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LINE SIZING FOR LIQUID
Basic principles
Calculation of pressure drop-flow rate relation in liquid lines is simplified by the near
incompressiblity of liquids.
For near isothermal conditions, the fluid viscosity does not change drastically from one end ofpipe run to the other.
Thus, a calculation method that assumes constant properties can be used over lengths of piping.
The calculation methods presented in this section:
1. Assume constant fluid properties
2. Applicable to pipe lengths with relatively constant temperature and no flashing
Momentum equation
General Consideration
When the momentum equation is written for a section of pipe carrying a fluid of constant fluidproperties, the resulting equation
is expressed as:
where:V1 = Upstream fluid velocity, ft/sec
V2 = Downstream velocity, ft/sec
P1 = Upstream pressure, psi
P2 = Downstream pressure, psi
Z1 = Upstream elevation, ftZ2 = downstream elevation, ft
hL = frictional head loss, ft
Y = acceleration of gravity
g = 32.17 ft/sec2
Figure below illustrates the condition for which this equation is written. This equation forms the
basis for pressure drop predictions using the Darcy Equation.
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Bernoulli Equation
When the frictional head loss term is omitted, the momentum equation becomes the bernoulli
equation. The Bernoulli equation was derived through a momentum balance on a frictionless fluid
Units
Each term in the momentum equation has the unit s of feet, which is the form presented incivil
engineerng textbooks and is used for computations in this section
Mechanical and chemical engineering textbooks use and equivalent form in which each term has
the dimensions of pressure.
Analysis of equation terms
Definition of terms
V2 terms represent acceleration effects in the fluidP terms represent pressure gradient effects
Z terms represent elevation effects
hL term represents the frictional pressure drop effect
Velocity term
Since acceleration effects are generally small for steady state flow in piping pressure drop
calculations, the V2 terms are usually ignored.
For a constant diameter pipe with an incompressible fluid, is identical to , and velocity
terms make no net contribution.
Pressure terms
y is the weight density and is expressed in units of , r,where :
where:
Y = weight density, lbf/ft3
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r = mass density, lbm/ft3
g = acceleration gravity, 32.17, ft/sec2
Gc = 32.17 (ft-lbf/lbm sec2)
For all practical situations, g = 32.17 ft/sec2 and there is no numerical distinction between y and
r
The computational convenience of the civil engineering form of the momentum equation arisesfrom the incorporation of the factor
Gc into y, weight density
Darcy and Fanning Equations
The momentum e quation has the frictional effects included in the term, and the methode for
calculating frictional effects is unspecified
Darcy and Fanning equations provide a means of calculating these friction effects.
Coefficient Darcy and Fanning equations can be calculated by Churchil Equation if the flow in
laminar condition and Chen equation if the flow in turbulent conditions.
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Compressor
Compressor is one of the fluid flow operation equipment. The objective of compressor is to
increase the gas stream pressure. Because of many limitation on materials and the shape of
compressor, it is usually used in the compression ratio of 3 to 8 for a centrifugal compressor up
to 12 to 24 for axial compressor.
To select the most satisfactory compression equipment, chemical engineers must consider a
wide variety of type, each of which has peculiar advantages for particular applications. Among the
major factors to be considered are flow rate, head or pressure, temperature linitations, methode of
sealing, method of lubrication, power consumtion serviceability, and cost.
Step in Compressor 0.0.2
1. Selecting Component and Thermodynamic Model
Before you could use the program, you must determine the component(s) will be processed.
Component DataBase for this free software is limited only for 45 components. Beside the
component, user should also select the Thermodynamic model will be used in the calculation.This free software is limited only for 4 model. This Thermodynamic model is used in the
determination of compressibility factor at suction and discharge condition. If user select Ideal
System for it, compressibility factor will be used is one at any condition. The others is used via
Equation Of State (EOS) and depend on Temperature, Pressure, mole fraction, and component's
critical properties.
2. Determination of Component(s)'s Mole Fraction
After component(s) and Thermocynamic model have selected, user must define their fraction on
the stream. User could define this at the end of user specification, but still could not calculate
before component(s)'s mole fraction is defined. If user do not know their composition, but their
molar flow rate (each component), then i t could b e used. Because of mole fraction only
determined if its total is unity, then user must normalize them by click Normalize button.
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3. User Specification Input
The next step of this program is specification of the condition of its operation. They are stream
condition and one of their efficiency (between adiabatic and polytropic). In this step, user couldenter a value for relative density or not. The difference of it is that if user enter a value of stream's
relative density, then program use that value for the determination of specific heat ratio of stream
via Champbell's Generalization(1). If i t is not be entered with a valid value or zero value, then
program automatically left it as blank and use the specific heat capacity of component(s) in
determining that specific heat ratio. the disadvantage of i t is that the program use ideal heat
capacity. Otherwise in the use of relative density on it , Chambell limitize the use of his
generalization for Hydrocarbon Compounds.
