = compressibility factor of gas, dimensionless R = gas constant = 10.73 ft3 psia/lb-moleR T = gas temperature, °R G = gas gravity (air = 1.00) P = gas pressure, psia Usually, an acceptable operational velocity is 50% of the above. In the above eqn. P is the maximum pressure in pipeline that is at

inlet section.

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Soln.

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Reynolds No.

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WEYMOUTH EQUATION

In USCS units, the Weymouth equation is stated as follows:

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In SI units, the Weymouth equation is as follows:

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PANHANDLE A EQUATION The Panhandle A Equation was developed for use in natural gas

pipelines, incorporating an efficiency factor . In this equation instead of pipe friction , pipeline efficiency is used. The general form of the Panhandle A equation is expressed in USCS

units as follows:

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PANHANDLE B EQUATION The Panhandle B equation, also known as the revised Panhandle

equation, is used in large diameter, high pressure transmission lines. In fully turbulent flow, it is found to be accurate for values of

Reynolds number in the range of 4 to 40 million. This equation in USCS units is as follows:

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FRICTION FACTOR The term friction factor is a dimensionless parameter that depends

upon the Reynolds number of flow. Two types of friction factor are commonly used :

i) Darcy friction factor.

ii) Fanning friction factor

Both friction factors are coorelated by the following equation :

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To avoid confusion, the Darcy friction factor is used and is represented by the symbol f.

Following regimes will be considered : Laminar flow : Turbulent flow

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Turbulent Flow

For turbulent flow, the friction factor is a function of the Reynolds number, pipe inside diameter, and internal roughness of the pipe.

Many empirical relationships for calculating f have been put forth by researchers.

The most popular correlations are :

i) The Colebrook-White

ii) and AGA equations

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Before we discuss the equations for calculating the friction factor in turbulent flow, it is appropriate to analyze the turbulent flow regime. Turbulent flow in pipes (Re > 4000) is subdivided into three separate regions as follows:

1. Turbulent flow in smooth pipes 2. Turbulent flow in fully rough pipes 3. Transition flow between smooth pipes and fully rough pipes

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COLEBROOK-WHITE EQUATION (between smooth pipes &fully rough pipes)

wheref = friction factor, dimensionlessD = pipe inside diameter, in.e = absolute pipe roughness, in.Re = Reynolds number of flow, dimensionless

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where f = friction factor, dimensionless D = pipe inside diameter, in. e = absolute pipe roughness, in. Re = Reynolds number of flow, dimensionless

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Turbulent flow in fully rough pipes Similarly, for turbulent flow in fully rough pipes, with Re being a large

number , f depends mostly on the roughness e and, therefore, the friction factor equation reduces to :

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AMERICAN GAS ASSOCIATION (AGA) EQUATION In 1964 and 1965, the American Gas Association (AGA) published a

report on how to calculate the transmission factor for gas pipelines to be used in the General Flow equation.

This is sometimes referred to as the AGA NB-13 method. Using the method outlined in this report, the transmission factor F is

calculated using the following method :

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Method of calculation F

First, F is calculated for the rough pipe (referred to as the fully turbulent zone) by the following equation :

D = INTERNAL DIAMETER. e = absolute pipe roughness Next, F is calculated based on the smooth pipe law (referred to as

the partially turbulent zone).

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Ft = Von Karman smooth pipe transmission factor D f = pipe drag factor that depends on the Bend Index (BI) of the pipe.

The pipe drag factor D f is a parameter that takes into account the number of bends, fittings, etc. Its value ranges from 0.90 to 0.99.

The Bend index is the sum of all the angles and bends in the pipe segment, divided by the total length of the pipe section under consideration

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Finally, the smaller of the two values of the transmission factor is used in the General Flow Equation

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Ques :

Using the AGA method, calculate the transmission factor and friction factor for gas flow in an NPS 20 pipeline with 0.500 in. wall thickness. The flow rate is 200 MMSCFD, gas gravity = 0.6, and viscosity = 0.000008 lb/ft-sec.

The absolute pipe roughness is 700 μ in. Assume a bend index of 60°, base pressure of 14.73 psia, and base temperature of 60°F.

gas property+flow eqn+ pdrop due to friction ch1,2_2

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