gadalla_shortcut models, retrofit design of distillation columns (2003)

0263–8762/03/$23.50+0.00# Institution of Chemical Engineers

www.ingentaselect.com=titles=02638762.htm Trans IChemE, Vol 81, Part A, September 2003

SHORTCUT MODELS FOR RETROFIT DESIGN OFDISTILLATION COLUMNS

M. GADALLA, M. JOBSON and R. SMITHDepartment of Process Integration, UMIST, Manchester, UK

S hortcut models are well established for grassroots design of distillation columns andhave been widely applied. However, no shortcut models are available that addressretro� t. Shortcut models are quicker to solve, do not have signi� cant convergence

problems and are more robust than rigorous models for column optimization. In particular,shortcut models for retro� t would be valuable for evaluating retro� t design options, forimproving the performance of existing distillation systems (columns and heat recoverysystems) and can be combined with detailed heat-integration models for optimizing existingheat-integrated distillation systems. This paper presents retro� t shortcut models for design ofboth reboiled and steam-stripped distillation columns. These models are primarily based on amodi� ed Underwood method, the Gilliland and Kirkbride correlations, the Fenske equation andthe material balances. The retro� t models are applicable for simple distillation columns,sequences of simple distillation columns, and complex distillation con� gurations, includingcolumns with side-strippers and side-recti� ers. The models � x both the column con� gurationsand the operating conditions, including steam � ow rates, and calculate the product � ow rates,temperatures and compositions, and the various heat duties. A comparison of the model resultswith those of rigorous models of existing distillation columns is presented to validate themodel.

Keywords: retro� t; complex column; heat-integration; thermal coupling; FUG method.

INTRODUCTION

In the design of simple and complex distillation columns,the calculation of minimum re� ux is a very important step.At minimum re� ux, the distillation column requires anin� nite number of stages. This theoretical condition setsthe operating limit of a real column. Minimum re� ux can bedetermined by rigorous simulation using a large number ofstages and specifying the recoveries of key components.However, the calculation may be dif� cult to converge.Instead, shortcut methods are more widely used to determineminimum re� ux. The best known shortcut method forcalculating minimum re� ux is the method of Underwood(1948). This method is based on two limiting assumptions,constant molar over� ow within each column section, andconstant relative volatilities throughout the column. It iseasy to use, with only recoveries of two key components andthermal condition of feed needing to be speci� ed. Thismethod is applicable to simple distillation columns, i.e.single-feed two-product columns with a single condenserand a single reboiler. The minimum condenser and reboilerduties and also the minimum vapour � ow rates in columnsections are obtained from the calculations. The methodgives good results for distillation systems with relativelyideal mixtures. However, for multi-component mixtures andfor systems with non-ideal vapour–liquid equilibrium beha-viour, the molar over� ow is not constant and the relative

volatilities change through the column (Seader and Henley,1998; Suphanit, 1999). Where the underlying assumptionsare not valid, the accuracy of the results will be compro-mised. Even in these cases, however, the estimation ofminimum vapour � ow rates is good in regions of constantcomposition, also known as pinch zones (King, 1980;Kister, 1992). Some improvements to the Underwoodmethod have been suggested to extend its applicability(e.g. King, 1980; Nandakumar and Andres, 1981a,b; Rev,1990; Suphanit, 1999).

Based on the Underwood equation, many researchershave proposed shortcut models for grassroots design ofnon-conventional distillation columns. The Fenske–Under-wood–Gilliland (FUG) is the most popular shortcut modelfor design. Petlyuk et al. (1965) and Stupin and Lockhart(1972) studied the energy consumption of fully thermallycoupled distillation compared with conventional columns.Cerda and Westerberg (1981) developed shortcut models fordesign of various complex distillation systems. Glinos andMalone (1985) developed a shortcut procedure for design ofa distillation column with a side-stripper. Carlberg andWesterberg (1989b) and Triantafyllou and Smith (1992)applied the Underwood equation to a three-column modelfor the design and analysis of fully thermally coupleddistillation columns. Suphanit (1999) developed shortcutmodels for various complex distillation column con� gura-tions, including side-strippers and side-recti� ers.

971

Since distillation is an energy-intensive process andrequires large capital investment, retro� t of distillationcolumns is carried out more often than is installation ofnew equipment. Retro� t projects of distillation processesaim to reuse the existing equipment more ef� ciently in orderto increase the pro� t. To carry out a retro� t study, retro� tmodels are necessary to � x the existing distillation design.No shortcut models are published for retro� t; rigorousmodels are generally applied within commercial simulationpackages. Established rigorous models are time-consumingand have convergence problems. Furthermore, they fail toconsider all design parameters simultaneously in the opti-mization of the whole system, particularly in heat-integrateddistillation columns. In contrast, shortcut models are quickerto solve and more robust for optimization, especially whenall design variables are considered simultaneously. They canalso be combined with detailed heat-integration models forimproving the energy ef� ciency of distillation systems.

In this paper, shortcut models for retro� t design ofdistillation columns are developed. These retro� t modelsare applicable for various reboiled and steam-strippeddistillation columns, including simple columns, columnswith side-strippers, side-recti� ers, and partial or full thermalcoupling. These models form the basis for a retro� t designmethodology (Gadalla, 2003; Gadalla et al., 2003a) fordistillation columns and the associated heat recoverysystems.

RETROFIT MODELS FOR REBOILEDDISTILLATION COLUMNS

Distillation columns require the input of energy toperform the required separation; in most applications,reboilers supply this energy. A distillation column using areboiler and condenser is known as a conventional distilla-tion column. In this section, a shortcut model for retro� tdesign of reboiled distillation columns is developed. Thisshortcut model is based on the model developed by Suphanit(1999) for grassroots design of complex distillationcolumns. Initially, a shortcut model is developed for retro� tdesign of simple distillation columns. Thereafter, a retro� tmodel is proposed for design of complex distillation con� g-urations (e.g. distillation columns with side-stripper, side-recti� ers, thermal coupling, etc.).

Basic Model Equations for Grassroots Design

This section summarises the previous shortcut models fordesign distillation columns developed by Suphanit (1999).This model is an improvement to the standard FUG method.The improvements concentrate on the limiting assumptionsof the FUG method: constant molar over� ow within eachcolumn section and constant relative volatilities throughoutthe column. In this model, the relative volatility of eachcomponent is the geometric mean of that at differentlocations in the column, i.e. top section, bottom sectionand feed stage. An enthalpy balance around column sectionsis carried out to accommodate changes in vapour � ow ratesat both minimum and actual re� ux conditions. The modi� edprocedure at the minimum re� ux conditions is as follows(Figure 1):

(1) Use the Underwood equation to estimate the minimumvapour � ow rates at the top and bottom pinch zones(Vmin,pinch, Vmin,pinch).

(2) An enthalpy balance around the top section (envelope1 in Figure 1) is performed to calculate the minimumcondenser duty and the minimum vapour � ow rate at thetop of the column (Vmin,top). Then, the correspondingreboiler duty is calculated by an overall enthalpybalance.

