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Evaporation_examples_from_Chapter_04

Evaporation_examples_from_Chapter_04 - 4.5 Evaporation and...

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4.5 Evaporation and Diffusion 4.5.4 Evaporation and Diffusion through Quiescent Air (page 286) z y a,1 , y j,1 or P a,1 , P j,1 volatile liquid (species j) z 1 y a,2 , y j,2 or P a,2 , P j,2 z 2 diffusion of contaminant (j) diffusion of air (a) bulk motion of air and j Figure 4.10 Evaporation of a volatile liquid (species j) from a container open at the top, partially filled with the volatile liquid. The evaporation mass flow rate (mass per time) is given in all cases by evap,j j j mN M = ± A (4-46) A log mean mol fraction (y am ) and a log mean partial pressure ratio (P am ) are defined as a,2 a,1 am a,1 yy y y ln y =    (4-53) and ( ) a,1 am a,1 PP P P ln P = (4-54) The mass transfer coefficient is defined as k G . For pure diffusion, k G is () ja G u21 a k RTz z y = D m (4-59) or, ja G a m P k z P = D (4-60) The molar flux (N j ) can be expressed as ( ) jG j , 1j , 2 Nk P y y =− (4-61) Alternatively, the molar flux (N j ) can be written instead as ( ) ( ) j G u molar,j,1 molar,j,2 G j,1 j,2 N kRTc c k P P = (4-62) Usually, points 1 and 2 correspond to the liquid-gas interface (subscript i) and the top of the container or tank (subscript 2 in Figure 4.10) respectively.

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Example 4.10 - Evaporation of PERC from a Nearly Empty Drum Given : A dry cleaning establishment uses perchloroethylene, commonly called PERC or “perk” (Cl 2 C=CCl 2 , CAS 127-18-4), as the fluid to clean clothes. PERC is a colorless liquid with a chloroform-like odor and a PEL of 100 PPM. The liquid arrives in a 55-gallon drum and is transferred to the cleaning equipment. A nearly empty drum with an open top is improperly stored inside the facility and a small pool of PERC in the bottom of the drum evaporates into the workplace. The drum has a cross-sectional area of 0.25 m 2 and a height, (z 2 – z 1 ), of 0.813 m. From the MSDS and Appendices A.8, A.9, and A.20, PERC has the following properties: - M = 165.8, ρ = 1.62 g/cm 3 - odor recognition threshold (high value) = 69. PPM - boiling point (BP) = 250. o F - vapor pressure, P v (at 20 ° C) = 14.0 mm Hg - D ja = 0.74 x 10 -5 m 2 /s To do : Estimate the rate at which PERC evaporates. Solution : In the far-field, P a,2 = P, since P j,2 0. At the liquid interface, the partial pressure of the PERC is equal to the vapor pressure at standard atmospheric conditions, P j,1 = 14.0 mm Hg. Thus, ( ) a,1 j,1 P P P 760. 14.0 mm Hg 746. mm Hg =− = = From Eq. (4-54), () a,2 a,1 am a,1 PP 760. 746. mm Hg P 753.0 mm Hg 760. P ln ln 746. P == =      The mass transfer coefficient (k G ) can be obtained from Eq. (4-60), ( ) 2 5 ja G 2 u21 a m m 760 mm Hg 0 74 10 s P kJ kN k kJ RTz z P kNm kPa m 8 314 293 15 K 0 813 m 753 0 mm Hg kmol K .. D . . . × −⋅ 9 G 2 kmol k 3 769 10 kPa m s . The molar flux is then found from Eq. (4-62), jG j , 1 j , 2 9 9 2 2 NkP P kmol 101.3 kPa kmol 3.769 10 14.0 0 mm Hg 7.034 10 760.0 mm Hg kPa m s m s =   ⋅⋅ Finally, the mass flow rate of the PERC is obtained from Eq. (4-46), 92 evap,j j j 2 kmol kg m N M A 7.034 10 166.0 0.25 m kmol ms ==× = -7 kg 2.92×10 s ± which is approximately 1.03 g/hr.
4.5.5 Evaporation of Single Component Liquids (page 291) U z N j U(z) P j (z) U P j, liquid air and vapor Figure 4.12

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Evaporation_examples_from_Chapter_04 - 4.5 Evaporation and...

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