Optimization of Distillation Separations Using Feed Splitting by a

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Optimization of Distillation Separations using Feed Splitting by a Homotopy Continuation Method Mohammad Asadollahi, Farhang Jalali Farahani, and J. D. Seader Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b03947 • Publication Date (Web): 23 Mar 2017 Downloaded from http://pubs.acs.org on March 29, 2017

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Industrial & Engineering Chemistry Research

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Optimization of Distillation Separations using Feed Splitting by a Homotopy Continuation Method Mohammad Asadollahi*, Farhang Jalali Farahani*, J.D. Seader**1 *Chemical Engineering Department, University of Tehran, Tehran, Iran ** Department of Chemical Engineering, University of Utah, Salt Lake City, UT 84112, USA ABSTRACT

It is a common procedure to save energy in industrial distillation towers by preheating and precooling the feed with heat transfer from the bottom and top products. An example is oil sweetening by distillation. It is shown here using simulation that if, before entering the unit, the oil feed is split into two streams, and only one of them is preheated, further savings of energy (up to 50%) can be achieved. The same results are achieved by splitting the feed to an ethaneethylene distillation column and precooling only one part of it just before entering the tower. In this study, the effects of feed splitting into hot and cold towers were investigated in order to reduce the duties of the reboiler or condenser, and the total annual cost (TAC). Also, consideration was given to obtaining a common design in order to achieve greater flexibility for the required operating schemes.

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Corresponding Author E-mail: [email protected].

ACS Paragon Plus Environment


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The investigation was carried out as an optimization problem defined by effective parameters affecting the reboiler and condenser duty and products recovery. Models for finding the best feed split-fraction ratio, optimal locations for the feeds, the number of trays required for a specified separation and the best operating pressure for a distillation column with feed splitting are presented. By using a homotopy continuation method in MATLAB, and connecting it to the ASPEN HYSYS simulator, the optimal values for decision variables were calculated. It is observed that the optimal feed-splitting technique leads to 49.2% reduction in energy demand in an oil sweetening process and a 24% reduction in reboiler duty and a 22% reduction in condenser duty in an ethane-ethylene separation process in comparison with conventional processes.

Keywords: Oil Sweetening, Ethane/Ethylene separation, Feed Splitting, Optimization, Homotopy Continuation 1.

Introduction

Apart from stabilization problems of ‘‘sweet’’ crude oil, ‘‘sour’’ crude oil, containing hydrogen sulfide, mercaptans, and other sulfur compounds, may cause unusual processing and environmental problems in oil-field production facilities. Hydrogen sulfide (H S), known as "sour gas", is a highly toxic natural component of crude oil that must be removed in the refining process. The primary and essential difference between regular crude oil and "sour" crude oil is the presence of hydrogen sulfide (H S).The concentration of H S determines the relative sweetness of crude oil which is represented by the crude oil reservoir specification. Along with stabilization, crude oil sweetening brings in what is called a ‘‘dual operation’’ which permits easier and safer downstream handling, and improves and upgrades the crude marketability. The reboiled stabilizer distillation towers are the most effective means to sweeten sour crude oils.


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The hot strippers are commonly operated at high temperature, utilizing high-duty reboilers. The desired objectives for any oil sweetening process are to obtain a stabilized, sweet product combined with a high percentage recovery of the crude oil. The main goal of this study is to reduce the amount of energy required by the reboiler in the hot stripper column by partially preheating the feed(s) by the bottoms. Typically, more than half of the heat distributed to a process plant ends up in the reboilers of distillation columns. By this, high-level energy is fed at the base of the column and about the same amount of energy is released at the top, unfortunately at a much lower temperature level. The difference between the two Gibbs energies can be seen as the necessary energy investment to reverse the mixing entropy and to separate the components of a given feed by a distillation process1-3. To find a solution to this problem, some researchers have proposed alternatives focused on the feed-splitting concept4. Thermal condition of the feed is one of the important schemes for the energy-efficient design of a distillation column. By exchanging heat with the bottom product or with any other available low-grade heat sources, the thermal condition of the feed may be altered to reduce the reboiler duty. There exists an efficiency associated with feed preheating because a portion of the thermal energy given to the feed reduces the reboiler duty5. An index of separability of a process is the relative volatility of the components to be separated. The easier separation with lower energy demand can be achieved for the higher relative volatility system. In this regard, process integration has been known as a proper method for reducing the energy requirement. Preheating the feed with feed-splitting is a common procedure for saving energy in industrial distillation towers. In the feed-splitting technique, there is an optimal fraction of the feed that leads to a minimum energy demand for the process. A method for achieving the best feed-splitting ratio is the subject of this study6-8.



