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Absorbers
4
Absorbers Introduction ................................................ 93 Hydrocarbon Absorber Design ......................... 93 Inorganic Absorbers ...................................... 94
Rules of Thumb for Chemical Engineers. DOI: 10.1016/B978-0-12-387785-7.00004-9 Copyright Ó 2012 Elsevier Inc. All rights reserved.
Packing Height for Mass Transfer in Packed Columns ..................................................... 95 Overall Mass Transfer Coefficient ..................... 98
92
Absorbers
93
Introduction There are two major types of absorption. In each case, a gas stream contacts the liquid absorbent, transfers components into the liquid, and therefore cleans the gas. Hydrocarbon absorption is very similar to distillation, with the vapor-liquid equilibrium driving the process, as discussed in Chapter 3. The absorber uses a lean oil in which the hydrocarbon components are much heavier than the component absorbed from the gas stream. There may or may not be a reboiler. The columns are often fitted with trays rather than packing. Canned computer distillation programs usually include hydrocarbon absorber options. Inorganic components are absorbed into aqueous solutions. When it is strictly a physical process, mass
transfer coefficients determine the column design. Packed towers are almost always utilized. Reactive absorption is when chemical reactions accompany the absorption of gases into liquid solutions. The design of reactive absorption processes should also use mass transfer film models, taking into account the chemical reactions [1]. In these processes, we define “solute” to mean the component in the gas stream that is absorbed into a liquid “solvent.” An Excel workbook, containing worked examples, accompanies this chapter.
Hydrocarbon Absorber Design Absorbers are used to remove hydrocarbons from natural gas. The “rich gas” enters the bottom of a column with trays or packing, flowing countercurrent to a “lean oil” with a molecular weight of about 100 to 200. For ambient temperature absorbers, a heavy lean oil is used with molecular weight of 180 to 200. Refrigerated absorbers use a lighter lean oil of molecular weight 120 to 140. The circulation rate of the oil depends on its molecular weight, so the lighter oil will have a lower circulation rate. However, the lighter oil will have higher vaporization losses [2]. For all detailed absorber designs, tray-to-tray calculations should be done using an appropriate computer program. Vendors will perform the calculations if the engineer lacks access to a program. However, preliminary designs can be done with the method given in this section. The 1947 Edmister short-cut method uses “absorption and stripping factors” to predict the performance of absorption into lean oils. Others have published Edmister’s chart (see Refs [1] or [2]) which gives curves for columns with 0.2 to infinite theoretical trays, and an abscissa with partially compressed scale. Because this graphical method is now of interest primarily for preliminary work, the chart is reworked and simplified in Figure 4-1. The primary assumptions for the method are: • Relative volatility between the key component and the lean oil is constant throughout the column.
• The average temperature of the column is representative of the overall column. • Vapor and liquid traffic are constant through the column. 1. Given: Composition of rich gas stream, mole fractions Feed rate of rich gas stream, moles/h Relative volatility of each component of rich gas with lean oil Mole fraction of each hydrocarbon in lean oil Desired recovery of key component from gas into the oil fraction Number of theoretical trays in the column 2. Use the chart (Figure 4-1) to find the absorption factor. For example, if the desired recovery of the key component is 75%, with six theoretical trays, the absorption factor is 0.80. 3. Calculate the required feed rate of the lean oil stream: Lo ¼ Ai ai;o V (4-1) Where Lo ¼ feed rate, lean oil, mol/h Ai ¼ Absorption factor from chart, for component i ai,o ¼ average relative volatility, hydrocarbon component i and lean oil V ¼ feed rate, rich gas, mol/h
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Rules of Thumb for Chemical Engineers
Figure 4-1. Absorption and stripping factors vs. stripping functions. (Adapted from [1].)
4. Calculate the absorption factor for each of the remaining components in the rich gas stream, using Equation 4-1 rearranged. 5. Use the chart to find the recovery fraction for each of the remaining components. For example, if the absorption factor is 0.33, the recovery fraction with six theoretical trays is 0.36. 6. For each component, calculate the mole fraction in the lean gas stream that leaves the column with: V Ynþ1;i Ei ðV Ynþ1;i Lo Yo;i Þ Y1;i ¼ (4-2) V
Where Y1,i ¼ component i in lean gas stream, mole fraction Ynþ1,i ¼ component i in rich gas stream, mole fraction Ei ¼ recovery fraction for component i Yo,i ¼ ai,o Xo,i ¼ equilibrium vapor concentration of component i in lean oil stream Xo,i ¼ component i in liquid phase of lean oil stream, mole fraction
Inorganic Absorbers Film theory is widely used to model absorption units. It assumes that the gas and liquid phases are well mixed, but separated from each other by a thin boundary layer. The boundary layer consists of a gas film and a liquid film. In each case the films are assumed to have little motion (no mixing) and mass transfer occurs by molecular diffusion. The diffusion rate is defined by absorption coefficients that depend on the concentration of the solute in the gas, at the interface, and in the liquid. The absorption coefficients require knowledge of the surface area of the boundary layer. This is difficult to
define. Instead, “volume coefficients” are determined experimentally for specific packings. When the solute is very soluble in the solvent, the gas film controls the mass transfer and KGA is used for calculations. When the solute has low solubility, the liquid film commands and KLA is preferred. However, the mass transfer calculations can use either value regardless of which side is controlling. For physical absorption, where there is no chemical reaction, the vapor-liquid equilibrium defines the driving force. Since the solvent usually leaves the column containing a dilute concentration of solute, use Henry’s Law
Absorbers
to model the system if the value of the coefficient is known. Henry’s Law is applicable for gaseous solutes (i.e., the solute has a vapor pressure well above the system pressure at the operating temperature), with a maximum 0.01 mole fraction in the solvent and pressure below 2 atmospheres. For some systems Henry’s Law is applicable outside this envelope; plot experimental data with the Henry’s Law expression to compare [7]. Rules of thumb for packed column absorbers: • Select liquid rates at least 25% to 100% greater than the theoretically calculated minimum rate. • Typical liquid rates are between 12 and 125 (m3/h)/ m2 (5 and 50 gpm/ft2) [7]. See Table 4-1. • Typical gas flow rates are between 40 and 70% of the calculated flooding rate. • Tower diameter should be at least eight times the packing size. • For packing factors from 10 to 60 (ft1), an empirical equation for the limiting pressure drop at flooding is [4]: DPflood ¼ 0:115 Fp0:7
(4-3)
95
Where: DPflood ¼ pressure drop at flooding, inches H2O per foot of packing • For higher values of the packing factor, assume 2.0 inches H2O per foot [4]. However, Strigle recommends that after determining the tower diameter and height based on mass transfer equations (next section), calculate the pressure drop. The design parameters should be iterated until a maximum pressure drop of 0.60 in H2O/ft with water as the solvent, or 0.40 in H2O/ft with other liquids, is found. For foaming systems, the maximum pressure drop should be 0.25 in H2O/ft [9]. • Choose a solvent: a) with high gas solubility, b) with low volatility, c) as non-corrosive as possible, d) with low cost and high availability, e) with relatively low viscosity, and f) with positive safety and toxicity profile. • Consider structured packing, rather than random dumped packing, for applications requiring very low pressure drop or when an existing column capacity must be increased (see Table 4-2). • For absorbers with chemical reaction, provide at least 33% excess of the reactant in the solvent [7].
