Trichloroethylene (TCE), a common industrial solvent, is often found at low concentrations in industrial waste waters. Stripping is a common process for removing sparingly soluble, volatile organic solutes such as TCE from aqueous solution. A wetted-wall column is used to study the stripping of TCE

Question

Trichloroethylene (TCE), a common industrial solvent, is often found at low concentrations in industrial waste waters. Stripping is a common process for removing sparingly soluble, volatile organic solutes such as TCE from aqueous solution. A wetted-wall column is used to study the stripping of TCE from water to air at a constant temperature of [latex]293 \mathrm{~K}[/latex] and total system pressure of 1 atm. The column inner diameter is [latex]4 \mathrm{~cm}[/latex] and the height is [latex]2 \mathrm{~m}[/latex]. In the present process, the volumetric air flow rate into the column is [latex]2000 \mathrm{~cm}^{3} / \mathrm{s}\left(2.0 imes 10^{-3} \mathrm{~m}^{3} / \mathrm{s} ight)[/latex] and the volumetric flow rate of water is [latex]50 \mathrm{~cm}^{3} / \mathrm{s}\left(5 imes 10^{-5} \mathrm{~m}^{3} / \mathrm{s} ight)[/latex]. Estimate [latex]K_{L}[/latex], the overall liquid phase mass transfer coefficient for TCE across the liquid and gas film. Assume that water loss by evaporation is negligible.

Accepted Answer

Relevant physical property data are provided below. The process is very dilute so that the bulk gas has the properties of air and the bulk liquid has the properties of water. The equilibrium solubility of TCE in water is described by Henry's law of the form

[latex]p_{A}=H \cdot x_{A}[/latex]

where [latex]H[/latex] is 550 atm at [latex]293 \mathrm{~K}[/latex]. The binary gas phase diffusivity of TCE in air is [latex]8.08 imes 10^{-6} \mathrm{~m}^{2} / \mathrm{s}[/latex] at [latex]1 \mathrm{~atm}[/latex] and [latex]293 \mathrm{~K}[/latex], as determined by the Fuller-Shettler-Giddings correlation. The binary liquid-phase diffusivity of TCE in water at [latex]293 \mathrm{~K}[/latex] is [latex]8.9 imes 10^{-10} \mathrm{~m}^{2} / \mathrm{s}[/latex], as determined by the Hayduk-Laudie correlation.

With this physical property information in hand, our strategy is to estimate the gas film coefficient [latex]k_{G}[/latex], the liquid film coefficient [latex]k_{L}[/latex], and then the overall mass-transfer coefficient [latex]K_{L}[/latex]. First, the bulk velocity of the gas is

[latex]v_{\infty}=\frac{4 Q_{g}}{\pi D^{2}}=\frac{4 \cdot\left(2.0 imes 10^{-3} \frac{\mathrm{m}^{3}}{\mathrm{~s}} ight)}{\pi(0.04 \mathrm{~m})^{2}}=1.59 \frac{\mathrm{m}}{\mathrm{s}}[/latex]

The Reynolds number for air flow through the inside of the wetted wall column is

[latex]R e=\frac{ ho_{ ext {air }} v_{\infty} D}{\mu_{ ext {air }}}=\frac{\left(1.19 \frac{\mathrm{kg}}{\mathrm{m}^{3}} ight)\left(1.59 \frac{\mathrm{m}}{\mathrm{s}} ight)(0.04 \mathrm{~m})}{1.84 imes 10^{-5} \frac{\mathrm{kg}}{\mathrm{m} \cdot \mathrm{s}}}=4113[/latex]

and the Schmidt number for TCE in air is

[latex]\mathrm{Sc}=\frac{\mu_{\mathrm{air}}}{ ho_{\mathrm{air}} D_{\mathrm{TCE}-\mathrm{air}}}=\frac{1.84 imes 10^{-5} \frac{\mathrm{kg}}{\mathrm{m} \cdot \mathrm{s}}}{\left(1.19 \frac{\mathrm{kg}}{\mathrm{m}^{3}} ight)\left(8.08 imes 10^{-6} \frac{\mathrm{m}^{2}}{\mathrm{~s}} ight)}=1.91[/latex]

where the properties of air are found from Appendix I. As the gas flow is not laminar [latex](\operatorname{Re}>2000)[/latex], equation (30-17)

