DESIGN OF A PACKED-BED ABSORPTION COLUMN CONSIDERING FOUR PACKING TYPES AND APPLYING MATLAB

In the present work, a packed bed absorption column is designed to recover certain amounts of ethanol contained in a gaseous stream. Four packing types (50-mm metal Hiflow rings, 50-mm ceramic Pall rings, 50-mm metal Top Pak rings and 25-mm metal VSP rings) are considered in order to select the most appropriate one in terms of column dimensions, pressure drop and mass-transfer results. Several design parameters were determined including column diameter (D), packing height (Z), overall masstransfer coefficient (Km) and gas pressure drop (P/Z), as well as the overall number of gas-phase transfer units (NtOG), overall height of a gas-phase transfer unit (HtOG) and the effective surface area of packing (ah). The most adequate packing to use for this absorption system constitutes the 25-mm metal VSP rings, since it provided the greatest values of Km (0.325 kmol/m.s), and ah (169.57 m), as well as the lowest values of both Z (0.6 m) and HtOG (0.145 m), meaning that it will supply the higher masstransfer conditions with the lowest column dimensions. The influence of both gas mixture (QG) and solvent (mL) feed flowrates on D, Z, Km, P/Z, NtOG and HtOG was also evaluated for the four packing considered. The design methodology was solved using computing software MATLAB version 7.8.0.347 (R2009a) (Math Works, 2009), and also Microsoft Excel.


INTRODUCTION
Gas-liquid operations are used extensively in chemical and petrochemical industries for transferring mass, heat and momentum between the phases.Among the most important gas-liquid systems employed nowadays is absorption, defined as a mass transfer operation at which one or more soluble components contained in a gas phase mixture are dissolved into a liquid solvent whose volatility is low under process conditions.The absorption process could be classified as physical or chemical.The physical absorption occurs when the target solute is dissolved into the solvent, while the chemical absorption takes place when the target solute reacts with the solvent.The removal efficiency of any physical absorption process will depend on the physical-chemical properties (density, viscosity, diffusivity, etc.) and feed flowrates of the gaseous and liquid streams; the type of mass-transfer contact surface (packing or plate); the operating temperature and pressure (commonly, lower temperatures will favor gas absorption by the liquid solvent); gas-liquid ratio; contact time between phases; and the solute concentration at the inlet gas stream.Gas-liquid absorption operations are usually accomplished in equipment named absorbers.
Absorbers are used to a great extent in industrial complexes and plants to separate and purify gaseous streams, to recover valuable products and chemicals, as well as for contamination control.The most common absorber types employed in industry are plate columns, packed towers, Venturi cleaning towers and spray chambers.Packed towers are widely used for gas-liquid absorption operations and, to a limited extent, for distillations (Perry and Chilton, 2008).A typical packed column consists of a vertical, cylindrical shell containing a support plate for the packing material, mist eliminators, as well Nexo Revista Científica / Vol. 29, No. 02, pp.83-104 / Diciembre 2016 as a liquid distributing device designed to provide effective irrigation to the packing (Benitez, 2009) (Figure 1).The liquid is fed at the top of the column and trickles down through the packed bed, exposing a large surface to contact the gaseous stream, which is supplied at the bottom of the tower (Ludwig, 1997) (Richardson and Harker, 2002).The tower packing, or fill, should provide a large interfacial surface between liquid and gas per unit volume of packed space, and also should have desirable hydrodynamic/hydraulic characteristics (Benitez, 2009).Packed-bed absorbers have been widely studied, analyzed and assessed in recent years either to design or evaluate a unit for a given application (Benitez, 2009)  The design approach of a packed-bed absorber usually involves the determination of geometrical parameters such as tower diameter (D) and packing height (Z), as well as some other mass-transfer and operational variables such as convective mass-transfer coefficients for gas and liquid streams; dry and overall pressure drops; as well as overall mass-transfer coefficient.A well designed packed-bed tower will provide the required mass-transfer contact between gas and liquid phases, with low pressure drop, small capital and operating costs, and high removal efficiencies.The use of simulation and modeling techniques to design, evaluate or optimize chemical processes, equipment and unit operations, either from the economic or technical point of view, have reached unprecedented levels in recent years (Boyadjiev, 2010) (Dimian and Bildea, 2008) (Finlayson, (2006).Among the most developed and common computer applications used today is the MATLAB ® software (Math Works, 2009), since it provides numerical methods which permit to solve numerous mathematical, statistical, financial, trigonometric, etc. functions by using special application fields referred to as toolboxes (Karris, 2004) (Nakamura, 2002).MATLAB ® software is considered a highlevel software package with many built-in functions, which is very easy to use, even for people without prior programming experience, and that make the learning of numerical and mathematical methods much easier and more interesting (Karris, 2004)   At the present work, a packed bed absorber is designed to recover certain amounts of ethanol contained in a CO2-rich gaseous stream coming from fermentation operations.Four different packing types (Pall ® , Hiflow ® , Top Pak ® and VSP ® ) were evaluated in order to determine which packing configuration provides the lowest column dimensions (tower diameter and packing height) as well as the highest mass-transfer coefficient for this application, without exceeding the maximum allowable pressure drop and also without affecting the requested removal efficiency.The influence of both liquid solvent and gas mixture feed flowrates on 4 important process parameters (tower diameter, packing height, gas pressure drop and overall mass-transfer coefficient) was assessed for the four packing, while the effect of this two flowrates on two design parameters (overall number of gas-phase transfer units; NtOG and overall height of a gas-phase transfer unit, HtOG) was also determined.The design methodology was solved using computing software MATLAB ® version 7.8.0.347 (R2009a) (Math Works, 2009), and also Microsoft Excel ® spreadsheet.

