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University of Miskolc
Faculty of Earth Science and Engineering
Petroleum and Natural Gas Institute
Analysis of Heavy Oil in a Two Phase-Flow
Thesis
Author’s name: Omunakwe Emmanuel Buduka,
petroleum engineering MSc student
Department supervisor: László Kis, assistant lecturer
Miskolc 2016
MISKOLCI EGYETEM
Műszaki Földtudományi Kar
KŐOLAJ ÉS FÖLDGÁZ INTÉZET
UNIVERSITY OF MISKOLC
Faculty of Earth Science & Engineering
PETROLEUM AND NATURAL GAS INSTITUTE ——————————————————————————————————————————————————————————————————————————————————————————
: H-3515 Miskolc-Egyetemváros, Hungary : (36) (46) 565-078 FAX: (36) (46) 565-077
e-mail: [email protected]
Diploma Thesis
Project Assignment
for
Omunakwe Emmanuel Buduka
Preliminary Title of Thesis:
Analysis of Heavy Oil in a Two Phase-Flow
Contents:
Review the literature regarding the two-phase flow pressure drop calculations.
Introduce the empirical methods for horizontal transportation.
Analyze the effect of temperature changes on pressure loss along the flowline during
multiphase flow of high-viscosity crude.
Investigate the effect of parameters affecting pressure drop.
Give recommendations for the supposed transporting scenarios.
Faculty Advisor: László Kis, assistant lecturer
Deadline of submission: 9 May 2016.
Zoltán Turzó, PhD
Head of Institute
Miskolc, 01 June 2015.
Proof Sheet for thesis submission for MSc students
Name of student: Omunakwe Emmanuel Buduka Neptune code: KK0Y36
Degree program: Petroleum Engineering
Department supervisor: László Kis Institute: University of Miskolc
Title of Thesis: Analysis of Heavy Oil in a two Phase-Flow
1. Statement of the degree program leader:
Thesis assignment was delivered to the student.
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The student have submitted the first draft of the Thesis work
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Undersigned agree/ do not agree to the submission of this Thesis.4
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5. The thesis (two copies + electronic version on CD) has been submitted
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___________________________
4 Thesis can be submitted regardless of the consultant's consent
Proof Sheet for thesis submission
for Petroleum Engineering MSc students
Name of student: Omunakwe Emmanuel Buduka
Neptune code: KK0Y36
Title of Thesis: Analysis of Heavy Oil in a two Phase-Flow
Declaration of Originality
I hereby certify that I am the sole author of this thesis and that no part of this thesis has been
published or submitted for publication.
I certify that, to the best of my knowledge, my thesis does not infringe upon anyone’s
copyright nor violate any proprietary rights and that any ideas, techniques, quotations, or any
other material from the work of other people included in my thesis, published or otherwise,
are fully acknowledged in accordance with standard referencing practices.
9 May 2016
Signature of the student
Statement of the Department Advisor1
Undersigned agree/ do not agree to the submission of this Thesis.
9 May 2016
Signature of
Department Advisor
The thesis has been submitted:
Date 9 May 2016.
Administrator of
Petroleum and Natural Gas Institute
1 Thesis can be submitted regardless of the consultant’s consent.
i
Table of Contents 1 Introduction ................................................................................................................ 1
1.1 Background Theories .......................................................................................... 2
2 Literature Review ....................................................................................................... 3
2.1 Challenges of heavy Oil ...................................................................................... 3
2.2 Effects of high viscosity on pipeline design........................................................ 3
2.3 Methods of transporting heavy oil ...................................................................... 4
2.3.1 Heating: ........................................................................................................ 4
2.3.2 Dilution ........................................................................................................ 7
2.3.3 Oil in water Emulsion .................................................................................. 9
2.3.4 Core-annular flow ...................................................................................... 10
2.3.5 Partial upgrading ........................................................................................ 10
2.4 Choice of Method .............................................................................................. 10
2.5 Importance of two-phase flow........................................................................... 11
2.6 Basic Principles of two-phase flow ................................................................... 12
2.7 Flow Patterns ..................................................................................................... 13
2.7.1 Bubble flow ................................................................................................ 13
2.7.2 Dispersed Bubble flow ............................................................................... 14
2.7.3 Slug Flow ................................................................................................... 14
2.6.4 Transition (churn) flow .................................................................................. 15
2.8 Flow Maps ......................................................................................................... 16
2.9 Superficial Velocity........................................................................................... 18
2.10 Gas Slippage .................................................................................................. 19
2.11 Liquid Holdup ............................................................................................... 20
2.12 Mixture Properties ......................................................................................... 21
2.13 Multiphase flow ............................................................................................. 23
2.14 Pressure Gradient Equations .......................................................................... 24
3 Empirical correlations for pressure drop calculations .............................................. 26
3.1 Beggs-Brill ........................................................................................................ 26
3.1.1 The flow patterns ....................................................................................... 27
3.2 Mukherjee-Brill ................................................................................................. 28
3.2.1 Phase Slippage and liquid holdup .............................................................. 28
3.2.2 Development of liquid holdup calculation ................................................. 29
3.2.3 Effects of Inclination and Viscosity ........................................................... 29
3.3 Fancher Brown .................................................................................................. 30
3.3.1 Methods of Predicting Pressure Gradient .................................................. 30
4 Investigation of a transportation problem ................................................................. 32
4.1 Statement of problem ........................................................................................ 32
4.1.1 Fluid Pvt Data ............................................................................................ 32
4.1.2 Pipeline Data .............................................................................................. 33
4.1.3 Measured viscosities .................................................................................. 33
4.1.4 Measured Density ...................................................................................... 34
4.1.5 Calculated density ...................................................................................... 34
4.2 Calculation and Results ..................................................................................... 34
4.2.1 Effect of the used empirical method .......................................................... 35
4.2.2 The Effect of condensate concentration on the pressure ........................... 38
4.2.3 The effect of diameter on the pressure ....................................................... 41
4.2.4 Calculation summary ................................................................................. 43
4.2.5 The effects of economic evaluation ........................................................... 44
5 Conclusion and Recommendations .......................................................................... 46
6 References ................................................................................................................ 48
7 Acknowledgment ...................................................................................................... 49
8 Appendices ............................................................................................................... 50
1
1 Introduction
The most economic means of transporting petroleum and natural gas ever since its
discovery in 1851 is by pressure pipelines. Transporting heavy oil tends to be highly
challenging due to the high viscosity effects which results to pressure drop along the
pipeline.
Several transportation methods of these crude is discussed such as the heating, dilution, oil
and water emulsion, core annular flow and partial upgrading, which is the most recent
method mentioned above. The flow patterns, importance of multiphase flow and empirical
correlations were also discussed in order to achieve the aim, which is investigating the
pressure drop along a given horizontal pipeline of 2000m. Also the viscosity and density
data used were measured and calculated.
However, the empirical correlations chosen were based on horizontal flow, investigating
the effects of condensate concentrations, pipe diameters and the base oil on how they
affects the pressure drop. Calculations were made using the using different correlations
such as the Beggs-Brill, Fancher-Brown and Mukherjee-Brill. The results were analysed
based on the chosen pipe diameter, condensate concentration and the base oil on different
situations. A comparison was also made between different pipe sizes and condensate
concentration in order to investigate the results and evaluate the economic cost involved in
implementing such design.
Therefore a conclusion was made based on the best results gotten from different pipe
diameters, condensate concentrations and the base oil, for the pipe design, the flow and
generally the aim which is the pressure drop. A solution to the transportation problem was
also made and possible means of encountering such cases in the near future.
2
1.1 Background Theories
Heavy oil transportation has existed in western Canada for a number of years because
Substantial reserves of proven oil have been restricted to local requirement, due to the
challenges involved
The steady-state simultaneous flow of petroleum liquids and gases in wells and surface
pipes is a common occurrence in the petroleum industry. However, oil wells produce
normally a mixture of liquids and gases to the surface while phase conditions usually
change along the flow path. Also, this results in the case of higher pressures, where at the
bottom of the well, the flow maybe single but with continuous production which leads to
pressure decrease, causing dissolved gases to evolved from the flowing liquid resulting to a
multiphase flow.
In some cases, both oil and gas wells can be vertical, inclined and also contain larger
horizontal sections. The importance of a proper description of flow behaviour in oil wells
cannot be overemphasized because the greatest challenge is the pressure drop in the well
and the most decisive part of the total production system. It therefore considers the
boundary of the drainage area, formation fluids first flow in the porous media surrounding
the well and wellbore.
The multiphase flow system is not just restricted to the above cases, but it’s also applied in
artificial lifting methods where a mixture of phases presents in the well tubing. Such as
Gas lifting where the injection of high pressure gas into the well at a specific depth, to a
multiphase system2.
The calculation of the pressure drop and analysis of the pressure traverse helps the
production engineer in the description of the multiphase flow phenomena for producing oil
and gas wells, is off great importance for the design and optimization problem in the
petroleum industry.
