The University of Texas at Austin
College of Engineering

CSTR

In this module we will explore how to solve problems for a single steady state CSTR involving multiple reactions. We will also explore how closely one can approach the performance of a PFR with a finite number of identical CSTRs in series.

The design Equation for a CSTR

is written for each component, where

When Q = Qf, the set of algebraic equations is solved for cj. If all the reactions are first-order, the set of equations will be linear and you should seek an analytical solution to the problem. This example will involve a set of first order reactions that will lead to a set of linear equations for the set of material balances. Therefore it will be possible to sort these balances to give a set of equations that can be represented by

Ac=cf

THE PROBLEM STATEMENT

The liquifaction of coal in a slurry reactor can be described by the following sequence.

k1 = 0.012 min-1

k2 = 0.046 min-1

k3 = 0.020 min-1 ; k-3 = 0.034 min-1

k4 = 0.040 min-1

where the values for the rate constants are those at 400 ºC. Coal particles less than 200 mesh are dissolved in a high temperature oil (250 ºC) saturated with hydrogen. This system can be modeled as a homogeneous reaction. All reactions are first order in the concentration of the hydrogen reactant.

THE QUESTIONS

  1. Develop the set of algebraic equations that will permit you to determine the concentration of coal, preasphaltines, asphaltines, and oil in the effluent of a 3 m3 CSTR operating at 400 ºC. The entering concentration of coal is 2 kmole/m3 and the volumetric feed rate is 0.01m3/min. Check your answer for the matrix A against the program when C, P, A, and O are designated as components 1, 2, 3, and 4, respectively.

    2.  

  2. A single 3 m3 CSTR has an effluent concentration for coal of 0.109 and for oils of 1.524 kmole/m3. The effluent concentration for a 3 m3 PFR with the same initial conditions gives the tabulated results. Notice how different concentrations are for the two cases. Can you explain why the two cases are so different?

    3. Component

    Concentration (kmole/m3)

    Coal

    0.000

    Preasphaltines

    0.075

    Asphaltines

    0.023

    Oils

    1.902
  3. Now run the simulation program to examine the effect of operating CSTRs-in-series on the final effluent concentration. The program plots the effluent concentration from each CSTR so you can compare the cumulative effect of operation in series with the total volume fixed at 3 m3 to the result in the 3 m3 PFR. Notice how close you approach the PFR performance as the number in series increases. Can you explain why this happens?
  1. How many CSTRs come within 10% of the final effluent concentration of oils for the PFR?
  2. How many CSTRs come within 5% of the final effluent concentration of oils for the PFR?
  3. How many CSTRs come within 5% of the final effluent concentration of oils for the PFR?