KINETICS EXPERIMENT

Background

This experiment illustrates a typical process development activity.  A chemical reaction has been studied in glassware and batch reaction data have been gathered.  The next step is to develop a bench-scale, continuous flow reactor as a prototype of subsequent pilot scale, semi-works, or commercial-scale reactors.  The prototype reactor has already been build and its flow diagram is attached as Figure 1.  Unfortunately, personnel changes have occurred, and the design basis for the prototype reactor has been lost.  Your job, as the chemical engineering group currently associated with this project is fourfold:

1. To analyze the batch kinetic data and to construct a kinetic model of the process.

2. To use the model to define suitable operating conditions for the prototype reactor to achieve 70% conversion of dye under laminar flow conditions.

3. To run the prototype reactor to obtain data on conversion versus mean residence time at one or more operating temperatures.

4. To analyze the prototype reactor data, to describe the reactor's performance relative to various standard reactor models, and to make recommendations for scaleup.

Your results should be given in a single, comprehensive report covering each of the above points.  Additional requirements and details on the various points are given in the following sections.

Batch Reaction Data

The reaction studied is the hydrolysis of crystal violet dye with an excess of sodium hydroxide in dilute aqueous solution.  The reaction is

 (C6H4N (CH3)2)3 CCl + NaOH  ® (C6H4N (CH3)2)3 COH + NaCl

Table I gives calibration data for the absorbance at 590 nm as a function of dye concentration.  (The spectrophotometer used for these measurements is different than those installed on the prototype reactor.)  Table II gives kinetic data for batch experiments at one initial dye concentration, two initial NaOH concentrations, and at three different temperatures.  These data should be used to fit a kinetic model.  A commonly used model for irreversible reactions of the form A + B ® Products is

 Rate = ko[exp(-DE/RT)] [A]n [B]m

 where ko, DE, n and m are fitted parameters.  It is desirable that n and m be chosen as integers whenever the data can be reasonably well fit by integral values.  See Chapter 7 in the new CRUD book.  Some of the preliminary work has already been done in Problem 7.4.
 

Definition of Operating Conditions


The prototype reactor consists of a helically coiled tube 10 m long and 3/8 inch in diameter.  It is placed in a water bath for temperature control.  You must pick flow rates, reactant concentrations and operating temperatures suitable for use in the prototype reactor.  Pick the same inlet dye concentration as used in the batch experiments.  Use an NaOH concentration and temperature within the range of the experimental data.  Otherwise, the model you have fit may not apply.  Estimate ?HR for the reaction. Then calculate the adiabatic ?T for the reaction to confirm that the reaction will be isothermal.

Two additional constraints should be imposed to ensure a reasonably simply analysis and scaleup.  The flow regime should be laminar, i.e., Re < 2000.  Also, the range of dye conversions should span 70% from both sides so that interpolation rather than extrapolation can be used.

To meet the additional constraints, you must calculate both Re and conversion as a function of mean residence time, ?.  The calculation of Re is straightforward.  That for conversion is more complicated since you do not know exactly how the prototype reactor will behave.  However, you do know that its performance will lie somewhere between those of a piston flow reactor and a CSTR (perfect mixer) with the same value of ?.  Also, in the analysis that will finally be required, two other reactor models should be considered.  These are a diffusion-free, laminar flow reactor and a laminar flow reactor with (radial) molecular diffusion.  Both of these laminar flow reactors assume a straight tube while the prototype reactor is coiled into a helix.  However, they should certainly provide a closer bound on performance than the CSTR.

Prototype Operation

You must make solutions of dye and NaOH sufficient to run the experiments. The spectrophototometers must be calibrated using the initial dye concentration as one point and the NaOH solution as the other point.  The piping allows these solutions to be pumped through the instruments while bypassing the reactor.  Be careful to use a low flow rate when the NaOH is pumped through the instruments.  The flow meters on the dye and NaOH solutions must also be calibrated.

Preheat the NaOH and the reactor water bath prior to initiating flow.  Then run long enough to achieve a good steady-state.  This will require 3 to 5 mean residence times, but the important thing is that the spectrophotometer concentrations become constant.  Run enough flow rates and adjust them as necessary to span the desired 70% conversion.  You will want to collect and weigh effluent samples to confirm the flow rates.

