To: Michael T. Timko & William Clark

From: Michael Bodanza, Martin Burkardt, Marcus Lundgren, Rachel Whalen

Date: 22 February 2015

Subject: Pressure-Swing Distillation Plant Design

Introduction

Pressure-Swing Distillation (PSD) is a system of two distillation columns operating at

different pressures. As the azeotrope shifts with pressure, this separation can circumvent this

limiting factor. From the first column, the exiting stream at the first azeotrope composition

becomes the feed for the second column, and the exiting stream at the second azeotrope

composition can be recycled to increase efficiency. The two product streams can in principal be

separated to purity.

Our team was requested to design a separation process using this method for an acetone – methanol

mixture. As an exploration in minimizing cost, a high-pressure distillation column (HPD) was also

designed to yield the same degree of separation.

The design specifications of the distillation require two product streams at 28% acetone

and a 95% acetone from 150 kgmol/hr feed of 60% acetone in methanol. On analysis, PSD was

determined to be the most cost-effective method to overcome the difficulty of this particular

separation. The PSD system will produce 78.4 kgmol/hr of 28% acetone and 71.6 kgmol/hr of 95%

acetone.

Methodology

Part 1: Experimental Data and Curve Fitting Models

Initially, it was required to fit experimental data to parameters; in particular the Wilson

equation was used. Using the provided VLE data1, the curves were fitted to the azeotrope

conditions: x1 = y1 = 0.78 at 328.7 Kelvin and 1.013 bar. From this set of conditions, α12/R and

α21/R could be determined.

To begin it was assumed that Φ ≈ 1 for both components at this low pressure. Noting also

the azeotrope conditions the equilibrium expressions reduced to the following:

ɣ1𝑎𝑧 =

𝑃

𝑃1𝑠𝑎𝑡 (1)

ɣ2𝑎𝑧 =

𝑃

𝑃2𝑠𝑎𝑡 (2)

The saturation pressure is readily determined from Antoine’s equation, with published

coefficients2 readily available.

MathCAD was incorporated in our solution with the built in solver function to determine

the two Wilson equation parameters (see Appendix): Λ12 and Λ21. The following equations were

used as inputs for MathCAD to solve for α12/R and α21/R:

Λ12 = (𝑉2

𝑉1)exp(

−𝛼12

𝑅𝑇) (3)

Λ21 = (𝑉1

𝑉2)exp(

−𝛼21

𝑅𝑇) (4)

With these α-values, a graph was constructed with modified Raoult’s Law:

ɣ1𝑃1𝑠𝑎𝑡𝑥1 = 𝑦1𝑃 (5)

ɣ2𝑃2𝑠𝑎𝑡𝑥2 = 𝑦2𝑃 (6)

The calculated and provided values were graphed in parallel to indicate the fit for data.

For pressures greater than 3 bar, Φ ≠ 1. For this reason the following equilibrium expression

was used and α-parameters were assumed to hold for increasing pressure:

ɣ1𝑃1𝑠𝑎𝑡𝑥1 = Φ1𝑦1𝑃 (7)

ɣ2𝑃2𝑠𝑎𝑡𝑥2 = Φ2𝑦2𝑃 (8)

Further definitions of Φ can be found in the appendix.

Part 2: Pressure-Swing Distillation and Optimizing Pressures

In order to choose pressures that are both reasonable and cost-effective, many high-

pressure systems were considered (see appendix) along with the given system (P = 1.013 bar = 1

atm) to find the best fit. Diagram 1 depicts the PSD system with column 1 and 2 operating at 1.013

bar and 2.8 bar, respectively. McCabe-Thiele analysis was used to determine the total number of

stages. Mass-balances were used to solve for the compositions and flow rates of bottoms (product) ,

distillate, and recycle streams. Reflux ratios were found assuming the optimal external reflux ratio

(L/D) is (1.1 – 2.0) times the minimum external reflux ratio (L/D).

Diagram 1: PSD system operating at 1.013 bar (1 atm) and 2.8 bar for column 1 and 2, respectively.