(3) The minimum vapour � ow rate at the bottom of thecolumn (Vmin,bottom) is calculated by enthalpy balancearound the reboiler (envelope 2 in Figure 1).

At the actual re� ux condition, the vapour � ow rate in the topsection (Vtop) is calculated by a material balance around thecondenser, assuminga value for the re� ux ratio, R=Rmin. Then,the vapour � ow rate in the bottom section (V 0

bottom) is calcu-lated by an enthalpy balance around the reboiler (Figure 2). Inthe standard FUG model, this vapour � ow rate is calculatedusing the thermal conditions at the feed stage.

Based on these improvements to the FUG method,Suphanit (1999) developed shortcut models for grassrootsdesign of reboiled distillation columns, including differentcolumn con� gurations, such as columns with side-strippersand side-recti� ers, and columns with side-exchangers. For agiven feed and required separation, the model calculates thenumber of theoretical stages in each section, assuming avalue for the ratio R=Rmin.

The basic model equations of the shortcut model arepresented for simple distillation columns with reboilers, asfollows. The Underwood equation at the feed stage can bewritten as:

X aixf ,i

ai ¡ fˆ 1 ¡ q (1)

Figure 1. Modi� cation of FUG method at minimum re� ux (Suphanit,1999).

Trans IChemE, Vol 81, Part A, September 2003

972 GADALLA et al.

The minimum vapour � ow rate and distribution of compo-nents with volatilities between those of the key componentsat the top pinch location is given by:

X aidi

ai ¡ fˆ Vmin,pinch (2)

The minimum vapour � ow rate at the bottom pinch locationis then calculated as follows:

V 0min,pinch ˆ Vmin,pinch ¡ (1 ¡ q)F (3)

The minimum re� ux ratio is then calculated:

Rmin ˆVmin,top

D

³ ´¡ 1 (4)

The Fenske equation is used to determine the minimumnumber of stages at total re� ux:

Nmin ˆ ln[(RLK=(1 ¡ RLK))=((1 ¡ RHK)=RHK)]ln[aLK=aHK]

(5)

To achieve a speci� ed separation between two key compo-nents, the actual re� ux ratio and the number of stages mustbe greater than their minimum values. The actual re� ux ratiois generally chosen, by economic considerations, as somemultiple of minimum re� ux. The corresponding number ofstages is then determined by suitable graphical methods orby an empirical correlation. The most successful andsimplest graphical correlation for the number of stageswas developed by Gilliland (1940) and slightly modi� edlater by Robinson and Gilliland (1950). Seader and Henley(1998) reviewed the various equations for the Gillilandcorrelation and presented a comparison of rigorous calcula-tions with the Gilliland correlation. The Gilliland correla-tion relates the number of stages to the minimum numberof stages, and minimum and actual re� ux ratios. The datafor this correlation are based on accurate calculations.

Molokanov et al. (1972) represented these data by a linewith the following equation:

c ˆ 1 ¡ exp1 ‡ 54:4x

11 ‡ 117:2x

³ ´x ¡ 1

x0:5

³ ´µ ¶(6)

x ˆ R ¡ Rmin

R ‡ 1(7)

c ˆN ¡ Nmin

N ‡ 1(8)

After calculating the total number of theoretical stagesinside the column, the location of the feed stage can beidenti� ed using the empirical equation of Kirkbride:

NR

NSˆ B

D

³ ´xfHK

xfLK

³ ´xbLK

xdHK

³ ´2" #0:206

(9)

Following the calculations of total number of stages and thefeed location, an energy balance is carried out to calculatethe condenser and reboiler duties (Seader and Henley,1998).

Retro� t Shortcut Model for Simple ReboiledDistil lation Columns

Figure 3 shows a simple distillation column (conventionaldistillation column). For an existing simple distillationcolumn, the basic model equations are solved simulta-neously with the material balance equations to build theretro� t shortcut model.

Material balances are carried out around the column forthe light and heavy key (LK, HK) components:

xbLK ˆ xfLKF(1 ¡ RLK)B

(10)

xdHK ˆ xfHKF(1 ¡ RHK)D

(11)

The Fenske equation is rewritten for an existing distillationcolumn to give the recovery of the key components as afunction of the minimum number of stages, as follows:

RLKRHK

(1 ¡ RHK)(1 ¡ RLK)ˆ

aLK

aHK

µ ¶Nmin

(12)

Figure 2. Modi� cation of FUG method at actual re� ux (Suphanit, 1999).

Figure 3. Simple distillation column with reboiler.


SHORTCUT MODELS FOR RETROFIT DESIGN 973

The Kirkbride correlation and the LK and HK componentmaterial balance equations are rearranged and solved simul-taneously, resulting in:

1 ¡ RLK

1 ¡ RHKˆ fKirk (13)

where

fKirk ˆ BD

³ ´xfHK

xfLK

³ ´µ ¶1=2 NR

NS

³ ´2:427

(14)

The term fKirk can be calculated for the existing distillationcolumn, where the number of stages in each section is givenand the top and bottom product molar � ow rates and themole fractions of the key components are known.

Equations (12) and (13) are solved simultaneously tocalculate the recovery of the HK component as follows:

1 ¡ RHK

RHKˆ 1 ¡ fKirk(1 ¡ RHK)

fKirk(1 ¡ RHK)1

fFensk(15)

1 ¡ RHK… †2‡RHK 1 ¡ RHK… † 1fFensk

¡ RHK

fKirk

1fFensk

ˆ 0

(16)

where

fFensk ˆaLK

aHK

³ ´Nmin

(17)

Equation (16) is quadratic in RHK. Since the recovery of theheavy key component, RHK must be positive and less thanunity; only the positive root of Equation (16) is accepted:

RHK ˆ 1 ¡ (fKirk ‡ 1)4(fFensk ¡ 1)

³ ´2

‡ 1(fFensk ¡ 1)fKirk

" #1=2

‡ fKirk ‡ 12fKirk(fFensk ¡ 1)

(18)

This equation calculates the recovery of the heavy keycomponent, given the values of the terms fKirk and fFensk.Then, the recovery of the light key component can bedetermined from Equations (13) and (18) as follows:

RLK ˆ 1 ¡ fKirk(1 ¡ RHK) (19)

From the existing total number of theoretical stages insidethe distillation column and for the existing operating condi-tions, the minimum number of stages which is required tocalculate the term fFensk is calculated from the Gillilandequation:

Nmin ˆ N (1 ¡ c) ¡ c (20)

where

c ˆ f (R, Rmin) (21)

Equations (14) and (17)–(21) represent the retro� t shortcutmodel for conventional distillation columns. This modelutilizes the Molokanov equation to represent the Gillilandcorrelation. However, any other suitable equation can besubstituted.

