Title: Determination of gas-free densities and relative amounts of gases in liquids in manufacturing processes
Abstract: Improved control of continuous processes that handle liquids. Data generated by this invention is used to control gas contents of liquids within optimum ranges, for instance in paper coating processes and in the manufacture of food products (ketchup), personal care products (shampoo), paints, and in any industry where information on entrained and/or dissolved gases, and related parameters such as true density of and gas solubility in process liquids, is employed to optimize processing. The amount of gas in a liquid is determined by subjecting a mixture of an incompressible liquid sample and a compressible gas to three or more different equilibrium pressure states, measuring the temperature and volume of the mixture at each of the pressure states, determining the changes in volume of the mixture between at least two different pairs of pressure states, and calculating the amount of gas in the liquid sample. The inventive apparatus includes: a reservoir for process fluid; piping through which fluid may be pumped, the piping being under the control of a pressure regulator which is capable of setting at least three different pressures P1, P2, and P3 in the apparatus; at least three fluid control valves V1, V2, and V3; a pressure gauge; a temperature gauge; and a density gauge.
Patent Number: 7,017,388 Issued on 03/28/2006 to Chen, et al.
| Inventors:
|
Chen; Qingyuan (Appleton, WI);
Franda; Robert Josef (Sherwood, WI)
|
| Assignee:
|
Appleton Papers, Inc. (Appleton, WI)
|
| Appl. No.:
|
841530 |
| Filed:
|
May 10, 2004 |
| Current U.S. Class: |
73/19.05; 73/19.01; 73/19.1; 73/23.33; 73/25.04; 73/29.01 |
| Current Intern'l Class: |
G01N 5/00 (20060101); G01N 7/00 (20060101); G01N 37/00 (20060101) |
| Field of Search: |
73/102,190.2,190.5,191,191.1,233.3,250.4,290.1,300.1,30,310.4,32R
|
References Cited [Referenced By]
U.S. Patent Documents
| 3673853 | Jul., 1972 | Griswold et al.
| |
| 3731530 | May., 1973 | Tanguy et al.
| |
| 3939693 | Feb., 1976 | Dumont.
| |
| 4056002 | Nov., 1977 | Arieh et al.
| |
| 4120192 | Oct., 1978 | Williamson.
| |
| 4168624 | Sep., 1979 | Pichon.
| |
| 4184359 | Jan., 1980 | Gracey.
| |
| 4365505 | Dec., 1982 | Holzl.
| |
| 4516580 | May., 1985 | Polanyi.
| |
| 4584866 | Apr., 1986 | Janssen.
| |
| 4862729 | Sep., 1989 | Toda et al.
| |
| 4863498 | Sep., 1989 | Soriente et al.
| |
| 4924695 | May., 1990 | Kolpak.
| |
| 5041990 | Aug., 1991 | Yabumoto.
| |
| 5129366 | Jul., 1992 | Chikamori et al.
| |
| 5295083 | Mar., 1994 | Yano et al.
| |
| 5365435 | Nov., 1994 | Stephenson.
| |
| 5621161 | Apr., 1997 | Leyse.
| |
| 5635631 | Jun., 1997 | Yesudas et al.
| |
| 5846831 | Dec., 1998 | Silvis.
| |
| 5932792 | Aug., 1999 | Dougherty.
| |
| 6138498 | Oct., 2000 | Hofer et al.
| |
| 6192737 | Feb., 2001 | Ohlrogge et al.
| |
| 6393893 | May., 2002 | Fetz et al.
| |
| 6496781 | Dec., 2002 | Chen et al.
| |
| 2003/0051531 | Mar., 2003 | Patashnick et al.
| |
| Foreign Patent Documents |
| 02124445 | May., 1990 | JP.
| |
Other References
Bergman et al., "On-Line Measurement of Coating Color Quality in Coater Supply
System", 1999 TAPPI Coating Conference, Toronto, Canada, 1999 (16 pages).
Mütek News, No. 7, Aug. 2001 (4 pages).
Pulse Air—V3, www.papec.com. Dec. 21, 2001 (3 pages).
Anton Paar, "On-line CO2 measurement in the beer and soft drink industry", Press
Release, Jul. 2001 (3 pages).
|
Primary Examiner: Williams; Hezron
Assistant Examiner: Rogers; David A.
Attorney, Agent or Firm: Birch, Stewart, Kolasch & Birch, LLP
Parent Case Text
This application is a divisional of application Ser. No. 10/046,240, filed on
Jan. 16, 2002, now U.S. Pat. No. 6,766,680 B2, the entire contents of which application
is hereby expressly incorporated by reference.
Claims
What is claimed is:
1. A method of determining the gas-free density of a mixture of an incompressible
liquid sample and a compressible gas which comprises subjecting said mixture to
at least three different equilibrium pressure states, measuring the temperature
and density of the mixture at each of the at least three pressure states, determining
the changes in density of the mixture between at least two different pairs of pressure
states, and calculating the gas-free density of said incompressible liquid sample
by using the equation
##EQU53##
wherein V is the volume of the gas-free liquid at ambient pressure, determined
by the equation
##EQU54##
wherein P
1, P
2, and P
3 are three different equilibrium
ambient pressures, and, ρ
1, ρ
2 and ρ
3
are the densities of the mixture measured at an equilibrium states P
1,
P
2 and P
3, respectively.
