# US 12,181,396 B2 · Rheology device and method

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- Number: US 12,181,396 B2
- Document ID: US12181396B2
- Status: Granted
- Kind: B2
- Application number: 17/365,381
- Filed: 2021-07-01
- Published: 2022-01-06
- Granted: 2024-12-31
- Earliest claimed: 2020-07-02
- Assignees: Opla Energy Ltd.
- Applicants: Opla Energy Ltd.
- Inventors: Hossein Khorshidian; Elvin Mammadov; Saied Afshari; Ahmad Alizadeh
- Web page: https://patentgrep.com/patent/US12181396B2

## CPC

- G01N 11/08: by measuring pressure required to produce a known flow
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)

## Abstract

A rheology device comprises an elongated body having a flow path defined therein, first and second pressure lines in communication with the first and second ends of the flow path, respectively, and a differential pressure sensor for measuring a difference in pressure between the first and second pressure lines. In embodiments, the pressure lines are filled with a spacer fluid different from the fluid in the flow path. Based on at least three measurements of difference in pressure and corresponding flow rates, a yield point, a consistency factor, and a power factor can be calculated, and a rheology model of the fluid can be generated. Related methods are described which allow fluid rheology models to be determined and updated frequently. The device and methods herein may be useful in oil and gas operations, for example for rheology and hydraulic modeling in drilling operations.

## Claims

### Claim 1

A rheology device for connection to a fluid flow line having a fluid flowing therethrough, the rheology device comprising:
an elongated body having a first end, a second end, and a fluid flow path defined in the elongated body, the fluid flow path extending between the first and second ends, the first and second ends configured for connection to the fluid flow line to allow fluid communication between the fluid flow line and the fluid flow path;
a differential pressure sensor;
a first pressure line having a first end, a second end, and an inner fluid passageway extending between the first and second ends, the first end coupled to the elongated body and in communication with the fluid flow path at or near the first end of the elongated body, and the second end coupled to and in communication with the differential pressure sensor; and
a second pressure line having a first end, a second end, and an inner fluid passageway extending between the first and second ends, the first end coupled to the elongated body and in communication with the fluid flow path at or near the second end of the elongated body, and the second end coupled to and in communication with the differential pressure sensor,
the differential pressure sensor for measuring at least three differences in pressure between the first and second pressure lines, each of the at least three differences in pressure corresponding to a different flow rate of the fluid, and the at least three differences in pressure and the corresponding different flow rates are used to determine a rheology model of the fluid;
a first fitting coupled to and in fluid communication with the first pressure line; and
a second fitting coupled to and in fluid communication with the second pressure line, the first and second fittings configured to allow a spacer fluid to be injected into the inner fluid passageways of the first and second pressure lines, respectively.

### Claim 2 (depends on 1)

The rheology device of claim 1, wherein the spacer fluid has a viscosity between about 500 cP and about 2500 cP.

### Claim 3 (depends on 1)

The rheology device of claim 1, wherein the differential pressure sensor is supported on an outer surface of the elongated by a clamp configured to dampen vibration.

### Claim 4 (depends on 1)

The rheology device of claim 1, wherein the fluid flow path is an inner bore of the elongated body.

### Claim 5 (depends on 1)

The rheology device of claim 1, wherein the fluid flow path is an annular space of the elongated body.

### Claim 6

A method for determining a rheology model for a fluid flowing in a fluid flow line, the method comprising:
a) using a sensor to measure a flow rate of the fluid in the fluid flow line;
b) determining a corresponding difference in pressure of the fluid between an upstream location and a downstream location of a fluid flow path, the fluid flow path being in fluid communication with the fluid flow line such that at least some of the fluid flows through the fluid flow path from the upstream location to the downstream location;
c) changing the flow rate of the fluid;
d) repeating steps a) to c) at least three times to provide at least three data pairs, each data pair having a respective flow rate and a respective difference in pressure;
e) calculating, based on the at least three data pairs, a yield point, a consistency factor, and a power factor; and
f) determining, based on the yield point, the consistency factor, and the power factor, a rheology model of the fluid; and
wherein the yield point (YP), the consistency factor (K), and the power factor (n) are calculated by:
Δ
⁢
P
L
=
4
⁢
K
D
⁢
(
8
⁢
V
D
)
n
⁢
(
3
⁢
n
+
1
4
⁢
N
)
n
⁢
1
1
-
X
⁢
(
1
1
-
aX
-
bX
2
-
cX
3
)
n
⁢
X
=
4
⁢
L
⁡
(
YP
)
D
⁢
ΔP
⁢
a
=
1
2
⁢
n
+
1
⁢
b
=
2
⁢
n
(
n
+
1
)
⁢
(
2
⁢
n
+
1
)
⁢
c
=
2
⁢
n
2
(
n
+
1
)
⁢
(
2
⁢
n
+
1
)
where, for each data pair, ΔP is the respective difference in pressure, L is a distance between the upstream location and the downstream location, D is a diameter of the fluid flow path, V is a velocity of the fluid which is the ratio between the respective flow rate and the cross-sectional area of the fluid flow path.

### Claim 7 (depends on 6)

The method of claim 6 wherein determining the corresponding difference in pressure is performed by a rheology device; the fluid flow path is defined in the rheology device; and the rheology device comprises a first pressure line and a second pressure line, and a first end of the first pressure line is in communication with the upstream location, and a first end of the second pressure line is in communication with the downstream location.

### Claim 8 (depends on 7)

The method of claim 7 comprising, prior to determining the corresponding difference in pressure, filling the first and second pressure lines with a spacer fluid.