In the application of the model for retro� t design,Equations (14) and (17)–(21) are solved simultaneouslyto simulate existing simple reboiled distillation columns.Equation (14) uses assumed values for the key componentrecoveries to initialize the calculations of the term fKirk. The

input data to the model are the feed speci� cations (i.e. � owrate, temperature, pressure, composition), and the number ofexisting stages in each section, as well as the operatingconditions (i.e. re� ux ratio, column temperature, columnpressure). The model output includes the key componentrecoveries, product compositions and � ow rates, and thecondenser and the reboiler duties.

The same retro� t model is applicable for sequences ofsimple distillation columns (Figure 4). In this case, the modelis applied directly and sequentially to each column in the sequ-ence, starting with the � rst column. In the column sequence,the number of existing stages in each section and the operatingconditions are � xed. The model calculates the product com-positions, � ow rates and temperatures, and the various duties.

Illustrative example 1: simple reboiled columnA simple reboiled distillation column separates a mixture

of aromatic hydrocarbons into two products. The feedmixture data and column speci� cations are given inTable 1. The task of the distillation column is to separatebenzene from toluene with 99% recovery of both key com-ponents. The physical properties of the feed mixture and theproducts are calculated by the Peng Robinson model.

The existing distillation column is modelled using rigor-ous simulation, to provide results as a basis for comparison.The rigorous simulation (HYSYS Process Simulation, 2001,Version 2.4.1, Hyprotech Ltd) uses the same physicalproperty calculations. A re� ux ratio of 2.082 is calculatedby HYSYS to separate the given feed mixture in the existingdistillation column into the top product with the required

Figure 4. Direct and indirect sequences of two simple reboiled distillationcolumns. (a) Indirect sequence; (b) direct sequence.

Table 1. Feed mixture data and column speci� cations(example 1).

Flow rate (kmolh¡1)

Feed mixtureBenzene 200Toluene 100Ethyl benzene 100m-Xylene 200o-Xylene 100Total 700

Feed conditionsPressure (bar) 2.0Temperature (¯C) 135.9

Column speci� cationsRectifying stages 15Stripping stages 15Column pressure (bar) 2.0


974 GADALLA et al.

speci� cations. A hundred theoretical stages are used tocalculate the minimum re� ux ratio in the rigorous simula-tion. In the retro� t shortcut calculations, the number ofexisting stages is speci� ed, as are the operating conditions,including the re� ux ratio. The model calculates the productkey component recoveries, � ow rates and temperatures, andthe duties of the condenser and reboiler. The results aresummarized in Table 2.

It is clear from Table 2 that the retro� t shortcut model isin very good agreement with the rigorous model. Thisagreement is expected for a simple distillation column; themaximum deviation is less than 1% compared with rigorousmodels. This good agreement between results validates theretro� t shortcut model.

Although the rigorous simulation provides a value for there� ux ratio for the retro� t shortcut calculations, the re� uxratio can also be calculated within the retro� t shortcutmodel. Therefore, the retro� t model can be applied inde-pendently of the rigorous simulations.

Retro� t Shortcut Model for Complex Disti l lationCon� gurations with Reboilers

In the complex column con� gurations considered, asingle feed is separated into more than two products,using a main column with a side-stripper or side-recti� er,as shown in Figure 5. Retro� t modelling for such complexcon� gurations is more dif� cult than for simple sequences.

Suphanit (1999) developed a shortcut model for grass-roots design of complex columns with side-strippers andside-recti� ers. This model calculates the number of theore-tical stages required for a given separation and feed speci-� cations. In this model, the complex con� gurations aredecomposed into thermodynamically equivalent sequencesof simple columns, as shown in Figure 5. This facilitates thedesign and analysis of the con� gurations. An indirectsequence of two thermally coupled simple columns isequivalent to a complex column with a side-stripper. Forthe complex column with a side-recti� er, the equivalentsequence is a direct sequence of two thermally coupledsimple columns. The connections between the simplecolumns are one vapour stream and one liquid stream.This connection is known as thermal coupling, because ofthe direct heat transfer between column sections. In thethermally coupled direct sequence, the downstream columnis fed by a liquid stream from the upstream column andreturns vapour to the upstream column, while in the ther-mally coupled indirect sequence, the downstream columnreturns liquid to the upstream column and receives a vapourphase feed from the upstream column. Using this decom-position technique, the design of such con� gurationsbecomes more systematic. Each simple column in theseequivalent sequences can be designed individually fromupstream to downstream columns.

In the indirect sequence equivalent to a complex columnwith a side-stripper, the thermal coupling is at the top of the� rst column, as shown in Figure 6. The vapour and liquid

Table 2. Retro� t shortcut and rigorous model results (example 1).

ParameterRigorous

model

Retro� tshortcutmodel

Top product � ow (kmol h¡1) 199.0 198.9Top product temperature (¯C) 104.4 104.4Condenser duty (kW) 5003 5002Bottom product � ow (kmol h¡1) 501.0 501.1Bottom product temperature (¯C) 158.7 158.8Reboiler duty (kW) 5431 5427Recovery of benzene to distillate (%) 99.00a 98.92b

Recovery of toluene to bottomproduct (%)

99.00a 98.87b

Re� ux ratio, R 2.082 2.082a

Minimum re� ux ratio, Rmin 1.931 1.967

aSpeci� ed; bratio of recoveries speci� ed (fKirkˆ 1).

Figure 5. Decomposition of reboiled complex distillation columns (with full thermal coupling), showing distribution of existing number of stages.



streams connecting the columns are assumed to be thevapour � owing to and liquid leaving a hypothetical partialcondenser of the � rst column. In this case, the vapour andliquid � ow in the top section of the � rst column are the feedand side-draw streams for the second column respectively.The net feed � ow for the second column is the top product� ow of the � rst column (D1). The modi� ed FUG shortcutmodel is applied to each column starting from the � rstcolumn, then moving to the second column. The assumptionof Carlberg and Westerberg (1989a), that the feed and side-draw streams are on the same stage, is applied in this model.

In a similar way, complex columns with side-recti� ers areanalysed; thermal coupling between the columns in this caseis at the bottom of the � rst column, as shown in Figure 7.The liquid and vapour streams in the bottom section of the� rst column are assumed to be the feed and side-draw forthe second column, respectively. The net feed � ow to thesecond column is the bottom product of the � rst column(B1). The modi� ed FUG method is applied to both columnsin the equivalent sequence of columns (Suphanit, 1999).

Based on these shortcut models for grassroots design andthe retro� t model developed for simple distillation columns,a retro� t model for complex columns with side-strippers andside-recti� ers is proposed (Figure 8):

(1) The complex column is decomposed into the thermody-namically equivalent sequence of simple columns. Theexisting stages are distributed into the correspondingcolumn sections (see Figure 5).

(2) The retro� t shortcut model is applied to each simplecolumn in the sequence, starting with the � rst column.The model � xes the number of existing stages in eachsection, and, for the given operating conditions, itcalculates product � ow rates and compositions, andthe duties of the reboilers and condensers.

