Download - Drilling Engineering - PE 311 Laminar Flow in Pipes and Annuli Non-Newtonian Fluids

Drilling Engineering

Prepared by: Tan Nguyen

Drilling Engineering - PE 311

Laminar Flow in Pipes and Annuli

Non-Newtonian Fluids



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



Pipe Flow – Power Law Fluids



Pipe Flow – Power Law Fluids

Frictional pressure drop in field unit:



Annular Flow – Power Law Fluids




Pipe Flow – Bingham Fluids



Annular Flow – Bingham Fluids




Summary



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



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)



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.