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This experiment involves the hydrolysis of a 4% solution of ethyl acetate, with an ion exchange resin acting as a catalyst. The feed solution is heated by circulating hot water in a stainless steel heat exchanger and then passes through a bed of catalyst beads. When a steady state has been reached the acetic acid in the reactor effluent is titrated with NaOH to determine the conversion. Runs made at several different feed rates and temperatures allow the activation energy of the reaction to be determined, and the possibility of diffusion control to be examined.

The apparatus includes two temperature indicator/controller units, either of which can be used to control the power to the water heater. The switch-selectable controlled temperature is that of the water leaving the water heater, or that of the reactor effluent. Thus the apparatus can also be used to study the transient behavior of a feedback control system as a function of the PID controller parameters, and also as a function of the variable delay corresponding to the choice of controlled variable and reactor feed rate.

(References refer to those listed at the end of the experiment description.)

You are employed by Dowpont Chemical Company as a chemical engineer in its Central Research Laboratory at Midlington, Michiware. The marketing group for ion exchange resins has become concerned that the only estimate of fluid-phase mass transfer that is available to technical customers who buy Dowpont resins is the old Wilke-Hougen (1) correlation, and they want, both as a service to customers and as a means of improving their technical image relative to their chief competitor, Rohm and Haas, to offer customers a modern-day check on pertinent fluid-phase transport. You have thus been commissioned by your CRL group leader, Dr. Ole Aginous, to use an 'easy' method of studying transport resistance in resin beds. To avoid the complexities of transient operation Aginous has proposed acid catalysis as the operation to study and you and he together have tentatively selected the chemical system and apparatus described here. A few runs are to be done to see if: (1) the system is indeed rate limited by fluid phase mass transfer (and not by intraparticle transfer or pore surface rate), (2) the system will be suitable - with or without modification - for an extensive study of fluid-phase transport, and (3) you can obtain, if possible, a preliminary check on the Wilke-Hougen correlation in both its original and modified form. If modifications to the equipment or chemical systems are required, suggest what form they should take. The report is primarily for Aginous, to help him plan further work, but if it is clear and professional he will pass it on to the Dowpont marketing group, enhancing your reputation in the company.

D. INTRODUCTION

The purpose of this experiment is to investigate the kinetics of the acid-catalyzed hydrolysis of ethyl acetate, using an immobilized anion ion-exchange resin as the catalyst. The temperature and flow rate dependence of the calculated reaction rate constant, and then the activation energy of the reaction, will be determined. The possible existence of transport effects will be examined.

The reaction to be studied is the liquid-phase hydrolysis of ethyl acetate (EtAC) to ethanol (EtOH) and acetic acid (HAc):

CH₃COOC₂H₅ + H₂O = CH₃COOH + C₂H₅OH

The catalyst is Rohm and Haas Amberlyst 15 ion exchange resin in the acid form. (The resin is put into acid form by contact with strong acid, e.g. 1 N HCl or H₂SO₄, and may be so regenerated.) The material used in this experiment is 20-50 mesh, 840 to 297 micrometer diameter, say 0.05 cm as an average. Presenting the catalyst in resin form, as a kind of insoluble acid, eliminates the need for subsequent neutralization or removal from the hydrolysate as would be required if a soluble acid were used, but requires that the ester be transported to, and the alcohol and acid be transported from, a phase boundary (the surface of the ion exchange resin). Thus it is possible that the rate at which the process proceeds will be limited by transport, reaction rate, or a combination of both. By appropriate variation of flow rates, concentrations, and temperature you are expected to quantify the factors affecting the reaction rate. Under the conditions of the experiment, the reaction may be treated as first order with respect to the ethyl acetate and as essentially irreversible (see below).

It is important to understand that the resin bed in this experiment functions as a true catalyst, no consumption of acid or net exchange of ions taking place. Thus, this fixed bed reaction operation can occur at steady-state and the "breakthrough curve" characteristic of an ion exchange separation process is not encountered.

Let the reaction be

A = B + D, rate = kC

with A = ethyl acetate (EtAc), B = acetic acid (HAc), D = ethanol (EtOH). Let C be the EtAc concentration, V be the running volume (we neglect volume occupied by the catalyst in defining the volume) of a plug flow reactor of total volume V_F, and let Q be the volumetric flow rate. Assuming first-order reaction, the steady state reactor equation is

dC/dV = -(1/Q)kC, C(0) = C₀

for

0 <= V <= V_F

and with k the reaction rate constant, assumed to be a function of temperature T (Kelvin) only.

