Fluid flow and pressure drop - part 2-

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Fluid flow and pressure drop - part 2-

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Chapter One

Fluid flow and pressure drop

1.5.2 Phase behavior
Phase behavior refers to the mole fraction ratio of vapor to liquid of the fluid and a prediction of its value as a function of pressure, temperature, and composition. For NGL and volatile oils, calculation of the fluid phase behavior is necessary for the determination of pressure drop-flow rate relations. If the fluid composition is known, flash calculations can be performed to determine the phase envelope and the relative amounts of liquid and vapor in the two-phase region.

1.5.3 Waxy crude
The design and operation of facility piping and pipelines carrying crudes with very high pour points or with high wax content require special consideration. This section discusses waxy crude, its behavior and special design, and operational challenges involved in both the design and operation of waxy piping and pipelines. Refer to Figure 1.6 for vapor-pressure-temperature relationship chart for light petroleum products.

1.5.3.1 Paraffin wax
Waxy crude contains heavy paraffins. Heavy paraffins are saturated hydrocarbons that typically contain between 18 and 34 carbon atoms in a chain. The wax formed is of crystalline structure and can be soft with a high percentage of trapped oil similar to Vaseline or can form hard deposits like candle wax.

1.5.3.2 Waxy crude behavior
When the temperature drops too low for wax to remain dissolved in a crude, it precipitates out of solution and deposits itself on the inside wall of facility piping and pipelines or inside facility process components. The “cloud point” or the “wax appearance temperature” (WAT) is defined as the temperature at which wax crystals can first be detected. When the temperature in facility piping or pipeline system drops below the cloud point, wax crystals begin to form and deposit. Any additional decrease in temperature causes additional wax to come out of solution until the crude in the piping system gels up. The temperature at which this occurs is called the “pour point.” When the crude in the pipe gels up, a certain force (yield stress) is required to shear the waxy crude and restart the flow.
In practice, a crude is considered to have a high wax content when there is more than 10% wax, while a crude is considered to have low wax content when there is less than 4%. Some examples of low-wax-content crudes are shown in Table 1.4. Even though the wax content of each of the crudes is 4%, there are significant differences in pour point, that is, the temperature at which the crude gels up. As is shown, the Malaysian Labuan crude would gel up at 48 °F (9 °C), while the Saudi Arabian light crude would gel only if the temperature drops below -32.8 °F (-36 °C).
Table 1.5 shows some examples of crude with high wax content and relatively high pour points. Temperatures in a pipeline between 68° and 86 °F (20-30 °C) are not uncommon, such as the shutdown of a subsea pipeline. Under this condition, these crudes will gel up. To understand the behavior of waxy crude, one needs to know the following:
Cloud point
Pour point
Wax content
Yield stress
Image
Figure 1-6 Vapor pressure for light hydrocarbons.


Name Density (kg/m3) Wax content
(shell) (%wt) Pour point
(ASTM D97) °C
Arabian Light
Kuwait
Basrah
Forties
Labuan 854
870
855
839
863 4
4
4
4
4 -36
-21
-12
0
9
Table 1.4 Low-wax-content crude oils

Name Density (kg/m3) Wax content (%wt) Pour point (ASTM D97) °C

Cabinda
Gamba
Shengli
Sarir
Beatrice
Bombay High
Taching
868
868
908
847
832
832
864
10
12
12
16
16
16
20
21
33
27
24
27
33
33
Table 1.5 High-wax-content crude oils

1.5.3.3 Wax prediction
The potential for wax formation in piping and pipelines can be predicted by sampling and analyzing the crude for the following properties:
Cloud point—cold finger technique or cross polar microscopy
Pour point—differential scanning calorimetry
Wax content—solid-phase analysis
Carbon distribution—gas chromatography

In order to achieve accurate results, it is imperative representative samples must be taken and that the correct experimental procedures be followed. Even if this is done, reproducibility is difficult, and one is very likely to get a range of results, rather than one definitive value, for example, cloud point.

1.5.3.4 Design and operational challenges
Waxy crude with high cloud points and pour points poses special design and operational challenges. These include the following:
Wax deposits on the internal pipe walls of flow lines and pipeline reduce internal diameter, which causes pressure and production losses.
Removal of wax deposits requires production shutdowns or extra pigging, which results in loss of revenue or extra costs.
Flow lines and pipelines may need to be designed with costly insulation to ensure the crude remains warm and above the wax deposition temperature.
Chemicals are added to prevent wax formation and deposition, which is expensive.
Chemicals may need to be injected before a shutdown to prevent crude from gelling up in the pipeline, if it cools below the pour point.

