Post on 21-Mar-2020
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Serra Negra – SP, 19 a 22 de Agosto de 2019
Euler-Lagrange numerical model for the sulfate scale
formation including the effects of adhesion and solid
crystal growth
Marina E. Mazuroski1, Vinicius G. Poletto1, Fernando C. De Lai1
André L. Martins2, Silvio L. M. Junqueira1
1Research Center for Rheology and Non-Newtonian Fluids – CERNN, Federal University of Technology - Paraná –
UTFPR, Curitiba-PR, Brazil, 81280-340,
mazuroski@alunos.utfpr.edu.br, vpoletto@utfpr.edu.br, fernandodelai@utfpr.edu.br, silvio@utfpr.edu.br 2Research and Development Center – CENPES, PETROBRAS, Rio de Janeiro-RJ, Brazil, 21941-915,
aleibsohn@petrobras.com.br
Abstract Scale deposition in downhole equipment and completion systems can cause productivity issues, with limited oil output,
equipment damage and safety issues. In this context, the experiment Dynamic Tube Blocking test, for instance, allows
the studying of crystal formation under different saturation, temperature and pressure conditions. However, the DTB,
like other related experiments, are run with low flow rates, which are far from representing the real downhole flow
environment. Furthermore, limitations arise in determining the scaling tendency of complex geometry parts such as
sand control screens and valves. This work proposes a numerical model for simulating liquid-solid flow for the scaling
formation process, incorporating the effects of crystal growth and adhesion. The solution is represented as a
continuous fluid phase evaluated through an eulerian approach, while the crystals in solid phase are portrayed as
discrete spherical particles with a lagrangian approach. Both are mathematically formulated with the Dense Discrete
Phase Model (DDPM) coupled with the Discrete Element Method (DEM), resulting into a four-way interaction
between the phases. The growth mechanism is simulated through User Defined Functions so that different particle
functions for the diameter growth are studied in a capillary tube as well as on a heterogeneous porous medium. The
constant force model represents adhesive forces, assessed through a repose angle study and then incorporated in the
DTB simulation. Further calibration of the numerical model will allow the prediction of the flow reaction to scale
formation phenomena like crystal growth and solids adhesion followed by deposition on a surface.
1. Introduction Secondary oil recovery can be achieved through
injection of seawater into production wells, which
maintains reservoir pressure and increases the oil
output. However, the mixture of incompatible seawater
and formation connate water triggers scale formation
and deposition, one of the most serious problems that
can affect hydrocarbon production environments.
Scaling decreases the productivity of the well through
the formation of a thick layer that can take place in
injection and production wells, pipelines, other
production facilities and equipment, causing blockage
and clogging the flow, severely increasing the pressure
drop in the production tubing. Precipitation can also
cause formation damage in the reservoir and increase
corrosion rates, resulting in safety issues to the
operation [1], [2].
The deposition process initiates because of the low
solubility of substances formed through the mixture of
injection and formation water containing
complementary salt ions. Combined with certain
temperature and pressure conditions of the system, and
influenced by other parameters, these salts may achieve
a supersaturated state, and precipitation prospect
increases drastically [3].
Depending on the reservoir and seawater compositions,
different types of scale can assemble, the most common
being sulfate and carbonate salts, such as barium
sulfate, strontium sulfate, calcium sulfate and calcium
carbonate [3].
At certain circumstances, an effective scale
management strategy helps assuring oil production
conditions. Most measures focus on reducing scale
potential, since the removal of deposited salts from
down hole equipment has a much higher cost [1], [4].
Common measures to prevent scale formation include
desulfation of injected water, which avoids only sulfate
scale, and use of inhibitors, chemicals designed to
restrain crystal formation and growth [1], [2]. The
classification of the inhibitor relies on the mechanism
of the scale prevention: Thermodynamic inhibitors act
by decreasing the ionic activity and therefore
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decreasing the super saturation of the solution. On the
other hand, kinetic inhibitors act on the adsorption of
the solid crystal surface, hindering the incorporation of
ions and, as a consequence, its growth [4].
