Investigation of the Static Pressure Drop and Production that Occurs
due to Flow Patterns in a Perforated Horizontal Wellbore
HASANAIN J. KAREEM1, HASRIL HASINI1, MOHAMMAD A.ABDULWAHID2
1Mechanical Engineering,
University Tenaga Nasional,
MALAYSIA
2Thermal Mechanical Engineering,
Southern Technical University,
IRAQ
Abstract: - This study examined the intricate interaction between flow patterns and production within a
perforated horizontal wellbore. The study precisely assessed the behavior of static pressure drop by utilizing an
array of flow regimes encompassing bubble, dispersed bubble, transitional bubble/slug, slug, stratified,
transitional slug/stratified wave, and stratified wave. Remarkably, an upward trend in static pressure drop was
observed with increasing water phase presence, while the converse was true for the air phase. Besides, the air
phase superficial velocity exhibited a direct correlation with the magnitude of pressure drop fluctuations. The
liquid production demonstrated a peak during bubble and slug flow regimes, followed by a descent during the
transition to stratified and stratified wave flow. This decline can be attributed to mixing pressure drops
localized during the perforations. Furthermore, an upward trend in average liquid production was observed with
increasing mixture superficial velocity, primarily due to the dominant presence of the water phase.
Additionally, the percentage of liquid production was positively associated with the water's superficial velocity
when the air's superficial velocity was held constant. While the experimental and numerical results were in
agreement for slugs and structured flows, there were discrepancies in the behavior of static pressure for
bubbles, small bubbles, and structured waves.
Key-Words: - flow patterns, static pressure drop, production optimization, multiphase flow, experimental and
numerical analysis, perforated horizontal wellbore.
Received: June 11, 2023. Revised: February 23, 2024. Accepted: April 5, 2024. Published: May 28, 2024.
1 Introduction
Perforated horizontal pipes were significantly
utilized in different sectors, ranging from water, oil,
and air to water treatment and chemical engineering
applications. It is for this reason that knowledge of
the flow governing mechanisms inside these
perforated horizontal wellbores was considered
paramount to production optimization. One of the
primary areas researchers focused on was the flow
patterns developed due to changes in surface
velocities of water and air inside these wellbores—
as these patterns directly led to pressure drop effects
along their lengths, consequently hampering output
procedures.
Several investigators in perforated horizontal
wellbores have taken up the flow patterns and
pressure gradient research. Flow patterns and
pressure gradients in horizontal pipes were studied
by [1] and [2] who found that larger pressure
gradients are associated with higher oil and water
surface velocities; this indicated observation of the
variations of the pipe's pressure gradient which
changed when the flow regime transitions were
done alongside with decreasing diameters of pipes
as a mechanism to increase pressure gradients.
The past studies considered particular flow
patterns. For instance, [3], delved into the impact of
slug flow patterns in horizontal pipes on pressure
drop and velocity profiles. In a different approach,
[4], identified stratified flow patterns in horizontal
pipes where air accumulated at the top and water at
the bottom without bubbles. Meanwhile, [5],
explored scattered bubbles, stratified, and slug flow
in horizontal pipes as part of their study. Similarly,
[6], investigated slug flow patterns and made an
interesting observation that an increase in liquid
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
208
Volume 19, 2024
flow rate results in a higher liquid holdup even
when gas flow is kept constant.
[7], investigated slug flow patterns and pressure
drop fluctuations associated with slug formation.
Bubble generation was noted when the superficial
water velocity exceeded the superficial air velocity.
[8], [9], [10], [11] and [12], investigated bubble
formation due to shear stress forces and discovered
that bubble size increased with longer horizontal
pipe lengths. [13], studied stratified wavy, slug, and
annular flow patterns in a horizontal pipe and found
an increase in wave size while transitioning from
stratified wave flow to slug flow. [14], demonstrated
connections between increased pressure drop and
both increased gas-liquid two-phase flow rate and
higher perforation density. [15], studied bubble flow
patterns, observing an increase in pressure drop with
increasing liquid flow rate.
[16], moreover, demonstrated a gradual increase
in total and friction pressure drops with increasing
wellbore length, with a lesser impact on mixing and
acceleration pressure drops. [17], attributed
increased pressure loss with increasing liquid flow
rate to friction loss. [18], observed bubble
accumulation at the upper pipe section due to
buoyancy forces and an increase in wave size with
pipe length. [19], explained that an increased mass
flow rate within the horizontal wellbore led to an
increase in pressure drop.
[20], found that pressure drop was higher in
perforated horizontal wellbores with a 90º angle
phase compared to those with 0º and 180º angle
phases due to the increased influence of mixing
pressure drop on increasing swirling. [21], observed
that liquid holdup increased when the liquid flow
rate increased, and they also noticed that the max
flux and pressure drop increased at an increased
liquid holdup fraction. [22], investigated flow
patterns and pressure drop in the horizontal pipe and
observed that the stratified flow pattern was
obtained through the horizontal pipe only when the
liquid flow was located at the bottom wall, while
gas flowed at the upper wall of the horizontal pipe.
They noted that the pressure drop increased by
increasing the liquid flow rate due to the friction
force effect.
Within this work, we embark upon an
experimental investigation of the flow dynamics
within a perforated horizontal wellbore featuring
two perforations and a phasing angle of °180. The
key focus of this investigation is centered on
changes taking place along the wellbore itself; these
modifications encompass pressure drop, flow
patterns, and production. Based on the experimental
outcomes, this research aims to understand the static
pressure drop behavior exhibited by diverse flow
patterns, namely bubble flow, transition
bubble/dispersed bubble flow, transition bubble/slug
flow, slug flow, stratified flow, transition
slug/stratified wave flow, and stratified wave flow.
These patterns emerge because of dissimilar
superficial mixture velocities between the air and
water phases. Furthermore, the influence of the
friction factor is examined through an analysis of
both unperforated and perforated pipes, utilizing the
aforementioned experimental results.
2 Experimental Apparatus
This study utilized a perforated horizontal pipe as
the primary apparatus for investigating the
phenomenon under investigation (Figure 1). Two
perforations are designed on a pipe in a vertical
direction with an exact angle of 180°. This design
was influenced by [23], work but used different
specifications for the horizontal pipe perforation as
well as the perforation setup.
Transparent Perspex (acrylic) is used to make
the primary channel, which is 3 m long and has an
internal diameter of 0.0381 m; it features two
perforations with an inner diameter of 0.004 m
placed at specific locations along its wall. Through
the pipe's transparency, scientists can take photos to
visually document flow patterns: this helps them see
variances in air and water superficial velocities.
This is primarily documented visually using a
high-speed camera (Vision Datum LEO720S) — as
shown in Figure 2. Capable of recording at 1,000
frames per second, this camera features a resolution
of 720 × 540 pixels that makes it adaptable for
different flow pattern visualizations. Tailoring the
recording range between 100 and 1,000 fps enables
a personalized approach to gathering data specific to
the flow regime being analyzed. It's an overview of
the tool we use: with information about its ability
and how we can adjust it to our advantage based on
what we are studying.
