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14.1-1

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14.1-1

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    1. 1 14.1-1 Pressures

    2. 2 API Power Law Model K = consistency index n = flow behaviour index Recently the API has published their API RP 13D. In this publication, the API recommends using a modified power law model to calculate pressure losses in pipes and annuli. For a power law, the shear stress is proportional to the shear rate, and passes through the origin. However, it does not plot as a straight line – it is shear thinning. The apparent viscosity decreases with increasing shear rate. The K in the above equation is the consistency index and has units of equivalent cp. The n is the flow behavior index, and represents the degree of non-Newtonian behavior that the fluid exhibits.Recently the API has published their API RP 13D. In this publication, the API recommends using a modified power law model to calculate pressure losses in pipes and annuli. For a power law, the shear stress is proportional to the shear rate, and passes through the origin. However, it does not plot as a straight line – it is shear thinning. The apparent viscosity decreases with increasing shear rate. The K in the above equation is the consistency index and has units of equivalent cp. The n is the flow behavior index, and represents the degree of non-Newtonian behavior that the fluid exhibits.

    3. 3 Rotating Sleeve Viscometer The API Power law tries to match shear rates from the viscometer with shear rates actually experienced inside the drillpipe and annulus. To do this we use the 600 and 300 rpm readings for pressure losses inside the drill pipe. We use the 3 and 100 rpm readings inside the annulus.The API Power law tries to match shear rates from the viscometer with shear rates actually experienced inside the drillpipe and annulus. To do this we use the 600 and 300 rpm readings for pressure losses inside the drill pipe. We use the 3 and 100 rpm readings inside the annulus.

    4. 4 Pressure Drop Calculations Example Calculate the pump pressure in the wellbore shown on the next page, using the API method. The relevant rotational viscometer readings are as follows: R3 = 3 (at 3 RPM) R100 = 20 (at 100 RPM) R300 = 39 (at 300 RPM) R600 = 65 (at 600 RPM) We will demonstrate with an example calculation.We will demonstrate with an example calculation.

    5. 5 We will calculate the pressure losses in the entire circulating system.We will calculate the pressure losses in the entire circulating system.

    6. 6 Inside the drillpipe we calculate n, K and average velocity.Inside the drillpipe we calculate n, K and average velocity.

    7. 7 Next we calculat the effective viscosity, and the Reynolds number.Next we calculat the effective viscosity, and the Reynolds number.

    8. 8 We calculate a and b to be used along with the Reynolds number to calculate the friction factor.We calculate a and b to be used along with the Reynolds number to calculate the friction factor.

    9. 9 Finally the pressure drop in the drill pipe.Finally the pressure drop in the drill pipe.

    10. 10 Repeat inside the drill collars. Remember to use the 300 and 600 rpm readings inside the drill string.Repeat inside the drill collars. Remember to use the 300 and 600 rpm readings inside the drill string.

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    13. 13

    14. 14 The new API publication recommends a simpler equation to calculate the pressure drop through the bit.The new API publication recommends a simpler equation to calculate the pressure drop through the bit.

    15. 15 Now we use the 3 and 100 rpm readings to calculate pressure losses in the annulus.Now we use the 3 and 100 rpm readings to calculate pressure losses in the annulus.

    16. 16 The DC OH annulus.The DC OH annulus.

    17. 17

    18. 18

    19. 19 The DP OH annulus.The DP OH annulus.

    20. 20

    21. 21

    22. 22

    23. 23 Pump pressure can now be calculated by summing all the pressure drops in the system.Pump pressure can now be calculated by summing all the pressure drops in the system.

    24. 24

    25. 25 Here we plot the circulating pressure as a function of the cumulative distanced from the standpipe.Here we plot the circulating pressure as a function of the cumulative distanced from the standpipe.

    26. 26 The HSP vs. distance from the standpipe.The HSP vs. distance from the standpipe.

    27. 27 Now combined.Now combined.

    28. 28 Same plotted vs. depth in the well.Same plotted vs. depth in the well.

    29. 29 Pipe Flow - Laminar In the above example the flow down the drillpipe was turbulent. Under conditions of very high viscosity, the flow may very well be laminar. If flow in the drillpipe is laminar the friction factor can be calculated with the above and used in the frictional pressure equation.If flow in the drillpipe is laminar the friction factor can be calculated with the above and used in the frictional pressure equation.

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