3
2 Literature Review
2.1 Challenges of heavy Oil
The challenges or difficulties encountered in the transportation of heavy oil can be
summarized in one word as viscosity. Viscosity can be defined as a measure of a fluid
resistance to flow. It describes the internal friction of a moving fluid. Its unit is the
centipoise (cP). It also has the following characteristics:
Viscosity generally increases as API gravity increases.
The viscosity of these crudes is very much greater than that of light crudes such
as (the Western Canada crude which is greater than the Alberta light crude).
In the range of flowing temperature which can be expected in a pipeline, small
difference in temperature has a major effect on viscosity4.
Also, it is said to be that from various researches carried out and literatures that these crude
have a very high pour point of about 20 °C. They are generally thixotropic, which means
their flow behaviour is time dependent.
2.2 Effects of high viscosity on pipeline design
In the most economic size of pipe design, the flow tends to be generally a
laminar rather than turbulent, because in the laminar flow pressure drop for a
given pumping rate is directly proportional to viscosity.
High pressure per mile will be encountered resulting in fairly close pump station
spacing.
In case where high viscosity oil rate is too high, to get an economic efficiency or
reasonable efficiency from centrifugal pump is limited, hence positive
displacement pumps are required.
If positive displacement pumps are used in a situation where temperature
variation will have an effect on pipeline flow capacity, the additional method is
used in adjusting the pumping rates1.
However, it’s important that we understand that these effects concerning the transportation
of heavy oils exist in almost all parts of the world which can be overcome. Heavy oil has
been pipelined in several areas such as California since early in the century; also some
extreme viscous oil is moved in pipeline systems in Venezuela and Indonesia. Basically,
4
some production from small wells scattered pools like in the case of Canada, these
difficulties are more of economic than technical, because heavy oil can be moved
economically by pipeline than by truck or rail1.
2.3 Methods of transporting heavy oil
The followings are the various ways or schemes by which to reduce the excessive power
consumption in pumping high viscous oil4.
1. Heating
2. Dilution
3. Oil water emulsions
4. Core annular flow
5. Partial field upgrading
2.3.1 Heating:
This method is well known and widely proven in several parts of the world, especially in
Venezuela and United States. The process consists in heating the crude in order to raise its
flowing temperature and hence reduce its viscosity to acceptable limits for transportation1.
Also, it is well known that viscosity decreases rapidly with increasing temperature.
Most heavy oil pipelines are specially designed below 500cP at the pump outlet. The
process of evaluating temperature and pressure profiles of heavy oil flow along pipelines
are always complicated and tedious. Thus, involves the solution of the first law of
thermodynamics (simultaneous solution of the total energy) and the mechanical energy
balance equations, over finite sections along the length of the pipeline1.
However, the heat loss from flowing fluids can be calculated by determining an overall
heat transfer coefficient which depends on the thermal conductivity of the pipe wall, and
the surrounding soil and also the ambient thermal conditions. Temperature and pressure
profiles at several flow rates for a typical heated oil line are shown in the Figure 11. The
cooling of the oil along the direction of flow, and its consequent increase in viscosity,
results in a hydraulic profile which is not a straight line. The curvature of the line is more
pronounced for more viscous material.
5
Another characteristic of the heating method is the fact that at a low flow rate, the pumping
pressure has a high value. This is due to the high viscosity effect caused by the rapid
decrease in temperature associated to the low fluid velocity, as shown in the Fig. 21 below.
Figure 1. Profile for typical heated oil line at different flow rates2
Thus, the heating method proves the fact that at a low flow rate the pumping pressure has a
high value. This is due to the high viscosity effect caused by the rapid decrease in
temperature which enables the low fluid velocity shown in Figure 21.
6
Figure 2. The effect of flow rate on the pumping pressure for different pipeline
lengths and diameters2
Another important aspect of heating heavy oil is the maximum distance between pumping
stations. This distance heavily depends on the flow rate of the crude oil.
The following are considerations in the design of hot pipeline transporting heavy oil
The heat losses which includes with special focus on insulation thickness
Temperature required to achieve optimum viscosity
The pipeline material used
The number of pumping stations
Coating and insulation type.
Prevention of plugging
Expansion of the pipeline
Start up and shut conditions
It should be noted that a direct fixed heater is generally used to raise the temperature of the
oil and the heaters can be natural gas or fuel oil fired4.
It is also important to know that variation of temperature due to flow rate changes causes a
longitudinal expansion of the pipeline. For above ground lines, expansion is absorbed by
expansion loops, and for buried lines thicker steel is required in order to absorb
longitudinal compression stresses.
7
Plugging must be prevented because generally it occurs when the lines are cooled down to
ambient temperature, therefore displacement oil must be used during start up and shut
down operations.
Let make certain assumptions, in order to calculate the temperature at any point along the
pipeline Moreau (1965)
𝑇 = 𝑇𝑔 + (𝑇𝑖 − 𝑇𝑔)𝑒−3.94×𝑈×𝑑𝑜×𝐿
𝑆𝑒𝑄 (1)
Where T = temperature of flowing oil, F
Tg = ground temperature, F
Ti = inlet temperature of oil into the pipeline, F
e = base of natural logs- - dimensionless
U = overall heat transfer coefficient, BTU/h/ft2/F
do= outside diameter of pipe, in
L = distance from inlet, in
Se = specific gravity of oil
c = specific heat of oil, BTU/lb/F
Q = flow rate, bbl/day
It should be noted that the distance that the oil will travel for a given temperature drop is
dependent upon the flow rate. Also to be noted that the above equation is for a stabilized
flowing condition which may take some time to reach or achieve.
2.3.2 Dilution
Dilution is an alternative method of reducing the pressure gradient in a heavy oil line by
blending a less viscous hydrocarbon such as condensate, natural gasoline or naphtha to the
heavy oil to reduce its viscosity. This method has been intensively applied in Canada,
U.S.A. and Venezuela4.
Figure 3. shows the reduction in viscosity that can be obtained by blending condensate
with heavy crude oils because of an exponential relationship between the resulting
viscosity of the mixture and the volume fraction of the diluent. Because of this
relationship, small percentages of diluent have marked effect on the viscosity of the
8
mixture and therefore it is evident that there is optimum percentage above which there is
little further reduction4.
Figure 3. Effect of dilution with condensate on crude viscosities of different API
gravity2
However, it is better to actually make test blends in the laboratory and to determine
viscosities experimentally. In such cases, pressure losses may be calculated by using
conventional methods, assuming isothermal one phase flow of a homogenous mixture with
a viscous value.
It’s imperative to note that diluent with similar characteristics to condensate can be
manufactured from any light crude in refineries from fractions normally used to produce
gasoline, Jet fuels and middle distillates. Many light types of crude can also be used
directly as diluent such with API gravity between 35 to 45 degrees1. Although a greater
volume is required to do the same job as condensate, because the cost of the crude is lower
than diluents as there are no manufacturing costs involved, therefore leading to the
requirement of large capacity of pipeline.
.
9
2.3.3 Oil in water Emulsion
This method involves a process where a high viscous hydrocarbon is been handled in the
form of an emulsion4. An extra heavy crude or bitumen is suspended in the water (the
external phase) in the form of micro spheres are stabilized with the addition of chemical
additives in order to achieve a reduction in the apparent viscosity of the heavy oil as occurs
in the case of a diluent or heat, therefore helping to reduce the amount of horsepower
required to pump the heavy crude through flow lines.
The design of a programme to apply the emulsion technology must consider the following
aspects:
Selection of the best chemical for the formation of the emulsion
Dispersion mechanism (mixers & homogenizers)
Disintegration of emulsion (breaking)
Rheological & stability characteristics of emulsion.
In selecting the accurate and suitable chemical you ensure that it has the ability to exhibit
the required stability of the emulsion under different conditions. The most relevant
parameter are temperature, hydrocarbon/water ratio, water salinity and pH. Also non-ionic
surfactants are the most effective in producing a more suitable and stable emulsion due to
their ability in producing smaller mean droplet size4, this produces an effect of the volume
of water on the viscosity of the emulsion, whereby viscosity decreases exponentially with
water content. Such reactions are greatly important in selecting the optimum amount of
water to be present in the emulsion.
The rheological behaviour of the emulsion must be assessed in order to predict pressure
losses. According to rheological models developed by states that the behaviour must be
Newtonian for oil content below 65% and for oil content above this value, the emulsion
behaves as a pseudoplastic fluid. As mentioned above that stability is one of the most
important properties of emulsions, since emulsion must possess the ability to withstand
severe handling through power equipment, valves and accessories. Finally, the emulsion
breaking or disintegration process is determined by temperature, water pH, water salinity
and surfactant concentration.
10
2.3.4 Core-annular flow
This method is practically based on the flow regime determined by laboratory loop test
analysis and field tests. This mode of transportation method uses a less viscous immiscible
fluid, where water is introduced into the flow to act as a lubricating layer which absorbs
the shear stress existing between the walls of the pipes and the fluid, reducing the
resistance to flow.