Part 3: High-Pressure Distillation and Optimizing Pressure

In order to complete a separation to the degree required, it is possible to shift the azeotrope

beyond that composition required with a high enough pressure. Using MathCAD, this high

pressure was determined once the azeotrope composition shifted past 28% acetone. The HPD

column is pictured below in Diagram 2. The calculations are similar to the ones around PSD

column, however, mass balances were run for the single column without any recycle loops.

Diagram 2: HPD column operating at 18.437 bar.

Part 4: Cost Estimation and Comparison

In an effort to find the most cost-effective column, the capital cost of various distilla t ion

systems were compared using the following tabulated cost equations3:

𝐶𝑜𝑙𝑢𝑚𝑛𝐶𝑜𝑠𝑡 = (2500 + 1200(0.5 + (𝑃

8.5−0.006∗𝑃))) ∗ 𝑁 (9)

𝑃𝑢𝑚𝑝𝐶𝑜𝑠𝑡 = (210 + 130 ∗ log10𝑃) ∗ 𝑃 (10)

Where P is in atm and N is the number of stages. While these equations assume the optimal interna l

reflux ratio (L/V) is 1.4 times the minimum, we apply them to our columns to give an estimation

of the total price.

Main Results and Discussion

Part 1: Experimental Data and Curve Fitting Models

To fit the provided data accurately, α12/R and α21/R were determined from the azeotrope

conditions. The α-values are, -17.437 K and 243.02 K, respectively. These values can be

extrapolated to model other system pressures.

The T-x-y and x-y graphs, shown below in Figure 2 and Figure 3, respectively, are slight

over estimates from the given data. This did not change the value of the azeotrope, so the Wilson

equation is still a useable model.

Figure 2: Comparison of model (lines) and physical data (points) in a T-x-y diagram.

Figure 3: Comparison of model (line) and physical data (points) in an x-y diagram.

Part 2: Pressure-Swing Distillation and Optimizing Pressures

The PSD system requires two varied pressures to operate. The first column is set to run at

1.013 bar (1 atm), whereas the second column was set to run at 2.8 bar (2.76339 atm). This reduces

the azeotrope composition by 18%. Under lower pressure differences, the number of stages

required increased dramatically, making these columns impractical. At higher pressure-swings, the

328

329

330

331

332

333

334

335

336

337

338

339

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

T (K

)

X, Y (acetone)

T-x-y Diagram at 1.01325 bar

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Y (A

ceto

ne)

X (acetone)

X-Y Chart at 1.01325 bar

number of stages is reduced, however, the trade-off between operating at a higher pressure and

reduced stages was not significant enough and was less cost effective. At the selected pressure

swing, it was determined that 10 stages in the lower pressure column and 18 in the high pressure

column were needed. Additional results can be found in the Appendix.

Part 3: High-Pressure Distillation and Optimizing Pressure

A very high pressure column is needed to push the azeotrope and perform distilla t ion

utilizing just one column. While theoretically this could be operated around 10 atm (the minimum

pressure required), our team deemed it would be less cost effective than others. For this reason, a

slightly pressure of 18.743 bar (18.498 atm) was chosen as this reduces the azeotrope composition

to 20% acetone. Under these conditions 16 stages are required to complete the separation. For

comparison, a column operating at 14.201 bar (14.015 atm) was also analyzed. However, as the

azeotrope composition (x1az = 0.25) is closer to the desired composition, the number of stages

increases and the price consequently increases by roughly 10% when compared to the higher

pressure column. Additionally, it is noted that the azeotrope will completely disappear around 27

bar, however, this will significantly increase the cost.

Part 4: Cost Estimation and Comparison

As a major factor and contribution to optimizing, minimizing capital cost is central to this

project. The equations used provide some estimations for the total cost, although are not strictly

applicable. Nevertheless, the PSD system is more effective than the HPD column. The two systems

cost $92,700 and $98,900, respectively. This is a 7% difference, which our team deems significant

to consider the PSD to be a more appropriate option for the company.

Part 5: Health and Safety Risks

Another significant impact on design, is the associated health and safety risks of this

mixture. Under high pressures and high temperatures a 50/50 mixture of the two components can

result in destructive situations including explosions and fires.4 This imposes a higher degree of

concern for a high-pressurized column and leads our team to further consider PSD to be the safer

option.

