$$\rightleftharpoonup{xx}$$
$$\longleftharp{xx}$$,
$$\longrightharp{xx}$$,
Chemical reactions are carried out in various types of reactors using catalysts in order to increase reaction rate and improve conversion. Reaction rate is temperature dependent thus it is strongly influenced by heat transfer. Additionally, reaction rate is effected by mass transfer since a reaction cannot take place faster than the rate at which reactants are supplied to the catalyst surface. Therefore, packed bed reactors are often preferred over batch reactors as rapid heat transfer is more feasible. In this video, the kinetics of a simple reaction in a packed bed reactor is analyzed. The reactor is operated at different conditions in order to determine the real reaction order and a parent rate constant, as the kinetics of real systems often deviate from what is expected.
Packed bed reactors can be modeled as a series of many equally sized CSTRs who's total volume and catalyst weight matches that of the packed bed reactor. This model is called the tanks-in-series model and is given by this equation. Here, i is the reactor number, CA0 is the feed concentration of the limiting reactant, and delta FAI is the change in fractional conversion of the limiting reactant. Finally, RAI is the rate of reaction, N is the number of tanks needed, and Tao is residence time. The forward rate for a catalytic reaction is almost always first order with respect to catalyst concentration and some positive order less than two with respect to reactant concentration. However, catalyst inhibition may alter reaction order, causing the reaction order to appear less than it actually is. Even reactants can inhibit the catalyst causing the reaction order to appear close to zero. For these reasons, catalytic reactions are described by the power law model where K prime is the apparent rate constant, CA is the concentration of the limiting reactant, and beta is the apparent reaction order. The model presupposes that catalyst concentration is constant. However, in practice, catalysts deactivate. Thus catalyst concentration should be modeled as a function of time. In the following demonstration, the kinetics of a typical reaction with a solid catalyst and liquid phase reactants and products is demonstrated. The reaction involves the breakdown of sucrose into glucose and fructose called sucrose inversion. The reaction is typically first order with respect to sucrose and with respect to catalyst sites. The rate constant is effected by heat and mass transfer, flow distribution, temperature, and catalyst activation. Thus the rate constant is determined experimentally for the specific system. Now that we have discussed the tanks-in-series model and how to deduce the reaction kinetics, let's take a look at the procedure itself.
Before you start, familiarize yourself with the apparatus. Select Perm from the unit item on the menu to access the permeameter schematic. In this experiment, the unit is operated using a distributed control system. Only bed number one, the organics tank, pump, and T505 temperature controller are used. By selecting Trend 50, all the data, the key process variables with respect to time can be obtained and collected into a spreadsheet. Now, open the inlet and exit valves to catalytic reactor bed number one. Make sure that the inlet and exit values to the other beds are closed as well as the control valve F531 and the on/off valve D531 on the city water supply.
Add dilute acid to the two liter tank. Turn on the feed pump to a constant speed and set the rotameter to obtain a desired flow of 40 to 70 milliliters per minute. Increase the speed of the feed pump if the rotameter cannot reach this range of flow. Feed the acid and then approximately 200 milliliters of deionized water to regenerate the catalyst by exchanging the cations such as sodium or calcium which are interacting with sulfonic acid anions. Next, prepare the sucrose feed solution and add one liter to the organics tank. Turn on the pump. Use the speed controller of the pump and the rotameter to adjust the speed flow as desired. Set the T505 temperature controller to auto and select a set point of 50 degrees Celsius. When the system has reached 50 degrees, move the set point to the final temperature of 60 degrees where the reaction is typically carried out.
First, use a test tube to collect at least 25 milliliters of the initial feed to have a sucrose sample before the reaction has started. Then wait until two bed residence times have passed and collect two sets of 25 milliliter samples at the drain which are 10 minutes apart. These samples will be analyzed using a polarimeter. To begin reactor shutdown, set T505 to zero output. Once the temperature begins to drop, shut off the reactor and then close the block valves on bed one. Now use a polarimeter to analyze the samples. A polarimeter is used because carbohydrates are enantiomers and rotate polarized light to a certain degree. Sucrose rotates the light to the right while the solution of glucose and fructose will rotate it to the left giving negative values. Turn on the sodium lamp and wait until a yellow light is seen. A uniform dark field is visible at the zero position of the dial. Transfer 25 milliliters of the reaction sample to the tube and place it into the polarimeter with the bulb near the eye piece facing up and then close the cover. Dark and light fringes can be observed through the lens if the reaction sample rotates polarized light. Rotate the dial until the fringes disappear and reveal a uniform dark field. Adjust the focus with the black dial and using the Vernier scale, read the rotation angle through the magnifying glass to determine the fraction conversion of sucrose.
Now let's take a look at the rate constant determination using the fractional conversion of sucrose in a packed bed reactor. The specific rotation D of each sugar can be found in the literature and is correlated to the measured rotation and the concentration. Concentration is then used to determine fractional conversion. This data is shown here, plotted against the degree of rotation. The higher the concentration of sucrose, the higher the positive degree of rotation. As the reaction progresses and sucrose is converted to glucose and fructose, the positive degree of rotation diminishes. Now let's take a look at the reaction kinetics of sucrose inversion at 60 degrees Celsius. Calculate the pseudo first order constant K prime for each feed concentration, which ignores the first order dependents of the catalyst. Then account for the first order dependence of the catalyst by dividing the pseudo first order rate constant by the concentration of the catalyst to give the second order rate constant K two. To determine the real reaction order for the data acquired, start with the generalized mole balance of the packed bed reactor with respect to catalyst weight W. Then determine the equations for each reaction order. Fit these equations to the data using a non-linear regression and determine the sum of squared errors to evaluate the fit. Now fit the data to the tanks-in-series model for the first order reaction and determine the number of tanks needed. A small number of tanks is calculated suggesting that the reaction deviates from ideal packed bed reactor behavior. This is most likely attributed to axial mixing and temperature fluctuations within the reactor. Finally, we can compare the reaction behavior of various kinetic orders, including first and second order packed bed reactor models with first and second order tanks-in-series models consisting of two tanks. It is clear that the fractional conversion for the first order packed bed reactor model more closely represents the observed behavior as matched to the known data point for 15 weight percent sucrose.
Solid catalysts are used in a wide range of applications and reactor setups as they are one of the most important fields in modern technology. A fluidized bed reactor utilizes solid catalyst suspended in fluid. The fluid, usually gas or liquid, is passed through solid catalyst particles at high enough velocities to suspend them and make them behave like a fluid. These types of reactors can be used for many different applications, one of which is the pyrolysis of lignocellulosic biomass. In this process, the thermal decomposition of biomass occurs resulting in oxygenated bio oils. Catalyst performance varies depending on operating conditions, which can be measured using a temperature programmed reaction. A temperature programmed reaction involves the steady increase of reaction temperature with the continuous monitoring of reactor effluent. Performance is then correlated to temperature enabling the determination of optimum operating temperature.
You've just watched Jove's introduction to packed bed reactors for catalytic reactions. You should now understand how to analyze the kinetics of the reaction and how to model behavior using the tanks-in-series model. Thanks for watching.
