Roberto Faustini MSc in Mechanical Engineer Department of Mechanical Energy Conversion Simón Bolívar University Sartenejas, Baruta, Edo. Miranda Apartado 89000 -Venezuela Tel: +58-(212) 9064134 e-mail:
[email protected]
Frank Kenyery Ph.D and Professor of the Department of Mechanical Energy Conversion Simón Bolívar University Sartenejas, Baruta, Edo. Miranda Apartado 89000 -Venezuela Tel: +58-(212) 9064134 e-mail:
[email protected]
3D Flow Modeling In One Helical-Axial Multiphase Pump Stage through CFD The application of the helical-axial technology in multiphase boosting have had a great acceptance in the oil industry, specially in production and transportation areas, allowing the offshore and onshore oil fields development in an economic way through the application of better production methods and schemes. Up to the date, the development of studies published on this type of technology has been based principally on experimental models. On the other hand, in the last 13 years analyses have been joining across simulations in Computational Fluid Dynamics (CFD) for improvements in design and prediction of the turbomachineries performance. Some simulations in helical-axial technology have been reported mainly in one-phase and permanent state conditions. For a better understanding of these pump performance simulations in two-phase flow are needed, especially with high gas volumetric fractions (GVF> 60 %) into each components (stator and rotor) and stage, bearing in mind realistic geometric factors and flow conditions in the entry and exit of the pump. The accomplishment of this study arises with the intention of the fluidynamic understanding of this technology working with two-phase flow (water-air) to verify hereby his theoretical performance and to propose improvements in the design using the program CFX V-5.7. The results show the performance of one stage of the pump with high GVF, where it can appreciate a deficiency in the performance of the pump stator, whereas the rotor performance shows a better efficiency and conduction of the fluids with which it is achieved a 3D model of what happens with the flow inside the pump, explaining his performance for certain conditions. Keywords: Multiphase boosting, helical-axial pump, multiphase pump, computational fluid dynamics (CFD)
Introduction The technical and commercial successful of helical-axial multiphase pumps have opened new perspectives in the oil technology. Nevertheless there are few publications about its design and construction. On the other hand, the development of new design methods in turbomachinery through 3D simulations using CFD has allowed the virtual verification of its development, gaining time and money in this process. The previous argument arise this investigation, in which is proposed the analysis of the stage performance of a known helical-axial pump across the modeling of his components (rotor and stator) and a stage with a GVF > 60% in CFD by means of the commercial program CFX-V5.7. This program uses 3D Navier-Stokes equations applied to one and two-phases models with which it is possible to predict the fluidynamics that governs the performance of this type of pumps to understand his functioning. In this way, the performance curves can be predicted to different conditions demonstrating that the CFD is an important and economic tool for the modeling and pump design, breaking the paradigms that focous the developments only in empirical relations and experimental tests through the construction of prototypes. Previous Work And State Of The Art The first works in multiphase pumping referred to the helical-axial technology date from the seventies and they were made to extend the applications of the electric submersible pumps (ESP) in oil wells. In the middle of the eighties, the multiphase boosting began to be of great interest for the production transport of satellite fields in deep waters, which in that time were developed under stand-alone platforms in the North Sea to reduce the associated costs to the offshore developments. The distances to the existing facilities were limited between 15 and 20 km due to the reservoir pressure available and multiphase pumps appeared to increase these distances providing energy to the gas-liquid
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mixture for the separation process in shore installations reducing the offshore handling costs [1]. Since 1973 the “Institut Française du Pétrole” (IFP) made tests in different pumps prototypes, increasing their capacities: 4500 bbl/day (1973), 15000 bbl/day (1979), and 20000 bbl/day (1983) [2]. In 1983, the IFP and Total Oil were associated, joined by Statoil in 1984 in a project called Poseidón, whose objective was the development of a complete system of production for operation under the sea level, able to extract the gas-petroleum mixture with high GVF from the well head, to compress it and to even transport it to great distances (up to 50 km) in an economic way compared with other methods of transportation, guaranteeing the easy operation and the low price in the maintenance of the equipment. Arnadeau, of the IFP, was one of the pioneers in the development of this technology through this program. [1][2][3] On the other hand, in 1991 the Cotap-Neptunia company, specialized in nuclear boilers for the French navy fleet, developed the multiphase pump Neptunia based on rotodynamic technology, which includes a rotor and stationary rectifier of axial geometry with NACA profiles (65-Serie). The first prototype consisted of a six stage pump able to operate with fractions of gas between 0 and 0.9, with pressure delivery capacities near the 300 Psi and with rotation speeds between 2000 and 6500 RPM. This pump has many applications regarding to oil fields with pressure decrement and deep water wells. From this last application, the company developed a system of pumping known like Nausicaa that was studied in the present investigation.