Advanced Artificial Lift Methods
Advanced Artificial Lift Methods – PE 571
Chapter 1 - Electrical Submersible Pump
Centrifugal Pump Theory – Inviscid Fluids – Single Phase
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Principles of an Centrifugal Pump
ESPs are multi stage centrifugal pumps. The two main components of a
centrifugal pump are the impeller and the diffuser.
The Impeller takes the power from the rotating shaft and accelerates the fluid.
The diffuser transforms the high fluid velocity (kinetic energy) into pressure.
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Geometry of an Centrifugal Pump
The main components of an ESP including:
Impellers
Casing
Diffusers
Shaft
Thrust washers
Bushing
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Impeller
Washer
Diffuser
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Geometry of an Centrifugal Pump
Impeller
Impeller
Diffuser
Diffuser
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
True Velocity Profile of Fluid Inside an Impeller
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Assumptions
Assumptions:
1. Two dimensions: radial and tangential direction.
2. The impeller passages are completely filled with the flowing fluid at all time
(no void spaces)
3. The streamlines have a shape similar to the blade’s shape
4. Incompressible, inviscid, and single phase fluid
5. The velocity profile is sysmetric.
The head calculated based on these assumptions is known as the
theoretical head
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Velocities at the intake and outlet of an impeller
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Velocities at the intake and outlet of an impeller
Exit Velocity Triangle
Entrance Velocity Triangle
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Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Velocity at One Point on the Impeller’s Blade
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Velocity at One Point on the Impeller’s Blade
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Velocity at One Point on the Impeller’s Blade
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Triangle Fluid Velocity
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Conclusion on Triangle Fluid Velocity
Known 3 operational parameters:
1. Angle, b: knowing pump blade geometry
2. Tangential velocity, U: knowing the rotational speed
3. Radial velocity, vr: knowing the flow rate.
Therefore, the velocity triangle is completely determined.
What we need now is to find the pressure increment developed by one impeller
as a function of those 3 operational parameters and the fourth one, namely the
fluid density
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Based on a Free Body Diagram
r
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R + dr
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Based on a Free Body Diagram
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Based on a Free Body Diagram
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Based on a Free Body Diagram
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Based on a Free Body Diagram
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Mass Balance
Mass balance equation under steady state conditions in cylindrical coordinate:
Note that the fluid at the outlet of the impeller has two components: vr and vq.
However, the change of vq respect to q is zero.
Hence:
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constant
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Mass Balance
The flow rate entering the pump intake is given (ri = r):
or
Rotational speed is related to the tangential velocity U by:
Hence, we know three parameters:
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Mass Balance
Three parameters:
Combining with the triangle velocity gives:
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Momentum Equation
For S.S; incompressible and single phase fluid; the momentum equations in the
cylindrical coordinates are given:
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Total Pressure Losses Along the Streamline
If the fluid is inviscid; No change of velocity in z and q (symmetric velocity)
direction; Neglect the pressure drop due to gravity:
Total derivative of pressure respect to the radius:
Therefore:
Streamline Trajectory
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Streamline Geometric Relationship
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Total Pressure Losses Along the Streamline
Therefore, the total pressure losses along the streamline can be express as:
From the triangle geometric relationship:
Hence:
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Total Pressure Losses Along the Streamline
Simplifying this equation gives
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Total Pressure Losses Along the Streamline
Finally, the pressure difference across a streamline is given:
Integrate this equation gives the pressure increase across one stage:
By definition:
Hence:
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Total Pressure Losses Along the Streamline
Using the geometrical relationships:
This equation can be expressed as the Euler Equation:
Field unit:
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Total Pressure Losses Along the Streamline
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Pump Head Definition
Definition for the pump head:
Head is an indirect measurement of pressure that does not depend on the fluid
density. That means for low viscous fluids, the pump performance can b uniquely
defined in terms of head.
In other words, the pump performance, in pressure, depends on the density of
the fluid being pumped, but when this performance is expressed in head, the
pump performance is independent of the fluid being pumped
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Pump Head Definition
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Head Losses
Due to the Leakage and recirculation of fluid inside the impleller.
Hydraulic losses including:
Diffusion loss due to divergence, or convergence
Fluid shock loss at the inlet
Mixing and eddying loss at the impeller discharge
Turning loss due to turning of the absolute velocity vector
Separation losses
Friction losses
Mechanical losses
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Leakage and Recirculation Losses
Recirculation
Leakage
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Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Leakage and Recirculation Losses
Theoretical diagram
Diagram with recirculation
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Leakage and Recirculation Losses
Head, H
Theoretical head (Euler head)
Leakage/Recirculation losses
Flow rate, Q
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Hydraulic Losses
Pumps are designed trying to achieve a no pre-rotation condition close to the
best efficiency point, since this condition minimize shock-losses. In other words,
shock losses increase as we move away from the BEP.
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Hydraulic Losses
Other losses including friction, mixing, change in direction of fluid, separation,
etc. also contribute significantly to the total losses due to hydraulic.
Head, H
Theoretical head (Euler head)
Hydraulic losses
Flow rate, Q
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Friction Losses
Friction losses increases with increasing flowrate and viscosity.
Head, H
Theoretical head (Euler head)
Friction losses
Flow rate, Q
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Mechanical Losses
These losses include disk friction and frictional losses in bearings. The most
significant loss is the thrust bearing loss. The mechanical losses do not have any
effect on head and capacity of a pump but increase the brake hoursepower.
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Total Losses
Theoretical head (Euler head)
Head, H
Hydraulic losses
Friction losses
Actual Head
Leakage/Recirculation losses
Flow rate, Q
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Horsepower
The hydraulic horsepower is the energy transmitted to the fluids by the pump.
The break horsepower is the energy required by the pump shaft to turn. Some of
this energy is dissipated inside the pump.
The ratio between the hydraulic horsepower and the break horsepower is the
pump hydraulic efficiency.
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Pump Performance
In practice, a pump is tested by running it at a constant speed and varying the
flow by controlling the choke. During the test, Q, DP, and the break horsepower
are measure at several points. The DP is then converted to head and the overal
efficiency of the pump is calculated. Based on these data, we can develop the
pump performance.
The performance curve of a centrifugal pump can be summarized in only one
curve of head vs. flowrate for all low viscous fluids.
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Pump Performance
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Pump Performance
Manufacturers also provide polynomial equations to describe the catalog pump
performance curves.
Electrical Submersible Pump
Advanced Artificial Lift Methods
Theoretical Head Developed by an Impeller
Pump Performance
Do the calculation for these correlations:
Electrical Submersible Pump