Multicomponent Distillation Shortcut Method

Journal of Applied and Industrial Sciences, 2013, 1 (3): 44-48, ISSN: 2328-4595 (PRINT), ISSN: 2328-4609 (ONLINE)

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Research Article

A short-Cut Method for Designing Multi-Component Fractionation Column Rawia. S.Hassan1 , Gurashi.A. Gasmelseed2, B. A. Karama3, and A.E Musa4 (1)

Faculty of graduate studies, University of Karary, Khartoum – Sudan Email : [email protected] (3) Faculty of graduate studies, University of Karary, Khartoum – Sudan (2) Department of Leather Technology, College of Applied and Industrial Sciences, University of Bahri, Khartoum – Sudan, P.O.Box 1660 Email : [email protected] Telephone: +249919634134 (4) Department of Leather Technology, College of Applied and Industrial Sciences, University of Bahri, Khartoum – Sudan, P.O.Box 1660 E mail: [email protected] (Received: June 11, 2013; Accepted: August 14, 2013) 

Abstract— Fractionation of multicomponent mixtures into top and side stream products depends on the relative volatility of the cut. As the cut consists of more than one component with specific true boiling point (TBP), its relative volatility can be calculated. In this method the component with the lowest relative volatility at the top above the feed tray is designated as a light key component (lk), all non-light keys,(nlk) are more volatile with volatilities greater than that of the light key. On the other hand the components with highest volatility at the bottom below the feed plate is designated as the heavy key component (hk), all nonheavy keys (nhk), are less volatile with relative volatilities less than that of the heavy key. Based on these facts, the designated light and heavy components will be taken as binary and the column will be designed accordingly. In this study a multicomponent fractionation column is designed by both the rigorous multicomponent design method and that of a simple binary Mc cabe Thiele method for the system C2 to C7 feed mixture. The results of the design parameters are considered to be good and in agreement.

Index Terms— Design, Multicomponent, Binary systems. I. INTRODUCTION

M

ulticomponent hydrocarbons need to be separated into top and side streams products in a fractionation column [1]. These streams are separated in cuts depending on their true boiling point temperature and their relative volatilities. The design of such columns is tedious and requires compositions, and physical properties of the top and bottom products [2]. The important parameter in the design is the number of theoretical stages which requires the application of Underwood and Gilly land correlations, the data therefore require on-line sampling on pilot scale with subsequent scaleup.

A new technique is developed taking into consideration the more volatile component or cut as the (lk) component and the less volatile component or cut as the heavy key (hk). The (nlk) are those which are more volatile than the (lk), while the nonheavy keys (nhk) are those which are less volatile than heavy keys [2]. The light and heavy are taken to be a binary system of the two components and the number of theoretical plates are determined by Mc cabe Thiele graphical method, and so are the other design parameters. The design parameters determined by both methods are to be compared and analyzed. II. MATERIALS AND METHODS A mixture of hydrocarbons C2 to C7 is taken as a multicomponent feed entering the fractionators as saturated liquid at a temperature of 120oC and a pressure of 13 bars. The equilibrium data are obtained using Antoine equation. The minimum number of theoretical stages is calculated by Fenske equation [3]. Compositions of the feed, distillate, bottom, and relative volatilities are specified and tabulated. The minimum reflux ratio is determined by Underwood equation [4] taking q-value equal to one as the feed is saturated liquid. The flow factor is calculated as well as the tray space and the column is operated at 85% of the flooding capacity, the number of theoretical trays is then calculated by Gilly land equation [6], the overall efficiency is calculated by O’nell equation[5], and hence the number of actual stages and the column height. The column down-comer, net, and active areas are specified as well as the diameter of the column at 85% of the flooding velocity. But as for the new technique, the equilibrium data are determined for the binary consisting of lk and hk, and Mc cabe Thiele plot is used to determine the number of the theoretical plates, other design parameters are calculated normally [6].