[4] Until 1992, the results and development in the helical-axial hydraulics were based mainly on experimental developments completed by eulerians simulations of single-phase flow. Little by little, the progress in flow simulations has increased considerably the roll of the CFD, and in the last 13 years, the use of powerful simulators based on 3D fluid dynamic through the Navier-Stokes equations has helped in the design of
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turbomachineries. Most of the analyses were made in singlephase flow and the characteristic curves through these simulations agree relatively well with the experimental data with a small tendency to over predict flow ranks. [1] [5] Tremante [5], Pordal[6], Stoleman [7], Goto [8,9], and Asuaje[10], among others researchers, have exposed the advantages of using the CFD in turbomachinery, reducing the time of design considerably, optimizing processes simply and eliminating the non satisfactory options quickly and reducing the associated costs to the new design. Falcimaigne [1] describes the state of the art in the helicalaxial technology till 2002. In reference of the CFD the investigator assure that there are few analyses in two-phase fluid and makes reference to investigations that have been made through the Fluent software on the hydraulics of these pumps, observing the distribution of the fluids in a stage (rotor/stator) and their consequences in the performance of the pump using a maximum gas volumetric fraction of 10% without taking into account the transference from mass between both phases. Cao [11] and his research group focused its investigations in the dynamic fluid simulation of a helical-axial rotor of Poseidón technology. At first, they mention that the hydrodynamic design of this type of technology is still a difficult task and there is not a directly guarantied model applicable for the design of the blades of the rotor. Until recent dates, the development process has been empirical through the experimentation of many rotors, being selected the one of better performance. This process requires a high consumption of time and money and for this reason arises the combination between the inverse design method and the direct analysis of the flow. The inverse method talks about the theoretical calculation of the geometry of the blade according to the specifications of the field of required flow, whereas the direct method talks about to the simulation of this geometry through CFD. The simulations were made to a GVF rank between 0% and 55% and were validated with experimental data. It was obtained that the height differential coefficient decreases as the GVF is increased. On the other hand, the investigators assure that the centrifugal force plays a dominant role in this type of rotors. The results through the simulations show the formation of a local region of low pressure in the intersection between the entrance and the wall of the bucket in where the gas blockade phenomenon can easily be caused.
The geometry of the rotor and stator was created using the program BladeGen 4.1. The rotor has a hub radius of 101.5 mm in the entrance side and 112.5 mm in the exit side; the shroud radius is constant throughout the rotor and equal to 125.0 mm. The rotor is made up of 5 NACA 65 blades. (Fig. 1)
Fig. 1 Rotor representation
The stator has a hub radius of 112.5 mm in the entrance side and 101.5 mm in the exit side; the shroud radius is constant throughout the stator and equal and to 125.0 mm. The stator is made up of 32 NACA 65 blades. The geometry of the real stator was created in another study that was made in the “Laboratorio de Conversión de Energía Mecánica” (LABCEM) of the Simón Bolívar University (USB). (Fig. 2)
Many of the turbomachinerie developments have arisen through modifications from prototypes without theoretical bases. Nevertheless, through the CFD a better understanding of the influence of certain parameters in the performance of a machine can be obtained, with the intention to improve the design through theoretical bases generated in studies. For cases of designs through inverse methods the CFD has allowed to validate and to optimize the entered parameters to generate geometry, under the described method, in a fast way and obtaining a clear vision of the flow development in 3D. [8] Geometry Creation
Mesh Creation The meshes were created using the program TurboGrid V1.06.00 For the rotor were placed static blocks of entrance and exit to 5.0 mm of the beginning and culmination of the profile. These blocks were extended approximately to 110.0 mm (average length of cord) as much in the entrance as in the exit.