Problem description
A gaseous mixture containing CO2 and ethanol, with a molar composition of 92 % CO2 and 8 % of the alcohol, is evolved from a fermentation process.The ethanol must be recovered by means of a countercurrent absorption process using water as the solvent (Figure 3).The gas mixture will enter the tower at a rate of 4000 m 3 /h, at 25 ºC (298 K) and 1.1 atm, while the solvent (water) will be supplied at a flowrate of 6500 kg/h and also at 298 K.The required recovery of ethanol will be 97.0 %, while the maximum pressure drop permitted for the gas stream should not exceed 250 Pa/m of packed height.It's desired to design a suited packed-bed absorber working at 70% of flooding and operating under isothermal conditions.For this application, four packing types will be evaluated (Figure 2 According to (Ludwig, 1997), the four packing types considered have the following performance and mass-transfer characteristics:  ; the solute gas is very diluted in the liquid phase (that is, the liquid phase can be catalogued as a dilute liquid solution), the system operates under isothermal conditions and there is no reaction between the dissolved solute (ethanol) and the solvent (water), it's assumed that the system obeys the Henry's law (Leye and Froment, 1986) (Matos and Hing, 1990) (Perry and Chilton, 2008) (Richardson and Harker, 2002) (Treybal, 1980).According to (Perry and Chilton, 2008) (Rogers, 2007), the value of the Henry's constant for an ethanol-water system operating at 25 ºC is H = 0.272 atm.Thus, the distribution coefficient () for the gas-liquid system (ethanol-water system) at 25 ºC and 1.1 atm is  = H/P = 0.272/1.1 = 0.229.

Packing hydraulic and mass-transfer parameters
The most important hydraulic/mass transfer characteristics of the four packing types selected are described in the Table 2 (Billet, 1989) (Perry and Chilton, 2008).

Inlet data
The inlet data necessary to carry out the design calculations are showed in Table 3: The molecular weight of the gas mixture (MG) was determined applying the equation ( 1): where yCO2(1) = 1yeth(1).The gas mixture density (ρG) at 25 ºC was determined using the Kay's method (Perry and Chilton, 2008), while the viscosity of the gas mixture (μG) was calculated using the following correlation (Pavlov, 1981): where μeth and μCO2 values are given in cP.
The amount of ethanol absorbed is; The amount of solvent liquid exiting the column is: The flow parameter (X), the pressure drop parameter under flooding conditions (Yflood) and the CS coefficient at flooding conditions (CSflood) were determined according to the equations (5) ( 6) and ( 7), respectively.
The gas velocity at flooding conditions (vGflood), the gas velocity (vG), and finally the tower diameter (D), were calculated by using the following correlations: Most packed-bed absorbers are designed to safely avoid flooding conditions and also to operate in the preloading region, with a gas-pressure drop limit of 200 -400 Pa/m of packed depth [4].In this approach, both the gas dry pressure drop (ΔP0/Z) and overall pressure drop (ΔP/Z) were determined for the absorption process using well-accepted equations.The liquid holdup influence was also taken into account, that is, when the packed bed is irrigated, the liquid holdup causes an increment of the pressure drop (Benitez, 2009) (Perry and Chilton, 2008).Prior to the determination of both pressure drops, it was necessary to determine several parameters first.Among those parameters are included the effective particle diameter (dP) [equation (11)]; the wall factor (KW) [eq.( 12)]; the gas-phase Reynolds number (ReG) [eq.( 13)]; the dry-packing resistance coefficient (ψ0) [eq.( 14)]; liquid mass velocity (GL) [eq.( 15)]; the liquid velocity (vL) [eq.( 16)]; the liquid-phase Reynolds number (ReL) [eq.( 17)]; liquid-phase Froude number (FrL) [eq.( 18)]; the ratio ah/a [eq.( 19)]; the effective specific surface area of packing (ah) [eq.( 20)]; and, finally, the liquid holdup (hL) [eq.( 21)].
The gas dry pressure drop per meter of packing height (ΔP0/Z) was determined according to the following correlation: Then, the gas overall pressure drop per meter of packing height (ΔP/Z) can be finally calculated:

Gas-phase diffusion coefficient:
The theory describing diffusion processes in binary gas mixtures at low to moderate pressures has been studied extensively in recent years, and is well developed nowadays.Since the absorption process is a binary gas system taking place at low-pressure, the gasphase diffusion coefficient can be estimated using the Wilke and Lee correlation (Benitez, 2009): where: Liquid-phase diffusion coefficient: Compared with the kinetic theory behind the gases behavior, which is well developed and available today, the theoretical basis of the internal structure of liquids and their transport characteristics are still insufficient to permit a rigorous treatment (Benitez, 2009) (Billet, 1989).Usually, liquid diffusion coefficients are several orders of magnitude smaller than gas diffusivities, and depend mostly on concentration profiles due to changes in viscosity, as well as some changes in the degree of ideality of the solution.To determine the liquid-phase diffusion coefficient in binary systems for solutes transport to aqueous solutions, the Hayduk and Minhas correlation was used (Benitez, 2009)

Mass transfer coefficients
To determine the mass transfer coefficients for both phases, two correlations were used which were obtained from an extensive study made by Billet and Schultes (Billet, 1989), that involved measurement and correlation of mass-transfer coefficients for 31 different binary and ternary systems, equipped with 67 different types and sizes of packings, in columns of diameter ranging from 6 cm to 1.4 m.

Operating and equilibrium lines
The operating line will be elaborated using the following data:  Mole fraction of ethanol in inlet gas mixture [yeth(1)] = 0.08  Mole fraction of ethanol in outlet gas mixture [yeth(2)] = 0.0024 While to elaborate the equilibrium line, the following expression will be used:

RESULTS AND DISCUSSION
The main physical parameters calculated for the gas mixture (that is, molecular weight, density and viscosity) are showed in Table 4, while the calculated tower diameter (D) and overall gas pressure drop (ΔP/Z) values for each packing type, among other important design variables, are showed in Table 5. Nexo Revista Científica / Vol. 29, No. 02, pp.83-104 / Diciembre 2016 Table 6 shows the calculated values of the diffusion and convective mass-transfer coefficients for both fluids (gas and liquid), whereas the values obtained of packing height (Z) and other significant flow and mass-transfer parameters are listed in Table 7, all of them for the four packing types selected.Finally, Table 8 presents a summary of the most important geometrical and mass-transfer parameters calculated for the four packing types.Figure 4 shows a graphical comparison between Z and D for each packing type; while the values obtained of gas pressure drop and overall mass-transfer coefficient for each packing are given in Figure 5 and Figure 6, respectively.The resulting values of tower diameter; gas pressure drop; overall mass-transfer coefficient and packing height for each packing as a function of gas mixture feed flowrate (QG) and liquid solvent feed flowrate (mL) are reported in Figure 7 and Figure 8, respectively.The behavior of the variables NtOG and HtOG with respect to QG and mL are showed in Figure 9 and Figure 10, respectively.Finally, both the operating and equilibrium lines are illustrated in Figure 11.directly related with the packing factor (Fp) value of each packing type, that is, if Fp increases so will increase the value of D. As for the calculated values of gas pressure drop (P/Z) (Figure 5), the VSP ® rings exhibited the highest value of this parameter (223 Pa/m), while the lowest value of this parameter corresponded to Hiflow ® rings, with 112 Pa/m.This variable depends on several factors, being the most important to consider (without taking into account the influence of the physical-chemical parameters of the fluids being handled) the gas mixture (QG) and solvent (mL) feed flowrates, mass-transfer surface area per unit volume of packing (a); packing porosity (), Fp and D. In general, P/Z will increase if a, mL and D decreases and if , QG or Fp increases.
Finally, VSP ® rings supplied the greater value of the overall volumetric mass-transfer coefficient (Km) (Figure 6) corresponding to 0.326 kmol/m 3 s, while the lowest value of this parameter belonged to Top Pak ® rings (0.068 kmol/m 3 s).The most influential variables on Km are the hydraulic factor Ch and the mass-transfer factor CV; as well as QG, mL, Fp, a, D and .In that case, the value of Km will increase with an increment of Ch, CV and a, as well as with a reduction of Fp, D and .On the other hand, an increment of QG and a reduction of mL will decrease the value of Km for the four packing types evaluated, according to the results showed in Figure 8 and Figure 9. Regarding to the results showed in Figure 8, an increment of the QG (maintaining constant the value of mL) will increase the value of D, P/Z and Z, while Km will decreases.On the other hand, an increment of the mL (keeping constant the value of QG) will increase the values of D and Km, while both P/Z and Z decrease for the four packing types.As for the results displayed in Figure 10, an increment of QG will increase both the overall height of a gasphase transfer unit (HtOG) and the overall number of gas-phase transfer units (NtOG) for all the four packing types evaluated.In contrast, the Figure 11 showed the opposite pattern, that is, both the HtOG and NtOG decrease with an increment of the water feed flowrate.The results obtained in both figures mean that both the eight of the apparatus required to accomplish the requested separation and the number of theoretical stages required to carry out the same separation in a plate-type apparatus will increase if QG increases (mL constant), and will decrease if mL increases (QG constant).Analyzing and summarizing the results showed in Table 9, the Pall rings supplied the highest value of D (1.221 m), while Hiflow ® rings provided the lowest value of P/Z (112 Pa/m).On the other hand, Top Pak ® rings presented the highest values of both HtOG (0.671 m) and Z (2.60 m), as well as the lowest values of D (0.921 m), Km (0.109 kmol/m 3 .s)and ah (55.66 m -1 ).Finally, VSP ® rings had the highest values of P/Z (223 Pa/m), Km (0.326 kmol/m 3 .s)and ah (169.57m -1 ), and the lowest values of both HtOG (0.148 m) and Z (0.60 m).It should be noted that the value of D obtained for VSP ® rings, which is the second highest value of D of all the packing types considered, is only 18.6 % higher than the lowest value of D obtained, corresponding to Top Pak ® rings (0.921 m).Considering the results obtained for the four packing types evaluated, it can be concluded that the most appropriate packing to use for this service or application is the VSP ® rings, since it supply the most economic geometrical results and the highest mass-transfer conditions.