(3) Owing to the thermal coupling, the procedure is iterative,as indicated in Figure 8. The procedure terminates oncethe calculatednumberof stages corresponds to the numberof existing stages in each thermally coupled column.

Figure 6. Modelling of thermal coupling for the sequence equivalent to a side-stripper.

Figure 7. Thermal coupling procedure for equivalent sequence of side-recti� er.


976 GADALLA et al.

Figure 9 shows column con� gurations with partial thermalcoupling, as well as fully thermally coupled sequences. In thepartially thermally coupled sequences, only some of the heatload of the condenser or the reboiler in the � rst column isshifted to the subsequent column. In the partially coupledindirect sequence, a side-cooler is installed at the top ofthe � rst column instead of the condenser. In the partiallycoupled direct sequence, a side-heater is installed at thebottom of the � rst column instead of the reboiler of the � rstcolumn.

The degree of thermal coupling for indirect coupledsequences is de� ned as the ratio of the liquid � ow rate at thetop of the column when using a side-cooler to that when noside-cooler is installed (Suphanit, 1999). Similarly, the degreeof thermal coupling for direct coupled sequences is the ratioof the vapour � ow rate at the bottom of the column whenusing a side-heater to that when no side-heater is installed.In uncoupled sequences, the degree of thermal coupling isequal to zero, which means there is no liquid or vapour fromthe subsequent column. In fully coupled sequences, this valueis unity; the duty of the side-cooler and side-heater is zeroand the total heat duty of the condenser and reboiler in the� rst column is shifted to the subsequent column. Suphanit(1999) developed a design model for the calculation of side-exchanger duties in partially thermally coupled complexcolumns. The model calculates the exchanger duty for anassumed degree of thermal coupling between columns and agiven temperature drop over the exchanger.

A similar retro� t model to that for fully coupledsequences (see Figure 8) is proposed for the partiallycoupled complex con� gurations. This retro� t model isbuilt by combining the retro� t model for simple columnsand the model of Suphanit (1999) for complex columns withside-exchangers. In this case, both column con� guration andoperating conditions are � xed. The model calculates theproduct � ow rates, temperatures and compositions, and theheat duties of the reboilers, condensers and side-exchangers.

Illustrative example 2: reboiled column with side-stripperAn existing complex column with a side-stripper sepa-

rates the feed mixture given in Table 1 into three products,as indicated in Table 3. This column con� guration is

Figure 8. Retro� t algorithm for complex column con� gurations.

Figure 9. Thermal coupled complex column con� gurations (direct andindirect sequences). (a) Partial thermal coupling; (b) full thermal coupling.



equivalent to two fully thermally coupled reboiled columns.The existing number of stages and column operating condi-tions are listed in Table 3. The task of the � rst column in thesequence is to separate between the toluene and ethylbenzene with 99% recoveries of each. The second columnthen recovers 99% of the benzene to the top product and99% of the toluene to the bottom product. The operatingre� ux ratio of the distillation column (i.e. second column inequivalent sequence) is 4.54. The physical properties ofthe feed and product streams are calculated by the PengRobinson model.

The retro� t shortcut model simulates the existing distilla-tion unit. The existing stages are speci� ed, as are theoperating re� ux ratio and the liquid recycle � ow rate fromthe second column to the � rst column. The simulationresults, summarized in Table 4, include the product � owrates and temperatures, the key component recoveries, thecondenser and reboiler duties, and the vapour � ow rate inthe thermal coupling connection. These results arecompared with rigorous simulation results (HYSYS), forthe same column and feed speci� cations.

It can be seen that the results of the retro� t shortcutmodels are in very good agreement with those of therigorous simulation. The deviation of the results for mostdesign variables is less than 1%, except for the reboiler ofthe second column, which shows a deviation of 6.8% in the

heat duty. The temperature difference of the various streamsis than 0.5¯C.

Conclusions

Retro� t models have been developed for reboiled distilla-tion columns. The models are applicable for simple distilla-tion columns and sequences of simple columns. The modelsalso apply to complex con� gurations of distillation columns,such as columns with side-strippers and side-recti� ers. Inthe calculations, the models � x both the given columncon� guration and operating conditions, and calculate theproduct � ow rates and compositions and the various heatingand cooling duties. Generally, very good agreement isobserved between the retro� t model and rigorous simulationresults for a well behaved mixture of hydrocarbons. Theretro� t shortcut models can initialize the rigorous modelcalculations.

RETROFIT MODEL FOR STEAM-STRIPPEDDISTILLATION COLUMNS

Some distillation applications, including crude oil distil-lation, use stripping steam as a vaporization mechanism.Live steam is injected directly into the bottom of the columnas a stripping agent. Steam is condensed in the condenserand can be separated from liquid hydrocarbons at the top ofthe crude oil column because it is immiscible with mosthydrocarbons.

In steam-stripped distillation columns, the column isdivided into two sections, the rectifying and strippingsections, as shown in Figure 10. Stripping steam reduces

Table 3. Column speci� cations for thermallycoupled indirect sequence (example 2).

Column 1 Column 2

Top stages 18 18Bottom stages 25 12Pressure (bar) 2.0 2.0


ParameterRigorous

model


Column 1Bottom product � ow (kmol h¡1) 399.4 399.7Bottom product temperature (¯C) 166.7 166.8Reboiler duty (kW) 7713 7644Bottom recovery of ethyl benzene (%) 99.0a 99.5

Thermal coupling (see Table 3)Vapour � ow (kmolh¡1) 829.0 825.6Liquid � ow (kmolh¡1) 525.7 525.7a

Column 2Reboiler duty (kW) 1732 1850Condenser duty (kW) 8987 8936Top product � ow (kmol h¡1) 198.0 198.9Top product temperature (¯C) 104.3 104.3Bottom product � ow (kmol h¡1) 102.7 101.4Bottom product temperature (¯C) 135.7 135.5Top recovery of benzene (%) 99.0a 99.0b

Bottom recovery of toluene (%) 99.0a 99.1b

Re� ux ratio 4.54a 4.54a

aSpeci� ed; brecovery ratio (fKirk) speci� ed. Figure 10. Simple distillation column using stripping steam.


978 GADALLA et al.

the partial pressure of the hydrocarbons in the strippingsection, which results in vaporisation. Figure 11 shows thetemperature pro� le through the steam-stripped distillationcolumn and compares it with that of a reboiled column. Ascan be seen, the stage temperature of the reboiled columndecreases continuously from the reboiler to the condenser.In the steam-stripped column, the vapour is generated by thereduction in the partial pressure of the liquid; the liquid itselfsupplies the heat of vaporization. The liquid temperaturereduces from the feed stage towards the bottom of thecolumn. The temperature pro� le of the steam-strippedcolumn shows a peak value at the feed stage (Suphanit, 1999).

The challenges for modelling steam-stripped columns arethat the conventional shortcut models for reboiled columns,such as the FUG model, cannot be applied directly. Thereason is that the separation characteristics, such as thetemperature pro� le and the vapour generation mechanism,are different in steam-stripped columns from those ofreboiled columns.