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Several publications deal with feed-splitting for single columns. Tavana and Shahhosseini6 applied the feed-splitting concept to a CO -ethane azeotropic process and reported a 56% reduction in energy demand in comparison with the conventional process under the same operating conditions. A case study by Soave and Feliu1 shows that feed splitting for a mixture of propane–benzene can decrease the reboiler and condenser duties dramatically compared to a conventional design. Babaei and Esfahany7 investigated the feed-splitting technique on three classical arrangements for a multicomponent separation in order to reduce the total annual cost (TAC). Their results showed that the feed splitting arrangement reduced TAC by 49.2 %. Lee et.al.8 found that splitting one of the rate-determining feeds and feeding them to different locations in a reactive distillation column leads to significant savings in TAC (10.4%) and a reduction of the operating cost (11.9%). In a cryogenic columns study, Soave et.al.2 and Salerno et.al.4 used feed splitting for demethanizer and ethane–ethylene separation towers in order to achieve a significant reduction in condenser duty. In this study, a homotopy continuation method was applied for finding the best feed splitfraction ratio, optimal locations for the feeds, and the number of trays required for a specified separation in a distillation column with multiple feeds. By using a homotopy continuation optimization method in MATLAB, in conjunction with the ASPEN HYSYS simulator, optimal values for decision variables were calculated. The main goal of this study was to reduce the reboiler and condenser duties as much as possible by considering the products recovery. In the first case study, the reboiler duty and oil recovery for an oil sweetening process are defined as objective functions and are optimized using the homotopy continuation method. In the second case study, an ethane-ethylene tower is optimized with respect to reboiler and condenser duties and products recovery.


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2. Brief description of the oil sweetening process Sour crude oil can be sweetened by using a reboiled stripper to remove H2S. A conventional process is shown in Fig.1. The production train consists of 1st and 2nd stage phase separators where the crude oil from the well is partially degassed by two stages of pressure reduction. The partially degassed oil is fed to the top tray of the reboiled stripper, where the gas moving up the column is enriched in the lighter components such as methane, ethane, and H S. Outlet oil from the bottom of the reboiled stripper enters a production tank which operates slightly above atmospheric pressure. 1st STAGE GAS

FEED FROM OIL

SOUR GAS

2nd STAGE GAS

TO DESALTING UNIT

nd

st

2 STAGE

1 STAGE PV

1 V-8

PRODUCTION TANK

HOT STRIPPER

Treated Water

V-6

Reboiler Air Cooler

Figure 1. Base Case: Typical Schematic of Hot Stripping Process. Process simulations for the reboiled stripper were carried out using ASPEN HYSYS. The feed to the process is given in Table S1. The feed was obtained by mixing gas of known composition (dry basis) and pure water, as shown in Fig.2. The Sour Peng-Robinson (PR– SOUR) equation of state was the most appropriate equation for this system. The simulation was done based on achieving simultaneous stripping and stabilization to give a 10 ppmw H S content in the outlet oil from the stripping column and the RVP of oil in the range of 8-10 psia. The



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purpose of the column simulation modeling was to determine the optimal acceptable column operating conditions in terms of maximum oil production and minimum energy consumption. HYSYS simulation optimized column operation and the number of theoretical stages. Several cases were run to establish an optimal number of theoretical stages, with respect to product quality and overall column efficiency. The operation of the stripping column was considered over a range of acceptable pressures and number of theoretical stages to achieve a high efficiency in terms of liquid product recovery, given the requirement to simultaneously meet the desired specification for H S content and RVP of the bottom product.

Figure 2. Process Feed preparation model.

2.1 Process sequences analysis


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In the arrangement shown in Fig.1, two-phase liquid streams from the 1st and 2nd separator stages are collected in the common header and routed to a hot stripper. This column is designed for a three-phase distillation operation using a V-L1-L2 model. The above case was simulated using Aspen Hysys with the inside-out method described by Seader et al.9, including consideration of two liquid phases when needed. Product results are presented in Table S2. 2.2 Hot Stripping Scheme Different cases were considered to evaluate the relationship between column operating pressure, reboiler duty, stabilized crude RVP, H S content, recovery efficiency and the number of stages for typical arrangement shown in Fig.1. The relationship between the number of theoretical column stages and RVP was established by fixing column pressure and gradually increasing the number of theoretical stages (assuming 100% tray efficiency). Once a reasonable number of column stages were defined, the column pressure was varied to assess the effect on the product recovery efficiency. Simulation cases were run in which the reboiler pressure was increased from just above atmospheric to a sufficiently high value to satisfy all product specifications. Again, the number of theoretical stages was investigated keeping all other column parameters constant. Several cases were then established by increasing the reboiler pressure (while keeping all other parameters fixed) until all product specifications were met. The selection of the optimal operating values for these variables was based on achieving the maximum crude oil product output from the stabilization plant combined with the minimum reboiler duty in the stripper. A feed-split philosophy was utilized for the column feed, where the bulk of the sour crude stream was preheated prior to feeding the center of the column and the remainder bypassed the column preheater and was introduced to the top of the column at a temperature below the



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bubble point at the given operating pressure. This subcooled feed acted as a direct condensing medium (internal reflux) and prevented excessive loss of the light fraction portion with the H S rich vapor stream leaving the column top. The effect of feed split was established in terms of heat required for the reboiler, product recovery, and RVP. 2.3 Simulation models Three stripper feed preheating models were considered for base case i.e. Fig.1. They are shown in Figs. 3, 4, and 5 as alternatives 2, 3, and 4, respectively. Alternative 1 did not preheat the feed, as shown in Fig. 1. In all three models, stripper operating conditions and number of stages were the same. Also, the exchanger temperature approach was kept constant. In the second alternative (Fig.3), all of the feed is preheated by the bottom product and injected into the top tray of the stripper tower as hot feed. As the liquid falls through the tower, it goes from top to bottom, and gets increasingly richer in the heavier components and increasingly leaner in the lighter components. This process has more energy saving than the no-preheat method of Fig. 1, and reduces the quantity of heat required for stripping within the column. In the third alternative (Fig.4), heat integration techniques were used in the simulation to preheat the stripper feed using hot bottom product. Only one part of the feed was preheated and then fed to the center of the column. The remaining stripper feed bypassed the column preheater and was introduced to the top of the column. This cold liquid feed acted as a direct condensing medium (internal reflux) and prevented excessive loss of the light fraction portion enriched with H S content leaving the column top. Two other parameters; top feed / center feed split flow ratio and hot feed stage location, were also investigated and chosen carefully to assess their effect.