2. The method of claim 1, wherein said at least three equilibrium pressure states
differ from one another at least to the extent that three different apparent densities
of said liquid differ from one another by at least 0.1%.
3. The method of claim 1, wherein said at least three pressure states differ
from one another by at least 0.1 psi.
4. The method of claim 3, wherein said at least three pressure states differ
from one another by at least 1 atmosphere.
5. A method for 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 gas-free density of the mixture;
b.) continuously mixing said solids and/or liquids with the liquid carrier component;
c.) determining the gas-free density, ρ, as defined in the method of claim 1;
d.) comparing the calculated gas-free density to the target gas-free density; and,
e.) if the calculated gas-free density is greater or less than the target gas-free
density, lowering or raising the amount of solids or liquids mixed in step b.).
6. A method of determining the amount of gas in a liquid which comprises subjecting
a mixture of an incompressible liquid sample and a compressible gas to at least
three different equilibrium pressure states, measuring the temperature and density
of the mixture at each of the at least three pressure states, determining the changes
in density of the mixture between at least two different pairs of pressure states,
and calculating the amount of said gas in said liquid sample by using the equation
##EQU55##
wherein V is the volume of the gas-free liquid at ambient pressure, determined
by the equation
##EQU56##
and V
s is volume of free gas under standard conditions and is determined
by the equation
##EQU57##
wherein P
1, P
2, and P
3 are three different equilibrium
ambient pressures, P
s and T
s are standard pressure and temperature,
ρ
1, ρ
2 and ρ
3 are the densities
of the mixture measured at an equilibrium states P
1, P
2 and
P
3, respectively.
7. A method for controlling the entrained gas content of a liquid or slurry being
flow-processed, the method comprising:
a.) setting a quantitative target for the free gas content of said liquid or slurry;
b.) continuously flowing said liquid or slurry and mixing an antifoam agent therewith;
c.) determining the volume percentage of free gas, x%, as defined in the method
of claim 2;
d.) comparing the calculated free gas content to the target free gas content; and,
e.) if the calculated free gas content is greater than the target free gas content,
raising the amount of antifoam agent mixed in step b.).
8. The method of claim 7, wherein the liquid or slurry being flow-processed is
a slurry of kaolin clay, calcium carbonate, titanium dioxide, or alumina trihydrate
being supplied as a coating to a paper substrate.
9. The method of claim 7, wherein the liquid or slurry being flow-processed is
ointment, cream, lotion, toothpaste, mayonnaise, ketchup, or lubricating grease
being packaged into a retail container.
10. In an apparatus comprising a reservoir for process fluid, piping through
which said process fluid may be pumped, and a deaerator unit, the improvement which
comprises locating means for detecting the volume percentage of free gas in said
process fluid by the method of claim 2 in working relationship to said deaerator unit.
11. The apparatus of claim 10, wherein a single such detection means is located
downstream of said deaerator unit and wherein said apparatus further comprises
an alarm capable of signaling the presence in said process fluid of a volume percentage
of free gas higher than a pre-specified level.
12. The apparatus of claim 10, wherein two such detection means are located,
respectively, upstream and downstream of said deaerator unit and wherein said apparatus
further comprises a comparator capable of determining and indicating the magnitude
of any difference in volume percentage of free gas in said process fluid upstream
of and downstream of said deaerator unit.
Description
FIELD OF THE INVENTION
This invention provides means for improving control of continuous processes
that handle liquids, and therefore provides benefits to manufacturers by enabling
them to effectively monitor and operate their processes. Data generated by this
invention can be used to control the gas contents of liquids within optimum ranges,
for instance in paper coating processes and in the manufacture of such products
as food products (ketchup, mayonnaise, syrup), personal care products (skin cream,
shampoo), pharmaceutical products, paints, petroleum blends, and the like. This
invention is useful in any industry where information on entrained and/or dissolved
air and other gases, and related parameters such as true density of and gas solubility
in process liquids, is employed to optimize processing.
BACKGROUND OF THE INVENTION
Those skilled in the arts of processing liquids desire to know how much air
and/or other gases are entrapped and dissolved therein for a variety of reasons.
Entrapped air can cause undesired foaming during processing, e.g. in papermaking
and in the preparation of foodstuffs, and can result in disruption of film products,
e.g. from paints. Entrained gases distort such processing parameters as density,
making precise control of processes impossible. Those skilled in the art know that,
generally, the more viscous a fluid being processed, the more difficult it is for
any entrained air to escape from it and consequently the greater the amount of
air bubbles likely to be accumulated therein. Also, as pressure on a fluid is lowered,
dissolved air or other gas therein tends to leave solution and form bubbles in
the fluid.
There are a number of instruments that are currently commercially available
for measuring the air or gas content in a liquid. Such instruments include Valmet's
COLORMAT, Mütek's GAS-60, Papec's PULSE))))AIR, Capella Technology's CAPTAIR,
Anton-Paar's CARBO 2100 CO
2 analyzer, and CyberMetrics' AIR TESTER.
Mütek's GAS-60, for instance, is said to be useful in the context
of minimizing pinholes (voids) in papermaking processes. Pinholes develop when
pressure is reduced and dissolved gases—which accumulate in the papermaking
process due to mechanical effects and chemical and biological reactions—are
released. The GAS 60 is installed on line and is used to determine the gas content
of entrained and dissolved gases in pulp suspensions. Having determined gas content,
process engineers are able to calculate how much (expensive) deaerating additive
should be used, and thus to avoid unnecessarily increased manufacturing costs due
to employing too much deaerating additive.
