Gadalla_shortcut Models, Retrofit Design Of Distillation Columns (2003)

0263–8762/03/$23.50+0.00 # Institution of Chemical Engineers Trans IChemE, Vol 81, Part A, September 2003

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SHORTCUT MODELS FOR RETROFIT DESIGN OF DISTILLATION COLUMNS M. GADALLA, M. JOBSON and R. SMITH Department of Process Integration, UMIST, Manchester, UK

S

hortcut models are well established for grassroots design of distillation columns and have been widely applied. However, no shortcut models are available that address retroŽ t. Shortcut models are quicker to solve, do not have signiŽ cant convergence problems and are more robust than rigorous models for column optimization. In particular, shortcut models for retroŽ t would be valuable for evaluating retroŽ t design options, for improving the performance of existing distillation systems (columns and heat recovery systems) and can be combined with detailed heat-integration models for optimizing existing heat-integrated distillation systems. This paper presents retroŽ t shortcut models for design of both reboiled and steam-stripped distillation columns. These models are primarily based on a modiŽ ed Underwood method, the Gilliland and Kirkbride correlations, the Fenske equation and the material balances. The retroŽ t models are applicable for simple distillation columns, sequences of simple distillation columns, and complex distillation conŽ gurations, including columns with side-strippers and side-rectiŽ ers. The models Ž x both the column conŽ gurations and 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 results with those of rigorous models of existing distillation columns is presented to validate the model. Keywords: retroŽ t; complex column; heat-integration; thermal coupling; FUG method.

volatilities change through the column (Seader and Henley, 1998; Suphanit, 1999). Where the underlying assumptions are not valid, the accuracy of the results will be compromised. Even in these cases, however, the estimation of minimum vapour  ow rates is good in regions of constant composition, also known as pinch zones (King, 1980; Kister, 1992). Some improvements to the Underwood method 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 researchers have proposed shortcut models for grassroots design of non-conventional distillation columns. The Fenske–Underwood–Gilliland (FUG) is the most popular shortcut model for design. Petlyuk et al. (1965) and Stupin and Lockhart (1972) studied the energy consumption of fully thermally coupled distillation compared with conventional columns. Cerda and Westerberg (1981) developed shortcut models for design of various complex distillation systems. Glinos and Malone (1985) developed a shortcut procedure for design of a distillation column with a side-stripper. Carlberg and Westerberg (1989b) and Triantafyllou and Smith (1992) applied the Underwood equation to a three-column model for the design and analysis of fully thermally coupled distillation columns. Suphanit (1999) developed shortcut models for various complex distillation column conŽ gurations, including side-strippers and side-rectiŽ ers.

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 an inŽ nite number of stages. This theoretical condition sets the operating limit of a real column. Minimum re ux can be determined by rigorous simulation using a large number of stages and specifying the recoveries of key components. However, the calculation may be difŽ cult to converge. Instead, shortcut methods are more widely used to determine minimum re ux. The best known shortcut method for calculating 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, and constant relative volatilities throughout the column. It is easy to use, with only recoveries of two key components and thermal condition of feed needing to be speciŽ ed. This method is applicable to simple distillation columns, i.e. single-feed two-product columns with a single condenser and a single reboiler. The minimum condenser and reboiler duties and also the minimum vapour  ow rates in column sections are obtained from the calculations. The method gives good results for distillation systems with relatively ideal mixtures. However, for multi-component mixtures and for systems with non-ideal vapour–liquid equilibrium behaviour, the molar over ow is not constant and the relative 971

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Since distillation is an energy-intensive process and requires large capital investment, retroŽ t of distillation columns is carried out more often than is installation of new equipment. RetroŽ t projects of distillation processes aim to reuse the existing equipment more efŽ ciently in order to increase the proŽ t. To carry out a retroŽ t study, retroŽ t models are necessary to Ž x the existing distillation design. No shortcut models are published for retroŽ t; rigorous models are generally applied within commercial simulation packages. Established rigorous models are time-consuming and have convergence problems. Furthermore, they fail to consider all design parameters simultaneously in the optimization of the whole system, particularly in heat-integrated distillation columns. In contrast, shortcut models are quicker to solve and more robust for optimization, especially when all design variables are considered simultaneously. They can also be combined with detailed heat-integration models for improving the energy efŽ ciency of distillation systems. In this paper, shortcut models for retroŽ t design of distillation columns are developed. These retroŽ t models are applicable for various reboiled and steam-stripped distillation columns, including simple columns, columns with side-strippers, side-rectiŽ ers, and partial or full thermal coupling. These models form the basis for a retroŽ t design methodology (Gadalla, 2003; Gadalla et al., 2003a) for distillation columns and the associated heat recovery systems.

RETROFIT MODELS FOR REBOILED DISTILLATION COLUMNS Distillation columns require the input of energy to perform the required separation; in most applications, reboilers supply this energy. A distillation column using a reboiler and condenser is known as a conventional distillation column. In this section, a shortcut model for retroŽ t design of reboiled distillation columns is developed. This shortcut model is based on the model developed by Suphanit (1999) for grassroots design of complex distillation columns. Initially, a shortcut model is developed for retroŽ t design of simple distillation columns. Thereafter, a retroŽ t model is proposed for design of complex distillation conŽ gurations (e.g. distillation columns with side-stripper, siderectiŽ ers, thermal coupling, etc.).

Basic Model Equations for Grassroots Design This section summarises the previous shortcut models for design distillation columns developed by Suphanit (1999). This model is an improvement to the standard FUG method. The improvements concentrate on the limiting assumptions of the FUG method: constant molar over ow within each column section and constant relative volatilities throughout the column. In this model, the relative volatility of each component is the geometric mean of that at different locations in the column, i.e. top section, bottom section and feed stage. An enthalpy balance around column sections is carried out to accommodate changes in vapour  ow rates at both minimum and actual re ux conditions. The modiŽ ed procedure at the minimum re ux conditions is as follows (Figure 1):

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

(1) Use the Underwood equation to estimate the minimum vapour  ow rates at the top and bottom pinch zones (Vmin,pinch, Vmin,pinch). (2) An enthalpy balance around the top section (envelope 1 in Figure 1) is performed to calculate the minimum condenser duty and the minimum vapour  ow rate at the top of the column (Vmin,top). Then, the corresponding reboiler duty is calculated by an overall enthalpy balance. (3) The minimum vapour  ow rate at the bottom of the column (Vmin,bottom) is calculated by enthalpy balance around the reboiler (envelope 2 in Figure 1). At the actual re ux condition, the vapour  ow rate in the top section (Vtop) is calculated by a material balance around the condenser, assuming a value for the re ux ratio, R=Rmin. Then, 0 the vapour  ow rate in the bottom section (Vbottom ) is calculated by an enthalpy balance around the reboiler (Figure 2). In the standard FUG model, this vapour  ow rate is calculated using the thermal conditions at the feed stage. Based on these improvements to the FUG method, Suphanit (1999) developed shortcut models for grassroots design of reboiled distillation columns, including different column conŽ gurations, such as columns with side-strippers and side-rectiŽ ers, and columns with side-exchangers. For a given feed and required separation, the model calculates the number of theoretical stages in each section, assuming a value for the ratio R=Rmin. The basic model equations of the shortcut model are presented for simple distillation columns with reboilers, as follows. The Underwood equation at the feed stage can be written as: X ai xf ,i ˆ1¡q (1) ai ¡ f Trans IChemE, Vol 81, Part A, September 2003

