10.8. ESTIMATION OF MASS-TRANSFER COEFFICIENTS FOR PACKED TOWERS

10.8A. Experimental Determination of Film Coefficients

The individual film mass-transfer coefficients and depend generally upon Schmidt number, gas and liquid mass velocities, and the size and shape of the packing. The interactions among these factors are quite complex. Hence, the correlations for mass-transfer coefficients are highly empirical. The reliability of these correlations is not too satisfactory. Deviations of up to 25% are not uncommon. A major difficulty arises because it is an overall coefficient or resistance that is measured experimentally, which represents the two film resistances in series. To obtain the single-phase film coefficient, the experiment must be so arranged that the other film resistance is negligible or can be approximately calculated.

To measure the liquid film mass-transfer coefficient , a system for absorption or desorption of very insoluble gases such as O₂ or CO₂ in water is used. The experiment gives , which equals (which can give H_L), since the gas-phase resistance is negligible.

To measure the gas-phase film coefficient , we desire to use a system such that the solute is very soluble in the liquid and the liquid-phase resistance is negligible. Most such systems, for example, NH₃–air–water, have a liquid-phase resistance of about 10%. By subtracting this known liquid-phase resistance (obtained by correcting data for absorption of CO₂ or O₂ to NH₃ data for ) from the overall resistance in Eq. (10.4-24), we obtain the coefficient or H_G. Details of these systems are discussed elsewhere (G1, S1, S2).

10.8B. Correlations for Film Coefficients

Correlations for experimental coefficients can be expressed in terms of H_L and H_G or and , which are related by Eqs. (10.6-39) and (10.6-40). For the first generation of packings, such as Raschig rings and Berl saddles, extensive correlations are available (T1). However, comprehensive data on the individual coefficients H_L and H_G for the newer packings, which have higher mass-transfer coefficients and capacity, are not generally available. These newer packings are more commonly used today.

However, as an alternative method for comparing the performance of different types and sizes of these newer random packings, the system CO₂–air–NaOH solution is often used (P2, S4). Air containing 1.0 mole CO₂ at 24°C (75°F) is absorbed in a packed tower using 1.0 N (4 wt %) NaOH solution (E2, E3, P2, S4). An overall coefficient K_Ga is measured.

In this system, the liquid film is controlling but the gas film resistance is not negligible. The fast chemical reaction between NaOH and CO₂ takes place close to the interface, which gives a steeper concentration gradient for CO₂ in the water film. Hence, the value of K_Ga is muc h larger than for absorption of CO₂ in water. Because of this, these experimental values are not used to predict the absorption for other systems in towers.

These experimental results, however, can be used to compare the performances of various packings. To do this, the ratio f_p of K_Ga for a given packing to that for -in. Raschig rings at a liquid velocity G_x of 5000 lb_m/h · ft² (6.782 kg/s · m²) and G_y of 1000 lb_m/h · ft² (1.356 kg/s · m²) is obtained; these are given in Table 10.6-1. The f_p value is a relative ratio of the total interfacial areas, since the reaction of CO₂ in NaOH solution takes place in the relatively static holdup pools and in the dynamic holdup. Some f_p data have been obtained at G_y = 500 lb_m/h · ft² instead of 1000 (E3). Eckert et al. (E2) showed that there is no effect of G_y in the range of 200–1000 lb_m/h · ft² on the overall K_Ga. This is expected where the liquid film resistance controls (S1). Values of f_p for various investigators agree within ±10% or less.

10.8C. Predicting Mass-Transfer Film Coefficients

For estimating the performance H_L(H_x) and H_G(H_y) of a new packing, the values of f_p can be used to correct the experimental H_x values for oxygen absorption or desorption and the H_y value for NH₃ absorption with -in. Raschig rings. These values must also be corrected for Schmidt number, liquid viscosity, and flow rates.