Papec's PULSE))))AIR_V3 is a sensor for the measurement of entrained air
and gases in process fluids. It is said to be useful in the pulp and paper industry
in connection with machine headboxes and white water systems, coatings, and brownstock
washers, in the secondary fiber industry (for effluent treatment), in the paint
industry, in oil bottling processes, in the processing of well drilling muds, and
in general in any application needing entrained air information.
Anton-Paar's CARBO 2100 CO
2 analyzer employs a patented impeller
method which is said to make it significantly faster that other commercially available
systems for measuring and monitoring tasks and also for regulating the CO
2
content of process liquids during production runs in the beer and soft drink industry.
It is believed that all of these instruments adopt a common approach, using Boyle's
Law. Boyle's law is given by the formula
P1V1=P2V2 (1)
where V
1 and V
2 are the volumes of the free gas in the
liquid at two different pressures, P
1 and P
2, respectively.
Being a "two-point measurement", this common approach measures the volume difference
ΔV=V
1-V
2 between P
1 and P
2, and
calculates the volumes of free gas, V
1 and V
2, from Boyle's
Law as
##EQU1##
More general formulas, which correlate the volumes of free gas with the pressures
being acted upon, can be derived from the Ideal Gas Law as
P1V1=n1RT1 (3)
and
P2V2=n2RT2 (4)
where R is the gas constant, and n
1, T
1 and n
2,
T
2 are moles of free gas and temperatures at P
1 and P
2,
respectively. In the case of n
1=n
2 and T
1=T
2,
equations (3) and (4) can be simplified to the equation of Boyle's Law given in
(1). Hence, Boyle's Law is, in fact, a special case of the Ideal Gas Law and is
valid only if the moles of free gas and temperatures at P
1 and P
2
are kept constant.
In practice, a portion of free gas, however, will be dissolved into the liquid.
The solubility of gas is, as a general rule, proportional to the gas pressure as
stated in Henry's Law
P=Hnd (5)
where P, H, n
d are the pressure of the gas being dissolved, the
constant of Henry's Law, and moles of dissolved gas, respectively. This unquestionably
makes n
1≠n
2 between P
1 and P
2,
causing a violation of Boyle's Law. Therefore, using Boyle's Law for a "two-point
measurement" is an unreliable approximation and can cause a significant amount
of error, especially when the pressure difference between the two points becomes large.
To cure this error, there have been some attempts to use Henry's Law to compensate
for the amount of the dissolved gas. This approach, however, is generally impractical,
inasmuch as the constants of Henry's Law are not available for many process liquids,
particularly for those containing multiple-components such as coating slurries.
Using the known constant of one liquid to approximate the constant of the others
may potentially introduce a considerable amount of error, because the solubility
of gases such as air changes dramatically from liquid to liquid. The solubility
of air in isooctane at standard temperature and pressure, for example, is more
than 100 times higher than the solubility of air in water.
SUMMARY OF THE INVENTION
The present invention provides methods and apparatuses for determining the entrained
gas content and/or the dissolved gas content of liquids. This invention provides
means for improving control of continuous processes that handle liquids, and therefore
provides benefits to manufacturers by enabling them to effectively monitor and
operate their processes. Data generated by this invention can be used for instance
to control the gas contents of liquids within optimum ranges, for instance in the
processing of foam such as shaving cream or ice cream and to minimize gas contents,
for instance in paper coating processes and in the manufacture of such products
as food products (ketchup, mayonnaise, syrups, various sauces), personal care products
(skin cream, shampoo, lotions, toothpaste), pharmaceutical products, herbicides,
paints, lubricating greases, petroleum blends, water softeners, and the like. This
invention is useful in any industry where information on entrained and/or dissolved
gas, and related parameters such as true density and solubility of process liquids,
is employed.
In one embodiment, this invention provides a method for controlling the entrained
gas content of a liquid or slurry being flow-processed. The liquid or slurry being
flow-processed may be—without limitation—a slurry of kaolin clay, calcium
carbonate, titanium dioxide, or alumina trihydrate being supplied as a coating
to a paper substrate. Alternatively—again without limitation—the liquid
or slurry being flow-processed is ointment, cream, lotion, toothpaste, mayonnaise,
ketchup, or lubricating grease being packaged into a retail container. The method
comprises: a.) setting a quantitative target for the free gas content of said liquid
or slurry; b.) continuously flowing said liquid or slurry and mixing an antifoam
agent therewith; c.) determining the volume percentage of free gas, x%, from the
formula
##EQU2##
wherein Vs is the volume of free gas under standard conditions and V is the
gas-free volume of the liquid carrier component; e.) comparing the calculated free
gas content to the target free gas content; and, f.) if the calculated free gas
content is greater than the target free gas content, raising the amount of antifoam
agent mixed in step b.).
In another embodiment, this invention provides an apparatus comprising a reservoir
for process fluid, piping through which the process fluid may be pumped, and a
deaerator unit, the improvement which comprises locating means for detecting the
volume percentage of free gas in the process fluid in working relationship to the
deaerator unit. In this apparatus, a single such detection means may be located
downstream of the deaerator unit and wherein the apparatus further comprises an
alarm capable of signaling the presence in the process fluid of a volume percentage
of free gas higher than a pre-specified level. Alternatively, the apparatus may
include two such detection means located, respectively, upstream and downstream
of the deaerator unit and the apparatus may further comprises a comparator capable
of determining and indicating the magnitude of any difference in volume percentage
of free gas in the process fluid upstream of and downstream of the deaerator unit.
