Fluid flow and pressure drop - Part 1 -Introduction-

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Fluid flow and pressure drop - Part 1 -Introduction-

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Fundamentals of Oil and Gas Processing Book
Basics of Gas Field Processing Book
Prediction and Inhibition of Gas Hydrates Book
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Chapter One

Fluid flow and pressure drop

1. Introduction to facility piping and pipeline systems

The produced Oil and gas fluid produced must be transported to a facility where it is separated into oil, water, and gas; treated to remove impurities such as H2S, CO2, H2O, and solids; processed into specific end products and refined or stored for eventual sales. Figure 1 is a simplified block diagram that illustrates the basic “wellhead to sales” concept. The diagram begins with wellhead choke, which is used to control the rate of flow from each well. The fluid from the well travels through a flow line to the production facility where the fluid is separated, conditioned, treated, processed, measured, and refined or stored.
The facility piping and pipeline systems associated with producing wells include, but are not limited to, the well flow line, trunk line, facility (on-plot) interconnecting equipment piping within the production facility, gathering or sales pipelines, and transmission pipelines. A brief description of the aforementioned facility piping and pipeline systems follows.

1.1.1 Flow line
A well flow line identifies a two-phase line from a wellhead to a production manifold. Flow lines range in size from 2 in. to 20 in.

1.1.2 Trunk line
A trunk line is a larger line that connects two or more well flow lines that carries the combined well streams to the production manifold. Trunk lines range from 10 in. to 42 in.

1.1.3 Manifold
A manifold is a combination of pipes, fittings, and valves used to combine production from several sources and direct the combined flow into appropriate production equipment.
A manifold may also originate from a single inlet stream and divide the stream into multiple outlet streams. Manifolds are generally located where many flow lines come together, such as gathering stations, tank batteries, metering sites, separation stations, and offshore platforms. Manifolds also are used in gas lift injection systems, gas/water injection systems, pump/compressor stations, gas plants, and installations where fluids are distributed to multiple units. A production manifold accepts the flow streams from well flow lines and directs the combined flow to either test, or production separators and tanks.

1.1.4 Facility (on-plot) interconnecting piping
Facility piping consists of piping within a well-defined boundary of processing plants, piping compressor stations, or pumping stations. The piping is used for conducting a variety of fluids within those boundaries as required.

1.1.5 Transmission line
A transmission line consists of a cross-country piping system for transporting gas or liquids. The inlet is normally the custody transfer point or the production facility boundary with the outlet at its final destination, for example, processing plants and refineries. Transmission lines are usually long and have large diameters.

1.1.6 Gathering line
A gathering line consists of the line downstream of field manifolds or separators containing fluid flow from multiple wells and leading to the production facility. The gathering line may handle condensed hydrocarbon liquids, water, and corrosive gas and may require special design considerations.
Image

Figure 1.1 Block diagram of “wellhead to sales” concept.
1.2 Introduction to fluid flow design
When designing facility piping and/or pipeline systems, it is essential to optimize the line size and determine pump and/or compressor requirements.
Several factors that should be considered when determining the size of a line to meet the design requirements are the following:
Volume of fluid
Distance
Pressure loss
1.2.1 Volume of fluid
The main consideration in line sizing is the volume of fluid that must be transported through the piping system. The exact volume is rarely known during the initial design stage. An estimate is normally made for initial design purposes. Excess capacity reduces line profitability, while too small a line might need to be expanded in the future.

1.2.2 Distance
For pipelines, the distance between the entry point and the delivery point must be known. The designer needs to know the type of terrain the pipeline must traverse and the elevation profile along the right-of-way as it affects pressure loss and power requirements. The designer must also be knowledgeable of environmental conditions, ecological, historical, and archaeological sites as they might impact the pipeline routing, thereby increasing the length of the pipeline.