Designers and pipeline operations personnel need to thoroughly evaluate the aforementioned factors when confronted with waxy crude. When deciding how to manage the production and transportation of waxy crude, it is imperative that one carefully consider both capital (CAPEX) and operating expenses (OPEX) over the life cycle of the field for different options.

1.5.3.5 Wax management
A development plan for a waxy crude field will be different and more likely more expensive than a nonwaxy crude. Thus, early prediction is important. There are commercially available wax prediction tools available that will predict the wax deposition rate. However, one needs to be cautious as the results may not be reliable.
There are several options to choose from when one needs to manage waxy crude production. These include the following:
Wax inhibitors, growth modifier, or dispersants
Pour point reducer
Dilution (reduces wax content)
Pipeline insulation
Heating or steam tracing the pipeline
Regular pipeline pigging

1.6 Flow conditions
1.6.1 Flow potential
The flow potential is the total pressure drop available to transport fluid in a section of pipe. This potential, the difference in inlet and discharge pressures, includes the elevation pressure effect due to hydraulic pressure in an inclined pipe. If the flow potential does not equal or exceed that required to flow a given quantity of fluid, a larger diameter pipe, pump, or compressor must be specified.

1.6.2 Flow regimes
When a fluid moves through a pipe, two distinct types of flow are possible, laminar and turbulent. Laminar flow occurs in fluids moving with small average velocities. As the velocity increases, a “critical” point is reached at which the flow regime changes to turbulent flow. This “critical” point varies depending upon the pipe diameter, the fluid density and viscosity, and the velocity of flow. Turbulent flow becomes apparent as the velocity is increased above a critical velocity. In laminar flow, the fluid particles move along the length of the pipe in a very orderly fashion, with little or no sideways motion across the width of the pipe.
Turbulent flow is characterized by random, disorganized motion of the particles, from side to side across the pipe as well as along its length. The two types of fluid flow are described by different sets of equations. In general, for most practical situations, the flow will be turbulent.
Image
Figure.1-7. Laminar and turbulent flow in pipes.
1.6.3 Reynolds Number
A useful factor in determining which type of flow is involved is the Reynolds number. This is the ratio of the dynamic forces of mass flow to the shear resistance due to fluid viscosity and is given by the following formulas.
Re = DVρ/ µ\ = 1488 DVρ/ µ = 124 dVρ/ µ Eq. 1-12

where
Re = Reynolds number, dimensionless
V = average gas velocity, ft/s
D = pipe inside diameter, ft
d = pipe inside diameter, in.
ρ = gas density, lb/ft3
μ = gas viscosity, lb/ft-s (1 cp = 0.000672 lb/ft-s (lb/ft./s))
μ\ = absolute viscosity, cP

The flow is considered to be laminar flow when the Reynolds number is below 2000.
Turbulent flow is said to exist when the Reynolds number is greater than 4000. When the Reynolds numbers is between 2000 and 4000, the flow is called critical flow, or undefined flow.
Therefore
Re <= 2000 Flow is laminar
Re > 4000 Flow is turbulent
2000 < Re <= 4000 Flow is critical flow
In terms of the more commonly used units in the gas pipeline industry, the following formula for Reynolds number is more appropriate:

Re = 1.35 x 10-5 (GQ/µd) Eq. 1-13
where
G = gas specific gravity (air = 1)
Q = gas flow rate, standard ft3/day (scfd)
d = pipe inside diameter, in.
μ = gas viscosity, lb/ft-s (1 cP = 0.000672 lb/ft-s)

Or
Re = 20,100 (GQg/ µ\ d) Eq. 1-14
µ\ = gas absolute viscosity, cP
Qg = gas-flow rate, MMscf/D

Reynolds number for liquids
The Reynolds number can be expressed in more convenient “oil field” terms. For liquids, asfollows:
Rel = 92.1 (SG) Ql/d µ\ Eq. 1-15

µ\ = absolute viscosity (cP),
d = pipe ID (in.),
(SG) = specific gravity of liquid relative to water,
Ql = liquid flow rate (BPD).