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Fig 2. Stator representation
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The model was simplified and the radial clearence was not taken into account. For the validation of the mesh it was used water simulations at 25°C, using a rotational speed of 5500 RPM, an entrance pressure of 22 psig and a flow of 302 m3/h, within the pump operation range given by the fabricant. To high GVF the pump needs to increase the speed of rotation to be able to raise pressure. As Caridad [12] and Bastardo[13], a difference in the results between two different grids less than 1% was chosen as the criterion to ensure mesh independence. Figure 5 shows how the the different grid sizes tend to stabilize with a greater number of elements. Therefore, it was selected the Grid B of 81680 nodes and 71371 elements, which have a variation of 0.54% in the results with respect to the following mesh (Fig 5).
GRID B 71371 ELEMENTS
GRID C 87632 ELEMENTS GRID A 50022 ELEMENTS
Q = 302.0 m3/h GVF = 0 %
Fig 5. Rotor mesh validation
Good results can be obtained simulating 1 channel interblade of the rotor with 6 channels interblades of the stator, giving a pitch ratio of 1.066 in the interphase. This parameter measures the relation between the surface of exit of the rotor and the surface of entrance of the stator. Using the same procedure and criteria of selection for the rotor a stator grid was selected. ∆P Vs # Elements (Estator) -20000
GRID B 32608 ELEMENTS
GRID C 50592 ELEMENTS
∆P[Pa]
-25000 -30000 -35000 -40000 5000
GRID A 15884 ELEMENTS
25000
45000 # Elements
GRID D 68256 ELEMENTS
65000
Fig 6. One interblade stator mesh validation
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It was selected the Grid C. One stator interblade grid has 50,592 elements and 57,273 nodes (Fig. 6). Therefore, 6 channels of the stator represent a mesh of 303,552 elements altogether. The disposition of the study under this way, instead of the analysis of a complete stage, arises by problems in capacities of data processing. The cases of study of two-phase models are more complex and require greater capacities of data processing due to the additional equations to solve for each finite volume. Physical Definition Once obtained the mesh, this one is loaded in the PreProcessor of the CFX 5.7 program, defining the physical models to use in the simulations, properties of the fluid and bondury conditions, among other details. The fluid dynamics within rotor and stator obeys to a series of hypotheses that simplify the complexity of the problem: permanent, isothermal and incompressible flow, without transference of mass between phases and axisimetric geometry. The physical models that were included were the following ones: Multiphasic model For the two-phase simulations the multiphasic particle model is used considering a continuous and dispersed phase. The air is the continuous phase and the water is the dispersed phase, mixed in a superior scale to the molecular one, where they can have differents fields of speeds and temperatures interacting in terms of transference in the interphase. A fog type flow was assumed, with a diameter of drop φd= 0.001 mm, where drag in the particle can be obteined without originating blockade in the simulation. For the drag, a value of CD=0,424 was assigned corresponding to a sphere that flows in a fluid for the Reynolds number values between 1x105 and 1x107, which correspond to the present simulations range. Turbulence Model The turbulence consists of fluctuations in the fluid field in time and space. It can have significant effects in the characteristics of the fluid, specially in 3D flow. The resolution of the Navier-Stokes equations in a direct way implies a computational power cost greater than the ones that have the present processors. The turbulence models are used to predict the effects of the turbulence with no need to solve on small scales the fluctuations. CFX has a series of models; many of them based on the RANS (Reynolds Averaged Navier Stokes) equations used for different applications. In the simulations carried out in this investigation it was used the k-ε model. This model is considered the standard in the industry and has been implemented in most of the investigation works giving good results. It offers a good commitment between precision of the results and robustness of calculations and has been catalogued like one of most prominent of the models. It is recommended in the manual of the program and also its use in previous works carried out by Cao [11], Caridad [12], Bastard [13] and Suarez [14] among others.
