1 Experimental and CFD study of an Electrical Submersible Pump’s (ESP) performance operating under Two-Phase Liquid-Liquid Flow and O/W emulsion Daniel Fernando Rozo Oviedo Deisy Steffania Becerra Tuta Department of Chemical Engineering, Universidad de los Andes, Bogotá, Colombia General objective To study and contrast the operation and performance of an Electrical Submersible Pump (ESP) considering two-phase liquid-liquid flow and O/W direct emulsion, through the analysis of key operational parameters and the characterization of its behavior using dimensionless variables. Specific objectives 1. To generate a computational CFD model of the ESP that accurately captures the operation of the system and validate it against experimental observations. 2. To analyze the effect of the rheological behavior of the tested fluid on certain operational parameters of the pump, such as total head, mechanical and hydraulic power and efficiency. 3. To identify the inversion point of emulsions inside the ESP. 4. To determine the effect of the operation of the ESP on the oil/water droplet size distribution and the mean droplet size.
Transcript
1
Experimental and CFD study of an Electrical Submersible Pump’s
(ESP) performance operating under Two-Phase Liquid-Liquid Flow
and O/W emulsion
Daniel Fernando Rozo Oviedo
Deisy Steffania Becerra Tuta
Department of Chemical Engineering, Universidad de los Andes, Bogotá, Colombia
General objective
To study and contrast the operation and performance of an Electrical Submersible Pump (ESP)
considering two-phase liquid-liquid flow and O/W direct emulsion, through the analysis of key operational
parameters and the characterization of its behavior using dimensionless variables.
Specific objectives
1. To generate a computational CFD model of the ESP that accurately captures the operation of the
system and validate it against experimental observations.
2. To analyze the effect of the rheological behavior of the tested fluid on certain operational
parameters of the pump, such as total head, mechanical and hydraulic power and efficiency.
3. To identify the inversion point of emulsions inside the ESP.
4. To determine the effect of the operation of the ESP on the oil/water droplet size distribution and
the mean droplet size.
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Experimental and CFD study of an Electrical Submersible Pump’s
(ESP) operating under Two-Phase Liquid-Liquid Flow and Water-Oil
emulsions
Daniel Fernando Rozo Oviedo
Deisy Steffania Becerra Tuta
Department of Chemical Engineering, Universidad de los Andes, Bogotá, Colombia
ABSTRACT
Electrical Submersible Pumps (ESPs) are one of the most common artificial lifting methods employed in the
extraction of crude oil worldwide. The main purpose of this work is to study the ESP’s performance under two
phase Liquid-Liquid flow and O/W emulsions. In this work both experimental and Computational Fluid Dynamic
(CFD) approaches were considered. A testing facility using a 4-stage Franklin Electric 1HP ESP in a 250L tank,
with a pipeline loop was constructed to carry out experiments at a constant rotational speed of 3450 rpm. The
pump’s performance was studied experimentally through the measurement of parameters such as torque, brake
power, flow rate, electrical current, and outlet pressure. Emulsion characterization was performed by measuring
the rheological behavior and particle size distribution. The commercial software STAR-CCM+ was used for the
CFD simulations. Water and oil single phase simulations were in good agreement with experimental data (MSE
of 3.58% for water, and 2.38% and 3.68% for the sunflower and mineral oil, respectively). For the two-phase L-
L simulations good agreement with experimental data was also observed (MSE of 5.38%) which have the inversion
point at 50% v / v oil and finally, stable emulsion phase inversion was found to occur at a 90% v/v oil concentration
where the particle size distribution is perfect monodisperse and viscosity increases.
recirculation, stage pressure drop and rotational speed,
giving a more comprehensive understanding of the
design and behavior observed for centrifugal pumps.
These models have been presented by authors as
Lobanoff (1992), Nelik (1999), Gulich (1999) and
more recently Nesbitt (2006). Specific emphasis on
ESP modelling and design has been carried out by
Takacs (2009). Analytical studies and models on the
behavior two phase flow and emulsions on centrifugal
pumps and particularly ESP systems are practically
non-existent given its inherent complexity for
predicting operational parameters such as hydraulic
power or head rise. Therefore, only experimental and
computational studies can be found, which provide
empirical or statistical models to predict several
fundamental variables.
2.2 Previous experimental studies
Single phase experimental studies and empirical
correlations have been developed early on by
institutions such as the Hydraulics Laboratory of
Lehigh University and the Ingersoll-Rand Company of
Philipsburg, New Jersey during years 1944-45. These
first systematic approaches were aimed to understand
the influence of the fluid’s viscosity on the
performance of the pumping equipment. Ippen (1945)
published the results gathered during those systematic
studies, which were performed on four different
centrifugal pumps with over 200 tests considering
various oils of different viscosities, in order to account
for the influence of varying Reynolds numbers against
fundamental parameters such as efficiency, head rise
and brake power. Since then, Hydraulic Institute (HI)
(1948) and more recently the KSB (2005) have updated
these studies and proposed empirical correlations and
correction factors accounting specifically on the fluid’s
viscosity for the design and expected performance of
centrifugal pumps. Empirical models have also been
proposed by Takacs and Turzo (2000) to account for
the effect of viscous fluids on the ESP operation. More
recently, Amaral et al. (2009) and Solano (2009)
further tested the empirical correlations and charts
provided by the HI and revealed that the correction
factors gave inappropriate estimations of the ESP
pressure rise for viscous fluids. Even more recent
studies have been conducted on the matter, Zhu et al
(2016), focusing on BEP and H-Q curve results for
different viscosity oils on a seven-stage ESP. Particular
analysis on stage performance and flow patterns is
conducted.
Despite all the available models and studies
performed on centrifugal pumps and ESPs, research
concerning two-phase L-L flow and emulsions has
begun recently. Most of the studies concerning two-
phase L-L mixture dynamics involve flow in pipelines,
as phase inversion prediction on pipe flow for water/oil
mixtures with varying oil viscosities carried out by
Arirachakaran et al. (1989) and analysis of the effect of
phase inversion on pressure gradients in pipelines as
conducted by Ioannou et al. (2004). Focusing on
centrifugal pumps and ESPs, Khalil et al. (2006) and
(2008) analyzed the rheological behavior of stable and
unstable O/W emulsions and determined that its
viscosity was the main factor which affected negatively
the pump’s performance.
