Mass transfer in plate columns

M.M. Sharma, R.A. Mashelkar, V.D. Mehta

► To cite this version:

M.M. Sharma, R.A. Mashelkar, V.D. Mehta. Mass transfer in plate columns. British Chemical Engineering, 1969, 14 (1), pp.70-76. hal-03650360

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mixture was taken and absorbed completely in aqueous potassium iodide solution in the case of chlorine and aqueous sodium hydroxide solution containing 1% wt/wt glycerol in the case of sulphur dioxide. The amount of chlorine and sulphur dioxide was determined iodometrically.

Amount of sodium dimethyldithiocarbamate in a mixture of sodium dimethyldithiocarbamate and sodium tetramethylthiuram disulphide was found by first filtering out the disulphide and then titrating the dithiocarbamate with standard iodine solution using starch as an external indicator.

Carbon dioxide was absorbed in a known volume and strength of aqueous sodium hydroxide solution (≈ 2 N). The total amount of the sodium hydroxide and sodium carbonate was determined by titrating the solution against standard hydrochloric acid solution using methyl orange as an indicator. The amount of sodium hydroxide in the solution was determined by precipitating carbonate as barium carbonate by the addition of sufficient amount of barium chloride and then titrating the same solution against standard hydrochloric acid solution using thymol blue as an indicator. The difference in the above two readings gave the amount of carbonate in the solution.

Carbon dioxide was also absorbed in aqueous solutions of lithium hydroxide (≈ 1 to 3 N) and barium hydroxide (≈ 0.2 M). The amount of unreacted hydroxide in the lithium hydroxide solution was determined by precipitating the soluble carbonate as barium carbonate by addition of sufficient amount of barium chloride and then titrating the same solution against standard hydrochloric acid solution using thymol blue as an indicator. The amount of unreacted hydroxide in aqueous solution of barium hydroxide was determined by titrating the clear solution against standard hydrochloric acid using thymol blue as an indicator. Carbon dioxide was absorbed in aqueous solutions of mono-ethanolamine and diethanolamine. The amount of carbon dioxide in the solution was found by adding a known amount of dilute sulphuric acid solution (at least 30% in excess of the likely requirements) which results in decomposing the carbamate into carbon dioxide. The volume of carbon dioxide evolved was then measured in an Orsat type of apparatus.

Carbon dioxide was absorbed in a known volume and strength of aqueous sodium carbonate-sodium bicarbonate solution. A known amount of the feed solution was added to a known volume of 0.1 N caustic soda solution so as to convert all the bicarbonate to carbonate; which was precipitated along with the rest of the carbonate as barium carbonate by adding an excess of 25% barium chloride solution. The unreacted sodium hydroxide was titrated against standard hydrochloric acid using phenolphthalein as an indicator. The same was repeated for the product solution. The bicarbonate formed was obtained by taking the difference of the two readings corresponding to the feed and the product solution.

Cuprous chloride was analysed by the modification of the method used for estimating ferrous ions. To the cuprous chloride solution was added a known volume of ferric chloride solution. This reacts with cuprous chloride according to the equation

$$CuCl + FeCl_3 = CuCl_2 + FeCl_3$$

The ferrous chloride was titrated against standard potassium dichromate solution using barium diphenylamine sulphonate as an indicator. The details of the methods have been reported by VOGEL (2).

### Apparatus

Work at essentially atmospheric pressure and a temperature of 30 ± 2°C was carried out in the following columns.

(a) A 15.5 cm i.d. perspex column fitted with a 7.5 cm (3 in. mild steel) or 10 cm (4 in. stainless steel) bubble cap at the centre.

(b) A 10 cm i.d. perspex column fitted with a 7.1 cm diameter stainless steel bubble cap at the centre.

(c) A 22.5 cm square model bubble cap stainless steel column having one side of perspex and provided with a perspex window on the opposite side, and fitted with a 10 cm (4 in. stainless steel) bubble cap at the centre and quarter

<table><caption>TABLE I—Details of bubble caps</caption><thead><tr><th>Cap specifications</th><th>7.5 cm cap<br>in<br>15.5 cm i.d.<br>column</th><th>10 cm cap<br>in<br>15.5 cm i.d.<br>column</th><th>7.1 cm cap<br>in<br>10 cm i.d.<br>column</th><th>10 cm cap<br>in<br>22.5 cm i.d.<br>column</th></tr></thead><tbody><tr><td>Material of construction</td><td>MS</td><td>SS</td><td>SS</td><td>SS</td></tr><tr><td>Diameter, cm</td><td>7.5</td><td>10</td><td>7.1</td><td>10</td></tr><tr><td>Height, cm</td><td>5.5</td><td>5.5</td><td>4.9</td><td>6.3</td></tr><tr><td>Inside diameter of the<br>riser, cm</td><td>4.55</td><td>6.4</td><td>4.5</td><td>6.7</td></tr><tr><td>Type of slots</td><td>Rectangular</td><td>Trapezoidal</td><td>Rectangular</td><td>Trapezoidal</td></tr><tr><td>Slot height, cm</td><td>2.51</td><td>2.5</td><td>1.6</td><td>2.3</td></tr><tr><td>Slot width, cm</td><td>0.6</td><td>top 0.5</td><td>0.5</td><td>top 0.2</td></tr><tr><td></td><td></td><td>bottom 1:2</td><td></td><td>bottom 0:8</td></tr><tr><td>Skirt clearance, cm</td><td>Zero</td><td>1.5</td><td>1</td><td>1</td></tr></tbody></table>

bubble caps at the four corners. Details of this column are given in Fig. 1. This is likely to act as a representative section of a large bubble cap plate column.

The pertinent details of the bubble caps are given in Table I.

It was found necessary to use a variety of columns mentioned above. Thus (for instance) for economic reasons Freon-12 as a carrier gas could be used only in the case of 10 cm diameter column. Most of the preliminary experiments for assessing the importance of various variables were done in 10 and 15.5 cm diameter columns. The 22.5 cm square column was used to obtain data which are likely to be useful for the design of industrial columns.