Procedure Vapor -liquid equilibrium is calculated by Antoine equation: ………..1 Where: Pvap= vapor pressure of the component A, B, C = Antoine constants T = absolute temperature in Kelvin For saturation feed at 120°C and 13 bar Table1 Antoine constants for the system C2 – C7 Component name Symbol A B Ethane C2H6 15.9 1580 Propane C3H8 15.7 1870 Iso butane C4H10 15.9 2200 Cis butane C4H8 15.8 2210 i-pentane C5H12 15.6 2350 Iso prene C5H8 15.9 2470 Cyclo hexane C6H12 15.8 2660 Toluene C7H8 16.3 3240

C -13.8 -25.1 -29.9 -36.2 -40.2 -39.6 -47.2 -47.2

III. RESULTS AND DISCUSSION The following data are obtained:

Component Name

Symbol

Ethane Propane Iso butane Cis butane i-pentane Iso prene Cyclo hexane Toluene

C2H6 C3H8 C4H10 C4H8 C5H12 C5H8 C6H12 C7H8

Table 2 Equilibrium relationship Vapor Distribution Pressure Coefficient Ki Pvi 123292.7 12.64 40256.2 4.13 18477.9 1.89 14598.1 1.5 7480.6 0.767 7265.7 0.745 3246.7 0.333 995.5 0.102

Component Feed Rate Kmol/h 0.93 17.09 14.06 18.05 14.93 1.62 12.29 30

Calculate from equilibrium relationship: Ki= Pvi/Pt Where: Pvi = vapour pressure of component i Pt = total pressure Minimum number of stages Fenske equation

Table 3 Composition of components C2 – C7 Component Feed D ,mole fraction W, mole fraction name mole fraction Ethane 0.0093 0.0475 0 Propane 0.1709 0.4196 0 Iso butane 0.1406 0.3462 0 Cis butane 0.085 0.1967 0.00105 i-pentane 0.1439 0.0004 0.2530 Iso prene 0.0162 0 0.28 Cyclo hexane 0.1229 0 0.2695 Toluene 0.3 0 0.5107 Where: D= distillate product, W= bottom product C2= Ethane; C3 = Propane; C4 = Iso butane, Cis butane; C5 = i-pentane, Iso prene; C6 = CYCLO HEXANE; C7 = TOLUENE Table 4 Calculation of Relative volatility of C2 – C7 Component Name αi = Pi/Pj Ethane 16.48 Propane 5.38 Iso butane 1.95 Cis butane 2.74 i-pentane 1 Iso prene 0.97 Cyclo hexane 0.43 Toluene 0.13 Pvi = vapour pressure of component i Pj = vapour pressure of component j lk = 2.74 , where lk is the relative volatility of the light key Table 5 Composition of light (cis-butane) and heavy (i-pentane) keys in top and bottom: Lk Hk xD,mole fraction 0.1967 0.0004 xB, mole fraction 0.0015 0.253 The mole fraction of XD and XB are experimental data Determination of minimum number of stages (Nm): Nm = 12.8 = 13 stages Minimum Reflux Ratio Rm Using Underwood equation: ………3

……….2

Where: Nm = minimum number of stages, xD =composition of the top product α = relative volatility, xw=composition of the bottom product

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For saturation feed condition, q=1, θ = 1.3 by trial and error Where: αi = relative volatility of component (i), XiF = composition of component ( i) in feed.