Similarly, Ibrahim and Maloka (2006) were one of
the first to conduct droplet size characterization of oil-
water dispersion flow in centrifugal pumps and
proposed a correlation to calculate the daughter droplet
size distribution characteristic diameters as a function
on inlet distribution. Later, Morales et al. (2012)
analyzed he droplet formation in oil/water flow through
centrifugal pumps and found out that an increase in the
pump speed implied a decrease in droplet size. They
also concluded that the effects of mixture flow rate,
water cut, and inlet droplet size distribution could be
negligible. Currently, Perissinotto (2017) evaluated the
forces acting on individual oil drops within an ESP’S
impeller using high-speed photography and flow
visualization techniques. This work verifies the
observations reported by Morales (2012). Moreover,
Bulgarelli (2018) in his PhD thesis broadly analyzed
the emulsions viscosity behavior and phase inversion
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phenomena within and ESP, analyzing factors as
droplet size distribution and effective viscosity.
V.2 Previous computational (CFD) studies
Several computational studies have been carried
out for single phase flows with different approaches
such as centrifugal pump design optimization (Qi et al.,
2012 Zhang et al., 2013), instantaneous pressure
fluctuation (Gonzales et al. 2002) and high viscosity
fluid flow. Shojaeefard et al. (2006) conducted
experimental and CFD simulation for a centrifugal
pump working with viscous fluids, they found good
agreement between simulation and CFD data when
solving RANS equations with SST 𝑘 − 𝜔 turbulence
model. Stel (2014) simulated a three-stage ESP where
only one seventh of the stage was consider reducing
computational cost. Flow on diffuser was found to be
affected by suction head of downstream impellers
which indicates that simulation with multistage ESP
geometries agree better with experimental results than
that based on single-stage pumps. Sudden-rising head
phenomena occurring when a centrifugal pump handles
high viscosity fluids was studied by Li (2014) who
implemented standard 𝑘 − 𝜖 turbulence model and
non-equilibrium wall function into RANS equations
and confirmed that the phenomena studied occurred
due to a flow transition from hydraulically rough
regime to hydraulically smooth regime. More recently
Babayigit et al. (2017) improved considerably the
accuracy of the pump performance calculation by
studying the effect of leakages and balance holes on a
radial flow centrifugal pump but with an increase in the
computational time and cost.
Most of the CFD studies carried out on ESP and
centrifugal pumps have considered only gas-liquid
two-phase flow and have widely studied phenomena
such as phase distribution, gas locking and even
cavitation phenomena. However, research on L-L flow
and emulsions is very scarce and has only been treated
experimentally, given the complexity required to
model key processes such as droplet coalescence and
break up. The most complete research done on the
matter is by Croce (2014) on his MSc thesis, where he
studied two-phase Oil-Water flow and emulsion
formation on a seven stage ESP. This work studied the
variation of the effective viscosity against the water
fraction of the emulsion and analyzed the effect of
phase inversion on the pumping performance. An
empirical model was suggested based on the existing
models for oil/water emulsion’s effective viscosity.
III. MATERIALS AND METHODS
3.1 Experimental Procedure
An experimental study was carried out to complement and validate the information gathered through the CFD simulations performed. This section describes the main experimental facility used, the properties of tested fluids properties tested and the general experimental procedure that was followed.
3.1.1 Testing fluids
Single phase experiments were carried out using
150L of tap water, sunflower and mineral oil. Firstly,
the tap water used was chemically characterized and its
properties are shown in Table 1. Table 1. Chemical properties of tap water (Salud, 2011; Silva et al., 2015)
Parameter Value
pH 7.8
Conductivity (μS/cm) 65.5
Dissolved Metals (mg/L) 0.098
Turbidity (NTU) 0.4
In this case, the number of radicals present in the
water capable of generating salts related to water
hardness are low. Therefore, no major impact of ions
present needs to be considered for any surfactant effect
on the experiments of two-phase flow.
Secondly, with regards to the sunflower and
mineral oil used, viscosity and density were measured
at 18 °C, using a DV2T digital viscometer and a
pycnometer. Results are show in Table 2.
Table 2. Measured properties of oils
Substance Density
[kg/m3]
Viscosity
[cP]
Sunflower Oil 922 68.87 Mineral Oil 863 31
Water 997 1.2
As for the emulsion study, 96% Sodium Dodecyl
Sulfate (SDS, CHEMI Co., Colombia) was used as
surfactant. All emulsion formulations were prepared
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with an emulsifier concentration of 5.75 mg/mL of
water/oil mixture.
3.1.2 Experimental facility
All experiments were carried out using a 4 inch 1
HP four-stages Franklin Electric Tri-Seal Electrical
submersible pump contained in a 250L polyethylene
tank as shown in Figure 6.
Figure 6: Experimental facility Diagram
A 1” stainless steel pipeline was used to avoid fluid
leakage. Several measuring devices were implemented
in the assembly. A 5 Nm HBM-T22 torque transducer
and Clipx signal conditioner device were used for in
situ, real time torque monitoring. Pressure was
measured at the pump’s outlet using a Sper Scientific
pressure meter of 50 bar and transducer. Pump’s
rotational speed, voltage and power were measured and
controlled, using an E3 Optidrive frequency drive.
Finally, flow was measured using a Flomec-OM025
mechanical oval gear flow-meter due to the high
viscosity of the emulsions studied.
The viscosity and particle size measures were taken
at the experimental facilities of Universidad de los
Andes (Colombia). Rheological behavior was
determined using a TA Instruments ARG 2 Rheometer
with a shear rate that varied from 1.45 s−1 to 145.2 s−1
at a temperature of 20°C. The geometry used to
perform viscosity measurements was a concentric
conical cylinder geometry of 28 mm diameter and 42
mm length. Particle size of emulsions was obtained by
blue laser diffraction using a Mastersizer 3000 with a
water cell. Deionized water with a refractive index of
1.33 was used as dispersant. Emulsion’s conductivity
was measured using a Mettler Toledo S47 Sevenmulti
pH/conductivity module.
3.1.3 Emulsification process
The emulsification process was carried out
introducing into the tank 135L of pure sunflower oil.
Due to the high hydrophilicity of SDS, it was added in
the concentration specified before to 15L of Tap water.