1.6.4 Pipe roughness
In laminar flow, the pipe wall roughness does not materially affect the pressure gradient.
In turbulent flow, the pipe wall roughness has a marked effect on the pressure gradient. As the Reynolds number increases, the fluid boundary layer on the pipe wall becomes thinner, exposing the irregularities in the pipe wall to the high velocity outside the boundary layer. Techniques for quantifying relative roughness, or ratio of wall irregularity height to pipe diameter, are discussed later in this chapter.

1.6.5 Rate
Fluid flow rate (V = Q/A) through a pipe is primarily controlled by pressure loss due to friction. The higher the flow rate, the higher the frictional pressure drop. Reducing frictional pressure drop requires lower velocities. The capacity of a pipe is determined by the velocity developed at the design or allowable pressure drop (flow potential).

1.6.6 Velocity limitations
When fluid flow rates increase, fluid velocities can increase until the pipe wall is actually damaged. The avoidance of pipe damage sets an upper limit on the capacity of the pipe. One criterion used to estimate the critical fluid velocity above which pipe damage may occur is found in API RP 14E, which suggests that a critical erosional velocity is expressed as

Ve = C / √ρ Eq. 1-16
where
ρ = mixture density (lbm/ft.3),
Ve = erosional velocity threshold (ft./s),
C = 125 for intermittent service,
= 100 for continuous service,
= 60 for corrosive service.

1.6.7 Temperature
Fluid temperature can affect the pressure drop-flow rate relations and thus affects the choice of pipe size. Fluid temperature can also affect the fluid density and thus influence the erosional velocity limitations.

1.6.7.1 Gas considerations
When a gas with even small amounts of heavier hydrocarbons (propane and heavier) is compressed and/or cooled sufficiently, the heavier components may condense into a separate liquid phase. The presence of two phases flowing concurrently in a pipe causes a considerably higher frictional pressure drop than an equivalent mass flow rate of gas in the same diameter pipeline.
The presence of even 1% by volume liquid phase can cause a 20-30% increase in frictional pressure drop. The presence of liquid can also increase elevation pressure drop. Since liquids tend to be much heavier than gases, the presence of liquid in the flow increases the effective fluid density, thus increasing hydrostatic pressure.

1.6.7.2 Liquid considerations
Temperature strongly influences liquid viscosity. Viscosity increases exponentially with decreasing temperature. The increasing viscosity causes a decreasing Reynolds number and an increasing frictional pressure gradient. If the Reynolds number becomes sufficiently low and the flow becomes laminar, the frictional pressure gradient becomes inversely proportional to viscosity. Quantitative methods for calculating temperature effects in liquids are discussed later in this chapter.
1.7 Special considerations
1.7.1 Emulsions
The characteristics of oil-water emulsions vary greatly and are difficult to characterize or predict. Caution should be exercised and experienced help sought in dealing with emulsion in fluid flow calculations.

1.7.2 Pigging
A pig is a spherical or cylindrical device that is pumped through a pipe.

1.7.2.1 Liquid removal
Liquid accumulation at the bottom of a gas pipeline can cause erratic “slug” flow of accumulated liquids and a reduction of the effective pipe cross-sectional flow area, which reduces line capacity. The passage of a pig through the line functions like a piston and pushes the accumulated liquid toward a slug catcher, thus restoring the line capacity. Pigs used for liquid removal are generally inflatable spheres, rather than like rubber balls. By adjusting the inflation pressure of the sphere, the tightness of fit in the pipe can be altered.

1.7.2.2 Corrosion protection
Water in a low section of pipe can become a corrosion hazard and must be removed.
Often, a slug of corrosion inhibitor is injected and a second slightly underinflated pig is run to allow the inhibitor to coat the pipe wall.

1.7.2.3 Cleaning
Special types of scrapper pigs are run to remove paraffin, scale, rust, or construction debris from the inside of the pipe wall.

1.7.2.4 Monitoring
Special monitoring pigs are run to inspect the condition of the pipe. Feeler gauges on the pipe wall can check for wall thickness loss due to corrosion. Inclinometers and other position sensors have been placed in pigs to monitor pipe movement due to soil shifting. Increasing sophisticated pigs are being used for a widening range of pipeline monitoring tasks.

1.7.2.5 Auxiliary equipment
Much care and planning must be exercised before pigging a pipeline. Special equipment to launch and receive pigs must be provided. Line, fittings, and valves must be examined to assure passage and controlled removal of the pig from the line.
Pig velocity and travel must also be controlled through fluid pumping rates, upstream and downstream pressures, and the use of “pig sig” equipment that provides positive external signal information about internal arrival or passage.