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9 1st STAGE GAS

FEED FROM OIL

2nd STAGE GAS

2nd STAGE

1st STAGE PV

V-8

V-1

SOUR GAS

TO DESALTING UNIT PRODUCTION TANK HOT STRIPPER

Treated Water

PREHEATER

Reboiler Air Cooler

Figure 3. Alternative 2.

1st STAGE GAS

FEED FROM OIL

2nd STAGE GAS

2nd STAGE

1st STAGE PV

V-8

V-1

SOUR GAS

TO DESALTING UNIT FEED SPLITTER

PRODUCTION TANK HOT STRIPPER

Treated Water

PREHEATER

Reboiler Air Cooler




10 1st STAGE GAS

FEED FROM OIL

2nd STAGE GAS

2nd STAGE

1st STAGE PV

V-8

V-5

SOUR GAS Vent Stream

TO DESALTING UNIT

FEED SPLITTER FLASH DRUM

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PRODUCTION TANK HOT STRIPPER

Treated Water

PREHEATER

Reboiler Air Cooler

Figure 5. Alternative 4. In alternative 4 shown in Fig.5, oil leaving from prior 2nd stage separator is fed to the flash drum separator, which is operated at tower bottom pressure. After separation of vapor and liquid in the flash drum, the vapor phase goes to the top of the stripper column. Liquid is split as in alternative 3. For alternatives 3 and 4, the stripper feed split fraction and feed entry locations were critical and were determined carefully. A homotopy optimization procedure was used to optimize these design parameters by varying the values around selected operation points and evaluating how they affected reboiler duty and liquid recovery. 2.4 Application of homotopy continuation method A widely used homotopy, H(x, t), consists of a linear combination of two real functions: f (x), whose zeroes are sought; and G(x), a function for which a zero is known or readily selected or obtained. Both functions must be smooth with twice-differentiable derivatives. Thus, H(x, t) = t f (x) + (1 − t) G(x) = 0

(1)


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Where t, the homotopy parameter, allows tracking of a solution path that connects the starting point, , at t = 0, to all ∗ , which are all solutions of f (x) = 0. Using numerical continuation, the parameter t is gradually varied, starting from t = 0 and without being confined, leading to a series of solutions to Eq. (1).Whenever the homotopy path crosses t = 1, a solution to f (x) = 0 is found. The three most widely cited G(x) functions are: The fixed-point (FP) function, G(x) = (x − ), (2)

the affine function, which adds a factor, A, to the FP function to improve scaling in the homotopy function, G(x) = A(x − ), (3)

Where A is often taken as the derivative of f(x) evaluated at , and the Newton (N) function, G(x) = f(x) – f ( ) (4)

The FPN (fixed-point and Newton) homotopies are used and formulated in two steps10-12, to give H(x, t) = tF(x) + (1 − t)G(x) F(x) = f(x) (x − )

(5)

(6)

G(x) = {(x − ) + F(x) − F( )} (7) H(x, t) = tF(x) + (1 − t) {(x − ) + F(x) − F( )}= 0

(8)

After simplification10. H(x, t) = (x − ) [1 + f (x) − t] = 0

(9)



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In many engineering equations, such as the MESH equations for distillation towers, the equations are nonlinear and difficult to solve analytically. Here, the homotopy continuation method is applied to solve optimization problems with high nonlinearity order. As the incidence of multiple roots, particularly in many chemical engineering applications has become evident, interest has mounted in developing ways to extend the method to find all solutions. At first, it was conjectured that all roots would lie on the homotopy path. Thus, it was only necessary to continue following the path from one solution to the next until the path approached infinity in the homotopy parameter12. That conjecture was applied in this study. 2.5 Initial simulation results for the hot stripping scheme The hot stripper column is regarded as the heart of the crude stabilization process. Thus, extensive stripper column optimization was carried out. It was found that a column utilizing 15 ideal stages gives a product that satisfies the required H S removal but not the RVP specification (8-10 psia) even when the column pressure was raised in excess of 100 psig. The results of this sensitivity analysis can be seen in Fig.6. It can be seen that each subsequent increase in operating pressure brings proportionately less benefit in terms of product recovery and RVP given the fixed H S specification of 10 ppmw (i.e. diminishing returns). As the operating pressure increases, the operating temperature of the column and, therefore, the required indirect heater energy input increases. Based on the above simulation cases and judgment, taking into consideration the additional operating costs and capital costs of purchasing and running high-pressure columns, an operating pressure of between 50 and 60 psig was chosen. The column was set to achieve the H S specification of below 10 ppmw, although the RVP specification of between 8.0 to 10 psia could not be achieved at the


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same time. The H S specification was chosen as the main specification to optimize while achieving the best possible RVP.