Analysis and Scaleup

If all has gone well, your experimental measurements should show that the prototype reactor performs less well than a piston flow reactor but better than laminar flow in a straight tube with or without diffusion.  At least that was the concept as conceived by the (now departed) design engineer.  Centrifugal forces due to the coiling induce a secondary flow that promotes radial mixing which gives a closer approach to piston flow than would be expected for a straight tube.  Analyze your experimental results in light of these expectations.  Then give a recommendation for scaleup to a flow rate of 250 kg/min.  This is roughly 1000 times more output than the pilot reactor. Should the large reactor consist of 1000 helically coiled tubes in parallel?  A reasonable design might be a single, larger diameter coiled tube or several straight tubes in parallel (as in a shell-and-tube heat exchanger).  Note, however, that radial mixing due to diffusion will decrease as tube diameter increases.  This will decrease conversion at the same ?.  Your recommendation must account for the decrease.

To understand the pilot scale reactor, you must be able to calculate the conversion in a straight-tube, laminar flow reactor with radial diffusion.  The best approach to doing this is to solve the governing partial differential equation.  It is sometimes possible to apply the axial dispersion model to a laminar flow reactor, but the reactor must be quite long for this to work.  Yours may not be long enough.

To perform the scaleup, you must consider heat generation since this may impose a limit on the tube diameter.  The temperature at every point in the reactor must remain within the limits of our laboratory results 30-45oC.  The inlet NaOH concentration for the full-scale reactor should be 0.04 moles/l.  You should consider whether or not it is necessary that the full-scale reactor operates in laminar flow.

Report Format

In preparing your final report, please observe the following guidelines.

Your report should be an intelligent presentation of your work in a format appropriate for presentation, say, by a pilot plant team to a supervisor.  SI units should be used.  Repetition of knowledge available in texts or references is generally not required.  However, reference to this information and presentation of the basic equations that you use are necessary.  When you finish your report, read it at least one more time.  Note that language and neatness of the report affect your grade considerably.

Complete documentation is required for an excellent report.  The reader must be able to reproduce all of your calculated results using the sample calculations as a guide.  For a computer program, you must submit a listing as well as input/output information, a flowsheet of the calculations and other explanatory material to assist the reader in understanding your work.

References

The primary source needed for the analysis is any good text on chemical reactor design.  The following reference may be useful to understand laminar flow in a straight tube with diffusion:

Cleland, F.A. and Wilhelm, R.H., "Diffusion and Reaction in a Viscous-flow
 Tubular Reactor," AIChE J., 2, 489 (1956).

Indeed, the calculations you need may already have been done in this paper, but you will have to figure out the notation and how the authors present their data.

See also Chapter 8 in the new CRUD book.

Chapter 9 in the same book discuss the axial dispersion model.  This model is simple but, unfortunately, it is applicable to laminar flow reactors only if they are quite long.

The secondary flows induced by coiling are discussed in

Nauman, E.B., "The Residence Time Distribution for Laminar Flow in Helically Coiled Tubes", Chem. Eng. Sci., 32, 287 (1977).

Note, however, that this paper ignores the (beneficial) effects of molecular diffusion.

 Tables

 TABLE I

CALIBRATION  DATA  FOR  SPECTROPHOTOMETER

Adsorbance, A 0 0.112 0.231 0.381 0.499 0.638 0.980 1.305
at 590 nm

ml of 7.72x10-5 M stock 0   2   4   6   8   10   15   20
dye solution diluted to
100 ml with deionized
water
 
 
 
 

TABLE II

KINETIC  DATA  FROM  HYDROLYSIS  OF  DYE  WITH  NaOH  IN  BATCH REACTOR
 

 RUN B1 B2 B3 B4

 Initial concentration 0.02 0.04 0.04 0.04
 of NaOH (after mixing
 with dye) moles/l

 Temperature, °C 30.0 30.0 38.0 45.0
 
  Time   A Time   A Time   A Time   A
  Min  Min  Min  Min

  0.0 0.88 0.0 0.88 0 0.88 0 0.88
  2.0 0.511 3.0 0.17 0.5 0.618 0.5 0.566
  4.0 0.300 3.6 0.12 1.0 0.434 1.0 0.364
  5.0 0.226 4.5 0.07 2.0 0.214 2.0 0.151
  6.0 0.172 6.0 0.03 3.0 0.105 3.0 0.062