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Molokanov et al. (1972) represented these data by a line with the following equation: µ³ ´³ ´¶ x¡1 1 ‡ 54:4x c ˆ 1 ¡ exp (6) 11 ‡ 117:2x x0:5 R ¡ Rmin xˆ (7) R‡1 N ¡ Nmin cˆ (8) N ‡1 After calculating the total number of theoretical stages inside the column, the location of the feed stage can be identiŽ ed using the empirical equation of Kirkbride: "³ ´³ ´³ ´2 #0:206 NR B xfHK xbLK ˆ (9) NS D xfLK xdHK

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

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

The minimum vapour  ow rate and distribution of components with volatilities between those of the key components at the top pinch location is given by: X ad i i ˆ Vmin,pinch (2) ai ¡ f The minimum vapour  ow rate at the bottom pinch location is then calculated as follows: 0 Vmin,pinch ˆ Vmin,pinch ¡ (1 ¡ q)F

The minimum re ux ratio is then calculated: ³ ´ Vmin,top Rmin ˆ ¡1 D

(3)

(4)

The Fenske equation is used to determine the minimum number of stages at total re ux: ln[(RLK =(1 ¡ RLK ))=((1 ¡ RHK )=RHK )] Nmin ˆ (5) ln[aLK =aHK ] To achieve a speciŽ ed separation between two key components, the actual re ux ratio and the number of stages must be greater than their minimum values. The actual re ux ratio is generally chosen, by economic considerations, as some multiple of minimum re ux. The corresponding number of stages is then determined by suitable graphical methods or by an empirical correlation. The most successful and simplest graphical correlation for the number of stages was developed by Gilliland (1940) and slightly modiŽ ed later by Robinson and Gilliland (1950). Seader and Henley (1998) reviewed the various equations for the Gilliland correlation and presented a comparison of rigorous calculations with the Gilliland correlation. The Gilliland correlation relates the number of stages to the minimum number of stages, and minimum and actual re ux ratios. The data for this correlation are based on accurate calculations. Trans IChemE, Vol 81, Part A, September 2003

RetroŽ t Shortcut Model for Simple Reboiled Distillation Columns Figure 3 shows a simple distillation column (conventional distillation column). For an existing simple distillation column, the basic model equations are solved simultaneously with the material balance equations to build the retroŽ t shortcut model. Material balances are carried out around the column for the light and heavy key (LK, HK) components: xfLK F(1 ¡ RLK ) B xfHK F(1 ¡ RHK ) ˆ D

xbLK ˆ

(10)

xdHK

(11)

The Fenske equation is rewritten for an existing distillation column to give the recovery of the key components as a function of the minimum number of stages, as follows: µ ¶N RLK RHK aLK min ˆ (12) aHK (1 ¡ RHK )(1 ¡ RLK )

Figure 3. Simple distillation column with reboiler.

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The Kirkbride correlation and the LK and HK component material balance equations are rearranged and solved simultaneously, resulting in: 1 ¡ RLK ˆ fKirk (13) 1 ¡ RHK where

fKirk

µ³ ´³ ´¶ = ³ ´ B xfHK 1 2 NR 2:427 ˆ D xfLK NS

(14)

The term fKirk can be calculated for the existing distillation column, where the number of stages in each section is given and the top and bottom product molar  ow rates and the mole fractions of the key components are known. Equations (12) and (13) are solved simultaneously to calculate the recovery of the HK component as follows: 1 ¡ RHK 1 ¡ fKirk (1 ¡ RHK ) 1 ˆ (15) RHK fKirk (1 ¡ RHK ) fFensk R 1 1 …1 ¡ RHK †2 ‡RHK …1 ¡ RHK † ¡ HK ˆ0 fFensk fKirk fFensk (16) where ³ fFensk ˆ

aLK aHK

´Nmin (17)

Equation (16) is quadratic in RHK. Since the recovery of the heavy key component, RHK must be positive and less than unity; only the positive root of Equation (16) is accepted: "³ #1=2 ´2 (fKirk ‡ 1) 1 RHK ˆ 1 ¡ ‡ 4(fFensk ¡ 1) (fFensk ¡ 1)fKirk ‡

fKirk ‡ 1 2fKirk (fFensk ¡ 1)

(18)

This equation calculates the recovery of the heavy key component, given the values of the terms fKirk and fFensk. Then, the recovery of the light key component can be determined from Equations (13) and (18) as follows: RLK ˆ 1 ¡ fKirk (1 ¡ RHK )

(19)

From the existing total number of theoretical stages inside the distillation column and for the existing operating conditions, the minimum number of stages which is required to calculate the term fFensk is calculated from the Gilliland equation: Nmin ˆ N (1 ¡ c) ¡ c

input data to the model are the feed speciŽ cations (i.e.  ow rate, temperature, pressure, composition), and the number of existing stages in each section, as well as the operating conditions (i.e. re ux ratio, column temperature, column pressure). The model output includes the key component recoveries, product compositions and  ow rates, and the condenser and the reboiler duties. The same retroŽ t model is applicable for sequences of simple distillation columns (Figure 4). In this case, the model is applied directly and sequentially to each column in the sequence, starting with the Ž rst column. In the column sequence, the number of existing stages in each section and the operating conditions are Ž xed. The model calculates the product compositions,  ow rates and temperatures, and the various duties. Illustrative example 1: simple reboiled column A simple reboiled distillation column separates a mixture of aromatic hydrocarbons into two products. The feed mixture data and column speciŽ cations are given in Table 1. The task of the distillation column is to separate benzene from toluene with 99% recovery of both key components. The physical properties of the feed mixture and the products are calculated by the Peng Robinson model. The existing distillation column is modelled using rigorous 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 physical property calculations. A re ux ratio of 2.082 is calculated by HYSYS to separate the given feed mixture in the existing distillation column into the top product with the required

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

(20)

where

c ˆ f (R, Rmin )

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

(21)

Equations (14) and (17)–(21) represent the retroŽ t shortcut model for conventional distillation columns. This model utilizes the Molokanov equation to represent the Gilliland correlation. However, any other suitable equation can be substituted. In the application of the model for retroŽ t design, Equations (14) and (17)–(21) are solved simultaneously to simulate existing simple reboiled distillation columns. Equation (14) uses assumed values for the key component recoveries to initialize the calculations of the term fKirk. The

Flow rate (kmol h¡1) Feed mixture Benzene Toluene Ethyl benzene m-Xylene o-Xylene Total Feed conditions Pressure (bar) Temperature (¯ C) Column speciŽ cations Rectifying stages Stripping stages Column pressure (bar)

200 100 100 200 100 700 2.0 135.9 15 15 2.0

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SHORTCUT MODELS FOR RETROFIT DESIGN Table 2. RetroŽ t shortcut and rigorous model results (example 1).