This solution was added to the tank. Emulsification
process was carried out using the pump as mixer
running at a rotational speed of 3450 rpm for 20
minutes. After the pump’s performance measurement
procedure was executed, as sample of 15 mL of the
emulsion present in the tank was moved from the
system out by using the valve found at the inferior part
of the assembly. Again, a quantity of 15L of SDS-water
solution described before was added to the tank and
emulsification procedure was repeated. This process
was repeated until all formulations from 90% Oil vol
emulsion to 10% Oil vol emulsion were studied.
Finally, a small quantity (25-50 mL) of the emulsion
moved from the tank was stored and used for
rheological, particle size and conductivity
measurements, before the phase separation of the
unstable emulsion.
3.1.4 Two-phase flow procedure
The process followed in for two-phase oil-water
experiments is the same described in the emulsification
process with absence of SDS on the water phase. Due
to the lack of surfactant, there was no emulsion
formation, so rheology and particle size was not
measured on these experiments.
3.1.5 Pump’s performance measurement
Pump’s performance was studied by measuring
several variables such as pump’s torque, power,
hydraulic head and electrical current at different flow
rates. For controlling flow rate, a 1” gate valve was
installed before the flow meter as shown in Figure 6.
This valve was closed until the desired flow rate was
reached. Once at the desired flow rate, the pump’s
performance was measured in situ using the devices
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mentioned in sub-section 1.2 for 1 minute. After the
valve is closed again to a new flow rate, this process
was repeated until all range of desired flows was
covered. The flow range covered went from 0 GPM to
20 GPM for all experiments.
3.2 CFD modelling
3.2.1 Geometry Model
The geometry was modelled and generated using
Autodesk Inventor 2019 taking into an account the real
measures and geometry of the pump used in the
experimental part of the project. Only the top part of
the pump and the stages were modeled (see Figure 7)
given that these parts are the ones that mix and move
the fluid on the real assembly.
Figure 7. Pump’s 3D CAD model where a) is a stage and b) is the
pump’s top part which contains the stages.
The pump shaft, which drives the rotor, is located
through the fluid domain. After the CAD modeling, the
parts must be exported into STAR- CCM+ v13.04 for
the internal volume to be extracted and the different
domains splitted (See Figure 8). Each of the stages was
spitted into two parts according to its movement: the
rotatory part (impeller) and the stationary part
(diffuser).
Figure 8. Domains of the pump in CFD
3.2.2 Spatial discretization
The geometry showed in Figure 7 was imported
to the commercial CFD Software STAR-CCM+
v13.04. There, the spatial discretization of the pump
was constructed using the automated mesh tool offered
by the software with a polyhedral mesh. Due to the
complexity of the geometry of the pump and its stages,
polyhedral mesh was chosen over other types of mesh
such as the tetrahedral or the trimmed (orthogonal)
mesh. Polyhedral meshing models create arbitrary
polyhedral cell shape which uses 5 times less cells than
the equivalent tetrahedral mesh for obtaining the same
solution accuracy (Siemens, 2018a). The fact that a
polyhedral cell has a greater number of sides than the
cells used on the other mesh types, allows the CFD
software to compute gradients and flow distributions
with greater accuracy even in edges and corners where
cells may likely have a couple of more neighbors (Peric
& Ferguson, 2005). Additionally, polyhedral mesh
have an average of 14 faces which allow 7 optimal flow
directions which lets simulations complete with a lower
computational time (Peric & Ferguson, 2005; Siemens,
2018a).
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Figure 9. Meshed pump geometry
The polyhedral mesh was constructed using the
Surface Remesher, Thin Mesher and Prism Layer
Mesher models. The thin mesher allows thin areas (as
the tips of the blade of the impeller shown in Figure 9)
to have a prismatic type volume mesh so that the
overall cell quality improves and convergence is aid
(Siemens, 2018a). A quantity of 4 thin layers was used
on the simulation. The prim layer mesh model
generates orthogonal prismatic cells next to wall
surfaces and boundaries which are necessary to
improve the accuracy of the near wall flow solution
(Siemens, 2018a). This is critical for determining
different variables such as separation (which affects
drag and pressure drop), forces and heat transfers at
walls. The principal components that define a prim
layer are its thickness, the number of cell layers and its
size distribution. For this case the values taken are
presented in Table 3.
Table 3. Prims Layer Characteristics
Size Distribution Geometric Progression
Total Thickness 0.5 mm
Number of Layers 4
The number of layers was stablished at 4 with a
growth rate of 1.3. The total thickness of the prims
layer was tuned to 3.5% of the base size of the core
volume mesh in order, to assure a correct value of the
dimensionless wall distance (𝑦+) whose expression is
shown in the next equation.
𝑦+ =𝑢𝜏𝑦
𝜈
(25)
Where 𝑢𝜏 is the friction velocity which represents
the scale of velocities near a solid boundary and is a
function of the surface shear stress and the density of
the fluid. The value of the y+ (using the two-layer
formulation) must be bigger than 30 so that the velocity
profile matches the law of the wall (log layer region) as
shown in Figure 10 (Wilcox & others, 1998) . Given
that not all fluid is in direct contact with a wall, the
prims layer was no applied to regions as the stage
interfaces, the inlet and the outlet.
Figure 10. Typical velocity profile for turbulent boundary layer
(Wilcox et al., 1998).
For the rest of the mesh a general base size of 1.4cm
was stablished by performing a mesh independence test
which will be shown in section 4.1.1. The mesh
independency test consists on the evaluation of the
several factors like computational time, memory
requirement, and solution accuracy of the simulation as
function of the number of cells which make up the
mesh. Base size selection was the one whose number
of cells present simultaneous optimal conditions of the
factors mentioned above. Target size and minimum
size were established at 100% and 3.5% with respect to
the base size. The minimum size was stablished so that
it matches the prims layer thickness
3.2.3 Physical model selection
The physical model selection was made based on
the different conditions that were given during the real
experimentation. First, given that the fluid inside the
ESP moves in all direction due to the rotatory nature of
it, the presence of turbulence which is anisotropic, and
the 3D geometry already made, the fluid was modelled
in the three space dimensions. The principal physical
equations that are solved in CFD are momentum
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conservation (Navier-Stokes equation (26)) and mass
conservation (continuity equation (27)).
