Packed Column Design - Packing Height Calculation Notes

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SCHOOL OF CIVIL, ENVIRONMENTAL & CHEMICAL ENGINEERING PROC2089 PROCESS PLANT DESIGN & ECONOMICS

Packed Column Design References 1. Sinnott, R.K., (1999), “Coulson & Richardson’s Chemical Engineering Design”, Vol. 6, Chapter 11. 2. Treybal, R.E., (1981), “Mass Transfer Operations”, McGraw-Hill, Chapters 6 & 8. 3. Peters, M.S., and Timmerhaus, K.D., (2003), “Plant Design and Economics for Chemical Engineers”, McGraw-Hill, Chapter 15. 4. Walas, S.M., Chemical Process Equipment-Selection and Design”, Butterworths, Chapter 13. Packed column design - Calculation of packing height Packing height using transfer units: For the case of solute A diffusing through stagnant and nondiffusing solvent B, the packing height z in a packed column is given by the following equation: y V * 1 (1 - y e ) lm z = dy KG aP y∫2 (1- y)(y - y e )

V2, y2

L2, x2

where V* = molar flow rate of gas per unit area, kmol/h.m2 L1, x1 KG = overall gas-phase mass transfer coefficient V1, y1 a = interfacial surface area per unit volume, m2/m3 P = total pressure, atm or bar y1, y2 = mole fractions of the solute in the gas at the bottom and top of the column, respectively ye = concentration in the gas that would be in equilibrium with the liquid concentration at any point When the concentration of the solute is small (less than 10%) the above equation is simplified as y V * 1 dy z = KG aP y∫2 (y - y e ) Packing height in terms of overall liquid-phase mass transfer coefficient, KL: x L * 1 dx z = KL aC t x∫2 (xe - x)

where L* = molar liquid flow rate per unit cross-sectional area, kmol/h.m2 Ct = total molar concentration, kmol/m2 = ρL = molecular weight of solvent

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z

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2 Packing height in terms of “Transfer Units” The equation for packing height z in terms of overall gas-phase mass transfer coefficient, KG may be viewed as a product of HOG and NOG: y V * 1 dy z = H OG N OG = K G aP y∫2 (y - y e ) NOG HOG where HOG = height of an overall gas-phase transfer unit NOG = number of overall gas-phase transfer units

Similarly, the equation for packing height z in terms of overall liquid-phase mass transfer coefficient, KL may be viewed as a product of HOL and NOL x V * 1 dx z = H OL N OL = K LaC t x∫2 (xe - x ) HOL

NOL

where HOL = height of an overall liquid-phase transfer unit NOL = number of overall liquid-phase transfer units

Estimation of the number of the transfer units, NOG 1. Graphical method 2. Algebraic equation 3. Using NOG vs. y1/y2 chart

1. Graphical method y1

The integral

dy

∫ (y - y

y2

e

)

is integrated graphically between the limits y1 and y2.

2. Algebraic calculations If the operating and equilibrium lines are straight and the system involves dilute mixtures y - y2 N OG = 1 Δy lm Δy 1 − Δy 2 where Δy lm = where Δy 1 = y 1 - y e1 and Δy 2 = y 2 - y e2 ⎛ Δy 1 ⎞ ln⎜ ⎟ ⎝ Δy2 ⎠ 3. Estimation of NOG • If the equilibrium and operating lines are straight and the solvent feed is free of solute, NOG can be estimated using the following relationship:

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⎡⎛ mV *⎞ y1 1 mV *⎤ ln ⎢⎜ 1+ ⎟ ⎥ where m is the slope of the equilibrium line mV * ⎝ ⎠ y2 L * L * ⎣ ⎦ 1L* Figure 11.39 (Sinnott) is a plot of the above equation. This chart is used for quick estimate of NOG and z. Optimum value for mV*/L* = 0.7 to 0.8 N OG =

Prediction of the height of a transfer unit (HTU)

• Experimental values of HTU are available as a function of type and size of packings in Sinnott and Perry’s handbook. If experimental values are not available for the system under consideration, predictive methods are used to estimate them. HOG and HOL are estimated using the following relationships: V* H OG = H G + m HL L* L* H OL = H L + HG mV * where HG = height of a transfer unit based on gas film, m HL = height of a transfer unit based on liquid film, m

Predictive methods

HG and HL values are estimated using two methods: 1. Cornell’s method (approximate) 2. Onda’s method (preferred method) 2. Onda’s method