Parameter Top product  ow (kmol h¡1) Top product temperature (¯ C) Condenser duty (kW) Bottom product  ow (kmol h¡1) Bottom product temperature (¯ C) Reboiler duty (kW) Recovery of benzene to distillate (%) Recovery of toluene to bottom product (%) Re ux ratio, R Minimum re ux ratio, Rmin

Rigorous model

RetroŽ t shortcut model

199.0 104.4 5003 501.0 158.7 5431 99.00a 99.00a

198.9 104.4 5002 501.1 158.8 5427 98.92b 98.87b

2.082 1.931

2.082a 1.967

a

SpeciŽ ed; bratio of recoveries speciŽ ed (fKirk ˆ 1).

speciŽ cations. A hundred theoretical stages are used to calculate the minimum re ux ratio in the rigorous simulation. In the retroŽ t shortcut calculations, the number of existing stages is speciŽ ed, as are the operating conditions, including the re ux ratio. The model calculates the product key component recoveries,  ow rates and temperatures, and the duties of the condenser and reboiler. The results are summarized in Table 2. It is clear from Table 2 that the retroŽ t shortcut model is in very good agreement with the rigorous model. This agreement is expected for a simple distillation column; the maximum deviation is less than 1% compared with rigorous models. This good agreement between results validates the retroŽ t shortcut model. Although the rigorous simulation provides a value for the re ux ratio for the retroŽ t shortcut calculations, the re ux ratio can also be calculated within the retroŽ t shortcut model. Therefore, the retroŽ t model can be applied independently of the rigorous simulations.

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RetroŽ t Shortcut Model for Complex Distillation ConŽ gurations with Reboilers In the complex column conŽ gurations considered, a single feed is separated into more than two products, using a main column with a side-stripper or side-rectiŽ er, as shown in Figure 5. RetroŽ t modelling for such complex conŽ gurations is more difŽ cult than for simple sequences. Suphanit (1999) developed a shortcut model for grassroots design of complex columns with side-strippers and side-rectiŽ ers. This model calculates the number of theoretical stages required for a given separation and feed speciŽ cations. In this model, the complex conŽ gurations are decomposed into thermodynamically equivalent sequences of simple columns, as shown in Figure 5. This facilitates the design and analysis of the conŽ gurations. An indirect sequence of two thermally coupled simple columns is equivalent to a complex column with a side-stripper. For the complex column with a side-rectiŽ er, the equivalent sequence is a direct sequence of two thermally coupled simple columns. The connections between the simple columns are one vapour stream and one liquid stream. This connection is known as thermal coupling, because of the direct heat transfer between column sections. In the thermally coupled direct sequence, the downstream column is fed by a liquid stream from the upstream column and returns vapour to the upstream column, while in the thermally coupled indirect sequence, the downstream column returns liquid to the upstream column and receives a vapour phase feed from the upstream column. Using this decomposition technique, the design of such conŽ gurations becomes more systematic. Each simple column in these equivalent sequences can be designed individually from upstream to downstream columns. In the indirect sequence equivalent to a complex column with a side-stripper, the thermal coupling is at the top of the Ž rst column, as shown in Figure 6. The vapour and liquid

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

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

streams connecting the columns are assumed to be the vapour  owing to and liquid leaving a hypothetical partial condenser of the Ž rst column. In this case, the vapour and liquid  ow in the top section of the Ž rst column are the feed and side-draw streams for the second column respectively. The net feed  ow for the second column is the top product  ow of the Ž rst column (D1). The modiŽ ed FUG shortcut model is applied to each column starting from the Ž rst column, then moving to the second column. The assumption of Carlberg and Westerberg (1989a), that the feed and sidedraw streams are on the same stage, is applied in this model. In a similar way, complex columns with side-rectiŽ ers are analysed; thermal coupling between the columns in this case is at the bottom of the Ž rst column, as shown in Figure 7. The liquid and vapour streams in the bottom section of the Ž rst column are assumed to be the feed and side-draw for the second column, respectively. The net feed  ow to the second column is the bottom product of the Ž rst column (B1). The modiŽ ed FUG method is applied to both columns in the equivalent sequence of columns (Suphanit, 1999).

Based on these shortcut models for grassroots design and the retroŽ t model developed for simple distillation columns, a retroŽ t model for complex columns with side-strippers and side-rectiŽ ers is proposed (Figure 8): (1) The complex column is decomposed into the thermodynamically equivalent sequence of simple columns. The existing stages are distributed into the corresponding column sections (see Figure 5). (2) The retroŽ t shortcut model is applied to each simple column in the sequence, starting with the Ž rst column. The model Ž xes the number of existing stages in each section, and, for the given operating conditions, it calculates product  ow rates and compositions, and the duties of the reboilers and condensers. (3) Owing to the thermal coupling, the procedure is iterative, as indicated in Figure 8. The procedure terminates once the calculated number of stages corresponds to the number of existing stages in each thermally coupled column.

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

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Figure 8. RetroŽ t algorithm for complex column conŽ gurations.

Figure 9 shows column conŽ gurations with partial thermal coupling, as well as fully thermally coupled sequences. In the partially thermally coupled sequences, only some of the heat load of the condenser or the reboiler in the Ž rst column is shifted to the subsequent column. In the partially coupled indirect sequence, a side-cooler is installed at the top of the Ž rst column instead of the condenser. In the partially coupled direct sequence, a side-heater is installed at the bottom of the Ž rst column instead of the reboiler of the Ž rst column.

Figure 9. Thermal coupled complex column conŽ gurations (direct and indirect sequences). (a) Partial thermal coupling; (b) full thermal coupling.