The primary pipe initiates an axial water flow
using a centrifugal pump. Instantaneously, an
electro-air compressor is used to introduce a radial
airflow through the perforations located along the
pipe's wall. The axial water flow has superficial
velocity values ranging from 0.27 to 0.55 m/s, while
the radial air flow's superficial velocities range from
0.066 to 33.1 m/s, as measured by two air flow
meters.
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
209
Volume 19, 2024
Fig. 1: Experimental Apparatus
Fig. 2: High-Speed Camera
2.1 Procedures Measurement
This study employed a series of five pressure
sensors to measure the static pressure drop of a two-
phase air-water flow along the perforated horizontal
pipe. The pressure sensor model utilized was the
WNK81mA, offering a micro pressure range of 0-20
kPa with an accuracy of 1%. These sensors,
powered by a 24 V supply, produce a current output
signal ranging from 4 to 20 mA (MilliAmperes). To
facilitate data acquisition, an analog signal
acquisition module with 1% accuracy was used to
convert the 4-20 mA signal into the RS485
communication protocol, enabling connection to a
laptop via a USB interface. This module is also
powered by a 24 V supply, as depicted in Figure 3.
The Modbus poll software served as a master
simulator, emulating a slave ID corresponding to the
pressure sensor, operating at a baud rate of 9,600
bits per second. The transmission of pressure sensor
data entailed receiving the signal through the data
acquisition unit, which then transmitted the
information to a laptop running the master Modbus
software. The recorded data was stored in Microsoft
Excel, as depicted in the diagram presented in
Figure 4.
Fig. 3: The Procedure of System Connection
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
210
Volume 19, 2024
Fig. 4: Diagram of the Transmission Signal of the
Sensor Pressure Transmitter
2.2 Mechanism of the Behavior of Static
Pressure Drop
Experimental observations revealed an inverse
relationship between the static pressure drop and the
presence of the air phase.
On the contrary, the presence of the water phase
demonstrated a direct correlation with the pressure
drop. According to [19], increased water
concentration increases the static pressure drop
value. Figure 5 depicts the air-water two-phase
mixture flow with varying densities and viscosities,
explaining the variance in pressure sensor readings.
[19], found a positive link between the static
pressure drop and the holdup fraction, which is the
ratio of water volume to total mixture volume.
Higher holdup fractions cause more water flow,
leading to increased flow resistance. Also, found a
negative link between pressure drop and void
fraction, which is the percentage of air volume to
total mixture volume. A higher vacancy fraction
leads to less water flow and lower flow resistance.
Fig. 5: Mechanism of Pressure Sensor Transmitter
2.2.1 Change in Flow Pattern with Elevated Air
Superficial Velocity
Figure 6 shows how flow patterns change when air
superficial velocity increases but water superficial
velocity remains constant. Cases 2.1 and 2.2 show a
bubble flow pattern with air dispersed inside the
continuous water phase. This pattern occurs when
the water's superficial velocity exceeds that of the
air, influenced by shear stress, surface tension, and
the differing viscosities and densities of the mixture
components. As a result, the air phase separates and
gathers in the upper part of the pipe due to buoyancy
forces.
2.2.2 Transitional Regimes:
As air superficial velocity increases (case 2.3), the
dispersed bubble flow transforms into a cloud-like
dispersed bubble flow. This transition is marked by
the formation of a larger concentration of non-
coalescing bubbles, resembling a "cloud." Further,
an increase in air velocity (case 2.4) leads to the
growth and shape transformation of bubbles. While
maintaining diverse sizes and shapes, the bubbles
exhibit a tendency towards sphericity. Notably, a
stratified/dispersed bubble flow is observed along
the horizontal pipe, characterized by bubble
merging, and consequently increasing bubble size
and quantity.
2.2.3 Plug Flow and Stratification:
Case 2.5 presents a plug flow pattern, with
elongated bubbles accumulating at the pipe's top
portion. These "bullet-shaped" bubbles, formed in
the fully developed flow region, result from the
coalescence of smaller bubbles. Notably, this pattern
appears stratified from an uphill perspective, while
exhibiting a bubble flow nature from a
comprehensive viewpoint. Conversely, stratified
flow occurs under higher air velocities (case 2.6).
This regime is characterized by air accumulating at
the upper pipe section due to buoyancy, while the
water phase flows downwards driven by gravity.
2.2.4 Slug Flow and Production Implications:
At even higher air superficial velocities (case 2.7),
slug flow manifests with significant wave peaks.
This pattern features air gaps formed by the
coalescence of smaller bubbles, separated by a water
layer developed in the fully developed flow region.
The high airflow dynamics result in lifted water,
leading to the formation of high peaks in the water
waves.
It is crucial to note that bubble flow patterns
persist near the bottom perforation due to the
concentrated water phase and surface tension.
However, case 2.8 highlights the emergence of a
large air gap near the upper perforation because of
high air velocity. This gap subsequently diminishes
in size towards the bottom perforation. Furthermore,
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
211
Volume 19, 2024
the water layer separating the air gaps increases with
higher air velocities, ultimately hindering the axial
flow of water and potentially leading to production
losses in perforated horizontal wells.
Fig. 6: Flow patterns in a horizontal perforated pipe
3 Numerical Analysis
3.1 Grid Independence Study
This study employed computational fluid dynamics
(CFD) software, specifically ANSYS FLUENT R3
(2019), to generate a three-dimensional (3D)
computational domain discretized using a
tetrahedral mesh. The research investigated a two-
phase transitional flow within a perforated
horizontal pipe. The pipe had a length of 3 m, an
internal diameter of 0.0381 m, and two perforations
with inside diameters of 0.004 m and a phasing
angle of 180°. This configuration aimed to simulate
the complexities of flow encountered in horizontal
wellbores.
Due to the computational demands and extended
simulation run time associated with a full-scale
model, a half-symmetric horizontal pipe was
employed along the y-axis. The symmetric method
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
212
Volume 19, 2024
was implemented to ensure the preservation of flow
patterns, velocity profiles, and total pressure drop
within the pipe by mirroring the pipe's geometry.
To account for the viscous effects within the
turbulent boundary layer near the pipe wall, a mesh
sensitivity analysis was conducted. The analysis
investigated four mesh sizes: 75,000 cells,
1,000,000 cells, 1,500,000 cells, and 2,000,000
cells. Each mesh configuration incorporated five
inflation layers, as illustrated in Figure 7. Grid
independence was established by demonstrating the
consistent, regular shape of the bubble flow pattern
within the perforated horizontal wellbore across
different mesh sizes. Additionally, the time required
for simulation convergence decreased with
increasing mesh refinement.
3.2 ANSYS Fluent Analysis Procedure
This study employed the ANSYS Fluent software,
utilizing the Volume of Fluid (VOF) model, to
simulate the flow patterns observed within a
perforated horizontal pipe. The simulations
incorporated the effects of gravity due to material
property discrepancies, promoting optimal flow
regimes. Additionally, implicit body force treatment
was implemented to ensure convergence by
balancing body forces and pressure gradients within
the momentum equations. To address pressure-
velocity coupling skewness, the Pressure-Implicit
with Splitting of Operators (PISO) method was
employed. Furthermore, the Staggering Pressure
Option (PRESTO) scheme, coupled with a second-
order upwind scheme, was utilized to solve the
momentum equations and perform pressure
interpolation. Turbulent flow and near-wall mesh
density treatment were achieved through the
application of the Renormalization Group (RNG)
and differential viscosity models, respectively.