Table 4-1 Maximum recommended liquid loading for random packings [9]
Packing Height for Mass Transfer in Packed Columns
Packing Size mm
in
Liquid Rate (gpm/ft2)
19 25 38 50 90
3 /4 1 1½ 2 3½
25 40 55 70 125
The following procedure gives a reasonable estimate for the height of packing. As written it neglects temperature change in the column; the temperature may change due to the heat of solution, heat of reaction, and heat of vaporization. This procedure is applicable to physical
Table 4-2 Comparison of random packing and trays for acid-gas absorption columns [2] Attribute
Random Packing
Trays
Pressure drop
Typically about 1/3 that of trays due to larger open area and lack of liquid head
Typical pressure drop for tower with 25 transfer stages Foaming
7 kPa (1 psi)
Each tray has a liquid head (typically 50 mm or 2 in. per tray) contributing to higher pressure drop through the column 21 kPa (3 psi)
Column diameter
No restriction if the size of the packing is small compared with the column diameter. Recommended for columns with diameter less than 1 m (3 ft)
Excellent performance due to low gas and liquid velocities and large open area
Comparable to random packing if downcomers are well designed. However, prediction of downcomer choke and aeration factors are uncertain.
(Continued)
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Rules of Thumb for Chemical Engineers
Table 4-2 Comparison of random packing and trays for acid-gas absorption columns [2]dcont’d Attribute
Random Packing
Trays
Solids
Solids tend to accumulate in packing voids.
Maldistribution
Most severe in large-diameter towers, where there are low liquid flowrates, and smaller packing. Maldistribution can be remedied with good distributor design, water-testing, and inspection. Fast movement of hydrogen molecule can result in reverse diffusion in packing Distributor turndown often restricts packing turndown to about 2 on the liquid flowrate. If steady liquid flowrate is used (e.g., pumparounds), turndown performance of packing can match or exceed trays. Ceramic and plastic packings are highly corrosionresistant at low cost Greater flexibility because packing is relatively easy to change to modify column characteristics
Handle solids much better than packing due to much higher gas and liquid velocities, and fewer locations on trays where solids can be deposited. Use trays with large sieve holes or large fixed valves when plugging and fouling are primary considerations. Inherently more robust
Hydrogen-rich systems Turndown
Resistance to corrosion Flexibility
absorption. See Table 4-3 for a list of data required for the calculations. The accompanying Excel workbook has a worked example. For systems with a fast chemical reaction, the concentration of solute in the solvent may be assumed to be nil throughout the column; this assumption decreases the calculated packing height. However, if there is a slow reaction the required packed height may be more than that calculated [1]. 1. Define the equilibrium curve. Use Henry’s Law, if applicable, to establish the concentration of solute in solvent that is in equilibrium with the gas feed stream concentration (y1) at the bottom of the column (x*). 1 x1 ¼
Moving valve trays typically achieve turndown of 4 to 5. Large diameter sieve holes or fixed valve trays typically achieve turndown of 2 to 2.5, which is comparable to packings. Corrosion-resistant alloys are expensive Fixed trays are relatively difficult and expensive to change
Table 4-3 Data required for absorber calculations Category
Data Required
Absorber Packed Column and System
Operating pressure, P Column diameter, D Packing type and size Absorption volume coefficient, KGA Henry’s Law coefficient, kH, or vaporliquid equilibrium data, evaluated at the average column temperature Molar flow rate, G1 Molecular weight of inert gas and solute, MG and MS Temperature Mole fraction of solute, feed stream, y1 Mole fraction of solute, exit stream, y2, or percent of solute to remove in the column Molecular weight of solvent, ML Temperature Density, rL Molar concentration of solute in the feed stream, x2 (important if the solvent is recirculated)
Gas Stream
y1 kH
2. Calculate the slope of the equilibrium curve. This is the minimum ratio of molar flow, L/G: L y2 y1 ¼ x2 x1 G min
Much less influence on turbulent contact on trays
Liquid Stream
Absorbers
3. Choose a liquid rate that is about 20% to 100% higher than minimum [7]. For example, with 50% excess liquid flow: L L2 ¼ 1:5 G1 G min 4. Assume that none of the solvent is vaporized. Determine the molar gas flow out of the column. G2 ¼
G1 ð1 y1 Þ ð1 y2 Þ
5. Close the material balance to find the actual concentration of solute in solvent at the bottom of the column. First compute the moles of solute in the liquid discharge. Then calculate the concentration and molar flow rate. Moles ¼ L2 x2 þ G1 y1 G2 y2 x1 ¼
Moles Moles L2 ð1 x2 Þ
L1 ¼ G1 þ L2 G2 6. Calculate the molal gas velocity using the average gas rate through the column. Gm ¼
97
8. Obtain the log-mean concentration driving forces with the following two expressions: ðy y ÞLM ¼
ð1 yÞLM ¼
ðy1 y1 Þ ðy2 y2 Þ ðy1 y1 Þ ln ðy2 y2 Þ ð1 y1 Þ ð1 y1 Þ ð1 y1 Þ ln ð1 y1 Þ
9. Calculate the number of transfer units required for absorption: NOG ¼
ðy1 y2 Þ ðy y ÞLM
10. Calculate the height of each transfer unit: HOG ¼
Gm KGA ð1 yÞLM
11. The overall packed height is found by multiplying the number of transfer units by the height of each transfer unit: Z ¼ NOG HOG The dimensions of a packed column are shown in Figure 4-2.