This linear equation is easily integrated to give

C(V_F) = C₀exp(-kV_F/Q)

where V_F is the total volume of the reactor. From the stoichiometry we have

C_F = C(V_F) = C₀ - C_B

where C_B is the effluent concentration of acetic acid (gmol/cm³), determined by titration. The feed concentration C₀ is found from the fact that the feed is made up by diluting 400 cm³ of EtAc (MW = 88.11) to 10 L with distilled water. The density of EtAc is 0.895 gm/cm³ at 25 C. The feed solution is thus 0.406 M.

From the integrated equation we have

kV_F/Q = ln(C₀/C_F)

or

k = (Q/V_F)ln(C₀/C_F)

If k follows an Arrhenius dependence on absolute temperature T (K), namely

k(T) = b₁exp(-E/RT)

where E is the activation energy, R is the gas constant, and b₁ is a parameter, then a plot of ln(k) vs. 1/T will be a straight line with slope -E/R. Note that, if Q is held constant while T is varied, a plot of ln(kV_F/Q) vs. 1/T will also have slope -E/R.

F. APPARATUS

Inspect the apparatus and prepare a schematic diagram, asking the assistant for help if necessary.

The reactor consists of a 3.7 cm ID, 53 cm long borosilicate tube surrounded by a water jacket. The catalyst section is supported by a 60 mesh stainless steel screen in a stainless ring at each end. The catalyst is packed to a depth of about 36 cm. The entrance and exit sections of the reactor are packed with glass beads to reduce dead volume and flow maldistribution. Flow through the jacket and the reactor is upward, in order to remove any air or vapor bubbles. A 1/16" stainless jacketed copper-constantan thermocouple is located in the reactor effluent, and is connected to a temperature indicator/controller.

The feed is supplied to the reactor from a 20 L tank by a magnetic-drive centrifugal pump. The feed consists of a mixture of absolute ethyl acetate in distilled water, 400 ml of EtAc diluted to 10 L. (EtAc MW = 88.11, density = 0.895 gm/ml)

To obtain isothermal operation of the reactor at any desired temperature, the feed is preheated in a small stainless steel heat exchanger (1 ft² area) and the reactor is jacketed. A magnetic-drive centrifugal pump circulates water from a 10 L electrically heated (1350 W) vessel through the heat exchanger and the jacket in parallel. A ball valve, normally open, may be used to control the hot water flow to the heat exchanger. The input to the active controller is normally a 1/16 inch stainless steel jacketed copper-constantan thermocouple mounted in the reactor effluent line. When the controller parameters have been properly tuned, the controller will hold the reactor effluent temperature to within 0.2 C of the set point.

A second indicator/controller has as input transducer a thermocouple mounted in the outlet line of the water heater, and a switch on the control box allows either thermocouple to be used as the controlled variable. Because the lags associated with flow through the heat exchanger and the reactor, and with the thermal capacitance of these units, control of the hot water temperature may be less susceptible to oscillation than control of the reactor effluent temperature.

A rotameter is used to monitor the feed flow rate. Either the rotameter may be calibrated initially, or the flow rate for each run can be measured by collecting a known volume (50 to 100 ml) for a measured time, in which case the rotameter is used only to assure constancy of flow during the run. The valve on the rotameter should be set wide open, and the valve downstream of the reactor should be used to set the flow rate. This maintains maximum pressure on the reactor, and reduces the possibility that ethyl acetate will vaporize at the higher temperatures.

Equipment for titrating the product stream samples includes a 50 ml burette, phenolphthalein indicator, and 0.1 N NaOH titrating solution. Typically a 50 ml sample is collected in an Erlenmeyer flask, a few drops of phenolphthalein dissolved in ethanol is added, and the sample is titrated to a phenolphthalein end point using 1.0 or 0.1 N NaOH.

Do runs at several, typically three, flow rates at roughly 30 C, then increase the reactor temperature to about 40 C and again make three runs, and then repeat at about 50 C. For each flow rate, allow a few reactor volumes of feed to pass through the reactor and then titrate a sample of product. Continue to titrate samples until the concentration of acetic acid is approximately constant. Note that at the highest temperature some of the EtAc may vaporize in the heat exchanger or catalyst bed. Look for and record the presence of bubbles in the bed.