1.7.3 Water hammer
The preceding discussion assumed that the fluid flow is steady-state. Transients have been assumed to be unimportant in the sizing of piping. One aspect of liquid flow line sizing in which transients can be extremely important involves “water hammer.” Whenever a valve in a liquid line is closed, all the liquid flowing in the pipe upstream of the closed valve must be slowed and brought to rest. Since this liquid column can be massive and is relatively incompressible, a large transient pressure at the downstream end of the pipe may be required. If the valve closure is abrupt, and the fluid initial velocity is sufficiently high, then a destructive pressure surge may result.
This pressure surge travels upstream in the flow line and may exceed the burst pressure of the pipe. The familiar knocking of household plumbing resulting from rapid faucet closure is an example of this pressure pulse deforming the piping and causing it to knock or hammer against its supports. “Water hammer” is mainly found only in liquid lines due to the near incompressibility of liquid.

1.7.4 Line packing
Fluid transient effects can also be important in long gas pipelines as a method of smoothing demand peaks. Since gas is much more compressible than liquid, potentially destructive liquid pressure surges do not occur as they may in liquid lines.
The compressibility of gas permits the pipeline to serve as a long, slender, pressure vessel for the storage of gas. By allowing the pressure levels in a gas pipeline to fluctuate, the instantaneous gas input to a pipeline does not have to equal the instantaneous gas offtake from the pipeline. The practice of pumping the line pressure up to a high pressure during periods of low demand permits the pipeline to deliver gas quantities in excess of its steady-state capacity under conditions of high demand. The process of raising pipeline operating pressures in anticipation of greater future demand is called “line packing.”

1.7.5 Line drafting
The process of drawing pipeline inventory down during periods of peak demand is called “line drafting.” While pipeline pack and draft are of small importance in production operations, gas transmission companies are quite sophisticated in using pack and draft to smooth their demand curves. The capacity to “pack” a gas pipeline is related to the difference in the normal operating pressure and the MAWP.

1.7.6 Phase flow regimes
1.7.6.1 Single-phase flow
Single-phase liquid flows are characterized by a virtually constant density but may be strongly influenced by viscosity effects. Single-phase gas flows are characterized by low viscosity, which result in high Reynolds numbers. Pipe wall roughness tends to be a more important effect in determining frictional pressure drop than does viscosity.
The density of gases varies greatly with both pressure and temperature and is the cause for the development of separate pressure drop-flow rate equations for two-phase flow.
In some single-phase flow conditions, a small volume of gas may be entrained in the liquid flow, such as a liquid dump line from a separator, or a small amount of liquid may be carried in the pipe in gas flow, such as the gas outlet line off a separator. These small amounts usually have a negligible effect on pressure loss and are not considered in single-phase flow calculations. However, there are certain flow conditions where sufficient volumes of a second gas or liquid phase exist to produce an appreciable effect on pressure loss. The pressure drop in such lines must be considered using techniques for two-phase flow.

1.7.6.2 Two-phase flow
When vapor and liquid flow in a pipe simultaneously, the flow situation becomes much more complicated. Liquid and vapor phases will distribute according to flow conditions, pipeline geometry, and the effect of gravity. Pressure drop-flow rate relations change as well. Using the best correlations available for pressure drop and liquid holdup, predictions may be in error by as much as +/- 20% for perfectly horizontal pipe and +/- 50% for inclined and looped systems. A phase diagram should be prepared for the flowing fluid. Plotting the anticipated flowing pressure and temperature will determine the number of phases present.
Generally, in production operations, two-phase flow exists from the wellbore to the first separator in the production facility. Gas from the separator is considered single-phase flow even though entrained liquids are present. Liquid from the separator is considered single-phase flow even though gas is present due to pressure drop through a liquid dump valve.
Different liquid and gas distributions in the pipe occur for different flow conditions.