ðG1 þ G2 Þ=2 p D2 =4
7. Find the vapor phase concentration of solute that would be in equilibrium with the liquid concentration at the bottom and top of the column. If there is an irreversible chemical reaction the equilibrium concentration is zero (y* ¼ 0). y1 ¼ kH x1 y2 ¼ kH x2
Figure 4-2. Nomenclature for packed tower absorber.
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Rules of Thumb for Chemical Engineers
Overall Mass Transfer Coefficient If KGA values are available for a known system, those of an unknown system can be approximated by: Dv ðunknownÞ 0:56 KGA ðunknownÞ ¼ KGA ðknownÞ Dv ðknownÞ (4-5)
Absorption coefficient data may be difficult to obtain. The values are specific to the gas-liquid system of interest, and change with both gas and liquid rate. Packing manufacturers often publish KGA values for the CO2caustic system, but these are of little use in predicting coefficients for other systems. The coefficient is a function of gas flow rate and liquid flow rate according to the relationship [7]. However, the KGA value reaches a maximum as the liquid rate is increased at constant gas rate, when a pressure drop of about 0.75 in H2O/ft is achieved for 2-inch and smaller sizes of random packings [9]. KGA f Lb Gc
Where: KGA ¼ gas film overall mass transfer coefficient, kgmol/s-m3-atm or lb-mol/h-ft3-atm Dv ¼ diffusivity of solute in gas, m2/s or ft2/h [5] The simplest gas diffusivity relationship is the Gilliland relationship:
(4-4)
Dv ¼ 0:0069
For liquid-film controlled systems, the value of exponent b lies between 0.22 and 0.34 depending on the characteristics of the packing. If data is not available assume that b ¼ 0.30. Assume exponent c ¼ 0.06 to 0.08. For gas-film controlled systems, the value of exponent b also lies between 0.22 and 0.34 (assume 0.30 if unknown). However, exponent c ranges from 0.67 to 0.80 and should be assumed to be 0.75 if unknown. In any event, the sum of b and c should be greater than 1.0.
T 3=2 ð1=MA þ 1=MB Þ0:5 1=3 1=3 2 P VA þ V B
(4-6)
Where: T ¼ absolute temperature, R MA and MB ¼ molecular weights of the two gases, A and B P ¼ total pressure, atm VA and VB ¼ molecular volumes of gases, cc/g-mol It is convenient that packing manufacturers have largely standardized the reporting of KGA values, based on a system of 1% carbon dioxide absorbed into a solution of 4% NaOH with 25% conversion to carbonate. Comparison of KGA values at the same liquid loading provides the overall mass transfer relationship among the packings. Using Table 4-4, convert the reported, or known, value of KGA for a specific packing to the value to use for a different packing type or size. Some commercial systems are listed in Table 4-5.
Example
Absorption of hydrogen chloride into water is gas-film controlled. The KGA at a liquid rate of 4 gpm/ft2 and gas rate of 3.5 ft/s is reported to be 14 lb-mol/h-ft3-atm. What is the KGA at a liquid rate of 10 gpm/ft2 and gas rate of 5.0 ft/s? Solution: 0:3 0:75 10 5 KGA ¼ ð14Þ ¼ 24 4 3:5
Table 4-4 Relative overall mass transfer coefficient for packings Packing Size Packing
Material
beta-RingÒ Cascade Mini-RingÒ FlexiringÒ Hy-PakÒ IMTPÒ
Metal Metal Metal Metal Metal
5
16 mm ( /8”)
1.68
25 mm (1”) 2.22 1.99 1.54 1.5 2.00
38 mm (1.5”)
1.80 1.32 1.26 1.66
50 mm (2”) 1.41 1.68 1.09 1.05 1.37
80 mm (3” or 3.5”) 1.13 1.30 0.69 0.87
Absorbers
99
Table 4-4 Relative overall mass transfer coefficient for packingsdcont’d Packing Size Packing
Material
5
16 mm ( /8”)
25 mm (1”)
38 mm (1.5”)
50 mm (2”)
80 mm (3” or 3.5”)
I-Ring Metal 3.12 2.68 1.98 1.56 0.98 Nutter Ring Metal 2.05 1.71 1.51 1.07 Pall Rings Metal 1.51 1.26 1.06 0.62 Ceramic 1.38 1.11 0.92 0.54 IntaloxÒ Saddles Raschig Rings Ceramic 1.13 0.94 0.80 0.50 Ceramic 1.63 1.00 0.56 Super IntaloxÒ Saddles Plastic 1.64 1.21 0.84 beta-RingÒ Plastic 1.29 1.07 Cascade Mini-RingÒ Plastic 1.61 1.19 1.16 0.95 0.60 FlexiringÒ Plastic 1.16 Intalox SnowflakeÒ Pall Rings Plastic 1.29 1.10 1.02 0.60 Jaeger Ring Plastic 1.63 1.20 1.09 0.98 0.59 Plastic 1.80 1.37 1.20 Tri-PackÒ Jaeger Saddle Plastic 1.54 0.97 0.59 Jaeger Low-Profile Ring Plastic 1.17 1.17 1.02 Tellerette Plastic 1.22 1.07 Comparison of KGA published by packing manufacturers for the CO2/NaOH system at 25 C at a liquid rate of 10 gpm/ft2 and gas rate of between 400 and 970 lb/ft2-h
Table 4-5 Commercially important absorption systems
Solute
Solvent
Type of Absorption