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Domain Discretization Numerical approaches are made in order to obtain real solutions of the flow through the Navier-Stokes equations. Reason why the equations are replaced by algebraic approaches that must be solved through numerical methods. On the case of the program CFX, this one is based on the finite volumes method. Many of the development schemes for CFX are based on approaches to expansion schemes (like Taylor series) for continuous functions. The numerical resolution of the equations modeled in convective terms was done under a hybrid method. It was used an Upwind modification scheme for the turbulence equations, in where the expansion series in the first term is truncated, diminishing the computational calculation costs. It is necessary to make reference that this scheme is the only one available for the resolution of turbulence in this program. For the mass and transport conservation equations, it was used a High Resolution advection scheme for being a precise and robust scheme, recommended by the CFX manual.
Fig 6. ∆P vs Q (Rotor)
Work Shemes The simulations were made mainly modifying variable like gas volumetric fraction (GVF) and flow rate. Simulations with the rotor at 5500 RPM, varying the total flow rate at the exit of the pump were made from 280 m3/h to 500 m3/h approximately and suction pressure of 22 Psi (151700 Pa) for volumetric fractions of gas (GVF) of 0.6, 0.7 and 0.8. Once obtained the results of velocity and volumetric fractions in the exit area of the rotor (5 mm after the edge of the blade) studied in the previous case for the case corresponding to GVF = 70%, this one was used like condition of entrance of the stator. Convergence Criteria and Data Collection The convergence criteria settled down under the parameters recommended in the manual of the CFX program, correspond to a maximum residual value of 0.0001 and a value of the maximum error in the mass balance of 3%. Once the solution is reached and it goes to the visualizer of the program for the results, it was settle down a unified criterion for the pressure data taking values in the rotor and stator. These values were took in a plane created in a cross section from the rotor and stator separated 5 mm from the blade at the entrance and exit. Numerical Results and Discussions A tendency of ∆P diminution exists as the GVF increases. For simulations with GVF near to 80% the behavior already is very unstable and only 3 points of operation could be obtained near the mass flow of better performance (370 m3/h). The ∆P for these pumping conditions is smaller to 120000 [Pa]; nevertheless, it is necessary to take into account that the mixture, when presenting greater GVF will be lighter and could be pumped with this increase of pressure (see Fig. 6).
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Fig 7. Rotor phases distribution @ 5500 RPM, GVF = 70% & Q=370 m3/h
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In Figure 7, the phases distribution for different span of he rotor was presented in an operation point corresponding to GVF=70% and Q=370 m3/h. An accumulation of the gas at the extrados of the blade exists, whereas in the intrados the heaviest phase is accumulated (water). The elimination of the tip clearence avoids the draining between the interblade channels of the rotor and therefore, an escape route of the liquid does not exist and is accumulated in the shroud. The suction zone, in the extrados of the blade, contains greater fractions of gas extended to almost half of the area when coming out of the interblade channel. GVF Influence on the Phases Distribution The Figure 8 shows the distribution of phases in an entrance plane of the rotor located above 5 mm of the blade leading edge for the better performance point(Q=370 m3/h) at 5500 RPM.
Fig 10. Rotor Phase distribution (Span=0.5), Q=370 m3/h
An approach to the previous figure for the blade zone can observe in the Fig. 11.
Fig. 8 Rotor Phases Distribution – Entrance plane (Q=370m3/h)
An almost homogenous flow can be saw at the entrance, in where they appear small zones of gas accumulation due to the influence of the blade leading edge when it turns. In the exit plane (Fig. 9) the influence of the centrifugal force of the rotor on the phases distribution can be observed under the simulated conditions.
Fig. 11 Rotor phase distribution (Span=0.5),Q=370 m3/h
A zone of water accumulation exists almost at the end of the intrados blade towards the trailing edge, which is thinner as the GVF is increased and also in the leading edge. The profile is surrounded in a zone of pure gas from the leading edge and it extends waters down, diminishing his thickness in the part of the intrados as it advances towards the trailing edge of the profile and extending itself of the extrados side. The rotor, secretes the phases and the stator and the following stages are affected, since there is no uniform distribution of the phases when coming out of the rotor. The flow deflection in the zones with high content of liquid and gas are different.