1.8 Volumetric and Mass Flow Rates
1.8.1 Volumetric Flow Rate
The volumetric flow rate (QV) of a system is a measure of the volume of fluid passing a point in the system per unit time. The volumetric flow rate can be calculated as the product of the cross-sectional area (A) for flow and the average flow velocity (v).
QV = A v Eq. 1-17
Where
QV =Volumetric flow rate, ft3/sec
A = Cross-sectional area, ft2
V = Velocity, ft/sec

Example 1-1:
A pipe with an inner diameter of 4 inches (4/12 ft.) contains water that flows at an average velocity of 14 feet per second. Calculate the volumetric flow rate of water in the pipe.
Solution:
QV =Av
= (π D2 /4) x v
= 3.14 x (4/12)2 x14 / 4
= 1.22 ft3 /sec

1.8.2 Mass Flow Rate
The mass flow rate (m) of a system is a measure of the mass of fluid passing a point in the system per unit time. The mass flow rate is related to the volumetric flow rate as shown in
Equation 1-18, where ρ is the density of the fluid.
m = ρ QV Eq. 1-18
where
QV =volumetric flow rate is in cubic feet per second, ft3 /sec
ρ = the density is in pounds-mass per cubic foot, lbm/ft3
m = mass flow rate measured in pounds-mass per second, lbm/sec.

Replacing in Equation 1-18 with the appropriate terms from Equation 1-17 allows the direct
calculation of the mass flow rate.
m = ρ A v Eq. 1-19

Example 1-2:
The water in the pipe of the previous example had a density of 62.44 lbm/ft3. Calculate the mass flow rate.
Solution:
m = ρ QV
m = 62.44 x 1.22
= 76.2 lbm/sec

1.9 Networks
Piping systems are composed of more than a single line of constant diameter pipe.
Several pipes may be manifolded together, and even runs of a single line may change diameter. For very complicated systems, hand calculations may be prohibitively complicated, and computer programs must be used. For simple series and parallel lines, composite pressure drop-flow rate relations can be calculated using a couple of simple procedures.

Image
Figure 1.8 Series and parallel piping systems.

1.9.1 Pipes in series
Pressure drops are additive in pipes in series. For two sections of pipe, the downstream section having a different diameter from the upstream section, the overall pressure drop can be calculated by determining the pressure drop of the upstream and downstream sections separately. The composite pressure drop is then calculated by adding the pressure drops of the upstream and downstream sections. Note that the volume flow rate (Q) is the same in the upstream and downstream segments of pipes in a series.
1.9.2 Pipes in parallel
For two pipe segments in parallel, the pressure drops are identical for each segment and the flow rates are additive. Figure 1.8 shows the comparison between these two conditions.
1.10 Continuity Equation
The continuity equation is simply a mathematical expression of the principle of conservation of mass. For a control volume that has a single inlet and a single outlet, the principle of conservation of mass states that, for steady-state flow, the mass flow rate into the volume must equal the mass flow rate out. The continuity equation for this situation is expressed by Equation
m inlet = m outlet 1-20
(ρAv)inlet = (ρAv)outlet 1-21

One of the simplest applications of the continuity equation is determining the change in fluid velocity due to an expansion or contraction in the diameter of a pipe.
Example 1-3:
Steady-state flow exists in a pipe that undergoes a gradual expansion from a diameter of 6 in. to a diameter of 8 in. The density of the fluid in the pipe is constant at 60.8 lbm/ft3. If the flow velocity is 22.4 ft/sec in the 6 in. section, what is the flow velocity in the 8 in. section?
Solution:
From the continuity equation we know that the mass flow rate in the 6 in. section must equal the mass flow rate in the 8 in. section. Letting the subscript 1 represent the 6 in. section and 2 represent the 8 in. section we have the following.
m1 = m2
ρ1 A1 v1 = ρ2 A2 v2
v2 = v1 (ρ1 / ρ2) (A1 / A2 )
= v1 (π r12 / π r22)
= 22.4 x 32 / 42 = 12.6 ft/sec

Example 1-4:
The inlet diameter of a pump shown in Figure 1-9 is 28 in. while the outlet flow through the pump is 9200 lbm/sec. The density of the water is 49 lbm/ft3.
What is the velocity at the pump inlet?
Solution:
Ainlet = ρ r2 = 49 x (3.14) (14/12)2
= 4.28 ft2
minlet = moutlet = 9200 lbm/sec
(ρ Av)inlet = 9200 lbm/sec
Vinlet = 9200 / ( 4.28 x 49 ) =43.9 ft/sec


Image
Figure 1-9- Centrifugal pump sketch for example 1-4.

