Worth 100 pts/ 20% of your final grade

Topics Covered: Excel Mass Balances, VBA Programming, Graphing, Basic ChE Principles

Problem Statement: Xylenes are used as raw materials for the manufacturing of polyesters which are

used for textile fibers, photographic film, and soft-drink bottles. The process to be added to an existing

facility involves the isomerization reactor where meta-xylenes (m-x) is converted to ortho-xylenes (o-x)

and para-xylenes (p-x). Note that all three of these compounds are isomers (same elemental

composition with different chemical structure). Therefore, they have the same molecular weight

(MW=106). For our purposes here we will assume that equal amounts of o-x and p-x are produced so

that the reaction proceeds as follows:

2 →

+

This liquid phase reaction is assumed to be irreversible and is approximated by first-order kinetics with a

1

rate constant of = 0.133 . The reaction is slightly endothermic (Δ =

295 − ) The simplified process is described below.

A liquid feed stream will enter the process at 2 atms and a temperature off 77F at a rate of 1.15 million

kg/day. The mass fractions of that feed stream are:

Feed Stream

Benzene

0.14

o-x

0.25

m-x

0.38

p-x

0.23

The feed stream goes through a distillation column where 99% (by mass) of the benzene is removed in

the distillate (the top of the distillation column at 80 F and 1 atm), the small amount of benzene and the

entire xylene stream comes out in the bottoms at atmospheric pressure (1 atm) and 283 F.

A centrifugal pump will be used to increase the pressure of the stream sufficiently to overcome the

pressure drop due to friction in each of the components of the process (see the additional information

given below). Following the pump, the stream will pass through a heat exchanger where the

temperature will be increased from 283 F to 500 F using steam. The hot pressurized stream will then be

fed into a well-mixed isothermal reactor (maintained with a steam jacket around the reactor) where

70% of the m-x will be reacted to form o-x and p-x. The product stream from the reactor is cooled as

much as possible with cooling water in another heat exchanger before entering the separation system.

The separation system will yield four streams with the following mass fractions and which are all the

same temperature.

Output stream

1

2

3

4

Technical Details.

Benzene

0

0

0

1

o-x

1

0

0

0

m-x

0

0.03

0.7

0

p-x

0

0.97

0.3

0

1) Assume that the separation system is isothermal (operates at constant temperature)

2) The separation system at the end of the process uses a complex scheme of multiple stages. For

this preliminary design, simply represent the separation system by a box labeled “separation

system” in your excel sheet

3) Assume countercurrent, single pass heat exchangers

4) Δ ℎ = Δ

5) The heat capacity for the xylene stream has the formula

a. ( ) = 41.7 + 0.153 ° 2 (° )

6) The density of xylenes is given by the equation

=

1+(1− )

= 49.9367; = 0.216174; = 619.996; = 0.23776

( 3) =

7) Saturated steam is available at 545 °

49.9367

( ) 0.23776

(1+(1−

)

619.996

0.216174

(1000 ) and Δ = 650 .

When used for the

heater and reactor, the amount of steam that is used is only that which is condensed, and the

condensate leaves as a saturated liquid.

8) Cooling water is available at 90 ° and has a maximum outlet temperature of 120 ° . The heat

capacity of water is 1

°

4.18

°

1

°

9) In selecting the temperature of the process stream leaving the cooler, observe the rule of them

that the minimum temperature difference (either Δ 1 Δ 2 ) for a heat exchanger is 10 °

10) The pressure drop due to friction in each of the units is estimated to be as follows:

Heat Exchanger

15 psi

Reactor

5 psi

Product cooler

15 psi

Separation system

165 psi

The outlet pressure from the separation system is atmospheric pressure. For this preliminary

design, the pressure drops in the pipes between the major components may be neglected. The

pipes are all the same diameter and there are no significant changes in elevation The pump has

an efficiency of 75% ( = 0.75)

Assignment

1) Sketch the process on a blank sheet of paper (10%)

2)

3)

4)

5)

6)

a. The purpose of this is for you to understand the process better and for you to be able to

perform the mass balances. Please take a photo or scan this and upload it with your final

assignment

Perform a mass balance on the process, one unit at a time to determine the flows of each type

of xylene and the benzene in the process (15%)

a. I would recommend that you do these by hand at first before you enter them into excel.

Put the mass balance in excel so that if one value changes the entire process automatically

updates. Hint: the cells need to be linked and functions of one another (Part of 20% see note

below)

Determine the enthalpy of heating up the xylene stream (before the reactor) and cooling down

the xylene stream (after the reactor). You will need to use the formula and program it as a VBA

function (15%)

a. Δ = ∫ ( )

b. The first heat exchanger takes the stream from the distillation column at 283 to 500 °

c. The second heat exchanger (or the cooler) cools the hot stream from the reactor from

500 ° to (a value you need to determine…hint: .Δ 2 = 10 ° )

In VBA program a function for the density of xylene and graph density vs temperature from =

300 600 (10%)

a. Need to make sure you follow the rules of making a good graph. Include axis labels, tick

marks, etc.

Determine how much cooling water is needed (5%)

a. Δ = 20 Δ

b. You know Δ from the integral above (this is for the exchanger or “cooler” after the

reactor), you know what Delta T should be, ℎ20 = 4.18

7) Determine how much steam is needed (5%)

a. Δ = Δ

b. You know Δ from the integral above (you should have done it twice, this is for the

exchanger before the reactor) you know Δ you are solving for the mass flow rate of

steam.

8) Calculate how much steam is needed to keep the reactor at 500 F. (5%)

a. Δ = 295 − = Δ

b. Determine how many moles of m-x are reacted to calculate Δ then divide by

Δ to determine mass of steam. Hint: 1 BTU = 252.2 calories

9) Calculate the volume of the reactor (10%)

0

=

=

=

0 (1 − ) (1 − )

You will get units of min….need to divide by the volumetric flow rate (use the density for

500 F of the Xylene Stream).

10) Calculate the size of the pump that is needed. (5%)

a. Add up all the pressure drops listed in the table in the technical details section

b. =

Δ

c. Units will be tricky here, need to convert psi = 2 to 2

d. Should get final units of

e.

−

To get value to Horsepower, multiply by total mass flow rate. Should get units of

1 ℎ = 550

Notes: Problems 6-10 could be done by hand, but I want you to enter them into excel. The goal is that if

I changed the conversion rate of m-x from 70% to 80% all of your numbers would update in the

workbook or if the total flow rate change. On that note, make sure you can do that before turning in

your assignment. 20% of your grade comes from having your excel document linked for the mass and

energy balances.

Your final deliverable is your excel workbook and a short summary of your results (answer each

question in a word document, make sure your density figure is in here as well).

Deliverables for Project

.

• Turn in word document giving me all of the answers asked for in the

Homework

Please make sure answers have units and are clearly labeled

Make sure that the figure of the density is properly formatted

• Turn in Excel Workbook, to get full points

• Needs to be clearly labelled

Units need to be shown

• Needs to be able to be navigated easily

Cells need to be linked together

.

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