The small perforated plate column consisted of a glass tube of 3.6 cm i.d. The gas was sparged through a perforated plate, the details of which are given below.

Hole diameter = 1.985 mm.

No. of holes = (9 and 17) on triangular pitch.

Percentage perforated area = 2.78 and 5.4%.

Material of construction = stainless steel and perspex.

This column was made of glass so that any significant change in the hydrodynamic behaviour due to a change in the carrier gas, viscosity, ionic strength or the presence of solids could be visually observed.

### Experimental

The experimental set-up used in the case of bubble cap plate column is given in Fig. 2.

Flow rates of the solute gas (ammonia, carbon dioxide, sulphur dioxide, chlorine) and the carrier gas (air, Freon-12, Freon-22, Freon-114) were adjusted to give from 0.5 to 10% of the solute in the gas mixture. The solute gas was metered either by a soap film meter or an accurately calibrated rotameter and the carrier gas was metered by a calibrated rotameter. A known volume of the absorbent was introduced into the column and the stop-watch started at the moment the solute gas was introduced in the column. The pressure of the gas mixture entering the column and temperature of the gas entering and leaving the column was recorded. The temperature of the absorbent at the beginning and at the end of the experiment was also recorded. After a definite time (varying from 5 to 45 min.), the liquid was taken out and analysed for the solute content. In the studies on the effect of solids formation on the value of effective interfacial area, a sample of the absorbent from the plate was withdrawn after definite intervals of time by means of a sample tube. The gas holdup tends to increase with an increase in the amount of solids on the plate, and hence even after a continuous withdrawal of the liquid from the plate, the submergence could be kept constant within ± 5%.

For the absorption of triethylamine, it was vapourised with air in a packed column, in the case of a bubble cap plate column and in a small sintered disc bubber in the case of the small perforated plate column. The outlet gas mixture from the packed column or the sintered disc bubber was analysed for the amine content. Then triethylamine vapour-air mixture was mixed with air to give about 1% of triethylamine in the gas mixture and then fed to the bubble cap plate column and the small perforated plate column.

Fresh solutions were always prepared in the case of air oxidation of cuprous chloride under neutral and acidic conditions, so as to minimise the error due to the oxidation by oxygen in the atmosphere. In the case of studies on the effect of solid on mass transfer the solutions were analysed after filtering the solution before and after a run.

<figure><img src="image_1.png" /><figcaption>Fig. 2 Experimental set up for the bubble cap plate column. 1—Gas cylinder. 2—Buffer vessel. 3—Rotameter. 4—Storage for liquid to be vapourised. 5—Capillary flowmeter. 6—Packed column. 7—Trap. 8—Scrubber. 9—Barometer. 10—Soap film meter. 11—Blower. 12—Liquid storage bottle. 13—Storage of absorbent liquid. 14—Bubble cap plate column. 15—Trap.</figcaption></figure>

The set up shown in dotted lines was used for the vapourisation of triethylamine.
<figure><img src="image_2.png" /><figcaption>**Fig. 3** Effect of ionic strength and viscosity on the effective interfacial area in perforated plate column. Superficial gas velocity
Submergence = 21 cm/sec
= 10 cm</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Fig. 4** Effect of solids formation on the effective interfacial area in 15-5 cm diameter bubble cap plate column. Superficial gas velocity
Submergence = 80 cm/sec
= 20 cm
● Ba(OH)$_2$ - CO$_3$
○ LIOH - CO$_3$</figcaption></figure>

For the evaluation of the interfacial area by the method of absorption accompanied by fast pseudo-first order reaction, values of the specific rate of absorption in some typical cases were experimentally found out by using a laminar jet apparatus. The principal design features of the apparatus were akin to those used by SHARMA and DANCKWERTS (3) and it was the same as that used by JHAVERI and SHARMA (4). By a combination of different jet diameter and lengths and liquid flow rate it was possible to cover a range of contact times from 0-019 to 0-04 sec.

In the case of absorption of oxygen from air into the aqueous solutions of cuprous chloride containing 3 M $CuCl_2$, the values of specific rate of absorption were found by using a stirred cell with pure oxygen. The stirred cell was the same as that used by JHAVERI and SHARMA (4) and had an effective interfacial area of 53 cm². A perspex stirrer with four flat blades was used.

In the case of some crucial systems which exhibit rather low gas phase diffusivities, experimental values of the diffusivities were obtained and compared with the predicted values. The method adopted was based on the original method of STEFAN and WINKELMAN and subsequently modified by LEE and WILKE (5). The liquid to be evaporated was contained in the vertical limb of a tube (6 mm i.d.), which was immersed in a constant temperature water bath. The carrier gas at the rate of about 1 cm³/sec was passed, which entered through the horizontal section of the tube. The pressure of the gas was recorded and the volume of the gas leaving the tube was metered by a soap film meter. The walls of the tube were of glass and the level of the liquid in the tube was measured by a travelling microscope. The values of the liquid level were recorded. The values of diffusivity were calculated in the manner suggested by RICHARDSON (6).

## Results and discussion

### Effective interfacial area

The theory of absorption accompanied by fast pseudo-first order reaction was used for finding the effective interfacial area under various hydrodynamic conditions. When the concentration of the reactant in the neighbourhood of the surface is very little different from that in the bulk, the dissolved gas undergoes a pseudo-first order reaction. The DANCKWERTS' model (7) then gives the specific rate of absorption $R$, g mole/cm² sec., as:

$$R = C^* \sqrt{Dk_2 [B]} + k_L^2 \quad \dots (1)$$

The condition to be satisfied is:

$$\sqrt{D k_2 [B]} \ll k_L (1 + [B]/ZC^*) \quad \dots (2)$$

where $k_2$ = second order reaction rate constant, cm³/g mole sec.; $D$ = diffusivity of the dissolved gas, cm³/sec.; $[B]$ = concentration of the reactant in the bulk of the solution, g mole/cm³; $k_L$ = liquid side mass transfer coefficient without reaction, cm/sec.; $Z$ = number of moles of the reactant reacting with one mole of the dissolved gas, and $C^*$ = solubility of the gas in the solution, g mole/cm³. When

$$Dk_2 [B] \gg k_L^2 \quad \dots (2a)$$

we get

$$R = C^* \sqrt{Dk_2 [B]} \quad \dots (3)$$

The specific rate of absorption then becomes independent of the

hydrodynamic conditions and becomes a unique function of the physico-chemical properties of the system.

