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Continuous Stirred Tank Reactor (CSTR)

Category: Chemical Engineering

Demonstrates: Differential equations; Dynamic simulation

Problem Description

A chemical reaction A → B takes place in a continuous stirred tank reactor (CSTR). The reactor is heated by a heating jacket containing a fluid at a constant temperature.

Calculate the changes in concentration and temperature over time inside the reactor when the first-order reaction takes place. The reaction rate is defined by:

r = ke-E/RTC

where r is the reaction rate [mol/cm3.s]; T is the temperature [K]; and C is the concentration of the reactant in the liquid [mol/cm3]. The density of the reactant is assumed to be constant regardless of temperature. Other parameters and operating conditions are as follows:

Volume of reactorV = 2000 cm3
Feed rateF = 10 cm3/s
Rate constant of reactionk = 7.86 x 1012 l/s
Activation energyE = 22500 cal/mol
Gas constantE = 1.987 cal/mol.K
Density of reactantρ = 1 g/cm3
Specific heat of reactantCp = 1 cal/g.K
Heat of reactionΔH = -10000 cal/mol
Heat transfer coefficient * AreaUA = 1.356 cal/s.K
Temperature of heat transfer medium  Tw = 350 K
Temperature of feedT0 = 300 K
Concentration of feedC0 = 5.0 x 10-6 mol/cm3

The following equations will be used:

Material and Heat Balances:

V(dC/dt) = FC0 - FC - Vr
VρCp(dT/dt) = FρCp(T0 - T) + (-ΔH)Vr - UA(T - Tw)

Initial Conditions:

t = 0 : C = C0, T = T0

The EQUATRAN source text for this problem is:

/* Continuous Stirred Tank Reactor (CSTR) */


VAR V = 2000 "Volume of reactor [cm3]", ..
F = 10 "Feed rate [cm3/s]", ..
k = 7.86E12 "Rate constant of reaction [1/s]", ..
E = 22500 "Activation energy [cal/mol]", ..
ro = 1 "Density of reactant [g/cm3]", ..
cp = 1 "Specific heat of reactant [cal/g.K]", ..
dH = -10000 "Heat of reaction [cal/mol]", ..
UA = 1.356 "Heat transfer coefficient [cal/s.K]", ..
T "Temp. of reactant [K]", ..
Tw = 350 "Temp. of heat transfer medium [K]", ..
T0 = 300 "Temp. of feed [K]", ..
t "Time [s]", ..
C "Concentration [mol/cm3]", ..
C6 "Concentration [mol/cm3]x1000000", ..
r "Reaction rate [mol/m3.s]", ..
C0 = 5.0E-6 "Concentration of feed [mol/cm3]", ..
R = 1.987 "Gas constant [cal/mol.K]"

/* Reaction Rate */
r = k*EXP(-E/R/T)*C

/* Material Balance */
V*C' = F*C0-F*C-V*r

/* Heat Balance */
V*ro*cp*T' = F*ro*cp*(T0-T)-dH*V*r-UA*(T-Tw)

/* Initial Conditions */
C # C0
T # T0

C6 = C * 1E6
INTEGRAL t[0,1000] STEP 10
TREND T,C STEP 100
OUTPUT1 t,T,C6 STEP 10

Enter the lines above into a new source text window, then click the Run button. No further input is required, so the results will be displayed imediately.

/* Continuous Stirred Tank Reactor (CSTR) */                            
------------------------------------------------------------------------------
   t            T            C         
------------------------------------------------------------------------------
0            300.0000     5.00000e-006
100.00000    302.5880     4.85051e-006
200.0000     304.0551     4.72524e-006
300.0000     304.8869     4.62786e-006
400.0000     305.3584     4.55663e-006
500.0000     305.6257     4.50688e-006
600.0000     305.7773     4.47329e-006
700.0000     305.8632     4.45117e-006
800.0000     305.9119     4.43688e-006
900.0000     305.9395     4.42779e-006
1000.0000    305.9551     4.42207e-006

A graph can be displayed to show the variation in the reactor conditions over time. Click the Graph icon on the toolbar, select Time as the X value, Temperature as Y1 and Concentration as Y2, the click Ok.

CSTR graph

The EQUATRAN file for this example can be downloaded from the link below:

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