The effectiveness of chemical inhibitors is influenced
by the thermodynamic conditions of the well,
composition of the water mixture, thermal stability of
the inhibitor and brine compatibility [5]. Mostly
important, the action of the inhibitors is only
accomplished by the injection in the seawater-brine
mixture at the downhole assembly. However, the
production zones in modern well completion systems
are not approachable by the injection lines, remaining
vulnerable. For instance, it is not possible to use
injection lines in Petrobras’s cableless intelligent well
completion design [6].
The downhole parts (e.g. internal control valves, sliding
sleeves valves, sand control screens, gravel packing)
are prone of inorganic scaling. For this reason, the
understanding of scale formation has been the subject
of studies for decades. Thermodynamic and kinetic
models are widely available in commercial softwares
such as MultiScale, GWB and SOLMINEQ. However,
while such computer packages are able to determine the
saturation of a system based on thermodynamic
conditions, they do not take into account the influence
of flow dynamics over the scale formation. Therefore,
miscalculations of the scaling risk arise
On the other hand, experimental tests are appropriate
for studying the hydrodynamic effects on scale
precipitation, and are usually combined with the results
from thermodynamic modelling. For instance, the
Dynamic Tube Blocking Test (DTB) is a common
experiment for evaluating scale formation dynamics in
a capillary tube by measuring the pressure drop
response of the flow of a supersaturated ionic solution.
Spite of the possibility of setting high pressure and high
temperature in the DTB, the flow rate is low, not
representing well production conditions.
Numerical modelling of the process of scale formation
may arise as a solution for the evaluation of the scaling
tendency in downhole parts with complex geometry,
like sand screens and SSV valves. Furthermore, the
numerical method is capable of implementing a more
extensive range of boundary conditions to represent
production conditions, such as high temperatures and
high pressures, which are difficult to manage in
experimental tests.
In this work it is described the developments into a
numerical model for the liquid-solid two-phase flow for
the simulation of the process of scale formation,
incorporating the effects of particle growth and particle
adhesion. A hybrid Euler-Lagrange approach is applied
for the formulation of the flow and the solid particles,
which mimic the precipitated sulfate crystals. The four-
way interaction between the phases allow the
evaluation of the particle effect over the flow field. The
numerical simulation is resorted by coupling the Dense
Discrete Phase Model (DDPM), able to compute either
dilute or dense particulate flows, to the Discrete
Element Method (DEM). The DEM incorporates the
influence of forces that arises from collision, friction
and adhesion among particles or between a particle and
a surface. In this work, a number of tests are presented
to explore the potentiality of the DDPM-DEM, like the
simulation of the particle growth in a capillary tube and
in a heterogeneous porous medium. The particle
adhesion is studied through the reproduction of the
angle of repose test and the adhesion into a capillary
tube.
2. Problem Formulation The scale formation process is envisioned as a two-
phase liquid-solid flow constituted of a liquid medium
with discrete solid particles, which mimic the
precipitated crystals of sulfate. The crystal formation
process is illustrated in Figure 1, which begins with a
supersaturated solution with the formation of small
nuclei (approximately 10-10 m). These nuclei will grow
or undergo secondary nucleation, which starts from
already existent nuclei. If the system conditions allow,
the clusters will grow to larger sizes (100 µm), and start
to agglomerate and adhere to other surfaces, constantly
breaking up and forming new groups. The numerical
model proposed in the present work comprises the
phenomena of crystal growth, agglomeration/adhesion
and crystal breakup.
Figure 1. Two-phase liquid-solid flow for the scaling
process including adhesion and growing effects.
The liquid-solid two-phase flow is formulated through
an Euler-Lagrange approach. The equations are
numerically simulated with the CFD-DEM coupling by
the Dense Discrete Phase Model (DDPM) [7] and the
Discrete Element Method (DEM) [8]. The mass and
momentum balance equations are adapted to
incorporate the influence of the solid phase through the
means of the fluid volume fraction (εβ), as seen in Eqs.