Absorption of lean carbon dioxide in aqueous solutions of sodium hydroxide and monoethanolamine serve as convenient systems to be used for finding the values of the effective interfacial area. The relevant physico-chemical data are available (8) and, in some cases were experimentally obtained.

There was some gas-side resistance which was taken into account for evaluating the values of effective interfacial area. For this purpose the overall gas-side mass transfer coefficients obtained in this work were used with the necessary corrections.

JHAVERI and SHARMA (4) have studied the kinetics of oxidation of cuprous chloride, which gives two main products, copper oxychloride under neutral conditions and cupric chloride under acidic conditions:

$$6 \text{ CuCl} + 3/2 \text{ O}_2 + 3 \text{ H}_2\text{O} = (3 \text{ CuO.CuCl}_2 \cdot 3 \text{ H}_2\text{O}) + 2 \text{ CuCl}_2 \quad \dots (4)$$

$$4 \text{ CuCl} + 4 \text{ HCl} + \text{O}_2 = 4 \text{ CuCl}_2 + 2 \text{ H}_2\text{O} \quad \dots (5)$$

The above reactions are second order in $[Cu^+]$ and first order in $[O_2]$. Under the conditions when absorption is accompanied by fast pseudo-first order reaction, the specific rate of absorption of gas will be given by

$$R = C^* \sqrt{D k_2 [B]^2} \quad \dots (6)$$

where $k_2$ = third order reaction rate constant (1/g mole)² sec⁻¹. The equation for the rate of absorption into a batch of liquid $i$,

$$- \frac{d [B]}{dt} = 4 Ra \quad \dots (7)$$

$$a = \frac{\ln [B]_i/[B]_f}{4 C^* t \sqrt{Dk_2}} \quad \dots (8)$$

where $a$ = effective interfacial area per unit volume, cm³/cm²; $[B]_i$ = initial concentration of cuprous chloride, g mole/l; $[B]_f$ = final concentrations of cuprous chloride, g mole/l, and $t$ = time of reaction, sec.

Equation 6 holds if,

$$Dk_2 [B]^2 \gg k_L^2 \quad \dots (9)$$

and

$$Dk_2 [B]^2 \ll k_L [B]/4 C^* \quad \dots (10)$$

When $k_L$ is significant compared to the term $Dk_2 [B]^2$, the value of effective interfacial area will be given by

$$a = \ln \left\{ \frac{[B]_i + \sqrt{[B]_i^2 + k_L^2/Dk_2}}{[B]_f + \sqrt{[B]_f^2 + k_L^2/Dk_2}} \right\} + 4 C^* t \sqrt{Dk_2} \quad \dots (11)$$

The relevant physico-chemical data required for the evaluation of effective interfacial area were taken from the work by JHAVERI and SHARMA (4).

Sample calculation for the evaluation of the effective interfacial area
System: Air-carbon dioxide and aqueous solution of sodium hydroxide.

(1) Column: 22.5 cm square column with a 10 cm diameter bubble cap at the centre and quarter bubble caps of 10 cm diameter at the four corners.

(2) Gas flow rate 25-791 l/sec.; superficial gas velocity = 51-5 cm/sec.

(3) Initial normality of NaOH: 2.699 N.

(4) Final normality of NaOH: 2.134 N.

(5) Inlet % of $CO_2$: 1-388.

(6) Outlet % of $CO_2$: 1-162.

(7) Average temperature of the liquid: 32-5°C.

(8) Overall mass transfer coefficient: $2.35 \times 10^{-4}$ g mole/cm² of dispersion atm sec.

The gas-side mass transfer coefficient ($k_g a$) for air-sulphur dioxide system, under similar hydrodynamic conditions is $4.05 \times 10^{-4}$ g mole/cm² atm sec.

The diffusivity of carbon dioxide in air is slightly different than that of sulphur dioxide in air and therefore the diffusivity correction is applied assuming that

$$k_g a \propto D_g t^{-5}$$

Therefore, the gas-side mass transfer coefficient for the case under consideration:

$$k_g a = \begin{aligned} & 4.05 \times 10^{-4} \sqrt{0.165/0.151} \text{ g mole/cm}^3 \text{ atm sec.} \\ & = 4.23 \times 10^{-4} \text{ g mole/cm}^3 \text{ atm sec.} \end{aligned}$$

The following equation gives the relationship between the overall
mass transfer coefficient and the individual mass transfer coefficients.

$$ \frac{1}{k_{\text{ga}}} = \frac{1}{k_{\text{ga}^2}} + \frac{1}{H k_{\text{Lna}}} \quad \dots \quad (12) $$

where $k_{LR}$ is the liquid-side mass transfer coefficient with reaction, which in this case is given by,

$$ k_{LR} = \sqrt[3]{Dk_{s}[B]} \text{ cm/sec.} \quad \dots \quad (13) $$

$H$ = Henry's constant, g mole/cm³ atm.

The solubility of CO₂ in an electrolyte solution can be estimated by using the expression given by SHARMA and DANCKWERTS (8)

$$ \log H/H_w = -K_s I $$

where $H$ = solubility of CO₂ in electrolyte solution, g mole/cm³ atm; $H_w$ = solubility of CO₂ in water, g mole/cm³ atm; $K_s$ = $t_4 + L + t_6$ l/g ion; $t$ = contribution due to various species, l/g ion, and $I$ = ionic strength, g ion/l.

The values of $K_s$ have been reported by VAN KREVELEN and HOFTIZER (9).