• this method is used to predict kG and kL values and is applicable for various packings Let aw is the effective wetted area of the packing −0 . 05 0.2 0 . 75 0 .1 2 ⎡ ⎛ L*m 2 ⎞ ⎛σc ⎞ ⎛ L*m ⎞ ⎛ L*m a ⎞ aw ⎟ ⎜ ⎟ = 1 - exp ⎢-1.45⎜ ⎟ ⎜ ⎟ ⎜ a ⎝σL ⎠ ⎢ ⎝ a μ L ⎠ ⎜⎝ ρ 2L g ⎟⎠ ⎝ ρ Lσ L a ⎠ ⎣ 2/3 1/ 3 −1 / 2 ⎛ L*m ⎞ ⎛ μ L ⎞ ⎛ ρL ⎞ kL ⎜ (ad p )0.4 = 0.0051 ⎜ ⎟ ⎜ ⎟ ⎟ ⎝ μ Lg ⎠ ⎝ a w μ L ⎠ ⎝ ρ LDL ⎠

⎛ V* ⎞ k G RT = K 5 ⎜⎜ m ⎟⎟ a Dv ⎝ a μV ⎠

0.7

⎛ μV ⎞ ⎜ ⎟ ⎝ ρ V DV ⎠

1/ 3

(ad p )-2.0

where K5 = 5.23 for packing sizes above 15 mm = 2.0 for packing sizes below 15 mm a = actual area of packing per unit volume, m2/m3 dp = packing size, m σc = critical surface tension for packing material, mN/m

⎤ ⎥ ⎥ ⎦

4 = 61 mN/m for ceramic = 75 mN/m for metal = 33 mN/m for plastic = 56 mN/m for carbon σL = liquid surface tension, N/m

Now HG and HL can be calculated using the following relationships: V* HG = kGa w P where kG = gas-film mass transfer coefficient, kmol/m2.s.atm V* = molar gas flow rate/cross-sectional area, kmol/m2.s HL =

L* k La w C t

where kL = liquid-film mass transfer coefficient, m/s L* = molar liquid flow rate/cross-sectional area, kmol/m2.s Ct = total concentration, kmol/m3 = ρL = molecular weight of solvent

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Tutorial 2 Packing height calculation 1. Ammonia content of a gas stream is reduced from 4.0 mole% to 0.5 mole% in a packed absorption tower at 293 K and 1.013 x 105 Pa. The inlet flow of pure water is 68 kmol/h and the total flow of inlet gas is 58 kmol/h. The tower diameter is 0.75 m. The packings are 25 mm Intalox saddles.

a) Estimate HOG values using Onda’s methods (Ans: 2.57 m using Onda’s method) b) Compare the packed-bed height values calculated using the HOG values obtained in the previous step NH3 -water equilibrium data are given in Table 1. 2. The gas SO2 is being scrubbed from air-SO2 mixture by pure water at 303 K and 1.013 x 105 Pa. The inlet gas contains 6.0 mole% SO2 and the outlet gas contains 0.3 mole% SO2. The tower cross-sectional area of packing is 0.44 m2. The inlet gas flow is 15 kmol inert air/h and the inlet water flow is 980 kmol inert water/h. The packing used are 38 mm Berl saddles.

Compare the packed-bed height values calculated using Onda’s methods. (Ans: 1.6 m using Onda’s method) 3. SO2 -water equilibrium data are given in Table 2. A flue gas containing 6.0% SO2 by volume is to be scrubbed with water in a tower packed with 1 inch metallic pall rings to remove the SO2 so that the exit gas will contain no more than 0.1 mole% SO2. The tower must treat 0.125 kg/s of flue gas at atmospheric pressure and 20oC and is to be designed using 60% of flooding velocity. The water flow rate is 5.0 kg/s. Operating conditions of the tower will be isothermal at 20oC and 1 atmospheric pressure.

Calculate the a) diameter of the column assuming liquid mass flow rate does not change much over the column height b) height of the packing using Onda’s method Some useful design data: At 20oC: ρL = 998 kg/m3 Average molecular weight of inlet gas = 31.1 kg/kmol -5 μv = 1.82 x 10 Pa.s DL = 1.7 x 10-9 m2/s 3 ρv = 1.29 kg/m μL = 1.00 x 10-3 Pa.s Dv = 1.45 x 10-5 m2/s The equilibrium curve, which is a plot of mole fractions of SO2 in the vapour (y) and liquid (x) phases, is nearly linear so it could be fitted by the following least-squares equation: y = 25.7x – 0.00063.

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