Example 1-5:
A piping system has a "Y" configuration for separating the flow as shown in Figure 1-10.
The diameter of the inlet leg is 12 in., and the diameters of the outlet legs are 8 and 10 in. The velocity in the 10 in. leg is 10 ft/sec. The flow through the main portion is 500 lbm/sec. The density of water is 62.4 lbm/ft3. What is the velocity out of the 8 in. pipe section?
Solution:
A8 = 3.14 x (4 /12)2 = 0.349 ft2
A10 = 3.14 x (5 /12)2 = 0.545 ft2
minlets = moutlets
m12 = m10 + m8
m8 = m12 - m10
(ρ Av)8 = m12 - (ρ Av)10
(ρ Av)8 = 500 – (62.4 x 0.545 x 10) = 159.9 lbm/sec
v8 = 159.9 / (0.349 x 62.4) = 7.3 ft/sec
Image
Figure 1-10- Flow lines sketch for example 1-5.
Fundamentals of Oil and Gas Processing
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Table of Contents
CHAPTER ONE ............................................................................................................... 8
FLUID FLOW AND PRESSURE DROP ...................................................................... 8
1. Introduction to facility piping and pipeline systems................................................................. 8
1.1.1 Flow line.......................................................................................................................................... 8
1.1.2 Trunk line ........................................................................................................................................ 8
1.1.3 Manifold .......................................................................................................................................... 8
1.1.4 Facility (on-plot) interconnecting piping...................................................................................... 8
1.1.5 Gathering line................................................................................................................................. 9
1.1.6 Transmission line........................................................................................................................... 9
1.2 Introduction to fluid flow design ................................................................................................ 9
1.2.1 Volume of fluid ............................................................................................................................... 9
1.2.2 Distance .......................................................................................................................................... 9
1.2.3 Pressure loss ............................................................................................................................... 10
1.2.4 Line size determination............................................................................................................... 10
1.2.4.1 Pressure drop considerations ............................................................................................ 10
1.2.4.2 Fluid velocity considerations .............................................................................................. 10
1.2.5 Wall thickness determination..................................................................................................... 10
1.2.5.1 Maximum internal/external pressure considerations ...................................................... 10
1.3 Fluid flow principles ................................................................................................................... 10
1.3.1 Pressure changes........................................................................................................................ 10
1.3.1.1 Acceleration effects ............................................................................................................. 10
1.3.1.2 Elevation effects................................................................................................................... 11
1.3.1.3 Frictional effects................................................................................................................... 11
1.3.2 Steady-state conditions .............................................................................................................. 11
1.4 Fluid types .................................................................................................................................... 11
1.4.1 Gases ............................................................................................................................................ 11
1.4.2 Crude oil........................................................................................................................................ 11
1.4.3 Water............................................................................................................................................. 11
1.4.4 Two-phase fluids.......................................................................................................................... 11
1.4.5 Combinations ............................................................................................................................... 12
1.5 Fluid characteristics ................................................................................................................... 12
1.5.1 Physical properties ...................................................................................................................... 12
1.5.1.1 Composition.......................................................................................................................... 12
1.5.1.2 Liquid Density....................................................................................................................... 12
1.5.2: Hydrocarbon gas physical properties ...................................................................................... 13
1.5.2.1: Molecular weight and apparent molecular weight.......................................................... 14
Example 1.1:.................................................................................................................................. 14
1.5.2.2: Apparent molecular weight of gas mixture...................................................................... 15
Example 1.2:.................................................................................................................................. 15
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1.5.2.3: Gas Specific Gravity and Density..................................................................................... 16
Example 1-3: ................................................................................................................................. 16
1.5.2.4: General Gas Law ..................................................................................................................... 16
1.5.2.5 Compressibility and compressibility factor (z) ................................................................. 17
Example 1-4: ................................................................................................................................. 17
Example 1-5: ................................................................................................................................. 18
Example 1-6: ................................................................................................................................. 19
1.5.2.6: Gas density at any condition of Pressure and temperature ......................................... 19
Example 1-7:.................................................................................................................................... 21
1.5.2.7: Gas volume at any condition of Pressure and temperature ......................................... 21
Example 1-8: ................................................................................................................................. 22
Example 1-9:.................................................................................................................................... 22
Example 1-10:................................................................................................................................. 22
Example 1-11:.................................................................................................................................. 22
Example 1-12:.................................................................................................................................. 23
1.5.3: Velocity of fluids (Liquid and gas), (ft/s)......................................................................................... 23
Example 1-13:.................................................................................................................................. 24
1.5.3.1 Maximum Recommended Velocity.......................................................................................... 25
1.5.4 Viscosity of Fluids............................................................................................................................ 25
1.5.2.1 Crude oil Viscosity.................................................................................................................... 26
1.5.2.2 Oil-Water Mixture Viscosity..................................................................................................... 28