Fig. 9 Rotor Phases Distribution – Exit plane (Q=370m3/h)
It is appraised a gas accumulation in the extrados of the blade, and a fine water layer in the periphery of the rotor shroud. Half of the channel interblade has pure gas, whereas the other half presents a two-phase mixture with values of GVF near the condition imposed in the entrance. This last zone reduces its size when coming out as the GVF is increased, thing that can be detailed in Fig. 10.
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Flow Rate Influence on the Phases Distribution The influence of the flow rate in the distribution of phases for a GVF equal to 70% can be observed in the Figure 12.
formation of an air pocket is reduced in the intrados and extended in the extrados as it advances towards the trailing edge. Next, a picture of the entrance and exit planes, separated to 5 mm of the trailing and leading edge is presented:
Fig. 14 Rotor Phases Distribution – Entrance plane (GVF =70%)
Fig. 12 Rotor Phase Distribution (Span 0.5), GVF=70%
The increase of the flow rate allows that the zones where the heavy fractions in the interblade channel tend to concentrate themselves in homogenous form and the zone of influence throughout the profile is extended, where a pocket with heavy fractions thickens is observed. In the Figure 13 it will be possible to detailed this.
Fig 15 Rotor Phases Distribution – Exit plane ( GVF=70%)
Fig. 13 Rotor Phase Distribution (Span=0.5), GVF=70%
A zone of water accumulation exists in the pressure side of the blade that extends towards the trailing edge, and that is reduced as the flow rate increases. In the leading edge the
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Figure 14 shows an homogenous distribution at the rotor entrance according to the flow conditions imposed. Nevertheless, a zone of influence by leading edge exists and forms air pockets which disappear as the flow rate increases. Figure 15, shows the existence of water accumulation zones in the shroud, which are diminishing their thickness as the flow rate increases. The zone of pure gas diminishing as the flow rate increases, and the mixture zone is increased.
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Stator Performance at GVF = 70% The phases distribution in the stator entrance is as it shows in Figure 15. The stator performance at GVF=70% can be appreciated in Figure 16, next.
Next, Figure 17, shows the distribution of phases in the stator in different planes and flow rates for a GVF=70%, after its passage by the rotor. It is possible to observe how there is not uniformity in the distribution of the phases and the liquid tends to concentrated in the shroud. The phases distribution for the flow rates is irregular and evidence that there is not a good effect for each blade. It is necessary to emphasize that the figure represent a determined moment in the operation of the pump and that this distribution of phases changes in the stator as the rotor turn. The streamlines of the continuous phase (air) in the Fig. 18 shows a disordered trajectory and appear small zones of recirculation.
Fig. 16 ∆P vs Q (GVF=70%)
In the previous graph (fig 16), it is possible to observe that as increases the flow rate there is an increment in the losses in the stator. For the simulated flow rates the pressure energy that had gained by the rotor is lost totally during the passage of the flow through the stator and the performance of the stage, therefore, it is translated in a general loss of pressure. Fig. 18 Stator Gas Streamlines (meridional plane), Q = 387m3/h & GVF = 70%
Nevertheless, the streamlines for the disperse phase (liquid) shown in Figure 19, evidence an ordered trajectory
Fig. 19 Stator Liquid Streamlines (meridional plane), Q=387m3/h & GVF=70%
Fig. 17 Stator Phase Distribution
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The flow conduction does not obey to a pattern and the blades do not lead the fluid in a regular way through their channels, reason why the performance of the stator is not adapted.