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The degree of thermal coupling for indirect coupled sequences is deŽ ned as the ratio of the liquid  ow rate at the top of the column when using a side-cooler to that when no side-cooler is installed (Suphanit, 1999). Similarly, the degree of thermal coupling for direct coupled sequences is the ratio of the vapour  ow rate at the bottom of the column when using a side-heater to that when no side-heater is installed. In uncoupled sequences, the degree of thermal coupling is equal to zero, which means there is no liquid or vapour from the subsequent column. In fully coupled sequences, this value is unity; the duty of the side-cooler and side-heater is zero and the total heat duty of the condenser and reboiler in the Ž rst column is shifted to the subsequent column. Suphanit (1999) developed a design model for the calculation of sideexchanger duties in partially thermally coupled complex columns. The model calculates the exchanger duty for an assumed degree of thermal coupling between columns and a given temperature drop over the exchanger. A similar retroŽ t model to that for fully coupled sequences (see Figure 8) is proposed for the partially coupled complex conŽ gurations. This retroŽ t model is built by combining the retroŽ t model for simple columns and the model of Suphanit (1999) for complex columns with side-exchangers. In this case, both column conŽ guration and operating conditions are Ž xed. The model calculates the product  ow rates, temperatures and compositions, and the heat duties of the reboilers, condensers and side-exchangers. Illustrative example 2: reboiled column with side-stripper An existing complex column with a side-stripper separates the feed mixture given in Table 1 into three products, as indicated in Table 3. This column conŽ guration is

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Table 3. Column speciŽ cations for thermally coupled indirect sequence (example 2).

Top stages Bottom stages Pressure (bar)

Column 1

Column 2

18 25 2.0

18 12 2.0

equivalent to two fully thermally coupled reboiled columns. The existing number of stages and column operating conditions are listed in Table 3. The task of the Ž rst column in the sequence is to separate between the toluene and ethyl benzene with 99% recoveries of each. The second column then recovers 99% of the benzene to the top product and 99% of the toluene to the bottom product. The operating re ux ratio of the distillation column (i.e. second column in equivalent sequence) is 4.54. The physical properties of the feed and product streams are calculated by the Peng Robinson model. The retroŽ t shortcut model simulates the existing distillation unit. The existing stages are speciŽ ed, as are the operating re ux ratio and the liquid recycle  ow rate from the second column to the Ž rst column. The simulation results, summarized in Table 4, include the product  ow rates and temperatures, the key component recoveries, the condenser and reboiler duties, and the vapour  ow rate in the thermal coupling connection. These results are compared with rigorous simulation results (HYSYS), for the same column and feed speciŽ cations. It can be seen that the results of the retroŽ t shortcut models are in very good agreement with those of the rigorous simulation. The deviation of the results for most design variables is less than 1%, except for the reboiler of the second column, which shows a deviation of 6.8% in the

Table 4. RetroŽ t shortcut and rigorous model results (example 2).

Parameter Column 1 Bottom product  ow (kmol h¡1) Bottom product temperature (¯ C) Reboiler duty (kW) Bottom recovery of ethyl benzene (%) Thermal coupling (see Table 3) Vapour  ow (kmol h¡1) Liquid  ow (kmol h¡1) Column 2 Reboiler duty (kW) Condenser duty (kW) Top product  ow (kmol h¡1) Top product temperature (¯ C) Bottom product  ow (kmol h¡1) Bottom product temperature (¯ C) Top recovery of benzene (%) Bottom recovery of toluene (%) Re ux ratio a

SpeciŽ ed; brecovery ratio (fKirk) speciŽ ed.

Rigorous model

RetroŽ t shortcut model

399.4 166.7 7713 99.0a

399.7 166.8 7644 99.5

829.0 525.7

825.6 525.7a

1732 8987 198.0 104.3 102.7 135.7 99.0a 99.0a 4.54a

1850 8936 198.9 104.3 101.4 135.5 99.0b 99.1b 4.54a

heat duty. The temperature difference of the various streams is than 0.5¯ C. Conclusions RetroŽ t models have been developed for reboiled distillation columns. The models are applicable for simple distillation columns and sequences of simple columns. The models also apply to complex conŽ gurations of distillation columns, such as columns with side-strippers and side-rectiŽ ers. In the calculations, the models Ž x both the given column conŽ guration and operating conditions, and calculate the product  ow rates and compositions and the various heating and cooling duties. Generally, very good agreement is observed between the retroŽ t model and rigorous simulation results for a well behaved mixture of hydrocarbons. The retroŽ t shortcut models can initialize the rigorous model calculations. RETROFIT MODEL FOR STEAM-STRIPPED DISTILLATION COLUMNS Some distillation applications, including crude oil distillation, use stripping steam as a vaporization mechanism. Live steam is injected directly into the bottom of the column as a stripping agent. Steam is condensed in the condenser and can be separated from liquid hydrocarbons at the top of the crude oil column because it is immiscible with most hydrocarbons. In steam-stripped distillation columns, the column is divided into two sections, the rectifying and stripping sections, as shown in Figure 10. Stripping steam reduces

Figure 10. Simple distillation column using stripping steam.

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SHORTCUT MODELS FOR RETROFIT DESIGN the partial pressure of the hydrocarbons in the stripping section, which results in vaporisation. Figure 11 shows the temperature proŽ le through the steam-stripped distillation column and compares it with that of a reboiled column. As can be seen, the stage temperature of the reboiled column decreases continuously from the reboiler to the condenser. In the steam-stripped column, the vapour is generated by the reduction in the partial pressure of the liquid; the liquid itself supplies the heat of vaporization. The liquid temperature reduces from the feed stage towards the bottom of the column. The temperature proŽ le of the steam-stripped column shows a peak value at the feed stage (Suphanit, 1999). The challenges for modelling steam-stripped columns are that the conventional shortcut models for reboiled columns, such as the FUG model, cannot be applied directly. The reason is that the separation characteristics, such as the temperature proŽ le and the vapour generation mechanism, are different in steam-stripped columns from those of reboiled columns. Suphanit (1999) developed a shortcut model for grassroots design of steam-stripped distillation columns. Based on this model, a retroŽ t model for design of steam-stripped distillation columns is proposed. First, a retroŽ t model is presented for simple distillation columns. Thereafter, a model is proposed for retroŽ t design of complex distillation conŽ gurations, including distillation columns with sidestrippers, side-rectiŽ ers and thermal coupling. Basic Model Equations for Grassroots Design The shortcut model developed by Suphanit (1999) for grassroots design of steam-stripped distillation columns is presented, as it is the foundation of the retroŽ t model. This model is applicable for simple and complex conŽ gurations of steam-stripped distillation columns. In this model, the Underwood equation and enthalpy balance are applied to a simple steam-stripped column to estimate the minimum vapour  ow rate in each section, and the minimum re ux ratio and the condenser duty. The dew point temperature is calculated to determine the temperature of the top product for a partial condenser; the bubble point temperature is calculated for a total condenser. The temperature of the bottom product is calculated by an enthalpy balance. The number of stages is calculated separately for each section of the column. In the rectifying section, the Fenske