Suphanit (1999) developed a shortcut model for grass-roots design of steam-stripped distillation columns. Basedon this model, a retro� t model for design of steam-strippeddistillation columns is proposed. First, a retro� t model ispresented for simple distillation columns. Thereafter, amodel is proposed for retro� t design of complex distillationcon� gurations, including distillation columns with side-strippers, side-recti� ers and thermal coupling.

Basic Model Equations for Grassroots Design

The shortcut model developed by Suphanit (1999) forgrassroots design of steam-stripped distillation columns ispresented, as it is the foundation of the retro� t model. Thismodel is applicable for simple and complex con� gurationsof steam-stripped distillation columns. In this model, theUnderwood equation and enthalpy balance are applied to asimple steam-stripped column to estimate the minimumvapour � ow rate in each section, and the minimum re� uxratio and the condenser duty. The dew point temperature iscalculated to determine the temperature of the top productfor a partial condenser; the bubble point temperature iscalculated for a total condenser. The temperature of thebottom product is calculated by an enthalpy balance.

The number of stages is calculated separately for eachsection of the column. In the rectifying section, the Fenske

equation is applied to determine the minimum number ofstages at total re� ux condition:

Nmin ˆ ln[(xdLK=xdHK)=(xLKFS=xHKFS)]ln[aLK=aHK]

(22)

The Gilliland correlation then determines the number ofstages in this section.

To apply such shortcut design equations as Equation (22),the relative volatilities and mole fractions of components in amixture of unknown composition are needed, where therelative volatilities are composition dependent. An iterativeapproach is needed to estimate product compositions andhence volatilities. Initial values for the recoveries of the lightand heavy key components are speci� ed, and initially, com-ponents lighter than the light key and those heavier thanthe heavy key are assumed to be fully recovered, to the dis-tillate and bottoms, respectively. The recoveries of the inter-mediate-boiling compounds, given relative volatility values,can be estimated using the Fenske equation (for total re� ux)and the Underwood equation (for minimum re� ux), andinterpolating between these conditions (King, 1980).

In the stripping section, the vapour � ow rate pro� le isnon-linear, as shown in Figure 12(a). Thus, to obtain a goodprediction of the number of stages, consecutive � ash calcu-lations are performed from the bottom stage towards thefeed stage. The number of stages is counted from the bottomstage until the stage vapour � ow rate reaches or exceeds thevapour � ow rate below the feed stage, as shown in Figure12(b). The bottom vapour � ow rate is obtained by an overallenthalpy balance. The vapour � ow rate below the feed stageis assumed to be the minimum vapour � ow rate at thebottom pinch of the column (Suphanit, 1999).

Retro� t Shortcut Model for Simple Disti llationColumns with Stripping Steam

The retro� t model for the rectifying section of simplesteam-stripped distillation columns is developed by solvingthe basic model equations simultaneously with the materialbalance equation for a given number of stages. Steam istreated as an inert gas that does not condense in the column,nor interact with the other components present, but doesaffect the partial pressure of the hydrocarbons. Vapour–liquid equilibrium and relative volatility are calculated basedon the hydrocarbon mixture at this partial pressure. The

Figure 11. Temperature pro� les or reboiled and steam-stripped distillation columns (Suphanit, 1999). (a) Conventional column; (b) steam-stripped column.



assumption that the steam is introduced at a temperature andpressure that allow it to remain in the vapour phase issupported by rigorous simulation results for crude oildistillation columns.

A material balance is carried out around the column forthe heavy key component, resulting in:

xdHK ˆ xfHKF(1 ¡ RHK)D

(23)

For an existing simple distillation column, the Fenske equa-tion is rewritten to give the recovery of the key componentsas a function of the minimum number of stages, as follows:

xdLK

xdHKˆ jSteam (24)

where

jSteam ˆ xLKFS

xHKFS

aLK

aHK

µ ¶Nmin

(25)

By solving Equations (23) and (24), the recovery of theheavy key component can be calculated by:

RHK ˆ 1 ¡ xdLKDxfHKFjSteam

(26)

The minimum number of stages in the rectifying section canbe calculated for the existing distillation column, where thenumber of stages is known and the operating conditions are� xed:

Nmin ˆ NR(1 ¡ c) ¡ c (27)

The retro� t model for the rectifying section is representedthrough Equations (25)–(27). These equations are solvedsimultaneously for given feed speci� cations, � xed operatingconditions and the existing number of stages, to calculatethe composition and � ow rate of the products.

For the stripping section, the retro� t model is based onconsecutive � ash calculations, as shown in Figure 13. Themodel determines the product composition for a givennumber of stages and steam � ow rate. The model calcula-tions start by assuming the bottom product composition.Then, in an iterative procedure, consecutive � ash calcula-tions are carried out from the bottom stage to the feed stage.Vapour–liquid equilibrium calculations and energy andmass balances are carried out for each stage to determinethe composition and � ow rate of the vapour and liquidphases in the column. In each step, the number of stages iscounted from the bottom stage to the feed stage. Then thebottom product composition is updated (through a linearrelation with the previous bottom composition). The itera-tions terminate when the calculated number of stages andexisting number of stages are identical. Hence, the correctbottom product composition is obtained.

The retro� t models for the rectifying and strippingsections comprise the retro� t model for simple steam-strippeddistillation columns. This model � xes the number of stagesin each section and, for the given operating conditions andsteam � ow rate, it calculates the product � ow rates, tempera-tures and compositions, and the condenser duty.

The same retro� t model is also applicable for sequencesof simple steam-stripped columns (e.g. Figure 14). The linkbetween each pair of columns in the indirect sequence is thetop product stream from the upstream column to the down-stream column. In the direct sequence, the bottom product

Figure 12. Stripping section of steam-stripped column. (a) Vapour � owpro� le; (b) stripping section.

Figure 13. Retro� t algorithm for stripping sections.


980 GADALLA et al.

from the upstream column feeds the downstream column.As seen in these con� gurations, the sequences are simplecolumns connected with no thermal coupling. Therefore, theretro� t model for simple steam-stripped columns is applieddirectly and sequentially to each simple column in thesecon� gurations, starting with the � rst column.

Illustrative example 3: simple steam-stripped columnAn equimolar C8–C23 mixture of normal paraf� ns is

separated into two products by a simple steam-strippeddistillation column. The feed data and column speci� cationsare given in Table 5. Superheated steam at 160¯C and 3 baris used as a stripping agent. The task of the distillationcolumn is to recover 95% of n-C14 to the top product and95% of n-C19 to the bottom product.