𝜕
𝜕𝑡∫ 𝜌𝑣𝑑𝑉𝑉
+ ∫ 𝜌𝑣 ⊗ 𝑣 ∙ 𝑑𝑎𝐴
= −∫ PI ∙ 𝑑𝑎𝐴
+
∫ 𝑇𝑠 ∙ 𝑑𝑎𝐴
+ ∫ 𝑓𝑏𝑑𝑉𝑉
+ ∫ 𝑠𝑢𝑉𝑑𝑉
(26)
𝜕
𝜕𝑡∫ 𝜌𝑑𝑉𝑉
+ ∫ 𝜌𝑣 ∙ 𝑑𝑎𝐴
= ∫ 𝑆𝑢𝑑𝑉𝑉
(27)
For solving these two equations a numerical
approach is necessary. In this case STAR-CCM+ uses
the finite volume discretization approach in which the
mathematical model shown above is transformed into
an algebraic equation system (Discretization
convention is shown in Figure 11).
Figure 11. Convention for the discretization of the transport
equation
The general transport equation in this scheme
becomes:
𝜕
𝜕𝑡(𝜌𝜙𝑉)0 + ∑ [𝜌𝜙(𝑣 ∙ 𝑎)]𝑓𝑓 = ∑ (Γ∇𝜙 ∙ 𝑎)𝑓𝑓 +
(𝑆𝜙𝑉)0
(28)
Where 𝜙 is the transported quantity. It can be seen
in equation (28) that the volume integral becomes the
mean value of the argument evaluated at the current
cell while the surface integral became a sum of the
property weighted by the face area over all of faces of
the cell. To solve the convective terms of the equation
several approaches can be made. In this case a second
order upwind approach (Equation (29)) was taken since
this scheme correctly estimates physical quantities in
the flow direction (as there is high convection on the
pump this direction is privileged), it is unconditionally
bounded (takes no negative values) and has high
precision in contrast with the downwind scheme which
is unconditionally unstable (Andersson et al., 2011).
(�̇�𝜙) = {�̇�𝑓(𝜙0 + 𝑠0(∇𝜙)0) 𝑓𝑜𝑟 �̇�𝑓 ≥ 0
�̇�𝑓(𝜙1 + 𝑠1(∇𝜙)1) 𝑓𝑜𝑟 �̇�𝑓 < 0 (29)
For the diffusive term in equation (28) a second-
order approach is taken by the CFD software involving
the cell values of 𝜙0 and 𝜙1 as shown in equation (30).
𝐷𝑓 = Γ𝑓[(𝜙1 − 𝜙0)�⃗⃗� ∙ 𝑎] (30)
Where Γ𝑓 is the diffusivity fase, a is the surface area
vector and 𝛼 is normalized vector normal to the cell
area. Segregated Flow solver is selected due to the
incompressible nature of the fluid used and because it
converges within less computational time than the
coupled flow solver. This model solves the equation of
motion and continuity in a uncouple manner and then,
linkage between the two is assured using a pressure-
correction equation following a Simple type algorithm.
To obtain how the system evolves in time, the
implicit unsteady model approach for solving the
temporal dependent parts of the equation showed above
was used. In this approach each physical time-step
involves a certain number of inner iterations in order to
converge to a solution for that given instant of time.
This fully implicit method is unconditionally bounded
which helps the solver convergence. The time step is
determined using the Courant number such that this
time step is shorter than the time it takes to transport
past the cell.
𝐶𝐹𝐿 =𝜌(Δ𝑥)2
Δt Γ (𝐷𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑒),
Δ𝑥
Δt v (𝐶𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑣𝑒) (31)
In the simulation case the time step was let by
default at a value of 5E-5s with a standard maximum
number of inner iterations of 80.
Turbulence is one of the most important factors on
fluid dynamic modeling due to the fact that it enhances
heat- and mass transfer rate. It is a decaying process
where a large turbulent structure (eddies) breaks up into
smaller and smaller until the flow becomes laminar
(Figure 12).
Figure 12. Energy flux from large to small scales (Andersson, et
al., 2012).
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Due to the chaotic nature of turbulence, it has
received a statistical treatment for its understanding.
Even though one-point quantitates do not recreate the
full statistics of the include they still include lots of
information such as the mean flow velocity and the
turbulent kinetic energy per unit of mass 𝑘. In the one
– point statistics velocity at any particular position and
time is divided into and average an a fluctuating part.
𝑣𝑖 = ⟨𝑣𝑖⟩ + 𝑢𝑖 (32)
This equation is known as the Reynolds
decomposition. Applying Reynolds decomposition to
the Navier -Stokes equation gives the next expression:
𝜕⟨𝑣𝑖⟩
𝜕𝑡+ ⟨𝑣𝑗⟩
𝜕⟨𝑣𝑖⟩
𝜕𝑥𝑗= −
1
𝜌
𝜕⟨P⟩
𝜕𝑥𝑖+ 𝜈
𝜕2⟨𝑣𝑖⟩
𝜕𝑥𝑗2 −
𝜕⟨𝑢𝑖𝑢𝑗⟩
𝜕𝑥𝑗 (33)
Equation (33) is known as the Reynold Average
Navier-Stokes (RANS) equation. The last term of this
equation −𝜌⟨𝑢𝑖𝑢𝑗⟩ is referred to as the Reynolds
stresses which is very important since it introduces a
coupling between the mean and fluctuating part of the
velocity field. To calculate the components of this
tensor, at thin layer adjacent to walls this tensor
becomes comparable to the viscus stress.
𝜌||⟨𝑢𝑖𝑢𝑗⟩|| ≈ μT ‖𝜕⟨𝑣𝑖⟩
𝜕𝑥𝑗+
𝜕⟨𝑣𝑗⟩
𝜕𝑥𝑗‖ (34)
This equation is the Boussinesq approximation
which treats eddies like molecules and introduces an
important term which is the turbulent viscosity which
can be seen as an eddy viscosity. Thus, if specific
details on turbulence are not important, it can interpret
the fluid as a pseudo-fluid with an increased viscosity
𝜈𝑒𝑓𝑓 = 𝜈 + 𝜈𝑇. Knowing the characteristic velocity (𝑢)
and scale of local turbulence (𝑙) enables to calculate
this viscosity in the following way.
This characteristic velocity and scale can be given
in term of the kinetic energy given to the turbulence 𝑘
and the energy dissipation rate 𝜖 which are obtained as
solution to their respective transport equations. This
turbulence modelled is called the 𝑘 − 𝜖 turbulence
model (Equation (35)) and given its robustness, its
solving speed and performance for a wide range of
flows it was selected for the one phase flow simulations
made.
