1. Advanced Artificial Lift Methods Electrical Submersible Pump Advanced Artificial Lift Methods – PE 571 Chapter 1 - Electrical Submersible Pump Affinity Laws

2. Advanced Artificial Lift Methods Electrical Submersible Pump 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 Laws Introduction to The Affinity Laws

3. Advanced Artificial Lift Methods Electrical Submersible Pump Theoretical centrifugal pump performance: In terms of revolution per minute N = 2  : Rearrange Introduction to The Affinity Laws Affinity Laws

4. Advanced Artificial Lift Methods Electrical Submersible Pump Define two new dimensionless parameters: Dimensionless head: Dimensionless capacity: Then the Euler equation can be plotted as: Introduction to The Affinity Laws Affinity Laws

5. Advanced Artificial Lift Methods Electrical Submersible Pump Introduction to The Affinity Laws Theoretical performance (Euler Equation) Actual Performance Affinity Laws

6. Advanced Artificial Lift Methods Electrical Submersible Pump 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. Introduction to The Affinity Laws Affinity Laws

7. Advanced Artificial Lift Methods Electrical Submersible Pump Introduction to The Affinity Laws Affinity Laws

8. Advanced Artificial Lift Methods Electrical Submersible Pump Any combinations that we can obtain the same point on the performance curve (same Q d and same H d ) are defined as equivalent states. Introduction to The Affinity Laws 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) QdQd HdHd Equivalent states

9. Advanced Artificial Lift Methods Electrical Submersible Pump 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. Introduction to The Affinity Laws Affinity Laws

10. Advanced Artificial Lift Methods Electrical Submersible Pump Let consider two different pump geometries: Dimensionless capacity: Dimensionless head Specific Speed Affinity Laws – Due to Pump Geometry

11. Advanced Artificial Lift Methods Electrical Submersible Pump From the dimensionless capacity gives: From the dimensionless head: Combining these two equations gives: Or: Specific Speed Affinity Laws – Due to Pump Geometry

12. Advanced Artificial Lift Methods Electrical Submersible Pump 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 Affinity Laws – Due to Pump Geometry

13. Advanced Artificial Lift Methods Electrical Submersible Pump 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 Affinity Laws – Due to Pump Geometry

14. Advanced Artificial Lift Methods Electrical Submersible Pump According to the definition, the specific speed is a dimensionless number. For different units: American industry: Specific Speed Affinity Laws – Due to Pump Geometry

15. Advanced Artificial Lift Methods Electrical Submersible Pump Result from Solano (2009) Affinity Laws – Due to Pump Geometry

16. Advanced Artificial Lift Methods Electrical Submersible Pump Result from Solano (2009) Affinity Laws – Due to Pump Geometry

17. Advanced Artificial Lift Methods Electrical Submersible Pump Result from Solano (2009) – Ns = 2900 Effect of Viscosity Affinity Laws – Due to Pump Geometry

18. Advanced Artificial Lift Methods Electrical Submersible Pump Result from Solano (2009) – Different Ns Affinity Laws – Due to Pump Geometry

19. Advanced Artificial Lift Methods Electrical Submersible Pump Expected Results for Viscous Fluids Affinity Laws – Due to Pump Geometry

20. Advanced Artificial Lift Methods Electrical Submersible Pump 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. Affinity Laws – Due to Pump Geometry

21. Advanced Artificial Lift Methods Electrical Submersible Pump Other Effects of Specific Speed Affinity Laws – Due to Pump Geometry

22. Advanced Artificial Lift Methods Electrical Submersible Pump 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. Affinity Laws – Due to Pump Geometry

23. Advanced Artificial Lift Methods Electrical Submersible Pump 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

24. Advanced Artificial Lift Methods Electrical Submersible Pump In summary: These are called the Affinity Laws. Affinity Laws – Due to The Speed

25. Advanced Artificial Lift Methods Electrical Submersible Pump Affinity Laws – Due to The Speed

26. Advanced Artificial Lift Methods Electrical Submersible Pump 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. Affinity Laws – Due to The Speed