1.2.3 Pressure loss
The pressure loss as the fluid flows through the piping system is a key factor in both facility and pipeline design. Available piping inlet pressure must be known, as well as if there is any particular outlet requirement at the delivery point.
The design process begins with sizing lines for a given fluid flow rate. One must conform to the following:
Applicable codes, standards, and recommended practices
Company design criteria as contained in applicable facility specifications
Local regulatory requirements
The design process requires determination of the line size and wall thickness.
1.2.4 Line size determination
1.2.4.1 Pressure drop considerations
Pressure drop is used to avoid the installation of excessive brake horsepower required to boost the pressure for transporting the fluid. It is used to conform to the available piping inlet and discharge pressures and the allowable pressure gradient standards.

1.2.4.2 Fluid velocity considerations
Fluid velocities are used to prevent excessive water hammer, erosive velocities, and liquids and/or solids from dropping out of the flow stream.

1.2.5 Wall thickness determination
1.2.5.1 Maximum internal/external pressure considerations
Internal burst pressure is based on initial well conditions and other flow line considerations.
The external collapse resistance is a consideration in offshore locations and in onshore locations where the overburden loads are large.
The applicable design standards are ASME B31.3, ASME B31.4, and ASME B31.8.

1.3 Fluid flow principles
1.3.1 Pressure changes
As a fluid flows through a pipe, its pressure changes. Calculation of these pressure changes is necessary to size pipe. Fluid pressure changes can occur due to the following:
Acceleration effects
Elevation effects
Frictional effects

1.3.1.1 Acceleration effects
Acceleration effects in production facility piping systems are generally negligible and are ignored.

1.3.1.2 Elevation effects
Elevation effects are a result of hydrostatic gravity effects and can occur even in still fluid in inclined pipes. Elevation effects are important in wellbore pressure gradients, cross-country pipelines, and subsea pipelines. They are less important in production facilities and process piping, except pump suction lines and flow lines.

1.3.1.3 Frictional effects
Frictional effects, or pressure drop, are of primary importance in production facilities, flow lines, and pipeline design. As a fluid travels down a pipe, flow is retarded by frictional shear stresses with the pipe walls. The pressure levels decrease downstream as energy is used to overcome the frictional effects. The only exception occurs in downwardly inclined sections of pipe where elevation effects may overcome the pressure-decreasing effects of friction. The faster the fluid travels in the pipe, the greater the frictional stresses and the greater the pressure gradient.

1.3.2 Steady-state conditions
Most piping design is performed assuming non-fluctuating flow conditions. Two situations in which transients must be taken into account involve “water hammer” in liquid lines and “line pack and draft” in gas lines. Considerations of the above conditions are necessary primarily for pipeline operations.

1.4 Fluid types
Facility piping and pipelines transport various types of fluids. These include the following:

1.4.1 Gases
Unprocessed natural gas (rich gas) consists primarily of methane with some heavier hydrocarbons.
Processed natural gas (lean gas) consists primarily of methane, although small amounts of heavier fractions may still be present.
Nonhydrocarbon components consist of nitrogen and hydrogen sulfide and carbon dioxide may also be present.
Natural gas liquids (NGLs) consist primarily of the intermediate-molecular-weight hydrocarbon components such as propane, butane, and pentanes plus.

1.4.2 Crude oil
Crude oil consists of the heavier hydrocarbon fractions that are generally liquid at atmospheric conditions in storage tanks. Volatile oils are stabilized to prevent excessive vapor formation or “weathering” in storage or transport tankers. Piped fluid will remain liquid due to adequate operating pressure.

1.4.3 Water
Produced well streams frequently contain dissolved salts and minerals that are usually
corrosive; thus, piping systems must also transport water.

1.4.4 Two-phase fluids
Two-phase fluids usually consist of natural gas and condensate or crude oil and associated
gas. Flow lines from the well to the production facility are designed for two-phase flow.