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CONCLUSIONS On the basis of the results obtained in this study the following thing can be concluded: • The use of the CFD for the performance prediction of a Helical-Axial Pump through the simulations of its components (rotor and stator), have shown to be an important tool to understand the hydrodynamic behavior in 3D in its interior, with which it is possible to improve the process of design of these machines in a fast and economic way compared with experimentation methods on prototypes. • The gas accumulation in the interblade channel of the rotor reduces the flow passage area and increases the two-phases losses. This accumulation is greater in distant points of the better operation performance. • An increase of the gas zone exists as the GVF is increased. • For high GVF the rotor secretes the phases, affecting the performance of the stator and future stages. • The stator performance is deficient for all the simulated cases since it does not recover the kinetic energy of the fluid that comes from the rotor. The phases distribution in the stator working to high fractions (GVF = 70%) is not uniform in the interblade channel. Nomenclature CFD = Computational Fluid Dynamics CD = Drag coefficient ESP = Electric Submersible Pump GVF = Gas Volume Fraction φd = drop diameter ACKNOWLEDGMENTS We are thankful to the support and disposition offered by professor Miguel Asuaje of the Simón Bolivar University (Venezuela) for the learning of the program. REFERENCES [1] Falcimaigne, J., Brac, J., Cgarron, Y., Paignier, P., and Vilagines, R., 2002, “Multiphase Pumping: Achievements and Perspectives”, Oil & Gas Science and Technology – Rev. IFP, Vol. 57 No. 1, 2002, pp 99-107. [2] Arnaudeau, M.P., 1988, “Development of a Two-Phase Oil Pumping System for Evacuationg Subsea Production Without Processing Over a Long Distance: Poseidon Project”, Offshore Technology Conference, OTC Paper No. 5648, Huston, Texas, pp. 271-279. [3] Falcimaigne, J., Durnado, P., Loupias, M., y Vilagines, R., 1994, “Multiphase Rotodynamic Pumps Extend their Operating Capabilities”, SPE Paper No. 28882, London, UK, pp. 153-160. [4] Reber J.D., Chaix J.E, Cotap Neptunia, 1995, “The Neptunia Multiphase Pump: Test Results and Applications”, Offshore Technology Conference, OTC Paper No. 7935, France, 8 pp.
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[5] Tremante A., Moreno N., Rey R., Noguera R., 2002, “Numerical Performance Prediction and Experimental Validation of an Axial Pump Under Two-Phase Flow (Liquid/Gas)”, ASME Engineering Technology Conference on Energy, Huston, Texas, 6 pp. [6] Pordal, H. S., Matice, C. J., Fry, T. J., 2005, “Computational fluid dynamics: a key analytical tool”, Hydrocarbon Processing Journal , pp. 85-91. [7] Stoleman, D., Saad, A., Cooper, P., 2001, “Designing Custom Pump Hydraulics Using Tradicional Methods”, 2001 ASME Fluid Engineering Division Summer Meeting, Proceedingf of ASME FEDSM2001-18067, New Orleans, USA, 9 pp. [8] Goto, A., Zangeneh, M., 2002, “Hydrodynamic Design of Pump Diffuser Using Inverse Design Method and CFD”, Journal of Fluid Engineering, Vol. 124, pp. 319-328. [9] Goto, A., Nohmi, M., Sakurai, T., Sogawa, Y., 2002, “Hydrodynamic Design System for Pumps Based on 3-D CAD, CFD, and Inverse Design Method”, Journal of Fluid Engineering, Vol. 124, pp 329-335. [10] Asuaje, M., Bakir, F., Kouidri, S., Noguera R., Rey, R., 2005 “Computer-aided design and optimization of centrifugal pumps”, Power and Energy Journal Proc. IMechE, Vol. 219 Part A, Paris, France, pp. 187-193. [11] Cao, S, Peng, G., Yu, Z., 2005, “Hidrodynamic Design of Rotodynamic Pump Impeller for Multiphase Pumping by Combined Approach of Inverse Design and CFD Analysis”. ASME Vol 127, pp. 330-338. [12] Caridad J., 2002, “Análisis y Predicción del Comportamiento de Bombas Electrosumergibles Manejando Flujo Bifásico”, M.S. Thesis, (in Spanish), Universidad Simón Bolívar, Venezuela. [13] Bastardo, R., 2003, ‘‘Simulación Numérica del Flujo Bifásico Líquido-Gas en el Difusor de una Bomba Centrífuga Multietapas,’’ M.S. Thesis, (in Spanish), Universidad Simón Bolívar, Venezuela. [14] Suarez L., 2005, “Análisis del Comportamiento de Separadores Rotativos para BES Mediante Simulaciones de Flujo Bifásico 3D”, M.S. Thesis, (in Spanish), Universidad Simón Bolívar, Venezuela.
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