Characterization of fluids with drag reducing additives in a couette device

Patent metadata

Field	Value
Publication number	US-10860753-B2
Application number	US-201315035072-A
Country	US
Kind code	B2
Filing date	Nov 7, 2013
Priority date	Nov 7, 2013
Publication date	Dec 8, 2020
Grant date	Dec 8, 2020

Abstract

A method is provided for characterizing fluid flow in a pipe where the fluid includes a drag reducing polymer of a particular type and particular concentration. A computational model is configured to model flow of a fluid in a pipe. The computational model utilizes an empirical parameter for a drag reducing polymer of the particular type and the particular concentration. The computational model can be used to derive information that characterizes the flow of the fluid in the pipe. The empirical parameter for the particular type and the particular concentration of the drag reducing polymer can be identified by solving another computational model that is configured to model turbulent Couette flow in a Couette device for a fluid that includes a drag reducing polymer of the particular type and the particular concentration. The empirical data needed for identification of the empirical parameter are obtained from Couette device experiments.

First claim

What is claimed is:

1. A method of characterizing fluid flow in a pipe where the fluid includes a drag reducing polymer of a particular type and particular concentration, the method comprising:
i) providing a Couette device that includes an annulus disposed between an outer annular surface and an inner annular surface and a sensor disposed adjacent the outer annular surface, wherein the sensor is configured to measure shear stress of fluid at the outer annular surface;
ii) providing a first computational model associated with the Couette device of i) to model turbulent Couette flow of a fluid based upon a flow representation consisting of an inner sublayer, an outer sublayer, and a turbulent core between the inner sublayer and the outer sublayer, wherein the first computational model includes an empirical parameter for the particular type and the particular concentration of the drag reducing polymer that is based on the shear stress of the fluid at the outer annular surface measured by the sensor, and wherein the first computational model further includes a first drag reduction parameter associated with the outer sublayer and a second drag reduction parameter associated with the inner sublayer, wherein both the first and second drag reduction parameters are based on the empirical parameter;
iii) loading a fluid into the annulus of the Couette device of i), the fluid including the particular type and the particular concentration of the drag reducing polymer, and operating the Couette device of i) to induce turbulent flow of the fluid in the annulus of the Couette device and to obtain related experimental data including shear stress of the fluid at the outer annular surface measured by the sensor;
iv) processing the first computational model of ii) in conjunction with the experimental data obtained in iii) on a data processor to solve for the empirical parameter of the first computational model;
v) providing a second computational model that is configured to model flow of fluid in a pipe, wherein the second computational model includes a drag reduction parameter that is a function of the empirical parameter as solved for in iv), and wherein the second computational model further includes a friction factor that is a function of the drag reduction parameter, wherein the friction factor relates pressure loss due to friction along a given length of pipe to the mean flow velocity through the pipe; and
vi) processing the second computational model on a data processor to derive information that characterizes the flow of fluid in the pipe.

2. A method according to claim 1 , wherein the drag reduction parameter is also a function of a dimensionless pipe radius.

3. A method according to claim 2 , wherein the second computational model is configured to relate the drag reduction parameter to the empirical parameter by an equation of the form:
D * =1+α * R +

where
D * is the drag reduction parameter,
α * is the empirical parameter, and
R + is the dimensionless pipe radius.

4. A method according to claim 1 , wherein the second computational model is configured to relate the friction factor to the drag reduction parameter by an equation of the form:

1

f
0.5

=

4
⁢

log
10

⁡

(

Re
⁢

⁢

f
0.5

)

+

8.2
⁢

D
*
2

-
8.6
-

12.2
⁢

log
10

⁢

D
*

where
f is the friction factor,
D * is the drag reduction parameter, and
Re is the Reynolds number of the flow in the pipe.

5. A method according to claim 4 , wherein the second computational model is further configured to relate the Reynolds number Re to a dimensionless pipe radius R + .

6. A method according to claim 4 , wherein the information derived in iv) includes a solution for the friction factor f for given flow conditions.

7. A method according to claim 6 , wherein the information derived in iv) includes a pressure drop over a given length of pipe based on the solution for the friction factor f.

8. A method according to claim 1 , wherein the second computational model is based upon a representation of the flow as two layers consisting of a viscous outer sublayer that surrounds a turbulent core.

9. A method according to claim 1 , wherein both the first and second drag reduction parameters are also based on a dimensionless torque G derived from the shear stress of the fluid at the outer annular surface measured by the sensor.

10. A method according to claim 9 , wherein:
the outer and inner annular surfaces of the Couette device of i) are concentric with respect to one another about a common center, wherein the outer annular surface is offset from the center by a first radius R and the inner annular surface is offset from the center by a second radius r 0 , wherein R is greater than r 0 ; and
the first computational model is configured to relate the first and second drag reduction parameters to the empirical parameter by equations of the following form:

D

o
*

=

1
+

α
*

2

⁢

(

1
-
η

)

⁢

G

2
⁢

⁢
π

D

i
*

=

1
+

α

Assignees

• Schlumberger Technology Corp

Inventors

• Barmatov Evgeny Borisovich
• Eskin Dmitry

Classifications

• G06F2113/14

  Pipes · CPC title

• G06F30/20 Primary

  Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) · CPC title

• G06F30/28 Primary

  using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD] · CPC title

• G01N11/04 Primary

  through a restricted passage, e.g. tube, aperture · CPC title

• G01N2011/006

  Determining flow properties indirectly by measuring other parameters of the system · CPC title