Solubility of CO₂ in water at 32.5°C in water = 2.51 × 10⁻⁴ g mole/cm³ atm. The initial solution contained 0.07 M Na₂CO₃. Taking this into account, reduction factor for the solubility of carbon dioxide = 0.416. Therefore, solubility of carbon dioxide in the aqueous hydroxide solution = 1.04 × 10⁻⁵ g mole/cm³.

The value of second order reaction rate constant was evaluated from the data reported by DANCKWERTS and SHARMA (8). It was assumed that the relative effect of the ionic strength on second order reaction rate constant is independent of temperature in the range of 20 to 35°C. The value of $k_s$ in the above solution at 32.5°C is equal to 39,600 l/g mole sec. The diffusivity of dissolved carbon dioxide in aqueous sodium hydroxide solution was obtained by assuming that $D_{L\mu}/T$ is constant.

Here $\mu$ is the viscosity of the solution and $T$ is the absolute temperature, °K.

The viscosity of the above aqueous sodium hydroxide solution was determined at 32.5°C by Ostwald Viscometer No. 1 and was found to be 1.47 cP. Hence $D_L$ = 1.22 × 10⁻⁵ cm²/sec.

On substitution of the above values in Equation 12, $Hk_{LR}$ works out to be 1.19 × 10⁻⁵ g mole/cm³ atmsec.

The value of $Hk_{LR}$ was found experimentally in a laminar jet apparatus and was found to be 1.232 × 10⁻⁵ g mole/cm³ atmsec. Thus the difference between the estimated value and the experimentally found value is only 3.5%.

The value of $Hk_{LR}$ found experimentally is now corrected for the change in average concentration of sodium hydroxide. (Since the change in initial and final normality of sodium hydroxide solution is only about 17%, an arithmetic average may be taken.)

$$ \begin{aligned} \text{Thus } Hk_{LR} &= (1.232 \sqrt{2.416}/2.699) \times 10^{-5} \text{ g mole/cm}^2 \text{ atmsec.} \\ &= 1.17 \times 10^{-5} \text{ g mole/cm}^2 \text{ sec.} \end{aligned} $$

The conditions for the validity of pseudo-first order reaction were satisfied. The value of $k_L$ obtained experimentally under similar hydrodynamic conditions by using aqueous sodium carbonate-bicarbonate buffers is 0.044 cm/sec. The value of $k_L$ for the above conditions is obtained by assuming that $k_L \propto D_{L0}^{-1}$.

$$ \begin{aligned} \text{Thus } k_L &= 0.044 \sqrt{1.22/1.81} \times 10^{-5} \text{ cm/sec.} \\ &= (0.044) \times (0.821) \text{ cm/sec.} \\ &= 0.0361 \text{ cm/sec.} \end{aligned} $$

This value is in reasonable agreement with that calculated by the correlation proposed by ANDREW (10).

Conditions 2 and 2a are satisfied.

$$ \begin{aligned} \sqrt{Dk_2[B]} &= 1.155 \ll k_L (1 + B/2 C^*) = 300 \\ \sqrt{Dk_2[B]} &= 1.335 \gg k_L^2 = 13 \times 10^{-4} \end{aligned} $$

Thus the values of $k_{ga}$, $k_{ga}$ and $k_{LR}$ may be substituted in Equation 12, when we get $a = 2.29 \text{ cm}^3/\text{cm}^3$.

Now $a'$, the effective interfacial area per unit floor area is given by,

$$ \begin{aligned} a' &= a \times S \\ &= 2.29 \times 12.6 \\ &= 28.8 \text{ cm}^2/\text{cm}^3 \text{ of floor area} \end{aligned} $$

where $S$ = submergence.

(Note that the submergence as defined here is the height of the bubble travel and is measured as the distance from half of the slot height to the top of the dispersion.)

### Bubble cap plate column

In the case of bubble cap plate column, interfacial areas determined under similar hydrodynamic conditions where lean carbon dioxide gas was absorbed in aqueous solutions of sodium hydroxide and

monoethanolamine were the same, but when aqueous solution of diethanolamine was used, the value of effective interfacial area was about 23% lower than that obtained from sodium hydroxide and monoethanolamine solution. This may be due to the higher values of $Dk_3[B]$ reported for diethanolamine solution in the literature. A similar behaviour was observed by VIDWANS in a packed column (11).

It appears from the above observation that the presence of electrolytes or the ionic strength is unlikely to affect the value of the effective interfacial area in a bubble cap plate column.

### Small perforated plate column

The values of effective interfacial area were also found by absorbing CO₂ diluted with air (≈ 1%), in aqueous sodium hydroxide solutions. An increase of the average normal strength from 1 to 4.5 N resulted in increasing the viscosity from 1 to 2.5 cP. Fig. 2 shows the values of effective interfacial area against the average normality of the sodium hydroxide solution. The curve indicates a distinct increase in the value of effective interfacial area with increasing concentration of sodium hydroxide.

Two systems were chosen, one containing 3 M CuCl₂ in HCl along with CuCl (average ionic strength = 10.5) and other containing solution of CuCl in 5 N HCl (average ionic strength ≈ 6). The viscosity of the two solutions were 2·3 and 0·998 cP respectively. It was found in the case of small perforated plate column the values of effective interfacial area for the above two solutions were 14.5 and 6 cm²/cm³ respectively, when the ionic strength was varied from 10.5 to 6 g ion/l. It appears therefore that in the case of the perforated plate column, there is a considerable effect of both ionic strength and viscosity on the value of effective interfacial area.

The effect of ionic strength on the bubble size and effective interfacial area has been well recognised (12-15). In an electrolyte solution there are small ionic bubbles, the presence of which can be explained by the electrostatic potential at the gas-liquid interface. Their size is very small. The interfacial area and the residence time provided by these ionic bubble clouds are disproportionate to the amount of gas contained in these small volumes. The presence of these small bubbles in electrolyte solutions can be observed when the supply of the gas to the column is discontinued and the calming down of the solutions is observed.

