Pumping crude oil by centrifugal impeller having different blade angles and surface roughness
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Abstract
Centrifugal pumps are extensively used in the oil and gas industries and the pump performance drops with higher viscosity and higher surface roughness of the pump impeller, and the impeller design parameters have significant effect on the pump performance. Through the present research, crude oil pumping behavior has been predicted, analyzed and compared with other fluids. A 3D flow simulation using Reynoldsaveraged Navier–Stokes (RANS) equation was performed by considering different blade angles and impeller surface roughness to pump crude oil, kerosene, gasoline, salinewater and water. Standard kε twoequation turbulence model was used for the turbulent closure of steady incompressible flow. The investigation shows that the blade angles have significant influence on the head, input power and efficiency of the impeller for different liquids. Higher head and power, and lower hydraulic efficiency were observed with higher surface roughness values.
Keywords
Centrifugal impeller Exit blade angle Viscosity Roughness Slip factorList of symbols
Abbreviations
 RANS
Reynoldsaveraged Navier–Stokes
 CFD
Computational fluid dynamics
 PS
Pressure side
 SS
Suction side
 LE
Leading edge
 TE
Trailing edge
Description
 B
Blade width (mm)
 C
Absolute fluid flow velocity (m/s)
 c_{eq}
Equivalence factor
 c_{m}
Meridional velocity component (m/s)
 c_{u}
Peripheral velocity component (m/s)
 D
Diameter (m)
 f
Fluid
 f_{i}
Body force (N)
 f_{R}
Roughness effect
 g
Acceleration due to gravity (m/s^{2})
 H
Head generated (m)
 ΔH
Hydraulic losses (m)
 k_{s}
Sand roughness (μm)
 k_{s}^{+}
Roughness Reynolds number
 m
Mass flow rate (kg/s)
 N
Impeller speed (rpm)
 P
Power consumed by pump (kW)
 p
Pressure (N/m^{2})
 Q
Volume flow rate (m^{3}/s)
 Re
Reynolds number
 r
Radius (m)
 t
Total blade thickness (mm)
 U_{j}
Threedimensional velocity vector
 U
Peripheral velocity (m/s)
 u_{τ}
Frictional velocity (m/s)
 w
Relative fluid velocity (m/s)
 w_{u}
Peripheral component of w (m/s)
 w_{s}
Relative velocity on suction side (m/s)
 y
Blade thickness
 z
Blade number
Greek symbol
 β
Blade angle (^{o})
 ε
Rate of kinetic energy dissipation (J/s)
 η
Hydraulic efficiency (%)
 k
Turbulence kinetic energy (J)
 µ
Dynamic viscosity (N s/m^{2})
 ν
Kinematic viscosity (m^{2}/s)
 ρ
Density of fluid (kg/m^{3})
 σ
Slip factor
 τ_{ij}
Viscous stress tensor
 τ_{w}
Shear stress at the wall (N/m^{2})
Subscript
 1
Inlet
 2
Outlet
 a
Actual
 h
Hub
 o
Eye
 s
Shaft
 th
Theoretical
 max
Maximum
Introduction
Nowadays centrifugal pump either as single stage or multistage is extensively used in upstream, midstream and downstream oil industries. For example, the upstream oil industry uses to lift fluid from the wellbore, to deliver fluid in the separation system, etc. Performance characteristics of a pump greatly depend on geometry and surface property of an impeller. Again, the viscosity which can be defined as resistance to flow has significant impact on head, efficiency and power consumption of the pump.
Many researchers reported analysis of centrifugal pump for the flow behavior, influence of geometric parameters, etc. (Kamimoto and Matsuoka 1956; Varley 1961; Stepanoff 1940; Lazarkiewicz and Troskolanski 1965). The works on inlet and exit blade angle shows that the performance can be altered, when the angles are modified. A higher exit blade angle was suggested by the researchers. Kamimoto and Matsuoka (1956) experimentally investigated the effect of exit blade angles and reported that the impeller with 30° exit angle has the best performance. For a double suction centrifugal pump, the head increment can be achieved by increasing exit blade angle and an improvement in efficiency by varying exit blade angles can be obtained (Varley 1961). The inlet blade angle modification of a radial impeller has been reported by Sanda and Daniela (2012), and Luo et al. (2008). They reported that performance enhancement is possible by this modification.