In the stream condition frame, program show in a taskbar what phase does the stream because a
compressor could only be used for a vapor phase stream and so if it's show Liquid with a red
color as the background, then user (and the program) could not calculate the operation.
There also a big taskbar available to tell user which part of specification that should be entered. If
the specification do not completed, i ts color will stil l be yellow and if the program could calculate(i.e. all inputs has entered) then its color will be green and it wil l tell you Ready To Calculate.
After calculation has been done, its color will be blue and its word say Solved. User could see
his/her compressor's parameters on the Result's Frame.
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Calculation:
It has been told you about user specification inputs that must be entered and about the
calculation of specific heat ratio. other important parameter on the calculation are:
Duty, which based on the compressibility factor of suction and discharge stream and not be
based on heat content of each streams.
Exponent, which is the ratio of k for adiabatic and n for polytropic. Exponent is required as the
parameter of compression ratio's significancy in the operation.
SCFM (standard cubic feet per minute), which is the standard flow rate of the stream, which onthe condition of 288 Kelvin and 100 kPa. In the user specification input, user could select the unit
of flow rate of the stream. They are ACFD (actual cubic feet per day), ACFM (actual cubic feet per
minute), ACMD (actual cubic meter per day), ACMM (actual cubic meter per minute) and their
standard.
More:
This free software is completed with a curve of only three profiles based on user specifications.
This could be loaded from Tools Menu. As like in the basic process calculation, curves also
could be generated if only user has entered all of inputs required.
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HEATING/COOLING
This software is created only for single phase fluid operation. Its mean you will not able to
calculate heating cooling system with phase change. And for information, this software is
developed with base of calculation:
1. Heat Duty = Heat content of outlet stream - Heat content of inlet stream
2. Heat content is calculated use specific heat capacity
a. For gas, specific heat capacity is calculated using ideal heat capacity
b. For liquids, specific heat capacity is taken from data of "Reklaitis"(see refference)
Equation (1):
Equation (2):
Heat Duty = HTout - HTin
,
3. Phase change Temperature is based on mixture's Saturated Temperature. The saturated
temperature of component is calculated by Lee-Kesler Correlation, and for mixture Kay's Rule
methode is use to calculate pseudocritical.
4.The limitation of software, both of Tout and Tin must greater than 0 K, and Tin must less than
1000 K.
Note:- "Phase is determined based on saturation condition and not based on Vapour-Lquid
Equilibrium".
- "Step for using heating/cooling software similar with compressor"
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Gas-Solid Cyclone
Input Variable
Inputs are parameter when we create a unit process. Input variables that you must enetered are:
1. Feed Gas condition and Parameters
a. Gas inlet velocity (Vc)b. Diameter of particle that 50% removed (Dpc)c. Gas temperatured. Gas pressure
e. Gas density ()
f. Solid density (s)
g. Gas viscosity ()
Note:- The diameter of particle that 50% removed and gas inlet velocity used to calculate width ofrectangular cyclone inlet duct (Bc)
so, if Bc is known another dimension of cyclone will get.- The number gas stream Turn in cyclone (Ne) is optional function. That's mean you can write thevalue or you can leave it and the software will assume it has value 5. But we recomended foryou to give value in this part.
2. Approximation to calculate pressure drop parameter
This part is equation to calculate pressure drop parameter and you must select one. We give you4 optional and there are:a. Lappleb. Stepherd and Lapple
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c. Casal and Martinet-Benetd. ter linden
What result will you get it?
This part show of calculation of the result. You can get the result in:
a. Calculation of result and this show on frame cyclone dimension
b. The cyclone figure with fractional efficiency
This form will show after you write the input and then click show figure .
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and if you click next then form of fractional efficiency will shows.
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System Reporting
In nawapanca we give facilities that can make you print the result in Microsoft Excell. How'screate this?After you find the result then click Report, without opened the microsoft excell.
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Note: 1. If you will print the result you must cl ick Report.2. You can select and change the dimension on Cyclon dimension with click one dimension
you want in Dimension unit (frame of cyclone dimension).
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Line Sizing Two Phase
This software is developed with two commonly used correlation.
