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Chemical and Biomedical Engineering Department USF page 1 of 4

Study in Startup Dynamics of a Continuous Stirred Tank Reactor (CSTR)

BackgroundA type of reactor commonly used in industrial processing is the stirred tank operated

continuously. It is usually referred to as the continuous-stirred tank reactor (CSTR) or

backmix reactor, and is used primarily for liquid phase reactions. More specifically,continuous stirred tanks are used for relatively slow reactions of liquids and slurries. Itsnormal operation is at steady stateand its assumed to be perfectly mixed.

Consequently, there is no time dependence or position dependence of the temperature, the

concentration, or the reaction rate inside the CSTR. In other words, the concentrationand temperature is the same at every point inside the reactor. Therefore, the temperature

and concentration in the exit stream are modeled as being the same as those inside the

reactor. This is an extremely helpful and important point because otherwise, in systems

where mixing is not ideal, we would not know the concentration of the exit stream usinga well-mixed model and would have to resort to other methods, such as residence-time

distributions to obtain meaningful results. (Fogler) Ideally, stirred tank reactors run most

efficiently when the liquid level is equal to the tank diameter, although at higherpressures slimmer diameters are more economical and would decrease residence times.

The residence time along with space velocity and product distribution are usually found

from a pilot plant. Also, the CSTR can either be used by itself or, as part of a series or

battery of CSTRs. A battery of four or five in series is often used. It is also important tonote that the mixer power input to a homogeneous reaction stirred tank is usually 0.1-0.3

kW/m^3, but three times this amount when heat is to be transferred.

There are many other types of reactors currently used in industry, such as batch reactors,

semibatch reactors, tubular reactors, and fluidized-bed reactors. The choice of reactor

will depend upon a number of factors, such as the rate of reaction and the desired

conditions in which the reaction must take place. Batch reactions are conducted in stirredtanks where the reagents are added batch-wise. They are used mostly for small daily

production rates, when the reaction times are long, or when some condition such as feed

rate or temperature must be programmed in some way. In addition, the batch reactor hasthe disadvantages of high labor costs per batch and the difficulty of large-scale

production.

Semibatch reactors have essentially the same disadvantages as batch reactors, but they

have the advantages of good temperature control and the capability of minimizing

unwanted side reactions through the maintenance of a low concentration of one of the

reactants. These reactors are used for two-phase reactions in which a gas is typicallybubbled continuously through a liquid.

Tubular flow reactors, mainly plug-flow reactors (PFR) and packed-bed reactors (PBR),

are suited to high production rates at short residence times (sec. or min.) and whensubstantial heat transfer is needed. They are relatively easy to maintain and they usually

produce the highest conversion per reactor volume of any of the flow reactors, but the

temperature within the reactor is difficult to control and hot spots can occur when thereaction is exothermic. It is important to remember that depending upon the conditions in

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which the reaction is taking place, one reactor may or may not be more suitable than

another. Note that sometimes in certain situations tubular flow reactors are no better than

CSTRs. For example, in catalyst packed reactors, the residence time distribution is often

as good as that of a five-stage CSTR battery. Also, for conversion under about 95% ofequilibrium, the performance of a five-stage CSTR battery approaches plug flow.

The fluidized-bed reactor is analogous to the CSTR in that its contents, thoughheterogeneous, are well mixed, resulting in an even temperature distribution throughoutthe bed. Although, the fluidized-bed reactor cannot be modeled as either a CSTR or a

tubular reactor (PFR or PBR) therefore requiring a model of its own. The fluidized-bed

is a catalytic reactor that can handle large amounts of feed and solids and has goodtemperature control; consequently, it is used in a large number of applications. The

catalyst particles used in fluidized beds are 0.1 mm in diameter. For the purpose of

comparison, the dimensions of the catalyst particles used in slurry and fixed beds are 1

mm and 2-5 mm in diameter respectively.

For the case of this experiment, consider the following saponification reaction (Ethyl

Acetate reacting with Sodium Hydroxide to form Sodium Acetate):

CH3COOC2H5(aq) + Na+OH

-(aq) CH3CH2OH (aq) + CH3COO

-Na

+(aq)

This reaction is first order with respect to both sodium hydroxide and ethyl acetate i.e.second order overall. The reaction carried out in the CSTR will eventually reach steady

state. The steady state conditions vary with the concentration of the reagents, flow rates,

volume of the reactor, and temperature of the reaction. This reaction has been reported1.

to have an activation energy of 39,900 J/mol and a pre-exponential factor of 1.05 x 10

6

L/mol sec.