Normally, pump designers design the pumps for water and they rarely test for different viscosities. Obviously, higher viscosity has detrimental effect on performance as the higher viscosity has more resistance to flow (Murakami et al. 1980; Telow 1942; Ippen 1946; Itaya and Nishikawa 1960). Again, the density effect has not been considered by the researchers. If the fluid is having higher viscosity or density it is inevitable to check amount of extra power consumption required and this will help energy auditing of a company. The power requirement of pump selection on the basis of the head requirement can be evaluated. Reports on centrifugal pump handling viscosity liquids shows that that the large exit angle exhibits an improvement in head and efficiency (Aoki et al. 1947; Ohta and Aoki 1996; Fard and Boyaghchi 2007). Li (2011) investigated the effect of various blade angles of an industrial oil and concluded that the blade exit angle has equal effects on head, power and efficiency. Shojaeefard et al. (2012) investigated both experimentally and numerically the effect of impeller exit angle for oil as working fluid and showed that increase of impeller outlet angle leads to improvement in the performance. Shigemitsu et al. (2011) performed experiment and numerical analysis on a mini turbopump and reported that the flow rate of the maximum efficiency shifts to a large flow rate due to the increase of the blade exit angle.
If any centrifugal pump works for a longer period, the surface gets deteriorated because of fouling, cavitation or erosion. The oil industry typically handles multiphase flow and the phases are oil, water gas and sand. There may be some corrosive gasses also such as H_{2}S. The acidic gas H_{2}S reacts with water and forms H_{2}SO_{4} which is highly reactive to the metal. Similarly CO_{2} or Cl gives ion for corrosion of metal. These corrosive gasses along with sandjetting effect accelerate the erosion. A small amount of sand can initiate pitting on the surface and the new surface is attacked by the reactive gasses or acids. Hence, the pump handling fluid from the well bore or at the surface production operations or at the downstream petroleum processing industries will develop micropitting and as a result there will be surface roughness. On one side the oil or the liquid hydrocarbon (HC) coats the surface and helps reducing the reaction, but at the same time it resists the flow through the pump. The highdensity fluid can have higher head but the pump may be running under offdesign condition. Hence, finally pump performance will be dropped.
Experiments for different surface roughness values were conducted by Varley (1961), but they did not report the interdependency of exit blade angle with surface roughness. Fard and Boyaghchi (2007) studied the influence of various blade exit angles to handle viscous fluids by computational and experimental methods. The investigation did not include roughness of wet wall. Li (2011) reported effect of exit blade angle, viscosity and roughness by CFD simulations, but the effect of inlet and outlet blade angle on roughness was not included.
Several researchers (Johnston and Rothe 1967; Johnston et al. 1972; Bayly and Orszag 1988) reported a lowenergy separated region, i.e., a boundary layer on pressure side which is unstable and tends to propagate from the hub and shroud surfaces on the suction side in the impeller. This kind of flow pattern develops jet wake flow. The analytical and experimental results (Dean and Senoo 1960; Tuzson 1993) show that a separated region because of acceleration and corresponding pressure increase from suction side to pressure side forming a separated region has its limitations. This kind of jet wake flow pattern is exhibited only under certain conditions.
Thus, the purpose of the present study is to investigate the combined effect of blade angles and surface roughness on impeller performance by numerical simulation for crude oil, kerosene, gasoline, salinewater, and water at different flow rates. The flow mechanism, nature and distribution of velocity and pressure in the pump at design and offdesign point were reported. Reason to find performance change due to viscosity effect in a centrifugal pump was performed at different conditions.
Numerical formulation
Features of impeller
Parameter  Dimension 