Another embodiment of this invention is a method for determining the amount
of gas in a liquid which comprises subjecting a mixture of an incompressible liquid
sample and a compressible gas to at least three different equilibrium pressure
states, measuring the temperature and volume of the mixture at each of the at least
three pressure states, determining the changes in volume of the mixture between
at least two different pairs of pressure states, and calculating the amount of
gas in the liquid sample by using the equation
##EQU3##
wherein V is the volume of the gas-free liquid in a sample chamber at ambient
pressure and V
s is determined by the equation
##EQU4##
wherein P
1, P
2, and P
3 are three different
equilibrium ambient pressures, P
s and T
s are standard pressure
and temperature, ΔV
1 and ΔV
2 are the volume difference
of the free air measured at an equilibrium state between P
1 and P
2
and P
2 and P
3, respectively. In preferred embodiments
of this embodiment of the invention, the at least three equilibrium pressure states
differ from one another at least to the extent that the three different volumes
differ from one another by at least 0.1% and/or the at least three equilibrium
pressure states differ from one another at least to the extent that three different
apparent densities of said liquid differ from one another by at least 0.1%. In
other preferred embodiments of this embodiment of the invention, the at least three
pressure states differ from one another by at least 0.1 psi and/or the at least
three pressure states differ from one another by at least 1 atmosphere. In this
embodiment of the invention, the determination of changes in volume may be accomplished
by measurement of volumes or by measurement of apparent densities.
The present invention also provides an apparatus that includes: a reservoir for
process fluid; piping through which the fluid may be pumped, said piping being
under the control of a pressure regulator which is capable of setting at least
three different pressures P1, P2, and P3 in the apparatus;
at least three fluid control valves V1, V2, and V3; a pressure
gauge; a temperature gauge; and a density gauge. This apparatus may be used for
obtaining data for use in determining amounts of air entrained or dissolved in
a fluid, by a method that comprises: providing the apparatus as described; collecting
stabilized pressure, temperature, and density data at a first pressure level; collecting
stabilized pressure, temperature, and density data at a second pressure level;
and collecting stabilized pressure, temperature, and density data at a third pressure level.
Yet another embodiment of this invention is 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. This method embodiment of the invention comprises:
a.) setting a quantitative target for weight-% of one or more solids and/or concentration
of one or more liquids to the liquid carrier component; b.) continuously mixing
said solids and/or liquids with the liquid carrier component; c.) filling a measurement
chamber with the blended mixture and allowing it to come to equilibrium; d.) recording
equilibrium temperature, T
1, the volume of the sample, V
1,
and equilibrium pressure, P
1; e.) increasing or decreasing the volume
of the mixture in the sample chamber, allowing the fluid to come to equilibrium,
and recording equilibrium temperature, T
2, sample volume, V
2,
and equilibrium pressure, P
2; f.) again, increasing or decreasing the
volume of the mixture in the sample chamber, allowing the fluid to come to equilibrium,
and recording equilibrium temperature, T
3, sample volume, V
3,
and equilibrium pressure, P
3; g.) determining the true density, ρ,
by employing the formula ρ=m/V wherein the mass, m, is the mass of the liquid
mixture sample, and, the gas-free volume of the liquid mixture, V, and the volume
percentage of free air or other gas, x%, are calculated from the formulas
##EQU5##
##EQU6##
wherein ΔV
1 is the volume difference of the free gas between
P
1 and P
2, ΔV
2 is the volume difference
of the free gas between P
2 and P
3, V
t1 is the
total volume of the liquid and entrained gas, and Vs is the volume of free air
or other gas under standard conditions and is calculated from the formula
##EQU7##
wherein these variables are provided by the data collected in steps d.-f.),
and standard conditions refer to P=P
S=1 atm, T=T
S=273 K;
h.) calculating the weight-% of solids and/or the liquid concentration in the mixture
with the equation
##EQU8##
wherein ρ
L is the density of the liquid carrier component,
k
i is the Additive Volume Coefficient (AVC) for each solid or liquid,
x
i is the weight-% dry for each solid or the concentration for each
liquid, (ρ
s)
i is the density of each solid or liquid,
and ρ is the true density of the mixture; i.) comparing the calculated weight-%
solids or concentration to the target weight-% solids or concentration; and, j.)
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.).
Another inventive method for automatically controlling the output of a continuous
process that requires mixing of a solid or liquid component with a liquid carrier
component of this invention includes the steps of: a.) setting a quantitative target
for weight-% of one or more solids and/or concentration of one or more liquids
to the liquid carrier component; b.) continuously mixing said solids and/or liquids
with the liquid carrier component; c.) diverting a fluid sample from the main piping
system into the sample measurement chamber and allowing the sample to come to equilibrium;
d.) recording equilibrium temperature, T
1, equilibrium density, ρ
1,
and equilibrium pressure, P
1; e.) adjusting the pressure of the fluid
in the sample chamber, allowing the fluid to come to equilibrium, and recording
equilibrium temperature, T
2, equilibrium density, ρ
2,
and equilibrium pressure, P
2; f.) again, adjusting the pressure of the
fluid in the sample chamber, allowing the fluid to come to equilibrium, and recording
equilibrium temperature, T
3, equilibrium density, ρ
3,
and equilibrium pressure, P
3; g.) determining the true density, ρ,
by employing the formula
##EQU9##
wherein the volume, V, is calculated from the formula
##EQU10##
wherein these variables are provided by the data collected in steps d.-f.);
h.) calculating the weight-% of solids and/or the liquid concentration in the mixture
with the equation
##EQU11##
wherein ρ
L is the density of the liquid carrier component,
k
i is the Additive Volume Coefficient (AVC) for each solid or liquid,
x
i is the weight-% dry for each solid or the concentration for each
liquid, (ρ
s)
i is the density of each solid or liquid,
and ρ is the true density of the mixture; i.) comparing the calculated weight-%
solids or concentration to the target weight-% solids or concentration; and, j.)