Within this investigation, air and water were
designated as the first and second phases,
respectively. To facilitate the acquisition of a more
accurate distribution pattern, the initial volume
fraction of water within the wellbore was assumed
to be 1, signifying a wellbore entirely filled with
water before air introduction. The contact angle
employed, which influences bubble composition,
was set at 36°. This selection ensured compatibility
with the interface between the air and water phases,
as corroborated by the findings of [4] and [5]. The
constant ratio of time steps with mesh element size
was (
3
101
x
t
,
4
101
and
5
101
s/m),
determined based on the completed flow patterns
along the perforated horizontal wellbore and also the
convergence of the simulation.
Figure 7 showcases the variations in void
fraction for various mesh sizes while simulating
slug flow with a superficial velocity of 0.5 m/s for
both air and water phases. Mesh size A (75,000
cells) exhibited an unclear slug flow pattern due to
the influence of the interface separating bubbles.
This effect was significantly less pronounced with
mesh size B (1,000,000 cells), which displayed a
distinct slug flow pattern with a quicker separation
of radial airflow emanating from the top perforation.
This phenomenon can be attributed to surface
tension and shear stress.
The simulation period for mesh size B required
approximately 7 days, corresponding to a simulation
time of 7.2 s. In contrast, mesh size C (1,500,000
cells) yielded a void fraction of the air phase that
resembled a stratified flow pattern, with a
simulation period of 9 days and a simulation time of
8.9 s. Finally, mesh size D (2,000,000 cells)
demonstrated a void fraction behavior indicative of
a stratified flow pattern. The increased mesh size in
this case exacerbated the impact of the interface,
hindering the separation of air near the pipe wall.
The simulation period for mesh size D was 13 days,
corresponding to a simulation time of 11.4 s.
Figure 8 shows the static pressure drop
distribution along the perforated horizontal pipe
with different mesh sizes. A decrease in static
pressure values is observed with increasing density
of the mesh size. In this study, mesh size B type
with (1,000,000 cells) was chosen as optimal
because the slug flow pattern shape was very clear
and the average static pressure drop value calculated
experimentally converged from mesh size
(1,000,000 cells), with a percentage error of 6.5%
while it was (10.6%, 16.5%, and 18.5%) that occurs
with (75,000 cells, 1,500,000 cells and 2,000,000
cells), respectively as explained in Table 1.
Furthermore, the simulation time associated
with mesh size B was deemed favorable considering
the available laptop specifications and the time
required for result analysis.
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
213
Volume 19, 2024
Table 1. Error percentage of comparison Static pressure drop calculated experimentally with different mesh cell
sizes
Number of cells
Average of static
pressure drop (pa)
numerical
Average of static
pressure drop (pa)
numerical
Error %
75000 cells
76.90
83.80
8.23 %
1,000,000 cells
80.40
83.80
4.29 %
1,500,000 cells
71.80
83.80
14.31 %
2,000,000 cells
70.04
83.80
16.42 %
Fig. 7: Grid Independence of the plane when the x-axial (water phase) and the y-radial (air phase)
Fig. 8: Static pressure drop distribution along the
pipe with different mesh sizes
3.3 Boundary Condition
The inlet boundary for two-phase flow is estimated
using the following equation proposed by [24].
The superficial velocity of air:
m
a
as A
Q
U
(1)
The superficial velocity of water:
m
w
ws A
Q
U
(2)
Where:
wam AAA
(3)
The inlet values for turbulent kinetic energy k,
and its dissipation rate ε, are estimated using the
following equation by [25].
in
,
Dskinin /
2/3
,
8/1
Re
16.0
I
(4)
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
214
Volume 19, 2024
Where: I is turbulence intensity for fully developed
pipe flow.
The outlet boundary is static pressure equal to
zero because the perforated pipe's end is open and
exhibits atmospheric pressure.
p = p° = 0 (5)
0 dz
dW
dy
dV
dx
dU mmm
(6)
The mixture of two-phase flow is assumed to be
a no-slip boundary condition on the wall of the pipe,
defined as:
0 mmm WVU
(7)
3.4 Governing Equations
The governing flow equations explain the solution
of the two-phase (air-water) flow through the
domain by balancing the mass and momentum
equations as a function of the volume fraction
values for each phase.
3.4.1 Conservation of Mass
The continuity equation is solved by the volume
fraction of one or more of the phases. This equation
has the following form for the
th
q
Liquid volume
fraction phase, [24], [25].
(8)
Where:
i j k
V U V W
(9)
pq
m
.
explains the mass transfer from
to
q
and
qp
m
.
is the mass transfer from
q
to
,: Source
term.
The general continuity equation for mixture
flow is given by [26].
0
mm
i
ddU
dt dx
(10)
3.4.2 Conservation of Momentum
The momentum equation is solved in the full range
as a function of the volume fractions of all phases,
illustrated by vectors through the properties and
defined as.
(11)
The general momentum equation for mixture
flow is defined as.
(12)
The error percentage is calculated using the
mean absolute percent error (MAPE) that finds
simply the average values of each column, as given
by [27].
(13)
3.5 The Analysis of the Flow Patterns in a
Perforated Horizontal Pipe (Numerical
Study)
Figure 9 and Figure 10 illustrate the diverse flow
regimes observed within a perforated horizontal
pipe under various superficial air and water
velocities. In Figure 9, the water superficial velocity
is held constant at 0.27 m/s, while the air superficial
velocity is incrementally increased. Case 1.1 depicts
the bubble flow regime, where the dispersed air
phase coexists with the continuous water phase.
This regime arises due to the dominance of
buoyancy and the contrasting physical properties
(viscosity and density) of the air and water phases.
The shear stress and surface tension of the water
phase, coupled with the density difference, facilitate
the formation of bubbles that accumulate at the
pipe's upper section. These bubbles exhibit varying
sizes and shapes but tend towards sphericity.
As evident in Case 1.2, increasing the air's
superficial velocity leads to the coalescence of
individual bubbles into larger entities. Further
augmentation of the airflow rate, as shown in Case
1.3, results in the formation of slug flow,
characterized by elongated air pockets separated by
water layers. The buoyancy force and varying
mixture concentrations (air and water) contribute to
the segregation of these air gaps within the pipe.
These distinct air pockets resemble large waves that
can potentially fill the entire pipe diameter. Case 1.4
demonstrates the further enlargement and merging
of air gaps into Taylor bubbles with increasing air
superficial velocity. Finally, Case 1.5 showcases the
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
215
Volume 19, 2024
stratified flow regime observed at a superficial air
velocity of 1.7 m/s. Buoyancy compels the air phase
to accumulate at the pipe's top, while gravity
governs the downward flow of the water phase.
Notably, a critical air superficial velocity of 2.6 m/s
(Case 1.6) is observed beyond which the radial air
flow overcomes the axial water flow, leading to an
undesirable reverse flow. This phenomenon
signifies a detrimental loss in oil production,
highlighting the importance of maintaining airflow
rates within acceptable limits. It is also noteworthy
that stratified flow is consistently observed at the
end of the pipe across all patterns, owing to the
insufficiency of axial water flow to completely fill
the pipe.
Figure 10 presents flow regimes obtained with a
higher water superficial velocity of 0.55 m/s,
exhibiting similar trends to those observed in Figure
7. Notably, Cases 2.7, 2.8, and 2.9 depict the
occurrence of stratified wave flow due to the high
air superficial velocity, which possesses sufficient
kinetic energy to entrain the water phase and
generate waves within the perforated pipe. Case 2.7
exemplifies the coexistence of stratified flow at the
upper perforations and bubble flow at the lower
perforations, attributed to the interplay of shear
stress, surface tension, and water phase
concentration. As the air superficial velocity
increases in Case 2.8, the flow regime transitions
from stratified to stratified wave flow, reflecting the
generation of numerous waves within the pipe due
to the high kinetic energy of the air phase. Case 2.9
showcases the transition from stratified wave to
annular flow at an air superficial velocity of 33.1
m/s.
The high air velocity propels the air phase
towards the pipe's center, forcing the water phase
towards the wall. While annular flow is prevalent
near the perforations, it transitions back to stratified
wave flow at a distance of 2-3 meters from the mean
inlet due to the influence of gravity on the water
phase. Furthermore, the insufficient kinetic energy
of the airflow in this case study (mentioned in Table
2) leads to the formation of stratified wave flow in
the central region of the perforated horizontal pipe.
Fig. 9: Flow patterns in the perforated horizontal pipe when
ws
U
= 0.27 m/s
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
216
Volume 19, 2024
Fig. 10: Flow patterns in the perforated horizontal pipe when
ws
U
= 0.55 m/s
Table 2. A case study of flow patterns
Test No.
Flow patterns
as
U
m/s
ws
U
m/s
Test No
Flow patterns
as
U
m/s
ws
U
m/s
Case 1.1
Bubble flow
0.066
0.27
Case 2.1
Bubble flow
0.066
0.55
Case 1.2
Transition
bubble/slug flow
0.1
0.27
Case 2.2
Transition
bubble/dispersed flow
0.1
0.55
Case 1.3
Slug flow
0.3
0.27
Case 2.3
Slug flow
0.3
0.55
Case 1.4
Taylor bubble
0.5
0.27
Case 2.4
Transition Slug/Taylor
0.5
0.55
Case 1.5
Stratified flow
1.3
0.27
Case 2.5
Taylor bubble
1.3
0.55
Case 1.6
Stratified flow
2.6
0.27
Case 2.6
Stratified flow
6.6
0.55
Case 2.7
Transition slug/ stratified
wave flow
10.5
0.55
Case 2.8
Stratified wave flow
19.8
0.55
Case 2.9
Transition stratified
wave/ annular flow
33.1
0.55
4 Result and Discussion
4.1 The Behavior of Static Pressure Drop
with the Bubble Flow Pattern
Figure 11 presents the behavior of static pressure
drop (Pa) over time (s) during the bubble flow
pattern in the perforated horizontal pipe (Case 1). At
the inlet region, the pressure drop values remain
constant due to the dominance of the water phase.
As the flow progresses towards the perforations
(sensor pressure l/d = 22 and 44), the increasing
mixing pressure drop in this region, caused by the
disparity in density between the air and water
phases, leads to increased pressure fluctuations.
The pressure drop exhibits a cyclical pattern,
increasing as the water phase passes through the
sensor's cross-sectional area and decreasing as the
bubble phase passes through. This trend continues
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
217
Volume 19, 2024
along the horizontal pipe, with the pressure drop
decreasing from inlet to outlet due to frictional
losses. The variation in pressure drop magnitude is
influenced by the size and kinetic energy of the
bubbles, with a higher concentration observed at
sensor pressure l/d = 66 due to its location in a fully
developed flow region.
Moreover, void friction increases with the
length of the perforated horizontal pipe. Finally, the
pressure sensor values in the outlet region remain
stable due to the low static pressure drop readings,
resulting in minimal oscillations.
Fig. 11: Bubble flow when the superficial air
velocity is 0.066 m/s, and the superficial water
velocity is 0.27 m/s
Figure 12 shows Case 2, which demonstrates a
reduction in fluctuation during the bubble flow
pattern with increased water superficial velocity.
Static pressure drop values increase with increasing
water superficial velocity due to the impact of water
phase concentration and density. Fluctuation during
this flow pattern is lower compared to Case 1 as
bubble size is smaller when superficial water
velocity is 0.55 m/s.
A decrease in bubble count is observed with
increasing water superficial velocity, resulting in
increased holdup fraction values and greater
distance between generated bubbles. Pressure sensor
values are more stable during this regime.
Fig. 12: Bubble flow when superficial air velocity is
0.066 m/s and superficial water velocity is 0.55 m/s
4.2 The Behavior of Static Pressure Drop
with Transition Bubble/ Slug Flow
Pattern
As shown in Figure 13 (Case 3), increasing the air
superficial velocity leads to the formation of a large
air gap separated by a water layer, known as the
transition bubble/slug flow pattern. This
phenomenon primarily occurs in the fully developed
region, where the mixture flow velocity reaches its
maximum value. Consequently, the static pressure
drop remains stable throughout the slug phase due to
minimal air phase fluctuations. In this scenario, the
pressure sensor effectively treats the air phase as a
single phase due to its reduced sensitivity to
individual bubbles.
Notably, the size of the bubbles influences the
static pressure drop, with larger bubbles resulting in
a higher pressure drop. The occurrence of this flow
pattern is dependent on the air's superficial velocity,
with faster velocities causing it to appear earlier.
4.3 The Behavior of Static Pressure Drop
with Transition Bubble/ Dispersed
Bubble Flow Pattern
Figure 14 (Case 4) illustrates the transition
bubble/dispersed bubble flow pattern resulting from
an increase in water superficial velocity while
maintaining a constant air superficial velocity. The
presence of more bubbles at the pressure sensor
location (l/d = 66) leads to increased fluctuations
due to the higher bubble count along the perforated
horizontal pipe.
In this flow pattern, individual bubbles have
equal kinetic energy, preventing them from merging
and forming larger bubbles. As a result, the pressure
sensor readings stay consistent with those observed
in Case 1.
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
218
Volume 19, 2024
Fig. 13: Transition bubble/slug flow when the
superficial air velocity is 0.1 m/s, and the superficial
water velocity is 0.27 m/s
Fig. 14: Transition bubble/dispersed flow when the
superficial air velocity is 0.1 m/s, and the superficial
water velocity is 0.55 m/s
4.4 The Behavior of Static Pressure Drop
with the Slug Flow Pattern
Figure 15 outlines Case 5, which examines the
behavior of static pressure drop during the slug flow
pattern. The static pressure drop values decrease
during the period from 5 to 10 seconds, indicating a
slug situation influenced by the air phase.
Conversely, an increase in static pressure drop from
10 to 15 seconds signifies the passage of the water
phase through a cross-sectional measurement region
of the pressure sensor. The oscillation of static
pressure drop value is attributed to differences in
density and viscosity between air and water phases.
The outlet pressure sensor also reflects the influence
of slug flow, with values and fluctuation of static
pressure drop decreasing as water superficial
velocity increases and holdup fraction rises.