The existing distillation column is simulated using boththe retro� t shortcut model and rigorous simulation(HYSYS). Both models use the Peng Robinson model forthe physical property calculations of the feed and productstreams. In the rigorous simulation, a steam � ow rate of1540kmol h¡1 and a re� ux ratio of 0.411 are predicted toseparate the given feed in the existing column into therequired speci� cation. When using the retro� t model, thenumber of stages in each section and the column operatingconditions are � xed. The steam � ow rate and re� ux ratiothat are obtained from the rigorous simulation are speci� ed.The retro� t model calculates the product � ow rates andtemperatures, the key component recoveries (or � ow rates)and the duty of condenser. These results are summarized inTable 6, and compared with those of the rigorous simula-tion. The table shows very good agreement between theretro� t model and rigorous simulation results.

Retro� t Shortcut Model for Complex Disti l lationCon� gurations with Stripping Steam

Complex distillation con� gurations may use steam forvaporisation rather than using reboilers. Such columns aresuitable for mixtures that are temperature sensitive, such ascrude oil.

Complex columns with side-strippers and side-recti� ers,such as those shown in Figure 15, are more complicated thandirect and indirect two-column sequences (see Figure 14).These con� gurations are modelled by the decomposition ofcomplex columns into the thermodynamically equivalentsimple sequences. The equivalent sequences shown inFigure 15 are fully thermally coupled. The thermal couplingis used in place of the condenser of the � rst column in theindirect sequence; the condenser of the second columnprovides re� ux for both columns. In the direct sequence,thermal coupling is used in place of the reboiler of the � rstcolumn; the reboiler of the second column provides vapourfor both columns. The thermal coupling connections in theindirect sequence are the vapour feed to the downstreamcolumn from the upstream column and the liquid streamfrom the downstream column to the upstream column. In thedirect sequence, the downstream column receives its feedfrom the bottom liquid of the upstream column and returns avapour stream to the upstream column.

Suphanit (1999) developed shortcut models for grassrootsdesign of complex steam-stripped column con� gurationswith side-strippers and side-recti� ers, similar to those forreboiled complex columns.

Based upon the shortcut model of Suphanit (1999) andthe retro� t shortcut model for simple steam-stripped distilla-tion columns, a retro� t model is proposed for complexcolumns with side-strippers and side-recti� ers, as follows:

(1) The complex column is decomposed into the thermo-dynamically equivalent sequence of simple columns.The existing stages are then distributed into the corre-sponding column sections, as indicated in Figure 15.

(2) The retro� t shortcut model is applied sequentially toeach simple column in the con� guration. The columncon� guration and numbers of existing stages in eachsection, and steam � ow rates are � xed. The � ow rates,temperatures and compositions of the products and thecondenser duties are calculated.

(3) Owing to the thermal coupling, the procedure is iterative.The procedure terminates once the calculated number ofstages corresponds to the number of existing stages.

Figure 14. Sequences of direct and indirect simple steam-stripped distilla-tion columns. (a) Indirect sequence; (b) direct sequence.

Table 5. Equimolar feed mixture data and column speci� cations(example 3).

C8–C23 mixture

Feed speci� cationsFlow rate (kmolh¡1) 1000Pressure (bar) 3.0Temperature (¯C) 300

Column speci� cationsRectifying stages 6Stripping stages 8Column pressure (bar) 3.0Flow rate of n-C14 to top product

(kmolh¡1; 95% recovery)59.38

Flow rate of n-C19 to bottom product(kmolh¡1; 95% recovery)

59.38

Table 6. Retro� t shortcut and rigorous simulation results (example 3).

ParameterRigorous

model


n-C14 in top product (kmol h¡1) 59.38a 61.51n-C19 in bottom product (kmol h¡1) 59.38a 59.96Top product � ow (kmolh¡1) 564.6b 564.0Top product temperature (¯C) 130.4 131.4Condenser duty (MW) 40.0 40.4Bottom product � ow (kmol h¡1) 435.4b 435.9Bottom product temperature (¯C) 224.6 225.8Steam � ow (kmol h¡1) 1540 1540a

Re� ux ratio 0.411 0.411a

aSpeci� ed; bwater-free basis.



In Figure 16, other con� gurations of steam-strippeddistillation columns with partial thermal coupling arecompared with fully thermally coupled sequences; thesecon� gurations use side-coolers and side-heaters. The retro� tmodel for fully coupled sequences is combined with themodel developed by Suphanit (1999), for the calculation ofside-exchanger duties, and extended to the partially coupled

con� gurations. In this case, both column con� guration andoperating conditions, including steam � ow rates, are � xed.The product � ow rates and compositions, and the duties ofthe condenser and side-exchanger are calculated.

Illustrative example 4: steam-stripped columnwith side-stripper

In this example, the same hydrocarbon feed mixture givenin Table 5 is separated into three products using a steam-stripped distillation column with a side-stripper (equivalentto the thermally coupled indirect sequence of two steam-stripped columns). The speci� cations for each column aregiven in Table 7, including the � ow rates of stripping steamand of the key components. Stripping steam, used for bothcolumns, is at 160¯C and 3 bar.

The existing distillation column is � rst simulated usingrigorous simulation. The re� ux ratio was calculated to be2.59 to meet the product speci� cations. When using theretro� t model in the simulation of the given distillationcolumn, the column speci� cations and the operating condi-tions are speci� ed, as indicated in Table 8. The results of thesimulation include the product � ow rates and temperatures,the key component � ow rates and the various heat duties.These results are compared with those from the rigoroussimulation. Both models use the Peng Robinson model forthe calculation of the physical properties of the feed andproduct streams.

The retro� t shortcut and rigorous simulation results showrelatively good agreement. Deviations are due to the com-plexity in the column con� guration, the presence of thestripping steam and the large number of components.Temperature differences of up to 7.6¯C and � ow rate differ-ences of products of up to 5.8% are observed. However, very

Figure 15. Decompositions of steam-stripped complex columns, showing distribution of existing number of stages (full thermal coupling).

Figure 16. Thermally coupled complex columns with steam (direct andindirect sequences) (a) Partial thermal coupling; (b) full thermal coupling.


982 GADALLA et al.

good agreement can be observed for key component � owrates, the condenser duty and the re� ux ratio.

Conclusions

New shortcut models have been developed for retro� tdesign of steam-stripped distillation columns. The modelsare applicable for various con� gurations of distillationcolumns, including simple columns, sequences of simplecolumns, complex columns with side-strippers, side-recti-� ers, and partial or fully thermally coupled sequences. Theretro� t models predict results in good agreement with theexisting rigorous simulations. These models can initialiserigorous calculations.

RETROFIT MODELLING FOR REFINERYDISTILLATION COLUMNS

Crude oil distillation is a process of great importance inthe re� ning industry. The process is energy and capitalintensive. Retro� t of these systems is a common designactivity aiming to increase pro� t by using the existingequipment more ef� ciently.

Generally, crude oil distillation units use a combination ofsteam-stripped and reboiled columns. For retro� t design of

such con� gurations, the new shortcut models developed forreboiled columns and steam-stripped columns can beapplied sequentially.