### Bubble cap plate column

The effect of the presence of solids which were generated *in situ* on the value of effective interfacial area was studied by absorbing carbon dioxide diluted with air in aqueous solutions of lithium hydroxide and barium hydroxide in the case of bubble cap plate column. Fig. 5 shows the effective interfacial area against the average solids concentration. It is found that the values of effective interfacial area are little affected by the presence of solids on a bubble cap plate column. This observation is important in the cases where there is a possibility of a sludge formation.

### Small perforated plate column

Fig. 5, however, shows that the values of effective interfacial area, although higher than that in the case of no solid formation, tend to decrease as the solids concentration increases in the case of a perforated plate column. In the case of bubble contactors also a similar behaviour was observed (12). The solid particles generated *in situ* are likely to prevent the coalescence of the bubbles and thus

<figure><img src="image_4.png" /><figcaption>Fig. 5 Effect of solids formation on the effective interfacial area and gas-side mass transfer coefficient in perforated plate column. Superficial gas velocity ≈ 21 cm/sec</figcaption></figure>

Submergence ≈ 10 cm
● Effective interfacial area.
○ Gas-side mass transfer coefficient.

alter the hydrodynamics in the cases where there is a fine dispersion. It is conceivable that the quantity of the particles as also the size of the particles are likely to play an important role on the effective interfacial area.

### Bubble cap plate column

When the values of effective interfacial area in the presence of solids on a bubble cap plate column are compared with the values
<figure><img src="image_5.png" /><figcaption>Fig. 6 Effect of superficial gas velocity on a', the effective interfacial area, cm³/cm³, in bubble cap plate column.</figcaption></figure>

Δ 22.5 cm square column, submergence = 13 cm.
○ 15.5 cm diameter column, submergence = 11 cm.

<figure><img src="image_6.png" /><figcaption>Fig. 7 Effect of submergence on a', the effective interfacial area, cm³/cm³, in bubble cap plate column.</figcaption></figure>

Δ 22.5 cm square column, superficial gas velocity = 88 cm/sec.
● 22.5 cm square column, superficial gas velocity = 51.5 cm/sec.
○ 15.5 cm diameter column, superficial gas velocity = 120 cm/sec.

<figure><img src="image_7.png" /><figcaption>Fig. 8 Effect of submergence on effective interfacial area in perforated plate column.</figcaption></figure>

Superficial gas velocity = 21 cm/sec.

<figure><img src="image_8.png" /><figcaption>Fig. 9 Effect of liquid viscosity on the gas-side mass transfer coefficient (15.5 cm diameter column).</figcaption></figure>

Submergence = 11 cm.
○ Superficial gas velocity = 120 cm/sec.

Δ Superficial gas velocity = 68.5 cm/sec.

of effective interfacial area in the absence of solids, it is found that in the case of Ba(OH)₂, the values tend to be slightly higher, whereas in the case of LiOH, they are slightly lower. This may be attributed to the uncertain values of C*√Dk₃ [B] for the above two systems. The values of C*√Dk₃ [B] for the LiOH-CO₂ system were taken from the work of NUSING and KRAMERS (16). The values of rate constants reported by NUSING and KRAMERS are about 20% lower than those reported by other workers and hence the necessary correction was applied. The rate constants for the systems Ba(OH)₂-CO₂ were assumed to be the same as that for the system NaOH-CO₂ at equal ionic strengths.

Fig. 6 shows that a', the effective interfacial area per unit floor area varies as 0.5 power of the gas flow rate.

Fig. 7 shows that a' varies as 5/6 power of the submergence.

### Small perforated plate column

When the submergence was increased in the small perforated plate column, the effective interfacial area decreased drastically (Fig. 8). This is conceivable since the quality of the dispersion suffered considerably at very high submergences. Further in a small column such as the above, wall effects and end effects are also likely to be present.

Experiments were done in the small perforated plate column with plates of percentage perforated area of 2.78 and 5.4% respectively. The values of overall gas-side mass transfer coefficient obtained in the case of 5.4% perforated area plate were about 8% higher than that in the case of 2.75% perforated area plate. It

appears that percentage perforated area is not very important at any given superficial gas velocity.

### Bubble cap plate column

Experiments conducted in the 15.5 cm diameter perspex column fitted with 7.5 or 10 cm bubble cap at the centre gave the same gas-side mass transfer coefficient for the absorption of sulphur dioxide (carrier gas-air) in aqueous solutions of sodium hydroxide at practically the same superficial velocities of the gas. Also experiments conducted in the 10.0 cm diameter perspex column fitted with a 7.1 cm bubble cap at the centre with different design of slots (see Table I) gave the same gas-side mass transfer coefficients for the absorption of sulphur dioxide (carrier gas-air) in aqueous solutions of sodium hydroxide at the same superficial velocities of the gas. This indicates that the size of the cap and the type of slots are unlikely to be important in so far as the mass transfer coefficient is concerned. This is also in conformity with the information available in the literature (17), that slots have little, if any, effect on vapour-liquid contacting over the usual range of operating conditions when the slots are at least three-fourths open.

Fig. 9 shows that k_ga values for the absorption of sulphur dioxide (carrier gas-air) in aqueous sodium hydroxide solutions are independent of the viscosity of the solution. The viscosity of the solution was varied from 1.25 to 3.0 cP by increasing the normality of the solution from about 1.8 to 5.2 N. Viscosities from 4.6 to 9.3 cP were obtained by adding sugar to the aqueous sodium hydroxide solution and the viscosity of 10.8 cP was obtained by adding glycerine to an aqueous sodium hydroxide solution. It can be seen from Fig. 4 that at relatively high viscosity and a low gas velocity, there is a decrease (about 10%) in the value of k_ga, but at higher velocities, the values of k_ga are almost independent of the viscosity of the absorbent. A plausible explanation is that at low velocities when the slots in a bubble cap open to an extent less than about three-fourths of the height of the slot, then the hydrodynamic behaviour of the system is perhaps dependent on the viscosity of the system. However, when slots are open to an extent greater than three-fourths of the height of the slots then the hydrodynamic behaviour is unlikely to be dependent on the viscosity of the absorbent. To some extent the effect could be visually observed at low velocities. The gas flow rate required to fully open the slot, as calculated by the equation reported by CROSS and RYDER (18) is 34 l/s in the case of 10 cm bubble cap fitted in a 15.5 cm diameter column. The corresponding flow rate required to open the slots to an extent equal to three-fourths of the height of the slot was found to be 15 l/s. (The gas flow rate at which k_ga was found to be independent of viscosity (Fig. 9) was 21.3 l/s.)