Shaft diameter, D _{ s }  40 mm 
Eye diameter, D _{ o }  182 mm 
Hub diameter, D _{ h }  55 mm 
Inlet diameter, D _{ 1 }  160 mm 
Inlet blade width, b _{1}  54 mm 
Outlet blade width, b _{2}  30 mm 
Inlet blade angle, β _{1}  17°, 23° and 28° 
Outlet blade angle, β _{2}  25°, 40° and 70° 
Blade number, z  7 
Outlet diameter, D _{ 2 }  365 mm 
Viscosity and density of different fluids
Fluid  Viscosity (N s/m^{2})  Density (kg/m^{3}) 

Water  1.002E3  997 
Salinewater  1.080E3  1031 
Crude oil  5.000E3  835 
Gasoline  5.000E4  720 
Kerosene  2.100E3  810 
Meshing and boundary conditions
Parameter  Description 

Flow domain  Single impeller 
Interface  Periodic 
Mesh/nature  Structural/hexahedral 
Nodes  634,161 
Elements  568,620 
Fluid nature  Water, salinewater, crude oil, gasoline and kerosene 
Inlet  Pressure 
Outlet  Mass flow rate 
Residual convergence value  1 × 10^{−5} 
Time taken for simulation  15 h 
Iteration steps  2000 
Mass imbalance  0.0001 % 
The equations for turbulent kinetic energy and dissipation rate can be written as:
The values of the closing constants are C _{ μ } = 0.09, C _{ ε1=}1.44, C _{ ε2} = 1.92, σ _{ k } = 1.0, and σ _{ ε } = 1.3.
To account for Reynolds number (Re > 10^{5}), the standard kε turbulence model was employed. Within AnsysCFX (2010), the kε turbulence model uses the scalable wallfunction approach to improve robustness and accuracy. Highresolution upwind discretization scheme was used for solving convection terms with central difference schemes for diffusion terms. AnsysCFX (2010) solver is a coupled solver and solves the hydrodynamic equations for velocity and pressure (u, v, w, p) as a single system. The simulations were carried out on 3.4 GHz core i73370 processor with 8 GB ram. Time per iteration was within 21 s.
From Fig. 1a it is clear that as β _{2} increases, the absolute exit velocity c _{2} also increases. Increase in c _{2} causes c _{ u2} to increase which results in increase in head.
The Eqs. (8) and (10) indicate that the increase in exit angle results in increase in c _{ u2 } which increases the input power.
The hydraulic losses and theoretical head (H _{th}) at design point differ from the offdesign conditions. The head and the corresponding efficiency are higher for a larger exit angle (Srinivasan 2008).
Surface roughness
Results and discussion
Problem setup
Initially, the pump geometry was designed and griddependency test (Fig. 2), check for turbulence model and validity of the CFD simulations were checked for water at design flow condition. The number of nodes was 550,000 for all the simulations as the variation of head with the increase in number of nodes were not significant. Further it was checked for accuracy of the CFD model and found that the results were predicting well (Bellary et al. 2014; Bellary and Samad 2014). After that the geometry was changed for different inlet and exit angles, and different surface roughness. The simulations were done for different fluids and for a wider operating range.
Effect of blade angles
From Eq. (7) it is obvious that the head increases with the increase in c _{ u2}. Equation (8) represents a drooping down straight line and says that a larger discharge angle produces a higher head than a smaller exit angle. The maximum change of the head curve due to the variation in discharge angle is almost same for the fluids. This implies that the effect of discharge angle on the head curve is independent of the fluid viscosity (μ = 5.0E − 4 to 50.0E − 4 Ns/m^{2}). Irrespective of viscosity, the maximum change in head due to the change in β _{2} remains almost same (Fig. 5). Thus, effect of discharge angle on head is independent of the viscosity of fluid being used.
For the same flow rate and discharge angle, the input power is more for denser fluids (Fig. 5b) and this is explained by Eq. (10). The increase in flow rate results in increase in power consumption. The density of crude oil, gasoline or kerosene is lesser than that of water or salinewater, which causes the lesser power consumption. Higher β _{2} increases c _{ u2 }; hence, the power consumption by the impeller is more (Eq. 10).
