Real time determination of gas solubility and related parameters in manufacturing processes
View Patent ↗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 ) - R T P 2 - P 1 g ( Δ P Q a ) ] ( 23 ) in which P 1 and P 2 are two different ambient pressures and ΔP=P 2 −P 1 , ρ 1 and ρ 2 are apparent densities of the liquid sample measured at P 1 and P 2 , respectively, R is the constant of the Ideal Gas Law, T is the liquid temperature, Q is the flow rate, g(ΔP/Q a ) is a function for determining the amount of gas being dissolved between P 2 and P 1 , and V s 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 ) - R T s P s ( P 1 P 2 - P 1 g ( Δ P Q a ) - g ( P 1 - P s Q a ) ) ( 27 ) in which P s and T s are standard pressure (1 atm) and temperature (0° C.), and g ( P 1 - P s Q a ) is a function for determining the amount of gas being dissolved between P 1 and P s .
1. A dual core-module apparatus comprising: an apparatus having piping for processing 2- or 3-phase fluids at a dynamic state, said apparatus including two core-modules each comprising a density and temperature gauge having a pressure gauge located upstream thereof and a pressure gauge located downstream thereof, said two core-modules being operatively joined together by a pressure changing device.
2. A measurement procedure of obtaining data, on a continuous basis, for use in determining amounts of gas entrained or dissolved in a 2- or 3-phase fluid, which procedure comprises the steps of:
providing an apparatus according to claim 1 ;
processing the said fluid at a flow rate such that the pressure level differs between each of the dual core-modules by at least 1 psi or at least to the extent that two different apparent densities of said fluid differ from one another by at least 0.2%;
collecting temperature, pressure and apparent density data from the first core-module while operating at steady-state conditions;
simultaneously collecting temperature, pressure and apparent density data from the second core-module while operating at steady-state conditions; and
calculating entrained/dissolved gas using the algorithms (22)-(24) and (28) which follow:
V
1
=
P
2
P
2
-
P
1
(
1
ρ
1
-
1
ρ
2
)
-
RT
P
2
-
P
1
g
(
Δ
P
Q
a
)
(
22
)
V
=
V
i
1
-
V
1
=
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
)
ρ
=
1
V
(
24
)
x
%
=
V
s
V
s
+
V
(
28
)
wherein: V 1 is volume of the free gas entrained into a liquid at P 1 ; P 1 and P 2 are ambient pressures at which the apparent densities of the liquid are measured; ρ 1 and ρ 2 are apparent densities of the liquid that contains entrained gas being measured at P 1 and P 2 , respectively; R is the constant of the Ideal Gas Law; T is temperature of the process liquid/solution measured by a temperature sensor, assuming that the temperature is kept constant between the two measurement points (T=T 1 =T 2 ); g(ΔP/Q a ) is a function through which the gas solubility coefficients at a dynamic state can be determined; P is pressure of the gas being dissolved; ΔP is pressure difference ΔP=P 2 −P 1 or ΔP=P II −P 1 ; Q is a flow rate; α is an index reflecting the weak influence of flow rate on gas solubility; V is the gas-free volume of the liquid; V t1 is total volume of the liquid that contains entrained gas being measured at P 1 ; ρ is the gas-free true density of the liquid; x% is volume percentage of free gas at P s and T s; and V s is volume of free gas at P s and T s .
3. A measurement procedure of obtaining data at a static state for use in determining amounts of air entrained or dissolved in a 2- or 3-phase fluid, which procedure comprises the steps of:
providing an apparatus according to claim 1 ;
subjecting/pressurizing the said fluid into the apparatus at a no-flow state;
collecting temperature, pressure and apparent density data at a first pressure level when there is no longer any significant change in data;
increasing or reducing the system pressure to levels that differ from one another by at least 1 psi or at least to the extent that two different apparent densities of said fluid differ from one another by at least 0.2%;
collecting temperature, pressure and apparent density data at a second pressure level when there is no longer any significant change in data; and
calculating entrained/dissolved gas using the algorithms (33) (32), (24), and (28):
V
s
=
T
s
T
P
1
P
2
P
s
(
P
2
-
P
1
)
(
1
ρ
1
-
1
ρ
2
)
=
RT
s
C
[
33
]
V
=
1
ρ
1
-
[
P
2
P
2
-
P
1
(
1
ρ
1
-
1
ρ
2
)
-
RT
C
]
[
32
]
ρ
=
1
V
(
24
)
x
%
=
V
s
V
s
+
V
(
28
)
wherein: V s is volume of free gas at P s and T s ; P s is atmospheric pressure=1 atm (14.7 psi); T s is standard temperature=0°C.; T is temperature of the process liquid/solution measured by a temperature sensor, assuming that the temperature is kept constant between the two measurement points (T=T 1 =T 2 ); P 1 and P 2 are ambient pressures at which the apparent densities of the liquid are measured; ρ 1 and ρ 2 are apparent densities of the liquid that contains entrained gas being measured at P 1 and P 2 , respectively; R is the constant of the Ideal Gas Law; C is the gas solubility coefficient at a static state; V is the gas-free volume of the liquid; ρ is the gas-free true density of the liquid; and x% is volume percentage of free gas at P s and T s .