  # 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 reactor V = 2000 cm3 Feed rate F = 10 cm3/s Rate constant of reaction k = 7.86 x 1012 l/s Activation energy E = 22500 cal/mol Gas constant E = 1.987 cal/mol.K Density of reactant ρ = 1 g/cm3 Specific heat of reactant Cp = 1 cal/g.K Heat of reaction ΔH = -10000 cal/mol Heat transfer coefficient * Area UA = 1.356 cal/s.K Temperature of heat transfer medium Tw = 350 K Temperature of feed T0 = 300 K Concentration of feed C0 = 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. 