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.).
Both of these two methods of this invention can be used in a process for continuously
coating a substrate, for instance where the substrate is a paper web and the solids
component comprises kaolin clay, calcium carbonate, titanium dioxide, or alumina
trihydrate, in a method that comprises: a.) setting a quantitative target for weight-%
of one or more solids to be coated onto a substrate; b.) continuously applying
the solids to the substrate via a carrier fluid; c.) measuring the apparent density
of the slurry; d.) determining the true density of the slurry; e.) calculating
the weight-% of solids in the slurry in the manner either of the former or the
latter general method; f.) comparing the calculated weight-% solids to the target
weight-% solids; and, g.) if the calculated weight-% is greater or less than the
target weight-%, lowering or raising the amount of solids applied in step b.).
Likewise, either of these two general methods of this invention can be
used in a process for controlling the output of a continuous process for preparing
a syrup. This method comprises: a.) setting a quantitative target for a concentration
of one or more carbohydrates, e.g. sucrose, and/or carbohydrate-containing liquids,
e.g. corn syrup and high fructose corn syrup, to be blended, along with water,
into a syrup; b.) continuously supplying the carbohydrate and/or carbohydrate-containing
liquid and a dilution liquid to a vessel and mixing said liquids to form a slurry;
c.) measuring the apparent density of the slurry; d.) determining the true density
of the slurry; e.) converting this true density to the calculated carbohydrate
concentration; f.) comparing the calculated carbohydrate concentration to the target
carbohydrate concentration; and, g.) if the calculated carbohydrate concentration
is greater or less than the target carbohydrate concentration, lowering or raising
the amount of carbohydrates and/or volume of carbohydrate-containing liquids supplied
in step b.).
In a third group of practical applications, this invention provides a method
for
controlling the output of a continuous process for preparing a carbonated beverage,
e.g. a soft drink, beer, or a carbonated wine. This method comprises: a.) setting
a quantitative target for a concentration of carbon dioxide to be blended into
an aqueous medium; b.) continuously 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 P
0, wherein P
0
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 P
0; d.) reducing
the aqueous medium pressure from P
0 to P
1 allowing the dissolved
carbon dioxide to start to be released back to the aqueous medium in a free-bubble
form; e.] reducing the aqueous medium pressure further from P
1 to P
2
allowing a sufficient amount of the dissolved carbon dioxide to be released
back to the aqueous medium in a free-bubble form; f.) measuring the change in volume
of the carbon dioxide liquid mixture at an equilibrium state between P
1 and
P
2; g.) reducing the aqueous medium pressure further from P
2 to
P
3 allowing more dissolved carbon dioxide to be released back to the
aqueous medium in a free-bubble form; h.) measuring the change in volume of the
carbon dioxide liquid mixture at an equilibrium state between P
2 and
P
3; i.) determining the volume of free carbon dioxide, V
s,
in the carbonated aqueous medium at the standard condition using the equation
##EQU12##
wherein P
1, P
2, and P
3 are three different
equilibrium ambient pressures, P
s and T
s are standard pressure
and temperature, ΔV
1 and ΔV
2 are the volume difference
of the free carbon dioxide measured at an equilibrium state between P
1 and
P
2 and P
2 and P
3, respectively; j.] calculating
the carbon dioxide concentration using the equation
##EQU13##
wherein V
s is the volume of free carbon dioxide determined in
i.] and V is the volume of carbonated aqueous medium in the sample chamber at a
preset "bottling" pressure P
0 upon which no free bubble should present;
k.) comparing the calculated carbon dioxide concentration to the target carbon
dioxide concentration; and, l.) 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 in step b.).
This invention also provides various analytical methods. One is a method for
determining the concentration of a solid or liquid component in a liquid carrier
component, which comprises measuring the apparent density of the mixture; determining
therefrom the true density of the mixture; and calculating the weight-% of solids
in the slurry in the manner taught above. Another is a method for determining the
true density of a solid or liquid component in a liquid carrier component, which
comprises measuring the apparent density of the mixture; and determining therefrom
the true density of the mixture. Another is a method for determining the entrained
air content of a liquid component, which comprises measuring the apparent air content
of the liquid at a variety of pressures; and determining therefrom the true entrained
air content of the liquid. Another is a method of characterizing a liquid by determining
its entrained air content, which comprises calculating the volume percentage of
free air, x%, in the liquid using the equation
##EQU14##
wherein V is the volume of the gas-free liquid in a sample chamber at ambient
pressure and V
s is determined by the equation
##EQU15##
wherein P
1, P
2, and P
3 are three different
equilibrium ambient pressures, P
s and T
s are standard pressure
and temperature, ΔV
1 and ΔV
2 are the volume difference
of the free air measured at an equilibrium state between P
1 and P
2
and P
2 and P
3, respectively.