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equation is applied to determine the minimum number of stages at total re ux condition: Nmin ˆ

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

(22)

The Gilliland correlation then determines the number of stages in this section. To apply such shortcut design equations as Equation (22), the relative volatilities and mole fractions of components in a mixture of unknown composition are needed, where the relative volatilities are composition dependent. An iterative approach is needed to estimate product compositions and hence volatilities. Initial values for the recoveries of the light and heavy key components are speciŽ ed, and initially, components lighter than the light key and those heavier than the heavy key are assumed to be fully recovered, to the distillate and bottoms, respectively. The recoveries of the intermediate-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), and interpolating between these conditions (King, 1980). In the stripping section, the vapour  ow rate proŽ le is non-linear, as shown in Figure 12(a). Thus, to obtain a good prediction of the number of stages, consecutive  ash calculations are performed from the bottom stage towards the feed stage. The number of stages is counted from the bottom stage until the stage vapour  ow rate reaches or exceeds the vapour  ow rate below the feed stage, as shown in Figure 12(b). The bottom vapour  ow rate is obtained by an overall enthalpy balance. The vapour  ow rate below the feed stage is assumed to be the minimum vapour  ow rate at the bottom pinch of the column (Suphanit, 1999). RetroŽ t Shortcut Model for Simple Distillation Columns with Strippi ng Steam The retroŽ t model for the rectifying section of simple steam-stripped distillation columns is developed by solving the basic model equations simultaneously with the material balance equation for a given number of stages. Steam is treated as an inert gas that does not condense in the column, nor interact with the other components present, but does affect the partial pressure of the hydrocarbons. Vapour– liquid equilibrium and relative volatility are calculated based on the hydrocarbon mixture at this partial pressure. The

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

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The minimum number of stages in the rectifying section can be calculated for the existing distillation column, where the number of stages is known and the operating conditions are Ž xed: Nmin ˆ NR (1 ¡ c) ¡ c

Figure 12. Stripping section of steam-stripped column. (a) Vapour  ow proŽ le; (b) stripping section.

assumption that the steam is introduced at a temperature and pressure that allow it to remain in the vapour phase is supported by rigorous simulation results for crude oil distillation columns. A material balance is carried out around the column for the heavy key component, resulting in: xdHK ˆ

xfHK F(1 ¡ RHK ) D

(27)

The retroŽ t model for the rectifying section is represented through Equations (25)–(27). These equations are solved simultaneously for given feed speciŽ cations, Ž xed operating conditions and the existing number of stages, to calculate the composition and  ow rate of the products. For the stripping section, the retroŽ t model is based on consecutive  ash calculations, as shown in Figure 13. The model determines the product composition for a given number of stages and steam  ow rate. The model calculations start by assuming the bottom product composition. Then, in an iterative procedure, consecutive  ash calculations are carried out from the bottom stage to the feed stage. Vapour–liquid equilibrium calculations and energy and mass balances are carried out for each stage to determine the composition and  ow rate of the vapour and liquid phases in the column. In each step, the number of stages is counted from the bottom stage to the feed stage. Then the bottom product composition is updated (through a linear relation with the previous bottom composition). The iterations terminate when the calculated number of stages and existing number of stages are identical. Hence, the correct bottom product composition is obtained. The retroŽ t models for the rectifying and stripping sections comprise the retroŽ t model for simple steam-stripped distillation columns. This model Ž xes the number of stages in each section and, for the given operating conditions and steam  ow rate, it calculates the product  ow rates, temperatures and compositions, and the condenser duty. The same retroŽ t model is also applicable for sequences of simple steam-stripped columns (e.g. Figure 14). The link between each pair of columns in the indirect sequence is the top product stream from the upstream column to the downstream column. In the direct sequence, the bottom product

(23)

For an existing simple distillation column, the Fenske equation is rewritten to give the recovery of the key components as a function of the minimum number of stages, as follows: xdLK ˆ jSteam (24) xdHK where jSteam

µ ¶N xLKFS aLK min ˆ xHKFS aHK

(25)

By solving Equations (23) and (24), the recovery of the heavy key component can be calculated by: RHK ˆ 1 ¡

xdLK D xfHK FjSteam

(26)

Figure 13. RetroŽ t algorithm for stripping sections.

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

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

Parameter

Rigorous model

RetroŽ t shortcut model

n-C14 in top product (kmol h¡1) n-C19 in bottom product (kmol h¡1) Top product  ow (kmol h¡1) Top product temperature (¯ C) Condenser duty (MW) Bottom product  ow (kmol h¡1) Bottom product temperature (¯ C) Steam  ow (kmol h¡1) Re ux ratio

59.38a 59.38a 564.6b 130.4 40.0 435.4b 224.6 1540 0.411

61.51 59.96 564.0 131.4 40.4 435.9 225.8 1540a 0.411a

a

SpeciŽ ed; bwater-free basis.

from the upstream column feeds the downstream column. As seen in these conŽ gurations, the sequences are simple columns connected with no thermal coupling. Therefore, the retroŽ t model for simple steam-stripped columns is applied directly and sequentially to each simple column in these conŽ gurations, starting with the Ž rst column. Illustrative example 3: simple steam-stripped column An equimolar C8–C23 mixture of normal parafŽ ns is separated into two products by a simple steam-stripped distillation column. The feed data and column speciŽ cations are given in Table 5. Superheated steam at 160¯ C and 3 bar is used as a stripping agent. The task of the distillation column is to recover 95% of n-C14 to the top product and 95% of n-C19 to the bottom product. The existing distillation column is simulated using both the retroŽ t shortcut model and rigorous simulation (HYSYS). Both models use the Peng Robinson model for the physical property calculations of the feed and product streams. In the rigorous simulation, a steam  ow rate of 1540 kmol h¡1 and a re ux ratio of 0.411 are predicted to separate the given feed in the existing column into the required speciŽ cation. When using the retroŽ t model, the number of stages in each section and the column operating conditions are Ž xed. The steam  ow rate and re ux ratio that are obtained from the rigorous simulation are speciŽ ed. The retroŽ t model calculates the product  ow rates and temperatures, the key component recoveries (or  ow rates) and the duty of condenser. These results are summarized in Table 6, and compared with those of the rigorous simulation. The table shows very good agreement between the retroŽ t model and rigorous simulation results.