A five-fold variation in gas-side diffusivity was obtained in the case of 10 cm diameter column, whereas three-fold variation was obtained in the case of 15.5 cm diameter column. The range covered was limited because of the high flow rates of the gas in which case for economic reasons only air could be used as carrier gas and only in some cases Freon-12 could be used as a carrier gas. Fig. 10 shows that k_ga varies as 0.5 power of the diffusivity.

### Small perforated plate column

In the case of the small perforated plate column, it was possible to achieve a nine-fold variation in the gas phase diffusivity by using a combination of variety of solutes and carrier gases. Fig. 10 shows that at a given superficial velocity of the gas, k_ga varies as 0.5 power of the gas phase diffusivity. As discussed by MEHTA and SHARMA (1) and VIDWANS (11) and SHARMA (12) Schmidt number is unlikely to be a correlating factor. In the evaluation of overall gas-side mass transfer coefficient it was assumed that there was no back mixing in the gas phase. This is a reasonable assumption in view of the relatively high velocity of the gas and the reported behaviour of sieve plate columns. The visual observation of the column did not indicate any significant change in the characteristics of the dispersion when a variety of carrier gases were used, at a given superficial velocity of the gas. Care was exercised to see that the average normality of sodium hydroxide solution used remained practically the same for all the runs. This could be achieved by a slight variation in the time of the experiment and the partial pressure of the gas.

It was ensured in the case of small perforated plate column that the observed variation of the overall gas-side mass transfer coefficient with the diffusivity of the gas was due to the variation of the true gas-side mass transfer coefficient, k_g, rather than partly due to the variation in k_g and partly due to the variation in effective interfacial area. The values of effective interfacial area obtained under similar hydrodynamic conditions for the systems air-CO₂ and Freon-CO₂ were found to be practically the same. This indicates

Fig. 9. The gas side mass transfer coefficient for the absorption of sulphur dioxide (carrier gas-air) in aqueous solutions of sodium hydroxide at the same superficial velocities of the gas. This indicates that the size of the cap and the type of slots are unlikely to be important in so far as the mass transfer coefficient is concerned. This is also in conformity with the information available in the literature (17), that slots have little, if any, effect on vapour-liquid contacting over the usual range of operating conditions when the slots are at least three-fourths open.

that of the trans- and end walls of the column. It shows that the gas-air power held at the same constant flow rate for the chain change.

Fig. 10. The gas side mass transfer coefficient for the absorption of sulphur dioxide (carrier gas-air) in aqueous solutions of sodium hydroxide at the same superficial velocities of the gas. This indicates that the size of the cap and the type of slots are unlikely to be important in so far as the mass transfer coefficient is concerned. This is also in conformity with the information available in the literature (17), that slots have little, if any, effect on vapour-liquid contacting over the usual range of operating conditions when the slots are at least three-fourths open.

Fig. 11. The gas side mass transfer coefficient for the absorption of sulphur dioxide (carrier gas-air) in aqueous solutions of sodium hydroxide at the same superficial velocities of the gas. This indicates that the size of the cap and the type of slots are unlikely to be important in so far as the mass transfer coefficient is concerned. This is also in conformity with the information available in the literature (17), that slots have little, if any, effect on vapour-liquid contacting over the usual range of operating conditions when the slots are at least three-fourths open.

Small. In the presence of oxidants, the same effect is observed when the gas side mass transfer coefficient is increased.
<figure><img src="image_9.png" /><figcaption>**Fig. 10** Effect of gas-side diffusivity on the gas-side mass transfer coefficient.</figcaption></figure>

● Perforated plate column, U = 21 cm/sec, S = 10 cm.

○ 15-5 cm diameter column, U = 68.5 cm/sec, S = 11 cm.

Δ 10 cm diameter column, U = 51 cm/sec, S = 16 cm.

<figure><img src="image_10.png" /><figcaption>**Fig. 11** Effect of superficial gas velocity on the gas-side mass transfer coefficient.</figcaption></figure>

Δ 22.5 cm square bubble cap plate column. Submergence = 11-8 cm.

○ 15-5 cm diameter bubble cap plate column, Submergence = 11 cm.

● Perforated plate column. Submergence = 10 cm.

<figure><img src="image_11.png" /><figcaption>**Fig. 12** Effect of submergence on the gas-side mass transfer coefficient.</figcaption></figure>

● 10 cm diameter column, superficial gas velocity = 40 cm/sec.

○ 15-5 cm diameter column, superficial gas velocity = 102.5 cm/sec.

Δ 22.5 cm in. × in. square column, superficial gas velocity = 65.5 cm/sec.

that in the above experiments $k_g$ was varying and not a. The effect of the presence of solids on the value of overall gas-side mass transfer coefficient was studied by absorbing chlorine diluted with air in aqueous sodium dimethyl dithiocarbamate solution. Fig. 4 shows the variation in $k_ga$ with solids formation in the case of the sparged contactor. The values of $k_ga$ are found to decrease with an increase in the solids concentration.

### Bubble cap plate column

Fig. 11 which is a log-log plot of $k_ga$ for the absorption of sulphur dioxide (carrier gas-air) in aqueous sodium hydroxide solution against gas velocity for 15.5 cm diameter column and 22.5 cm square column as well as the sparged contactor shows that $k_ga$ varies as 0.75 power of the gas flow rate.