Conventionally, the design of crude oil distillation units iscarried out by the speci� cation of the cut point and gaptemperatures, or product � ow rates (Watkins, 1979). Rigor-ous model-based simulations apply this conventionalmethod for design of crude oil distillation systems, i.e. thesimulators specify the cut point and gap temperatures for theproduct separations. Conventional shortcut models (e.g.FUG) require the speci� cation of key components for therequired separation. In the shortcut models of Suphanit(1999), key components (generally pseudo-components)are speci� ed for each pair of successive products. Realcomponents can be speci� ed as the key components forthe separation of the light ends.

To apply the retro� t shortcut models presented in thispaper, the product compositions need to be expressed interms of recovery of light and heavy key components [seefor example Equations (10) and (23)]. A systematicapproach has been developed (Gadalla et al., 2003b) fornominating key components and specifying their recoveriesfrom the converged simulation results for an existing crudeoil distillation column.

Illustrative Example 5: Crude Oil Distillation ColumnAn industrial atmospheric crude oil distillation unit

processes 100,000 barrels per day (2610 kmol h¡1) ofcrude oil at 25¯C and 3 bar into � ve products: light naphtha(LN), heavy naphtha (HN), light distillate (LD), heavydistillate (HD), and residue (RES). Superheated steam at260¯C, 4.5 bar, is used as a stripping agent.

The true boiling point data (crude assay) of the crude oilare shown in Table 9; these data are based on the textbookexample of Watkins (1979). The crude assay is represented

Table 7. Column and product speci� cations (example 4).

Column speci� cations Column 1 Column 2

Rectifying stages 6 8Stripping stages 8 4Column pressure (bar) 3.0 3.0Steam � ow (kmolh¡1) 1100 100n-Dec � ow in top product (kmolh¡1) 59.4n-C19 � ow in bottom product (kmol h¡1) 59.4


ParameterRigorous

model


Column 1Bottom product � ow (kmol h¡1) 454.5a 448.1Bottom product temperature (¯C) 236.5 237.3n-C19 � ow in bottom product (kmol h¡1) 59.4b 59.48b

Steam � ow (kmol h¡1) 1100b 1100b

Thermal coupling (see Table 7)Vapour � ow (kmolh¡1) 1940 1875Liquid � ow (kmolh¡1) 261 224

Column 2Top product � ow (kmol h¡1) 277.5a 273.4Top product temperature (¯C) 127.8 128.7n-Dec � ow in top product (kmolh¡1) 59.4b 59.3Bottom product � ow (kmol h¡1) 268.5a 278.5Bottom product temperature (¯C) 228.1 235.7Condenser duty (MW) 30.7 30.8Steam � ow (kmol h¡1) 100b 100b

n-C13 � ow in bottom product (kmol h¡1) 57.8 61.2Re� ux ratio 2.59 2.59b

aWater-free basis; bspeci� ed.

Table 9. Crude assay data (example 5).

Percentage distilled (vol) TBP (¯C)

0 ¡3.05 63.5

10 101.730 221.850 336.970 462.990 680.495 787.2

100 894.0

Density ˆ 865.4kg m¡3.



using 25 pseudo-components, using the oil characterizationtechnique embedded within HYSYS. The physical proper-ties of each pseudo-component (e.g. molecular weight,vapour pressure, boiling temperature, critical properties,etc.) are calculated using the Peng Robinson model, andare then extracted from HYSYS. The key components forthe separation of each pair of products are shown inTable 10. The composition of the feed in terms of thesepseudo-components and their boiling temperatures and � owrates is given in Table 11.

The column con� guration is shown in Figure 17, whichalso shows the equivalent sequence of four thermallycoupled columns. Table 12 gives the existing stages ineach section of the column, the operating conditions, thesteam � ow rates, the pump-around temperature differencesand the degree of thermal coupling, which is de� ned as theliquid � ow rate at the top of the column when using pump-around to that when no pump-around is installed.

The existing atmospheric unit is simulated using theretro� t shortcut model. In the calculations, the existingstages in the rectifying and stripping sections are � xed,and the operating conditions including steam � ow rates arespeci� ed. The re� ux ratio, the temperature drops over thepump-arounds, and the degree of thermal coupling are thenspeci� ed. The retro� t shortcut model calculates the product� ow rates and temperatures, the pump-around duties and� ow rates, the duties of the condenser and reboilers, and thekey component � ow rates. These results are summarised in

Table 13, and are used to initialise the calculations of therigorous simulation (HYSYS), for the same column andfeed speci� cations and the operating conditions. The resultsof both models are compared in Table 13.

Table 13 shows that the results predicted by the retro� tshortcut model are in good agreement with those obtainedfrom the rigorous simulations; no signi� cant deviations areobserved. The maximum temperature difference is 10¯C andthe deviations in � ow rates are all less than 7%. Othervariable results are in very good agreement.

Table 10. Key components for the separation of each pair of products(see Figure 17).

Successive products

Keycomponent

LN andHN

HN andLD

LD andHD

HD andRES

Light key 4 7 11 13Heavy key 6 9 14 16

Table 11. Feed composition of crude oilmixture (derived from assay data).

Componentnumber

NBP(¯C)

Flow rate(kmolh¡1)

1 9 110.92 36 106.93 61 139.34 87 175.85 111 175.86 136 169.77 162 169.48 187 166.29 212 156.6

10 237 140.111 263 127.912 288 115.613 313 106.214 339 101.315 364 94.516 389 84.617 414 73.918 447 95.219 493 61.820 538 49.221 584 54.522 625 39.323 684 40.224 772 28.225 855 26.6

Total 2610.6

Figure 17. Atmospheric crude oil distillation column, showing the equivalent sequence of simple columns. (a) Complex con� guration; (b) equivalentsequence.


984 GADALLA et al.

As can be seen, the distillation column con� guration isvery complex with many side-strippers and pump-arounds,and it has a large number of components (25 ‘pseudo-components’ ‡ 1 ‘water’), so this good agreement is animportant result. It illustrates the adequacy of the retro� tshortcut model and supports the application of the newmodel for retro� t studies. These retro� t studies may includeevaluating design options for retro� t, such as adding pump-arounds, and assessing trade-offs between using strippingsteam and reboiling. In addition, the model can beembedded within an optimisation framework, and can becombined with a detailed heat integration model for increas-ing energy ef� ciency of the distillation unit (Gadalla, 2003;Gadalla et al., 2003a). Furthermore, the retro� t model caninitialise the rigorous model calculations by providing theproduct � ow rates and the pump-around duties and � owrates for a given feed, and existing number of stages andoperating conditions.

CONCLUSIONS

A new set of shortcut models for retro� t design ofcomplex distillation columns has been developed. Thesemodels are applicable for various con� gurations of distilla-tion columns, including simple columns, sequences ofsimple columns, complex columns with side-strippers orside-recti� ers, and partially or fully thermally coupledsequences. Distillation columns with either a reboiler orstripping steam are accounted for. For a given columncon� guration and operating conditions, the model calculatesthe � ow rates, temperatures and compositions of the productand internal streams, and the various heat duties. The resultsobtained compare very well with rigorous simulation results.