Table 5. Equimolar feed mixture data and column speciŽ cations (example 3). C8–C23 mixture Feed speciŽ cations Flow rate (kmol h¡1) Pressure (bar) Temperature (¯ C) Column speciŽ cations Rectifying stages Stripping stages Column pressure (bar) Flow rate of n-C14 to top product (kmol h¡1; 95% recovery) Flow rate of n-C19 to bottom product (kmol h¡1; 95% recovery)

1000 3.0 300 6 8 3.0 59.38 59.38

Trans IChemE, Vol 81, Part A, September 2003

RetroŽ t Shortcut Model for Complex Distillation ConŽ gurations with Stripping Steam Complex distillation conŽ gurations may use steam for vaporisation rather than using reboilers. Such columns are suitable for mixtures that are temperature sensitive, such as crude oil. Complex columns with side-strippers and side-rectiŽ ers, such as those shown in Figure 15, are more complicated than direct and indirect two-column sequences (see Figure 14). These conŽ gurations are modelled by the decomposition of complex columns into the thermodynamically equivalent simple sequences. The equivalent sequences shown in Figure 15 are fully thermally coupled. The thermal coupling is used in place of the condenser of the Ž rst column in the indirect sequence; the condenser of the second column provides re ux for both columns. In the direct sequence, thermal coupling is used in place of the reboiler of the Ž rst column; the reboiler of the second column provides vapour for both columns. The thermal coupling connections in the indirect sequence are the vapour feed to the downstream column from the upstream column and the liquid stream from the downstream column to the upstream column. In the direct sequence, the downstream column receives its feed from the bottom liquid of the upstream column and returns a vapour stream to the upstream column. Suphanit (1999) developed shortcut models for grassroots design of complex steam-stripped column conŽ gurations with side-strippers and side-rectiŽ ers, similar to those for reboiled complex columns. Based upon the shortcut model of Suphanit (1999) and the retroŽ t shortcut model for simple steam-stripped distillation columns, a retroŽ t model is proposed for complex columns with side-strippers and side-rectiŽ ers, as follows: (1) The complex column is decomposed into the thermodynamically equivalent sequence of simple columns. The existing stages are then distributed into the corresponding column sections, as indicated in Figure 15. (2) The retroŽ t shortcut model is applied sequentially to each simple column in the conŽ guration. The column conŽ guration and numbers of existing stages in each section, and steam  ow rates are Ž xed. The  ow rates, temperatures and compositions of the products and the condenser duties are calculated. (3) Owing to the thermal coupling, the procedure is iterative. The procedure terminates once the calculated number of stages corresponds to the number of existing stages.

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

In Figure 16, other conŽ gurations of steam-stripped distillation columns with partial thermal coupling are compared with fully thermally coupled sequences; these conŽ gurations use side-coolers and side-heaters. The retroŽ t model for fully coupled sequences is combined with the model developed by Suphanit (1999), for the calculation of side-exchanger duties, and extended to the partially coupled

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

conŽ gurations. In this case, both column conŽ guration and operating conditions, including steam  ow rates, are Ž xed. The product  ow rates and compositions, and the duties of the condenser and side-exchanger are calculated. Illustrative example 4: steam-stripped column with side-stripper In this example, the same hydrocarbon feed mixture given in Table 5 is separated into three products using a steamstripped distillation column with a side-stripper (equivalent to the thermally coupled indirect sequence of two steamstripped columns). The speciŽ cations for each column are given in Table 7, including the  ow rates of stripping steam and of the key components. Stripping steam, used for both columns, is at 160¯ C and 3 bar. The existing distillation column is Ž rst simulated using rigorous simulation. The re ux ratio was calculated to be 2.59 to meet the product speciŽ cations. When using the retroŽ t model in the simulation of the given distillation column, the column speciŽ cations and the operating conditions are speciŽ ed, as indicated in Table 8. The results of the simulation 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 rigorous simulation. Both models use the Peng Robinson model for the calculation of the physical properties of the feed and product streams. The retroŽ t shortcut and rigorous simulation results show relatively good agreement. Deviations are due to the complexity in the column conŽ guration, the presence of the stripping steam and the large number of components. Temperature differences of up to 7.6¯ C and  ow rate differences of products of up to 5.8% are observed. However, very Trans IChemE, Vol 81, Part A, September 2003

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Table 7. Column and product speciŽ cations (example 4). Column speciŽ cations

Column 1

Column 2

6 8 3.0 1100

8 4 3.0 100 59.4

Rectifying stages Stripping stages Column pressure (bar) Steam  ow (kmol h¡1) n-Dec  ow in top product (kmol h¡1) n-C19  ow in bottom product (kmol h¡1)

59.4

good agreement can be observed for key component  ow rates, the condenser duty and the re ux ratio. Conclusions New shortcut models have been developed for retroŽ t design of steam-stripped distillation columns. The models are applicable for various conŽ gurations of distillation columns, including simple columns, sequences of simple columns, complex columns with side-strippers, side-rectiŽ ers, and partial or fully thermally coupled sequences. The retroŽ t models predict results in good agreement with the existing rigorous simulations. These models can initialise rigorous calculations. RETROFIT MODELLING FOR REFINERY DISTILLATION COLUMNS Crude oil distillation is a process of great importance in the reŽ ning industry. The process is energy and capital intensive. RetroŽ t of these systems is a common design activity aiming to increase proŽ t by using the existing equipment more efŽ ciently. Generally, crude oil distillation units use a combination of steam-stripped and reboiled columns. For retroŽ t design of

Table 8. RetroŽ t shortcut and rigorous model results (example 4).

Parameter Column 1 Bottom product  ow (kmol h¡1) Bottom product temperature (¯ C) n-C19  ow in bottom product (kmol h¡1) Steam  ow (kmol h¡1) Thermal coupling (see Table 7) Vapour  ow (kmol h¡1) Liquid  ow (kmol h¡1) Column 2 Top product  ow (kmol h¡1) Top product temperature (¯ C) n-Dec  ow in top product (kmol h¡1) Bottom product  ow (kmol h¡1) Bottom product temperature (¯ C) Condenser duty (MW) Steam  ow (kmol h¡1) n-C13  ow in bottom product (kmol h¡1) Re ux ratio

Rigorous model

RetroŽ t shortcut model

454.5a 236.5 59.4b 1100b

448.1 237.3 59.48b 1100b

1940 261

1875 224

277.5a 127.8 59.4b 268.5a 228.1 30.7 100b 57.8 2.59

273.4 128.7 59.3 278.5 235.7 30.8 100b 61.2 2.59b

a

Water-free basis; bspeciŽ ed.