While operating at a high pressure (e.g. high temperature), a special lab safety issue arises

which is the back-up controller for the temperature. Therefore the system can easily be shut down

in case of an emergency. Along with a temperature controller, there must be release valve for

pressure in-order to control the device. The idea is similar to the temperature controller—if a

situation arises where pressure build-up occurs and must be decreased immediately, opening the

valve will assist in doing so. The vessels that the high pressure reactions take place in must also

be stabilized and periodically tested to make sure that the vessel can withstand the high stress after

a period of usage (“Lab Safety Manual”).

A leak will drastically increase the risk of fire or even an explosion. To extinguish a fire in

the plant, an alcohol-foam or dry chemical should be used because water will not function as an

extinguishant. When heated, these compounds may form fairly hazardous compounds such as

carbon dioxide, carbon monoxide, and formaldehyde—further confirming the need for fail-safe

release valves. Methanol is also considered dangerous to the environment, especially the soil,

which leads us to believe the plant should not operate near farms or local water supplies in the

event that an accident does occur.

Conclusions and Recommendations

From our initial set of data, we were able to conclude some reasonable modeling

coefficients that would allow us to make predictions at higher pressures and more severe

conditions; this calculations can have a high degree of impact on the distillation design.

In our best estimation it is reasonable for us to conclude that PSD to be the more reasonable

design selection. This method allows for lower pressure columns which are both cost-effective and

safe. While the costs of PSD and HPD are comparable, raising the pressure significantly increases

risk of explosions and fire.

After comparing a few higher-pressure systems, it is our recommendation to run a PSD

system with one column operating at 1.013 bar and the other at 2.8 bar. This will effectively reduce

the cost compared to other system pressures.

It may be beneficial to analyze other pressure combinations to find the minimum cost of

the given system. As a first pass, however, our calculations can provide a reasonable guide to

further investigation.

References

1. Van Winkle M.: vapor-liquid equilibria. Ind.Eng.Chem. 48 (1956) 142-146.

2. "National Institute of Standards and Technology." National Institute of Standards and

Technology. N.p., n.d. Web. 18 Feb. 2016.

3. “Analysis, Synthesis, and Design of Chemical Prcoesses” by R.C. Bailie, W.B. Whiting,

J.A. Shaeiwitz and D. Bhattacharyya, 4th Edition, Prentice-Hall PTR, Upper Saddle

River, New Jersey, 2012.

Appendix

All calculations for this project were mainly done using Microsoft Excel and Mathcad. The following equations were used to define calculation parameters:

𝑙𝑛ɣ1 = − ln(𝑥1 +Λ12𝑥2) + 𝑥2(Λ12

𝑥1 + Λ12𝑥2−

Λ21Λ21𝑥1 +𝑥2

)

𝑙𝑛ɣ2 = −ln(𝑥2+ Λ21𝑥1)− 𝑥1(Λ12

𝑥1+ Λ12𝑥2−

Λ21Λ21𝑥1 +𝑥2

)

These are known as Wilson’s equations where: γ1 & γ2 are correction factors Λ12 & Λ21 are Wilson constants dependent on temperature

x1 is the liquid composition of acetone, x2=1-x1 and is the liquid composition of methanol.

Part 2: Pressure-Swing Distillation and Optimizing Pressures

Figure 4: The figure shows the y vs x graph for both 1.03125 bar and 2.8 bar. The red line is at a pressure of

1.03125 bar and the grey line is at a pressure of 2.8 bar.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y1

x1

Pressure Swing (P1=1.01325 bar, az1=0.78),(P2=2.8 bar, az2=0.60)

Column 1 Pressure 1.01325 bar (1 atm)

Column 2 Pressure 2.8 bar (2.76339 atm)

Feed Flowrate 150 𝑘𝑔𝑚𝑜𝑙

ℎ𝑟

Z=xF (Feed Composition) 0.6

Fmix= 460.44

XB1 (Bottoms composition of Column 1) 0.28

XB2 (Bottoms composition of Column 2) 0.95

XD1 (Recycle composition of Column 1 to 2) 0.703

XD2 (Recycle composition of Column 2 to 1) 0.646 𝐿

𝑉 Column 1 Minimum: 0.545

Optimal: 0.683

𝐿

𝑉 Column 2 Minimum: 0.587

Optimal:0.74

𝐵1̇ 78.36𝑘𝑔𝑚𝑜𝑙

ℎ𝑟

𝐵2̇ 71.64𝑘𝑔𝑚𝑜𝑙

ℎ𝑟

𝐷1̇ 382.08𝑘𝑔𝑚𝑜𝑙

ℎ𝑟

𝐷2̇ 310.44𝑘𝑔𝑚𝑜𝑙

ℎ𝑟

Number of Stages for Low Pressure Column 10 Stages (9 and one reboiler)

