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Advanced Artificial Lift Methods

Electrical Submersible Pump

Advanced Artificial Lift Methods – PE 571

Chapter 1 - Electrical Submersible Pump

Affinity Laws

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We know that the pump performance curve obtained experimentally by the

manufacturer is valid for:

One pump hydraulic design and size

Single phase flow of low viscosity fluids

Pump operating at a constant and known rotational speed

How is the pump performance affected by the following:

Different Impeller and diffuser hydraulic design

Different impeller and diffuser size

Different rotational speeds

Different fluid viscosity

Multiphase flow

Affinity LawsIntroduction to The Affinity Laws

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Theoretical centrifugal pump performance:

In terms of revolution per minute N = 2:

Rearrange

Introduction to The Affinity Laws

Affinity Laws

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Define two new dimensionless parameters:

Dimensionless head:

Dimensionless capacity:

Then the Euler equation can be plotted as:


Affinity Laws

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Theoretical performance (Euler Equation)

Actual Performance

Affinity Laws

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The relationship between the dimensionless head and dimensionless flow rate is

unique.

This relationship (the red line) does not depend on the rotational speed. For

example, with N = 3600 RPM, then we can plot one performance curve. With N =

2000 RPM, we can now plot another performance curve. These two curves

should line-up one on the top of another. In other words, if we consider one point

on the performance curve, there are many different combinations between N, Q,

and H to attain this point.


Affinity Laws

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Affinity Laws

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Any combinations that we can obtain the same point on the performance curve

(same Qd and same Hd) are defined as equivalent states.


Affinity Laws

Red curve for a certain N1 and a set of Q = (Qa1, Qa2, … Qan) and H = (Ha1, Ha2, …Han)

Blue curve for a certain N2 and a set of Q = (Qb1, Qb2, … Qbn) and H = (Hb1, Hb2, …Hbn)

Qd

Hd

Equivalent states

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Therefore, based on this analysis, we can estimate the changes in the pump

performance due to:

Changes in pump geometry

Changes in rotational speed and pump size

These are the basics of the Affinity Laws.


Affinity Laws

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Let consider two different pump geometries:

Dimensionless capacity:

Dimensionless head

Specific Speed

Affinity Laws – Due to Pump Geometry

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From the dimensionless capacity gives:

From the dimensionless head:

Combining these two equations gives:

Or:

Specific Speed


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Define the specific speed as

We can come to several conclusions: if the two pumps are similar then

1. The specific speed will stay the same.

2.It does not depend on the pump speed on the performance curve.

3.It does not depend on the flow rate on the performance curve.

4.The physical meaning of the specific speed has no practical value and the

number is used as a “type number”.

Specific Speed


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Specific Speed

The value of the specific speed changes with pump geometry and that is why it is

commonly used as a “type number” to classify pumps


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According to the definition, the specific speed is a dimensionless number.

For different units:

American industry:

Specific Speed


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Result from Solano (2009)


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Result from Solano (2009) – Ns = 2900Effect of Viscosity


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Result from Solano (2009) – Different Ns


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Expected Results for Viscous Fluids


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Specific Speed

Several conclusions:

1. For a certain pump size and a certain rotational speed, pumps with higher

values of specific speed will have higher values for the bep flow rate

2.For a certain design and a certain rotational speed, pumps with higher values

of specific speed will have a smaller diameter and as a result will develop less

head.


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Other Effects of Specific Speed


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Other Effects of Specific Speed

For a given flow rate, maximum efficiency is attained by pumps of specific

speeds in the range of 2000 – 3000.

As specific speed increases, the pump design changes from purely radial to

strictly axial flow.

The pump efficiency falls of very rapidly for Ns < 1000. This is mainly because

the impellers have long, narrow passages which result in large friction losses and

greater disk friction loss. The amount of leakage also becomes a significant

portion of the impeller capacity.

For the radial type impeller, the high head and low flow rates indicate

improvement in efficiency is obtained through the minimization of leakage and

recirculation.


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In the next section, we will focus on the changes of the pump performance for

one specific pump geometric design but different sizes.

For two equivalent states:

Assuming the pump efficiency is also equal under these equivalent states:

Affinity Laws – Due to The Speed

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In summary:

These are called the Affinity Laws.


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Keep in mind that this theory is based on the assumptions: inviscid fluids, and

streamline flow of fluids along impeller and diffuser channels. Therefore, Affinity

Laws are not applicable for high viscous fluids.


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