Table 6 Calculation of Rm for separation of C2 – C7 Component name

Component name Ethane Propane Iso butane Cis butane

0.052 0.553 1.03 0.37

i-pentane Iso prene Cyclo hexane Toluene TOTAL

-0.0013 0 0 0 1.78

Where: ρv = density of the vapor phase ρl= density of the liquid phase Densities at the top of the distillation column ρv= 3.67 Kg/m3 ρl= 738 Kg/m3 Densities at the bottom of distillation column ρv= 2.16 Kg/m3 ρl= 578 Kg/m3 Taking tray spacing = 0.6 m Flow factor at the top = 0.03 Flow factor at the bottom = 0.02 KT = 0.18 KB = 0.16

Rm= 0.78 R actual = 1.5 * Rm = 1.18 Where R actual = R X = (R-Rm) /(R+ 1) …………..4 [7] Y = 1- X0.33 ………5 N = (Nmin + Y)/(1-Y) = 21.5 = 22 stages Column Efficiency EO= 51 – 32.1 log (αi* μi) …….6 μi = average viscosity= ∑ μi xi, αi = relative volatility of light key E0= 65.4 Na = 22/0.654= 34 stages Height of the column Ht = (Na – 1 ) *C + (Na /10) * C + 0.1 Ht ….7

Where: KT and KB are constants at the top and bottom respectively Velocity at the top = 2.8 m/s Velocity at the bottom = 2.3 m/s Operation at 85% flooding rate Velocity at the top = 2.38m/s Velocity at the bottom = 1.9 m/s Calculation of volumetric flow rates At the top =41900/3.67/3600 = 3.17 m3/s At the bottom 41900 /2.17 / 3600= 3.7 m3/s Area of the column Top = 3.17/ 2.38= 1.33 m2 Bottom = 3.7/1.98 = 1.8 m2 Column cross sectional area TOP = 1.33 / 0.88 = 1.5 m2 Bottom 1.8/0.88 =2.04 m2 Diameter of column:

Where: Ht = Height of the column. C = tray Space = 0.6 [8] Ht = 24 m Flow Rates: Feed = 160 Ton/h. Top Product = 20.94 T/h. Bottom Product = 139.06 T/h Vapor rate = D (1+R) = 41.9 T/h LT = DR = 21.06 T/h LB = F + LT L / V (top) = 0.5 L / V (bottom) = 2.5 Column diameter: The column diameter must be selected so that flooding does not occur, however at the same time vapor velocities that are high for greater plate are needed. In these calculations, operation at 85% of flooding velocity is taken, this velocity determined from equation

………. (8) Flow Factor

…………….9

………..10 DT = 1.38m, DB = 1.61 m Where: DT = column diameter at the top, DB = column diameter at the bottom Column diameter = 1.61 m Column area = 2 m2 Down comer area (12 % Ac) = 0.24 m2 Net Area = 2.5 – 0.3 = 1.8 m2 Active area = Ac – 2Ad = 1.56 m2 Hole area (10% Aa) = 0.156 m2 Hole diameter = 5 mm Plate thickness = 5 mm Area of one hole = 1.96*10-5 Number of holes = 7945 holes Binary Design Method: this is Mc.Thiele Method

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LK HK

Table 7 Identification of Light and Heavy component Component name xf xD xW Cis- butane 0.085 0.1967 0.00105 I-pentane 0.1493 0.0004 0.2530

Where: xf = composition in feed Data for vapor-liquid equilibrium curve in term of relative volatility ..................11

x 0 Y 0

0.05 0.123

0.1 0.23

Relative volatility for light component = 2.74 0.2 0.3 0.4 0.5 0.6 0.7 0.4 0.53 0.64 0.73 0.8 0.86

0.8 0.92

0.9 0.96

1.0 1

Figure 1: Mccabe Thiele graphical method Where y axis is the composition of light key in vapor phase and x axis is the composition of light key in liquid phase

Design parameter N Eo Na Ht D At Ad An Aa Ah Plate thickness Hole diameter Number of holes

Table 8 Comparison of multicomponent and binary design methods Multi component method Mc Thiele method 22stages 19 stages 65.4% 62.3% 34 stages 31 stages 24m 22 m 1.5 m2 1.7 m2 2 2m 2.3 m2 2 0.24 m 0.27 m2 2 1.8 m 2.02 m2 2 1.56m 1.76 m2 0.156 0.176 m2 0.5mm 0.5mm 0.5 mm 0.5 mm 7945 8963

