Advanced Degassing for Water Treatment

Understanding Degassing in Water Treatment

Degassing is a critical process in water treatment, particularly after advanced purification steps like reverse osmosis (RO). Its primary purpose is to remove dissolved gases, such as carbon dioxide (CO₂) and oxygen, from the water. This guide focuses on the principles and calculations for designing packed column degassers to effectively remove dissolved CO₂.

The Challenge of Dissolved Carbon Dioxide

Groundwater and other sources often contain dissolved CO₂. In water, CO₂ exists in equilibrium with bicarbonate (HCO₃⁻) and carbonate (CO₃²⁻) ions.

Equilibrium Equation: CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻ ⇌ 2H⁺ + CO₃²⁻

During the reverse osmosis process, semipermeable membranes efficiently remove dissolved ions like HCO₃⁻ and CO₃²⁻, channeling them into the concentrate stream. However, dissolved CO₂, being a non-ionic gas, can largely pass through the RO membrane. This leads to a decrease in the pH of the permeate (treated water), making it more acidic.

Acidic water can be detrimental to downstream processes, as many membranes are sensitive to low pH conditions and can be damaged or experience reduced performance. Therefore, removing dissolved CO₂ post-RO is essential to re-establish a neutral pH before further treatment or distribution. This is typically achieved using "strip towers" or degassers.

Fundamental Principles of Degasser Design

The design of a degasser, especially a packed column stripper, relies on understanding gas-liquid mass transfer principles.

Henry's Law and Constant

Henry's Law describes the relationship between the concentration of a gas in a liquid and its partial pressure in the gas phase at equilibrium. The dimensionless Henry's constant (H) is crucial for calculating this equilibrium. It varies with temperature.

The dimensionless Henry's constant at a given temperature (T) can be calculated using:

$H_T = H \cdot e^{-\frac{\Delta H}{R} \left(\frac{1}{T} - \frac{1}{293.15 \text{ K}}\right)}$

Where:

• $H_T$ = Dimensionless Henry's constant at temperature T
• $H$ = Dimensionless Henry's constant at 20°C (293.15 K)
• $\Delta H$ = Standard enthalpy change for solution in water, in $10^3 \text{ kcal/kmol}$ ($4.184 \times 10^3 \text{ kJ/kmol}$)
• $R$ = Universal gas constant, $1.987 \text{ kcal/(kmol} \cdot \text{K)}$ ($8.314 \text{ J/(mol} \cdot \text{K)}$)
• $T$ = Absolute temperature in Kelvin (K)

Table 1: Dimensionless Henry Constants at 20°C (293.15 K) for Various Substances

Minimum Air/Water Ratio and Stripping Factor

To achieve a desired removal percentage of a contaminant, a minimum air/water ratio is required. If the actual air/water ratio is below this minimum, the desired final concentration cannot be reached because equilibrium will be established prematurely.

The minimum air/water ratio changes with temperature. If the inlet concentration of the contaminant, $C_0$, and the desired outlet concentration, $C_u$, are known, along with the Henry's constant, the minimum air/water ratio ($Q_{a,min} / Q_{w}$) can be determined.

The stripping factor (S) is defined as the ratio of the actual air/water ratio to the minimum air/water ratio:

$S = \frac{(Q_a / Q_w)}{(Q_{a,min} / Q_w)}$

• If $S < 1$, the stripping column will not achieve the target concentration.
• If $S = 1$, the column operates at the minimum air/water ratio.
• Typically, S is greater than 1 for efficient operation.

Degasser Design Procedure

Designing a packed column degasser involves several steps to determine its dimensions and operating parameters.

Step 1: Define Design Criteria and Select Packing

Crucial design criteria include:

• Packing Factor ($C_f$): Specific to the chosen packing material.
• Air/Water Ratio: Determined based on desired removal and Henry's constant.
• Gas Pressure Drop: A typical value for packed columns is $50 \text{ Pa/m}$ ($0.002 \text{ psi/ft}$).

Table 2: Data for Common Packing Gaskets

Step 2: Determine Fluid Densities and Eckert Curve X-Value

The Eckert pressure drop curve is used to size the column's cross-section. The x-coordinate of the Eckert curve is given by:

$x = \frac{G_m}{L_m} \sqrt{\frac{\rho_L}{\rho_G}}$

Where:

• $\rho_L$ = Density of water [kg/m³]
• $\rho_G$ = Density of gas (air) [kg/m³]
• $G_m / L_m$ = Mass flux ratio gas/water (dimensionless)

A. Water Density ($\rho_L$) Calculation

The density of water changes with temperature. For a given temperature $T_2$ relative to a reference temperature $T_1$ (e.g., $T_1 = 293 \text{ K}$ or $20^\circ \text{C}$), the volume change $\Delta V$ can be estimated:

$\Delta V = V_0 \cdot \beta \cdot \Delta T$

Where:

• $\Delta V$ = Volume change [m³]
• $V_0$ = Original volume (e.g., $1 \text{ m}^3$)
• $\beta$ = Coefficient of cubic expansion for water, $0.21 \times 10^{-3} \text{ K}^{-1}$ at $293 \text{ K}$
• $\Delta T = T_2 - T_1$ = Temperature difference [K]

The new volume is $V_0 + \Delta V$. The density can then be calculated as:

$\rho_L = \frac{Mass}{V_0 + \Delta V}$

B. Air Density ($\rho_G$) Calculation

The density of air at a certain temperature ($T$) can be determined using the ideal gas law:

$\rho_G = \frac{P \cdot M}{R \cdot T}$

Where:

• $P$ = Prevailing air pressure ($101 \text{ kPa}$ or $1 \text{ atm}$ for atmospheric strippers)
• $M$ = Molar mass of air ($28.97 \text{ kg/kmol}$ or $0.02897 \text{ kg/mol}$)
• $R$ = Universal gas constant ($8314 \text{ J/(kmol} \cdot \text{K)}$ or $8.314 \text{ J/(mol} \cdot \text{K)}$)
• $T$ = Absolute temperature in Kelvin (K)

C. Mass Flux Ratio ($G_m/L_m$)

This ratio is determined from the known air flow rate ($Q_a$) and water flow rate ($Q_w$):

$\frac{G_m}{L_m} = \frac{Q_a}{Q_w}$

Where:

• $Q_a$ = Air flow rate [m³/s]
• $Q_w$ = Water flow rate [m³/s]

Step 3: Determine 'y' on the Eckert Curve

Given the calculated x-value (typically between 0.02 and 3.0), the corresponding y-value on the Eckert curve can be found graphically or approximated by the formula:

$y = 0.505 \cdot x^{0.089} \cdot e^{(-0.523 \cdot x)}$

This formula represents the approximate red curve in typical Eckert graphs.

Step 4: Calculate Gas Mass Flux ($G_m$)

The mass flux of the gas can be determined from the y-value of the Eckert curve:

$y = \frac{G_m^2 \cdot C_f}{\rho_G (\rho_L - \rho_G) \cdot g} \cdot (\frac{\mu_L^{0.1}}{\rho_L^{0.9}})$

Where:

• $G_m$ = Mass flux of gas [kg/(m²·s)]
• $C_f$ = Packing factor
• $g$ = Gravitational acceleration ($9.81 \text{ m/s}^2$)
• $\mu_L$ = Dynamic viscosity of water [kg/(m·s)]

Dynamic Viscosity of Water ($\mu_L$) For water in the temperature range of 283 K to 293 K ($10^\circ \text{C}$ to $20^\circ \text{C}$), the dynamic viscosity can be estimated by:

$\mu_L = \frac{1}{0.000185 \cdot T - 0.046}$

Where:

• $\mu_L$ = Dynamic viscosity of water [kg/(m·s)]
• $T$ = Temperature in Kelvin (K)

Once $\mu_L$ is known, $G_m$ can be calculated.

Step 5: Calculate Water Mass Flux ($L_m$) and Column Cross-Section

The mass flux of the water ($L_m$) can be calculated from the gas mass flux and the mass flux ratio:

$L_m = G_m \cdot \frac{L_m}{G_m}$

Finally, the cross-sectional area (A) of the stripping column can be determined using the water flow rate ($Q_w$) and its density ($\rho_L$):

$A = \frac{Q_w \cdot \rho_L}{L_m}$

The column diameter can then be calculated from the cross-sectional area.

Mass Transfer Coefficients and Column Height

To determine the required height of the stripping column, the overall mass transfer coefficient and individual diffusion coefficients are needed.

Diffusion Coefficients

Mass transfer occurs via diffusion from the water phase to the air phase. The diffusion coefficient depends on temperature and the properties of the diffusing substance (CO₂) and the medium (water or air).