Fig. 15: Slug flow when superficial air velocity is 0.3 m/s
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
219
Volume 19, 2024
4.5 The Behavior of Static Pressure Drop
with the Stratified Flow Pattern
Figure 16 (Case 6) depicts the stratified flow
pattern, where the air phase accumulates at the top
of the horizontal pipe due to the buoyant force
acting on the lighter air. Conversely, the water phase
settles at the bottom of the pipe due to the
gravitational force acting on the denser water. In this
flow pattern, the pressure sensor is primarily
sensitive to the air phase; consequently, the static
pressure drop values exhibit greater stability.
However, some fluctuations are observed in the
pressure sensor readings at l/d = 22 and l/d = 44, as
these locations are close to the perforations where
the mixing pressure drop, arising from the
interaction between radial and axial flow phases,
exerts an influence.
Additionally, the superficial velocity of the
mixture flow demonstrates instability within this
range. Beyond this region, at l/d = 66, the static
pressure drop values become more stable as the
mixture flow reaches the fully developed region and
moves further away from the influence of the
perforations.
Fig. 16: Stratified flow when superficial air velocity
is 1.3 m/s
4.6 The Behavior of Static Pressure Drop
with Transition Slug/ Stratified Wave
Flow Pattern
Figure 17 (Case 7) depicts the transition from slug
flow to a stratified wave flow pattern as the air
superficial velocity increases. This transition is
accompanied by a rise in void fraction compared to
Case 5. The high kinetic energy of the air phase
leads to the formation of waves within the pipe,
while the increased void fraction and decreased
holdup fraction result in a reduction of the water
layer separating the air gaps.
Fig. 17: Transition slug/ stratified wave flow when superficial air velocity is 10.5 m/s
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
220
Volume 19, 2024
4.7 The Behavior of Static Pressure Drop
with the Stratified Wave Flow Pattern
Figure 18 showcases Case 8, illustrating the
formation of a stratified wave flow pattern under
constant superficial water velocity and high
superficial air velocity. The substantial air velocity
effectively entrains the water phase, leading to the
generation of high-amplitude waves on the interface
between the two phases. These waves play a critical
role in the observed pressure drop behavior. The
kinetic energy associated with the wave motion
directly influences the static pressure drop, with
higher kinetic energy corresponding to a greater
pressure drop and vice versa.
In Figure 19, Case 9, it is evident that the
stratified wave flow pattern is semi-stable. The
waves formed in this case exhibit higher peaks
compared to the previous Case 8, and this is
contingent upon the kinetic energy when the
superficial water velocity is 0.55 m/s. Additionally,
when the superficial water velocity is increased, a
slight fluctuation is observed, leading to the
formation of waves at regular intervals.
Consequently, the pressure drop increases due to the
augmented mixture of superficial velocity.
Fig. 18: Stratified wave flow when the superficial
air velocity is 19.8 m/s
4.8 The Behavior of Static Pressure Drop of
Flow Patterns with l/d
4.8.1 Influence of l/d Ratio on Static Pressure
Drop
Figure 20 illustrates the impact of l/d on static
pressure drop (Pa) across various flow patterns
while maintaining a constant water superficial
velocity and varying air superficial velocity. The
results demonstrate fluctuations in static pressure
drop when l/d ranges from approximately 20 to 60.
Beyond this range, a continuous reduction is
observed towards a stable state indicative of fully
developed flow. This region signifies the
achievement of a steady-state regime with a well-
defined mixture flow profile. Notably, a peak in
pressure drop occurs at l/d = 22, attributed to the
reduction in axial flow hindering radial flow and
consequently increasing the mixing pressure drop.
This phenomenon is particularly evident during
bubble, dispersed bubble, and slug flow regimes.
In contrast, stratified flow exhibits a stable
decline in static pressure drop along the perforated
horizontal pipe as l/d increases. This behavior arises
from the air and water phases approaching equal
superficial velocities, resulting in the pressure
sensor being primarily influenced by the air phase.
This flow pattern manifests due to the air phase
accumulating at the upper portion of the horizontal
pipe, while the water phase accumulates at the
bottom.
During stratified wave flow, the observed
oscillations in static pressure drop are directly
linked to the kinetic energy of the generated waves.
Higher kinetic energy translates to increased static
pressure drop.
4.8.2 Impact of Water Superficial Velocity
Figure 21 depicts the influence of increasing water
superficial velocity on the behavior of static
pressure drop. Notably, the trend becomes smoother
with less pronounced fluctuations, likely due to the
presence of a higher holdup fraction. This
observation aligns with the decreasing trend in static
pressure drop values as the flow regime transitions
from bubble to stratified with increasing air
superficial velocity. Bubble flow exhibits the
highest static pressure drop, followed by a decrease
in the stratified flow regime. This disparity can be
attributed to the pressure sensor in the stratified flow
pattern solely experiencing the influence of the air
phase. Furthermore, the transition between flow
regimes is governed by the increasing air superficial
velocity.
Lastly, the static pressure drop associated with
stratified wave flow surpasses that of slug and
stratified flow patterns. This phenomenon is
attributed to the number and size of generated
waves. A greater number and size of waves
contribute to a higher static pressure drop, as the
kinetic energy of the mixture flow during this
pattern is significantly higher compared to other
regimes.
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
221
Volume 19, 2024
Fig. 19: Stratified wave flow when the superficial air velocity is 33.1 m/s
Fig. 20: The behavior of static pressure drop when
superficial water velocity is 0.27 m/s
Fig. 21: The behavior of static pressure drop when
superficial water velocity is 0.55 m/s.
4.9 Impact of Friction Factor through the
Unperforated and Perforated Horizontal
Pipes
Figure 22 illustrates the relationship between the
friction factor through perforated and unperforated
horizontal pipes and the Reynolds number of
mixture flow ( ). A decrease in friction factor is
observed with an increased Reynolds number of
mixture flow, in accordance with Equations (8) and
(9). Perforation roughness, as described by Equation
(9), is dependent on universal velocity, density of
perforations, and perforation diameter relative to a
perforated horizontal pipe.
The friction factor value is 0.031 when the
Reynolds number is 9162, decreasing to 0.025 when
the Reynolds number is 21380, as determined by the
Haaland Equation (Equation 8). Using Equation (9),
the friction factor is calculated as 0.03146 at a
Reynolds number of 9162 and decreases to 0.02512
at a Reynolds number of 21380. The resulting error
percentage is 1.4% at a Reynolds number of 9162
and 0.48% at a Reynolds number of 21380.
Therefore, it can be concluded that the
comparison of friction factor values (perforated and
unperforated horizontal pipe) approaches each other
with increasing Reynolds numbers due to the
reduced impact of friction at higher Reynolds
numbers and vice versa.
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
222
Volume 19, 2024
Fig. 22: Friction factors with the unperforated and
perforated horizontal pipes
4.10 Comparison between Experimental and
Numerical Results
Figure 23 presents a comparison between the
experimental and numerical results for the static
pressure drop along the pipe. The behavior of the
pressure drop curve exhibits a distinct increase at
the point l/d = 44 (length-to-diameter ratio). This
can be attributed to the combined effects of the flow
pattern (bubble, dispersed bubble, and slug flow) at
this location and the presence of the perforated
section. Additionally, the interaction between the air
and water phases (two-phase flow) contributes to
the pressure rise at this point. Furthermore, the
mixing and frictional pressure drops are also
intensified due to the flow characteristics.