Use for each temperature three flow rates, roughly 40, 80, and 160 ml/min. Thus 9 runs in total are required.

The first goal of the data analysis is to calculate the reaction rate constant k for each run. For runs at the same temperature, k will be plotted as a function of flow rate Q. Then, for runs at the same flow rate Q, a plot of ln(k) vs. 1/T will be examined and the activation energy will be determined from the slope of the plot, if the data lie close to a straight line.

If the activation energy is independent of flow rate, the implication is that the reaction is not diffusion controlled. If, however, the activation energy is lower at low flow rates, the implication is that the reaction is diffusion controlled. This argument is based on the assumption that the activation energy for diffusion is expected to be lower than that for the reaction itself. Increasing flow shifts the "apparent" activation energy from one characteristic of diffusion to one characteristic of reaction.

We may also plot k vs. Q at constant T. If k does not depend on Q the reaction is not diffusion controlled. If k increases with Q we have evidence for diffusion control. We might expect diffusion control to be more apparent at higher temperatures because, again referring to activation energies, reaction rates increase more rapidly with temperature than do diffusion rates.

It is possible to see if the reaction rate is controlled by diffusion through the fluid film at the particle interface. We will calculate the concentration gradient needed to transfer EtAc at the observed reaction rate across the fluid film, and compare this to the maximum concentration gradient available, namely the average of the inlet and outlet concentrations of EtAc. If the required gradient is relatively small, then the fluid film resistance is not controlling.

Finally, if the reaction is fully diffusion-controlled, the EtAc concentration in the catalyst pores is essentially zero, and the reaction rate constant k will be equal to the overall mass transfer coefficient per unit volume k _f a _p . As shown below, k _f a _p can be calculated from the modified Wilke-Hougen correlation (1).

If r is large, the fluid film resistance is controlling. Conversely, if r is small, the concentration gradient across the film is small and the reaction is controlled by the kinetics of diffusion and reaction in the catalyst pores.

As an alternate procedure, compare the calculated reaction rate constant k with the overall mass transfer coefficient k _f a _p from the Wilke-Hougen correlation. If they are roughly equal, we have evidence for diffusion control. If k is less than k _f a _p , we have evidence for reaction control.

The analyses suggested above fail to address one situation that you could encounter: strong evidence of diffusional control external to the particles, based on the sensitivity of k to flowrate, but the mass transfer coefficient calculated from Wilke-Hougen is too high to fit the data, indicating that some other step in the process must be controlling. But what other step, external to the particles, can control? Note that Wilke-Hougen gives a coefficient that is inversely proportional to d _p ^1.5. If the bed is channeling, the effective particle size may be equivalent to clumps of particles and the apparent discrepancy could be explained by the need to use an effective particle size larger than 0.5 mm.

 I. REPORT (in the context of the scenario)

Re-read the scenario and be sure that your report emphasizes the central problem the work was to address.

From the feed and effluent concentrations for each run, determine the apparent rate constant k for each flow-temperature combination. For a fixed temperature, plot the rate constant as a function of volumetric flow rate Q (cm³/s). If k does not depend on Q, you have strong evidence that the process is not diffusion controlled. If k increases with Q, the converse is true.

 For a fixed flow, plot ln(k) as a function of (1/T). The slope of the line (if the line is straight) is -E/R, where E is the activation energy. (In general the activation energy for a chemical reaction is greater than E for a diffusion-controlled process.) Calculate the apparent activation energy.

Discuss how calculated quantities (from both experiment and theory) may be uncertain because of uncertainties in the quantities from which they were calculated. (For example, are departures from linearity in the ln(k) vs. (1/T) plot significant, and how reproducible are the effluent concentration values?)

 J. REFERENCES

1. Perry, R.H. and C.H. Chilton, "Chemical Engineers' Handbook,

5th Ed." McGraw-Hill, New York (1973), Section 16-20.

2. Anon., Dowex: "Ion Exchange," Dow Chemical Co., Midland, Mich. (1958) esp. sec. 3, pp. 12-18, and p. 69.

3. Kunin, R. "Ion Exchange Resins 2nd ed." Wiley, New York, (1958) esp. Ch. 12, Catalysis with Ion Exchange Resins.

4. "Encyclopedia of Polymer Technology," Ion Exchange Polymers.