Mohamad Jamialahmadi, Hans Mller-SteinhagenUniversity of Auckland

Auckland, New Zealand

A Basic program for IBM PC-compatible computers optimizes the design of packed absorption or stripping columns with respect to operating and installation costs.

The program provides a plot of column costs as a function of absorption/stripping factor, from which the final design conditions can be determined. The calculated results are in good agreement with two operating installations.

### BACKGROUND

Packed columns are widely used for vapor/liquid mass transfer operations such as absorption and stripping. They have particular advantages such as economical operation with enhanced performance and low pressure drops.1-5

The general design algorithm for a packed column consists of the following main steps:

- Calculation of the average slope of the vapor/liquid equilibrium curve, mav
- Selection of a value for the absorption factor
- Hydraulic design of the column
- Process design of the column
- Pricing of the column.

The data necessary to carry out the design of packed absorption and stripping columns are physical properties of the system, vapor/liquid equilibrium data, absorption factor, and gas or liquid flow rate. Of these parameters, only the absorption factor, FABS, is unknown (see Equation 1 in box).

To find the most economical column dimensions, Steps 2 through 5 should be repeated for different values of FABS. This procedure requires an iterative search and involves complex and arduous calculations.

Colburn suggested that the optimum value of the absorption factor may lie between 0.6 and 0.8.6 This recommendation reduces the calculations considerably.

However, alternative designs should be taken into consideration both from technical and economical points of view. Without the aid of a computer, these calculations are time-consuming and subject to errors.

A review of existing literature shows that no comprehensive computer program has been proposed so far. To fill this gap, a new computer program designs packed absorption and stripping columns based on recommended models and correlations from the literature.

The program covers three major areas:

- The hydraulic design of packed columns, namely pressure drop per foot of packing, column inside diameter, and percentage of column flooding (see Nomenclature box).
- The process design of the packed column, i.e., the computation of the height of packing, number of packing beds, HETP, number of theoretical plates, and column shell height.
- The estimation of the optimum value of the absorption factor based on column pricing.

### HYDRAULIC DESIGN

The capacity of a packed column is determined by its cross-sectional area which usually is estimated from generalized pressure-drop curves like those given by Norton Company.7

The data necessary to determine the column cross sectional area and its diameter are the gas and liquid phase flow rates.

Of these two parameters only one is known: the gas flow rate in the case of absorption and the liquid flow rate in the case of stripping. The second flow rate is determined using an estimated absorption factor, FABS, and the average slope of the vapor-liquid equilibrium curve (Equation 1).

After that, the pressure drop per foot of packing, the column diameter, and the percentage of column flooding are calculated.

### AVERAGE SLOPE

The slope of the equilibrium curve at any point is given by Equations 2a and 2b, for stripping and absorption, respectively. Therefore, the average slope of the vapor/liquid equilibrium curve can be expressed for stripping as in Equation 3, and for absorption as in Equation 4.

For stripping, the range from x1 to xN (or the range from y1 to yN for absorption) is divided into 30 equal parts. For each value of x (or y for absorption) a value of y (or x* in absorption) is obtained from equilibrium data by linear interpolation or by a polynomial fit.

With the calculated value of Mav, the missing value of the gas or liquid flow rate can be determined from an assumed value of the absorption factor.

### COLUMN DIAMETER

The generalized pressure-drop correlation given by Norton Co. is used to determine the column cross-sectional area and diameter.7 This correlation contains pressure-drop curves ranging from 0.05 to 1.5 in. H2O/ft packing and for flooding conditions. The curves can be curve-fitted by an equation in the form of Equation 5, where X and Y are defined as shown in Equations 6 and 7.

Values of the packing factor, PF, can be found in standard mass-transfer literature. The coefficients in Equation 5 are given in Table 1.

Following the original presentation, pressure drops listed in Table 1 are in in. H2O/ft packing. For pressure drops not specified in Table 1, Y values are obtained by interpolation.

Finally, the percentage flooding is estimated as shown in Equation 8. The computer first reads the necessary input data, then calculates Mav and the unknown flow rate.

After that, the column cross-sectional area for a pressure drop corresponding to 60-80% flooding is determined by the variation of Gs in Equation 7.

### PROCESS DESIGN

Conventionally, the height equivalent to a theoretical plate (HETP) concept is used to design packed columns. The HETP concept is a discrete, rather than a continuous, model and HETP values vary not only with type and size of packing, but also with the flow rates of both phases.

For every system, HETP also varies with the phase concentrations.8 Therefore, the use of the height of a transfer unit (HTU) concept is preferred, since it is derived from the continuous and countercurrent nature of gas/liquid contacting.

If the HTU values for gas and liquid phases are known, these values can easily be combined to give the HETP value.9 In this program, the HTU concept is used to determine the height of packing required for any desired separation.