Fig. 12 shows that $k_ga$ for the absorption of chlorine (carrier gas-air) in aqueous sodium hydroxide solutions varies as -0.67 power of the submergence. It is likely that this relationship may not hold at all the gas velocities. In particular at very high gas velocities, the overall gas-side mass transfer coefficients may tend to be constant with submergence or they may tend to increase, depending on how the behaviour of the gas bubbles deviates from the normal chain bubbling pattern, as also how the amount of entrainment changes with submergence.

### Small perforated plate column

In the case of the small perforated plate column the effect of the presence and absence of solids on the value of $k_{L}$a was studied by oxidation of acidic and neutral solutions of cuprous chloride under the same conditions of ionic strength and viscosity. It is indicated that although the presence of solids leads initially to an increase in the value of effective interfacial area, it results in the reduction in the value of true liquid-side mass transfer coefficient, $k_{L}$.

### Bubble cap plate column

Fig. 13 shows that $k_{L}$, the true liquid side mass transfer coefficient, varies as -0.5 power of the submergence.

Fig. 14 shows that $k_{L}$, the liquid side mass transfer coefficient, varies as 0.25 power of the gas velocity.

PORTER, KING, and VARSHNEY (19), have found the values of $k_{L}$a and a in a 3 ft diameter bubble cap plate column. They have calculated the interfacial area by chemical method and the liquid-side mass transfer coefficient by physical absorption experiments. Under the same hydrodynamic conditions their values of $k_{L}$ are somewhat higher than those reported in this work. The relative variation of $k_{L}$ with respect to superficial gas velocity up to the values of superficial gas velocity of 75 cm/sec. is the same as that reported in this work (that is $k_{L} \propto U^{0.25}$). However, for superficial gas velocities greater than 75 cm/sec., they have reported a decrease in $k_{L}$a and a with an increase in the superficial gas velocity; which they have attributed to a change in the hydrodynamic behaviour of the dispersion on the plate. No such effect was observed in this work. The effective interfacial area found by these workers are somewhat closer to what this work indicates.

EDULJEE (20) has analysed the A.I.Ch.E. data and has proposed a correlation for the number of gas phase transfer units. If the same expression is written down in terms of the overall gas-side mass transfer coefficient, then we find that the powers of submergence and gas velocity in the correlation of gas-side mass transfer coefficient are the same as in this work. Also, by the theory of gas phase diffusion coefficients, the terms giving temperature, pressure and molecular weight can be combined together to show that the proper correlating factor will be square root of the gas-side diffusivity. However, the powers of temperature and pressure terms are 1/2 and

### Symbols used

a = effective interfacial area per unit volume of dispersion, cm³/cm²;

a' = effective interfacial area per unit floor area, cm³/cm²;

[B] = concentration of reactant in the bulk, g mole/cm²;

[B]a = initial concentration of reactant in the bulk, g mole/cm²;

[B]t = final concentration of reactant in the bulk, g mole/cm²;

C* = solubility of the solute gas in a given electrolyte solution, g mole/cm²;

H = Henry's constant, g mole/cm² atm;

Cw* = solubility of carbon dioxide in water, g mole/cm² atm;

Dg = diffusivity of solute in the gas phase, cm³/sec;

Dg = diffusivity of the dissolved solute gas in solvent, cm³/sec;

kS = second order reaction rate constant, litre/g mole sec;

kS = third order reaction rate constant (litre/g mole)⁻¹ sec⁻¹;

kOa = overall gas-side mass transfer coefficient, g mole/cm² of dispersion atm sec;

kOa = gas-side mass transfer coefficient, g mole/cm² of dispersion atm sec;

kLg = liquid-side mass transfer coefficient with reaction, cm/sec;

S = submergence, cm;

t = reaction time, sec;

U = superficial gas velocity, cm/sec;

μ = viscosity of the solutions, cP.

<figure><img src="image_12.png" /><figcaption>**Fig. 13** Effect of submergence on true gas and liquid-side mass transfer coefficient in 22.5 cm square model bubble-cap plate column.</figcaption></figure>

Δ Gas-side mass transfer coefficient, U = 97.5 cm/sec.

○ Liquid-side mass transfer coefficient, U = 89.8 cm/sec.

<figure><img src="image_13.png" /><figcaption>**Fig. 14** Effect of superficial gas velocity on the true gas and liquid-side mass transfer coefficient in 22.5 cm square model bubble cap plate column.</figcaption></figure>

Δ Gas-side mass transfer coefficient. Submergence = 11-8 cm.

○ Liquid-side mass transfer coefficient. Submergence = 9-3 cm.
—1/4, respectively, as against the theoretical powers of 3/4 and
—1/2 respectively. Since most of the A.I.Ch.E. work was at
essentially atmospheric pressure, the effect of pressure could not be
discerned properly.

The powers of diffusivity, gas velocity and submergence in so far
as their effect on overall mass transfer coefficients is concerned are
the same as reported by ANDREW (10). However, our values of
the constants in the correlation for overall mass transfer coefficients
and effective interfacial area are significantly different from those
reported by ANDREW (10). It is likely that this discrepancy arises
out of the way submergence is defined.

## Conclusion

(1) It has been shown that the presence of electrolytes, ionic strength, viscosity, presence of solids etc., do not affect the mass transfer in a bubble cap plate column. However, in the case of a small perforated plate column, where there is a fine dispersion, these factors have a profound influence on the mass transfer.