[latex]\frac{k_{c}D}{D_{A B}}\frac{P_{B,L B}}{P}=0.023\,\mathrm{Re}^{0.83}\mathrm{Sc}^{0.44}[/latex] (30-17)

is appropriate for estimation of [latex]k_{c}[/latex]. Therefore

[latex] \begin{gathered} k_{c}=\frac{D_{A B}}{D} 0.023 \operatorname{Re}^{0.83} \mathrm{Sc}^{0.44}=\left(\frac{8.08 imes 10^{-6} \mathrm{~m}^{2} / \mathrm{s}}{0.04 \mathrm{~m}} ight) \ (0.023)(4113)^{0.83}(1.91)^{0.44}=6.17 imes 10^{-3} \mathrm{~m} / \mathrm{s} \end{gathered} [/latex]

for a dilute solution where [latex]p_{B, l m} / P[/latex] is essentially 1 . The conversion to [latex]k_{G}[/latex] is

[latex]k_{G}=\frac{k_{c}}{R T}=\frac{6.17 imes 10^{-3} \frac{\mathrm{m}}{\mathrm{s}}}{\left(0.08206 \frac{\mathrm{m}^{3} \cdot \mathrm{atm}}{\mathrm{kg} \mathrm{mol} \cdot \mathrm{K}} ight)(293 \mathrm{~K})}=2.57 imes 10^{-4} \frac{\mathrm{kg} \mathrm{mol}}{\mathrm{m}^{2} \cdot \mathrm{s} \cdot \mathrm{atm}}[/latex]

The liquid-film coefficient is now estimated. The Reynolds number for the falling liquid film is

[latex]\operatorname{Re}_{L}=\frac{4 ho_{L} \dot{V}_{L}}{\pi D \mu_{L}}=\frac{4 \cdot\left(998.2 \frac{\mathrm{kg}}{\mathrm{m}^{3}} ight)\left(5 imes 10^{-5} \frac{\mathrm{m}^{3}}{\mathrm{~s}} ight)}{\pi \cdot(0.04 \mathrm{~m})\left(9.93 imes 10^{4} \frac{\mathrm{kg}}{\mathrm{m} \cdot \mathrm{s}} ight)}=1600[/latex]

and the Schmidt number is

[latex]\mathrm{Sc}=\frac{\mu_{L}}{ ho_{L} D_{\mathrm{TCE}-\mathrm{H}_{2} \mathrm{O}}}=\frac{\left(9.93 imes 10^{-4} \frac{\mathrm{kg}}{\mathrm{m} \cdot \mathrm{s}} ight)}{\left(998.2 \frac{\mathrm{kg}}{\mathrm{m}^{3}} ight)\left(8.90 imes 10^{-10} \frac{\mathrm{m}^{2}}{\mathrm{~s}} ight)}=1118[/latex]

where the properties of liquid water at [latex]293 \mathrm{~K}[/latex] are found in Appendix I. Equation (30-20)

[latex]{\frac{k_{L Z}}{D_{A B}}}=0.433(8{\bf c})^{1/2}\left({\frac{ ho_{L}^{2}g z^{3}}{\mu_{L}^{2}}} ight)^{1/6}({\bf R e}_{L})^{0.4}[/latex] (30-20)

is appropriate for estimation of [latex]k_{L}[/latex] :