A. Diffusion Coefficient of CO₂ in Water ($D_L$) The Hayduk-Laudie relation estimates the diffusion coefficient of CO₂ in water:

$D_L = \frac{13.26 \times 10^{-5}}{\mu_W^{1.14} \cdot V_B^{0.589}}$

Where:

• $D_L$ = Diffusion coefficient of CO₂ in water [cm²/s ($10^{-4} \text{ m}^2/\text{s}$)]
• $\mu_W$ = Dynamic viscosity of water [cP] ($1 \text{ kg/(m·s)} = 1000 \text{ cP}$)
• $V_B$ = Molar volume of CO₂ at its standard boiling point [liter/mole] (For CO₂, $V_B = 0.0340 \text{ liter/mole}$ at $T_B = 194.6 \text{ K}$)

B. Diffusion Coefficient of CO₂ in Air ($D_G$) The Wilke-Lee modification of the Hirschfelder-Bird-Spotz relation can be used for diffusion in gas:

$D_G = \frac{1.858 \times 10^{-3} \cdot T^{1.5} \cdot (M_A^{-1} + M_B^{-1})^{0.5}}{P \cdot r_{AB}^2 \cdot f(k \cdot T / \epsilon_{AB})}$

Where:

• $D_G$ = Diffusion coefficient of CO₂ in air [cm²/s ($10^{-4} \text{ m}^2/\text{s}$)]
• $T$ = Temperature [Kelvin]
• $M_A$ = Molecular weight of CO₂ ($44.01 \text{ g/mol}$)
• $M_B$ = Molecular weight of air ($28.97 \text{ g/mol}$)
• $P$ = Air pressure ($1.01 \times 10^5 \text{ Pa}$ or $1 \text{ atm}$)
• $r_{AB}$ = Average collision distance ($r_A + r_B$) / 2 [nm]
  • $r_A$ (for CO₂) = $0.369 \cdot (V_B)^{1/3} \cdot (T_{B,A})^{1/3} = 0.369 \cdot (0.0340)^{1/3} \cdot (194.6)^{1/3} \approx 0.395 \text{ nm}$
  • $r_B$ (for air) = $0.3711 \text{ nm}$
• $\epsilon_{AB}$ = Molecular attraction energy $\sqrt{\epsilon_A \cdot \epsilon_B}$ [ergs ($10^{-7} \text{ J}$)]
  • $\epsilon_A / k$ (for CO₂) = $1.21 \cdot T_{B,A} = 1.21 \cdot 194.6 \approx 235.4 \text{ K}$ (where $k$ is Boltzmann's constant)
  • $\epsilon_B / k$ (for air) = $78.6 \text{ K}$
• $k$ = Boltzmann's constant ($1.38 \times 10^{-16} \text{ g·cm}^2/(\text{s}^2 \cdot \text{K})$ or $1.38 \times 10^{-23} \text{ J/K}$)
• $f(k \cdot T / \epsilon_{AB})$ = Collision function.
  • Let $ee = \frac{k \cdot T}{\epsilon_{AB}}$.
  • $f(ee) = (0.237 \cdot ee - 0.258)^{0.147}$

C. Dynamic Viscosity of Air ($\mu_G$) The dynamic viscosity of air depends on temperature:

$\mu_G = 4.79 \times 10^{-26} \cdot T^{0.5} \cdot \frac{1}{\delta^2} \cdot \frac{1}{P_L}$

Where:

• $\mu_G$ = Dynamic viscosity of air [kg/(m·s)]
• $m$ = Mass of an "air molecule" ($4.79 \times 10^{-26} \text{ kg}$)
• $\delta$ = Diameter of an "air molecule" ($3.7 \times 10^{-10} \text{ m}$)
• $P_L$ = Air pressure [Pa]
• $k$ = Boltzmann constant ($1.38 \times 10^{-23} \text{ J/K}$)

Total Mass Transfer Constant ($K_L \cdot a$)

The overall mass transfer constant, $K_L \cdot a$, combines the individual mass transfer coefficients and the wetted surface area:

$\frac{1}{K_L \cdot a} = \frac{1}{k_L \cdot a_w} + \frac{1}{H \cdot k_G \cdot a_w}$

Where:

• $K_L \cdot a$ = Total mass transfer constant [s⁻¹]
• $k_L$ = Liquid-side mass transfer coefficient [m/s]
• $k_G$ = Gas-side mass transfer coefficient [m/s]
• $a_w$ = Wetted surface area of the packing [m²/m³]
• $H$ = Dimensionless Henry's constant

Onda Correlations for Mass Transfer Coefficients

The Onda correlations are widely used empirical relationships to determine $a_w$, $k_L$, and $k_G$.