Typical KGA (lb-mol/h-ft3-atm)
Henry’s Law Constant kH [ p / x [8] kH;px
C
Acetone Water Physical 1.95 4600 Acrylonitrile Water Physical 5.0 2800 Ammonia Dilute Acid Physical 13 (Note 4) 0.94 4100 Ethanol Water Physical 0.30 6500 Formaldehyde Water Physical 4.4 (Note 3) 0.017 6800 Hydrogen Chloride Water Physical 14 (Note 4) 0.03 0 Hydrogen Fluoride Water Physical 6.0 (Note 4) e e Sulfur Dioxide Water Physical 2.2 (Note 3) 46.1 3100 Sulfur Trioxide Water Physical 20 (Note 1) e e Benzene and Toluene Hydrocarbon Oil Physical e e Butadiene Hydrocarbon Oil Physical e e Butanes and Propane Hydrocarbon Oil Physical e e Naphthalene Hydrocarbon Oil Physical e e Carbon Dioxide Aqueous Sodium Hydroxide Irreversible Chemical 1.5 (Note 3) e e Hydrochloric Acid Aqueous Sodium Hydroxide Irreversible Chemical e e Hydrocyanic Acid Aqueous Sodium Hydroxide Irreversible Chemical 4.4 (Note 3) e e Hydrofluoric Acid Aqueous Sodium Hydroxide Irreversible Chemical e e Hydrogen Sulfide Aqueous Sodium Hydroxide Irreversible Chemical 4.4 (Note 3) e e Chlorine Water Reversible Chemical 3.4 (Note 3) 608 2500 Carbon Monoxide Aqueous Cuprous Ammonium Salts Reversible Chemical e e MEA or DEA Reversible Chemical (Note 2) e e CO2 and H2S DEG or TEG Reversible Chemical e e CO2 and H2S Nitrogen Oxides Water Reversible Chemical 18000 2000 The Henry’s Law constant (units: atm) listed here is the reciprocal, representing volatility, at 298.15 K. Use this expression to adjust for temperature: kH
1 1 ¼ kH exp C ðatmÞ T 298:15 (Continued)
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Rules of Thumb for Chemical Engineers
Table 4-5 Commercially important absorption systemsdcont’d
Solute
1. 2. 3. 4.
Solvent
Type of Absorption
Typical KGA (lb-mol/h-ft3-atm)
Henry’s Law Constant kH [ p / x [8] kH;px
C
2-inch ceramic Intalox saddles at a liquid rate of 7.5 gpm/ft2 and gas rate of 1200 lb/ft2-h [7] Refer to [7] for a discussion of this system #2 plastic Super IntaloxÒ packing at a liquid rate of 4 gpm/ft2 and gas velocity of 3.5 ft/s; liquid film controlled [7] #2 plastic Super IntaloxÒ packing at a liquid rate of 4 gpm/ft2 and gas velocity of 3.5 ft/s; gas film controlled [7]
Nomenclature Ai G D Dv Ei FP G Gm HOG KGA kH L Lo MA and MB NOG P T V VA and VB x y Xo,i Y1,i Ynþ1,i
¼ Absorption factor from chart, for component i ¼ vapor rate, moles/time ¼ tower diameter, m or ft ¼ diffusivity of solute in gas, m2/s or ft2/h ¼ recovery fraction for component i ¼ packing factor ¼ gas rate, moles/time ¼ molal gas velocity, moles/time/m2 or moles/time/ft2 ¼ height of a transfer unit with gas-film resistance, m or ft ¼ gas film overall mass transfer coefficient, kg-mol/s-m3-atm or lb-mol/ h-ft3-atm ¼ Henry’s law constant ¼ liquid rate, moles/time ¼ feed rate, lean oil, mol/h ¼ molecular weights of the two gases, A and B ¼ number of transfer units with gas-film resistance ¼ total pressure, atm ¼ absolute temperature, R ¼ feed rate, rich gas, mol/h ¼ molecular volumes of gases, cc/g-mol ¼ mole fraction, liquid phase ¼ mole fraction, vapor phase ¼ component i in liquid phase of lean oil stream, mole fraction ¼ component i in lean gas stream, mole fraction
Yo,i [ ai,o Xo,i Z ai,o
¼ equilibrium vapor concentration of component i in lean oil stream ¼ height of packed section of column, m or ft ¼ average relative volatility, hydrocarbon component i and lean oil
References
[1] Coker AK. Ludwig’s Applied Process Design for Chemical and Petrochemical Plants. 4th ed, vol. 2. Gulf Professional Publishing; 2010. [2] Gas Processors Suppliers Association (GPSA). Engineering Data Book, SI Version. 12th ed, vol. 2; 2004. [3] Kenig E, Seferlis P. Modeling Reactive Absorption. Chemical Engineering Progress, January, 2009:65–73. [4] Kister H. Ask the Experts: Acid-Gas Absorption. Chemical Engineering Progress, June, 2006:16–7. [5] Marreo T, Mason E. Gaseous Diffusion Coefficients. Journal of Physical and Chemical Reference Data. American Institute of Physics, 1972; 1:3. [6] McCabe W, Smith J, Harriott P. Unit Operations of Chemical Engineering. 7th ed. (New York): McGraw-Hill, Inc; 2004. [7] McNulty K. Effective Design for Absorption and Stripping. Chemical Engineering, November, 1994. [8] Sander R. Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry (Version 3), www.henrys-law.org; 1999. [9] Strigle Jr R. Packed Tower Design and Applications. 2 ed. Gulf Publishing Co; 1994.