1. Gas film coefficient H_y

Using the NH₃ absorption data corrected for the liquid film resistance of approximately 10%, H_G has been found to vary as G_y to an exponent between 0.3 and 0.4 (S1, T1) for values of G_y up to about 700 lb_m/h · ft² (0.949 kg/s · m²). A value of 0.35 is used. For liquid flows of G_x from 500 to 5000 lb_m/h · ft² (0.678–6.782 kg/s · m²), H_y varies as , with the value of used. Also, the value of H_y has been found to be proportional to of the gas phase. A value for H_y of 0.74 ft (0.226 m) is obtained from the correlation for -in. Raschig rings for the NH₃ system (S1) corrected for the small liquid film resistance of 10% at G_x = 5000 lb_m/h · ft² (6.782 kg/s · m²) and G_y = 500 lb_m/h · ft² (0.678 kg/s · m²). The value of G_y = 500 will be used instead of 1000, since there is no effect of G_y on f_p in this range. For the NH₃ system, N_Sc = 0.66 at 25°C. Then, for estimation of H_G for a new solute system and packing and flow rates of G_x and G_y using SI units,

Equation 10.8-1

where f_p for the new packing is given in Table 10.6-1 and H_G is in m.

2. Liquid film coefficient H_x

For gas flow rates up to loading or about 50% of the flooding velocity, the effect of G_y on H_x is small and can be neglected (S1). Using the oxygen desorption data, H_x is proportional to the liquid . The N_Sc = 372 at 25°C for O₂ in water and the viscosity μ is 0.8937 × 10⁻³ kg/m · s. Data for different packings show that H_x is proportional to (G_x/μ) to the 0.22–0.35 exponent, with an average of (G_x/μ)^0.3. A value of H_x = 1.17 ft (0.357 m), where G_x = 5000 lb_m/h · ft² is obtained from the correlation (S1) for the O₂ system and -in. Raschig rings. Then, to predict H_x for a new solute system and packing at velocities of G_x and G_y using SI units,

Equation 10.8-2

These equations can be used for values of G_y up to almost 1000 lb_m/h · ft² and G_x up to 5000 and remain below loading.

EXAMPLE 10.8-1. Prediction of Film Coefficients for CO2 Absorption Predict HG, HL, and HOL for absorption of CO2 from air by water in a dilute solution in a packed tower with -in. metal Pall rings at 303 K (30°C) and 101.32 kPa pressure. The flow rates are Gx = 4.069 kg/s · m2 (3000 lbm/h · ft2) and Gy = 0.5424 kg/s · m2 (400 lbm/h · ft2). Solution: From Appendix A.3-18, for CO2 at 1 atm, pA = 1.86 × 103xA. Hence, yA = pA/1.0 = 1.86 × 103xA (mole fraction units). Also, from Appendix A.3-3 for air at 303 K, μ = 1.866 × 10−5 kg/m · s and the density ρ = 1.166 kg/m3. The diffusivity for CO2 at 276.2 K from Table 6.2-1 is 0.142 × 10−4 m2/s. Correcting this to 303 K by Eq. (6.2-45), DAB = 0.142 × 10−4 (303/276.2)1.75 = 0.1670 × 10−4 m2/s. Hence, From Table 10.6-1 the relative mass-transfer coefficient for -in. metal Pall rings compared to that for -in. Raschig rings is fp = 1.34. Substituting into Eq. (10.8-1), From Appendix A.2-4, the viscosity of water at 303 K is 0.8007 × 10−3 kg/m · s and the density ρ = 995.68 kg/m3. At 298 K the viscosity of water is 0.8937 × 10−3 kg/s · m. From Table 6.3-1, the DAB of CO2 in water is 2.00 × 10−9 m2/s at 25°C. Using Eq. (6.3-9) to correct it to 303 K, DAB = (0.8937 × 10−3/0.8007 × 10−3)(303/298) (2.00 × 10−9) = 2.270 × 10−9 m2/s. Then, Substituting into Eq. (10.8-2), To calculate the value of HOL, the molar flow rates are calculated, where for dilute air, V = Gy/MW = 0.5424/28.97 = 0.01872 kg mol/s · m2, and for water, L = Gx/MW = 4.069/18.0 = 0.2261 kg mol/s · m2. Substituting into Eq. (10.6-58), The percent resistance in the gas film is 0.001575(100)/0.2322 = 0.68%. This shows that for a very insoluble gas, even though HG is similar in value to HL, the large value of m causes the gas-phase resistance to be very small. Hence, HOL ≅ HL. For a soluble gas like NH3, where m = 1.20 at 303 K compared to 1.86 × 103 for CO2, the percent resistance in the gas film would be about 90%. (See Problem 10.8-1.) The different gas and liquid Schmidt numbers for NH3 would have only a small effect on the results.