Real time monitoring of non-Newtonian fluids
Systems and methods for determining the yield stress of a non-Newtonian fluid in real time are provided. A pressure loss and/or liquid rise technique, an ultrasonic technique, and/or a penetrometer technique can be used to determine the yield stress of a non-Newtonian fluid. The ultrasonic technique can include a longitudinal wave approach and/or a shear wave approach. The methods and systems are non-invasive and only require slight modifications to the piping containing the non-Newtonian fluid in order to measure the yield stress.
1. A system for determining yield stress of a non-Newtonian fluid, the system comprising:
a pipe containing the non-Newtonian fluid;
a differential type pressure transmitter connected to a first point of the pipe and a second point of the pipe, the pipe containing therein a fully-developed laminar flow of the non-Newtonian fluid between the first point and the second point;
a processor;
a machine-readable medium in operable communication with the processor and having instructions stored thereon that, when executed by the processor, solve equations (1), (2), and (3) in order to determine the yield stress of the non-Newtonian fluid; and
a flow meter connected to the pipe and configured to measure a velocity of the non-Newtonian fluid,
the differential type pressure transmitter being configured to measure a first pressure of the pipe at the first point and a second pressure of the pipe at the second point,
the yield stress of the non-Newtonian fluid being determined in real time by the processor using the difference between the first pressure and the second pressure as an input to equation (1), and
equations (1), (2), and (3) being as follows
Δ
P
L
=
f
ρ
V
2
2
D
(
1
)
f
=
64
Re
+
64
Re
(
He
6.2218
Re
)
0.958
(
2
)
H
=
D
2
ρ
τ
y
μ
2
(
3
)
where ΔP is the difference between the first pressure and the second pressure, L is a predetermined length of the pipe between the first point and the second point, D is a predetermined diameter of the pipe between the first point and the second point, o is a predetermined density of the non-Newtonian fluid, f is a frictional coefficient of the non-Newtonian fluid, V is the velocity of the non-Newtonian fluid in the pipe between the first point and the second point measured by the flow meter, μ is a viscosity of the non-Newtonian fluid, Re is a Reynolds number of the non-Newtonian fluid in the pipe between the first point and the second point, He is a Hedstrom number of the non-Newtonian fluid in the pipe between the first point and the second point, and ty is the yield stress of the non-Newtonian fluid.
2. The system according to claim 1 ,
the flow meter being further configured to adjust a flow of the non-Newtonian fluid in the pipe to ensure that it is fully-developed laminar flow between the first point and the second point.
3. A method for determining yield stress of a non-Newtonian fluid, the method comprising:
providing the system according to claim 1 ;
measuring the difference between the first pressure and the second pressure using the differential type pressure transmitter; and
determining the yield stress of the non-Newtonian fluid using the processor and the machine-readable to solve equations (1), (2), and (3) with the difference between the first pressure and the second pressure being an input to equation (1).
4. The method according to claim 3 , the yield stress being determined in real time without any sample of the non-Newtonian fluid being removed from the pipe.