Inline rheology/viscosity, density, and flow rate measurement
A system for performing inline measurements of flow rate, density, and rheology of a flowing fluid is disclosed, comprising: (a) a rheology measurement subsystem comprising: a horizontal tube of internal radius r H ; means for measuring a velocity profile of a test fluid flowing through said horizontal tube at a distance x 0 from its upstream end; and means for determining wall shear stress at a boundary between said flowing fluid and an inner surface of said horizontal tube; (b) a density measurement subsystem comprising: a vertical tube of internal radius r V in fluid connection with said horizontal tube; a pressure sensor for measuring the pressure of said test fluid within said vertical tube at a location y 1 ; and, (c) a pressure sensor for measuring the pressure of said test fluid within said vertical tube at a location y 2 downstream from y 1 and displaced vertically from y 1 by a distance Δh.
1. A method for performing inline rheology and density measurements on a test fluid having a density ρ, comprising:
flowing said test fluid through a horizontal tube of internal radius r H having an upstream end and a downstream end;
measuring, via a velocity profile measurement device, a velocity profile v(r) at a distance x 0 from said upstream end for at least one value of r, 0≤r≤r H ;
determining, via a processor, a shear rate {dot over (γ)}(r);
calculating radius-dependent shear stress as a function of shear rate (rheogram) τ({dot over (γ)}) for at least one value of r, 0≤r≤r H ;
calculating at least one rheology parameter of said test fluid
η
(
γ
.
)
=
τ
(
γ
.
)
γ
.
;
flowing said test fluid through a vertical tube of internal radius r V ;
measuring, via a first pressure sensor, a first pressure of said test fluid within said vertical tube at a location y 1 ;
measuring, via a second pressure sensor, a second pressure of said test fluid within said vertical tube at a location y 2 ; and
determining, via the processor, said density p of said test fluid in said vertical tube based on the first measured pressure and the second measure pressure.
2. The method according to claim 1 , wherein said step of determining a shear rate comprises differentiating said velocity profile with respect to radius,
γ
.
(
r
)
=
d
v
d
r
.
3. The method according to claim 1 , wherein said step of calculating a radius-dependent shear stress comprises:
measuring a pressure difference ΔP H between pressures of said test fluid measured at two locations x 1 and x 2 , x 1 upstream of x 0 , x 2 downstream of x 0 ;
calculating shear stress as a function of radius
τ
(
r
)
=
Δ
P
H
2
L
r
,
where L=x 2 −x 1 ; and,
combining said shear stress as a function of radius with said shear rate as a function of radius to produce a rheogram (curve of shear stress as a function of shear rate).
4. The method according to claim 1 , wherein said step of flowing said test fluid through a horizontal tube comprises flowing said test fluid through a horizontal tube under conditions of laminar flow.
5. The method according to claim 1 , wherein said step of measuring a velocity profile comprises using a velocity profile measurement device selected from the group consisting of an imaging NMR spectrometer; an ultrasound velocimetry system; an optical velocimetry system; a pitot tube array; and an array of thermal flow sensors to measure said velocity profile.
6. The method according to claim 1 , wherein said test fluid is selected from the group consisting of single-component liquids, mixtures of liquids, solutions, suspensions, emulsions, colloids, slurries, pastes, creams, foams, media containing one or more liquids mixed with gas bubbles, media containing one or more liquids mixed with solid matter, and media containing one or more liquids mixed with gas and solid matter.
7. The method according to claim 1 , wherein said test fluid is non-Newtonian, a yield-stress material, a potable liquid, an edible non-liquid material that can be pumped through a tube, or any combination thereof.
8. The method according to claim 1 , wherein said test fluid comprises a fluid selected from the group consisting of oil-based drilling fluid, water-based drilling fluid, synthetic drilling fluid, fracturing fluid, crude oil, refined oil, an oil/water mixture, any of the above containing particulate matter, and any of the above to which a viscosifier has been added.
9. The method according to claim 1 , wherein said test fluid is a potable liquid.
10. The method according to claim 1 , wherein said step of measuring a velocity profile comprises:
passing said test fluid through an imaging NMR spectrometer; and,
imaging said test fluid as it passes through said imaging NMR spectrometer.
11. The method according to claim 10 , wherein said step of imaging said test fluid comprises imaging said test fluid by using an NMR imaging technique comprising a pulsed gradient spin echo sequence.
12. The method according to claim 10 , wherein said step of passing said test fluid through an imaging NMR spectrometer comprises passing said test fluid through an NMR spectrometer comprising a permanent magnet.