1.5.2.3 Viscosity of gases..................................................................................................................... 28
1.5.5 Phase behavior............................................................................................................................ 29
1.5.6 Waxy crude................................................................................................................................... 30
1.5.6.1 Paraffin wax .......................................................................................................................... 30
1.5.6.2 Waxy crude behavior........................................................................................................... 30
1.5.6.3 Wax prediction...................................................................................................................... 32
1.5.6.4 Design and operational challenges ................................................................................... 32
1.5.6.5 Wax management................................................................................................................ 33
1.6 Flow conditions ........................................................................................................................... 33
1.6.1 Flow potential ............................................................................................................................... 33
1.6.2 Flow regimes................................................................................................................................ 33
1.6.3 Reynolds Number........................................................................................................................ 34
1.6.4 Pipe roughness............................................................................................................................ 35
1.6.5 Rate ............................................................................................................................................... 35
1.6.6 Velocity limitations....................................................................................................................... 35
1.6.7 Temperature................................................................................................................................. 35
1.6.7.1 Gas considerations.............................................................................................................. 35
1.6.7.2 Liquid considerations............................................................................................................... 35
1.7 Special considerations............................................................................................................... 36
1.7.1 Emulsions ..................................................................................................................................... 36
1.7.2 Pigging .......................................................................................................................................... 36
1.7.2.1 Liquid removal ...................................................................................................................... 36
1.7.2.2 Corrosion protection ............................................................................................................ 36
1.7.2.3 Cleaning ................................................................................................................................ 36
1.7.2.4 Monitoring ............................................................................................................................. 36
1.7.2.5 Auxiliary equipment ............................................................................................................. 36
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1.7.3 Water hammer ............................................................................................................................. 36
1.7.4 Line packing ................................................................................................................................. 37
1.7.5 Line drafting.................................................................................................................................. 37
1.7.6 Phase flow regimes..................................................................................................................... 37
1.7.6.1 Single-phase flow................................................................................................................. 37
1.7.6.2 Two-phase flow .................................................................................................................... 37
1.8 Volumetric and Mass Flow Rates ............................................................................................. 38
1.8.1 Volumetric Flow Rate.................................................................................................................. 38
Example 1-14:.................................................................................................................................. 38
1.8.2 Mass Flow Rate ........................................................................................................................... 38
Example 1-15: ............................................................................................................................... 38
1.9 Networks ....................................................................................................................................... 39
1.9.1 Pipes in series.............................................................................................................................. 39
1.9.2 Pipes in parallel ........................................................................................................................... 39
1.10 Continuity Equation .................................................................................................................. 40
Example 1-16: ............................................................................................................................... 40
Example 1-17: ............................................................................................................................... 40
Example 1-18: ............................................................................................................................... 41
1.11 Average pipeline pressure....................................................................................................... 42
1.12 Fluid head, friction losses, and Bernoulli’s equation......................................................... 42
1.12.1 Fluid head................................................................................................................................... 42
1.12.1.1 Pressure head....................................................................................................................... 42
1.12.1.2 Velocity head ......................................................................................................................... 42
1.12.1.3 Elevation head and Relationship between Depth and Pressure ................................ 42
Example 1-19:.................................................................................................................................. 43
Example 1-20: ............................................................................................................................... 44
CHAPTER 2 .................................................................................................................... 44
FRICTION LOSSES & PRESSURE DROP EQUATIONS ...................................... 45
2.1 Friction losses ............................................................................................................................. 45
2.2 Bernoulli’s equation.................................................................................................................... 45
2.3 Pressure drop equations ........................................................................................................... 46
2.3.1 Darcy-Weisbach equation .......................................................................................................... 47
2.3.2 Fanning equation......................................................................................................................... 47
2.3.3 Moody and fanning friction factor comparison ........................................................................ 48
2.3.4 Calculation procedure................................................................................................................. 49
2.3.5 Effects of elevation changes...................................................................................................... 51
2.3.6 Effects of viscosity........................................................................................................................... 51
2.3.7 Hazen-Williams equation ....................................................................................................... 52
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2.3.7.1 “C” factors ............................................................................................................................. 53