4000 recovery & reb duty vs base pressure

3500

w) Reboiler duty (k

1000 1500

3000

2000 2500 3000

2500

3500 4000

2000 70 1500

re ss ure (p sig )

60 50

40

1000 93.5

93.4

30

se p

93.3 Oi l re 20 93.2 cove 93.1 ry(kg 93.0 dry p 10 92.9 rodu ct / k 92.8 g dry feed)

ba

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6. Hot Stripping Simulation Results (15 ideal stages, variable column pressure) At a fixed column pressure of 50-60 psig and given the fixed H S specification of 10 ppmw or less, the number of ideal stages was optimized. It was seen that each increase in the number of ideal stages resulted in an improvement in product recovery, however, this increase in the number of ideal stages resulted in diminishing returns, with proportionately less improvement in terms of crude oil product recovery as the number of ideal stages is increased. This is represented in Fig 7. It was found that a column utilizing 8-10 theoretical stages could meet the required specifications, while simultaneously achieving the maximum crude oil recovery and minimum reboiler duty specification.



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If total feed to the plant is preheated (Fig.3) then the light components from the top of the column will escape based on their lower vapor pressure and the oil recovery of the stripper will decrease. It was observed that each step increase in feed temperature resulted in a reduction in product recovery and required reboiler duty. As shown in Fig. 8 and Fig. 9, by utilizing heat from the hot crude oil product in order to preheat the feed (heat integration techniques), the amount of reboiler required duty decreased and heat recovery increased. As it is obvious, heat integration will reduce product recovery, but saves energy which reduces operating and fixed costs related to the reboiler. Consequently, sometimes the impact in absolute numbers of saving or recovering only 1% of the crude oil by distillation would be tremendous. An alternative, which improves product recovery, is to split the feed to the column and preheat only one part and feed it to the middle of the column. Simulation cases were studied for a range of column feed split ratios to establish the optimal relationship between final product recovery, RVP, and the required energy input.

3018 3016

93.46

3014 93.44

Reboiler duty(kw) Oil Recovery %

3012

93.42

3010 3008

93.40

Oil Recovery %

Reboiler Duty(kw)

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3006 93.38 3004 3002

93.36 2

4

6

8

10

12

14

Number of Trays

Figure 7. (60 psig) base pressure, Product recovery (%) and reboiler duty (kW) as a function of the number of ideal stages.


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15

3000 Reboiler Duty(kw)

2800

Reboiler Duty(kw)

2600 2400 2200 2000 1800 1600 1400 140

150

160

170

180

190

200

Temperature(F)

Figure 8. Reboiler duty (kW) vs. Column feed temperature (°F).

0.934 Oil Recovery% 0.932

Oil Recovery %

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.930

0.928

0.926

0.924 150

160

170

180

190

200

Temperature(F)

Figure 9. Oil & Heat Recovery (%) vs. column feed temperature (°F). Fig. 10 shows that the quantity of reboiler heat required to achieve the separation was strongly influenced by the feed split ratio. Increasing the cold feed fraction (decreasing the hot feed fraction) increased the reboiler heat requirement. The product recovery increased when more colder liquid was directed to the top of the column, Fig. 10 shows that the optimal column



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feed split was established by introducing 50- 60% of the feed to the top of the column, with 4050% of the preheated feed being introduced to the column feed point at the 5th ideal separation stage, Fig.11.

93.5 2500

2000 92.5 1500

92.0

Reboiler Duty(kw)

Oil recovery %

93.0

1000 Reboiler Duty(kw) Oil recovery %

91.5

500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Cold Feed Fraction

Figure 10. Reboiler Duty (Kw) and plant recovery (%) vs. column cold feed fraction.

1700

1680 Reboiler Duty(kw) Oil recovery %

93.2

1660

93.0

1640

92.8

1620

92.6

1600

92.4

Reboiler Duty(kw)

93.4

Oil Recovery %

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1580 0

2

4

6

8

10

12

Feed Tray Condidate

Figure 11. Best feed location for hot feed fraction. (The trays counted from the top down)


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2.6 Optimization Step MATLAB facilitates data exchange, visualization of computed results in the form of plots and tables, and implements many efficient and robust core numerical computing methods. By using the homotopy continuation optimization method in MATLAB, by means of path tracking with the continuation toolbox of CL MATCONT, developed by Dhooge et al. (2006)13, and connecting it with ASPEN HYSYS simulator process software14-15. Table 1 illustrates the definition of the optimization problem and its elements. All equality constraints are checked by the simulator. MESH equations around a tray of a distillation9. , + , + , + , + , + , = (10)

= [ =

+./ + ∑$)"#$ − &$ − '$ ( - ] "ℎ+ − ∆- (

0, ℎ+

+ ∑$)"#$ − &$ − '$ ( -

= [

+ ∑$)"#$ − &$ − '$ ( -

=

2 0, ∆ℎ

= - [

(11)

(12)

= - [[

2 ≤ j≤ N

+& ] "ℎ+

+./

− ∆-

1 ] ∆ℎ

(+(

+' ) 0, ℎ+ ] 1≤ j≤ N

(13)

(14)

(15)

+ ∑$)"#$ − &$ − '$ ( -

= 3 - # 4, ℎ5,

+& ]

∆ℎ1 + (

+' ) 0, ∆ℎ2 ]

(17)