A large exit angle favors efficiency enhancement (Fig. 5). The efficiency is maximum at the best efficiency point and gets reduced uniformly to the right of the best efficiency point. At this point, secondary and profile losses are minimum and at the offdesign points the secondary and shock losses increases which increases total hydraulic losses resulting in reduced efficiency (Srinivasan 2008). The efficiency for crude oil, salinewater, gasoline or kerosene is lower than that for water. The decrease in efficiency, while pumping the crude oil and salinewater is due to the disc friction losses over the outsides of the impeller shroud and hub due to viscous effect. The results agree with the results of Gulich (2010) and Li (2008).
The static pressure and kinetic energy reaches a peak value at the impeller exit. This is due to the energy transfer by the impeller to the fluid. Lowest pressure exists at the suction side (near the leading edge) of the impeller. With the increase in blade angle, the pressure difference between outlet and inlet increases. The liquids with large β _{2} have higher pressure difference because of the decrease in velocity at the impeller outlet for large β _{2} (Fig. 5). This agrees with the existing analytical results (Lazarkiewicz and Troskolanski 1965; Srinivasan 2008).
For a radial blade impeller jet wake flow pattern can be observed if sin(β) is relatively lesser than the ratio of the average velocity on the seperating streamline and circumferential velocity (Tuzson 2000). However, with backward curved vanes, the blades lean strongly backwards making sin(β) relatively large and the above statement does not hold good. Hence, jet wake flow pattern shown in Fig. 3 was not observed in the pumps (Tuzson 2000).
Effect of surface roughness
As stated earlier in this paper that the surface roughness helps dropping performance and it is supposed to have less performance if water is pumped. The following discussion tries to highlight its effect for different viscosity fluid and the design aspects of blade angles.
Combined effect of exit blade angle and roughness
In a total combined increase in β _{2} and k _{s} values increases the head and this leads to an increase in input power with a moderate fall in efficiency.
Hence, it is recommended that in case of crude oil pumping if the priority is to transport oil to a greater height, high surface roughness value and large exit angle can be introduced with a little compromise in efficiency. In other scenarios, if power saving and a fair overall pumping performance is a criterion, it is advised to select a moderate roughness value and exit blade angle.
Conclusions

The blade exit angle has higher influence on the head, shaft power and hydraulic efficiency while the inlet blade angle has lower effect on the parameters. Large exit blade angle always augments head generation with increased input power consumption. Increase in exit blade angle increases the hydraulic efficiency till the design point. At offdesign points, the efficiency decreases for higher exit blade angles because of different losses.

Higher viscosity liquids have lower head generation at the same exit blade angle. An increase in fluid density results in increased power consumption at various blade exit angles.

The efficiency drops with increase in surface roughness due to surface roughness effect, flow losses and external disc friction. Higher surface roughness helps getting higher head.

Combined effect of increase in exit blade angle and surface roughness shows an in increase in head with negligible increase in efficiency.

In crude oil industry, for high head oil transportation and more production, increase in surface roughness value with large exit blade angle is effective. Hence, prior to application, the design may consider design itself if there is possibility of surface deterioration with course of time. This will help reducing the total energy consumption.

From energy saving point of view and a fair overall crude oil pumping performance, a moderate selection in surface roughness value and exit blade angle is suggested, and this can be implemented while designing the component.
Notes
Acknowledgments
The authors would like to acknowledge Indian Institute of Technology Madras for the NFSC grant (Grant code: OEC/1011/529/NFSC/ABDU) to conduct this research.
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