(1) and (2), and the momentum coupling term, Fpβ
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[N/m³]. Such equations are able to model either dilute
or dense particulate flows.
0t
u (1)
T
p
t
p
u u u
u u g F
(2)
The solid phase is represented by discrete spherical
particles individually tracked in Lagrangian referential,
with the position xp individually calculated from the
velocity up in Eq. (3), which is obtained by the linear
momentum balance in Eq. (4). The particle angular
momentum balance is also calculated, through Eq. (5).
[ ]
[ ]
p j
p j
d
dt
xu (3)
[ ]
[ ] [ ] [ ] [ ]
[ ] [ ]
p j
p D j G j VM j PG j
SL j DEM j
dm
dt
uF F F F
F F
(4)
[ ]
[ ] [ ]
p j
D j DEM j
dI
dt
ωT T (5)
The forces in Eq. (4) arise from the flow effects, such
as the drag force, the virtual mass force, the pressure
gradient, the Saffman lift and the Magnus lift. The
particle-particle or particle-wall interactions result in
collision, frictional or adhesion forces. The torques,
from Eq. (5), represent the drag torque and the contact
torque, respectively. The equations for these forces are
summarized in Table 1.
Table 1. Forces acting on particles.
Forces
Drag [ ]
[ ] [ ] [ ] [ ]2
Re18( )
24
D p j
D j p j j p j
p p
Cm
d
F u u (6)
Gravity and buoyancy
[ ] [ ]
p
G j p j
p
m
gF (7)
Virtual mass [ ] [ ] [ ] [ ]VM j VM p j j p j
p
DC m
Dt
F u u (8)
Pressure gradient [ ] [ ] [ ] [ ]PG j p j j j
p
m
F u u (9)
Saffman lift [ ] [ ] [ ] [ ] [ ]( )SL j SL p j j j p j
p
C m
F u u u (10)
Contact
[ ] [ , ] [ , ] [ , ] [ , ]DEM j n i j i j t i j i j F F n F t
[ ] [ , ] [ , ]n j n n n p i j i jk F u n
[ ] [ ]t j a n jF F
,
0 if
min( , ) if
n adh
n adhadh n adhi j
s
f g m m s
F
(11)
(12)
(13)
(14)
Torques
Drag [ ] [ ] [ ]d j j p jC T ω
1/2 1
[ ] [ ] [ ]6,45Re 32,1Rej j jC
(15)
(16)
Contact [ ]
[ ] [ ] [ ] [ ]
[ ]2
p p j
DEM j ij t j r n j
p j
d
ωT n F F
ω (17)
The fluid and particulate phase numerical solution are
calculated separately, initiated with the convergence of
the fluid phase by finite volume method, followed by
the solid phase injections into the domain. The particles
velocity and angular velocity are individually
determined by implicit numeric integration, with the
particle-fluid forces calculations based on the fluid
flow field. Their position is then estimated through the
Crank-Nicholson scheme. Collision and adhesion
forces are computed only upon identification of contact
among particles between a particle and a surface, and
fulfillment of adhesion criteria.
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The particles in a collision are treated are soft-spheres
that can overlap each other. The force generated can be
calculated through various models, with the spring-
dashpot system being a simple and effective one,
described by Eq. (12). It takes into account the particles
spring coefficient kn [N/m] damping coefficient ηn
[N.s/m] and the superposition extent [7]. The friction
foces are calculated through the Coulomb model,
defined in Eq. (13).
The adhesion effects are mainly calculated through the
contact force achieved during collision. Several
adhesion force models are proposed in literature, with
different input variables. The simplest one presented is
the constant adhesive force model, which activates
based on a determined minimum distance δadh [m]
between particles or particles and boundaries, inflicting
a constant force value Fn,adh [N] based on the solids
mass [8]. The model is described by the Eq. (14).