[latex] \begin{gathered} k_{L}=\frac{D_{A B}}{z} 0.433(\mathrm{Sc})^{1 / 2}\left(\frac{ ho_{L}^{2} g z^{3}}{\mu_{L}^{2}} ight)^{1 / 6}\left(\mathrm{Re}_{L} ight)^{0.4} \ =\frac{8.9 imes 10^{-10} \frac{\mathrm{m}^{2}}{\mathrm{~s}}}{2 \mathrm{~m}} 0.433 \cdot(1118)^{1 / 2} \ \left(\frac{\left(998.2 \frac{\mathrm{kg}}{\mathrm{m}^{3}} ight)^{2}\left(\frac{9.8 \mathrm{~m}}{\mathrm{~s}^{2}} ight)(2 \mathrm{~m})^{3}}{\left(9.93 imes 10^{-4} \frac{\mathrm{kg}}{\mathrm{m} \cdot \mathrm{s}} ight)^{2}} ight)^{1 / 6}(1600)^{0.4}=2.55 imes 10^{-5} \mathrm{~m} / \mathrm{s} \end{gathered} [/latex]

Since the process is dilute, Henry's law constant in units consistent with [latex]k_{L}[/latex] and [latex]k_{G}[/latex] is

[latex]H=550 \mathrm{~atm} \frac{M_{\mathrm{H}_{2} \mathrm{O}}}{ ho_{L, \mathrm{H}_{2} \mathrm{O}}}=(550 \mathrm{~atm})\left(\frac{18 \mathrm{~kg}}{\mathrm{~kg} \mathrm{~mol}} ight)\left(\frac{1}{993.2 \mathrm{~kg} / \mathrm{m}^{3}} ight)=9.968 \frac{\mathrm{atm} \cdot \mathrm{m}^{3}}{\mathrm{~kg} \mathrm{~mol}}[/latex]

The overall liquid mass-transfer coefficient, [latex]k_{L}[/latex], is

[latex]\frac{1}{K_{L}}=\frac{1}{k_{L}}+\frac{1}{H k_{G}}=\frac{1}{2.55 imes 10^{-5} \frac{\mathrm{m}}{\mathrm{s}}}+\frac{1}{\left(9.96 \frac{\mathrm{atm} \cdot \mathrm{m}^{3}}{\mathrm{~kg} \mathrm{~mol}} ight)\left(2.57 imes 10^{-4} \frac{\mathrm{kg} \mathrm{mol}}{\mathrm{m}^{2} \cdot \mathrm{s} \cdot \mathrm{atm}} ight)}[/latex]

or [latex]k_{L}=2.52 imes 10^{-5} \mathrm{~m} / \mathrm{s}[/latex]. As [latex]K_{L} \cong k_{L}[/latex], the process is liquid film mass-transfer controlling, which is characteristic of interphase mass-transfer processes involving a large value for Henry's law constant.

Question 30.4: Trichloroethylene (TCE), a common industrial solvent, is oft...

Related Answered Questions

Estimate the distance a spherical drop of liquid water, originally 1 mm in diameter, must fall in quiet, dry air at 323 K in order to reduce its volume by 50%. Assume that the velocity of the drop is its terminal velocity evaluated at its mean diameter and that the water temperature remains at ...

Verified Answer:

Consider the remediation trench shown in Figure 30.7, a very simple process to treat contaminated wastewater before discharge to a lake or river. The remediation trench consists of a narrow outdoor open channel with an air sparger aligned along the bottom of the trench. Wastewater containing a ...

Verified Answer:

Verified Answer:

In a humidification apparatus, liquid water flows in a thin film down the outside of a vertical, circular cylinder. Dry air at 310 K and 1.013 × 10^5 Pa (1 atm) flows at right angles to the 0.076-m diameter, 1.22-m-long vertically aligned cylinder at a velocity of 4.6 m/s. The liquid film ...

Verified Answer:

The dissolution of lead from lead-soldered joints in household piping is a possible health problem. If the water flowing through the pipe is mildly acidic, then some of the lead will dissolve from the inner surface of the lead-soldered pipe section into the water. New drinking water requirements ...

Verified Answer:

Verified Answer: