ChemE 140Polystyrene Reactor Design

24 November 2013

Submitted By:Apurva Pradhan

apurva.pradhan@berkeley.edu;23461924Sonal Rangnekar

srangnekar@berkeley.edu;23662940Aditya Raghunathan

raghunathan.aditya@berkeley.edu;23637569Ross Udod

rossudod@gmail.com;23880119

Contents

1 Introduction 21.1 What is the Problem? . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Design Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Contributing Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Design Approach 3

3 Results 4

4 Recommended Design 5

5 Appendix 65.1 Appendix A: Derivations . . . . . . . . . . . . . . . . . . . . . . . . . 65.2 Appendix B: Given Constants . . . . . . . . . . . . . . . . . . . . . . 135.3 Appendix C: Supplementary Charts and Graphs . . . . . . . . . . . . 145.4 Appendix D: MATLAB Code . . . . . . . . . . . . . . . . . . . . . . 15

6 References 22

1

1 Introduction

1.1 What is the Problem?

We are charged to design a Plug Flow Reactor (PFR) that polymerizes styrene intopolystrene through the use of the initiator molecule azobisisobutyronitrile (AIBN).The reactor is to be optimized on a cost basis for the production of polystyrene atthe rate of 1000 kg/hr. The process flow diagram for the polystyrene plant is givenin Figure 1.

Figure 1: Schematic of Polystyrene Plant

1.2 Design Specifications

As per Figure 1, stream P must contain 1000 kg/hr of polystyrene. The initiatorenters through stream I at a concentration of 0.022 mol/L, and all unconvertedinitiator leaves through stream P . Because we require so little initiator, we canapproximate that it contributes negligible volume to the mixture stream that entersthe PFR. Styrene enters the plant through stream F, and unconverted styrene is splitin an equilibrium stage at the evaporator to either exit the plant in stream P or berecycled into the input stream for the PFR via recycle stream R. The ratio of therecycle stream R to the feed stream F is determined to be 1. The PFR is set tooperate at a steady temperature of 60◦C. [Figure 1]

1.3 Contributing Costs

The three major contributing costs to this plant are the infrastructure cost of thePFR, which is proportional to it’s volumetric capacity, the cost of styrene monomer

2

in stream F , which is proportional to the weight flow (kg/hr) of the molecule, andthe cost of energy per second (dollars per Watt) needed to overcome the pressuredrop across the reactor. These three costs are dependent on the volume of the PFR,which is dependent on the single-pass conversion of styrene in the PFR. Therefore,finding a minimum cost for operating this plant determines a specific volume for thePlug Flow Reactor and a specific feed rate of styrene.

2 Design Approach

We optimized the conversion for the reactor by determining the conversion whereoperation cost was a minimum. The total cost is a sum of individual costs forreactor size, input feed, and power needed to overcome the pressure drop. Eachcomponent has its own cost which contributes to the total cost for operation. Theexpressions for each component were determined from constraints and data in theproblem statement.

The PFR (plug flow reactor) design equation gives volume as a function of monomerconverted into polymer. Specific rates for initiator depletion and monomer conversioncan be found in equations A-6 and A-7. Constants can be found in Appendix B.The differential equation was solved numerically using MATLAB’s ode45 differentialequation solver with a relative tolerance of 10−18. Conversion was plotted as afunction of reactor volumes up to 1000 m3. [Figure C-1]

A mass balance on polystyrene gives the relationship between production of thepolymer and a conversion of styrene monomer. The desired production of 1000kg/hr of polystyrene is substituted into the mass balance to express volumetric flowinto the reactor as a function of only conversion. Two additional mass balances onstyrene with control volumes selected around the reactor and the separator combinewith the desired recycle ratio to give input feed as a function of volumetric flow intothe reactor. The concentration of initiator was at least 5 orders of magnitudes lowerthan the concentration of styrene and assumed to be negligible. Further detail isgiven from equations A-8 to A-21.

The pressure drop was determined by the friction factor, given as a function ofreactor length, adjusted for reactor volume. The Reynolds number for the system wasprovided as a function of diameter, axial velocity, viscosity, and density. Substitutionof the friction factor and the Reynolds number into the Blasius relation gives adifferential equation for pressure drop. The reaction tube diameter and the density

3

of the reactor mixture is given in Appendix B. The axial velocity is determined by afunction of volumetric flow rate and cross section area. The viscosity is a function ofaverage molecular weight, given in the design problem. The differential equation forpressure drop was rewritten in terms of initiator conversion and monomer conversion.Details are provided in A-22 to A-33. A system of differential equations for initiatorconversion, monomer conversion and pressure drop were solved simultaneously usingMATLAB’s ode45 integrator with a relative tolerance of 10−18.

The total cost was determined as a weighted sum of the three components. Differentcombinations of conversion and styrene feed required multiple iterations in order toplot a curve as a function of conversion.

3 Results

Our calculations indicate that a non-linear relationship exists between the total costof running the PFR per hour and the single-pass conversion of the styrene monomer[Figure 2]. This relationship matches the prediction that there exists a minimum costthat corresponds to a certain monomer conversion that fixes the rest of the reactordesign. We determine the minimum cost of operating the reactor to be $88,240. Thecorresponding value of single-pass conversion of styrene is 36.5%. By choosing thissingle-pass conversion, we fixed the initiator conversion, reactor volume, the styrenefeed, the average molecular weight of the polystyrene product, the pressure drop andthe volumetric flow rate. These values are given in Appendix C [Table C-1]. Ourcalculations also show that the single-pass conversions of the initiator and styrenemonomer have asymptotic behavior with increasing PFR volume, and the pressuredrop across the reactor decreases as the reactor volume increases. These plots aregiven in Appendix C.

4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8x 105

Conversion

Tota

l Cos

t

Student Version of MATLAB

Figure 2: Plot of the total reactor cost as a function of styreneconversion. A non-linear relationship is evident. The green circle

denotes the minimum cost ($88240) at the optimal volume (165m3)

4 Recommended Design

We recommend that the polystyrene plant have a Plug Flow Reactor with a volumet-ric capacity of 165 m3. The optimal single-pass conversion for this reactor is 36.5%to produce 1000 kg/hr of polystyrene, therefore the input flow of styrene in stream Fmust be 1369 kg/hr. At atmospheric pressure, stream F has a velocity of 3 m3/hr.This design produces a mixture of polystyrene with an average molecular weight of460 g/mol. The overall conversion of styrene due to this design is 73.0%.

As explained in the previous section of this report, these physical conditions areoptimized according to a general economic analysis of this plant. The cost for aPFR of this volume is $33074. The cost for the styrene feed is $55135, and theenergy cost for the reactor is $33. These latter two numbers are given on an hourlybasis, while the PFR cost is for the entire lifetime of the reactor. Therefore ourmethods of simply adding the individual costs to obtain a total cost can be considered

5

improper. Nevertheless, this gives an approximate indication of the relative cost ofthe design.

5 Appendix

5.1 Appendix A: Derivations

Figure A.1: Diagram of a polystyrene plant with an isothermal PFR

In a polystyrene plant, a continuous process is used to produce 1000 kg/h of polystyrenein an isothermal PFR. Following the reactor, volatile monomer (styrene) in the prod-uct stream is recovered by evaporation and recycled. Liquid product from the evap-orator includes dissolved styrene and a minor amount unreacted initiator.

The design equation is:

dx

dv=−riQi

(1)

where ri is the rate of reaction and Qi is the input flow rate.

Rate of conversion of initiator and monomer:

6

−rI = kdCI (2)

−rM = kp

(2kdCIkt

) 12

CM (3)

where kd is 0.85 ∗ 10−5s−1, kp = 145Lmol−1s−1, kt = 5.8 ∗ 107Lmol−1s−1, CI is theconcentration of initiator, and CM is the concentration of monomer.

Using the definition of conversion and composition of flow,

Ci = (1− xi)Cio (4)

Qi = QCio (5)

where Ci is the concentration of species i, xi is the conversion of species i, Cio isinitial concentration of species i, Q is the overall volumetric flow rate, and Qi is thevolumetric flow rate of species i.

The design equation can be rewritten as a function of conversion.

initiator:dx

dv=kd (1− xI)

Q(6)

monomer:dx

dv=kp

(2kdCI

kt

) 12

(1− xM)

Q(7)

where xM is the conversion of monomer and xI is the conversion of initiator.

The stoichiometry of the system reveals that the total mass of monomer reactedequals the total mass of polymer produced because it is a simple addition reaction.

∑(Mi +Mj)→

∑(Mi+j) (8)

7

where Mi and Mj are radical chains of an arbitrary length of i monomers and jmonomer respectively, and Mi+j is a polymer chain of length i+ j monomers. Eachmonomer has a constant mass, and the number of monomers reacted is conserved sothat the overall mass of the polymer formed is conserved.

mass monomer reacted = mass polymer formed (9)

The definition of conversion allows the mass of polymer formed to be rewritten as afunction of monomer consumed.

xM ∗mass monomer in = mass polymer formed (10)

Next, we performed a mass balance on the polymer with the reactor, operating atsteady state, as the control volume.Equation 10 is substituted for the generation term.

dm

dt= 0 = xMmMIn −mpOut (11)

where mMIn is the mass of the monomer in and mpOut is the mass of polymer flowingout. No polymer flows into the reactor.

Dividing the mass flow rate by the density gives the volumetric flow rate.

xMQMρstyrene = mpOut (12)

where xM is conversion of monomer, QM is volumetric flow rate of monomer in, andρ is density of the mixture.

The problem statement assumes that the concentration of initiator is negligible andthe mixture is uniform with ρstyrene = ρpolystyrene = ρmixture = 909.3kg ·m−3. Thisgives

8

QM = Q (13)

ρ = constant (14)

Q =mpOut

xM · ρ(15)

A basis of 1000 kg/hr of polystyrene produced gives

Q =1000kg/hr

xM · ρ(16)

A plot of many different volumetric flow rates corresponding to conversions from 0.1to 0.95 was evaluated using MATLAB.The specified recycle ratio of 1 gives the relationship between fresh styrene andrecycle feed.

R

F= 1 (17)

where R is the flow of styrene in the recycle stream and F is the flow of styrene inthe fresh feed stream.

The mass balance on the recycle junction gives:

F +R = Q (18)

Again, the initiator concentration is assumed to be negligible.

Substituting using the recycle ratio gives input feed as a function of reactor flowrate.

2F = Q (19)

F =Q

2(20)

9

Input feed is converted to mass by multiplication of density.

F =Q

2ρ (21)

The pressure drop is given as a differential equation defined for a friction factorf .

f = −dPdx

(D

2ρv2

)(22)

where dPdx

is the differential change of pressure as reactor length increases, D is thediameter of the reactor (0.1 m), ρ is the density of the mixture, and v is the velocityof axial flow.

The volume of the cylindrical plug flow reactor is given by

V = πD2

4x (23)

where V is reactor volume, D is the diameter of the reactor, and x is reactor length.Differentiation gives

dV =πD2

4dx (24)

dx =4

πD2dV (25)

Substitution into equation A-22 gives:

f = −dPdV

(4

πDρv2

)(26)

10

The velocity is a function of volumetric flow rate and area given by:

V =Q

A(27)

The friction factor obeys the Blasius relation

fmass =0.079

Re1/4(28)

where Re is the Reynold’s number. The Reynold’s number is defined as

Re =Dvρ

µ(29)

where D is diameter, v is axial velocity, ρ is density, and µ is axial viscosity.

Combining and rearranging equations A-28 through A-30 gives:

−dPdV

(4

πDρv2

)=

0.074(Dvρµ

) 14

(30)

−dPdV

=0.079πDρv2

4·(Dvρ

µ

) 14

(31)

where D is diameter, v is axial velocity, ρ is density, and µ is viscosity.

The viscosity was experimentally determined to be

ln( µ

1Pa · s

)= −13.04 +

2013T1K

+M0.18w

(3.915wp − 5.437w2

p +

(0.623 +

1387T1K

)w3p

)(32)

11

where wp is the weight fraction of polymer in the mixture, T is the temperature ofthe system in Kelvin, and Mw is the average molecular weight of polystyrene givenby

Mw =

(2 + 3

√2ktkdCi

(CM,0 − CM)

)Mw,st (33)

The results from combining equations A-31 to A-33 is visible in a plot solved numer-ically.

The total cost of the reaction is weighted differently for each of the three com-ponents.

C = $200 ∗ V + $70 ∗ min + $0.00015 ∗ p (34)

where V is the volume of the reactor in m3, min is the input feed in kg/hr, and p isthe power needed to overcome the drop in pressure caused by increased viscosity.

The mass flow rate is given by:

min = Qρ (35)

where Mw,styrene is 104.15g ·mol−1 and ρ is a density of 909.3kg/m3.

The power for the pump is given by

P = Q∆P (36)

where Q is volumetric flow in m3/s and ∆P is pressure drop in pascals.

Combining the previous three equations gives

12

C = $200 ∗ V + $70Qρ+ $0.00015 ∗Q∆P (37)

The values of V ,Q, and ∆P can be plugged in to equation A-38 from equations A-7,A-16, and A-31 to A-33, and can be solved for V and ∆P numerically and for Q bysubstitution through Matlab.

We determined the solution by iterating for different values of xM and Q, and aminimization of operation costs. The minimum operation cost was found to be$88243 for a conversion of 0.365.

5.2 Appendix B: Given Constants

Physical properties:ρstyrene = ρpolystyrene = ρmixture = 909.3kg ·m−3

Mw,styrene = 104.15g ·mol−1

Diameter of the PFR: D = 0.1m

Kinetic Rate Constants:kd = 0.85 ∗ 10−5s−1

kp = 145L ·mol−1s−1

kt = 5.8 ∗ 107L ·mol−1s−1

Costs:Cost per Volume of Reactor = $200/m3

Cost of Feed = $70/(kg/hr)Cost of Power = $0.15/kW

13

5.3 Appendix C: Supplementary Charts and Graphs

Table C-1: Design values that describe the PFR. These values weredetermined by fixing the running cost and monomer conversion of the

reactor

Table 1: Design values that describe the PFR. These values were determined by fixing the running cost and monomer conversion of the reactor.!

Total Cost $ 88242.91 Conversion of monomer 0.3652 Conversion of initiator 0. 8137 Reactor Volume 165.3707 m3 Styrene Feed 1369.1128 kg/hr Reactor Pressure Drop 4.612 x 108 Pa Average molecular weight of polystyrene 459.6683 g/mol Volumetric Flow rate 8.3649 x 10-4 m3/s

0 100 200 300 400 500 600 700 800 900 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Volume [m3]

Con

vers

ion

InitiatorMonomer

Student Version of MATLAB

Figure C-2: Plot of the single-pass conversion of styrene monomer andInitiator as a function of reactor Volume. This relationship matches our

prediction that the species conversion behaves asymptotically withreactor volume. The Initiator and Styrene monomer conversions are

represented by dashed and solid lines respectively.

14

0 100 200 300 400 500 600 700 800 900 1000−2.5

−2

−1.5

−1

−0.5

0 x 1020

Volume [m3]

Pres

sure

[Pa]

Student Version of MATLAB

Figure C-3: Plot of the pressure drop in the PFR as a function ofreactor volume. This relationship confirms our prediction that pressure

will continue to drop as the reactor volume increases.

5.4 Appendix D: MATLAB Code

function[]=Apurva_PFR()

%ChemE140 Design Project

%

%Group Members: Apurva Pradhan, Aditya Raghunathan, Sonal Rangnekar, Ross

%Udod

%

%November 24, 2013

close all;clear all;clc

conversion =0.1:0.0001:.95;

data(:,1)=conversion;

for i=1:length(conversion)

[Mw_poly,dP,Volume,Q]=Radke_PFR(conversion(i));

feed=1000/((1-conversion(i))*2);%feed styrene in kg/hr

15

vdata(i,1)=200*Volume;%cost per volume

fdata(i,1)=70*feed;%cost per kg/hr feed

pdata(i,1)=0.15*((dP*2*feed)/(3600*909.3))/1000;%cost per kw

totdata(i,1)=vdata(i,1)+fdata(i,1)+pdata(i,1);%total cost

end

[totalcost,iindex]=min(totdata);

cons=data(iindex,1);

[Mw_poly,dP,Volume,Q]=Radke_PFR(cons);

disp([’The total cost [$] is: ’,num2str(totalcost)])

disp([’The conversion of monomer [X_m] is: ’,num2str(cons)])

disp([’The conversion of initiator [X_i] is: ’,num2str(0.8137)])

disp([’The Reactor Volume [m^3] is: ’,num2str(Volume)])

disp([’The Feed [kg/h] is: ’,num2str(1000/(cons*2))])

disp([’The pressure drop [Pa] is: ’,num2str(dP)])

disp([’The Average Molecular weight of the polymer [g/mol] is: ’,num2str(Mw_poly)])

disp([’The volumetric flow rate [m^3/s] is: ’,num2str(Q)])

%Plot solution:

%figure

plot(conversion,totdata)

xlabel(’Conversion’)

ylabel(’Total Cost’)

grid on

hold on

scatter(0.3652,88242.9105)

[coni]=graphs_PFR(cons);

function[Mw_poly,dP,Volume,Q]=Radke_PFR(con)

m = 1000/(con*3600);

Q = m/909.3;

%--------------------------------------------------------------------------

%This script calculates and plots the pressure and conversions as a

%function of reactor volume for the polymerization of styrene in a

%Plug-Flow-Reactor (PFR). The reaction mechanism is the following:

%I = 2R

%R + M = M1.

%Mn. + M = Mn+1

16

%Mn. + Mm. = polymer

%--------------------------------------------------------------------------

%Solve system of differential equations numerically via ode45:

%1) Define volume interval.

V = [0 1000]; %.Volume. [m3]

%2) Define initial conditions.

Xio = 0; %Initial conversion of I.

Xmo = 0; %Initial conversion of M.

Po = 0; %Initial pressure. [Pa]

Xo = [Xio Xmo Po];

[Vout,X] = ode45(@rates,V,Xo);

%--------------------------------------------------------------------------

%Plot solution:

% figure

% plot(Vout,X(:,1))

% axis([V(1) V(2) 0 1])

% xlabel(’Volume [m3]’)

% ylabel(’Conversion of Initiator’)

% grid on

%

% figure

% plot(Vout,X(:,2),’r’)

% axis([V(1) V(2) 0 1])

% xlabel(’Volume [m3]’)

% ylabel(’Conversion of Styrene’)

% grid on

%

% figure

% plot(Vout,X(:,3),’g’)

% xlabel(’Volume [m3]’)

% ylabel(’Pressure [Pa]’)

% grid on

% %--------------------------------------------------------------------------

%Determine reactor volume and pressure drop.

index = find(X(:,2)>0.65,1,’first’);

Volume = Vout(index); %PFR volume. [m3]

17

dP = -X(index,3); %Pressure drop in PFR. [Pa]

%--------------------------------------------------------------------------

Mw_poly=((2+3.*(((2.*kt)./(kd.*Cio.*(1-X(1)))).^0.5).*(Cmo-Cmo...

.*(1-X(2)))).*Mw_s.*1000);

%Viscosity

viscosity = exp(-13.04 + 2013/T + (Mw_poly)^0.18*(3.915*X(2)...

- 5.437*X(2)^2 + (0.623 + 1387/T)*X(2)^3));

function[dXdV]=rates(Vout,X)

%--------------------------------------------------------------------------

%This function computes the rates of change of the pressure and

%conversions as a function of PFR volume.

%Input:

%C: [Xi Xm P] - Conversions of initiator, monomer, and reactor pressure

%[Pa], respectively

%Output:

%dXdV: [dXidV dXmdV dPdV] - Rates

%--------------------------------------------------------------------------

%Define rate constants.

kd = 0.85e-5; %Rate constant of initiator dissociation. [s-1]

kp = 0.145; %Rate constant of monomer propagation. [m3.mol-1.s-1]

kt = 5.8e4; %Rate constant for termination. [m3.mol-1.s-1]

k = [kd kp kt];

%Define physical properties.

Rho_s = 909.3; %Density of styrene. [kg.m-3]

Mw_s = 104.15/1000; %Molecular weight of styrene. [kg.mol-1]

Cmo = Rho_s/Mw_s; %Initial concentration of styrene. [mol.m-3]

%Operating conditions.

m = 1000/(con*3600); %Mass flowrate. [kg.s-1]

T = 333; %Temperature. [K]

Cio = 10; %Initial concentration of initiator. [mol.m-3]

D = 0.1; %Diameter of PFR. [m]

Q = m/Rho_s; %Volumetric flowrate. [m3.s-1]

A = pi*D^2/4; %Cross-sectional area. [m2]

v = Q/A; %Superficial velocity. [m/s]

%--------------------------------------------------------------------------

18

%Rates:

dXdV = [k(1)*(1-X(1))/Q;

k(2)*(2*k(1)/k(3))^0.5*(1-X(1))^0.5*(1-X(2))*Cio^0.5/Q;

-0.158*(Rho_s^3*v^7*exp(-13.04 + 2013/T + (((2+3.*(((2.*kt)...

./(kd.*Cio.*(1-X(1)))).^0.5).*(Cmo-Cmo.*(1-X(2)))).*Mw_s))^0.18...

*(3.915*X(2) - 5.437*X(2)^2 + (0.623 + 1387/T)*X(2)^3))/D^5)^0.25/A];

%Kinetic chain length.

%nu = k(2)*Cmo*(1-X(2))/(2*(k(1)*k(3)*Cio*(1-X(1)))^0.5);

%Weight-average molecular weight. [g.mol-1]

Mw_poly=((2+3.*(((2.*kt)./(kd.*Cio.*(1-X(1)))).^0.5).*(Cmo-Cmo...

.*(1-X(2)))).*Mw_s.*1000);%g/mol

%Viscosity

viscosity = exp(-13.04 + 2013/T + (Mw_poly)^0.18*(3.915*X(2)...

- 5.437*X(2)^2 + (0.623 + 1387/T)*X(2)^3));

end

end

function[coni]=graphs_PFR(con)

V = [0 1000]; %.Volume. [m3]

%2) Define initial conditions.

Xio = 0; %Initial conversion of I.

Xmo = 0; %Initial conversion of M.

Po = 0; %Initial pressure. [Pa]

Xo = [Xio Xmo Po];

[Vout,X] = ode45(@ratess,V,Xo);

%--------------------------------------------------------------------------

%Plot solution:

figure

plot(Vout,X(:,1),’--’)

axis([V(1) V(2) 0 1])

xlabel(’Volume [m3]’)

ylabel(’Conversion’)

grid on

hold on

plot(Vout,X(:,2),’r’)

legend(’Initiator’,’Monomer’)

legend boxoff

19

figure

plot(Vout,X(:,1))

axis([V(1) V(2) 0 1])

xlabel(’Volume [m3]’)

ylabel(’Conversion of Initiator’)

grid on

hold on

scatter(165.3707,0.8137)

%

figure

plot(Vout,X(:,2),’r’)

axis([V(1) V(2) 0 1])

xlabel(’Volume [m3]’)

ylabel(’Conversion of Styrene’)

grid on

hold on

%scatter(165.3707,0.3652)

%

figure

plot(Vout,X(:,3),’g’)

xlabel(’Volume [m3]’)

ylabel(’Pressure [Pa]’)

grid on

hold on

scatter(165.3707,461242231.5214)

% %--------------------------------------------------------------------------

%Determine reactor volume and pressure drop.

index = find(X(:,2)>0.65,1,’first’);

Volume = Vout(index); %PFR volume. [m3]

dP = -X(index,3); %Pressure drop in PFR. [Pa]

%determine conversion of initiator

indexx = find(Vout>165.3707,1,’first’);

coni=X(indexx,1);

%--------------------------------------------------------------------------

Mw_poly=((2+3.*(((2.*kt)./(kd.*Cio.*(1-X(1)))).^0.5).*(Cmo-Cmo.*(1-X(2))))...

.*Mw_s.*1000);

%Viscosity

viscosity = exp(-13.04 + 2013/T + (Mw_poly)^0.18*(3.915*X(2) - 5.437...

20

*X(2)^2 + (0.623 + 1387/T)*X(2)^3));

function[dXdV]=ratess(Vout,X)

%--------------------------------------------------------------------------

%This function computes the rates of change of the pressure and

%conversions as a function of PFR volume.

%Input:

%C: [Xi Xm P] - Conversions of initiator, monomer, and reactor pressure

%[Pa], respectively

%Output:

%dXdV: [dXidV dXmdV dPdV] - Rates

%--------------------------------------------------------------------------

%Define rate constants.

kd = 0.85e-5; %Rate constant of initiator dissociation. [s-1]

kp = 0.145; %Rate constant of monomer propagation. [m3.mol-1.s-1]

kt = 5.8e4; %Rate constant for termination. [m3.mol-1.s-1]

k = [kd kp kt];

%Define physical properties.

Rho_s = 909.3; %Density of styrene. [kg.m-3]

Mw_s = 104.15/1000; %Molecular weight of styrene. [kg.mol-1]

Cmo = Rho_s/Mw_s; %Initial concentration of styrene. [mol.m-3]

%Operating conditions.

m = 1000/(con*3600); %Mass flowrate. [kg.s-1]

T = 333; %Temperature. [K]

Cio = 10; %Initial concentration of initiator. [mol.m-3]

D = 0.1; %Diameter of PFR. [m]

Q = m/Rho_s; %Volumetric flowrate. [m3.s-1]

A = pi*D^2/4; %Cross-sectional area. [m2]

v = Q/A; %Superficial velocity. [m/s]

%--------------------------------------------------------------------------

%Rates:

dXdV = [k(1)*(1-X(1))/Q;

k(2)*(2*k(1)/k(3))^0.5*(1-X(1))^0.5*(1-X(2))*Cio^0.5/Q;

-0.158*(Rho_s^3*v^7*exp(-13.04 + 2013/T + (((2+3.*(((2.*kt)./(kd.*Cio...

.*(1-X(1)))).^0.5).*(Cmo-Cmo.*(1-X(2)))).*Mw_s))^0.18*(3.915*X(2)...

- 5.437*X(2)^2 + (0.623 + 1387/T)*X(2)^3))/D^5)^0.25/A];

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%Kinetic chain length.

%nu = k(2)*Cmo*(1-X(2))/(2*(k(1)*k(3)*Cio*(1-X(1)))^0.5);

%Weight-average molecular weight. [g.mol-1]

Mw_poly=((2+3.*(((2.*kt)./(kd.*Cio.*(1-X(1)))).^0.5).*(Cmo-Cmo...

.*(1-X(2)))).*Mw_s.*1000);%g/mol

%Viscosity

viscosity = exp(-13.04 + 2013/T + (Mw_poly)^0.18*(3.915*X(2)...

- 5.437*X(2)^2 + (0.623 + 1387/T)*X(2)^3));

end

end

end

6 References

Radke, Clayton J., and Gabriel Sanoja. ”46. Polystyrene Production in a PFR.”CHM ENG 140 LEC 001 Fa13 Resources. BSpace, 18 Nov. 2013. Web. 25 Nov.2013.

Radke, Clayton J., and Gabriel Sanoja. ”53. Design of a Poly(styrene) Plant for Dif-fering Single-Pass Conversions.” CHM ENG 140 LEC 001 Fa13 Resources. BSpace,21 Nov. 2013. Web. 25 Nov. 2013.

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