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Drilling Engineering - PE 311 Laminar Flow in Pipes and Annuli Non-Newtonian Fluids. Frictional Pressure Drop in Pipes and Annuli. When attempting to quantify the pressure losses in side the drillstring and in the annulus it is worth considering the following matrix:. - PowerPoint PPT Presentation
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Drilling Engineering
Prepared by: Tan Nguyen
Drilling Engineering - PE 311
Laminar Flow in Pipes and Annuli
Non-Newtonian Fluids
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
Drilling Engineering
Prepared by: Tan Nguyen
Pipe Flow – Power Law Fluids
Drilling Engineering
Prepared by: Tan Nguyen
Pipe Flow – Power Law Fluids
Frictional pressure drop in field unit:
Drilling Engineering
Prepared by: Tan Nguyen
Annular Flow – Power Law Fluids
Frictional pressure drop in field unit:
Drilling Engineering
Prepared by: Tan Nguyen
Pipe Flow – Bingham Fluids
Drilling Engineering
Prepared by: Tan Nguyen
Pipe Flow – Bingham Fluids
Drilling Engineering
Prepared by: Tan Nguyen
Pipe Flow – Bingham Fluids
Frictional pressure drop in field unit:
Drilling Engineering
Prepared by: Tan Nguyen
Annular Flow – Bingham Fluids
Frictional pressure drop in field unit:
Drilling Engineering
Prepared by: Tan Nguyen
Summary
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:
11
12
sec128)3.0/12(5.4097.8
803.1*48248
nw
w ddv
sftdd
qv /803.1)5.4097.8(488.2
80488.2 222
122
ftpsiftpsi
ddvK
dLdp n
nn
n
1000/9.77/0779.00.02080.312
4.5)097144,000(8.3)9,400(1.80
0208.02
144000
0.3
1.3
0.31
112
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/100ft2 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. (lbfxSn/100ft2 = 479 eq cp)
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/100ft2 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.