Finally, this invention provides various methods of identifying samples
of unknown constitution. One such method comprises comparing its entrained air
content with a collection of entrained air contents, for a variety of known compounds,
determined in the manner taught above. Another comprises comparing its true density
with a collection of true densities, for a variety of known compounds, determined
by use of the relationship
##EQU16##
Another comprises comparing its % solids with a collection of % solids, for
a variety of known compounds, determined according to the relationship
##EQU17##
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will be more fully understood from the detailed description
given hereinbelow and from the accompanying drawings. These drawings are provided
by way of illustration only, and thus do not in any way limit the present invention.
In particular, it is noted that the hardware configurations depicted in these drawings
are illustrative only (and not to scale). Those skilled in the art can easily develop
alternative hardware configurations that will likewise obtain the benefits of the
present invention.
FIG. 1 is a schematic representation of an indirect measurement apparatus embodiment
of the present invention (measuring density, calculating volume).
FIG. 2 is a schematic representation of an industrial coating line having an
on-line measurement system in accordance with the present invention integrated
into it.
FIG. 3 is a schematic representation of a fruit canning line having a Distributed
Control System operating in accordance with this invention.
FIG. 4 is a schematic representation of a direct measurement apparatus embodiment
of the present invention (measuring volume, e.g. using a piston in a cylinder).
FIG. 5 is a schematic representation of a coating system including a deaeration
module in accordance with this invention.
DETAILED DESCRIPTION OF THE INVENTION
The following symbols are used from Equation [1] through [38]:
P1, P2, P3: Different equilibrium ambient
pressures measured by a pressure sensor
P: Pressure of the gas being dissolved
V1, V2, V3: Volumes of the free gas entrained
into a liquid at P1, P2, and P3, respectively
n1, n2, n3: Moles of the free gas entrained
into a liquid at P1, P2, and P3, respectively
ρ1, ρ2, ρ3: Equilibrium
apparent densities of the liquid that contains entrained gas being measured at
P1, P2, and P3, respectively
ρ: Gas-free true density of the liquid
V: Gas-free volume of the liquid
Vt1: Total volume of the liquid that contains entrained gas being
measured at P1
ΔV1: The volume difference of the free gas measured at
an equilibrium state-between P1 and P2 (a measurable value)
ΔV2: The volume difference of the free gas measured at
an equilibrium state between P2 and P3 (a measurable value)
R: The constant of the Ideal Gas Law
T: Equilibrium temperature of the process liquid/solution measured by a
temperature sensor, assuming that the temperature is kept constant between the
three measurement points (T=T1=T2=T3)
H: The constant of Henry's Law
n*: Moles of the dissolved gas at P1
nd: Moles of the dissolved gas at P
n′1, n′2, n′3: Moles
of the normalized free gas at P1, P2, and P3,
respectively (with n* being neglected for the purpose of solving the constant of
Henry's Law explicitly)
Pg: Gas pressure inside the entrained gas bubbles
σ: Liquid surface tension
r: The medium radius of the entrained gas bubbles
Ps, Ts: Atmospheric pressure, Ps=1 atm
(14.7 psi) and standard temperature, Ts=25° C.
ns, Vs: Moles and volume of free gas at Ps
and Ts
x%: Volume percentage of free gas at Ps and Ts
mpyc: Mass of the liquid mixture sample collected by a pycnometer
Vpyc: Volume of the pycnometer
m: Mass of the liquid mixture sample
The following key equations are used in this application:
H: Henry's Law constant.
##EQU18##
Usage: determining the solubility, in terms of the magnitude of H, for one
specific gas dissolved into different liquids or for different gases dissolved
into one specific liquid; calculating the amount of dissolved gas using Henry's
law P=Hnd (Equation [5]) at a specific pressure, P.
Applied Method: direct measurement. For an indirect measurement,
##EQU19##
are needed to be substituted into [25].
V: gas-free volume of the liquid mixture being measured.
##EQU20##
Usage: being a parameter used in [34] for determining the volume percentage
of free gas, x%, at standard pressure and temperature (this parameter can be used
in a similar formula for determining the volume percentage of free gas at other
pressures as well); being a parameter used in [35] for determining the true density
of the gas-free liquid.
Applied Method: direct measurement.
V
s: the volume of free gas at the atmospheric pressure.
##EQU21##
Usage: converting the volume of free gas from one specific pressure to that
at the atmospheric pressure, which can further be used in [34] for determining
the volume percentage of free gas, x%, at the standard condition.
Applied Method: direct measurement.
x%: volume percentage of free gas at standard pressure and temperature.
##EQU22##
Usage: determining the volume percentage of free gas, x%, at the standard condition.
Applied Method(s): both direct and indirect measurements.
ρ: true density of gas-free liquid.
##EQU23##
Usage: calculating the true density of gas-free liquid using a pycnometer
preferably in a lab scenario, which can further be used as a reliable basis for
determining % solids.
Applied Method: direct measurement (lab method).
ρ: true density of gas-free liquid.
##EQU24##
Usage: calculating the true density of gas-free liquid in a production environment
scenario, which can further be used as a reliable basis for determining % solids.
Applied Method: direct measurement.
V: gas-free volume of the liquid in 1 unit of mass of liquid mixture.
