US 6,847,898 B1 · Real time determination of gas solubility and related parameters in manufacturing processes

Abstract

Methods and apparatuses for determining entrained and/or dissolved gas content of gas-liquid mixtures. Data generated is used to control the True (air-free) or Apparent (air-containing) Density or Entrained Air content of liquids within optimum ranges, e.g. in paper coating processes and in the manufacture of food products, personal care products, pharmaceutical products, paints, petroleum blends, etc. For example, an indirect method of continuously determining the amount of gas entrained in a liquid, by: continuously measuring the temperature, flow rate, and apparent density of the mixture at two different pressure states, and calculating the volume percentage of the gas in the liquid by using equation (28) x ⁢ % = V s V s + V ( 28 ) wherein V is the volume of the gas-free liquid calculated by equation (23) V = 1 ρ 1 - [ P 2 P 2 - P 1 ⁢ ( 1 ρ 1 - 1 ρ 2 ) - RT P 2 - P 1 ⁢ g ⁡ ( Δ ⁢ ⁢ P Q a ) ] ( 23 ) in which P1 and P2 are two different ambient pressures and ΔP=P2−P1, ρ1 and ρ2 are apparent densities of the liquid sample measured at P1 and P2, respectively, R is the constant of the Ideal Gas Law, T is the liquid temperature, Q is the flow rate, g(ΔP/Qa) is a function for determining the amount of gas being dissolved between P2 and P1, and Vs is determined by equation (27) V s = T s T ⁢ P 1 ⁢ P 2 P s ⁡ ( P 2 - P 1 ) ⁢ ( 1 ρ 1 - 1 ρ 2 ) - RT s P s ⁢ ( P 1 P 2 - P 1 ⁢ g ⁡ ( Δ ⁢ ⁢ P Q a ) - g ⁡ ( P 1 - P s Q a ) ) . ( 27 )

Claims24

Dependent claims

A method for automatically controlling the output of a continuous process with a liquid carrier that contains one or more gases, the method comprising the steps of:

a.) setting a quantitative target for volume-% of one or more gases in the liquid carrier;
b.) calculating the volume percentage of said gas in said liquid sample by using equation (28)
x
⁢
%
=
V
s
V
s
+
V
(
28
)
wherein V is the volume of the gas-free liquid calculated by equation (23)
V
=
1
ρ
1
-
[
P
2
P
2
-
P
1
⁢
(
1
ρ
1
-
1
ρ
2
)
-
RT
P
2
-
P
1
⁢
g
⁡
(
Δ
⁢
⁢
P
Q
a
)
]
(
23
)
in which P1 and P2 are two different ambient pressures and ΔP=P2−P1, ρ1 and ρ2 are apparent densities of the liquid sample measured at P1 and P2, respectively, R is the constant of the Ideal Gas Law, T is the liquid temperature, Q is the flow rate, and g(ΔP/Qa) is a function through which the gas solubility coefficients at a dynamic state are determined;
and VS is determined by equation (27)
V
s
=
T
s
T
⁢
P
1
⁢
P
2
P
s
⁡
(
P
2
-
P
1
)
⁢
(
1
ρ
1
-
1
ρ
2
)
-
RT
s
P
s
⁢
(
P
1
P
2
-
P
1
⁢
g
⁡
(
Δ
⁢
⁢
P
Q
a
)
-
g
⁡
(
P
1
-
P
s
Q
a
)
)
.
(
27
)
in which Ps and Ts are standard pressure (1 atm) and temperature (0° C.), P1, P2, Ps, ΔP, ρ1, ρ2, R, Q, and T are the same as defined in this claim, and
g
⁡
(
P
1
-
P
s
Q
a
)
is a function for determining the amount of gas being dissolved between P1 and Ps;
c.) comparing the calculated volume-% gas to the target volume-% gas;
and,
d.) if the calculated volume-% gas in the liquid carrier is greater or less than the target volume-% gas, lowering or raising the amount of gas in the liquid carrier.