1. Mendes, A.M.; Madeira, L.M.; Magalhaes, D.; Sousa, J.M.,An Integrated Chemical Engineering Lab

Experiment, Chem Eng Education 38, 168 (2004)

Information on Sensor Used

The progress of this reaction can be observed by monitoring the conductivity of the

reaction mixture as a function of time with a conductivity probe (F igure 1). The probesfunction is to measure the conductivity, i.e. the ability of the solution to conduct an

electrical current between two electrodes (F igure 2). Through the help ofLogger Pro

this electrical current can be measured. (Verni er manual , www.vern ier.com)

Conductivity is measured in units or Siemens (S) ( historically mhos ohms-1

)and can be

written in terms of resistance and the cell constant:

(conductivity, S) k = K/Rwhere K = cell constant (cm

-1)

R = resistance (ohms)

The cell constant (K) is written in terms of area and distance: (cell constant) K = d/Awhere A = area of the electrode surface

d = distance between the two electrode

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--------1 cm---------

--------1cm---------

F igure 1Conductivity Probe Figure 2electrode plates on the probe

It is important to note that typically there is much variation in the instrumentation used to

measure conductivity, but for the case of this experiment, the Vernier Conductivity Probewill be used. Also, conductivity tests are not indicative of the types of ions presentonly

the amounts.

Note: The conductivity sensor has a switch to select the range of conductivities beingmeasured. Please make sure an appropriate range is selected before you begin

the CSTR run.

The electrical conductivity of the system is present due to the ions that form from thereactant, sodium hydroxide (NaOH), and the product, sodium acetate (NaOCOCH3).

Initially, only NaOH contributes to the electrical conductivity, but as the reaction

proceeds, both NaOH and NaOCOCH3will contribute. Therefore, conductivity can beused to provide a measure of conversion. However, we must calibrate the sensor to relate

the conductivity to the relative amounts of both species present.

Theory

Figure 2typical depiction of stirred tank reactor

First note that because of the overflow out, the volume of the tank remains constant.

Also we can neglect the effect of concentration on density at these dilute conditions and

so the flow out is the sum of the two flows in. Let us define the following variables:

E-1

Fj0moles/hr

Fjmoles/hr

Njmoles

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0

0

( 2 ) / ; ( 0)

( 2 ) / ; ( 0)

A

Ai A A B A A

B

Bi B A B B B

dCFC FC VkC C V C t C

dt

dCFC FC VkC C V C t C

dt

02 2

AAAi

VkCFCFC

V = volume of the CSTR, in m3

F= inlet flow rate of the stream containing A m3/hr = inlet flow rate of stream containing

B

Fout=flow rate of the outlet stream = 2*F, since reactor volume is constantCAi=concentration of A = NaOH in the inlet stream, mole/m

3

CBi=concentration of B = NaAc in the inlet streamCA=concentration of A in the outlet streamCB=concentration of B in the outlet stream

Reaction rate= -kCACB moles/m3/hr, assumed to be first order with respect to A and B.

When the general mole balance equation is written for A and B we get

Accumulation of A= Input of A - Output of AConsumption of A due to reaction

Accumulation of B=Input of BOutput of B - Consumption of B due to reaction

Now since V is constant we can take it out of the differential and get two differentialequations to follow the changes (dynamics) in concentration of both species. The initial

conditions are;

(1)

(2)

Note that, by stoichiometry, the concentrations of the products sodium acetate (C) andethanol (D) will be equal (CC= CD). Note also that since both feed streams and the initial

reactor charge have the same 0.01 M concentration, CA+ CB+ CC+ CD= 0.01 at alltimes.

For steady state, the time derivatives in equations (1) and (2) are zero and:

(3) and (4)

Since we will use equal concentration of CAand CBin the inlet stream, the concentrationin the outlet will also be equal at steady state, since according to the reaction

stoichiometry one mole of A reacts with one mole of B. Hence CAi=CBiand CA=CB. Forthis particular case, equations

(3) and (4) become identical: (steady state) (5)

Our goal; Obtain the rate constant k by fitting equations (1) and (2) to the experimental

data and then obtain the steady state concentration of NaOH from equation (5).

2

2

A

Ai A A B

B

Bi B A B

dVCFC FC VkC C

dt

dVCFC FC VkC C

dt

2 0

2 0

Ai A A B

Bi B A B

FC FC VkC C

FC FC VkC C

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