Number of Stages for High Pressure Column 17 Stages (16 and one reboiler)

Feed Tray Location for Low Pressure Column 6th stage after reboiler

Feed Tray Location for High Pressure Column 5th stage after reboiler

Table 1: The following table summarizes the results of the pressure swing distillation at 1.01325 bar (1 atm) and 2.8

bar (2.76339 atm).

Part 3: High-Pressure Distillation and Optimizing Pressure

Column 1 Pressure 18.437 bar

Number of Stages 16 Stages (15 Stages and 1 reboiler)

Location of Feed Tray 9th stage after reboiler

�̇� 150 𝑘𝑔∗𝑚𝑜𝑙

ℎ𝑟

Z 0.6

�̇� 71.64 𝑘𝑔∗𝑚𝑜𝑙

ℎ𝑟

XB 0.95

�̇� 78.36 𝑘𝑔∗𝑚𝑜𝑙

ℎ𝑟

XD 0.28 𝐿

𝑉

Minimum: 0.689 Optimal: 0.7995

Table 2: This table summarizes the results of the high pressure distillation at 18.437 bar of pressure:

Part 4: Additional Calculations

Calculations

Flow Rate Calculations for Pressure Swing Distillation F = B1+B2

Fz = (B1* XB1) + (B2*XB2)

150(0.6) = B1(0.28) + (150-B1)(0.95)

B1 = 78.36 𝑘𝑔∗𝑚𝑜𝑙

ℎ𝑟

B2 = 71.64 𝑘𝑔∗𝑚𝑜𝑙

ℎ𝑟

D1 = D2 + B2

D1*XD1 = (D2*XD2) + (B2*XB2) (D2 + 71.64)(0.703) = D2(0.646) + 71.64(0.95)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y1

x1

x-y at P=18.743 bar

D2 = 310.44𝑘𝑔∗𝑚𝑜𝑙

ℎ𝑟

D1 = 382.08 𝑘𝑔∗𝑚𝑜𝑙

ℎ𝑟

Fmix = F + D2

Fmix*Zmix = (FZ) + (D2*XD2) Fmix =150 + 310.44

Fmix =460.44 𝑘𝑔∗𝑚𝑜𝑙

ℎ𝑟

460.44(Zmix) = 150(0.6) + ???=D2(???=XD2) Zmix = 0.67

Equipment Cost for Pressure Swing Distillation Column Cost:

= ($2,500 + $1,200[0.5+{1𝑎𝑡𝑚

(8.5−(0.006∗1atm)}])*10Stages column 1+ ($2,500 +

$1,200[0.5+{2.76339𝑎𝑡𝑚

(8.5−(0.006∗2.76339atm)}])*17Stages Column 2

= $91,757.86

Pump Cost = ($210 + $130*log101atm)*1atm + ($210 + $130*log102.76339atm)*2.76339atm = $948.90 Total Cost = $92.706.76

Flow Rate Calculations for High Pressure Distillation

F = D + B Fz = (B*XB)+(D*XD) 150(0.6) = B(0.28)+(150-D)(0.95)

D =78.36 𝑘𝑔∗𝑚𝑜𝑙

ℎ𝑟

B = 71.64 𝑘𝑔∗𝑚𝑜𝑙

ℎ𝑟

Equipment Cost for High Pressure

Distillation Column Cost = ($2,500 + $1,200[0.5+{18.4979𝑎𝑡𝑚

(8.5−(0.006∗18.4979atm)}])*16 Stages

=$91,936.29

Pump Cost = ($210 + $130*log1018.497atm)*18.497atm=$6,931.64 Total Cost = $98,867.54

Part 5: MathCAD Files

See attached documents for MathCAD Files including additional calculations.