However, besides the annular flow pattern, it’s important to note that other flow patterns
can be developed where two immiscible liquids are flowing in a pipe. This technology is
being studied in Venezuela presently by Marven and Intevep, affiliated companies of
Petroleos de Venezuela4.
2.3.5 Partial upgrading
This is also a new concept which consists an infield partial upgrading of the heavy crude
and bitumen, which modifies the crude composition for the purpose of making it less
viscous to be able to be transported, without significantly altering the refining
characteristics. This method have recorded successful results in some part of the world
such as the Resource Technology Associates (RTA), Boulder Colorado, where the
Geotrater process was used which consist of a thermal treatment of the heavy crudes in a
vertical tubular reactor4. The aim is to improve the crude transportability by lowering the
viscosity and pour point and increasing API gravity4.
2.4 Choice of Method
In choosing or selecting the most economical method for the pipeline transportation of
various oils. The choice depends upon many variables such as viscosity of the oil, cost and
availability of diluents and fuel, soil temperatures and conditions, the distance the oil is to
be moved or transported.
For the purpose of this research, the considered method of diluents is used with base oil
and condensate. Measured data were gotten from different percentage of dilution and in
respect to the pipe diameter, length and densities, thereby monitoring the rate of pressure
reduction along the flow path. The determination of the most appropriate method for
11
pipeline transportation of heavy oils is dependent upon number of factors, but the most
significant is the economic one, therefore some of the major factors are the followings:
Pipeline length
Climate
Existing facilities
Diluent availability
Water disposal
Electricity supply
Topographical profile
Type of crude oil
Environment
Markets.
For very long pipeline in a cool region or country, dilution or emulsion might be better
choices, as heating might require larger investment in heaters and insulated pipes, because
the emulsions used for long distance can be made to be very stable over long periods of
time. Also some crudes oil is suitable to form very stable emulsions at low surfactant
concentration influencing operating cost.
However, heated pipeline may be feasible in warm parts of the world like Venezuela and
California, as the low horsepower requirement and the use of non-insulated pipes may
minimize the initial investment and operating cost. In a case where there is shortage of
diluents, the heating and dilution methods on the marketing strategy which may also
change or influence the overall economic survey and make or create a platform of some
transportation methods more attractive than others.
2.5 Importance of two-phase flow
This is important for designing gas-liquid transportation systems, which will lead to the
development of empirical correlations which can be used to develop a model and predict
the pressure drop using the given parameters as stated earlier.
12
2.6 Basic Principles of two-phase flow
The multiphase flow is more complex than the single-phase flow. Due to the fact that the
sing-phase flow is more defined and most often have analytical solutions developed by
previous research works over the years. In terms of two-phase flow, its greatest problem is
the calculation of the pressure drop along the pipe which requires a careful observation
with high degree of accuracy. Also, predicting the phase conditions becomes more difficult
due to the introduction of the second phase. The following principles are outlined by2, for
the multiphase flow problem
That for any multiphase problem, the number of variables affecting the pressure
drop is enormous. In addition, the thermodynamic parameters for each phase
several variables describing the interaction of two phases (interfacial tension
etc).
The two-phase mixture is compressible that is the density depends on the actual
flowing pressure and temperature, since in most flow problems temperature and
pressure varies in a wide range, the effect must be properly accounted for.
Frictional pressure losses are much more difficult to be described since the it
involves more than one phase, in contact with the pipe wall which leads to
difficulty in multiphase mixture velocity which is more different to that of the
single-phase laminar or turbulent flows, adding to the difficult of pressure drop
prediction.
In addition to the pressure losses, energy loss is also observed which is called
the slippage loss. This happens due to the great difference in densities of the
liquid and the gas phases. In other words, it means that the slippage loss greatly
influences or contributes to the total pressure drop.
Physical phenomena and pressure losses considerably vary with the spatial
arrangement in the pipe of the flowing phases, conventionally called the flow
pattern, enabling different correlations to be used in calculating the pressure
drop which is the vital focus of the work.
It’s important to note that due to the complexity of the two-phase flow, early research by
several scholars, shows there was no evidence or proper documentation of necessary
differential equations which was used to resolve this problem rather a general simple
energy equation was used. This equation allows for a simple treatment of the two-phase
13
flow problem and has resulted to numerous models employed for the calculation of the
phases in order to ensure engineering accuracy2. Therefor a suitable empirical correlations
model based on horizontal pipe flow is used to determine the accurate pressure drop on
different situations, depending on the pipe diameters, condensate concentrations and the
base oil.
2.7 Flow Patterns
This is the arrangement by which liquid and gas, flowing together in a pipe taking different
geometrical configuration related to each other. Also, the flow pattern which occurs in
vertical, inclined and horizontal pipes have many common features but there is a basic
difference.
In horizontal flow, which is the purpose and focus of this research, considers the effect of
gravity which is pronounced compared to the other such as vertical flows, leading to the
separation of the gas from the heavier fluid phase and travels to the top (surface) of the
pipe. The following classification of flow patterns are universally accepted as proposed
by2.
Bubble flow
Dispersed bubble flow
Slug flow
Transition (churn) flow
2.7.1 Bubble flow
The bubble flow patterns occurs when the gas flow velocities are at the range of low to
medium, then the gas phase takes the form of distributed discrete bubbles rising in the
continuous liquid phase. Due to their low density, the gas tends to overtake the liquid
particles, leading to the formation of the gas slippage.
In this case, the liquid remains in contact with the pipe wall, which makes the calculation
of the pressure losses simpler.
14
Figure 4. Bubble flow Pattern2
2.7.2 Dispersed Bubble flow
In the dispersed bubble flow pattern, assuming the liquid velocity is relatively high why
the gas velocity is low, it means that the resistance of gas phase is small i.e. small bubbles
will be distributed along the continuous liquid phase which has a velocity rate. Thus, this
will result to no formation of slippage because of both phases travels at the same velocity.
It is seen that the multiphase mixture can also behaves like a homogenous phase, therefore
the mixture density can be calculated as є = λ since no formation of slippage occurred from
the liquid holdup2.
2.7.3 Slug Flow
The slug flow patterns helps to eliminate or diminish the continuous liquid phase present in
bubble and dispersed bubble flow patterns, because the liquid slugs and large bubbles
begins to follow each other in succession. Also, the separation of the Taylor bubbles which
contains in the pipe cross-sectional area are done by the liquid slugs occupying the pipe
cross section, containing small amounts of distributed gas bubbles2.
15
Figure 5. Slug flow pattern2
2.6.4 Transition (churn) flow
In this case, the shear forces destroy both the Taylor bubbles and liquid slugs which are
formed in the slug flow pattern, due to the high rate of gas present which are greater than
in the liquid slug flow and therefore the phase is not continuous.
Moreso, as the liquid slug’s collapses they are lifted by the smaller Taylor bubbles of
discrete shape. The liquid makes or undergoes an oscillatory motion in constant alternating
directions2. Also when there is an increase in gas rates, transition takes place which
eventually leads to the formation of the annular flow, governed by two mechanisms, the
liquid film stability and bridging. This is due to the fact that at low liquid rates, there will
be an increase in gas velocity which stabilizes the liquid film and annular flow can
develop. Also at higher liquid rates, higher gas velocities are needed to overcome the
bridging of the liquid phase and off course results to the annular flow2.
16
Figure 6. Transition (churn) flow pattern2
2.8 Flow Maps
It’s imperative to evaluate the determination of the actual flow pattern, the individual
boundaries of the visually observed flow patterns are usually plotted on so called flow
pattern maps. That is. graphical representations of the ranges of occurrence for each pattern
which is described by different empirical correlations by several researcher, as stated in2,
naming several authors whom were first to propose such map in a vertical flow in oil wells,
by using two dimensional parameter groups given as follows.
𝑁𝑙𝑣 = 1.938𝑣𝑠𝑙 × √𝜌𝑙
𝜎𝑙
4 (2)
𝑁𝑔𝑣 = 𝑣𝑠𝑔 √𝜌𝑙
𝑔𝜎𝑙
4= 1.938𝑣𝑠𝑔 √
𝜌𝑙
𝜎𝑙
4 (3)
The above parameters are called the liquid and gas velocity number, respectively, which
depends on their values according to the2, flow pattern in the figure below.
17
Figure 7. Vertical flow pattern map2
From the figure 7 above, it helps to find out the actual flow pattern irrespective of the
condition involved in the phases. Its also recalled that mechanistic models flow map are
the most comprehensive among the flow maps in a two-phase system. Therefore according
to this work, we will be considering the Aziz-Govier-Fogarasi2. flow pattern map.The
contionous efforts of committed and practising engineers and researcher which has led to
the great improvement of the calculation of pressure drop predictions, can therefore be said
that though not all all emperical mthods have successfully cover all aspects but the areas of
flow pattern maps which has contributed in a wide range of accuracy.