The momentum balance equation then receives the
solid and fluid volumetric fraction, and the volume-
averaged fluid-particle forces in each mesh control
volume, followed by a new solution of the continuous
phase by the finite volume method, new particle
injections, the update of the particle forces and so on.
3. Results and discussions The DDPM-DEM numerical model capabilities are
demonstrated though reproduction of literature results
The fluid-particle interaction forces are evaluated by
comparing the experimental results of Mordant and
Pinton [9] of beads abandoned from rest in water. The
numerical results for acceleration curves reaching
terminal velocity are presented and compared with
numerical results in Figure 2. The calculation of the
fluid-particle forces is accurate.
Figure 2. Comparison of simulated (DDPM) and
experimental [9] results for the acceleration curves of beads
abandoned in water.
The computation of the particle’s collisional force
imping normally on a surface is also verified, since
such force affects the adhesion mechanism included in
the numerical model. Gondret, Lance and Petit [10]
showed experimental results for particle rebound
acceleration, which is correlated to the numerical
calculations obtained via DDPM-DEM. The
comparison, as seen in Figure 3, indicates good
agreement and reinforces the numerical model capacity
of accurately reflecting wall effects into solid discrete
particles.
Figure 3. Comparison of DDPM-DEM numerical and
experimental [10] results for the acceleration curve of a
single particle impinging normally on a surface normal.
Finally, the scale formation process is considered as a
particle deposition into a surface followed by a particle
bed formation. Therefore, a dense solid two-phase flow
is observed, which necessarily affects the fluid flow by
imposing a pressure drop. To fulfill such verification,
experimental results for the transient bed formation of
a liquid-solid flow in a horizontal channel are displayed
in Figure 4. The numerical result reproduces the bed
formation process, resulting in a bed of comparable
dimensions to the experimental one. Furthermore, at 50
s, the fluid velocity field indicates that the fluid
accelerates above the bed, corroborating the particle’s
effect into the flow field.
Figure 4. Reproduction of literature results for the
horizontal liquid-solid flow with bed formation.
Dynamic Tube Blocking Test simulation parameters
were based on Santos [11] experimental set up with
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water flowing in laminar regime through a 0,5 mm tube
with length of 1,0 m, which is shortened to 0,0625 m to
reduce the mesh size. The solid phase is considered
mono disperse with constant diameter and properties,
cast in accordance to that of barium sulfate crystals.
The main parameters are listed in Table 2.
Table 2. Numerical test parameters
Tube diameter dt (mm) 0,5
Tube length, L (m) 1,0
Fluid flow, Q (mL/min) 10
Fluid specific mass, ρβ (kg/m³) 1000
Fluid viscosity, µβ (cP) 1,0
Reynolds number, Reβ 4,2x102
Particle diameter, dp (µm) 70
Solid specific mass, ρp (kg/m³) 4500
The boundary conditions are set so that water enters the
domain with uniform velocity, developing along the
tube length, with the no-slip condition throughout the
tube walls. Particles are injected from a surface
injection positioned in the fully developed flow region.
The DDPM-DEM requires a number of parameters to
be set up, which are listed on Table 3. A soft-sphere
approach is used to determine the deformation and
elasticity of the contact between two particles, given by
Eq. (12).
Table 3. DDPM-DEM parameters.
Fluid inlet velocity, uβ (m/s) 0,85
Particle injection velocity 1,7
Particle injection points 9
Particle flow (part/s) 18x103
Spring coefficient, kn (N/m) 30
Particle-particle restitution
coefficient, ep-p 0,75
Particle-wall restitution
coefficient, ep-w 0,75
Fluid time step, Δtβ (s) 5x10-4
Particle time step, Δtp (s) 5x10-6
For the DTB simulations, the domain is discretized with
mesh elements able to compute the laminar flow and
boundary layer effects with less than 10% deviation
from the analytical solution for the velocity and
pressure profiles. The cross-section and the axial-
section view of the mesh with 6,2x104 elements is
shown in Figure 5. The particles are injected through
nine injections points, tending to settle down in the tube
wall, and being dragged by the flow toward the pressure
outlet. The main response variable of DTB
experimental test is the pressure differential along the
pipe, as presented in Figure 5. The pressure increases
due the action of the particles, stabilizing after the solid
phase starts leaving the domain and the particle number
stays approximately constant within the geometry.