1.4.5 Combinations
Produced well fluids contain the following:
Hydrocarbons (gases and liquids)
Water
Varying amounts of CO2 and H2S
Liquid hydrocarbons and some water combine both physically and mechanically to form an emulsion that has a higher viscosity value than that of oil or water.

1.5 Fluid characteristics
1.5.1 Physical properties
The physical properties of the transported fluid play an important role in determining the pipe diameter and selecting the pipe material and the associated equipment. They are also important in determining the power required to transport the fluid. The most important fluid properties that affect piping and pipeline design are the following:
Composition
Density
Viscosity
Vapor pressure
Water content
CO2 and H2S content

1.5.1.1 Composition
Well stream compositions are usually stated as mole fractions. Knowledge of composition is necessary to predict fluid properties such as density, viscosity, and phase behavior. If a compositional analysis is not available, one must rely on a “black oil” characterization in which API gravity, gas gravity, gas-oil ratio, and water-liquid ratio are given. The use of empirical black oil property correlations provides reasonable values for density, viscosity, and phase behavior.

1.5.1.2 Density
There are several definitions of fluid density that are used in upstream oil and gas operations, such as density, specific gravity or relative density, and API gravity. The density of a fluid is defined as mass per unit volume with unit lbm/ft.3 (kg/m3). Density is a thermodynamic property and is a function of pressure, temperature, and composition. Liquid densities are higher than gas densities and are affected less by pressure and temperature. Gas densities are increased by increasing pressure and decreased by increasing temperature. The density of a fluid is an important property in calculating the elevation pressure drop since elevation pressure drop is the product of density and elevation change.
A liquid’s density is often specified by giving its specific gravity relative to water at standard conditions of 60 °F and 14.7 psia (15.6 °C and 101.4 kPa). Thus,

ρ = 62.4 (SG) Eq. 1.1

where
ρ = density of liquid (lb/ft.3),
SG = specific gravity of liquid relative to water.

API gravity is a special function of relative density. It is a reverse graduation scale of relative density, where lighter fluids have higher API gravities. For example, a light oil would typically have an API gravity between 30 and 40, while water would have an API gravity of 10. API gravity is defined as

0API = 141.5/(Sp.Gr @ 60 Deg F) - 131.5 Eq. 1.2

The density of a mixture of oil and water can be determined by the volume weighted average of the two densities and is given by

ρ = [ ρwQw + ρoQo ] / QT Eq. 1.3

where
ρ = density of liquid (lb/ft.3),
ρo = density of oil (lb/ft.3),
ρw = density of water (lb/ft.3),
Qw = water flow rate (BPD),
Qo = oil for rate (BPD),
QT = total liquid for rate (BPD).

The specific gravity or relative density of a liquid is indicated relative to water, and that of a gas is indicated relative to air. The specific gravity is measured at certain pressure and temperature conditions. Usually “Standard” conditions which are taken as 60 °F (15.6 °C) and 14.7 psi (1.01325 bar)

The average specific gravity of some oil field liquids are the following:
Crude oil 0.825
Condensate 0.75
Butane 0.58
Table 1- 2 specific gravity of some oil fluids.

The specific gravity of an oil and water mixture can be calculated by

(SG) m = [(SG)wQw + (SG)oQo] / QT Eq. 1.4

where
(SG)m = specific gravity of liquid,
(SG)o = specific gravity of oil,
(SG)w = specific gravity of water,
Qw = water flow rate (BPD),
Qo = oil for rate (BPD),
QT = total liquid for rate (BPD).

Unlike liquid, which is incompressible, gas is compressible. Gas density is a function of pressure, temperature, and molecular weight. The specific gravity or relative density of a natural gas at standard conditions of pressure and temperature is determined by its apparent molecular weight. It is often expressed as a specific gravity, which is the ratio of the density of the gas at standard conditions of pressure and temperature to that of air at standard conditions of pressure and temperature. Since the apparent molecular weight of air is(28.97), approx.. 29 lb/lb-mole (kg/kmole), the specific gravity of a gas is given by

S = MW / 29 Eq. 1.5

where
S = specific gravity of gas relative to air,
(MW) = apparent molecular weight of gas.