𝜈𝑇 = 𝐶𝜇𝑘2
𝜖 (35)
Other model widely used is the 𝑘 − 𝜔 turbulence
model where 𝜔 ∝ 𝜖/𝑘 is the specific dissipation.
Turbulent viscosity expression using this model is
shown in equation.
𝜈𝑇 =𝑘
𝜔 (36)
The advantage of this model with respect to the
𝑘 − 𝜖 one is the performance in low turbulence regions
and it superiority in predicting the law of the wall when
the model is used in the viscous sublayer shown in
Figure 10. 𝑘 − 𝜔 does not need wall function or two-
layer approximations to solve the viscous layer so there
is no need on refining the mesh. For this reason, for two
phase flow simulation where boundary layers are
larger, this turbulence model was used.
Two phase flow was modelled using the VOF
model presented in section 1.2 due to the weak
interaction an immiscibility of the oil and water used
for experimentation.
Motion on the pump was modeled by using Rigid
Body Motion (RBM) in which the impellers are seen as
solid bodies which undergoes rotation due to the
application of angular momentum which is specified by
the frecuency of this motion. In this case angular
velocity of the impellers was stablished at 3450 rpm
which is the real velocity of the pump.
3.2.4 Boundary and initial conditions
The geometry presented before has three boundary
surfaces which must be defined (see Figure 13). The
first one is the inferior surface of the pump which is the
inlet of it. Given that it is the entrance of mass to the
pump system it was defined as a Mass Flow Inlet in
which the value of the flow introduced depended on the
volumetric flow and the density of the fluid which was
going to be simulated. It is also important to state that
for two phase flow simulations the initial volumetric
fraction was specified on the VOF multiphase solver
where for simulations with 50% oil volume fraction or
oil lower concentration the continuous phase was
specified as water while for the resto of the simulations
the continuous phase was stablished as oil.
18
Figure 13. Geometry boundary definition
The second boundary are the pump walls. Given
that experimentally the pump is filled with the fluid
which it is going to work with, the wall was modelled
as adiabatic wall with the standard settings of the CFD
software. The outlet surface is the face through which
fluid exist the pump, therefore it was modelled as an
outlet with a split ratio of 1. The initial fluid velocity
was set as 0 m/s and the pressure was initialized at the
atmospheric pressure of Bogotá (74660.5 Pa) given
that the experiments were performed at that location.
IV. RESULTS AND DISCUSSION
4.1 Mesh independence test
The mesh independence test for water was carried
out. In this, 4 meshes were evaluated to find the optimal
relationship between the number of cells,
computational time and the percentage of error found
in the simulations regarding to the experimental results
taken at the University de los Andes.
4.1.1 Mesh independence for water
First, the number of cells was modified using the values in Table 4. However, it is important to emphasize that the base size parameter was kept constant for the 4 types of mesh, with the value of 1.4 cm.
Table 4. Mesh specifications for the mesh independence test
Name
Target
surface
size (cm)
Minimum
surface
size (cm)
Mesh
Density
Growth
Factor
Number
of Cells
Coarse 4.89 0.069 1.0 1.0 2’292.421
Base 1.39 0.051 1.0 1.0 3’922.029
Fine 1.33 0.042 1.4 0.70 4’478.402
Ultrafine 0.84 0.027 1.1 0.90 7’690.488
Figure 14 shows the application of this mesh
independence test for water. As can be seen, there is a general decreasing trend for the head error as the number of mesh cells increases. Thus, when comparing the absolute head error obtained between the experimental and simulation data, it is possible to demonstrate that increasing the number of cells (fine and ultra fine mesh) there is no significant reduction of the computational error, given that all are around 2%, in contrast to the coarse mesh.
All of above can be axpleined by the fact that, the
use of the Eealizable 𝑘 − 𝜀 turbulence model for single-phase simulations generally involves a modification of the ε equation. This modification involves a production term for turbulent energy dissipation that is not found in either the standard models. So, it is important to realize that this model is better suited to flows in which the strain rate is large and includes flows with strong streamline curvature and rotation, as ESP. Therefore, it is perfect for the validation of complex flows such as boundary layer, rotating and shear flows (Andersson et al., 2012).
Figure 14. Mesh independent test results for Water
Additional to the head absolute error, Figure 14
shows the total computational time for each case study. This computational time, as expected, increases significantly from one mesh type to another because the cell count increases from one mesh type to another, which greatly increases the number of equations to be solved. Consequently, to obtain a minimum error and a reasonable computational time, the “Base” (B) mesh was used.
19
4.2 Performance of ESP
The performance of the pump was studied using
different types of fluids, such as single-phase flow
(water, sunflower oil and mineral oil), two-phase flow
and O/W emulsions, to make a comparison of the main
operating conditions as Head, efficiency and hydraulic
and break power for the experimental data and CFD
simulations.
4.2.1 Single-phase flow
4.2.1.1 Water
At first, CFD simulations is compared with
experimental results for water flow to validate
numerical methodology. The results obtained are
presented in Figure 15.
Figure 15. Head and Efficiency curves for water
As shown in Figure 15, there is a good agreement
between the experimental results and those obtained
from the simulation in CFD, given that the RMS error
are 3.58% for head and 10.7% for efficiency. In this
case, the BEP was found at a volumetric flow of 20
𝑔𝑝𝑚 on both simulation and experimental data.
Likewise, a comparison between experimental and
CFD results for mechanical and hydraulic power was
made, Figure 16 shows that the experimental data also
agrees with the CFD model on these operational
parameters, where the RMS error is 11.1% and 4.72%
for the hydraulic and mechanical power, respectively.
Figure 16. CFD analysis of cavitation for water
On the other hand, given that the curves of the
manufacturer of the ESP used are not available due to
an adaptation of a new motor of greater power to avoid
operational failures when working with high viscosity
fluids, a cavitation analysis was performed by
evaluating the minimum pressure in the diffuser and
impellers. Therefore, the magnitude of the pressure
obtained at each of these points was compared with
respect to the water vapor pressure at 18°C. Hence, it
is possible to show in Figure 17 that the pump has a
higher pressure in all the points than the water vapor
pressure, so it does not present cavitation.
Figure 17. CFD analysis of cavitation for water
5.2.1.2 Sunflower and mineral Oil
The same analysis of operational parameters of the
pump for mineral and sunflower oil was developed. It
is important to note that, due to the increase in
viscosity, the maximum flow reached by the pump
during the experiments is 20 𝐺𝑃𝑀. The results are
presented in Figure 18.