The HTU values of gas and liquid phase are computed using the Bolles and Fair model.1

This model was recommended recently by Vital, et al., following an extensive literature survey.10

### PACKED BED HEIGHT

The height of packing required to achieve a desired separation in the gas or liquid phase is given by Equation 9, where NTUog is the number of overall gas transfer units and HTUog is the height of one overall gas transfer unit.

### TRANSFER UNITS

If the solute concentration is small, the number of overall transfer units can be calculated as a function of the gas concentration (Equation 10). The operating line relates the composition of vapor and liquid phases at any cross section of the column (Equations 11 and 12).

Therefore, the value of NTUog may be obtained by integrating Equation 10 in conjunction with the operating line. The trapezoid method is used for integration in this program.

### TRANSFER UNIT HEIGHT

No method is entirely satisfactory for predicting the height of a transfer unit. Based on a recent literature review, Vital, et al., recommend the improved Monsanto method by Bolles and Fair (Equations 13 and 14).10 1

Values for a and b are 1.24 and 0.6 for rings and 1.11 and 0.5 for saddles. The packing parameters for gas and liquid phases (PFG and PFL, respectively) are given by Bolles and Fair in the form of two sets of curves for Raschig rings (metal and ceramic), Berl saddles, and Pall rings.1 These curves were fitted to Equations 15 and 16.

The coefficients for each type of packing are listed in Tables 2 through 9. The coefficient CFL in Equation 14 is computed from Equation 17.

Equation 17 was obtained by curve-fitting data given by Bolles and Fair.1

The relationship between the overall height of the transfer units and the height of the individual film transfer units (HTU1 and HTUg) is used to obtain HTUog and then HETP (Equations 18 and 19).

The height of gas and liquid phase transfer units can then be obtained by simultaneously solving Equations 9-18. The first estimate for the height of packing, Z, is Z = NTUog. As recommended by Bolles and Fair, the calculated value of HTUog is multiplied by a safety factor of 1.7.1

### NUMBER OF BEDS

In packed columns, the packing is divided into beds of equal height, with a maximum height of 6 m. For packed columns with a packing in excess of 6 m, number of the packing beds is calculated as shown in Equation 20.

Spacing-equal to the column inside diameter-is also considered between each two beds. Hence, the height of the column shell is given by Equation 21.

NTUog, HTUog, height of packing, number of packing beds, HETP, number of theoretical plates, and column shell height are computed in sequential stages.

### PRICING OF COLUMN

In the pricing portion of the program, the optimum value of the absorption factor is determined from the column costs. For this reason, the total purchasing price of the column is divided into the following components:

- Cost of shell including heads and skirt
- Cost of internals and externals
- Cost of packing.

The total cost of alternative column design is determined for different values of the absorption factor. The results are then plotted against the absorption factor to find the most practical and economical absorption factor.

The sections to follow present correlations for the column costs. These correlations were determined by curve fitting data given by Timmerhaus and Peters and by the Stanford Research Institute.11 12 If more recent values are available, these correlations may be replaced.

### SHELL, HEADS, AND SKIRT

The price of column shell, heads, and skirt is determined on the basis of weight and construction material.

Data required to calculate the weight of column shell, heads, and skirt are column inside diameter, height, and thickness. The method for calculating the first two values has already been discussed.

The column shell thickness required to resist the internal pressure can be calculated by Equation 22, with ID being the column inside diameter in in., S the allowable stress, and E the joint efficiency, which is 1 for columns.

For packed columns taller than 15 m, the wall thickness calculated by Equation 22 is insufficient to withstand the combined stress of wind and weight. Bergman suggests that the wall thickness of the lower sections of the column be increased by 0.06 in. for each 6 m of height above 15 m.13

A corrosion allowance of 0.12 in. is also added to the calculated wall thickness. If severe corrosion is anticipated, the allowance should be increased to 0.2 in.

Finally, the estimated wall thickness is rounded up to the nearest manufacturing standards based on the criteria given in Table 10.

### WEIGHT CALCULATIONS

The weight of the column shell is determined by Equation 23, where pm is 0.283 lb/cu in. for carbon steel and 0.29 lb/cu in. for stainless steel. T is the rounded shell wall thickness.

A support skirt consists of a cylindrical shell with the same diameter as the column shell and a height of 3-5 m. The wall thickness of the skirt is determined with respect to the diameter and the height of the column:

0 < HETP 10: Ts = 0.3 in.

10 < HETP 20: Ts = 0.4 in.

20 < HETP 25: Ts = 0.5 in.

The weight of the skirt with an average height of 4 m is determined using the above data and Equation 23.

The two heads closing the ends of the column shell are assumed to be 2:1 ellipsoidal with diameter and wall thickness identical to that of the column shell. The combined weight of the heads is computed from Equation 24.