The density of a gas under specific conditions of pressure and temperature is given by

ρg = 2.7 SP/TZ Eq. 1.6

ρg= 0.093 ((MW)P)/TZ lb/ft3 Eq. 1.7

where
ρg = density of gas (lb/ft.3),
P = pressure (psia),
T = temperature (°R),
Z = gas compressibility factor,
S = specific gravity of gas relative to air,
(MW) = apparent molecular weight of the gas.

1.5.1.3 Viscosity
Viscosity is a measure of a fluid’s internal resistance to flow. It is determined either by
measuring the shear force required to produce a given shear gradient or by observing the
time required for a given volume of liquid to flow through a capillary or restriction.
When measured in terms of force, it is called absolute or dynamic viscosity. When measured
with respect to time, it is called kinematic viscosity. A fluid’s kinematic viscosity
is equal to its absolute viscosity divided by its density. The unit of absolute viscosity is
poise or centipoise (cP). The unit of kinematic viscosity is stoke or centistokes (cSt). The
relationship between absolute and kinematic viscosity is given by

μ = γρ Eq. 1.8

where
μ = absolute viscosity (cP),
γ = kinematic viscosity (cSt),
ρ = density (lb/ft.3),
SG = specific gravity relative to water.
In the metric system, if the absolute viscosity is given in centipoise, then the kinematic viscosity is in centistokes and the unit of density to use in Equation 8 is g/cm3. Since water has a density of 1 g/cm3, Equation 8 can be rewritten:

m = (SG)γ Eq. 1.9

where
m = absolute viscosity (cP),
(SG) = specific gravity of liquid relative to water,
γ = kinematic viscosity (cSt).
As shown in Figure 1.2, liquid water at 70 °F has an absolute viscosity of approximately one centipoise (cP). The common English system unit of viscosity is lbm/ft./s. The conversion between metric and English units are listed in the next table

Multiply By To obtain
ft2/sec 92903.04 Centistokes
lbf-sec/ft2 (lb/ft-sec) 47880.26 Centipoises
Centipoises 1/density (g/cm3) Centistokes
lbf-sec/ft2 (lb/ft-sec) 32.174/density (lb/ft3) ft2/sec
Centipoise 0.000672 lbm/ft-sec
Table 1- 2 Viscosity conversion factors

Image
Figure 1.2 Physical properties of water.

Fluid viscosity varies with temperature. For liquids, viscosity decreases with increasing temperature. The viscosity of oil is highly dependent on temperature and is best determined by measuring the viscosity at two or more temperatures and interpolating to determine the viscosity at any other temperature. When data are not available, the viscosity of a crude oil can be approximated from Figures 1.3, and 1.4, provided the oil is above its cloud point temperature, that is, the temperature at which wax crystals begin to form when the crude oil is cooled. Figures 1.3, and 1.4, present kinematic viscosity for “gas-free” or stock tank crude oils. Although viscosity is generally a function of API gravity, it is not always true that a heavier crude (lower API gravity) has a higher viscosity than a lighter crude (higher API gravity). Therefore, Figure 1.3 should be used with caution. As shown in Table 1.3, the viscosity of crude varies from very low to very high.

Crude Country Density (15 °C) (kg/m3) Viscosity (40 °C) cSt

Ekofisk Arabian Light Kuwait Bintulu Schoonebeek Langunillas Boscan
Norway Saudi Arabia Kuwait Sarawak Netherlands Venezuela Venezuela
804
859
870
886
904
967
1005
2
6
10
6
200
800
20,000
Table 1.3. Represents the independence of viscosity on crude oil density.
Image
Figure 1-3, typical viscosity-temperature curves for crude oils
Image
Figure 1-4, Oil viscosity vs. gravity and temp. (Courtesy of Paragon Eng. Services, Inc.)