He focused on the bubble and slug flow patterns, but its limitation was the flow pattern
prediction.This flow pattern was based on vertical oil wells for the prediction of the
pressure drop in the multiphase system, its also important to know that our focus and aim
lies on the horizontal pipeline, but for reference and in accordance with every research
which is required to include various works done on the same topic by evaluating and
making corrections in order to suit and fit the present research work model to be able to
achieve it puropose, which is to develop a empirical model bys using the Prosper software,
for a horizontal pipeline transporting heavy oil and to know the basic cuases of the
pressure drop along the flow path. Therefore the basic equation for the Aziz-Govier-
Fogarasi, according to2, flow pattern is given below, where the authors used their own flow
18
pattern map in the figure. The coordinates axes of the map, in contrary to most other maps,
are dimensioned variables as given below2.
𝑁𝑥 = 𝑣𝑠𝑔 (𝜌𝑔
0.00764)
1/3
[(72
𝜎𝑙) (
𝜌𝑙
62.4)]
1/4
(4)
𝑁𝑦 = 𝑣𝑠𝑙 [(72
𝜎𝑙) (
𝜌𝑙
62.4)]
1/4
(5)
Where 𝜌𝑙 = liquid density, lb/cuft,
𝜌𝑔 = gas density, lb/cuft,
𝑣𝑠𝑙 = liquid superficial velocity, ft/s,
𝑣𝑠𝑔= gas superficial velocity, ft/s,
𝜎𝑙 = interfacial tension, dyne/cm.
2.9 Superficial Velocity
In a two-phase flow, the calculation of the velocities of the gas and the liquid particles it’s
of great challenge because of the irregular motion comparing to that of the single-phase
flow, where its estimation is totally different2. In order to calculate the velocities in the
two-phase flow, we employ a special parameter known as superficial velocity, because it
considers the cross-sectional average velocity in a given pipe transporting a fluid fully
occupied with the given phase. Therefore, to do this it’s based on the in situ rate and the
pipe cross-sectional area as given below2.
𝑣𝑠 =𝑞𝑠𝑐𝐵(𝑃,𝑇)
𝐴𝑃 (6)
Also, considering the rate of production at standard conditions, its vital or important to
know the thermodynamic parameters of the phases involved, at the given temperature and
pressures, while the produced water is seen as negligible, the liquid and gas superficial
velocities can now be written and calculated from the following equations2.
𝑣𝑠𝑙 = 6.5 × 10−5 𝑞𝑜𝑠𝑐𝐵𝑜(𝑃,𝑇)
𝐴𝑃 (7)
19
𝑣𝑠𝑔 = 1.16 × 10−5 𝑞𝑜𝑠𝑐[𝐺𝑂𝑅−𝑅𝑠(𝑃,𝑇)]𝐵𝑔(𝑃,𝑇)
𝐴𝑃 (8)
Defining individual parameters
Where 𝑞𝑜𝑠𝑐 = oil flow rate, STB/d
Bo = oil volume factor at pressure and temperature, bbl/STB,
Bg = gas volume factor at pressure and temperature, ft3/scf,
GOR = gas-oil ratio at standard conditions, scf/STB,
Rs = solution gas-oil ratio at pressure and temperature, scf/STB,
Ap = pipe cross sectional area, ft2.
2.10 Gas Slippage
This is the process by which gas overtakes a liquid when they flow together in a vertical or
inclined pipe, due to their different in velocities. It is a basic phenomenon in a two-phase
flow that requires a high standard of understanding. The gas slippage is caused by the
following factors according to2.
The difference in density of gas (light phase) and liquid (dense phase) which
results in force acting on the gas phase leading to an increase in the gas
velocity.
Their energy losses occurring in both phases in the direction of flow which is
less in the gas phase than in the liquid phase. Thus, gas moves faster.
Since pressure decreases in the direction of flow, it therefore means that gas
is incompressible practically, gas expands and takes the shape of the
containing vessel, leading to an increase in its velocity
The above factors facilitate the effects of an increase in gas, relative to that of the liquid
phase. This causes the increase in mixture density, compared to that of the no-slip case,
where the two phase flow at identical velocities. The amount of slippage is governed by so
many factors such as the flow pattern, phase densities, the pipe size, etc.
Finally, the gas slippage is always significant at low liquid rates and diminishes with
increase in liquid rates as frictional pressure drop takes over. This is also describes with the
drift-flux model which, according to2, give the average cross-sectional velocity of the gas
phase in a two-phase mixture as:
20
𝑣𝑔 = 𝐶0𝑣𝑚 + 𝑣𝑏 (9)
Where 𝑣𝑔 = gas velocity, ft/s,
𝐶0 = distribution factor, -,
𝑣𝑚 = mixture velocity, ft/s,
𝑣𝑏 = bubble rise velocity, ft/s.
The distribution factor Co reflects the velocity and concentration distribution over the pipe
cross-section and can attain a value between 1.0 and 1.5. Relative to that, it can be said that
mixture velocity is the sum of individual phase’s superficial velocities. The term Vb
represents the terminal rising velocity of a single gas bubble or swarm of bubbles. It can be
calculated according to2. As
𝑣𝑏 = 1.53√𝑔𝜎𝑙(𝜌𝑙−𝜌𝑔)
𝜌2𝑙
4= 0.79√
𝜎𝑙(𝜌𝑙−𝜌𝑔)
𝜌2𝑙
4 (10)
Where 𝜌𝑙 = liquid density, lb/cuft,
𝜌𝑔 = gas density, lb/cuft,
𝜎𝑙 = interfacial tension, dyne/cm.
Also, the slip velocity between the phases can be calculated from the gas liquid phase
velocities as given below;
𝑣𝑠 = 𝑣𝑔 − 𝑣𝑙 (11)
2.11 Liquid Holdup
In a two-phase flow system, the liquid holdup is calculated based on the actual liquid
content of a pipe section from the given flow rates entering the pipe section. This
parameter is known as the no-slip liquid holdup. It is given by equation 12.
𝜆𝑙 =𝑞𝑙(𝑃,𝑇)
𝑞𝑙(𝑃,𝑇)+𝑞𝑔(𝑃,𝑇) =
𝑣𝑠𝑙
𝑣𝑠𝑙+𝑣𝑠𝑔 =
𝑣𝑠𝑙
𝑣𝑚 (12)
Where 𝜆𝑙 is the liquid holdup.
Considering the sum of the liquid and gas volumes which must be equal to the pipe
sections volumes. Therefore, the relationship of the gas and gas void fraction is introduced.
21
Now, let’s consider a relatively short pipe section containing a flowing two-phase mixture
as given below.
𝜆𝑙 = 1 − 𝜆𝑙 (13)
Also, if the pipe length is decreased to an infinitesimal dl, its ratio approaches to the cross
sectional liquid contact called liquid holdup and it is denoted by the symbol 𝜀𝑙. This applies
to the gas content and gas void fraction 𝜀𝑔2. Employing both phases with a cross sectional
area denoted by Ap𝜀𝑙 and Ap𝜀𝑔 respectively. The actual velocities can now be written as;
𝑣𝑔 =𝑣𝑠𝑔
𝜀𝑔 𝑎𝑛𝑑 𝑣𝑙 =
𝑣𝑠𝑙
𝜎𝑙 (14)
Therefore the gas void ratio and the liquid holdup is also given as
𝜀𝑔 =𝑣𝑠𝑔
𝐶0𝑣𝑚+𝑣𝑏 (15)
𝜀𝑙 = 1 − 𝜀𝑔 = 1 −𝑣𝑠𝑔
𝐶0𝑣𝑚+𝑣𝑏 (16)
Liquid holdup can also be derived from the definition of the slip velocity by substituting
the equation of the gas and liquid phase velocities into the slip velocity, we get
𝑣𝑠 =𝑣𝑠𝑔
1−𝜀𝑙−
𝑣𝑠𝑙
𝜀𝑙 (17)
Therefore the above equation can be solved for liquid holdup 𝜀𝑙
𝜀𝑙 =𝑣𝑠−𝑣𝑚+√(𝑣𝑚−𝑣𝑠)2+4𝑣𝑠𝑣𝑠𝑙
2𝑣𝑠 (18)
The liquid holdup, calculated from either equation (5) and (7), includes the effect of gas
slippage and must therefore always be greater than or equal to the no-slip liquid holdup, ie
1 ≥ 𝜆𝑙, this indicates the difference in magnitude of the actual gas slippage. The value of
the 𝜀𝑙 gives the proportion of the pipe cross-section occupied by the liquid phase in the
flowing two-phase mixture2. If the liquid holdup is known, the two-phase mixture density
can be easily calculated which is the main purpose of this research.
2.12 Mixture Properties
The mixture properties in a two-phase flow help to evaluate and facilitate the solutions of
the vital and relevant equations, which describes the behaviour of two-phase flows. In this
case, the calculation of the individual parameters is based on the thermodynamics
properties of the fluids such as mixture density and viscosity. Therefore two-phase mixture
22
density can understand the densities of the phases and the liquid holdup respectively. The
calculation can be done from the liquid holdup and no-slip mixture density2.