### COST CALCULATIONS

The cost of a shell with two heads and skirt is obtained from Equation 25. The column weight (W) is the sum of the weights of the shell, heads, and skirt.

CI refers to the Marshall & Swift (M&S) equipment cost index. At the time the correlation was developed, CI was 790.

The material factor (MF) is 1 for carbon steel, 1.7 for 304 stainless steel, and 2.1 for 316 stainless steel.

### COLUMN INTERNALS

The purchasing of internal fittings (such as distributors, etc.) per bed of packing is estimated from Equation 26.

Here, MF is 1 for carbon steel, 1.24 for 304 stainless steel, and 1.35 for 316 stainless steel.

### COLUMN EXTERNALS

In a packed column, each bed normally has a manhole and a platform. The platforms are connected via ladders, which are usually un-caged up to the first platform and caged thereafter.

The approximate installation cost of flanged manholes is estimated as a function of the column wall thickness from Equations 27a and 27b.

The total material cost for the platforms is obtained from Equation 28. Finally, the cost of the material for ladders is computed by Equation 29.

### PACKING

The cost of different types and sizes of packing used in the program are listed in Table 11. The final price of the packed column is obtained by adding the price of the column shell, heads, and skirt to the price of internals, externals, and packing.

### EXAMPLES

The predictions of the computer program compare well with two column designs, one of them for an existing column in the petrochemical industry.

### SO2 ABSORPTION

Sulfur dioxide produced by the combustion of sulfur in air is absorbed in water. The feed gas rate is 0.048 kmol/sec of 8% (vol/vol) SO2.

When designing an absorption column to recover 95% of the sulfur dioxide, the required input data are as shown in Table 12.

The calculated plot of total column cost vs. absorption factor is shown in Fig. 1. As discussed, the optimum value of the absorption factor is between 0.6 and 0.8.

At less than 0.6, the cost of the column remains almost constant despite the increasing absorption rate. At greater than 0.8, the cost of the column increases rapidly with decreasing liquid rate. (Exceptions to this rule are possible if the absorption is followed by a difficult or expensive desorption [high FABS], or if no desorption is required, [low FABS].)

Pure SO2 will be recovered from the solution by steam stripping. Therefore, the column was designed for FABS = 0.8, as the higher concentration will favor the stripper design.

This value for FABS was chosen to obtain a somewhat higher concentration of SO2 in the water, which is beneficial for the subsequent stripping process.

The column design data for an absorption factor of 0.8 are given in Table 13.

### METHANOL STRIPPING

This example has been provided by the process engineering department of Razi Petrochemical Complex, Iran.

Process condensate containing 1,110 ppm methanol is stripped with steam. The flow rate of the condensate is 0.9656 kmol/sec.

When designing a stripper to reduce the methanol content to approximately 50 ppm, the required input data are as shown in Table 14.

Fig. 2 shows the cost of the column as a function of the stripping factor. Dimensions of the column corresponding to a stripping factor of 1.1 are given in Table 15. These values are in good agreement with the actual column design.

### REFERENCES

- Bolles, W.L., and Fair, J.R., 1. Chem. Eng. Symp. Series, No. 56, 1979, pp.33-35.
- Porter, K.E., and Jenkins, J.D., "Interrelationship between industrial practice and academic research in distillation and absorption," 1. Chem. Eng. Symp. Series, No. 56, 1979.
- Fair, J. R., and Bolles, W.L., "Distillation in practice," AIChE Today Series, 1978.
- Perry's Chemical Engineers' Handbook, 6th Ed., McGraw Hill, New York, 1984.
- Bolles, W.L., and Fair, J.R., Chem. Eng., Vol. 89, 14, July 21, 1982, p. 109.
- Colburn, A.P., Trans. Am. Inst. Chem. Eng., Vol. 35, 1939, p. 211.
- Ludwig, E.E., Applied Process Design for Chemical and Petrochemical Plants, Vol. 2, 2nd Ed., Gulf Publishing Co., 1979.
- Treybal, E.R., Mass Transfer Operations, 3rd. Ed., McGraw-Hill, New York, 1980.
- Jamialahmadi, M., "Studies in Distillation in Packed Columns," MS thesis, Department of Chemical Engineering, University of Aston in Birmingham, 1979.
- Vital, J., Grosse], S.S., and Olsen, P.I., Hydrocarbon Processing, December 1984, p. 75.
- Peters, M.S., and Timmerhaus, K.D., Plant Design for Chemical Engineers, 3rd Ed., New York, McGraw-Hill, 1980.
- Stanford Research Institute, data supplied by Headquarters of Iranian Petrochemical Complex, Tehran.
- Bergman, E.O., Trans. A.S.M.E., 1955, 77, p. 863.

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