The introduction of stratified wave flow further
contributes to the pressure increase at l/d = 44. This
phenomenon is associated with the high air flow rate
(while maintaining a constant water flow rate) and
the wave formation characteristic of this flow
pattern. The unsteady nature of the flow,
corresponding to a two-phase flow not yet reaching
a stable state, further amplifies the pressure drop
behavior. Conversely, for slug and stratified flows
(occurring at air-to-water flow rate ratios near
unity), the pressure drop curve becomes more
streamlined and stable. This is because these flow
patterns represent a closer approximation to single-
phase flow, leading to a steady state along the pipe.
4.10.1 Steady-State Flow Characteristics
Under steady-state conditions, the flow regime
exhibits a clear stratification, with the air phase
occupying the upper portion of the pipe due to
buoyancy, while the water phase flows downwards
driven by gravity. Since the static pressure drop is
measured at the upper surface, it is primarily
influenced by the air phase (acting as a single phase)
due to its significantly lower density and viscosity
compared to water. Additionally, the compressible
nature of air and the minimal frictional effect further
contribute to its negligible impact on the pressure
drop.
4.10.2 Flow Pattern Dependence and
Convergence
The analysis reveals a general trend of decreasing
static pressure drop along the horizontal pipe with
increasing air flow rate (while maintaining a
constant water flow rate), reflecting the transition
between different flow patterns. Notably, the
pressure drop converges to a small value (close to
atmospheric pressure) at the outlet region (l/d = 88)
for all flow patterns. This implies that the pressure
drop difference at the outlet is negligible.
Figure 24 visually demonstrates the comparison
between experimental and numerical results by
presenting the air fraction contours extracted
numerically along the perforated wellbore. This
visualization underscores the clear relationship
between the flow patterns observed in the fully
developed region.
4.10.3 Error Analysis
Table 3 summarizes the calculated error percentages
(using Equation 6) for the different flow patterns.
An increased error percentage (12.49%) is observed
for stratified wave flow due to the elevated air flow
rate inducing water wave formation. These waves
contribute to increased fluctuations in both
experimental and numerical data, leading to a higher
error percentage. Conversely, flow patterns
exhibiting behavior closer to single-phase flow
(streamline), namely slug and stratified flows,
demonstrate lower error percentages (3.67% and
1.53%, respectively).
Figure 25 complements the analysis by
illustrating the occurrence of the reverse flow region
when the radial air flow rate surpasses the axial
water flow rate, as detailed in Figure 9 (Case 1.6).
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
223
Volume 19, 2024
Table 3. Percentage Error of Flow Patterns Comparison
Air Flow
rate (l/m)
Water Flow
rate (l/m)
Average of
experimental
results
Average of
numerical
results
Flow Patterns
٪ Error
0.05
15
86.08
77.25
Bubble Flow
10.25 %
0.1
15
89.83
80.10
Dispersed Bubble Flow
10.83 %
0.5
15
83.80
80.72
Slug Flow
3.67 %
5
15
90.04
91.42
Stratified Flow
1.53 %
15
15
475.38
416.2
Stratified Wave Flow
12.49 %
Fig. 23: The comparison of static pressure drop between experimental and numerical results
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
224
Volume 19, 2024
Fig. 24: The comparison of flow patterns between experimental and numerical results
Fig. 25: Reverse flow region
4.11 Measuring Liquid Product Quantity in
Horizontal Wells
This study explores a method for measuring the
quantity of liquid product extracted from a
horizontal wellbore during a production process.
The extracted liquid, typically a multiphase mixture
of oil, water, and gas, requires separation at
petroleum installations to obtain the final product,
crude oil. The wellbore's productivity, ultimately
determining its success, is directly correlated with
the amount of oil produced. Traditionally, the
productivity index, developed for single-phase flow,
has been used to estimate productivity in some
cases. However, this approach assumes that the
liquid flowing out of a perforated horizontal pipe
directly translates to the amount of oil produced,
which is not entirely accurate in multiphase flow
situations.
The proposed method for measuring the liquid
product quantity utilizes a dedicated setup featuring
two tanks: a 20-liter test tank for collecting the
liquid product over a specified time and a holding
tank for accumulating the returned liquid before
reinjection into the storage tank (Figure 26). When
the two-phase flow enters the test tank, the air
components separate and are released upwards due
to their lower density compared to the water, which
settles at the bottom due to gravity.
To determine the liquid quantity, the weight (in
kilograms) is measured using a scale and then
divided by the fixed measurement time (two
minutes) established using a stopwatch. Control
valves 1 and 2 are employed to manage the opening
and closing of the pipe after each reading. For
measurement, valve 1 is closed, and valve 2 is
opened, allowing the liquid in the test tank to be
weighed.
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
225
Volume 19, 2024
Fig. 26: Procedure to measure the quantity of the liquid product
Standard parameter measurements are
conducted with valve 1 open, valve 2 closed, and
valve 3 open, maintaining a closed system.
To minimize measurement errors, the process is
repeated approximately six times for each reading,
with the final liquid quantity value determined by
averaging the collected measurements. Additionally,
a three-minute waiting period is implemented
between each measurement to ensure system
stability and allow for potential pressure fluctuations
to subside. This multi-step approach offers a
standardized and reliable method for measuring the
liquid product quantity in horizontal wells,
facilitating accurate wellbore productivity
assessments, and optimizing oil production
processes.
Figure 27 A–E demonstrates an increase in the
quantity of liquid product collected with increasing
air superficial velocity when water superficial
velocity is kept constant. In Figure 27 A, when
ws
U
= 0.27 m/s, the quantity of the liquid product begins
to increase from a value of 0.17 kg/s. When
as
U
=
0.066 m/s, the amount increases until a value of
as
U
= 0.33 kg/s is reached. When
as
U
= 1.32 m/s, both
bubble and slug flows are observed. The quantity of
the liquid product gradually decreases (during the
transition from slug to stratified flow) that occurs
during
as
U
= 10 m/s. After this velocity, the quantity
is almost stable (during the transition from stratified
to stratified wave flow). The reason for obtaining
constant values of the liquid product is that the
increase in the amount of air will have a minimum
impact on the quantity of water. At the same time,
the effect of friction and the mixing pressure drop
between air and water decreased.
Figure 27 B exhibits similar behavior to Figure
27 A, with an increased drop in liquid product
observed at air superficial velocities greater than
as
U
= 10 m/s (stratified wave flow) because of the
impact of the increased velocity of the air phase.
With an increase in the water superficial velocity (
ws
U
= 0.45 m/s) as indicated in Figure 27 C, it is
observed that the quantity of the liquid product
increases up to 0.46 kg/s when (
as
U
= 0.066 m/s)
occurs during the bubble flow. On the contrary, a
sharp drop in the value of the liquid product is
observed with an increase in the air's superficial
velocity. This drop will continue till it reaches about
as
U
= 0.43 kg/s, then return to an increase. It
occurred because of an increase in the void fraction
value through a transition from the stratified flow to
the stratified wave flow pattern that caused a loss in
the liquid product.