Therefore, the flow is sensible to the particle’s effect,
elucidating the potential of the DDPM-DEM to take
into account the effects of the particle adhesion and
growth, to be implemented in the sequence.
Figure 5. Results for solid-liquid numerical solution with
pressure response from the fluid.
The growth phenomenon is represented through
diameter variations, which are implemented via user
defined functions (UDF), coupled with the DDPM-
DEM model. The expressions programmed in the
UDFs correlate the diameter value with variables such
as time, space and material properties. The diameter
values varied from 30 to 70 µm, with collision
parameters remaining the same as Table 3. Results for
the DTB including the effects of diameter growth are
presented in Figure 6 by different growing patterns
used for the functions.
In the simulation with diameter growing with flow
time, shown in Figure 6 (a), all particles grow
uniformly, while in the results showed in Figure 6 (b),
particles grow as their residence time in the domain
increases, achieving their maximum size at a larger
distance from the entrance. The diameter variation with
the longitudinal position, depicted in Figure 6 (c) ,
displays similar behavior as in Figure 6 (b), although
their growth is related to their distance from the inlet.
The diameter function (d) and the longitudinal and
radial growth diameter function (e) are both evaluated
with nine injection points to better illustrate size
differences. The particles grow when they move closer
to the outlet and to the walls. The expression is written
so that they shrink if they move toward the tube center,
indicating the possibility of diameter change in both
ways. The radial and longitudinal simulation also
demonstrates the possibility of using several variables
in a same function. The DDPM-DEM model is versatile
when responding to different diameter functions with
the flow reacting accordingly to the particle size
changes, as shown by the gravity influence on heavier
particles.
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Figure 6. Simulation of the liquid-solid flow with diameter
varying with: (a) Flow time; (b) Residence time; (c)
Longitudinal position; (d) Radial position and (e)
Longitudinal and radial position.
The particulate flow with the effect of diameter growth
is simulated in a heterogeneous porous medium
conceived as a staggered array of cylinders. In order to
observe the particle retention, the array has an
anisotropic and an isotropic region regarding the
variation of the porosity, φ [-], and the pore throat, pt
[mm], minimum distance between adjacent cylinders,
as depicted in Figure 7. The particles enter the domain
with a diameter smaller then the minimum pore throat
size, passing through without plugging the media. The
UDF is programmed with a residence time function that
activates after 5 seconds of particle injections, making
the diameter change from 0,5 to 1,0 mm, blocking the
smaller pore regions. The problem parameters are
detailed in Table 4.
Figure 7. Porosity and pore throat spatial variation for the
staggered array of cylinders.
Table 4. Porous media geometry and simulation parameters.
Porous media dimensions (mm) 180 x 90
Anisotropic region length (mm) 90
Isotropic region length (mm) 90
Pore throat (mm) 2,4-0,6
Fluid density, ρβ (kg/m³) 1181
Fluid viscosity, µβ (Pa·s) 0,0195
Flow Reynolds number, Reβ 100
Particle diameter range, dp (mm) 0,5-1,0
Particle density, ρp (kg/m³) 1181
Spring coefficient, kn (N/m) 80
Particle-particle restitution
coefficient, ep-p 0,90
Particle-wall restitution
coefficient, ep-w 0,60
Fluid time step, Δtβ (s) 1x10-2
Particle time step, Δtp (s) 1x10-5
The particles in the domain just before the diameter
change starts are shown in Figure 8 (a) and after 3
seconds of growth in Figure 8 (b). Particles near the
outlet are trapped, because the pore throat is lower than
the respective diameter. This shows an appropriate
response from the DDPM-DEM, which is able to
acknowledge the growth of an agglomerate of particles
near a wall, respecting the boundary conditions set.