Homotopy function: H1(x, t) = (x - ) [1+ 6 (x)-t]

(18)


1 ≤ j≤ N

(16)


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18 H2(x, t) = (x - ) [1+ 6 (x)-t]

(19)

Where 6 (x) is first optimization function (i.e. sweet oil recovery) and 6 (x) is the second optimization function (i.e. reboiler duty). Table 1. Definition of optimization problem Optimization Problem Objective Functions: Sweet oil recovery & Reboiler Duty Variables: lower

upper

limit

limit

pressure(psig)

1

100

number of trays

1

15

feed split ratio

0

1

overhead vap feed tray

1

15

hot fraction feed ray

1

15

constraints: H2S concentration(ppmw)

8

2.7 Results of Homotopy optimization


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The results of the homotopy optimization are reported in Table 2 and graphically shown in Fig.12. Table 2. Results of homotopy optimization paths. Variable

Starting Point

Global Optimum

Tower base pressure

50

57.8108

6

8.3849

0.5

0.5895

Vent stream location

1

1.06743

Preheated stream

2

5.8989

(psig) Number of trays Cold feed fraction

location



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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Figure 12. Homotopy paths for seeking decision parameters in optimization step.

2.8 Results


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To properly evaluate the simulation results, comparisons were made with the conventional scheme (Fig.1). Consideration was given to obtaining a common design for certain items in order to achieve greater oil recovery for the required operating schemes. The simulation cases were run with a target H S specification of 10 ppmw and results for all of the four cases studied are shown in Table 3. Table 3. Oil sweetening Column Results. Reboiler Base Sweetening

H2S Oil

SWEET OIL

No Of ALTERNATIVES

Description

Process

Pressure

DUTY

Recovery

FLOWRATE

(psig)

(KW)

(%)

(Barrel/Day)

Trays

RVP

(ppmw)

(psia)

at Final Stage

1(BASE CASE)

Cold Feed

10

60

3133

93.30

10121

6.69

4

10

60

1649

92.37

10020

7.47

8

10

60

1930

93.46

10141

7.25

5.68

10

60

1609

93.46

10141

7.25

10

8.3849**

57.8108

1592

93.46

10141

7.25

10

Feed

HOT 2 STRIPPING

Preheat 3

Feed Split FEED

4*

FLASH & SPLIT FEED

4

FLASH & SPLIT

*: The generated results before optimization by homotopy continuation. **: Round to 8 in simulator. Actually number of trays to be round to the closest real number for simulator input.

The simulated results of a non-preheated column (Fig.1) is considered as the base case to compare with the alternative proposals of preheating the feed. In comparing the 2nd alternative (Fig.3) to the base case, significant reduction in reboiler duty is achieved, but unfortunately at the same time the amount of oil recovery is reduced. In this case, the decrease of reboiler duty is



22

47% but the sweet oil flow rate is not acceptable. It was found that a column utilizing the feed split technique can overcome the problem of oil recovery. By using the feed split concept in alternative 3 (Fig.4) in comparison with the base case, the reboiler duty decrease is 38% while at the same time the sweet oil flow rate increases. A further improvement occurs in alternative 4 (Fig.5) where the reboiler duty is less than alternative 2 and the oil recovery percent is greater. The amount of energy saving, in this case, is 49% while the sweet oil flow rate is 120 barrel/day greater than base case production capacity. Alternative 4 shows the best performance in this case study. The results are presented graphically in Figs.13 and 14.

3400 Alternative's Duty

3200 3000 2800

Duty(kw)

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 44

2600 2400 2200 2000 1800 1600 1400 Alter 1(Base case)

Alter 2

Alter 3

Alter 4

Alternatives

Figure 13. Reboiler duty results. There are several useful results from using the feed split technique for the stripper. One is that the vapor load on the column decreases when feed splitting is applied. This is because hot liquid feed (preheated portion) is directed to a point lower in the column and the cold return liquid act as internal reflux and condenses the vapor upon contact in the upper part of the


Page 23 of 44

23

column. Since the vapor volume is much larger than the liquid volume, a decrease of vapor flow in the column makes it possible to decrease the column diameter. In Fig.15 the calculated tower diameter for all alternatives are shown.

93.4

Oil Recovery %

93.2

93.0

92.8

92.6 Alternatives Oil recovery %

92.4

92.2 Alter 1(Base case)

Alter 2

Alter 3

Alter 4

Alternatives

Figure 14. Oil recovery results.

1.6 Tower Diameter 1.5

1.4

Diameter(m)

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.3

1.2

1.1

1.0

0.9 base case

Alternative 2

Alternative 3

Alternative 4

Alternatives

Figure 15. Tower diameter results.



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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 44

24

An economic analysis was made in order to select the most suitable alternative for this study. It utilized equipment sizing and cost feature of the Aspen Icarus Process Simulator (IPE,2010) (Aspen capital cost estimator) using the utility costs listed in Table S3. Net present value (NPV) was determined by calculating the costs (negative cash flows) and benefits (positive cash flows) for each period of an investment. Each cash inflow/outflow was discounted back to its present value (PV) and then summed, giving: R8 "20( "1 + i(8

Where t is the time of the cash flow, i is the discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk); the opportunity cost of capital, R 8 is the net cash flow i.e. cash inflow – cash outflow, at time t. Given the (period, cash flow) pairs (t,R 8 ) where N is the total number of periods, the net present value NPV is given by: NPV (i, N)= =

A

>?