Absorbers Introduction ................................................ 93 Hydrocarbon Absorber Design ......................... 93 Inorganic Absorbers ...................................... 94
Rules of Thumb for Chemical Engineers. DOI: 10.1016/B978-0-12-387785-7.00004-9 Copyright Ó 2012 Elsevier Inc. All rights reserved.
Packing Height for Mass Transfer in Packed Columns ..................................................... 95 Overall Mass Transfer Coefficient ..................... 98
92
Absorbers
93
Introduction There are two major types of absorption. In each case, a gas stream contacts the liquid absorbent, transfers components into the liquid, and therefore cleans the gas. Hydrocarbon absorption is very similar to distillation, with the vapor-liquid equilibrium driving the process, as discussed in Chapter 3. The absorber uses a lean oil in which the hydrocarbon components are much heavier than the component absorbed from the gas stream. There may or may not be a reboiler. The columns are often fitted with trays rather than packing. Canned computer distillation programs usually include hydrocarbon absorber options. Inorganic components are absorbed into aqueous solutions. When it is strictly a physical process, mass
transfer coefficients determine the column design. Packed towers are almost always utilized. Reactive absorption is when chemical reactions accompany the absorption of gases into liquid solutions. The design of reactive absorption processes should also use mass transfer film models, taking into account the chemical reactions [1]. In these processes, we define “solute” to mean the component in the gas stream that is absorbed into a liquid “solvent.” An Excel workbook, containing worked examples, accompanies this chapter.
Hydrocarbon Absorber Design Absorbers are used to remove hydrocarbons from natural gas. The “rich gas” enters the bottom of a column with trays or packing, flowing countercurrent to a “lean oil” with a molecular weight of about 100 to 200. For ambient temperature absorbers, a heavy lean oil is used with molecular weight of 180 to 200. Refrigerated absorbers use a lighter lean oil of molecular weight 120 to 140. The circulation rate of the oil depends on its molecular weight, so the lighter oil will have a lower circulation rate. However, the lighter oil will have higher vaporization losses [2]. For all detailed absorber designs, tray-to-tray calculations should be done using an appropriate computer program. Vendors will perform the calculations if the engineer lacks access to a program. However, preliminary designs can be done with the method given in this section. The 1947 Edmister short-cut method uses “absorption and stripping factors” to predict the performance of absorption into lean oils. Others have published Edmister’s chart (see Refs [1] or [2]) which gives curves for columns with 0.2 to infinite theoretical trays, and an abscissa with partially compressed scale. Because this graphical method is now of interest primarily for preliminary work, the chart is reworked and simplified in Figure 4-1. The primary assumptions for the method are: • Relative volatility between the key component and the lean oil is constant throughout the column.
• The average temperature of the column is representative of the overall column. • Vapor and liquid traffic are constant through the column. 1. Given: Composition of rich gas stream, mole fractions Feed rate of rich gas stream, moles/h Relative volatility of each component of rich gas with lean oil Mole fraction of each hydrocarbon in lean oil Desired recovery of key component from gas into the oil fraction Number of theoretical trays in the column 2. Use the chart (Figure 4-1) to find the absorption factor. For example, if the desired recovery of the key component is 75%, with six theoretical trays, the absorption factor is 0.80. 3. Calculate the required feed rate of the lean oil stream: Lo ¼ Ai ai;o V (4-1) Where Lo ¼ feed rate, lean oil, mol/h Ai ¼ Absorption factor from chart, for component i ai,o ¼ average relative volatility, hydrocarbon component i and lean oil V ¼ feed rate, rich gas, mol/h
94
Rules of Thumb for Chemical Engineers
Figure 4-1. Absorption and stripping factors vs. stripping functions. (Adapted from [1].)
4. Calculate the absorption factor for each of the remaining components in the rich gas stream, using Equation 4-1 rearranged. 5. Use the chart to find the recovery fraction for each of the remaining components. For example, if the absorption factor is 0.33, the recovery fraction with six theoretical trays is 0.36. 6. For each component, calculate the mole fraction in the lean gas stream that leaves the column with: V Ynþ1;i Ei ðV Ynþ1;i Lo Yo;i Þ Y1;i ¼ (4-2) V
Where Y1,i ¼ component i in lean gas stream, mole fraction Ynþ1,i ¼ component i in rich gas stream, mole fraction Ei ¼ recovery fraction for component i Yo,i ¼ ai,o Xo,i ¼ equilibrium vapor concentration of component i in lean oil stream Xo,i ¼ component i in liquid phase of lean oil stream, mole fraction
Inorganic Absorbers Film theory is widely used to model absorption units. It assumes that the gas and liquid phases are well mixed, but separated from each other by a thin boundary layer. The boundary layer consists of a gas film and a liquid film. In each case the films are assumed to have little motion (no mixing) and mass transfer occurs by molecular diffusion. The diffusion rate is defined by absorption coefficients that depend on the concentration of the solute in the gas, at the interface, and in the liquid. The absorption coefficients require knowledge of the surface area of the boundary layer. This is difficult to
define. Instead, “volume coefficients” are determined experimentally for specific packings. When the solute is very soluble in the solvent, the gas film controls the mass transfer and KGA is used for calculations. When the solute has low solubility, the liquid film commands and KLA is preferred. However, the mass transfer calculations can use either value regardless of which side is controlling. For physical absorption, where there is no chemical reaction, the vapor-liquid equilibrium defines the driving force. Since the solvent usually leaves the column containing a dilute concentration of solute, use Henry’s Law
Absorbers
to model the system if the value of the coefficient is known. Henry’s Law is applicable for gaseous solutes (i.e., the solute has a vapor pressure well above the system pressure at the operating temperature), with a maximum 0.01 mole fraction in the solvent and pressure below 2 atmospheres. For some systems Henry’s Law is applicable outside this envelope; plot experimental data with the Henry’s Law expression to compare [7]. Rules of thumb for packed column absorbers: • Select liquid rates at least 25% to 100% greater than the theoretically calculated minimum rate. • Typical liquid rates are between 12 and 125 (m3/h)/ m2 (5 and 50 gpm/ft2) [7]. See Table 4-1. • Typical gas flow rates are between 40 and 70% of the calculated flooding rate. • Tower diameter should be at least eight times the packing size. • For packing factors from 10 to 60 (ft1), an empirical equation for the limiting pressure drop at flooding is [4]: DPflood ¼ 0:115 Fp0:7
(4-3)
95
Where: DPflood ¼ pressure drop at flooding, inches H2O per foot of packing • For higher values of the packing factor, assume 2.0 inches H2O per foot [4]. However, Strigle recommends that after determining the tower diameter and height based on mass transfer equations (next section), calculate the pressure drop. The design parameters should be iterated until a maximum pressure drop of 0.60 in H2O/ft with water as the solvent, or 0.40 in H2O/ft with other liquids, is found. For foaming systems, the maximum pressure drop should be 0.25 in H2O/ft [9]. • Choose a solvent: a) with high gas solubility, b) with low volatility, c) as non-corrosive as possible, d) with low cost and high availability, e) with relatively low viscosity, and f) with positive safety and toxicity profile. • Consider structured packing, rather than random dumped packing, for applications requiring very low pressure drop or when an existing column capacity must be increased (see Table 4-2). • For absorbers with chemical reaction, provide at least 33% excess of the reactant in the solvent [7].
