1. Drilling Engineering Prepared by: Tan Nguyen Drilling Engineering - PE 311 Laminar Flow in Pipes and Annuli Non-Newtonian Fluids

2. Drilling Engineering Prepared by: Tan Nguyen When attempting to quantify the pressure losses in side the drillstring and in the annulus it is worth considering the following matrix: Frictional Pressure Drop in Pipes and Annuli

3. Drilling Engineering Prepared by: Tan Nguyen Pipe Flow – Power Law Fluids

4. Drilling Engineering Prepared by: Tan Nguyen Pipe Flow – Power Law Fluids Frictional pressure drop in field unit:

5. Drilling Engineering Prepared by: Tan Nguyen Annular Flow – Power Law Fluids Frictional pressure drop in field unit:

6. Drilling Engineering Prepared by: Tan Nguyen Pipe Flow – Bingham Fluids

7. Drilling Engineering Prepared by: Tan Nguyen Pipe Flow – Bingham Fluids

8. Drilling Engineering Prepared by: Tan Nguyen Pipe Flow – Bingham Fluids Frictional pressure drop in field unit:

9. Drilling Engineering Prepared by: Tan Nguyen Annular Flow – Bingham Fluids Frictional pressure drop in field unit:

10. Drilling Engineering Prepared by: Tan Nguyen Summary

11. Drilling Engineering Prepared by: Tan Nguyen Examples Example 1: A Cement slurry that has a flow-behavior index of 0.3 and a consistency index of 9400 eq cp is being pumped in an 8.097x4.5 in. annulus at a rate of 200 gal/min. Assuming the flow pattern is laminar, compute the frictional pressure loss per 1000 ft of annulus. Also estimate the shear rate at the pipe wall. Mean velocity: Frictional pressure loss: Shear rate at the pipe wall:

12. Drilling Engineering Prepared by: Tan Nguyen Examples Example 2: a. Calculate the velocity of a fluid flowing through a 5’’ 19.5 lbm/ft drillpipe with I.D. = 4.276’’ at 150 GPM. b. Determine the pressure loss in the above situation if the fluid is a Bingham Plastic fluid with a plastic viscosity of 20 cp, a yield point of 15 lbf/100ft 2 and density of 10 ppg. (1 lbf/100ft2 = 0.479 Pa) c. Calulate the pressure loss in the above situation if the fluid was a power law fluid with the flow behavior index of 0.75 and a consistency index of 70 eq cp. (lbfxS n /100ft 2 = 479 eq cp)

13. Drilling Engineering Prepared by: Tan Nguyen Examples Solution: a. Calculate the velocity of a fluid flowing through a 5’’ 19.5 lbm/ft drillpipe with I.D. = 4.276’’ at 150 GPM. b. Determine the pressure loss in the above situation if the fluid is a Bingham Plastic fluid with a plastic viscosity of 20 cp, a yield point of 15 lbf/100ft 2 and density of 10 ppg. c. Calulate the pressure loss in the above situation if the fluid was a power law fluid with the flow behavior index of 0.75 and a consistency index of 70 eq cp.