8) "@(

?

(21)

The results are shown in Figures 16 to 18. Alternative 4 gave the highest NPV,


Page 25 of 44

25

9.8e+5 9.6e+5

Capital Cost(US$)

9.4e+5 9.2e+5 9.0e+5 8.8e+5 8.6e+5 8.4e+5 8.2e+5 Base Case

Alternative 2

Alternative 3

Alternative 4

Alternatives

Figure 16. Capital cost results.

1.1e+6

1.0e+6

Operating Cost(US$)

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


9.0e+5

8.0e+5

7.0e+5

6.0e+5

5.0e+5 Base Case

Alternative 2

Alternative 3

Alternative 4

Alternatives

Figure 17. Operating cost results.



26

6.4e+7

6.3e+7

NPV (US$)

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 44

6.2e+7

6.1e+7

6.0e+7

5.9e+7 Base Case

Alternative 2

Alternative 3

Alternative 4

Alternatives

Figure 18. NPV results. 3. Second Case Study 3.1 Brief description of Ethylene-Ethane Distillation Process Fig.19 shows the different process units of an industrial Olefin plant. As shown, the (C2) fraction from E-3311 in Step 3, being free of acetylene, is fed to the C2 splitter (T-3501), which operates at a pressure of approx. 8.8 bar and has 60 ideal trays. The column feed is presented in Table S4. In this study of the C2 splitter, the column feed configuration using the feed-splitting concept was modified to achieve a new optimized arrangement. The base-case arrangement is shown in Figure 20, while five feed-splitting arrangements are shown in Figs. 21-25. These five arrangements use cooling (rather that heating) of the feed or a fraction of it by heat exchange with the top product. Flash drums are provided to separate the feed or portions of it into vapor and liquid streams that are fed to the column at optimal locations. The most complex


Page 27 of 44

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


27

modification is Alternative 3-PA in Fig. 25, which shows four feed streams, one of which is a stream withdrawn from the column and recycled back. All of the alternative arrangements were optimized using the homotopy continuation procedure described above. The optimization problem is defined in Table 4. The homotopy continuation paths are shown in Figure 26, with the results listed in Tables 5-7, and shown graphically in Figs. 27-30. As shown in the best configuration, Fig. 25, feed (stream 35-1) is precooled in two steps, first, it flows through a gas chiller box, where it is cooled by remaining heat sink capacity of the overhead product. This stream is further cooled via pump around the system using the liquid from the tray 15. Then two-phase feed at -52°C is fed to a flash drum separator before feeding to T-3501. The liquid stream flows on level control to the lower section of the ethane/ethylene tower (T-3501). The gas flow from the flash drum is split, via flow-ratio control. One portion of the stream is condensed in the tower overhead exchanger at -72°C, reduced in pressure across a flow control valve, and fed to the top of the T-3501 as reflux. The remaining gas from the flash drum is fed through the Turbo Expander, where the pressure and temperature are reduced to 8.8 bar and -55°C before being fed to the tower. This stream also has the option of going through a Joule-Thomson pressure-control valve instead of the Expander when the Expander is down for maintenance or repairs. The on-spec overhead ethylene leaves T-3501 at a temperature of -57°C, then expands to 1 bar through a pressure control valve with its temperature reduced to -76°C. This ethylene stream exchanges heat countercurrently in both Tower side exchanger (E-3501) and gas chiller box (New HEX) and then is heated to 18°C and fed to ethylene compressor.



28

The bottom product of the T-3501, consisting of the ethane fraction, is vaporized and heated to ambient temperature, further superheated, and recycled to the cracking furnaces. STEP 1

STEP 2

STEP 3

PROPYLENE

CONDENSATE

STEAM

MEA WASH FEED PREHEATING

T-3101

C2H4/C2H6 SEPARATION

C1/C2 SEP ARATION

T-3401

T-4001

T-3501

T-3301

T-4301

C4+

ETHANE

CRACKING

E-3313 E-3311

ETHYLENE ABSORBER

C-2501


E-3011

H 1101-1501

CRACKED GAS COMPRESSION

PRECOOLING AND DRYING

1.C2/C3 SEPARATION 2.C3/C4 SEPARATION 3.C4/C5 SEPARATION


LOW TEMPERATURE SECTION

Figure 19. Flowsheet of the Olefin process. 35-2 CONDENSER

E-2111

C3/C4 SEPARATION

C2/C3 SEP ARATION

PROPANE

FEED

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 44

LT

PG

LIT

35-1 FEED TRAY

TC LC

REBOILER

35-7

Figure 20. Base-case process.