Table 4-1 Maximum recommended liquid loading for random packings [9]
Packing Height for Mass Transfer in Packed Columns
Packing Size mm
in
Liquid Rate (gpm/ft2)
19 25 38 50 90
3 /4 1 1½ 2 3½
25 40 55 70 125
The following procedure gives a reasonable estimate for the height of packing. As written it neglects temperature change in the column; the temperature may change due to the heat of solution, heat of reaction, and heat of vaporization. This procedure is applicable to physical
Table 4-2 Comparison of random packing and trays for acid-gas absorption columns [2] Attribute
Random Packing
Trays
Pressure drop
Typically about 1/3 that of trays due to larger open area and lack of liquid head
Typical pressure drop for tower with 25 transfer stages Foaming
7 kPa (1 psi)
Each tray has a liquid head (typically 50 mm or 2 in. per tray) contributing to higher pressure drop through the column 21 kPa (3 psi)
Column diameter
No restriction if the size of the packing is small compared with the column diameter. Recommended for columns with diameter less than 1 m (3 ft)
Excellent performance due to low gas and liquid velocities and large open area
Comparable to random packing if downcomers are well designed. However, prediction of downcomer choke and aeration factors are uncertain.
(Continued)
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Rules of Thumb for Chemical Engineers
Table 4-2 Comparison of random packing and trays for acid-gas absorption columns [2]dcont’d Attribute
Random Packing
Trays
Solids
Solids tend to accumulate in packing voids.
Maldistribution
Most severe in large-diameter towers, where there are low liquid flowrates, and smaller packing. Maldistribution can be remedied with good distributor design, water-testing, and inspection. Fast movement of hydrogen molecule can result in reverse diffusion in packing Distributor turndown often restricts packing turndown to about 2 on the liquid flowrate. If steady liquid flowrate is used (e.g., pumparounds), turndown performance of packing can match or exceed trays. Ceramic and plastic packings are highly corrosionresistant at low cost Greater flexibility because packing is relatively easy to change to modify column characteristics
Handle solids much better than packing due to much higher gas and liquid velocities, and fewer locations on trays where solids can be deposited. Use trays with large sieve holes or large fixed valves when plugging and fouling are primary considerations. Inherently more robust
Hydrogen-rich systems Turndown
Resistance to corrosion Flexibility
absorption. See Table 4-3 for a list of data required for the calculations. The accompanying Excel workbook has a worked example. For systems with a fast chemical reaction, the concentration of solute in the solvent may be assumed to be nil throughout the column; this assumption decreases the calculated packing height. However, if there is a slow reaction the required packed height may be more than that calculated [1]. 1. Define the equilibrium curve. Use Henry’s Law, if applicable, to establish the concentration of solute in solvent that is in equilibrium with the gas feed stream concentration (y1) at the bottom of the column (x*). 1 x1 ¼
Moving valve trays typically achieve turndown of 4 to 5. Large diameter sieve holes or fixed valve trays typically achieve turndown of 2 to 2.5, which is comparable to packings. Corrosion-resistant alloys are expensive Fixed trays are relatively difficult and expensive to change
Table 4-3 Data required for absorber calculations Category
Data Required
Absorber Packed Column and System
Operating pressure, P Column diameter, D Packing type and size Absorption volume coefficient, KGA Henry’s Law coefficient, kH, or vaporliquid equilibrium data, evaluated at the average column temperature Molar flow rate, G1 Molecular weight of inert gas and solute, MG and MS Temperature Mole fraction of solute, feed stream, y1 Mole fraction of solute, exit stream, y2, or percent of solute to remove in the column Molecular weight of solvent, ML Temperature Density, rL Molar concentration of solute in the feed stream, x2 (important if the solvent is recirculated)
Gas Stream
y1 kH
2. Calculate the slope of the equilibrium curve. This is the minimum ratio of molar flow, L/G: L y2 y1 ¼ x2 x1 G min
Much less influence on turbulent contact on trays
Liquid Stream
Absorbers
3. Choose a liquid rate that is about 20% to 100% higher than minimum [7]. For example, with 50% excess liquid flow: L L2 ¼ 1:5 G1 G min 4. Assume that none of the solvent is vaporized. Determine the molar gas flow out of the column. G2 ¼
G1 ð1 y1 Þ ð1 y2 Þ
5. Close the material balance to find the actual concentration of solute in solvent at the bottom of the column. First compute the moles of solute in the liquid discharge. Then calculate the concentration and molar flow rate. Moles ¼ L2 x2 þ G1 y1 G2 y2 x1 ¼
Moles Moles L2 ð1 x2 Þ
L1 ¼ G1 þ L2 G2 6. Calculate the molal gas velocity using the average gas rate through the column. Gm ¼
97
8. Obtain the log-mean concentration driving forces with the following two expressions: ðy y ÞLM ¼
ð1 yÞLM ¼
ðy1 y1 Þ ðy2 y2 Þ ðy1 y1 Þ ln ðy2 y2 Þ ð1 y1 Þ ð1 y1 Þ ð1 y1 Þ ln ð1 y1 Þ
9. Calculate the number of transfer units required for absorption: NOG ¼
ðy1 y2 Þ ðy y ÞLM
10. Calculate the height of each transfer unit: HOG ¼
Gm KGA ð1 yÞLM
11. The overall packed height is found by multiplying the number of transfer units by the height of each transfer unit: Z ¼ NOG HOG The dimensions of a packed column are shown in Figure 4-2.