151 more elements

A method for automatically controlling the output of a continuous process that requires mixing of a solid or liquid component with a liquid carrier component, the method comprising the steps of:

a.) setting a quantitative target for weight-% in the liquid carrier component of one or more solids and/or for concentration of one or more liquids in the liquid carrier component;
b.) continuously mixing said solids and/or liquids with the liquid carrier component;
c.) determining the true density, ρ, by employing equation (24)
ρ
=
1
V
(
24
)
wherein the volume, V, is calculated from equation (23)
V
=
1
ρ
1
-
[
P
2
P
2
-
P
1
⁢
(
1
ρ
1
-
1
ρ
2
)
-
RT
P
2
-
P
1
⁢
g
⁡
(
Δ
⁢
⁢
P
Q
a
)
]
(
23
)
in which P1 and P2 are two different ambient pressures and ΔP=P2−P1, ρ1 and ρ2 are apparent densities of the liquid sample measured at P1 and P2, respectively, R is the constant of the Ideal Gas Law, T is the temperature of the liquid sample, Q is the flow rate, and g(ΔP/Qa) is a function through which the gas solubility coefficients at a dynamic state are determined;
d.) calculating the weight-% of solids and/or the liquid concentration in the mixture from the true density ρ so determined;
e.) comparing the calculated weight-% solids or concentration to the target weight-% solids or concentration;
and,
f.) if the calculated weight-% solids or concentration is greater or less than the target weight-% solids or concentration, lowering or raising the amount of solids or liquids mixed in step b.).

59 more elements

An indirect method for determining gas solubility coefficients for a gas-liquid mixture at a dynamic state, the method comprising the steps of:

a.) subjecting the said gas-liquid mixture to flow at several different flowrates, Q1, Q2, . . . , Qi;
b.) measuring two different apparent densities of the mixture and two related ambient pressures at which the apparent densities are determined at each of the flow rates;
c.) acquiring off-line the true, gas-free liquid density, ρ*, through one-time measurement;
d.) determining the gas solubility coefficients, A0, A1, A2, . . . , Ai, by solving a group of linear equations (19)
A
0
+
A
1
⁡
(
Δ
⁢
⁢
P
Q
a
)
+
A
2
⁡
(
Δ
⁢
⁢
P
Q
a
)
2
+
⋯
+
A
i
⁡
(
Δ
⁢
⁢
P
Q
a
)
i
=
S
1
⁢

Q
=
Q
1
⁢
⁢
A
0
+
A
1
⁡
(
Δ
⁢
⁢
P
Q
a
)
+
A
2
⁡
(
Δ
⁢
⁢
P
Q
a
)
2
+
⋯
+
A
i
⁡
(
Δ
⁢
⁢
P
Q
a
)
i
=
S
2
⁢

Q
=
Q
2
⁢
⁢
A
0
+
A
1
⁡
(
Δ
⁢
⁢
P
Q
a
)
+
A
2
⁡
(
Δ
⁢
⁢
P
Q
a
)
2
+
⋯
+
A
i
⁡
(
Δ
⁢
⁢
P
Q
a
)
i
=
S
i
⁢

Q
=
Q
i
(
19
)
in which Q1, Q2, . . . , Qi, are the different flow rates generated for obtaining the gas solubility coefficients at a dynamic state, ΔP is the difference of the said two ambient pressures at each of the flow rates, a is an index reflecting the weak influence of flow rate on gas solubility, and S1, S2, . . . , Si are intermediate variables determined by equation (20)
S
1
=
1
RT
⁡
[
P
I
⁡
(
1
ρ
I
-
1
ρ
*
)
-
P
II
⁡
(
1
ρ
II
-
1
ρ
*
)
]

Q
=
Q
1
S
2
=
1
RT
⁡
[
P
I
⁡
(
1
ρ
I
-
1
ρ
*
)
-
P
II
⁡
(
1
ρ
II
-
1
ρ
*
)
]

Q
=
Q
2
…
S
i
=
1
RT
⁡
[
P
I
⁡
(
1
ρ
I
-
1
ρ
*
)
-
P
II
⁡
(
1
ρ
II
-
1
ρ
*
)
]
⁢

Q
=
Q
i
(
20
)
in which PI and PII are two different ambient pressures measured at each of the flow rates, ρI and ρII are apparent densities of the gas-liquid mixture measured at PI and PII, respectively, R is the constant of the Ideal Gas Law, T is the liquid temperature, Q is the flow rate, and ρ* is the predetermined gas-free liquid density as defined in c.);
e.) attaining the gas solubility function
g
⁡
(
Δ
⁢
⁢
P
Q
a
)
=
A
0
+
A
1
⁡
(
Δ
⁢
⁢
P
Q
a
)
+
A
2
⁡
(
Δ
⁢
⁢
P
Q
a
)
2
+
…
+
A
i
⁡
(
Δ
⁢
⁢
P
Q
a
)
i
upon the solution of the gas solubility coefficients, A0, A1, A2, Ai.