𝜌𝑛𝑠 = 𝜌𝑔𝜆𝑙 + 𝜌𝑔𝜆𝑔 (19)
Or a density including the effect of gas slippage
𝜌𝑚 = 𝜌𝑔𝜀𝑙 + 𝜌𝑔𝜀𝑔 (20)
Also, it important to note that the above equations actually depends on the temperature and
pressure valid at the given pipe section, assuming the water flow rate is zero, and then the
liquid density equals the in situ density of the oil phase. Finally, in order to analyse the
situation, the equation below is considered when the effects of the dissolved gas in the oil
phase is included;
𝜌𝑜 =350.4𝛾𝑜+0.0764𝛾𝑔𝑅𝑠(𝑃,𝑇)
5.61𝐵𝑜(𝑃,𝑇) (21)
The gas density is also determined as shown,
𝜌𝑔 = 2.7𝛾𝑔𝑃
𝑍𝑇𝑎 (22)
Where γo = specific gravity of oil,
γg = specific gravity of gas,
Ta = absolute temperature, R,
Z = gas deviation factor,
Rs = solution gas-oil ratio at pressure and temperature, scf/STB,
Bo = oil volume factor at pressure and temperature, bbl/STB.
Similarly, the calculation of the mixture viscosity is done in the most common way, by
using the no-slip holdup equation2.
𝜇𝑛𝑠 = 𝜇𝑙𝜆𝑙 + 𝜇𝑔𝜆𝑔 (23)
Another frequently applied expression is given as
𝜇𝑚 = 𝜇𝜀𝑙𝑙𝜇𝜀𝑔
𝑔 (24)
Therefore, the viscosity can now be calculated from this equation;
𝜇𝑚 = 𝜇𝑙𝜀𝑙 + 𝜇𝑔𝜀𝑔 (25)
Where: 𝜇𝑙= liquid viscosity at pressure and temperature, cP,
𝜇𝑔= gas viscosity at pressure and temperature, cP.
23
2.13 Multiphase flow
It’s said that the most of the pressure drop calculation of a horizontal pipeline models were
developed for two discrete phases, usually liquid and gas, therefore called two-phase flow
methods. Let’s consider a phase where there is pure oil or water but a mixture of oil and
water. We apply the mixing rule in order to evaluate the actual flow rates of the
components. If the flowing is a mixture of oil and water, then the superficial velocities of
the liquid and gas phases are determined by the following equations below2:
𝑣𝑠𝑙 = 6.5 × 10−5 𝑞𝑙𝑠𝑐
𝐴𝑝[𝐵𝑜(𝑃, 𝑇)
1
1+𝑊𝑂𝑅+ 𝐵𝑤(𝑃, 𝑇)
𝑊𝑂𝑅
1+𝑊𝑂𝑅] (26)
𝑣𝑠𝑙 = 1.16 × 10−5 𝑞𝑙𝑠𝑐
𝐴𝑝[𝐺𝐿𝑅 − 𝑅𝑠(𝑃, 𝑇)
1
1+𝑊𝑂𝑅] 𝐵𝑔(𝑃, 𝑇) (27)
Defining the each individual parameter of the above both equations:
Where: 𝑞𝑙𝑠𝑐 = liquid flow rate, STB/d,
𝐵𝑜 = oil volume factor at pressure and temperature, bbl/STB,
𝐵𝑤= water volume factor at pressure and temperature, bbl/STB,
𝐵𝑔 = gas volume factor at pressure and temperature, ft3/scf,
GLR = gas liquid ratio at standard conditions, scf/STB,
𝑅𝑠 = solution gas-ratio at pressure and temperature, scf/STB,
WOR = water-oil ratio at standard conditions, -,
𝐴𝑝 = pipe cross sectional area, ft2.
More so, in a multiphase flow system, the thermodynamic parameters, density and
viscosity of the liquid phases are always found as already explained above in the previous
sections of this literature. This approach has its limitation since oil-water mixtures may
behave very differently from this assumption. But we know that liquid density is always
affected by oil slippage, a phenomenon which has the same properties compare to that of
the gas slippage, where the lighter oil particles overtakes the denser (heavier) water phase.
Due to this fact, it’s said to be that mixture density increases beyond the value calculated
from a mixing rule. The viscosity of oil-water mixture may sometime exhibit non-
Newtonian behaviour, if the emulsion is formed. Its density can be calculated from the
expression below, with regards to the above limitation2.
24
𝜌𝐿 = 𝜌𝑂𝑊𝑂𝑅
1+𝑂𝑊𝑅+ 𝜌𝑤
1
1+𝑊𝑂𝑅 (28)
Then the actual density of formation water is found from its specific gravity and volume
factor:
𝜌𝑤 =350.4𝛾𝑤
5.61𝐵𝑤(𝑃,𝑇)=
𝛾𝑤
𝐵𝑤(𝑃,𝑇) (29)
2.14 Pressure Gradient Equations
The pressure gradient equations focus on the most challenge which is the calculation of the
pressure distribution along the pipeline, which is the aim of this research. This is due to the
pipe complexity of the flow phenomena in any of the flow patterns and the existence of
many flow patterns.
However, it is difficult to analyse the differential equations, the conversation of mass and
momentum, because it applies to both phases of the flow. In order to overcome this
challenge, the consideration is that the multiphase flow mixture is treated as a homogenous
fluid and which helps to write up the General Energy (Bernoulli) equation for the particular
hypothetical phase2. This equation helps to describe the conversation of energy between
two points (lying close to each other) in an inclined pipe; this can be solved by the function
of the pressure gradients equations.
Also, different pressure drops empirical correlations models from previous research work
will be investigated, which will be compared and help to derive our model for the
calculation of the pressure drop along the pipeline, with a given parameters such as the
flow rates, length and pipe sizes.
𝑑𝑝
𝑑𝑙=
𝑔
𝑔𝑐𝜌𝑚 sin 𝛼 + (
𝑑𝑝
𝑑𝑙)
𝑓+
𝜌𝑣𝑑𝑣𝑚
𝑔𝑐𝑑𝑙 (30)
Where α = pipe inclination angle, measured from the horizontal, radians
Note that in a vertical pipe α = 90 and sin α =1.0, hence dl = dh, and the above equation
can be rewritten in function of the vertical distance h as
𝑑𝑝
𝑑𝑙=
𝑔
𝑔𝑐𝜌𝑚 + (
𝑑𝑝
𝑑ℎ)
𝑓+
𝜌𝑣𝑑𝑣𝑚
𝑔𝑐𝑑ℎ (31)
25
It is clearly seen from the above equations the pressure gradients dp/dl or dp/dh is
composed of three terms describing the different kinds of energy changes occurring in any
pipe. Also, among all the second serves as most focused because, it’s irreversible pressure
losses are due to the fluid friction, which is conveniently expressed with the Darcy-
Weisbach equation helped by the friction factor.
(𝑑𝑝
𝑑𝑙)
𝑓= 𝑓
𝜌2𝑣
2𝑔𝑐 (32)
Where f = friction factor, -,
gc = 32.2 a conversion factor, -,
d = pipe diameter, in.
From equation (32), the friction factor f, is a function of the Reynolds number NRe and the
pipes relative roughness and is usually determined from the moody diagram. Therefore, the
most important component of the pressure gradient is listed according to their relative
importance for an inclined and a vertical pipe, respectively, using the field measurements.
The hydrostatic components represent the change in potential energy in the multiphase
flow due to the gravitational force acting on the mixture. This is usually found from the
mixture density which includes the effect of the slippage. As discussed already, the
mixture density from equation 19, and the frictional components represents the
irreversible pressure losses in the second term from the equations above, occurring in the
pipe due to fluid friction on the pipe inner wall.
26
3 Empirical correlations for pressure drop calculations
Empirical two-phase pressure drop correlations were first classified by Orkiszewski a
scientist, who indicated the flow patterns that is, the effective of the differential spatial
arrangements of two phases.
However, several research and consideration have been investigated and also carried out to
finalise the most important empirical correlations needed for the determination of pressure
drop in transportation of heavy oil. Therefore, for the purpose of this work, we should be
considering the following correlations which are in relations with the PROSPER software
used for the calculations:
Beggs-Brill correlation
Fancher Brown correlation
Mukherjee-Brill correlation
3.1 Beggs-Brill
The Beggs-Brill correlation is based on gas-liquid flow in inclined pipes, which he
investigated and determine the erect of pipe inclination angle or liquid holdup and pressure
losses5. He concentrated his correlation for liquid holdup and friction factor in order to
predict pressure gradients for two-phase flow in horizontal pipes at an angle for many flow
pressure gradients for two-phase in pipes at all angles for any conditions.