C1/C2 SEPARATION

C2H4/C2C6 SEPARATION

Page 29 of 44

29

TOP PRODUCT CONDENSER

PCV-3501 LT

PG

COLD FEED

LIT

E-3501

T-3501

FLASH DRUM

35-1 FCV

LIQUID TC LC

REBOILER

Bott


CONDENSER

TOP PRODUCT PCV-3501 LT

PG

E-3501

35-1 FCV

LIT

VAP 2

FLASH DRUM 2

VAP1

FLASH DRUM 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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


LIQ 2 T-3501 LIQ1 TC LC

REBOILER

Bott




30

TOP PRODUCT CONDENSER

PCV

LT

PG

35-1 FCV

COLD FEED

SPLITER

FRAC 1

FLASH DRUM

VQP1

LIT

E-3501

T-3501

FRAC2

LIQ1 TC LC

REBOILER

Bott

Figure 23. Alternative 3. TOP PRODUCT

VAP 2

35-1 FCV

E-3501

COLD FEED

LT

PG

LIT

FLASH DRUM 2

VAP 1

SPLITER

FRAC 1

CONDENSER

PCV-3501

FLASH DRUM 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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 44

T-3501

LIQ 2 FRAC 2

LIQ TC LC

REBOILER

Bott



Page 31 of 44

31 TOP PRODUCT CONDENSER

PCV

FFC

SPLITER

FRAC1 VQP1

2

NEW HEX

LIT

PCV

E-3501

FC

15 16

NC

T-3501

EXPANDER

FLASH DRUM

FRAC2

Ethylene

LT

PG

FC

Pre cold feed

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3 4

LIQ1 PCV TC

LIQ from Tray 15 35-1

LC

REBOILER

LIQ to Tray 16

Bott

Figure 25. Alternative 3-PA, Optimized new arrangement for the Ethane/Ethylene column. Table 4. Definition of the optimization problem. Optimization Problem Objective Functions: Condenser & Reboiler Duty Variables: lower limit

upper limit

Feed split ratio

0

1

Feed location of stream 2

1

60


1

60


1

60

constraints: Overhead product purity (% mol)

>99.94



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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 44

32 Overhead mass flow rate (kg/h)

>65658

Table 5. Results of homotopy optimization paths. Variable

Starting Point

Local Optimum

Global Optimum

0.05

0.558

0.1314


26

26.13

25.999


36

36.0435

41.3405


24

38.9996

41.8019

Cold feed fraction


Page 33 of 44

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


33

Figure 26. Homotopy paths for seeking decision parameters in optimization step.

Table 6. Simulation results for different alternatives in their optimized state Heat Duty(MW)

Column overhead mass flow

Alternatives Condenser

Reboiler

rate (KG/H)

Base case

19.86

18.81

65658.20

Alternative 1

16.67

16.20

65986.14

Alternative 2

16.65

16.19

65986.15



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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 44

34 Alternative 3

16.13

15.68

65986.15

Alternative 3-PA2

15.18

14.75

65986.16

Alternative 4

16.49

16.02

65986.14

Table 7. Ethylene recovery and Reflux ratio results

Alternatives

2

Ethylene recovery %

Column Reflux ratio

Base case

0.998

2.69

Alternative 1

0.998

2.26

Alternative 2

0.998

2.24

Alternative 3

0.998

2.14

Alternative 3-PA

0.998

2.03

Alternative 4

0.998

2.22

Pump Around


Page 35 of 44

35

21

condenser duty (MW)

20

19

18

17

16

15 conventional

alter 1

alter 2

alter3 alter3 with PA alter 4

Alternatives

Figure 27. Condenser duty (MW).

20

19

Reboiler duty (MW)

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


18

17

16

15

14 conventional

alter 1

alter 2


Alternatives

Figure 28. Reboiler duty (MW).



36

2.8

Reflux Ratio

2.6

2.4

2.2

2.0

1.8 conventional

alter 1

alter 2


Alternatives

Figure 29. Reflux ratio in different alternatives.

5

4

Energy Recovery (MW)

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 44

3

2

1

0

conventional

alter 1

alter 2


Alternatives

Figure 30. Amount of Energy Recovery (MW).


Page 37 of 44

37

In Fig. 31, the calculated tower diameter for all alternatives compared with the conventional (base case) separation process of ethane / ethylene is shown.

3.9 Tower Diameter 3.8

Tower Diameter(m)

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.7

3.6

3.5

3.4

3.3 conventional

alter 1

alter 2


Alternatives

Figure 31. Tower diameter sizing (m). An economic analysis was performed to select the most suitable solution for this study. The results of this evaluation compared with the classic separation of an ethylene-ethane mixture, the base case, are shown in Figs. 32-33, where the best case is alternative 3-PA.



38

2.8e+6 Capital Cost($)

Capital Cost($)

2.7e+6

2.6e+6

2.5e+6

2.4e+6

2.3e+6

2.2e+6 Base Case

Alter 1

Alter 2

Alter 3

Alter 3-PA

Alter 4

Alternatives

Figure 32. Capital coat evaluation (US$).

1.1e+7 Operating Cost($ 1.1e+7

Operating Cost($)

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 44

1.0e+7

9.5e+6

9.0e+6

8.5e+6 Base Case

Alter 1

Alter 2

Alter 3

Alter 3-PA

Alter 4

Alternatives

Figure 33. Operating coat evaluation (US$).


Page 39 of 44

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


39

4. Conclusion When applying a feed-splitting concept to an oil-sweetening process, it is possible, with heat exchange between the bottom product and a portion of the feed, to decrease the energy demand of the reboiler and, at the same time, increase further the oil recovery. Similarly, in an ethane/ethylene distillation column by splitting the feed and exchanging it with the top product, the energy demand can be significantly reduced. In this study, the energy consumption was optimized by seeking the optimal location16 of the feed trays using homotopy continuation. It was observed that the best scheme for an oil sweetening process gave a 49.2% reduction in energy demand. For an ethane-ethylene distillation, a 24% reduction in reboiler duty, and a 22% reduction in condenser duty were achieved in comparison with a conventional process.