ðG1 þ G2 Þ=2 p D2 =4
7. Find the vapor phase concentration of solute that would be in equilibrium with the liquid concentration at the bottom and top of the column. If there is an irreversible chemical reaction the equilibrium concentration is zero (y* ¼ 0). y1 ¼ kH x1 y2 ¼ kH x2
Figure 4-2. Nomenclature for packed tower absorber.
98
Rules of Thumb for Chemical Engineers
Overall Mass Transfer Coefficient If KGA values are available for a known system, those of an unknown system can be approximated by: Dv ðunknownÞ 0:56 KGA ðunknownÞ ¼ KGA ðknownÞ Dv ðknownÞ (4-5)
Absorption coefficient data may be difficult to obtain. The values are specific to the gas-liquid system of interest, and change with both gas and liquid rate. Packing manufacturers often publish KGA values for the CO2caustic system, but these are of little use in predicting coefficients for other systems. The coefficient is a function of gas flow rate and liquid flow rate according to the relationship [7]. However, the KGA value reaches a maximum as the liquid rate is increased at constant gas rate, when a pressure drop of about 0.75 in H2O/ft is achieved for 2-inch and smaller sizes of random packings [9]. KGA f Lb Gc
Where: KGA ¼ gas film overall mass transfer coefficient, kgmol/s-m3-atm or lb-mol/h-ft3-atm Dv ¼ diffusivity of solute in gas, m2/s or ft2/h [5] The simplest gas diffusivity relationship is the Gilliland relationship:
(4-4)
Dv ¼ 0:0069
For liquid-film controlled systems, the value of exponent b lies between 0.22 and 0.34 depending on the characteristics of the packing. If data is not available assume that b ¼ 0.30. Assume exponent c ¼ 0.06 to 0.08. For gas-film controlled systems, the value of exponent b also lies between 0.22 and 0.34 (assume 0.30 if unknown). However, exponent c ranges from 0.67 to 0.80 and should be assumed to be 0.75 if unknown. In any event, the sum of b and c should be greater than 1.0.
T 3=2 ð1=MA þ 1=MB Þ0:5 1=3 1=3 2 P VA þ V B
(4-6)
Where: T ¼ absolute temperature, R MA and MB ¼ molecular weights of the two gases, A and B P ¼ total pressure, atm VA and VB ¼ molecular volumes of gases, cc/g-mol It is convenient that packing manufacturers have largely standardized the reporting of KGA values, based on a system of 1% carbon dioxide absorbed into a solution of 4% NaOH with 25% conversion to carbonate. Comparison of KGA values at the same liquid loading provides the overall mass transfer relationship among the packings. Using Table 4-4, convert the reported, or known, value of KGA for a specific packing to the value to use for a different packing type or size. Some commercial systems are listed in Table 4-5.
Example
Absorption of hydrogen chloride into water is gas-film controlled. The KGA at a liquid rate of 4 gpm/ft2 and gas rate of 3.5 ft/s is reported to be 14 lb-mol/h-ft3-atm. What is the KGA at a liquid rate of 10 gpm/ft2 and gas rate of 5.0 ft/s? Solution: 0:3 0:75 10 5 KGA ¼ ð14Þ ¼ 24 4 3:5
Table 4-4 Relative overall mass transfer coefficient for packings Packing Size Packing
Material
beta-RingÒ Cascade Mini-RingÒ FlexiringÒ Hy-PakÒ IMTPÒ
Metal Metal Metal Metal Metal
5
16 mm ( /8”)
1.68
25 mm (1”) 2.22 1.99 1.54 1.5 2.00
38 mm (1.5”)
1.80 1.32 1.26 1.66
50 mm (2”) 1.41 1.68 1.09 1.05 1.37
80 mm (3” or 3.5”) 1.13 1.30 0.69 0.87
Absorbers
99
Table 4-4 Relative overall mass transfer coefficient for packingsdcont’d Packing Size Packing
Material
5
16 mm ( /8”)
25 mm (1”)
38 mm (1.5”)
50 mm (2”)
80 mm (3” or 3.5”)
I-Ring Metal 3.12 2.68 1.98 1.56 0.98 Nutter Ring Metal 2.05 1.71 1.51 1.07 Pall Rings Metal 1.51 1.26 1.06 0.62 Ceramic 1.38 1.11 0.92 0.54 IntaloxÒ Saddles Raschig Rings Ceramic 1.13 0.94 0.80 0.50 Ceramic 1.63 1.00 0.56 Super IntaloxÒ Saddles Plastic 1.64 1.21 0.84 beta-RingÒ Plastic 1.29 1.07 Cascade Mini-RingÒ Plastic 1.61 1.19 1.16 0.95 0.60 FlexiringÒ Plastic 1.16 Intalox SnowflakeÒ Pall Rings Plastic 1.29 1.10 1.02 0.60 Jaeger Ring Plastic 1.63 1.20 1.09 0.98 0.59 Plastic 1.80 1.37 1.20 Tri-PackÒ Jaeger Saddle Plastic 1.54 0.97 0.59 Jaeger Low-Profile Ring Plastic 1.17 1.17 1.02 Tellerette Plastic 1.22 1.07 Comparison of KGA published by packing manufacturers for the CO2/NaOH system at 25 C at a liquid rate of 10 gpm/ft2 and gas rate of between 400 and 970 lb/ft2-h
Table 4-5 Commercially important absorption systems
Solute
Solvent
Type of Absorption
Typical KGA (lb-mol/h-ft3-atm)