The begs-brill basic equation is derived and written up with the pipe length, L instead of
vertical depth coordinate because of the pipe is considered to be inclined. Also they took
into account all three components of the multiphase pressure drop; that is the elevation,
friction, and acceleration which can also be the kinetic term5:
𝑑𝑝
𝑑𝑙 =
(𝑑𝑝
𝑑𝑙)
𝑒𝑙+ (
𝑑𝑝
𝑑𝑙)
𝑓
1−𝐸𝑘 (33)
They express the component of the pressure gradients as:
(𝑑𝑝
𝑑𝑙)
𝑒𝑙=
1
144𝜌𝑚 sin 𝛼 =
1
144 [𝜌𝑙𝜀𝑙(𝛼) + 𝜌𝑔(1 − 𝜀𝑙(𝛼))] sin 𝛼 (34)
(𝑑𝑝
𝑑𝑙)
𝑓 = 1.294 × 10−3 𝑓
𝜌𝑛𝑠 𝑉2
𝑚
𝑑 (35)
27
Ek = 2.16 × 10−4 𝑣𝑚 𝑣𝑠𝑔𝜌𝑛𝑠
𝑃 (36)
Where: 𝜌𝑚 = mixture density, lb/cu ft,
𝜌𝑛𝑠 = no-slip mixture density, lb/cu ft,
𝜀𝑙(𝛼) = liquid holdup at an inclination angle of 𝛼, -,
𝛼 = pipe inclination angle, measured from the horizontal, rad,
f = friction factor, -,
𝑣𝑚 = mixture superficial velocity, ft/s,
𝑣𝑠𝑔= gas superficial velocity, ft/s,
p = pressure, psi,
d = pipe diameter, in.
3.1.1 The flow patterns
In the Beggs-Brill correlation, flow patterns are determined for horizontal flow only, using
empirically developed flow pattern map. Since this map is valid for horizontal flow only,
actual flow patterns in inclined or vertical cases cannot be predicted2. In this approach,
flow pattern is a correlating parameter only and does not indicate the actual flow pattern.
Therefore, two parameters were used to describe the horizontal flow patterns transitions,
that is, the no-slip liquid holdup 𝜆𝑙, and Froude number 𝑁𝐹𝑟 , which is defined belwo2:
𝜆𝑙 = 𝑣𝑠𝑙
𝑣𝑚 (37)
𝑁𝐹𝑟 =𝑣2
𝑚
𝑔𝑑= 0.373
𝑣2𝑚
𝑑 (38)
Where; 𝑣𝑠𝑙= liquid superficial velocity, ft/s,
𝑣𝑚= mixture superficial velocity, ft/s,
d = pipe diameter, in.
28
Figure 8. Flow pattern map of Beggs-Brill5
The Figure 8, above depicts the modified flow pattern map of the Beggs-Brill correlation,
designated for horizontal flow patterns and indicated the different boundaries of the flow
patterns as shown in the map.
3.2 Mukherjee-Brill
This correlation is developed for all pipe inclination angles, where they considered two set
of empirical equations, one each for uphill and downhill flow. Also it’s the first correlation
to consider the change of flow patterns with pipe inclination, using a large experimental
data base, covering the uphill and downhill flow patterns6.
The liquid holdup equation is a function of dimensionless liquid and gas velocity numbers
in addition to liquid viscosity number and angle of inclination. The mentioned parameters
defined the flow pattern transition uniquely in inclined two-phase flow.
3.2.1 Phase Slippage and liquid holdup
In an inclined two-phase pipe flow, a substantial part of the total pressure drop losses
maybe contributed by the hydrostatic pressure difference. The relative contribution of
friction gradient and hydrostatic gradient may be dictated by the prevailing flow patterns,
angle of inclination, and direction of flow6.
29
Base on their assumptions that the void fraction is a unique fraction of quality and physical
properties of the fluids. This is probably true where homogenous flow can be assumed or
during bubble flow at very low gas flow rates. Similar situations may also arise where the
phase velocity is very high, so that friction pressure drop governs the total pressure loss.
The concept of slip velocity comes from the physical phenomenon called slippage, which
is used to describe the natural phenomenon of one phase slipping past the other in two-
phase pipe flow. There are several causes for slippage between phases, frictional resistance
to flow or irreversible energy losses in the direction of flow are much less in the gas phase
than in the liquid phase.
3.2.2 Development of liquid holdup calculation
Several liquid holdup measurements at uphill and downhill inclination angles from 0 to ±
90 from horizontal were obtained accordingly6. In correlating this data, at each uphill and
downhill angle void fraction was plotted as a function of superficial gas velocity for fixed
superficial liquid velocity. The basic equation of the Mukherjee-Brill correlation is stated
as6:
𝐻𝑙 = 𝑒𝑥𝑝 [(𝑐1 + 𝑐2 sin 𝜃 + 𝑐3𝑠𝑖𝑛2𝜃 + 𝑐4𝑁2𝑙)
𝑁𝑐𝑠𝑔𝑣
𝑁𝑐6𝑙𝑣
] (39)
Where: 𝐻𝑙 = liquid hold up, -,
C = empirical constant, -,
Ngv = gas velocity number. 𝑣𝑠𝑔 = [𝜌𝑙
(𝑔𝜎)]
0.5
,
g = gravitational acceleration, ft/sec2,
𝑁𝑙 = liquid viscosity number, 𝜇𝑙 = [𝑔
(𝑝𝑙𝜎3)]
0.5
.
3.2.3 Effects of Inclination and Viscosity
The begs-brill correlation focuses basically on the liquid hold up, relating the importance
on the flow which passes through maximum and minimum at fixed inclination angles of
approximately +50 and -50 respectively6. The second degree polynomial function of the
form 𝑐1 + 𝑐2 sin 𝜃 + 𝑐3𝑠𝑖𝑛2𝜃 was selected by plotting liquid holdup for different angles of
inclination at a fixed liquid and gas velocity numbers6. This relation was also confirmed by
comparing results of other equation forms in trial runs of the regression analysis.
30
3.3 Fancher Brown
The Fancher Brown correlation was chosen in this work based on the fact that the Prosper
software acknowledges its importance in the vertical flow; therefore it established a
pressure traverse by using a 23/8𝑖𝑛 outside diameter tubing for varying liquid flow rates as
produced with varying gas liquid rate7. It was further intended to establish the reliability of
known methods for calculating pressure traverses.
Another objective of this correlation was to obtain sufficient pressure traverse data to allow
accurate prediction of the pressure traverse in 2in tubing for vary liquid flow rates, and for
any gas-liquid ratio in the range of the test carried out7.
3.3.1 Methods of Predicting Pressure Gradient
The Fancher-Brown used the method of measured data from previous different 49 wells,
34 flowing wells and gas-lift wells to predict the pressure gradients, which they related to
the Poettmann and Carpenter correlation, covering only a limited range of flow rates and
gas liquid ratios. The basic equation was derived from the irreversible energy-loss term,
evaluated by back calculation using the field data to determine the pressure gradients from
the following equation.
𝑓 = 7.413 × 1010𝜌𝑑5 × [𝑑𝑝
𝑑𝐻] − 𝜌𝑣𝑞2 × 𝑚2 (40)
Where f = fanning type friction factor,
𝜌 = Flowing density, lb/ft3
𝑑𝑝
𝑑𝐻= Pressure gradient, Psi/ft,
q = oil flow rate, bbl/day,
d = diameter of pipe, ft.
31
1.4737× 10−5 𝑚𝑄/𝐷7
Figure 9. Back calculated friction factor7
The figure above shows that the funning-type friction factor was plotted against the
Reynolds number. Also, that the scattering points in this correlation suggests that an
important parameter was neglected according to the Fancher-Brown correlation7.
32
4 Investigation of a transportation problem
The transportation problem was investigated by using the dilution method whereby the
base oil was diluted with a condensate. The effect of the used empirical method, the
condensate concentration and the pipe diameter on the pressure gradients along the pipe
were investigated using the PROSPER software. The best correlation with best fit for the
prediction of the pressure drop will be selected for the subsequent calculations and
investigations for the purpose of this research because of its accuracy in predicting the
pressure gradients for two-phase flow in horizontal pipes.
In addition, series of calculations were done using the PROSPER software in order to
determine the best results whereby different pipe diameters in 3 different situation and
percentage of condensate viscosities and known densities were used, helping to investigate
the behaviour of the pressure gradients along the pipe length with the effects of the
surrounding temperature, thereby making the oil more viscous to flow.
4.1 Statement of problem
A 2000 meter long pipe transporting heavy oil in a horizontal direction and was not
subjected to a flow test.
A PROSPER model is built.
The data was not matched.
An empirical correlation model is chosen to predict the GOR values along the
pipe in respect to the base oil, condensate concentration and an increase in pipe
diameter sizes in order for the reduction of pressure drop.
4.1.1 Fluid Pvt Data
Table 1: The available Pvt Data used in the calculation
Solution GOR 0, 100, 200, 300, 400, 500 scf/stb
Gas Gravity 0.8
Density Table 3.
Viscosity Figure 9.