Figure 27 D explains the value of the liquid
product at
ws
U
= 0.55 m/s. It was observed that the
value of the liquid product is
ws
U
= 0.55 kg/s when
as
U
= 0.066 m/s and 1.32 m/s, respectively (when
the transition from bubble to slug flow occurs).
However, the liquid product increases during the
transition from slug to stratified flow. Otherwise,
the drop in the liquid product occurs when the
transition from stratified flow to stratified wave
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
226
Volume 19, 2024
flow occurs, and this drop gets the shape of the
concavity in the curve of values of the liquid
product. Then it is increased when the air's
superficial velocity is greater than
as
U
= 40 m/s.
Figure 27 E depicts an increase in the liquid
product value during bubble flow and the transition
from bubble to slug flow, reaching approximately
0.69 kg/s. However, a simultaneous drop in the
liquid product value occurs during the transition
from slug to stratified wave flow. This drop
indicates fluctuations in the liquid product value due
to its dependency on the generated waves. These
waves lead to instability in the values and help
increase the quantity of the liquid product.
Figure 28 illustrates a direct correlation between
the average liquid product and the mixture's
superficial velocity. This is attributed to the
combined effect of an increasing holdup fraction,
due to a higher water phase presence, and a larger
volume flow rate associated with higher velocities.
Table 4 presents details on the liquid product
behavior observed during increased water
superficial velocity.
Several Key Observations:
1. Positive Correlation: The quantity of liquid
product exhibits a positive correlation with
increasing water superficial velocity, primarily
due to the rising holdup fraction.
2. Flow Regime Dependence: For bubble and
slug flow regimes (air superficial velocity
between 0.066 m/s and 1.32 m/s), the liquid
product increases with rising water superficial
velocity.
3. Flow Regime Transition: A decrease in the
liquid product is observed during the transition
from slug flow and stratified flow to stratified
wave flow.
4. Water Velocity Impact: A sharper decline in
the liquid product is observed at high water
superficial velocities compared to lower ones.
5. Stratified Wave Flow: In some instances,
stratified wave flow can exhibit an increase in
the liquid product due to wave generation,
leading to a higher holdup fraction and friction
factor. However, increasing the air phase can
counteract this effect by increasing the void
fraction and decreasing the holdup fraction,
resulting in a significant drop in the liquid
product.
6. Mixing Pressure Drop: An increase in mixing
pressure drop near perforation regions
contributes to a further decrease in the liquid
product. This phenomenon arises due to the
hindering effect of air radial velocity on water
axial velocity, creating a bottleneck region that
restricts water flow and consequently, reduces
the liquid product (particularly evident in
stratified and stratified wave flows).
7. Stratified Flow: The stratified flow regime,
characterized by two distinct phases with air
accumulating at the top and water settling at the
bottom due to buoyancy and gravity,
respectively, exhibits a decrease in the liquid
product. This is because high air superficial
velocity has minimal influence on the water
phase, except at the interface between the two
phases. Notably, some stratified wave flow data
points show higher liquid product values
compared to stratified flow due to the influence
of generated waves.
8. Constant Air Velocity: When air superficial
velocity is maintained constant, the percentage
of liquid product increases proportionally with
increasing water superficial velocity.
Table 4. Data of average liquid product with water superficial velocity
No
Water Superficial Velocity m/s
Average of liquid product kg/s
1
0.27
0.561917
2
0.36
0.71945
3
0.45
0.91445
4
0.55
1.07135
5
0.63
1.298933
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
227
Volume 19, 2024
Fig. 27(A–E): The quantity of the liquid product obtained with different air superficial velocities, with the
water superficial velocity kept constant
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
228
Volume 19, 2024
Fig. 28: Behavior of the average liquid product when increased water superficial velocities
5 Conclusion
This study investigated the relationship between
pressure drop and the various flow patterns
observed in perforated horizontal pipes. The
predicted flow patterns included bubble flow,
transition bubble/dispersed bubble flow, transition
bubble/slug flow, slug flow, stratified flow,
transition slug/stratified wave flow, and stratified
wave flow. The impact of the friction factor was
analyzed using experimental data from both
unperforated and perforated pipes. Additionally, the
study examined the behavior of liquid products
within these flow patterns within the perforated
horizontal wellbore.
Based on the Presented Experimental Results,
the Following Conclusions can be drawn:
The static pressure drop decreases with the air
phase but increases with the water phase flow
due to the concentration of water density.
Transitions between flow patterns occurred
with increasing superficial air velocity while
maintaining constant superficial water velocity.
Fluctuations in pressure drop were more
pronounced at higher superficial air velocities
and decreased with lower water holdup
fractions.
Stratified wave flow exhibited the highest peak
in static pressure drop due to the significant
kinetic energy of the waves in this pattern,
although it also offered greater stability due to
being solely influenced by the air phase.
High holdup fractions in bubble flow patterns
resulted in elevated static pressure drop values,
while lower values were observed in stratified
and stratified wave flow patterns due to
increased void fractions.
The quantity of liquid product increased with
higher water superficial velocity, corresponding
to a rise in the holdup fraction value.
Liquid product exhibited an increase during
bubble and slug flow patterns but decreased
during the transition from slug and stratified
flow to stratified wave flow.
The average liquid product increased with
greater mixture superficial velocity as a result of
a larger water phase contribution.
The percentage of the liquid product increased
with higher water superficial velocity while
maintaining constant air superficial velocity.
While good convergence between experimental
and numerical results was observed for slug and
stratified flow patterns, some discrepancies in
pressure drop behavior were found during the
bubble, transition bubble/dispersed bubble flow,
and stratified wave flow patterns.
Acknowledgement:
The authors would like to acknowledge the financial
support received from the Ministry of Education
Malaysia under the Fundamental Research Grant
Scheme (FRGS) scheme (20180110FRGS) that
enable the work to be carried out.
Nomenclature:
friction factor of the unperforated pipe
friction factor of the roughness
perforation
A
universal velocity ()
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
229
Volume 19, 2024
diameter of the perforations ()
viscosity of mixture flow
density of mixture flow ()
a
A
Area cross-section of air
2
m
w
A
Area cross-section of water
2
m
m
A
Area cross-section of mixture phase
2
m
m
Re
Mixture Reynolds number
in
U
Velocity of water phase
sm/
m
U
Mixture superficial velocity
sm/
as
U
Air superficial velocity
sm/
ws
U
Water superficial velocity
sm/
perforation density
Q
volume flow rate of water
D
Diameter of mean pipe
m
V
Mixture superficial velocity at – Y
sm/
m
W
Mixture superficial velocity at – Z
sm/
Length of the pipe
References:
[1] Al-Wahaibi, T., Smith, M., & Angeli, P.
(2007). Effect of drag-reducing polymers on
horizontal oil–water flows. Journal of
Petroleum Science and Engineering, 57(3-4),
334-346.
[2] Al-Wahaibi, T., Al-Wahaibi, Y., Al-Ajmi, A.,
Al-Hajri, R., Yusuf, N., Olawale, A. S., &
Mohammed, I. A. (2014). Experimental
investigation on flow patterns and pressure
gradient through two pipe diameters in
horizontal oil–water flows. Journal of
Petroleum Science and Engineering, 122,
266-273.