Figure 8. Particle growth in an anisotropic array of
staggered cylinders.
The adhesion model is tested with the software Rocky
DEM, which already has implemented the adhesion
equations. The variation of the adhesion distance is
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analyzed by verifying the rest angle of an agglomerate
of particles in a vertical tube that lifts up. The particles
then arrange themselves in a horizontal flat tray, with
the angle formed by the pile measured. The parameters
for the simulation are listed on Table 5. It is relevant to
notice that although the spring-dashpot collision force
model is also used, as stated in Eq. (12), Rocky DEM
utilizes the Young Modulus as input for the spring
coefficient calculation.
Table 5. Adhesion force model test parameters.
Tube diameter, D (m) 0,1
Tube length, L (m) 0,7
Particle diameter, dp (m) 0,025
Particle density, ρp
(kg/m³) 1650
Particle-particle
restitution coefficient, ep-
p
0,30
Particle-wall restitution
coefficient, ep-w 0,30
Particle-particle friction
coefficient, µp-p 0,7
Particle-wall friction
coefficient, µp-w 0,5
Young Modulus (N/m²) 1x108
Particles injected 6000
Particle time step, Δtp (s) 1x10-4
In the constant force adhesion model described in
Section 2 it is necessary to specify the adhesive force
intensity as well as the sphere of influence of the
adhesion around the particles. Figure 9 shows the
results varying the minimum adhesion distance from
zero to 1x10-3 m. The increase in this value produced in
a larger portion of particles subjected to the constant
adhesion force. As a result, the particles became more
agglomerated, culminating in adhesion forces strong
enough to hold them inside the vertical tube.
Figure 9. Rest angle test results for different adhesion
distances.
The adhesion model is also tested in the Dynamic Tube
Blocking Test geometry, with the coupling of the
softwares ANSYS Fluent and Rocky DEM. The first
simulates de fluid flow phase, using the parameters
listed in Table 2, while the second calculates the solid
phase with the adhesion effects included. The solutions
communicate and influence one another.
The parameters for the particles are listed in Table 6,
with the results shown in Figure 10.
Table 6. Solid phase parameters for adhesion simulations in
DTB geometry.
Particle diameter, dp
(µm) 25
Particle density, ρp
(kg/m³) 4500
Particle-particle
restitution coefficient, ep-
p
0,3
Particle-wall restitution
coefficient, ep-w 0,3
Particle-particle friction
coefficient, µp-p 0,3
Particle-wall friction
coefficient, µp-w 0,3
Young Modulus (N/m²) 1x106
Particle flow (part/s) 18x103
Particle time step, Δtp (s) 1x10-4
Figure 10. Results for the constant adhesion force model in
a capillary tube.
The necessary force for particles to visibly adhere to the
wall was set as 250 times their weight. Even though the
adhesion criteria is met near the particle injection
surface, the flow pushes the attached solids along the
wall length and produce a thin particle layer that
spreads through the tube instead of accumulating near
the entrance, revealing a great impact of the fluid phase
in this phenomenon, even with the great magnitude of
the adhesion force set.
4. Conclusions.
Inorganic scaling formation and deposition in oilfield
downhole equipment and completion systems can
provoke serious issues ranging from productivity
reduction to increased corrosion rates and equipment
damage. A numerical model to simulate the scaling
process as a solid-liquid flow, including the effects of
crystal growth and adhesion is proposed, an
advantageous alternative to expensive and limited
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experimental tests and a complement to the several
thermodynamic models available, which do not include
relevant hydrodynamic effects in their calculations.
The method proposed uses an Euler-Lagrange approach
with the DDPM-DEM model with four-way coupling.