##EQU25##
Usage: being a parameter used in [34] for determining the volume percentage
of free gas, x%, at standard pressure and temperature (this parameter can be used
in a similar formula for determining the volume percentage of free gas at other
pressures as well); being a parameter used in [37] for determining the true density
of the gas-free liquid.
Applied Method: indirect measurement.
ρ: true density of gas-free liquid.
##EQU26##
Usage: calculating the true density of gas-free liquid in 1 unit of mass of
liquid mixture, which can further be used as a reliable basis for determining % solids.
Applied Method: indirect measurement.
V
s: the volume of free gas at the atmospheric pressure.
##EQU27##
Usage: converting the volume of free gas from one specific pressure to that
at the atmospheric pressure, which can further be used in [34] for determining
the volume percentage of free gas, x%, at the standard condition.
Applied Method: indirect measurement.
In the disclosure that follows, every measured parameter, pressure, apparent
density,
temperature, and change in volume should be understood to be an equilibrium value.
The relationship between the gas pressure, P
g, inside gas bubbles
entrained in a liquid and ambient pressure, P, in equilibrium can be expressed
(according to the Young-Laplace Equation) as
##EQU28##
If the size of the entrained gas bubbles is sufficiently large, the second item
in (6) will be relatively small and insignificant, e.g.,
##EQU29##
atm (1.4 psi) when r≧1 mm (0.079"). The gas pressure, P
g, inside
the gas bubbles can then be replaced by the ambient pressure, P, with a sufficiently
high accuracy.
Under these circumstances, the ambient pressure can consequently be substituted
into the ideal gas law PV=nRT, giving the volumes of free gas in a liquid at different
pressures
##EQU30##
NOTE: assuming T=T
1=T
2=T
3
The volume differences, ΔV
1 and ΔV
2, between
P
1-P
2and P
2-P
3 are the reflection of
the change in volume of the entrained gas only, since the liquid itself is incompressible.
Equations (7), (8), and (9) can therefore be combined to
##EQU31##
ΔV
1 and ΔV
2, in general, can
be determined either DIRECTLY by measuring the changes in volume; or INDIRECTLY
by measuring the changes in apparent density.
By assuming that the unit of mass equals 1, the relationships between these two
options can readily be found as
##EQU32##
Equations (10) and (11) can be rewritten as
##EQU33##
In equilibrium, by applying Henry's Law, the amounts of the dissolved gas at
P
1,
P
2, and P
3, respectively, can be written as
P1=Hn* (16)
P2=H└n*+(
n1-n2)┘ (17)
P3=H└n*+(
n1-n3)┘ (18)
Equations (14)-(18) are a group of underdetermined linear equations, which,
in theory, have an infinite number of solutions. Such equations, nevertheless,
have a unique solution if any one of the variables can be determined. For the purpose
of determining the constant of Henry's Law, H, explicitly, it is arbitrarily to
neglect n* at this moment. This would allow (17) and (18) to be simplified as
P2=H(
n′1-n′2) (19)
P3=H(
n′1-n′3) (20)
or
##EQU34##
This manipulation actually assumes that the amount of the dissolved gas follows
P=H′(n-n*) that has a curve with a slope being parallel to P=Hn. n′
3
can then be obtained from (21) as
##EQU35##
By substituting n′
3 back into (15), n′
1 can
be solved as
##EQU36##
Likewise, n′
2 can also be solved from (14)
##EQU37##
The constant of Henry's Law, H, can therefore be determined from (19)
##EQU38##
Let P
1×[(17)-(16)]
HP1n1-HP1n2=P1(
P2-P1) (26)
##EQU39##
n
1 can finally be solved from (27)-(26), substituting (25) for H.
##EQU40##
The volume of free gas, V
1, at P
1 is then attainable
##EQU41##
and the gas-free volume of the liquid, V, can also be determined
##EQU42##
To determine the moles of free gas, n
s, at the atmospheric pressure,
P
s, the difference of dissolved gas, Δn
s, between P
1
and P
s should first be calculated from Henry's Law
##EQU43##
n
s can then be expressed as
##EQU44##
The volume of free gas, V
s, at the atmospheric pressure, P
s,
is therefore
##EQU45##
Alternatively, V
s could be determined with the use of the
Ideal Gas Law and equation (29), above
##EQU46##
The volume percentage of free gas, x%, at P
s and T
s can
thus be attained as
##EQU47##
DIRECT MEASUREMENT (for true density). For a laboratory measurement, the gas-free
true density, ρ, can be determined using a pycnometer, or a similar device.
A pycnometer is a device for determining the specific gravity of liquids and solids.
In this case, by weighing the mass, m
pyc, of the liquid mixture sample
and dividing the known volume, V
pyc, of the pycnometer, the true density,
ρ, turns out to be
##EQU48##
Or, for an online application, these mass and volume measurements could be obtained
by incorporating a load cell (a weight measurement instrument) into a controlled-volume
sample chamber such as is demonstrated in FIG. 4. Such a device would provide a
simple method of obtaining the data required to calculate percent entrained air,
percent dissolved air, Henry's Law constant, and true density of a solution in
real-time. In this application, true density would be determined via formula (35-B)
##EQU49##
where m is the mass of the fluid in the sample chamber and V is the gas-free
volume of the liquid.
INDIRECT MEASUREMENT (for true density). In case of the indirect measurement,
the gas-free volume of the liquid, V, in 1 unit of mass of liquid mixture is
##EQU50##
and the true density is
##EQU51##
This method of indirectly determining air-free volume of liquid, and ultimately
its true density, from the inverse of measured density, is demonstrated in FIG.