20
Figure 18. Head and efficiency curve of sunflower oil
Figure 19. Head and efficiency curve of mineral oil
As the previous results, the simulation and the
experimental data have a great agreement, given that
the RMS error is 2.38% and 3.68% for the sunflower
and mineral oil, respectively. Figure 18 and Figure 19
presents the head profile obtained for the two oils,
which is significantly lower compared to the water
curve. This degradation in the performance of the pump
is related to the increase in friction losses generated by
the increase in the viscosity of the fluids and hydraulic
losses, as the exchange of low momentum due to
nonuniform velocity distributions, caused by the action
of work transfer from the blades, deceleration of the
liquid, angle of incidence between liquid flow and
blades and local flow separations (See section 5.2.1.3).
Consequently, the pump requires a greater input of
power and generates a reduction in the efficiency of the
ESP (Figure 19). Hence, the efficiency is significantly
affected because it was reduced approximately 25%
regarding to the water and BEP moves to lower flow
rates when the viscosity increases.
In addition, experimental model of viscosity
correction created by Hydraulic Institute (HI-USA) for centrifugal pumps of section 1.1.3 is shown in Figure 18 and Figure 19, for both fluids. As can be seen, the viscosity correction does not properly match the experimental results obtained, since the curve obtained has a linear behavior. Likewise, the experimental model is given for a specific pump geometry, thus that all the internal and external losses derived from the impeller and diffusers geometry are not considered, so the head obtained at shut-off condition for oils is equal to the water curve, in contrast to experimentation.
Similarly, an analysis of the mechanical and
hydraulic power required for the pumping was made. Figure 20 presents the power profile required by the pump for mineral and sunflower oil. As can be seen, the experimental results agree with those obtained in the CFD simulations for both fluids, the RMS error for the hydraulic power is 0.97% and 0.5%, while for the mechanical power RSM error is 5.2% and 4.2%, for sunflower and mineral oil, respectively. When making a comparison with the results obtained for water, it is possible to show that the increase in viscosity generates a growth directly proportional to the power required for pumping.
21
Figure 20. Experimental and CFD results of a) Hydraulic and b)
Break power of mineral and sunflower oil.
5.2.1.3 Effect of viscosity and geometry on pump
performance
The Figure 21 shows curves of total head versus streamwise location at a 3450 𝑟𝑝𝑚 rotation speed for operation with several fluid viscosities shut-off. As it can be observed, the performance of the radial-flow pump deteriorates continuously with viscosity, which is caused by an increase of friction losses in the hydraulic channels and hydraulic losses. Theoretically, all monophasic fluids must have the same head in shut-off, however, it is possible to demonstrate that this is not fulfilled in this case due to the geometry of the pump used. In addition, it is possible to see that since they are centrifugal pumps in series, the head is cumulative and increases gradually in each stage.
Figure 21. Total head averaged along stream location for ESP
Figure 22. Impeller velocity profile of shut-off for a) Water, b) Sunflower Oil, c) Mineral Oil
22
As compared in Figure 23, from inlet of stage 1 to the
outlet of stage 4, the total head increase boosted for the
impeller of each stage, however, in the diffusers it is
possible to show a loss of pressure since it does not
impart energy to the fluid since it does not impart
energy to the fluid.
Figure 23. Total head averaged along streamwise location of
stage 3
Therefore, it is important to analyze the losses generated by the impeller's geometry. First, the hydraulic losses of the system generated by the incidence. Under the designed flow rate, the flow angle at the inlet of the blade usually is equal to the blade angle, which can meet the design requirements of no incidence entrance. When the flow rate changes, the flow angle at the inlet of the blade usually is not equal to the blade angle any more. Incidence at the inlet can lead to flow separation on the blade surface (Bing et al, 2012). The Figure 22 shows the absolute velocity profiles at the impeller, which is greater in the output. In this case, when the incidence is more, flow changes
its direction abruptly while passing through the blade
passage, generating less efficiency. This results in the
greater dissipation of the green zone of velocity for
mineral oil and sunflower, compared to water
Second, the increase in viscosity of the fluid results in
the increase of boundary layers in the lower upper
walls of the blades, which generates a change in the
direction of fluid within the impeller. However, it also
has three-dimensional effects when it modifies the
relative velocity distribution and there are adverse
pressure gradients, which cannot be compensated by
the curvature of the blade or the Coriolis force, the
trajectories will bend taking the movement a
transversal component from the convex to concave
faces (vortices). This produces secondary flow
formation, leading to internal losses. As can be seen
in
Figure 24 there is the presence of vortices near the tip
of the blades, causing the operation of the pump to
move away from the nominal of the machine.
Therefore, the secondary flow also appears in the
recirculation region between the boundary layers at
the root of the blades. Therefore, the velocity profile
for oils presents a greater quantity of sequential flows
that generates a degradation in their performance, in
contrast to water.
Third, an increase in hydraulic losses causes a
diminishment in the outlet relative flow angle, which
is a very important hydraulic parameter in the design
and operation of the centrifugal pumps. The outlet
relative flow angle as a function of the liquid flow rate
is presented in Figure 25. It is possible to show that
the angle decreases with the increase in viscosity but
remains constant for the volumetric flows evaluated. It
is worth mentioning that the diminution of β2 does not
represent a loss but a decrease in the ability of the
impeller to change the kinetics momentum of the
working fluid (Caridad et al.,2008), referred to a
decrease in head produced by the pump.
Figure 24. Impeller relative velocity profile for a) Water, b) Sunflower Oil and c) Water
23
Figure 25. Outlet relative Flow angle as a function of the liquid
flow rate.
In the internal flow field of impeller, disk friction
loss is defined as the linear loss caused at the wall
boundary layer of the blade, the impeller chamber and
so on, under the effects of fluid viscosity. Disk friction
loss is defined as:
Where 𝑍 is the number of blades, 𝜆 is the friction
resistance coefficient, 𝐷𝑖 is equivalent hydraulic
diameter of impeller, 𝑈1, 𝑈2 are the average relative
velocities of inlet and outlet, respectively (Bing et al.,
2012). Figure 26 shows the curves of the skin friction
loss, the trends of which are the same with different
blade angles. As the flow rate increases, the disk
friction loss will increase sharply. This also explains
the degradation of the operation of the pump for more
viscous fluids, because the less the exit angle, the
greater the friction losses, which is directly related to
the viscosity.