The model showed its capacity of perceiving the solid
phase influence on the fluid phase through the pressure
differential increase following the injection of solid
particles in a fully develop fluid flow. Crystal growth is
represented through User Defined Functions with
expressions for the particles diameter. Results for the
simulation in the DTB geometry (capillary tube) and in
a heterogeneous porous media demonstrated the
versatility of UDFs and the ability of the method in
adjusting particle forces calculations according to the
size of the spheres and respecting boundary conditions.
Finally, the adhesion mechanism is evaluated through a
rest angle test, elucidating the influence of the constant
adhesion force input parameters into the pile
morphology. The adhesion forces into the liquid-solid
flow are testes in the DTB geometry, with results
revealing a significant influence of the flow in the
particles deposition throughout the geometry, which
needed a great adhesion force to compensate for this
effect. Further study calibration of the DDPM-DEM
applied for the DTB problem will refine the model’s
capacity of simulating the solid-liquid flow with an
accurate representation of the growth and adhesion
effects of the scaling process.
5. Acknowledgments
The authors are grateful to the Brazilian Petroleum
Agency (ANP), the Human Resources Program for the
Petroleum and Gas Sector PRH-ANP (PRH10 –
UTFPR) and CENPES-PETROBRAS for the provided
financial support.
6. References [1] A. A. Olajire, “A review of oilfield scale
management technology for oil and gas
production,” J. Pet. Sci. Eng., vol. 135, pp.
723–737, 2015.
[2] M. S. Kamal, I. Hussein, M. Mahmoud, A. S.
Sultan, and M. A. S. Saad, “Oilfield scale
formation and chemical removal: A review,”
J. Pet. Sci. Eng., vol. 171, no. January, pp.
127–139, 2018.
[3] A. B. BinMerdhah, A. A. M. Yassin, and M.
A. Muherei, “Laboratory and prediction of
barium sulfate scaling at high-barium
formation water,” J. Pet. Sci. Eng., vol. 70, no.
1–2, pp. 79–88, 2010.
[4] C. Fan, A. Kan, P. Zhang, and M. Tomson,
“Barite Nucleation and Inhibition at 0 to
200°C With and Without Thermodynamic
Hydrate Inhibitors,” SPE J., vol. 16, no. 2, pp.
20–22, 2011.
[5] S. J. Dyer and G. M. Graham, “The effect of
temperature and pressure on oilfield scale
formation,” J. Pet. Sci. Eng., vol. 35, no. 1–2,
pp. 95–107, 2002.
[6] M. F. Da Silva, C. C. Jacinto, C. Hernalsteens,
M. Nobrega, M. Defilippo Soares, E.
Schnitzler, and L. B. Nardi, “Cableless
Intelligent Well Completion Development
Based on Reliability,” Offshore Tecnhology
Conf., no. July, pp. 1–10, 2017.
[7] B. Popoff and M. Braun, “A Lagrangian
Approach to Dense Particulate Flows,” in
Proceedings of the ICMF 2007, 6th
International Conference on Multiphase Flow,
2007.
[8] P. A. Cundall and O. D. L. Strack, “A discrete
numerical model for granular assemblies,”
Géotechnique, vol. 29, no. 1, pp. 47–65, 1979.
[9] N. Mordant and J. Pinton, “Velocity
measurement of a settling sphere,” Eur. Phys.
J., vol. 352, pp. 343–352, 2000.
[10] P. Gondret, M. Lance, and L. Petit, “Bouncing
motion of spherical particles in fluids,” Phys.
Fluids, vol. 14, no. 2, pp. 643–652, 2002.
[11] H. F. L. Santos, B. B. Castro, M. Bloch, A. L.
Martins, H. E. P. Schlüter, M. F. S. Júnior, C.
M. C. Jacinto, and F. F. Rosário, “A Physical
Model for Scale Growth during the Dynamic
Tube Blocking Test,” OTC Bras., no. Figure 1,
pp. 1–20, 2017.