The signi� cance of the new shortcut models is that theyare intended speci� cally for retro� t design, and they can beapplied to complex column con� gurations. Furthermore,these models account for the changes in relative volatilityand molar over� ow through the column, overcoming theunderlying limitations of the previous shortcut models. Theretro� t models are reliable for very complex con� gurations,including a large number of well-behaved components(crude oil distillation). The models also apply to otherdistillation applications, such as naphtha fractionation,petrochemicals separation, etc.

The retro� t models provide a basis for optimising andimproving the operating conditions of existing distillationcolumns for energy-related, economic and environmentalbene� ts. The models can also be applied to calculate theadditional heating and cooling requirements for increasedthroughput to an existing distillation process. The modelscan be utilised to assess retro� t modi� cations, such asadding side-coolers or replacing stripping steam with areboiler. Furthermore, these models can be combined withhydraulic models, for the calculation of column diameters,to assess the effect of increasing throughput on the hydrauliccapacity of an existing distillation column.

NOMENCLATURE

B molar � ow rate of bottom productD molar � ow rate of top productdi molar � ow rate of component i in top productF molar � ow rate of feed

Table 12. Speci� cations of atmospheric crude oil distillation column(example 5).

Columnspeci� cations

Column1

Column2

Column3

Column4

Rectifying stages 9 10 8 9Stripping stages 5 5 7 6Column pressure

(bar)2.5 2.5 2.5 2.5

Feed preheatingtemperature (¯C)

365

Vaporisationmechanism

Steam Steam Reboiler Reboiler

Steam � ow(kmolh¡1)

1200 250

Pump-around DT(¯C)

30 50 20

Degree of thermalcoupling

0.5 0.2 0.6

Top product � ow(kmolh¡1)

680.7

Bottom product� ow (kmolh¡1)

633.9 149.8 652.8 493.0

Re� ux ratio 0.41 0.42 1.47 4.77

Table 13. Results of atmospheric crude oil distillation column (example 5).

ParameterShortcutmodel

Rigorousmodel

Column 1Bottom product � ow rate (kmol h¡1) 633.9a 624.0Bottom product temperature (¯C) 334.7 333.4Key component � ow rate in bottom

product (kmol h¡1)83.5 83.5b

Pump-around duty (MW) 12.87 12.87b

Pump-around � ow rate (kmolh¡1) 2187a 2187b

Pump-around temperature drop (¯C) 30.0b 27.1Steam � ow rate (kmolh¡1) 1200b 1200b





Pump-around temperature drop (¯C) 50.0b 47.0Steam � ow rate (kmolh¡1) 250b 250b





Pump-around temperature drop (¯C) 20.0b 21.4Reboiler duty (MW) 9.38 9.38b

Column 4Top product � ow rate (kmol h¡1) 680.7 691.4Top product temperature (¯C) 76.9 77.1Key component � ow rate in top

product (kmol h¡1)174.6 175.5

Bottom product � ow rate (kmol h¡1) 493.0 491.5Bottom product temperature (¯C) 189.6 191.2Key component � ow rate in bottom


Condenser duty (MW) 52.20 52.10Reboiler duty (MW) 6.72 6.72b

Re� ux ratio 4.77b 4.79

aIndirectly speci� ed; bspeci� ed.



N total number of theoretical stagesNmin minimum number of stages at total re� uxR re� ux ratioRmin minimum re� ux ratioNR number of stages in rectifying sectionNS number of stages in stripping sectionRHK recovery of heavy key component to bottom productRLK recovery of light key component to top productxbLK mole fraction of light key component in bottom productxdHK mole fraction of heavy key component in top productxdLK mole fraction of light key component in top productxf,i mole fraction of component i in feedxfHK mole fraction of heavy key component in feedxfLK mole fraction of light key component in feedxHKFS liquid mole fraction of heavy key component on feed stagexLKFS liquid mole fraction of light key component on feed stageq liquid fraction of feed at feed stage conditionsVbottom molar vapour � ow rate in bottom section at actual re� uxVmin,pinch minimum molar vapour � ow rate at top pinchVmin,pinch minimum molar vapour � ow rate at bottom pinchVmin,top minimum molar vapour � ow rate in top sectionVmin,bottom minimum molar vapour � ow rate in bottom sectionVtop molar vapour � ow rate in top section at actual re� uxaLK volatility of light key component relative to a reference

componentaHK volatility of heavy key component relative to a reference

componentai volatility of component i relative to a reference componentf roots of Underwood equationfFensk Fenske term to simplify Equation (12)fKirk Kirkbride term to simplify Equation (13)c Gilliland termjSteam steam stripping term to simplify Equation (24)

REFERENCES

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Carlberg, N.A. and Westerberg, A.W., 1989b, Temperature-heat diagram forcomplex columns. 3. Underwood’s method for the Petlyuk con� guration,Ind Eng Chem Res, 28(9): 1386–1397.

Cerda, J. and Westerberg, A.W., 1981, Shortcut methods for complexdistillation columns: 1. Minimum re� ux, Ind Eng Chem Proc Des Dev,20(3): 546–557.

Gadalla, M., 2003, Retro� t design of heat-integrated crude oil distillationsystems, PhD Thesis, UMIST, Manchester, UK.

Gadalla, M., Jobson, M. and Smith, R., 2003a, Increase capacity anddecrease energy for existing re� nery distillation columns, Chem EngProg, 99(4): 44–50.

Gadalla, M., Jobson, M., Smith, R. and Boucot, P., 2003b,Design of re� nerydistillation processes using key component recoveries rather than conven-tional speci� cation methods, submitted to Trans IChemE, Part A, ChemEng Res Des (submitted).

Gilliland, E.R., 1940, Multi-component recti� cation, estimation of thenumber of theoretical plates as a function of the re� ux ratio, Ind EngChem, 32(9): 1220–1223.

Glinos, K. and Malone, M.F. 1985, Minimum vapor � ows in a distillationcolumn with a side stream stripper, Ind Eng Chem Proc Des Dev, 24(4):1087–1090.

King, C.J., 1980, Separation Processes, 2nd edition (McGraw-Hill,New York), Chap. 9, p 418, 426, 434.

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Nandakumar, K. and Andres, R.P., 1981, Minimum re� ux conditions. 2.Numerical-solution, AIChE J, 27(3): 460–465.

Petlyuk, F.B., Platonov, V.M. and Slavinskii, D.M., 1965, Thermodynami-cally optimal method for separating multi-component mixtures, Int ChemEng, 5(3): 555.

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ADDRESS

Correspondence concerning this paper should be addressed to DrM. Jobson, Department of Process Integration, UMIST, PO Box 88,Manchester M60 1QD, UK.E-mail: [email protected]

The manuscript was received 15 July 2002 and accepted for publicationafter revision 30 July 2003.


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gadalla_shortcut models, retrofit design of distillation columns (2003)

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