Figure 26. Disk friction losses for single phase fluids.
Finally, to evaluate the influence of viscosity in the
performance of each stage of the ESP, Figure 27
presents pressure head and efficiency curves as a
function of the flow rate for water and sunflower oil.
As it can be seen, all stages have almost the same
stable profile for water, but the profile gradually falls
around 36%, as the volumetric flow increases.
However, it is possible to see that the first stage has a
different behavior with less degradation, because the
effects of hydraulic losses are lower compared to the
other stages. Similarly, the efficiency remains the
same for all stages, where it is possible to show that
BEP is given for the flow rate of 20 𝐺𝑃𝑀 except for
the first stage, because this point is given for larger
volumetric flows that were not evaluated.
On the other hand, when evaluating the oil curve
is possible to show that the stage 1 generates more
head and is more efficient. This is due to the passage
through the stages, the hydraulic and friction losses
increase due to the viscosity, generating a deviation in
the impeller output angle of the pump 𝛽2, greater
amount of secondary flow and incidence. This stage
has BEP higher than the others evaluated. Similarly,
the behavior of the head has the same profile for the
other stages, having a degradation significantly higher
of 47%. In addition, the efficiency has a constant
performance in stages 2, 3 and 4, whose BEP is 15
𝐺𝑃𝑀. In addition, with respect to other operational
∆ℎ𝑠𝑓 = 𝑍𝜆𝑈1
2 + 𝑈22
4𝑔𝐷𝑖
(37)
24
parameters of the pump such as mechanical and
hydraulic power and shear cup are equal for all stages.
Figure 27. Head and efficiency curve for a) water and b)
sunflower oil
5.2.2 Two-phase curves
Mixing patterns are very important when studding
the performance of an ESP in presence of a two-phase
flow because this can affect velocity distribution as
well as pressure gradients along the stages of the pump
due to differences in the individual viscosity of the
liquids present. A CFD analysis was made to observe
this flow pattern through the pump, but to make sure
that the results acquired on the simulation are reliable,
an analysis and comparison between head, efficiency
and power curves obtained computationally and
experimentally was made.
Figure 28. a) Head and b) efficiency curves for two phase water-oil flow where circle marks correspond to CFD and square marks
to experimental
As seen in Figure 28 there is good agreement between
experimental and CFD data, with an overall average
RMS of 5.72%. A trend is observed for the Head in
Figure 28 where there is a better agreement for high
oil concentration data, than for low concentration data
where the deviance between CFD and experimental
results is higher. The effect of the increment of
viscosity of the mixture on the pump is seen clearly in
Figure 28. As oil fraction in the mixture diminishes,
the head and the efficiency increase due to a reduction
in the viscosity of the flow. For this reason, viscosity
of the oil-water mixture was studied as a function of
composition.
25
Figure 29. Experimental and CFD Viscosity data of oil-water
mixture
Figure 29 shows the plot of viscosity as function of
the oil concentration. Initially the viscosity increases
gradually with the increase of oil fraction, but at a
concentration near 50% v/v there is a sudden increase
in viscosity, which is due to phase inversion from W/O
to O/W unstable emulsion, after which the viscosity
diminishes abruptly and then increases gradually again
until the end. The phase inversion effect can also be
seen in Figure 28 where the head and efficiency
obtained experimentally are much smaller than those
of other compositions which is a consequence of the
increment of the viscosity of the mixture. The fact that
there is phase inversion on oil-water mixture with no
surfactant shows that there exists a weak interaction
between the two phases.
Figure 30. Chemical Structure of triglyceride which is the main
component of Sunflower Oil
As seen in Figure 30, the main components of sunflower oil are triglyceride that come mainly from linoleic acid and oleic acid. These structures present large carbon tales which are nonpolar and are the main reason why there is no interaction between water and this type of oil, but due to the presence of high
electronegative oxygen atoms on the head of this structure, there is a small polarity in this section of the molecule which may slightly interact with the water in the mixture and be responsible for the phase inversion.
It is also important to observe in Figure 29 that the CFD simulation did not capture this phase inversion. This is due to the use of the VOF model which, as stated in section 1.2 of the literature review, does not consider an interaction term between the phases and it does not model correctly a phase disperse in another given that it would need a mesh with base size inferior to the size of the droplets reason why it is not able to capture this phenom. It is also important to highlight in the comparison between experimental and CFD viscosity data that high oil concentration unstable emulsions present better agreement than those of low concentration as occurred with the head and efficiency results. This occurs because in unstable O/W emulsions (without surfactant) as the continuous phase is polar, resistance to coalescence may present given the formation of electrical double layers due to preferential absorption of ions from the water phase (Pal, 1993). This causes that oil phase disperse through the mixture which is why inversion is possible but as Figure 29 shows, when water is the disperse phase oil is not uniformly distributed and tends to flocculate which is a consequence of the non-interaction assumed by the VOF model.
Flow pattern in the third stage impeller was
studied for three different compositions: 80%, 50% and 20% oil. As seen in Figure 33, low oil concentration mixture presents most of the oil fraction near the shaft of the pump while the outer parts are mostly composed of pure water. This implies that there is not a uniform distribution of the disperse oil phase in the outgoing mixture which is not compatible with phase inversion theory which needs that the disperse phase fraction droplets increase and so coalesce between these droplets.
A similar situation occurs for the mixing patter of
50% oil unstable emulsion. As shown in Figure 33, the oil again does not distribute uniformly but concentrates in the shaft of the pump. Given the greater viscosity of the oil with respect to water, a greater drag force is needed for it to move while water having less viscosity moves easier, causing that the places where there is lower velocity in the impeller, oil concentrates.
26
Figure 31. Third impeller velocity profile of 50% Oil CFD
simulation
As seen in Figure 31, velocity near the shaft is
lower than in any other point of the impeller. It is also
important to notice that oil is also present on the
internal parts of the blades while water is present at the
outer part of them; this also is because of the velocity
distribution shown given that water has a higher
density than oil it locates itself in the high velocity
regions of the blade which is an effect of the
centrifugal effect of the impellers rotation (Croce,
2014).
Normally phase distribution inside the impeller
would change when approaching phase inversion due
to the sudden increase of the mixture viscosity but
given that there is no uniform distribution of any of the
phases on the profiles shown in Figure 33, water is
always found on the fastest parts of the impeller while
oil is going to be found in the slower parts. For the last
volume profile where water is the disperse phase, a
more uniform distribution is observed throughout the
impeller, water does not maintain at any specific
position. Due to the appearance of phase inversion, stability
of the mixtures was observed for any indication of interaction between the phases.