A. Wetted Surface Area ($a_w$) $a_w = a_t \left( 1 - e^{-1.45 \cdot Re_L^{0.1} \cdot Fr_L^{-0.05} \cdot We_L^{0.2} \cdot (\sigma_C / \sigma)^{0.75}} \right)$

Where:

• $a_t$ = Specific surface area of the packing [m²/m³]
• $\sigma$ = Surface tension of water [kg/s² (N/m)]
• $\sigma_C$ = Critical surface tension of the packing material [kg/s² (N/m)]
• $Re_L$ = Liquid Reynolds number
• $Fr_L$ = Liquid Froude number
• $We_L$ = Liquid Weber number

Dimensionless Numbers:

• Liquid Reynolds Number ($Re_L$): $Re_L = \frac{L_m \cdot d_P}{\mu_L}$
• Liquid Froude Number ($Fr_L$): $Fr_L = \frac{L_m^2}{g \cdot d_P \cdot \rho_L^2}$
• Liquid Weber Number ($We_L$): $We_L = \frac{L_m^2 \cdot d_P}{g \cdot \sigma \cdot \rho_L}$

Where:

• $L_m$ = Mass flux of water [kg/(m²·s)]
• $d_P$ = Nominal diameter of the packing [m]
• $\mu_L$ = Dynamic viscosity of water [kg/(m·s)]
• $\rho_L$ = Density of water [kg/m³]
• $g$ = Gravitational acceleration ($9.81 \text{ m/s}^2$)

B. Liquid-Side Mass Transfer Coefficient ($k_L$) $k_L = 0.0051 \cdot (\frac{L_m}{a_t \cdot \mu_L})^{2/3} \cdot (\frac{\mu_L}{\rho_L \cdot D_L})^{1/2} \cdot (\frac{\rho_L \cdot D_L \cdot a_t}{\mu_L})^{1/2}$

Where:

• $D_L$ = Diffusion coefficient of CO₂ in water [m²/s]

C. Gas-Side Mass Transfer Coefficient ($k_G$) $k_G = 5.23 \cdot (\frac{G_m}{a_t \cdot \mu_G})^{0.7} \cdot (\frac{\mu_G}{\rho_G \cdot D_G})^{1/3} \cdot (\frac{\rho_G \cdot D_G \cdot a_t}{\mu_G})^{1/2}$

Where:

• $G_m$ = Mass flux of air [kg/(m²·s)]
• $\mu_G$ = Dynamic viscosity of air [kg/(m·s)]
• $\rho_G$ = Density of air [kg/m³]
• $D_G$ = Diffusion coefficient of CO₂ in air [m²/s]

Conditions for Onda Correlations:

• Nominal packing diameter ($d_P$) must be less than $0.0508 \text{ m}$ ($2 \text{ inches}$).
• Liquid mass flux ($L_m$) should be between $0.8$ and $43 \text{ kg/(m²·s)}$.
• Gas mass flux ($G_m$) should be between $0.014$ and $1.7 \text{ kg/(m²·s)}$.
• For packing $0.0508 \text{ m}$ ($2 \text{ inches}$) or larger, the calculated $K_L \cdot a$ value should be multiplied by a safety factor of $0.75$.

Column Height Determination

The height ($L$) of the stripping column is calculated using the following formula:

$L = \frac{Q_w}{A \cdot K_L \cdot a} \cdot \ln \left( \frac{C_0 - \frac{C_0}{S}}{C_u - \frac{C_0}{S}} \right)$

Where:

• $L$ = Column height [m]
• $Q_w$ = Water flow rate [m³/s]
• $A$ = Cross-sectional area of the column [m²]
• $K_L \cdot a$ = Total mass transfer constant [s⁻¹]
• $C_0$ = Inlet concentration of contaminant (e.g., $100%$)
• $C_u$ = Desired outlet concentration ($1 - \text{removal rate}$)
• $S$ = Stripping factor

AquaChain Engineering Tip

When performing an initial pilot study for degasser design, always verify the actual packing factor ($C_f$) and specific surface area ($a_t$) provided by the packing manufacturer against the generic values, as variations can significantly impact mass transfer efficiency and pressure drop calculations.

Frequently Asked Questions

Q1: Why is CO₂ removal particularly important after reverse osmosis? A1: Reverse osmosis membranes are very effective at removing ionic species like bicarbonate, but dissolved CO₂ passes through, lowering the pH of the treated water. This acidic water can damage downstream equipment or membranes, making CO₂ removal essential for pH stabilization.

Q2: What is the significance of the stripping factor (S) in degasser design? A2: The stripping factor indicates how far the system operates from equilibrium. An S value greater than 1 means the column has sufficient capacity to achieve the desired removal, while S less than 1 suggests that the target concentration will not be met due to equilibrium limitations.

Q3: Are there any alternatives to packed column degassers for CO₂ removal? A3: While packed columns are common, other methods include spray towers, tray columns, and membrane contactors. The choice depends on factors like desired removal efficiency, flow rate, footprint, and operating costs. For very high purity requirements or specific gas compositions, membrane contactors can offer advantages.

Learn more about related processes: Deaeration Technology