(2) Generalised correlations have been derived for bubble cap plate column on the basis of the work in the model column, which may be useful for a rational design of the industrial equipment.

$$ (1) \quad k_g a = 2.5 \times 10^{-4} \quad U^{0.75} S^{-0.67} D_g^{0.5} \text{ g mole/cm}^3 \text{ atm sec.} $$
or $$ k_g a = 6.17 \quad U^{0.75} S^{-0.67} D_g^{0.5} \text{ sec.}^{-1}. $$

$$ (2) \quad k_L a = 6.97 \quad U^{0.75} S^{-0.67} D_L^{0.4} \text{ sec.}^{-1}. $$

$$ (3) \quad a' = 0.535 \quad U^{0.5} S^{0.83} \text{ cm}^3\text{/cm}^3. $$

$$ \begin{array}{l} (4) \quad k_g = 4.67 \times 10^{-4} \quad U^{0.85} S^{-0.5} D_g^{0.8} \text{ g mole/cm}^3 \text{ atm sec.} \\ \text{or} \\ \quad k_g = 11.5 \quad U^{0.85} S^{-0.5} D_g^{0.5} \text{ cm/sec.} \end{array} $$

$$ (5) \quad k_L = 13 \quad U^{0.85} S^{-0.5} D_L^{0.5} \text{ cm/sec.} $$

## ACKNOWLEDGEMENT

Two of us (R.A.M. and V.D.M.) wish to thank the University Grants Commission for an award of a scholarship which enabled this work to be carried out.

## REFERENCES

1. MEHTA, V. D., and SHARMA, M. M., Chem. Engng. Sci., 1966, 21, 361.

2. VOGEL, A. A., 'Textbook of Quantitative Inorganic Analysis', Longman, Green and Co., New York (2nd ed.).

3. SHARMA, M. M., and DANCKWERTS, P. V., Chem. Engng. Sci., 1963, 18, 729.

4. JHAVERI, A. S., and SHARMA, M. M., ibid., 1966, 22, 1.

5. LEE, C. Y., and WILKE, C. R., Industr. Engng. Chem., 1954, 46, 2381.

6. RICHARDSON, J. F., Chem. Engng. Sci., 1959, 10, 234.

7. DANCKWERTS, P. V., Industr. Engng. Chem., 1951, 43, 1460.

8. DANCKWERTS, P. V., and SHARMA, M. M., The Chemical Engineer, 1966, 281, CE 244.

9. VAN KREVELEN, D. W., and HOPTIZER, P. J., 'Sur la Solubilities der gas dianzes solutions aqueous', Chim. Ind., XXI em, Int. Chim. Ind., 1948, p. 188.

10. ANDREW, S. P. S., Alta Technologia Chemica Processi di Scambia, Academic Nationale die Licenci, Rome, 1961, p. 153.

11. VIDWANS, A. D., 'Mass transfer in packed columns', M.Sc. (Tech.) Thesis, Bombay University, 1966.

12. SHARMA, M. M., and MASHELKAR, R. A., Paper presented at Tripartite Chemical Engineering Conference, Montreal, September 1968.

13. BRAULICK, W. J., FAIR, J. R., and LERNER, B. J., A.I.Ch.E. Journal, 1965, 11, 73.

14. YOSHIDA, F., and AKITA, K., ibid., 1965, 11, 9.

15. MARRUCCI, G., and NICODEMO, L., Chem. Engng. Sci., 1967, 22, 1257.

16. NUSING, R. A. T. O., and KRAMERS, H., ibid., 1958, 8, 81.

17. HENGTSEBACK, R. J., 'Distillation principles and design procedures', Reishold Publishers Corp. (1961), p. 43.

18. CROSS, C. A., and RYDER, H. J., J. Appl. Chem., 1952, 2, 51.

19. PORTER, K. E., KING, M. B., and VARSINEY, K. C., Trans. Instn. Chem. Engng., 1966, 44, T 274.

20. EDULIER, H. E., Brit. Chem. Engng., 1965, 10, No. 2, 103.

## CONTRIBUTORS

<figure><img src="image_14.png" /><figcaption>M. M. SHARMA,
B.Chem.Eng., M.Sc.
(Tech.) Bombay Uni-
versity, Lecturer in
Chemical Engineering
during 1959-61 - Bombay
University, Ph.D. Chem-
ical Engineering - Cam-
bridge University (1964),
Professor of Chemical
Engineering since Sep-
tember 1964. Research
Interests - Mass Trans-
fer with Chemical Re-
action, performance of
mass transfer equip-
ment, vapour-phase
catalytic reaction, etc.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>R. A. MASHELKAR,
B.Chem.Eng., Bombay
University - working for
Ph.D. in Chemical En-
gineering.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>V. D. MEHTA,
B.Chem.Eng., M.Sc.
(Tech.) in Chemical En-
gineering (Bombay Uni-
versity), working as
Assistant Chemical En-
gineer inNirtonSynthetic
Fibres and Chemicals,
since April 1966.</figcaption></figure>

## Dropping the Pilot

The North Western Branch in conjunction with the Yorkshire Branch and British Chemical Engineering is organising a symposium entitled 'Dropping the Pilot' at the University of Manchester Institute of Science and Technology on Friday, March 21st, 1969, from 9.30 a.m. to 5.00 p.m. Seven papers will be presented.

1. 'The Function of Pilot Planting in a Large Chemical Complex.'
Dr C. W. SUCKLING, I.C.I. Mond Division.

2. 'Some General Aspects of Scale Up Practices'.
Mr M. D. WYNNE, I.C.I. Heavy Organic Chemicals Division.

3. 'Development of a Reactor for Processing Solids with Partial Melting...Isomerisation of Potassium Phthalate to Terephthalate'.
Dr Z. NOVOSAD, V. SVAB, J. MALEK, and V. BAZANT, The Czechoslovak Academy of Science, Prague.

4. 'The Roll of Laboratory Studies in the Design of Industrial Crystallisers'.
Dr J. W. MULLIN, University College, London.

5. 'Reducing or Eliminating the Pilot Plant in Fixed Bed Adsorption'.
Dr J. W. CARTER, University of Birmingham.

6. 'Scale up in Absorption and Distillation'.
Professor S. P. S. ANDREW, I.C.I. Agricultural Division.

7. 'To Full Scale Production Direct from the Laboratory'.
Dr G. T. SCHUCH, The Badger Co. Inc., Cambridge, Mass.

Further details, including synopses and registration details, will appear in the February issue of British Chemical Engineering.

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