Henry’s Law Constant kH [ p / x [8] kH;px
C
Acetone Water Physical 1.95 4600 Acrylonitrile Water Physical 5.0 2800 Ammonia Dilute Acid Physical 13 (Note 4) 0.94 4100 Ethanol Water Physical 0.30 6500 Formaldehyde Water Physical 4.4 (Note 3) 0.017 6800 Hydrogen Chloride Water Physical 14 (Note 4) 0.03 0 Hydrogen Fluoride Water Physical 6.0 (Note 4) e e Sulfur Dioxide Water Physical 2.2 (Note 3) 46.1 3100 Sulfur Trioxide Water Physical 20 (Note 1) e e Benzene and Toluene Hydrocarbon Oil Physical e e Butadiene Hydrocarbon Oil Physical e e Butanes and Propane Hydrocarbon Oil Physical e e Naphthalene Hydrocarbon Oil Physical e e Carbon Dioxide Aqueous Sodium Hydroxide Irreversible Chemical 1.5 (Note 3) e e Hydrochloric Acid Aqueous Sodium Hydroxide Irreversible Chemical e e Hydrocyanic Acid Aqueous Sodium Hydroxide Irreversible Chemical 4.4 (Note 3) e e Hydrofluoric Acid Aqueous Sodium Hydroxide Irreversible Chemical e e Hydrogen Sulfide Aqueous Sodium Hydroxide Irreversible Chemical 4.4 (Note 3) e e Chlorine Water Reversible Chemical 3.4 (Note 3) 608 2500 Carbon Monoxide Aqueous Cuprous Ammonium Salts Reversible Chemical e e MEA or DEA Reversible Chemical (Note 2) e e CO2 and H2S DEG or TEG Reversible Chemical e e CO2 and H2S Nitrogen Oxides Water Reversible Chemical 18000 2000 The Henry’s Law constant (units: atm) listed here is the reciprocal, representing volatility, at 298.15 K. Use this expression to adjust for temperature: kH
1 1 ¼ kH exp C ðatmÞ T 298:15 (Continued)
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Rules of Thumb for Chemical Engineers
Table 4-5 Commercially important absorption systemsdcont’d
Solute
1. 2. 3. 4.
Solvent
Type of Absorption
Typical KGA (lb-mol/h-ft3-atm)
Henry’s Law Constant kH [ p / x [8] kH;px
C
2-inch ceramic Intalox saddles at a liquid rate of 7.5 gpm/ft2 and gas rate of 1200 lb/ft2-h [7] Refer to [7] for a discussion of this system #2 plastic Super IntaloxÒ packing at a liquid rate of 4 gpm/ft2 and gas velocity of 3.5 ft/s; liquid film controlled [7] #2 plastic Super IntaloxÒ packing at a liquid rate of 4 gpm/ft2 and gas velocity of 3.5 ft/s; gas film controlled [7]
Nomenclature Ai G D Dv Ei FP G Gm HOG KGA kH L Lo MA and MB NOG P T V VA and VB x y Xo,i Y1,i Ynþ1,i
¼ Absorption factor from chart, for component i ¼ vapor rate, moles/time ¼ tower diameter, m or ft ¼ diffusivity of solute in gas, m2/s or ft2/h ¼ recovery fraction for component i ¼ packing factor ¼ gas rate, moles/time ¼ molal gas velocity, moles/time/m2 or moles/time/ft2 ¼ height of a transfer unit with gas-film resistance, m or ft ¼ gas film overall mass transfer coefficient, kg-mol/s-m3-atm or lb-mol/ h-ft3-atm ¼ Henry’s law constant ¼ liquid rate, moles/time ¼ feed rate, lean oil, mol/h ¼ molecular weights of the two gases, A and B ¼ number of transfer units with gas-film resistance ¼ total pressure, atm ¼ absolute temperature, R ¼ feed rate, rich gas, mol/h ¼ molecular volumes of gases, cc/g-mol ¼ mole fraction, liquid phase ¼ mole fraction, vapor phase ¼ component i in liquid phase of lean oil stream, mole fraction ¼ component i in lean gas stream, mole fraction
Yo,i [ ai,o Xo,i Z ai,o
¼ equilibrium vapor concentration of component i in lean oil stream ¼ height of packed section of column, m or ft ¼ average relative volatility, hydrocarbon component i and lean oil
References
[1] Coker AK. Ludwig’s Applied Process Design for Chemical and Petrochemical Plants. 4th ed, vol. 2. Gulf Professional Publishing; 2010. [2] Gas Processors Suppliers Association (GPSA). Engineering Data Book, SI Version. 12th ed, vol. 2; 2004. [3] Kenig E, Seferlis P. Modeling Reactive Absorption. Chemical Engineering Progress, January, 2009:65–73. [4] Kister H. Ask the Experts: Acid-Gas Absorption. Chemical Engineering Progress, June, 2006:16–7. [5] Marreo T, Mason E. Gaseous Diffusion Coefficients. Journal of Physical and Chemical Reference Data. American Institute of Physics, 1972; 1:3. [6] McCabe W, Smith J, Harriott P. Unit Operations of Chemical Engineering. 7th ed. (New York): McGraw-Hill, Inc; 2004. [7] McNulty K. Effective Design for Absorption and Stripping. Chemical Engineering, November, 1994. [8] Sander R. Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry (Version 3), www.henrys-law.org; 1999. [9] Strigle Jr R. Packed Tower Design and Applications. 2 ed. Gulf Publishing Co; 1994.