337 more elements

A method for controlling the output of a process for preparing a carbonated beverage, which method comprises:

a.) setting a quantitative target for a concentration of carbon dioxide to be blended into an aqueous medium;
b.) supplying carbon dioxide to the aqueous medium in a vessel and mixing those components to form a carbonated aqueous medium in the vessel at a preset “bottling” pressure P0, wherein P0 is the produced “bottling” pressure inside a sealed carbonated beverage container, at which pressure all of the free carbon dioxide is dissolved into the aqueous medium;
c.) diverting a carbonated aqueous medium sample from the vessel into a sample measurement chamber at the same “bottling” pressure P0;
d.) reducing the aqueous medium pressure from P0 to P1 allowing the dissolved carbon dioxide to start to be released back to the aqueous medium in a free-bubble form while the volume of the sample measurement chamber to be expanded correspondingly;
e.) reducing the aqueous medium pressure further from P1 to P2 allowing more dissolved carbon dioxide to be released back to the aqueous medium in a free-bubble form while the volume of the measurement chamber to be expanded further;
f.) measuring the change in volume of the carbon dioxide liquid mixture between P1 and P2;
g.) determining the volume of free carbon dioxide, Vs, in the carbonated aqueous medium at the standard condition using equation (37)
V
s
=
T
s
T
⁢
P
1
⁢
P
2
P
s
⁡
(
P
2
-
P
1
)
⁢
Δ
⁢
⁢
V
-
RT
s
C
(
37
)
in which P1 and P2 are two different ambient pressures, ΔV is the change in sample volume between P1 and P2, Ps and Ts are standard pressure and temperature, T is the temperature of the liquid sample, C is the gas solubility coefficient at a static state, and R is the constant of the Ideal Gas Law;
h.) calculating the carbon dioxide concentration using equation (28)
x
⁢
%
=
V
s
V
s
+
V
(
28
)
wherein Vs is the volume of free carbon dioxide determined in step g.) and V is the volume of carbonated aqueous medium in the sample chamber at a preset “bottling” pressure P0 upon which no free bubble should present;
i.) comparing the calculated carbon dioxide concentration to the target carbon dioxide concentration;
and,
j.) if the calculated carbon dioxide concentration is greater or less than the target carbon dioxide concentration, lowering or raising the volume of carbon dioxide supplied.

57 more elements

A method for controlling the output of a process for preparing a carbonated beverage, which method comprises:

a.) setting a quantitative target for a concentration of carbon dioxide to be blended into an aqueous medium;
b.) supplying carbon dioxide to the aqueous medium in a vessel and mixing those components to form a carbonated aqueous medium in the vessel;
c.) diverting a carbonated aqueous medium sample from the vessel into a sample measurement chamber at the first pressure state, P1, with the presence of free carbon dioxide bubbles in the aqueous medium;
d.) reducing the aqueous medium pressure to the second pressure state, P2, allowing more dissolved carbon dioxide to be released back to the aqueous medium in a free-bubble form while the volume of the measurement chamber to be expanded correspondingly;
e.) measuring the change in volume of the carbon dioxide liquid mixture between P1 and P2;
f.) determining the volume of free carbon dioxide, Vs, in the carbonated aqueous medium at the standard condition using equation (37)
V
s
=
T
s
T
⁢
P
1
⁢
P
2
P
s
⁡
(
P
2
-
P
1
)
⁢
Δ
⁢
⁢
V
-
RT
s
C
(
37
)
in which P1 and P2 are two different ambient pressures, ΛV is the change in sample volume between P1 and P2, Ps and Ts are standard pressure and temperature, T is the temperature of the liquid sample, C is the gas solubility coefficient at a static state, and R is the constant of the Ideal Gas Law;
g.) determining the volume of aqueous medium, V, in which no free carbon dioxide bubble is present, by equation (36)
V
=
V
t1
-
[
P
2
⁢
Δ
⁢
⁢
V
P
2
-
P
1
-
RT
C
]
(
36
)
in which Vt1 is the volume of gas-liquid mixture in the sample chamber at P1;
h.) calculating the carbon dioxide concentration using equation (28)
x
⁢
%
=
V
s
V
s
+
V
(
28
)
wherein Vs is the volume of free carbon dioxide determined in step f.) and V is the volume of aqueous medium, in which no free carbon dioxide bubble is present, as defined in step g.);
i.) comparing the calculated carbon dioxide concentration to the target carbon dioxide concentration;
and,
j.) if the calculated carbon dioxide concentration is greater or less than the target carbon dioxide concentration, lowering or raising the volume of carbon dioxide supplied.

83 more elements

Dependencies are inferred from the claim text.

Real time determination of gas solubility and related parameters in manufacturing processes

Life of this patent

Real time determination of gas solubility and related parameters in manufacturing processes

Life of this patent

Abstract

Claims24