Percent deviation -15.7 -4.9 -9.7 -9.0 11.7 13 11.1 10.8 11.3 11.3 0 0 11.3

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From figure 1 = 0.29 Number of theoretical stages = 19 stages Column Efficiency EO= 51 – 32.1 log (αi* μi) μi = average viscosity E0= 62.3% N = 19/0.623 = 29 stages Height of the column Ht = (Na – I ) *C + (Na /10) * C + 0.1 Ht Where: Na= Actual number of stages Ht = Height of the column C = tray Space = 0.6 Ht = 22 m Flow Rates- Feed = 160 Ton/h Top Product = 20.94 T/h Bottom Product = 139.06 T/h Vapor rate = D (12+2.2) = 67 T/h. LT = DR=46T/h, LB = F + LT = 206 T/h L / VT = 0.69, L / VB= 2.8 Where: LT, LB = liquid rate at the top and bottom VT, VB = vapor rate at the top and bottom Column diameter

Column cross sectional area AT=1.76 / 0.88=2 m AB =2.04 /0.88 =2.3m2 Diameter of the column DT = 1.59 m DB = 1.7m Column area = 2.3 m2 Down comer area (12 % Ac) = 0.27 m2 Net Area = 2.02 m2 Active area = Ac – 2Ad = 1.76 m2 Hole area (10% Aa) = 0.176 m2 Hole diameter = 5m Plate thickness = 5mm Number of holes = 9677 holes IV. CONCLUSIONS The multicomponent method using the (lk) and (hk) as binaries is comparatively similar to the method of Mccabe Thiele for binary graphical method. It is observed that the maximum deviations is 15% in the number of theoretical stages, other deviations fall between 11.7% and 0.0% which is acceptable for the design. The new method is simple, saves time and accurate. It is recommended that more case studies have to be designed and compared to confirm and verify the new design technique. Acknowledgement

Flow Factor

The authors wish to thank the University of Karary, Faculty of graduate studies for supporting this work for Ph.D Thesis in chemical engineering. REFERENCES

Densities at the top of distillation column ρv= 2.54Kg/m3 ρl= 641Kg/m3 Densities at the bottom distillation ρv= 2.44 Kg/m3 ρl= 626 Kg/m3 Taking tray spacing = 0.6 m Flow factor at the top = 0.04. Flow factor at the bottom = 0.17 KT = 0.19 KB = 0.17 Velocity at the top = 3.0 m/s Velocity at the bottom = 2.7 m/s For 85% flooding Velocity at the top = 3.0 * 0.85 = 2.55 m/s Velocity at the bottom=2.7* 0.85 = 2.3 m/s Volumetric flow metric rates At the top =41900/2.54 /3600 = 4.5 m3/s At the bottom 41900/2.441/ 3600= 4.7 m3/s Area of the column Top = 4.5/2.55 = 1.76 m2 Bottom = 4.7 / 2.3 = 2.04 m2

[1]. Treybal, R.E. (1984). Mass Transfer Operation, MCGraw Hill, New York. [2]. Fair, J.R, Bells, W.L. (1968).,Multicomponent Distillation, J.Chem.Eng., 951,165. [3]. Fenske, M.R. (1931). Distillation Design, J. of Ind. Eng. Chem, 24,482. [4]. Underwood, A.J. (1948). Distillation, J.of chem.Eng.progress, 44,603. [5]. O Connel, H.E. (1946). Separation Efficiency, Trans Am Inst Chem.Eng.42,741 [6]. Gilliland, ER. (1990). Separation Processes, J of Ind. Chem, 32, 1220. [7]. Luyben, W.L. (2007). Process Modeling and Simulation and Control, MCGrow Hill, New York. [8]. Dale, E, Edger, T.F. and Duncan, A.M.(1998).Process Dynamics and Control, John Willy and Sons, New York.

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Multicomponent Distillation Shortcut Method

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