1. AGA (American Gas Association) Equation
Basis: - High gas-liquid ratios
- Duckler for frictional component pressure drop
- Flanigan for elevation component at pressure drop
Overall two phase pressure drop
Defined as
Pt = Pf + Pe
Frictional component of pressure drop is
Elevation component of pressure drop is
Calculation procedure
1. Determine the following liquid volume fraction
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2. Determine the mixture viscosity for the Duckler
3. Calculate the superficial liquid velocity
4. Calculate the superficial gas velocity
5. Calculate the mixture velocity
6. Calculate the friction factor ratio
7. Calculate the two-phase mixture density
8. Calculate an estimate for the mixture Reynolds number
9. Determined a better estimate for the Duckler liquid holdup fraction (HLD), using and the
Reynolds number
10. Recalculate the mixture density (k) using the improved estimate of HLD.11. Using this new value of k, recalculate the mixture Reynolds number (Re)
12. Go back to step 9 to determined a new value for HLD. Continue this iterative procedure
until convergence.
13. Calculate the single phase friction factor
14. Calculate the frictional pressure drop
15. Determined the Flanigan liquid hold-up fraction
16. Calculate the elevation component17. Calculate the overall two-phase pressure drop
2. API (American Petroleum Institute)
Basis assumptions: - pressure drop is less than 10% P1- Bubble or mist flow exist- No elevation changes- No irreversiblr energy transfer between phases
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Calculation procedure
1. Determine the following liquid volume fraction
2. Determine the mixture viscosity for the Duckler
3. Calculate the superficial liquid velocity
4. Calculate the superficial gas velocity
5. Calculate the mixture velocity
6. Calculate the two-phase mixture density
m= W/(Qg+QL)
8. Calculate an estimate for the mixture Reynolds number
9. Calculate Darcy friction factor (fn)10. Calculate the frictional pressure drop
11. Determined the Flanigan liquid hold-up fraction
12. Calculate the elevation component
13. Calculate the overall two-phase pressure drop
Where:
Pt = Total two phase pressure drop, psi
Pf = Frictional component of pressure drop, psi
Pe = Elevation component of pressure drop, psi
fn = single friction factorftpr = friction factor ratio
k = two phase mixture density, lb/ft3
Vm = mixture of velocity, ft/sec
Lm = pipeline length, miles
d = pipe inside diameter, inches
Hlf = Flanigan liquid holdup fraction
Ze = sum of vertical elevation rises of pipe
(no elevation drops are considered), ft
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= flowing liquid volume fraction
QL = liquid flow rate at flowing conditions, ft3/secQg = Gas flow rate at flowing conditions, ft3/secn = mixture viscosity, cpL = liquid viscosity, cpg = Gas viscosity, cp
VSL = Superficial liquid velocity, ft/secA = Cross sectional area of pipe, ( d2)/4, ft2.VSg = Superficial gas velocity, ft/sec = -ln ()
= Density of liquid, lb/ft3g = Density of gas, lb/ft3HLD = Duckler liquid holdup fraction
( for the first estimate (assumption))
Re = Mixture Reynolds numberfn = Darcy friction factor
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Line Sizing for Gases
Basic Principles
Calculation of pressure drop-flow rate relations in single-phase gas lines differs from pressure drop
determination in single-phase liquid lines, because of the variation of gas density with pressure
and temperature changes.While liquids are nearly incompressible, the density of gases varies strongly with temperature,
and more imporantly, with pressure.The momentum wquation assumed that fluid density was
constant over the pipe segment under consideration. There are two ways of compensanting for
constant fluid density in the momentum equation:
1. Momentum equation may be applied segmentally over sufficiently short pipe segments, so that
the gas density is effectively constant over each segment. Differ gas densities are applied
in each segment. This approach uses computer where the increased
computational effort of multi-segmental evaluation is not problem.
2. For hand calculations, some closed form integration of an essentially differential momentum
equation is required. If effect elevations are ignored, and real gas behavior law of the
form:
where:P = fluid pressure, psia = fluid density, lbm/ft3Z = Gas compressibility factorR = universal gas constant, 1545 ft-lbf/lb-mole oRT = Fluid temperature, oTM = Molecular weight of gas, lbm/lb-mole
Is assumed, the a closed form integration of the momentum equation is possible. The resultingintegrated form is the basis for each of the several gas flow equations that are discussed
in this section.
Even though each of the gas flow equations are different due to the refinement of the basic gas
equation to different sets of experimental data, they are similar.
Each equation calculates flowline capacity when inlet and outlet pressure are given.
Volumetric flow rates calculated by each of the gas equations are at some standard condition
of pressure and temperature.
Most equations contain an empirical correction factor known as an efficiency factor to permit
adjusment of calculated results with field data.