Water salinity 0
Impurities (CO2, N2, H2S) None
Bubble Point Pressure 2500 psig at 200 °C
Bo 1.214 rb/stb
33
4.1.2 Pipeline Data
Table 2: The pipeline data
Parameter Value
Pipeline Length 2000 meter
Pipeline internal diameter 3.548 in, 4.026 in, 4.506 in
Pipeline inside roughness 0.0006 in
Temperature of surroundings 10 °C
Over heat transfer coefficient 7 BTU/h/ft2/F
Total pipe height above origin 0 ft
Fluid inlet temperature 50 °C
4.1.3 Measured viscosities
The measured viscosities of the base and condensate concentration
Figure 10. Measured viscosity values
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 10 20 30 40 50 60 70 80
Din
am
ic V
isco
sity
[cP
]
Temperature [°C]
10% concentration
20
30
40
50
66
0
34
4.1.4 Measured Density
Table 3: shows the different calculated densities used in the pipe diameters.
Density (kg/m3)
Base 905
10% 889.84
20% 874.68
30% 859.52
40% 844.36
50% 829.2
66% 804.94
4.1.5 Calculated density
Figure 11. Shows the graphical representation of the temperature dependency of the
density
4.2 Calculation and Results
The PROSPER software is used to calculate the following and to estimate the correlation
needed for the pipeline design and determining the pressure gradients:
The effect of the used empirical method.
The Base oil on different pipe diameter sizes.
The effects of the condensate concentration on the pressure drop using three
different concentrations.
The effects of the different pipe diameter sizes on the pressure drop.
The effect of the GOR on the pressure drop.
The effect of economic considerations.
700
750
800
850
900
950
1000
0 20 40 60 80 100
Den
sity
, k
g/m
3
Temperature, ͦͦC
35
4.2.1 Effect of the used empirical method
In this case, the used empirical method will be able to predict the best correlation after
investigating their effects on the pressure drop, using base oil with a 3.548in pipe diameter
and a 20% condensate concentration with a 4.026in pipe diameter size.
Case 1.
Figure 12. 0% condensate of 3.548 in pipe diameter of beggs-brill correlation.
The Figure 12. above showed a solution of the Beggs-Brill correlation whereby as the
GOR values increases along the pipeline, the pressure drop is reduced with the effect of the
diameter and surrounding temperature.
Case 2.
The Francher-Brown correlation is shown below in Figure 13, proved to be similar
solutions compared to that of the Beggs-Brill correlation. The GOR values are seen as they
increase along the pipe length with same pipe diameter of 3.548 in, as the pressure drop
reduces.
36
Figure 12. 0% condensate of 3.548in pipe diameter of Fancher-Brown correlation.
Also the correlation above showed that the surrounding temperature along the pipe is
increased.
Case 3.
Figure 13. 0% condensate of 3.548 in, pipe diameter of Mukherjee-Brill
correlation.
In this case, the Mukherjee-Brill correlation only showed the solution of the pressure drop
and the surrounding temperature along the pipeline, why the values of the GOR could not
be estimated, and does not give an accurate or similar result compared to the already
discussed correlations above.
37
Case1
Figure 14. 20% condensate of 4.026in pipe Beggs-Brill correlation.
As it is clearly seen in the Figure 14 above, the solution from the correlation showed the
same with pressure drop continuously reducing in a similar way compared in the previous
pipe diameter of 3.548in. The GOR values are clearly seen and continue to decrease along
the pipeline effecting the pressure reduction.
Case 2
Figure 15. 20% condensate of 4.026in pipe Fancher-Brown correlation.
The Fancher-Brown correlation also showed a similar solution but with a slight difference
when used with same condensate and pipe diameter as seen in the Beggs-Brill correlation.
The GOR values are also seen clearly.
Case 3
38
Figure 16. 20% condensate of Mukherjee-Brill correlation.
The Mukherjee-Brill correlation also showed the same solution as in the previous case of
3.548in pipe diameter even when the condensate concentration is increased, the GOR
values cannot be estimated along the pipe length but predicting only the pressure drop, and
however will not be considered as a good correlation in the subsequent investigations.
Therefore, the Beggs-Brill correlation is chosen to be used for the subsequent calculations
and investigation of the pressure drop because of its accuracy and similar solution to the
Fancher-Brown correlation. Its GOR values solution fits to what is expected in the design
and transportation of the crude.
.
4.2.2 The Effect of condensate concentration on the pressure
The effect of condensate concentration on how they affect the pressure drop along the
pipeline will be investigated by using the following scenario
Base oil with 0% condensate concentration of 3.548in pipe
10% Condensate concentration of 3.548in pipe.
30% condensate concentration of 3.548in pipe.
66% condensate concentration of 3.548in pipe.
39
Case 1
Figure 17. 0% condensate concentration of 3.548in pipe.
From Figure 17 and with a zero percent condensate, the outcome of the simulated results
for the pressure drop was higher than that observed for the case of 10% condensate
concentration as indicated in Figure 18 below. Additionally, sensitivity for the effect of an
increase in GOR was done and the results shown in Table 4 below. As can be seen from
Figure 17, an increase in GOR results in a corresponding increase in pressure drop along
the pipeline due to the additional mass of the gas phase. Ultimately, lesser outlet pressures
are obtained when the GOR increases.
Case 2
Figure 18. 10% condensate concentration on 3.548 in pipe.
40
Figure 18 indicates that the addition of the condensate concentration to the base oil results
in a decreased pressure drop along the pipeline. Sensitivity for increasing GOR values was
done and Table 5 shows the results from the calculation.
Case 3
Figure 19. 30% condensate concentration of 3.548in pipe
The effect of an increase in concentration is a decrease in density of the oil. This produces
a reduction in pressure required to initiate fluid flow. Figure 19 shows the result of
pressure drop for 30% condensate concentration. In comparison with the previous two
scenarios, much lower pressure drop values were recorded for 30% condensate
concentration and this result in higher outlet pressure even at increasing GOR values.
Case 4
Figure 20. 66% condensate concentration of 3.548in pipe
41
With the addition of 66% condensate to the base oil, the pressure drop reduction was
maximal and the changes in pressure drop with increasing GOR cannot be easily
interpreted from the inlet to the outlet. The transportation of this oil will be faster than in
all previous cases. Results of the simulation can be found in Table 8 of the appendix.
4.2.3 The effect of diameter on the pressure
The effect of the diameter on the pressure drop along the pipeline transportation of the
crude is investigated using different pipe diameters sizes and the Base oil in three different
cases, such as:
Base oil with a 3.548in pipe diameter.
Base oil with a 4.026in pipe diameter.
Base oil with a 4.506in pipe diameter.
Case 1
Figure 21. 0% condensate concentration of 3.548in pipe.
The size of the pipe diameter determines and influences the pressure drop such that the
pressure drop decreases with an increase in pipe diameter. However, the reduction of the
pressure from 65bars to 34.54bar for the case of 0 scf/STB GOR, is as a result of high
density of the oil is and it can only be optimized by the addition of the condensate or an
increase in temperature of the surrounding.
42
Case 2
Figure 22. 0% condensate concentration of 4.026 in pipe.
In Figure 22 above, as it is clearly seen, the outlet pressure is reduced from 32.5bar to
48.75bar for the 0 scf/STB case. This is as a result of an increase in the pipe diameter, with
same base oil and comparing it to the previous case of 3.548 in size pipe. The values of the
GOR between the first and second are almost the same but with a slight different.
Case 3
Figure 23. 0% condensate concentration of 4.506 in pipe.
Similarly, Figure 23 shows a much reduced pressure drop for a 4.026 in pipe. Outlet
pressure values between 48.75bar to 55.42bar were observed for the range of GOR
investigated. This emphasizes that larger the pipe diameter the smaller the pressure losses.
43
4.2.4 Calculation summary
4.2.4.1 Comparison of the pressure drop results between the base and condensate
concentration.
Table 4. The pressure drop difference for the Base oil
Crude
Sample
Pipe Size
(in)
GOR Outlet
Pressure(bar) 𝑑𝑝 = 𝑝𝑖𝑛 − 𝑝𝑜
( bar)
Base Oil (0%
Condensate)
3.548 0 54.7604 7.239
100 53.6203 11.379
200 49.5016 15.498
300 45.568 19.432
400 42.1688 22.831
500 37.6758 27.324
4.026 0 58.8867 6.113
100 58.525 6.47
200 55.8594 9.1406
300 53.625 11.375
400 51.9742 13.0258
500 50.1109 14.889
4.506 0 61.0594 3.940
100 60.891 4.109
200 59.231 5.769
300 57.310 7.769
400 56.7845 8.2155
500 55.7882 9.2118
From Table 4 above it is clear that the pressure drop along the pipe length was influenced
mostly by the pipe diameter. The larger diameter recorded a lower pressure drop compared
to others, and the investigation was done using the base oil.
However, from this we will investigate and record the pressure drop along the pipe length
and see how the condensate and different pipe diameters sizes will affect the reduction of
the pressure drop.