•

Nomenclature Abbreviation: GA = Genetic Algorithm HEX = Heat Exchanger MESH = Mass, Equalization, Summation and Heat NPV = Net Present Value PA = Pump Around RVP = Reid Vapor Pressure Latin Letters: f = Original function # = molar feed flow rate G = Combination of the fixed point and Newton functions



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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 44

40

H = Homotopy function h = molar enthalpy ℎ = ideal gas molar enthalpy i = The discount rate i = component j = stage 0, = equilibrium ratio for vapor–liquid m = stage N = number of trays Q = rate of heat transfer R 8 = The net cash flow t = Homotopy parameter t = The time of the cash flow U = liquid side stream molar flow rate

= molar vapor flow rare

W = vapor side stream molar flow rate x = Unknown variable , = liquid mole fraction z = overall mole fraction in combined phases Greek Letters: α,β,γ,δ,η,θ,µ = New functions ∆-+./ = molar enthalpy of vaporization ∆ℎ+ = vapor molar enthalpy change


Page 41 of 44

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


41

∆ℎB = liquid molar enthalpy change • Supporting Information for publication

The below tables are supplied as supporting information; Table S1. Oil production unit feed. Table S2. Heat and material balance for liquid product of base arrangement. (Refer to Figure 1.) Table S3. Utility cost estimation. Table S4. Ethane/Ethylene column feed. This information is available free of charge via the Internet at http://pubs.acs.org/.

References (1)

Giorgio, S.; Feliu, J. A. Saving energy in distillation towers by feed splitting. App. Therm. Eng. 2002, 22, 889–896.

(2)

Giorgio, S.; Gamba, S.; Pellegrini, L.

A.; Bonomi, S. Feed-Splitting Technique in

Cryogenic Distillation. Ind. Eng. Chem. Res. 2006, 45, 5761-576. (3)

Lee, E. K.; Wong, D. S. H. Shortcut design of complex distillation Part 1. Basic theory and applications to multi-feed columns. Chin. Inst. Chem. Eng. 2008, 39, 519–527.

(4)

Salerno, D.; Garcia, H. A.; Wozny, G. Ethylene separation by feed-splitting from light gasses. Energy. 2011, 36, 4518-4523.

(5)

Deshmukh, B. F.; Malik, R. K.; Bandyopadhyay, S. Efficient Feed Preheat Targeting for Distillation by Feed Splitting. Europ. Comp. Aided. Proc. Eng. 2005.

(6)

Tavana, Y.; Shahhosseini, S.; Hosseini, S. H. Feed-splitting technique in the extractive distillation of CO2–ethane azeotropic process. Sep. Purification. Tech. 2014, 122, 47–53



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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 44

42 (7)

Babaie, O.; Nasr Esfahany, M. The effects of feed splitting and heat integration in classical arrangements on cost minimization in separation of ternary mixture”. Chem. Eng. Proc. 2013, 63 , 37– 43.

(8)

Lee, H. Y.; Jan, C. H.; Chien I. L.; Huang H. P. Feed-splitting operating strategy of a reactive distillation column for energy-saving production of butyl propionate. Taiwan. Inst. Chem. Eng. 2010, 41, 403–413.

(9)

Seader, J. D.; Henley, E. J. Separation process principles.’’, John Wiley and Sons, New York, 1998.

(10) Rahimian,

S. K.; Jalali, F.; Seader, J. D.; White, R. E. A new homotopy for seeking all

real roots of a nonlinear equation. Comp. Chem. Eng. 2011, 35, 403–411. (11) Jalali,

F.; Seader, J. D. Homotopy continuation method in multi-phase multi-reaction

equilibrium systems. Comp. Chem. Eng. 1999, 23, 1319-1331. (12) Rahimian,

S. K.; Jalali, F.; Seader, J. D.; White R. E. A robust homotopy continuation

method for seeking all real roots of unconstrained systems of nonlinear algebraic and transcendental equations. Ind. Eng. Chem. Research. 2011, 50, 8892-8900. (13) Dhooge,

A.; Govaerts, W. Cl_matcont: a continuation toolbox in Matlab. In Proceedings

of the 2003 ACM symposium on Applied computing. 2003. (14) Govaerts,

W.; Kuznetsov, Y.; Dhooge, M. MATCONT and CL MATCONT: Continuation

toolboxes in matlab. Gent University and Utrech University. Tech. Rep. 2011. (15) Singh,

B. P.; Singh, R.; Kumar, M. V. P.; Kaistha, N. Steady State Analysis Of Reactive

Distillation Using Homotopy Continuation. Chem. Eng. Research and Design. 2005, 83, 959–968.


Page 43 of 44

43 (16) Viswanathan,

J.; Grossmann, I. E. Optimal feed locations and number of trays for

distillation columns with multiple feeds. Ind. Eng. Chem. Res. 1993, 32 , 2942-2949.

TOP VENT

COLD FRAC

DISTILLATION TOWER

SPLITTER

VAPOR

FLASH DRUM

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


HOT FRAC

HEAT-EX PRODUCT

LIQ

REBOILER FEED

HOT DISTILLATE



Page 44 of 44

44

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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

Optimization of Distillation Separations Using Feed Splitting by a

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