1.5.1.4 Crude oil Viscosity.
The best way to determine the viscosity of a crude oil at any temperature is by measurement. If the viscosity is known at only one temperature, Figure 1-5 can be used to determine the viscosity at another temperature by striking a line parallel to that for crudes “A,” “C,” and “D.” Care must be taken to assure that the crude does not have its pour point within the temperature range of interest. If it does, its temperature-viscosity relationship may be as shown for crude “B.”
Solid phase high-molecular-weight hydrocarbons, otherwise known as paraffins, can dramatically affect the viscosity of the crude sample. The cloud point is the temperature at which paraffins first become visible in a crude sample. The effect of the cloud point on the temperature viscosity curve is shown for crude “B” in Figure 1-3. This change in the temperature-viscosity relationship can lead to significant errors in estimation. Therefore, care should be taken when one estimates viscosities near the cloud point.
The pour point is defined as the lowest temperature (5 0F) at which the oil will flow.
The lower the pour point, the lower the paraffin content of the oil.
Figure 1-3, typical viscosity-temperature curves for crude oils. (Courtesy of ASTM D-341.)
(Light crude oil (300–400API), Intermediate crude oil (200–300), & Heavy crude oil (less than 200 API)

In the absence of any laboratory data, correlations exist that relate viscosity and temperature, given the oil gravity. The following equation relating viscosity, gravity, and temperature was developed by Beggs and Robinson after observing 460 oil systems:

µ = 10x -1 Eq. 1-10
where
µ = oil viscosity, cp,
T = oil temperature, 0F,
x = y (T)−1.163,
y = 10z
z = 3.0324 – 0.02023G,
G= oil gravity, API@ 60 0F.
Figure 1-6 is a graphical representation of another correlation.

1.5.1.5 Oil-Water Mixture Viscosity
The viscosity of produced water depends on the amount of dissolved solids in the water as well as the temperature, but for most practical situations, it varies from 1.5 to 2 centipoise at 500F, 0.7 to 1 centipoise at 1000F, and 0.4 to 0.6 centipoise at 1500F.
When an emulsion of oil and water is formed, the viscosity of the mixture may be substantially higher than either the viscosity of the oil or that of the water taken by themselves. The modified Vand’s equation allows one to determine the effective viscosity of an oil-water mixture and is written in the form

µeff = (1+2.5 ϕ +10 ϕ2) µc Eq. 1- 11

where
µeff = effective viscosity, cp
µc = viscosity of the continuous phase (Oil), cp
Φ = volume fraction of the discontinuous phase (Water).

1.5.1.6 Viscosity of gases
Viscosity of a fluid relates to the resistance to flow of the fluid. Higher the viscosity, more difficult it is to flow. Viscosity is a number that represents the drag forces caused by the attractive forces in adjacent fluid layers. It might be considered as the internal friction between molecules, separate from that between the fluid and the pipe wall.
The viscosity of a gas is very small compared to that of a liquid. For example, a typical crude oil may have a viscosity of 10 centipoise (cp), whereas a sample of natural gas has a viscosity of 0.0019 cp.
Viscosity may be referred to as absolute or dynamic viscosity measured in cp or kinematic viscosity measured in centistokes (cSt). Other units of viscosity are lb/ft-sec for dynamic viscosity and ft2/s for kinematic viscosity.
Fluid viscosity changes with temperature. Liquid viscosity decreases with increasing temperature, whereas gas viscosity decreases initially with increasing temperature and then increases with further increasing temperature.

Figure 1-5 can be used to estimate the viscosity of a hydrocarbon gas at various conditions of temperature and pressure if the specific gravity of the gas at standard conditions is known. It is useful when the gas composition is not known. It does not make corrections for H2S, CO2, and N2. It is useful for determining viscosities at high pressure.

Image
Figure 1-5 Hydrocarbon gas viscosity.
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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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