44
Table 5. Pressure difference of condensate concentration
Crude Sample Pipe Size
(in)
GOR Outlet
Pressure(bar) 𝑑𝑝 = 𝑝𝑖𝑛 − 𝑝𝑜
( bar)
Condensate
concentration
(10%)
3.548 0 55.4612 9.538
100 54.9313 10.068
200 50.8607 14.139
300 47.5366 17.139
400 44.2358 20.764
500 40.4352 24.564
4.026 0 59.3531 5.646
100 59.1235 5.876
200 56.5912 8.408
300 54.8122 10.187
400 53.0959 11.904
500 51.3495 13.6505
4.506 0 61.5489 3.451
100 61.2309 3.769
200 59.8110 5.189
300 58.6010 6.399
400 57.5859 7.414
500 56.5906 8.409
4.2.5 The effects of economic evaluation
The economic evaluation of facility investment is one of the most critical tasks involve in
the conceptual phase in pipeline transportation of heavy oil. Due to the commitment of
resources spending when a decision is made. Also, the evaluation also involves cash flow
considering all capital requirements and revenues, which includes the following analytical
steps8;
i. Project planning.
ii. Construction of pipeline cost.
iii. Projection of all expenditure and revenues.
iv. Cash flow that is maximization of profits.
However, the above mentioned should be properly considered and the availability pipeline
protection and creation of awareness during the design should be stated out in the chosen
area. The essential element of economic evaluation is project cash flow analysis which is
the profits and the purpose of any embarking projects. Therefore, these require quantifying
all monetary items and extend of the project, because all expenditure and revenues should
be encountered for the analysis in forms of quantity and within the estimated time or
prediction period.
45
As the values of the GOR reduces in table 5, the pressured drop along the pipe also
reduced. The pipe with large diameter sizes recorded lower pressure drop and the
condensate concentration has an effect on the base oil compared to the pressure drop
values as seen in table 4.
46
5 Conclusion and Recommendations
The major problem in transporting heavy oil is the high viscosity effects which results to
pressure drop along the pipeline. Several methods of viscosity reduction were analysed
such as the dilution and emulsion methods. The minimization of cost, availability of
diluents and surrounding temperatures and the conditions, the distance the oil is to be
moved. The importance of two-phase flow, choice of design of the pipeline and its
economic evaluation were discussed.
A Prosper model was built and a correlation chosen to calculate the pressure drops in a
horizontal pipeline of 2000 m. This was determined by series of investigations using the
base oil, condensate concentrations, different pipe diameters, the GOR values and
surrounding temperatures which influences the rate of pressure drop along the pipeline.
The solution to the transportation problem can be solved by using different cases as
discussed earlier:
Since size of the pipe diameter determines and influences the pressure drop
such that the GOR values can increase constantly in a large pipe diameter.
However, the loss of the pressure from 65bars to 34.54bar is as a result of high
viscosity of the oil which produces a high pressure loss but with an addition of
condensate and an increase in the pipe diameter from 3.548 in to 4.026 in and
temperature of the surrounding. Therefor the pressure drop is 30.46bars.
In Figure 22 above, the outlet pressure is increased from 32.5bar to 48.75bar,
which is 16.25bars pressure drop reduction. This is as a result of an increase in
the pipe diameter of 4.026 in, with same base oil and comparing it to the
previous case of 3.548 in size pipe where the pressure drop was 32.5bars.
With an increase of pipe diameter of 4.506 in and 50% condensate
concentration addition to the base oil, the pressure drop reduction was maximal
and was 63.395bars.
A large pipe diameter size of either 4.026in or 4.506in and approximately 30%
to 40% condensate concentration, should be considered during design and
evaluation of cost and markets demand, because the outlet pressure is increased
to 58.826bars and 61.506bars respectively compared to the base oil flowing in
the 3.548 in pipe.
47
The addition of 30% condensate concentration to the base oil with a pipe
diameter of 3.548 in showed a slight pressure drop difference of 55.0875bar to
55.1281bars.
For a very long pipeline transporting heavy oil, the dilution or emulsion method
might be a better choice, as heating the pipeline might require larger investment
and cost. Also the emulsion method provides more stability over a long period
of time.
Recommendation
In pipeline transportation of heavy oil, the minimization of the cost of design, the
availability of the diluents for the reduction of viscosity, the soil temperatures and the
conditions, the distance the oil is to be moved should be considered. A large diameter pipe
size should be used, because the larger the size, the smaller the pressure drop and the
market demand should be a factor in considering the investment cost in order to maximize
profits.
48
6 References
1. Moreau, B.L. The pipeline transportation of heavy oils. Heavy oil seminar, the
petroleum society of C.I.M, Calgary, May 5, 1965, P. 252
2. Takacs, G. Ph.D (2012.): Production engineering fundamentals vol 1., University of
Miskolc. pp.:33-61.
3. Guevara, E. et al, Core Annular flow: the most economical method for the
transportation of viscous hydrocarbons, the 4th Unitar, Aug 1985, 5 (194), P 531
4. D. Escojido. Maraven S.A. transportation of heavy crude oil and natural bitumen.
Part 1, Lagunillas, Estado Zulia, Venezuela. P.
5. B.H Beggs (U. of Tulsa) J.P (U.of Tulsa) A study of two-phase flow in inclined
pipes, Society of Petroleum Engineers, Journal of Petroleum. May 1973, vol 25.
6. Hermanta Mukherjee, and James .P. Brill, Liquid holdup correlations for inclined
two-phase flow, Society of Petroleum Engineers. Johnston-macco Schlumberger.
May 1983.
7. George .H. Fancher and Kermit .E. Brown, Prediction of pressure gradients for
multiphase floe in inclined pipes, Society of Petroleum Engineers, The U of Texas,
Austin, and March 1963.
8. Hyung-Jin Kim. An economic evaluation system for building construction projects
in the conceptual phase. Department of Research and development, Kunwon
Engineering Co. Ltd, Seoul, Kina 2004.
49
7 Acknowledgment
I would like to express my deepest appreciation to God almighty for his grace and love, my
advisor, Dr Zoltán Turzó and László Kis for their unwavering support, guidance and the
great opportunity to work with them. Their constant approaches in making sure this work
was concluded and great efforts to my thesis, without them and persistent help this
research would not have been possible.
A special thanks to László Kis for his support with computer software which made a
valuable contribution to my thesis. Thank you so much, I’m really grateful.
I would also say a special thank you to my family, relatives and friends for always
inspiring, supportive and for believing in my future.
Finally, I would like to say a big thank you to the University of Miskolc, academic staffs of
the Petroleum Engineering Department, for always been there and making sure that all that
is needed is made available during the period of my study here.
50
8 Appendices
APPENDIX A
Table 6. Pressure difference of condensate concentration
Crude Sample Pipe Size
(in)
GOR Outlet
Pressure(bar) 𝑑𝑝 = 𝑝𝑖𝑛 − 𝑝𝑜
( bar)
Condensate
concentration
(20%)
3.548 0 55.0489 9.951
100 54.7016 10.298
200 52.6215 12.378
300 47.4094 17.590
400 43.941 21.059
500 39.9344 25.065
4.026 0 59.0281 5.971
100 58.7539 6.246
200 58.2285 6.771
300 54.7569 10.243
400 52.9344 12.065
500 51.0047 13.995
4.506 0 61.3438 3.656
100 60.9874 4.012
200 60.6556 4.344
300 58.5625 6.437
400 57.525 7.475
500 56.5094 8.490
APPENDIX B
Table 7. Pressure difference of condensate concentration
Crude Sample Pipe Size
(in)
GOR Outlet
Pressure(bar) 𝑑𝑝 = 𝑝𝑖𝑛 − 𝑝𝑜
( bar)
Condensate
concentration
(30%)
3.548 0 55.1094 9.890
100 54.8844 10.481
200 54.5187 10.481
300 48.3482 16.651
400 45.0531 19.946
500 41.3734 23.626
4.026 0 58.9875 6.012
100 58.8632 6.136
200 58.6625 6.337
300 55.2681 9.731
400 53.4203 11.579
500 51.6783 13.321
4.506 0 61.1812 3.818
100 61.1002 3.899
200 60.8835 4.116
300 58.8553 6.144
400 57.8104 7.189
500 56.7245 8.275
51
APPENDIX C
Table 8. Pressure difference of condensate concentration.
Crude Sample Pipe Size
(in)
GOR Outlet
Pressure(bar) 𝑑𝑝 = 𝑝𝑖𝑛 − 𝑝𝑜
( bar)
Condensate
concentration
(66%)
3.548 0 64.4719 0.528
100 64.4512 0.548
200 64.4403 0.559
300 64.4313 0.568
400 64.2271 0.772
500 64.1129 0.887
4.026 0 64.7969 0.203
100 64.7571 0.242
200 64.7462 0.253
300 64.6982 0.301
400 64.4948 0.505
500 64.3906 0.609
4.506 0 64.9986 0.0014
100 64.9974 0.0026
200 64.9965 0.0035
300 64.9913 0.0087
400 64.6871 0.312
500 64.6674 0.332