1. Such a device provides a simple method of obtaining the data required to calculate
percent entrained air, percent dissolved air, Henry's Law constant, and true density
of a solution in real-time.
The volume of free gas, V
s, at the standard conditions, in 1 unit
of mass of liquid mixture is
##EQU52##
The volume percentage of free gas, x%, at P
s and T
s can
be calculated in the same manner as demonstrated in (34).
If even greater accuracy is required than that resulting from the preceding equations,
the assumption upon which equation (25) is based can be eliminated. The solution
for these key equations can then be found using iteration techniques. Such techniques
are well known to those skilled in the art of deriving mathematical solutions to problems.
While the focus of the discussion in this application is often on "air", this
invention can also be applied to the determination of amounts of any gas that is
entrained and/or dissolved in any liquid. For instance, one important application
of this invention is in the manufacture and processing of carbonated beverages,
in which much more carbon dioxide gas than air is entrained and dissolved in the
liquid carrier. Likewise, the present invention can be applied to processes conducted
under an inert atmosphere, in which the gas may be nitrogen, helium, or another
"inert" gas instead of (or in addition to) air.
U.S. Pat. No. 6,496,781 B1, MIXTURE CONCENTRATION CONTROL IN MANUFACTURING PROCESSES,
issued on Dec. 17, 2002. Some (but by no means all) embodiments of the present
invention can be used to make certain control methods described in that patent
even more accurate. Accordingly, the entire disclosure of that patent is hereby
expressly incorporated by reference.
EXAMPLES
Example 1
Entrained Air: Apparatus for the Indirect Measurement of Entrained and Dissolved
Air Content in Liquids
FIG. 1 depicts a particular hardware configuration that used the indirect measurement
option described above. The apparatus of FIG. 1 takes measurements in a "no flow"
state. Apparatus 10 of FIG. 1 includes a reservoir for process fluid, from
which the fluid may be pumped by through piping which is under the control of a
pressure regulator which is capable of setting at least three different pressures
P1, P2, and P3 in the system. Each of these pressures may
be either higher or lower than the preceding pressure. For instance, the measurement
sequence could be P1<P2<P3, or P1>P2
and P1<P3, or any other combination. Also, these pressures may
be set based on system constraints or testing objectives. Flow of the fluid in
the piping is controlled by three valves V1, V2, and V3. This
particular apparatus also includes a pressure gauge 12 and a density and
temperature gauge 14.
A measurement procedure is carried out on apparatus 10 as follows. Valves
V1 and V2 are opened to permit fluid pumped from the reservoir to
fill the piping. Valve V3 is partially closed to ensure that measurement
gauges 12 and 14 are filled with the fluid. The pressure regulator
is set to P1 and valve V2 is closed to pressurize pressure gauge
12 to P1. Valve V1 is closed. Subsequently, pressure, temperature,
and density data at pressure level P1 is collected until there is no longer
any change in the data. (It is noted that initial changes in density and pressure
result from air dissolving into or coming out of the fluid.) For the case where
P1<P2<P3, the pressure regulator is set to P2
and valve V1 is opened to pressurize pressure gauge 12 to P2.
Valve V1 is closed. Subsequently, pressure, temperature, and density data
at pressure level P2 is collected until there is no longer any change in
the data. Finally, the pressure regulator is set to P3 and valve V1
is opened to pressurize pressure gauge 12 to P3. Valve V1
is closed. Subsequently, pressure, temperature, and density data at pressure level
P3 is collected until there is no longer any change in the data. The three
sets of stabilized pressure, temperature, and density data may then be used in
the processes of the present invention, which are described in detail hereinabove.
Example 2
Entrained Air: Optimizing Deaerator Operations in Coating Processes
Certain coating processing environments require that excessive entrained
gases should be removed from the coating liquids prior to distributing the coating
liquids onto the substrate. This is because entrained gas bubbles, especially larger
ones, deteriorate coating quality and result in coating defects such as intolerable
pinholes. Deaeration is therefore highly desirable where excessive entrained gas
bubbles are presented. With the rapidly advancing technology of high-speed jet
and curtain coating, in which thin liquid sheets are either injected or allowed
to fall freely onto a substrate to be coated, any entrained large gas bubbles may
even cause the breakdown of the integrity of the free coating liquid sheet. Thus,
deaeration is a must for high-speed jet and curtain coating applications.
One application of the present invention, as depicted in FIG. 5, incorporates
this invention both before and after the deaerator in a curtain coater piping system.
The percent entrained air and percent dissolved air measurements provided before
and after the deaerator unit improve the manufacturing process by enabling optimization
of the deaerator unit, based upon determination of its process-specific deaeration
efficiency. Process parameter adjustments (degree of vacuum, rotation speed of
the deaerator, etc.) are made based upon the differences in "before" and "after"
values. The output from the upstream apparatus embodiment is compared to that from
the downstream apparatus embodiment to calculate the efficiency of air removal,
and process parameters are changed to enhance the amount of air removed by the
deaerator unit.
In addition to coating processes, other typical applications for deaerator systems
include the packaging of ointments, creams, lotions, toothpaste, mayonnaise, ketchup,
and lubricating grease.
Example 3
Entrained Air: Quality Control in Coating Application Systems
In Example 2, the deaerator units can be used to minimize waste costs due to
the
manufacture of off-q