2.3.7.2 Applicability........................................................................................................................... 53
2.4 Gas flow ........................................................................................................................................... 54
2.4.1 Gas Flow Equations......................................................................................................................... 54
2.4.1.1 General Flow Equation............................................................................................................. 54
2.4.1.2 Friction Factor.......................................................................................................................... 56
2.4.1.3 Colebrook-White Equation ...................................................................................................... 58
Example 2.1 ..................................................................................................................................... 59
2.4.1.4 Transmission Factor................................................................................................................. 60
Example 2.2 ..................................................................................................................................... 61
2.4.1.5 Modified Colebrook-White Equation....................................................................................... 62
Example 2.3 ..................................................................................................................................... 62
2.4.1.6 American Gas Association (Aga) Equation............................................................................... 63
Example 2.4 ..................................................................................................................................... 63
2.4.2 Low Pressure Gas Flow.................................................................................................................... 64
2.4.2.1 Oliphant equation................................................................................................................. 64
2.4.2.2 Spitzglass Equation .................................................................................................................. 65
Example 2.5 ..................................................................................................................................... 65
2.4.3 Empirical gas flow equations........................................................................................................... 65
2.4.3.1 Weymouth equation............................................................................................................. 65
Where............................................................................................................................................. 66
Example 2.6 ..................................................................................................................................... 66
Example 2.7 ..................................................................................................................................... 66
2.4.5.2 Panhandle “A” equation ...................................................................................................... 67
2.4.5.3 Panhandle “B” equation .......................................................................................................... 68
Example 2.8 ..................................................................................................................................... 69
2.4.5.4 Institute of Gas Technology (IGT) Equation .................................................................... 70
Example 2.9 ..................................................................................................................................... 70
2.4.6 Selection of gas flow equations ...................................................................................................... 71
2.4.6.1 General equation ..................................................................................................................... 71
2.4.6.2 Weymouth equation................................................................................................................ 71
2.4.6.3 Panhandle “B” equation .......................................................................................................... 71
2.4.6.4 Spitzglass equation .................................................................................................................. 71
2.4.6.5 Oliphant equation.................................................................................................................... 71
2.4.6.6 IGT equation ............................................................................................................................ 71
2.4.7 Steam equations - Babcock equation....................................................................................... 71
CHAPTER THREE ................................................................................................................. 72
TWO-PHASE FLOW ............................................................................................................. 72
3.1 Introduction..................................................................................................................................... 72
3.2 Factors that affect two-phase flow................................................................................................... 72
3.2.1 Liquid volume fraction .................................................................................................................... 73
3.2.2 Pipeline profile ................................................................................................................................ 73
3.2.3 Liquid holdup................................................................................................................................... 73
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3.2.4 Two-phase flow regimes................................................................................................................. 73
3.2.4.1 Horizontal flow regimes........................................................................................................... 73
3.2.4.1.2 Elongated bubble (plug flow): .......................................................................................... 74
3.2.4.1.4 Slug flow; .......................................................................................................................... 74
3.2.4.2 Vertical flow regimes............................................................................................................... 75
3.2.4.2.1 Bubble flow....................................................................................................................... 75
3.2.4.2.3 Churn (transition) flow ..................................................................................................... 76
3.2.4.2.4 Annular-mist flow............................................................................................................. 76
3.3 Two-phase pressure loss.................................................................................................................. 77
3.4 Two-phase liquid holdup.................................................................................................................. 77
3.5 Two-phase flow correlations............................................................................................................ 77
3.5.1 Beggs and Brill equation.................................................................................................................. 78
3.5.2 API RP 14E equation........................................................................................................................ 78
3.5.3 AGA equations ................................................................................................................................ 79
3.5.4 Calculation procedure ..................................................................................................................... 79
Example 3.1 ..................................................................................................................................... 82
Example 3.2 ..................................................................................................................................... 86
3.6 Sizing Criteria for Gas/Liquid Two-Phase Lines................................................................................. 86
a. Erosional velocity. ................................................................................................................................ 86
b. Minimum Velocity................................................................................................................................ 87
.................................................................................................................... 88
Fundamentals of Oil and Gas Processing
Basics of Gas Field Processing
Basics of Corrosion in Oil and Gas Industry
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