[3] Razavi, S. Y., & Namin, M. M. (2011).
Numerical model of slug development on
horizontal two-phase flow. In Proceedings of
The International Conference on Recent
Trends in Transportation, Environmental and
Civil Engineering (pp. 14-15).
[4] Pham, H., Wen, L., & Zhang, H. (2012).
Numerical simulation and analysis of gas-
liquid flow in a T-junction
microchannel. Advances in Mechanical
Engineering, 4, 231675.
[5] Vásquez, F., Stanko, M., Vásquez, A., De
Andrade, J., & Asuaje, M. (2012). Air–water:
two phase flow behavior in a horizontal pipe
using computational fluids dynamics
(CFD). WIT Transactions on Engineering
Sciences, 74, 381-392.
[6] Hassanlouei, R. N., Firouzfar, H., Kasiri, N.,
& Khanof, M. H. (2012). A simple
mathematical model for slug liquid holdup in
horizontal pipes. Scientia Iranica, 19(6),
1653-1660.
[7] Liu, D., Ling, X., & Peng, H. (2016).
Comparative analysis of gas–liquid flow in T-
junction microchannels with different inlet
orientations. Advances in Mechanical
Engineering, 8(3), 1687814016637329.
[8] Santos, R. M., & Kawaji, M. (2010).
Numerical modeling and experimental
investigation of gas–liquid slug formation in a
microchannel T-junction. International
Journal of Multiphase Flow, 36(4), 314-323.
[9] Arias, S., Legendre, D., & González-Cinca, R.
(2012). Numerical simulation of bubble
generation in a T-junction. Computers &
fluids, 56, 49-60.
[10] Shi, Y., Tang, G. H., & Xia, H. H. (2014).
Lattice Boltzmann simulation of droplet
formation in T-junction and flow-focusing
devices. Computers & Fluids, 90, 155-163.
[11] Chandra, A. K., Kishor, K., Mishra, P. K., &
Alam, M. S. (2016). Numerical investigations
of two-phase flows through enhanced
microchannels. Chemical and Biochemical
Engineering Quarterly, 30(2), 149-159.
[12] Wong, V. L., Loizou, K., Lau, P. L., Graham,
R. S., & Hewakandamby, B. N. (2017).
Numerical studies of shear-thinning droplet
formation in a microfluidic T-junction using
two-phase level-SET method. Chemical
Engineering Science, 174, 157-173.
[13] Vieira, R. E., Kesana, N. R., McLaury, B. S.,
Shirazi, S. A., Torres, C. F., Schleicher, E., &
Hampel, U. (2014). Experimental
investigation of the effect of 90 standard
elbow on horizontal gas–liquid stratified and
annular flow characteristics using dual wire-
mesh sensors. Experimental thermal and fluid
science, 59, 72-87.
[14] Qiji, S. U. N., & Xu, W. A. N. G. (2014).
Horizontal Well Bottom-Hole Pressure Drop
Steam Flooding Numerical Calculation. Adv.
Petrol. Explorat. Dev., 7(2), 76-79.
[15] Talley, J. D., Worosz, T., & Kim, S. (2015).
Characterization of horizontal air–water two-
phase flow in a round pipe part II:
Measurement of local two-phase parameters
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
230
Volume 19, 2024
in bubbly flow. International Journal of
Multiphase Flow, 76, 223-236.
[16] Hua, L., Yan, L., Xiaodong, P., Xindong, L.,
& Laichao, W. (2016). Pressure drop
calculation models of wellbore fluid in
perforated completion horizontal wells. IJHT,
International Journal of Heat and
Technology, 34(1), 65-72.
[17] Morshed, M., Amin, A., Rahman, M. A., &
Imtiaz, S. (2016, July). Experimental and
computational analysis of pressure response in
a multiphase flow loop. In AIP Conference
Proceedings (Vol. 1754, No. 1). AIP
Publishing.
[18] Hon, L. T., & Pao, W. (2017). CFD
Simulation of Two-phase Slug Flow Liquid
Carryover in T-junction Corresponds to
Various Diameter Ratio. UTP Technical
Report. DOI: 10.13140/RG. 2.2.
20419.20008.
[19] Sun, F., Yao, Y., Li, X., Zhao, L., Ding, G., &
Zhang, X. (2017). The mass and heat transfer
characteristics of superheated steam coupled
with non-condensing gases in perforated
horizontal wellbores. Journal of Petroleum
Science and Engineering, 156, 460-467.
[20] Azadi, M., Aminossadati, S. M., & Chen, Z.
(2016). Large-scale study of the effect of
wellbore geometry on integrated reservoir-
wellbore flow. Journal of Natural Gas
Science and Engineering, 35, 320-330.
[21] Hamad, F. A., Faraji, F., Santim, C. G. S.,
Basha, N., & Ali, Z. (2017). Investigation of
pressure drop in horizontal pipes with
different diameters. International Journal of
Multiphase Flow, 91, 120-129.
[22] Baghernejad, Y., Hajidavalloo, E., Zadeh, S.
M. H., & Behbahani-Nejad, M. (2019). Effect
of pipe rotation on flow pattern and pressure
drop of horizontal two-phase
flow. International Journal of Multiphase
Flow, 111, 101-111.
[23] Wen, J., Yang, M., Qi, W., Wang, J., Yuan,
Q., & Luo, W. (2018). Experimental analysis
and numerical simulation of variable mass
flow in horizontal wellbore. International
Journal of Heat & Technology, 36(1).
[24] Hasanain. et al. (2017). "Numerical Analysis
of Two-Phase Flow Patterns in Vertical and
Horizontal Pipes." Wseas Transactions on
Fluid Mechanics, 12, 131-140.
[25] Abdulkadir, M. (2011). Experimental and
computational fluid dynamics (CFD) studies
of gas-liquid flow in bends, University of
Nottingham. PhD, thesis.
[26] Versteeg, H. K., & Malalasekera, W.
(2007). An introduction to computational fluid
dynamics: the finite volume method. Pearson
education.
[27] Ortiz-Vidal, L. E., Mureithi, N., & Rodriguez,
O. M. H. (2014). Two-phase friction factor in
gas-liquid pipe flow. Revista de Engenharia
Térmica, 13(2), 81-88.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed to the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself.
The authors would like to acknowledge the financial
support received from the Ministry of Education
Malaysia under the Fundamental Research Grant
Scheme (FRGS) scheme (20180110FRGS) that
enable the work to be carried out.
Conflict of Interest
Please check the following as appropriate:
o All authors have participated in (a) conception
and design, or analysis and interpretation of the
data; (b) drafting the article or revising it
critically for important intellectual content; and
(c) approval of the final version.
o This manuscript has not been submitted to, nor
is under review at, another journal or other
publishing venue.
o The authors have no affiliation with any
organization with a direct or indirect financial
interest in the subject matter discussed in the
manuscript
o The authors have affiliations with organizations
with direct or indirect financial interest in the
subject matter discussed in the manuscript:
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.21
Hasanain J. Kareem, Hasril Hasini, Mohammad A. Abdulwahid
E-ISSN: 2224-347X
231
Volume 19, 2024