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such conŽ gurations, the new shortcut models developed for reboiled columns and steam-stripped columns can be applied sequentially. Conventionally, the design of crude oil distillation units is carried out by the speciŽ cation of the cut point and gap temperatures, or product  ow rates (Watkins, 1979). Rigorous model-based simulations apply this conventional method for design of crude oil distillation systems, i.e. the simulators specify the cut point and gap temperatures for the product separations. Conventional shortcut models (e.g. FUG) require the speciŽ cation of key components for the required separation. In the shortcut models of Suphanit (1999), key components (generally pseudo-components) are speciŽ ed for each pair of successive products. Real components can be speciŽ ed as the key components for the separation of the light ends. To apply the retroŽ t shortcut models presented in this paper, the product compositions need to be expressed in terms of recovery of light and heavy key components [see for example Equations (10) and (23)]. A systematic approach has been developed (Gadalla et al., 2003b) for nominating key components and specifying their recoveries from the converged simulation results for an existing crude oil distillation column. Illustrative Example 5: Crude Oil Distillation Column An industrial atmospheric crude oil distillation unit processes 100,000 barrels per day (2610 kmol h¡1) of crude oil at 25¯ C and 3 bar into Ž ve products: light naphtha (LN), heavy naphtha (HN), light distillate (LD), heavy distillate (HD), and residue (RES). Superheated steam at 260¯ C, 4.5 bar, is used as a stripping agent. The true boiling point data (crude assay) of the crude oil are shown in Table 9; these data are based on the textbook example of Watkins (1979). The crude assay is represented

Table 9. Crude assay data (example 5). Percentage distilled (vol) 0 5 10 30 50 70 90 95 100 Density ˆ 865.4 kg m¡3.

TBP (¯ C) ¡3.0 63.5 101.7 221.8 336.9 462.9 680.4 787.2 894.0

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

LN and HN

HN and LD

LD and HD

HD and RES

Light key Heavy key

4 6

7 9

11 14

13 16

using 25 pseudo-components, using the oil characterization technique embedded within HYSYS. The physical properties of each pseudo-component (e.g. molecular weight, vapour pressure, boiling temperature, critical properties, etc.) are calculated using the Peng Robinson model, and are then extracted from HYSYS. The key components for the separation of each pair of products are shown in Table 10. The composition of the feed in terms of these pseudo-components and their boiling temperatures and  ow rates is given in Table 11. The column conŽ guration is shown in Figure 17, which also shows the equivalent sequence of four thermally coupled columns. Table 12 gives the existing stages in each section of the column, the operating conditions, the steam  ow rates, the pump-around temperature differences and the degree of thermal coupling, which is deŽ ned as the liquid  ow rate at the top of the column when using pumparound to that when no pump-around is installed. The existing atmospheric unit is simulated using the retroŽ t shortcut model. In the calculations, the existing stages in the rectifying and stripping sections are Ž xed, and the operating conditions including steam  ow rates are speciŽ ed. The re ux ratio, the temperature drops over the pump-arounds, and the degree of thermal coupling are then speciŽ ed. The retroŽ 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 the key component  ow rates. These results are summarised in

Table 11. Feed composition of crude oil mixture (derived from assay data). Component number

NBP (¯ C)

Flow rate (kmol h¡1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

9 36 61 87 111 136 162 187 212 237 263 288 313 339 364 389 414 447 493 538 584 625 684 772 855

110.9 106.9 139.3 175.8 175.8 169.7 169.4 166.2 156.6 140.1 127.9 115.6 106.2 101.3 94.5 84.6 73.9 95.2 61.8 49.2 54.5 39.3 40.2 28.2 26.6

Total

2610.6

Table 13, and are used to initialise the calculations of the rigorous simulation (HYSYS), for the same column and feed speciŽ cations and the operating conditions. The results of both models are compared in Table 13. Table 13 shows that the results predicted by the retroŽ t shortcut model are in good agreement with those obtained from the rigorous simulations; no signiŽ cant deviations are observed. The maximum temperature difference is 10¯ C and the deviations in  ow rates are all less than 7%. Other variable results are in very good agreement.

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

Trans IChemE, Vol 81, Part A, September 2003

SHORTCUT MODELS FOR RETROFIT DESIGN Table 12. SpeciŽ cations of atmospheric crude oil distillation column (example 5). Column speciŽ cations Rectifying stages Stripping stages Column pressure (bar) Feed preheating temperature (¯ C) Vaporisation mechanism Steam  ow (kmol h¡1) Pump-around DT (¯ C) Degree of thermal coupling Top product  ow (kmol h¡1) Bottom product  ow (kmol h¡1) Re ux ratio

Column 1

Column 2

Column 3

Column 4

9 5 2.5

10 5 2.5

8 7 2.5

9 6 2.5

Steam

Steam

Reboiler

Reboiler

1200

250

30

50

20

0.5

0.2

0.6

365

680.7 633.9

149.8

652.8

493.0

0.41

0.42

1.47

4.77

Table 13. Results of atmospheric crude oil distillation column (example 5). Parameter Column 1 Bottom product  ow rate (kmol h¡1) Bottom product temperature (¯ C) Key component  ow rate in bottom product (kmol h¡1) Pump-around duty (MW) Pump-around  ow rate (kmol h¡1) Pump-around temperature drop (¯ C) Steam  ow rate (kmol h¡1) Column 2 Bottom product  ow rate (kmol h¡1) Bottom product temperature (¯ C) Key component  ow rate in bottom product (kmol h¡1) Pump-around duty (MW) Pump-around  ow rate (kmol h¡1) Pump-around temperature drop (¯ C) Steam  ow rate (kmol h¡1) Column 3 Bottom product  ow rate (kmol h¡1) Bottom product temperature (¯ C) Key component  ow rate in bottom product (kmol h¡1) Pump-around duty (MW) Pump-around  ow rate (kmol h¡1) Pump-around temperature drop (¯ C) Reboiler duty (MW) Column 4 Top product  ow rate (kmol h¡1) Top product temperature (¯ C) Key component  ow rate in top product (kmol h¡1) Bottom product  ow rate (kmol h¡1) Bottom product temperature (¯ C) Key component  ow rate in bottom product (kmol h¡1) Condenser duty (MW) Reboiler duty (MW) Re ux ratio

Shortcut model

Rigorous model

633.9a 334.7 83.5

624.0 333.4 83.5b

12.87 2187a 30.0b 1200b 149.8a 256.1 69.9 18.03 2305a 50.0b 250b 652.8a 282.7 149.7

12.87b 2187b 27.1 1200b 140.5 265.9 69.9b 18.03b 2305b 47.0 250b 673.3 286.2 149.7b

11.25 5790a 20.0b 9.38

11.25b 5790b 21.4 9.38b

680.7 76.9 174.6

691.4 77.1 175.5

493.0 189.6 168.2

491.5 191.2 168.2b

52.20 6.72 4.77b

a

Indirectly speciŽ ed; bspeciŽ ed.