CONCLUSIONS
The Pall ® rings provided the greatest value of tower diameter (D) [1.An increment of the gas mixture feed flowrate (QG) (keeping constant mL) increases the values of D, P/Z and Z, while Km decreases for the four packing types considered.An increment of the solvent feed flowrate (mL) (maintaining constant QG) will increase the values of D and Km, while both P/Z and Z decreases for the four packing types evaluated.An increment of QG will increase the values of both the HtOG and the overall number of gas-phase transfer units (NtOG) for the four packing types.Both the HtOG and NtOG decrease with an increment of mL.The most adequate packing to use on this absorption system is the VSP ® rings since it provided the highest mass-transfer conditions with the lowest column dimensions.Nexo Revista Científica / Vol. 29, No. 02, pp.83-104 / Diciembre 2016 SEMBLANZA DE LOS AUTORES Amaury Pérez Sánchez: Obtuvo el grado de Ingeniero Químico en la Universidad de Camagüey "Ignacio Agramonte Loynaz", Cuba, donde actualmente es profesor instructor e investigador auxiliar.Trabaja en líneas de investigación relacionadas con la transferencia de calor y masa en plantas procesadoras de alimentos y biotecnológicas, además del empleo de simuladores de procesos para evaluar y/o diseñar procesos, sistemas u operaciones unitarias.

Figure 4 .Figure 5 .
Figure 4. Comparison between Tower Diameter and Packing Height as a function of packing

Figure 9 .
Figure 9. Calculated Tower Diameter; Gas Pressure-Drop; Overall Mass-Transfer Coefficients and Packing Height values for the different packing types as a function of Solvent (Water) Feed Flowrate.

Figure 10 .
Figure 10.Calculated HtOG and NtOG values for each packing type as a function of Gas Mixture Feed Flowrate.

Figure 11 .
Figure 11.Calculated HtOG and NtOG values for each packing type as a function of Liquid Solvent (Water) Feed Flowrate.

Table 1 .
Performance and mass-transfer characteristics of the different packing considered (Ludwig, 1997), 1997)

Table 4 .
Calculated physical parameters

Table 5 .
Tower diameter and pressure drop results for each packing type

Table 6 .
Diffusion and mass-transfer coefficients for each packing type

Table 8 .
Summary of the most important packed column design parameters for the four packing considered