Figure 32. 50% Oil Sample Separation
Figure 32 shows that a homogeneous mixture is obtained after pumping showing simulation volume fraction profile wrong. Interaction can be seen in picture b) where overthought phase separation has already happened there are still droplets of oil present in the aqueous phase. 5.2.3 Emulsions
ESP’s performance with emulsion was studied experimentally by measuring the head and calculating the efficiency for different compositions.
Figure 33. Oil volume fraction profile for the third stage impeller of a) 80%, b) 50% and c) 20% oil composition CFD simulations
27
Figure 34. Experimental Efficiency and Head curves data as
function of stable composition emulsion.
As shown in Figure 34, the emulsion composition
plays a major role on the performance of the ESP,
where the head goes from 16 m for high oil
composition to nearly 35 m. As the composition of oil
in emulsion diminishes, the head delivered as well as
the efficiency increase; this is caused by the decrease
of viscosity of emulsions and the increase of its
density. Due to the addition of the surfactant the
superficial tension between phases is reduced and
coalescence between droplets is decreased which
enable the coexistence of oil and water in a mixture.
However, the presence of a second phase in a
continuum have consequences on the physical
properties of it even when the disperse liquid is at very
low concentrations. In the case of the emulsion made,
they are high concentration emulsions, so the
rheological behavior is governed by droplet interaction
and size distribution.
Figure 35. Emulsion viscosity as function of oil volumetric
composition
Figure 35 shows the behavior of viscosity of the
emulsions at a constant shear rate of 30 𝑠−1. It is
important to highlight that the viscosity of 90% oil
emulsion is much higher than the viscosity of the rest
of the compositions. As in the case of unstable
emulsion, the sudden increase in the viscosity indicates
the phase inversion point. The reason why this point is
so far in the oil composition is because of the nature of
the surfactant. Since SDS has a high hydrophilic
character (HLB =40) and has a high concentration on
the emulsion, the horizontal inversion frontier in the
formulation-composition diagram (Figure 5) tends to
expand, this occurs since normal emulsions (the ones
that obey Bancroft rule) become more stable and so
abnormal emulsion present at extreme composition
values. To probe this point superficial tension between
water and oil was measured with and without SDS.
Table 5. Superficial tension comparison using SDS surfactant
SDS concentration
(mg/ml)
Interface
Surface Tension
(mN/m)
0 35.9
5.75 4.5
As seen in Table 5, SDS reduces superficial
tension between sunflower oil and water by a factor of
8 in the concentration used on experimentation, which
stabilizes the phases and increases the region A- area
as well as the hysteresis zone of the diagram (Figure
36) which is why phase inversion starts to occur from
28
a composition of 70% oil in the viscosity composition
diagram.
Figure 36. Formulation composition diagram with hysteresis
zone in blue
Viscosity is also affected by the interaction
between droplets and its size distribution, which is
why they were measured.
Figure 37. Particle size distribution for different composition
emulsion
Particle size distribution in Figure 37 shows that as the concentration of oil diminishes the distribution becomes less monodisperse.
Viscosity increases when the internal phase
(which in this case is oil) becomes high and the drop
size is monodisperse as is the case of the 90% oil
emulsion which is perfectly monodisperse (in the
sense that it presents as a standard normal
distribution). Also, viscous behavior changes as the
particle size becomes less monodisperse, this causes
that the emulsion present a stronger shear thinning
behavior. For observing the behavior of the
pseudoplastic behavior, viscosity of the emulsions
made was adjusted to the Carreau viscosity model
(Equation (38)) using the optimization tool Solver of
the software of Microsoft Excel®.
Figure 38. Behavior of the power index as a function of oil
composition for Carreau Viscosity model
The power index n is smaller than 1 for all compositions which indicates the pseudoplastic nature of the emulsions made. It is seen that out of the hysteresis zone (below 70% oil composition) the power index increments with the increase of water in the mixture, this confirms the fact that as the particle distribution becomes smaller, the shear thinning nature diminishes.
V. CONCLUSIONS
• Using the realizable 𝑘 − 𝜀 model for single phase
simulations allows that the normal stress is
positive under all flow conditions, providing a
satisfactory accuracy when estimating head curves
for ESP.
• Due to the slight polar head of the triglycerides
that make up the sunflower oil there is a weak
interaction between water and oil phase without
surfactant which enables the formation of an
unstable dispersion that suffers phase inversion.
• The experimental data validated the results of the
CFD simulations. The VOF model, although it
does not consider the interaction between the
phases, allows to adequately model the behavior of
the pump.
𝜇𝑒𝑓𝑓(�̇�) = 𝜇𝑖𝑛𝑓 + (𝜇0 − 𝜇𝑖𝑛𝑓)(1 + (𝜆�̇�)2)𝑛−12
(38)
29
• Phase inversion was achieved for unstable (with
no surfactant) and stable emulsion at a volumetric
oil fraction of 50% and 90%, respectively.
• VOF model was not able to capture oil-water
mixture phase inversion because of the
nonuniform distribution of the phases on the
impellers and the lack of interaction terms in the
model.
• Mixing profile showed that due to its high density
and lower viscosity, water tends to be found in the
high velocity region of the impeller while oil is
found on the slower ones.
• Phase inversion without surfactant express itself as
a sudden increment in the viscosity of the mixture
while in stable emulsion this increment occurs
gradually due to a greater hysteresis region caused
by the presence of surfactant.
• Viscosity of emulsions tend to increase as the
droplet size distribution becomes monodisperse
which tends to occur for phase inversion.
VI. FUTURE WORK
Develop a model in CFD that allows modeling the
formation of emulsions inside the ESP and validate it,
using the experimental data obtained in this study.
Likewise, continue with the analysis of the pump
performance using other types of fluids, such as non-
Newtonian as CMC, in order to identify the effect of
the shear rate on the fluid and the operating parameters
of the pump.
ACKNOWLEDGMENTS
Mr. Nicolas Rios Ratkovich and master’s degree teaching assistant at Universidad de los Andes, Mr. Juan Pablo Valdes, are acknowledged for their ongoing theoretical and simulation support. Finally, Ms Alexandra Cediel Ulloa for their experimental support on this study.
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