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52.10 6.72b 4.79

985

As can be seen, the distillation column conŽ guration is very complex with many side-strippers and pump-arounds, and it has a large number of components (25 ‘pseudocomponents’ ‡ 1 ‘water’), so this good agreement is an important result. It illustrates the adequacy of the retroŽ t shortcut model and supports the application of the new model for retroŽ t studies. These retroŽ t studies may include evaluating design options for retroŽ t, such as adding pumparounds, and assessing trade-offs between using stripping steam and reboiling. In addition, the model can be embedded within an optimisation framework, and can be combined with a detailed heat integration model for increasing energy efŽ ciency of the distillation unit (Gadalla, 2003; Gadalla et al., 2003a). Furthermore, the retroŽ t model can initialise the rigorous model calculations by providing the product  ow rates and the pump-around duties and  ow rates for a given feed, and existing number of stages and operating conditions. CONCLUSIONS A new set of shortcut models for retroŽ t design of complex distillation columns has been developed. These models are applicable for various conŽ gurations of distillation columns, including simple columns, sequences of simple columns, complex columns with side-strippers or side-rectiŽ ers, and partially or fully thermally coupled sequences. Distillation columns with either a reboiler or stripping steam are accounted for. For a given column conŽ guration and operating conditions, the model calculates the  ow rates, temperatures and compositions of the product and internal streams, and the various heat duties. The results obtained compare very well with rigorous simulation results. The signiŽ cance of the new shortcut models is that they are intended speciŽ cally for retroŽ t design, and they can be applied to complex column conŽ gurations. Furthermore, these models account for the changes in relative volatility and molar over ow through the column, overcoming the underlying limitations of the previous shortcut models. The retroŽ t models are reliable for very complex conŽ gurations, including a large number of well-behaved components (crude oil distillation). The models also apply to other distillation applications, such as naphtha fractionation, petrochemicals separation, etc. The retroŽ t models provide a basis for optimising and improving the operating conditions of existing distillation columns for energy-related, economic and environmental beneŽ ts. The models can also be applied to calculate the additional heating and cooling requirements for increased throughput to an existing distillation process. The models can be utilised to assess retroŽ t modiŽ cations, such as adding side-coolers or replacing stripping steam with a reboiler. Furthermore, these models can be combined with hydraulic models, for the calculation of column diameters, to assess the effect of increasing throughput on the hydraulic capacity of an existing distillation column. NOMENCLATURE B D di F

molar molar molar molar

 ow rate  ow rate  ow rate  ow rate

of bottom product of top product of component i in top product of feed

GADALLA et al.

986 N Nmin R Rmin NR NS RHK RLK xbLK xdHK xdLK xf,i xfHK xfLK xHKFS xLKFS q Vbottom Vmin,pinch Vmin,pinch Vmin,top Vmin,bottom Vtop aLK aHK ai f fFensk fKirk c jSteam

total number of theoretical stages minimum number of stages at total re ux re ux ratio minimum re ux ratio number of stages in rectifying section number of stages in stripping section recovery of heavy key component to bottom product recovery of light key component to top product mole fraction of light key component in bottom product mole fraction of heavy key component in top product mole fraction of light key component in top product mole fraction of component i in feed mole fraction of heavy key component in feed mole fraction of light key component in feed liquid mole fraction of heavy key component on feed stage liquid mole fraction of light key component on feed stage liquid fraction of feed at feed stage conditions molar vapour  ow rate in bottom section at actual re ux minimum molar vapour  ow rate at top pinch minimum molar vapour  ow rate at bottom pinch minimum molar vapour  ow rate in top section minimum molar vapour  ow rate in bottom section molar vapour  ow rate in top section at actual re ux volatility of light key component relative to a reference component volatility of heavy key component relative to a reference component volatility of component i relative to a reference component roots of Underwood equation Fenske term to simplify Equation (12) Kirkbride term to simplify Equation (13) Gilliland term steam stripping term to simplify Equation (24)

REFERENCES Carlberg, N.A. and Westerberg, A.W., 1989a, Temperature-heat diagram for complex columns. 2. Underwood’s method for side strippers and enrichers, Ind Eng Chem Res, 28(9): 1379–1386. Carlberg, N.A. and Westerberg, A.W., 1989b, Temperature-heat diagram for complex columns. 3. Underwood’s method for the Petlyuk conŽ guration, Ind Eng Chem Res, 28(9): 1386–1397. Cerda, J. and Westerberg, A.W., 1981, Shortcut methods for complex distillation columns: 1. Minimum re ux, Ind Eng Chem Proc Des Dev, 20(3): 546–557. Gadalla, M., 2003, RetroŽ t design of heat-integrated crude oil distillation systems, PhD Thesis, UMIST, Manchester, UK. Gadalla, M., Jobson, M. and Smith, R., 2003a, Increase capacity and decrease energy for existing reŽ nery distillation columns, Chem Eng Prog, 99(4): 44–50.

Gadalla, M., Jobson, M., Smith, R. and Boucot, P., 2003b, Design of reŽ nery distillation processes using key component recoveries rather than conventional speciŽ cation methods, submitted to Trans IChemE, Part A, Chem Eng Res Des (submitted). Gilliland, E.R., 1940, Multi-component rectiŽ cation, estimation of the number of theoretical plates as a function of the re ux ratio, Ind Eng Chem, 32(9): 1220–1223. Glinos, K. and Malone, M.F. 1985, Minimum vapor  ows in a distillation column 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. Kister, H.Z., 1992, Distillation Design (McGraw-Hill, New York), Chap. 3, p 113. Molokanov, Y.K., Korablina, T.P., Mazurina, N.I. and Nikiforov, G.A. 1972, Int Chem Eng, 12(2): 209. Nandakumar, K. and Andres, R.P., 1981, Minimum re ux conditions. 1. Theory, AIChE J, 27(3): 450–460. 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, Thermodynamically optimal method for separating multi-component mixtures, Int Chem Eng, 5(3): 555. Rev, E., 1990, The constant heat transport model and design of distillation columns with one single distributing component, Ind Eng Chem Res, 29(9): 1935–1943. Robinson, C.S. and Gilliland, E.R., 1950, Elements of Fractional Distillation, 4th edition (McGraw-Hill, New York, USA). Seader, J.D. and Henley, E.J., 1998, Separation Process Principles (Wiley, New York), Chap. 9, p 499. Stupin, W.J. and Lockhart, F.J., 1972, Thermally coupled distillation–A case history, Chem Eng Prog, 68(10): 71. Suphanit, B., 1999, Design of complex distillation systems, PhD Thesis, UMIST, Manchester. Triantafyllou, C. and Smith, R., 1992, The design and optimization of fully thermally coupled distillation columns, Trans IChemE, Part A, Chem Eng Res Des, 70(2): 118–132. Underwood, A.J.V., 1948, Fractional distillation of multi-component mixtures—calculation of minimum re ux, J Inst Petrol, 32: 614–626. Watkins, R.N., 1979, Petroleum ReŽ nery Distillation, 2nd edition (Gulf, Texas, USA).

ADDRESS Correspondence concerning this paper should be addressed to Dr M. 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 publication after revision 30 July 2003.

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