General Considerations
Assumption:
- Isothermal
- No work is performed
- Steady state conditions
- friction factor (f) is constant
Determining specific volume at upstream conditions
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Rearranging and solving for ,we have:
where:
Qg = Gas flow rate, MMSCFDP1 = upstream pressure, psiaP2 = downstream, psiaS = specific gravity of gasZ = compressibility factor for gasT = gas flowing temperaturefD = Darcy friction factord = pipe inside diameter
The "Z" factor is assumed to be constant but in reality it will change from point 1 to point 2, thus
it is chosen form an average pressure defined as follows:
Approximation of general equation for small pressure drops
This equation yields reasonable results when P1-P2 < 10% of P1
Weymouth Equation
Weymouth's data base consisted of pipes having diameters ranging from 0.8 to 11.8 inchies, thusthe equation is most accurate for pipes having a diameter less than 12 inches. For larger pipe,Weymouth equation becomes increasingly conservative, that is, predictive flow capacitiesbecome increasingly less compared to actual flow capacities.
Assumptions:
- Turbulent flow, high reynolds number exist and- Friction factor is dependent upon relative roughness (/D)
For fixed absolute roughness (), the friction factor was assumed as
Substitution of the above friction value into the general equation for gas yields the Weymouth
Equation.The Weymouth equation is of the form
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where:
Qg = volumetric flow rate, MMSCFDP1 = upstream pressure, psiaP2 = downstream, psiaS = specific gravity of gasZ = compressibility factor for gas
d = pipe inside diameterL = pipeline length, feetT1 = gas flowing temperature, oR
Assuming a temperature of , a gas compressiblity factor of 1.0 and specific gravity of 0.6 equation
reduces to
where:
Qg1 = volumetric flow rate, SCFDLm = pipeline length, miles
Panhandle Eastern Equations
General considerations
Two gas flow equations were developed by Panhandle Eastern for calculating flow rates in large
diameter, 12 inches and above, cross country gas transmission lines.
Panhandle equation that have revised is best used for larger diameter pipes. This equation hasrevised exponents and includes the gas compressiblity factor. It assumes that the friction factorcan be represented by a straight line of constant negative slope (fD=C/Ren) in the moderateReynolds number region of the Darcy Friction Factor diagram.
where:Q = Volumetric gas flow rate, MMSCFDd = pipe inside diameterP1 = upstream pressure, psiaP2 = downstream, psiaLm = pipeline length, milesS = specific gravity of gasZ = compressibility factor for gasT = gas flowing temperatureE = Efficiency factor
= 1.0 for brand new type= 0.95 for good operating conditions= 0.92 for average operating conditions= 0.85 for unfavourable operating conditions
AGA Equation
General considerations
Most contemporary and most accurate of the gas equations in use. Contains several features
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lacking in the earlier gas equations. Contains explicit inclusion of gas compressibilty factoreffects with the "Z" factor being evaluated at effective average pressure in the line segment.Includes an elevation correction factor lacking in the original versions of the other equations.
Includes a transmission factor (F) that is related to the fanning Friction Factor (ff). This factordepends on pipe relative roughness, and for sufficiently low Reynolds number, it includes aReynolds number effect. Its assumes an isothermal flow.
The AGA equations is expressed as
where:
Q = Volumetric gas flow rate, ft3/D @ T0 and P0T0 = Temperature base, oRP0 = Pressure base, psiad = pipe inside diameterP1 = upstream pressure, psiaP2 = downstream, psiaT = gas temperature, oRLm = pipeline length, milesS = specific gravity of gasF = transmission factorEc = elevation correction factorZs = compressibil ity factor
Elevation correction factor(Ec)
where:h1 = elevation of pipeline inlet, fth2 = elevation of pipeline outlet, ft
Compressiblity factor at average conditions (Za)Its determined from average pressure (Pa), fluid flowing temperature() and by use of a generalizedcompressibility chart. Average pressure (T) is determined from the following equation:
Transmission factor (F)For high Rynolds number it is determined from the following equation
For a flow Re less than critical Re, the transmission factor is calculated according to the folowingequation:
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This equation is implicit in and must be solved iteratively.The flow Re is calculated according tothe following equation:
where: = gas viscosity, lbm/ft-sec
While the critical Re is calculated using the following equation
Spitzglass Equation
Modification of general equation that was developed for piping that would operate nearatmospheric pressure. It is derived by making the following assumptions:
a. f = (1 + 3.6/d + 0.03 d) (1/100)
b. T = 520oRc. P1 = 15 psid. P < 10% P1
with the above assumptions, and expressing pressure drop in terms of inches of water, theSpitzglass equationcan be converted to oil filds units.
Substituting P = 0.036 hw; P1=15 psi; and T = 520 oR, we have:
where:
Qg = volumetric flow rate, MMSCFD, at 14.7 psig and 60oF
hw = pressure loss, inches of water
d = pipe inside diameter
S = specific gravity of gas
L = pipeline length, feet
Note:
- specific gravity for air = 1
- For standard conditions P = 14.7 psi and T = 520oR