### Claim 9 (depends on 7)

The method of claim 7, wherein the rheology device comprises a differential pressure sensor and the corresponding difference in pressure is determined by the differential pressure sensor.

### Claim 10 (depends on 6)

The method of claim 6, wherein the sensor is a flowmeter; the fluid flow path is defined in the flowmeter, the upstream location is an inlet of the flowmeter; and the downstream location is an outlet of the flowmeter.

### Claim 11 (depends on 6)

The method of claim 6 wherein the rheology model is determined using:
τ=YP+KYn
where τ is shear stress, YP is the yield point, K is the consistency factor, Y is shear rate, and n is the power factor.

### Claim 12 (depends on 6)

The method of claim 6 wherein calculating the yield point, the consistency factor, and the power factor comprises an approximation, the approximation comprising:
for each data pair:
assigning an initial value to each of the yield point, the consistency factor, and the power factor;
determining a Reynolds number based on the respective flow rate and the initial values of the yield point, the consistency factor, and the power factor;
determining a flow regime based on the Reynolds number and the initial values of the yield point, the consistency factor, and the power factor;
calculating a calculated difference in pressure based on the flow regime;
calculating a squared error based on the respective difference in pressure and the calculated difference in pressure; and
minimizing a summation of the respective squared errors of the at least three data pairs,
wherein the yield point, the consistency factor, and the power factor are calculated based on the summation.

### Claim 13 (depends on 12)

The method of claim 12 wherein the Reynolds number NRe for each data pair is:
N
R
⁢
e
=
4
⁢
ρ
⁢
Q
j
π
⁢
μ
e
⁢
D
⁢
c
where ρ is the density of the fluid, Qj is the respective flow rate, D is a diameter of the fluid flow path, and c and μe are respectively:
c
=
1
-
1
2
⁢
n
+
1
⁢
(
Y
⁢
P
Y
⁢
P
+
K
[
8
⁢
(
3
⁢
n
+
1
)
⁢
Q
j
n
⁢
π
⁢
D
3
]
n
)
⁢
μ
e
=
Y
⁢
P
+
K
[
(
3
⁢
n
+
1
n
⁢
c
)
⁢
(
8
⁢
Q
j
π
⁢
D
3
)
]
n
(
3
⁢
n
+
1
n
⁢
c
)
⁢
(
8
⁢
Q
j
π
⁢
D
3
)
where n is the initial value of the power factor, YP is the initial value of the yield point, K is the initial value of the consistency factor.

### Claim 14 (depends on 13)

The method of claim 13 wherein, for each data pair, determining a flow regime comprises calculating a Reynolds number threshold NReC:
N
R
⁢
e
c
=
(
4
⁢
(
3
⁢
n
+
1
)
n
⁢
y
)
1
1
-
z
where y and z are, respectively:
y
=
log
⁡
(
n
)
+
3
.
9
⁢
3
5
⁢
0
⁢
z
=
1
.
7
⁢
5
-
log
⁡
(
n
)
7
.

### Claim 15 (depends on 14)

The method of claim 14 wherein, for each data pair, the calculated difference in pressure ΔPjcalc is:
Δ
⁢
P
j
c
⁢
a
⁢
l
⁢
c
=
3
⁢
2
⁢
ρ
⁢
L
⁢
Q
j
2
π
2
⁢
D
5
⁢
f
where, if the Reynolds number NRe is less than the Reynolds number threshold NReC, f is:
f
=
4
N
R
⁢
e
⁢
(
3
⁢
n
+
1
n
)
and where, if the Reynolds number NRe is greater than the Reynolds number threshold NReC, f is:
f=yNRe−z.

### Claim 16 (depends on 15)

The method of claim 15 wherein, for each data pair, the squared error ej is:
ej=(ΔPjexp−ΔPjcalc)2
where ΔPjexp is the respective difference in pressure.

### Claim 17 (depends on 16)

The method of claim 16 wherein the summation is minimized using:
E
⁡
(
n
,
K
,
τ
y
)
=
∑
j
=
1
N
e
j
⁢
n
,
K
,
τ
y
=
arg
⁢
min
n
,
K
,
τ
y
⁢
E
,
subject
⁢
to
:
n
,
K
∈
(
0
,
∞
)
⁢
and
⁢
τ
y
∈
[
0
,
∞
)
where τy is the yield point and N is the number of data pairs, to calculate the yield point, the consistency factor, and the power factor.

### Claim 18 (depends on 6)

The method of claim 6 comprising repeating steps a) to e) and updating the rheology model based on the yield point, the consistency factor, and the power factor to provide an updated rheology model.

### Claim 19 (depends on 18)

The method of claim 18 comprising comparing the updated rheology model with the rheology model for monitoring the composition of the fluid.

### Claim 20 (depends on 6)

The method of claim 6 comprising generating a hydraulic model based on the rheology model.

### Claim 21 (depends on 6)

The method of claim 6 wherein the fluid is a drilling fluid or a drilling mud in a system for drilling a wellbore and wherein for a section of the wellbore, the Reynolds number R is:
R
=
4
⁢
n
⁢
ρ
⁢
V
⁢
D
⁡
(
1
-
a
⁢
X
-
b
⁢
X
2
-
c
⁢
X
3
)
μ
w
(
3
⁢
n
+
1
)
where ρ is the density of the fluid and μw is:
μ
w
=
[
D
⁢
Δ
⁢
P
4
⁢
L
]
n
-
1
n
[
K
1
-
X
]
1
n
.