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

• US 7,559,223 B2
• Filed: 12/13/2004
• Issued: 07/14/2009
• Est. Priority Date: 08/21/2003
• Status: Expired due to Fees

• Current Assignee: Appvion Operations, Inc.
• Original Assignee: Appleton Papers Incorporated (Oldapco PDC Corp.)
• Inventors: Franda, Robert Josef, Chen, Qingyuan
• Primary Examiner(s): Williams; Hezron
• Assistant Examiner(s): Shabman; Mark
• Application Number:
  US11/009,044
• Publication Number:
  US 20050109078A1
• Time in Patent Office: 1,674 Days
• Field of Search: 73/190.5, 73/190.4, 738/613.55, 702/24, 702/25
• US Class Current: 73/19.05
• CPC Class Codes: G01N 2013/025 Measuring foam stability
• CPC Class Codes: G01N 33/0016 by regulating a physical variable, e.g. pressure or temperature
• CPC Class Codes: G01N 33/143 containing sugar
• CPC Class Codes: G01N 33/34 Paper
• CPC Class Codes: G01N 7/14 by allowing the material to emit a gas or vapour, e.g. water vapour, and measuring a pressure or volume difference determining urea G01N33/48742
• CPC Class Codes: G01N 9/26 by measuring pressure differences

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)

$\begin{array}{cc}x\%=\frac{V_s}{V_s+V}& \left(28\right)\end{array}$
wherein V is the volume of the gas-free liquid calculated by equation (23)

$\begin{array}{cc}V=\frac{1}{{\rho }_1}-\left[\frac{P_2}{P_2-P_1}\left(\frac{1}{{\rho }_1}-\frac{1}{{\rho }_2}\right)-\frac{RT}{P_2-P_1}g\left(\frac{\Delta P}{Q^a}\right)\right]& \left(23\right)\end{array}$
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/Q^a) is a function for determining the amount of gas being dissolved between P₂ and P₁, and V_s is determined by equation (27)

$\begin{array}{cc}{V}_s=\frac{T_s}{T}\frac{P_1{P}_2}{P_s\left(P_2-P_1\right)}\left(\frac{1}{{\rho }_1}-\frac{1}{{\rho }_2}\right)-\frac{R{T}_s}{P_s}\left(\frac{P_1}{P_2-P_1}g\left(\frac{\Delta P}{Q^a}\right)-g\left(\frac{P_1-P_s}{Q^a}\right)\right)& \left(27\right)\end{array}$
in which P_s and T_s are standard pressure (1 atm) and temperature (0° C.), and

$g\left(\frac{P_1-P_s}{Q^a}\right)$
is a function for determining the amount of gas being dissolved between P₁ and P_s.

Claims

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;

$\begin{array}{cc}{V}_1=\frac{P_2}{P_2-P_1}<br><br>\left(\frac{1}{{\mathrm{\rho <br><br>}}_1}-\frac{1}{{\mathrm{\rho <br><br>}}_2}\right)-\frac{\mathrm{RT}}{P_2-P_1}<br><br>g<br><br>\left(\frac{\mathrm{\Delta <br><br>}<br><br><br><br>P}{Q^a}\right)& \left(22\right)\\ V=V_{i<br><br><br><br>1}-V_1=\frac{1}{{\mathrm{\rho <br><br>}}_1}-\left[\frac{P_2}{P_2-P_1}<br><br>\left(\frac{1}{{\mathrm{\rho <br><br>}}_1}-\frac{1}{{\mathrm{\rho <br><br>}}_2}\right)-\frac{\mathrm{RT}}{P_2-P_1}<br><br>g<br><br>\left(\frac{\mathrm{\Delta <br><br>}<br><br><br><br>P}{Q^a}\right)\right]& \left(23\right)\\ \mathrm{\rho <br><br>}=\frac{1}{V}& \left(24\right)\\ x<br><br><br><br>\%=\frac{V_s}{V_s+V}& \left(28\right)\end{array}$

wherein;

V₁ is volume of the free gas entrained into a liquid at P₁;

P₁ and P₂ 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 P₁ and P₂, 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=T₁=T₂);

g(Δ

P/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;

Δ

P is pressure difference Δ

P=P₂−

P₁ or Δ

P=P_II−

P₁;

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 P₁;

ρ

is the gas-free true density of the liquid;

x% is volume percentage of free gas at P_s and T<sub>s; and

Vs</sub> 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);

$\begin{array}{cc}{V}_s=\frac{T_s}{T}<br><br>\frac{P_1<br><br>P_2}{P_s<br><br>\left(P_2-P_1\right)}<br><br>\left(\frac{1}{{\mathrm{\rho <br><br>}}_1}-\frac{1}{{\mathrm{\rho <br><br>}}_2}\right)=\frac{{\mathrm{RT}}_s}{C}& \left[33\right]\\ V=\frac{1}{{\mathrm{\rho <br><br>}}_1}-\left[\frac{P_2}{P_2-P_1}<br><br>\left(\frac{1}{{\mathrm{\rho <br><br>}}_1}-\frac{1}{{\mathrm{\rho <br><br>}}_2}\right)-\frac{\mathrm{RT}}{C}\right]& \left[32\right]\\ \mathrm{\rho <br><br>}=\frac{1}{V}& \left(24\right)\\ x<br><br><br><br>\%=\frac{V_s}{V_s+V}& \left(28\right)\end{array}$

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=T₁=T₂);

P₁ and P₂ 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 P₁ and P₂, 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.