Collection and Analysis of Rate Data Dr. A.K.M. Shafiqul Islam

Example 5-3 We shall use the reaction and data in Example 5-1 to illustrate how to use regression to find  and k’.

Solution Combined rate law and mole balance equation Integrating with the initial conditions when t=0 and C A =C A0 Substituting the initial concentration C A0 =0.05 mol/dm 3

We first assume a value of  and k and calculate t for the concentrations of A in the table. Calculate the sum of squares of difference between the measured time t mi and the calculated time t ci. For N measurements

First guess  =3 and k’=5 with C A0 =0.05, then we get Now we make calculation for each measurement of concentration and fill in column 3 and 4. Example, for C A =0.038 mol/dm 3 Next we calculate the squared difference

Evaluation of Laboratory Reactors The successful design of industrial reactors lies primarily with the reliability of the experimentally determined parameters used in the scale-up. It is essential to design equipment and experiments that will generate accurate and meaningful data. There is no single comprehensive laboratory reactor that could be used for all types of reactors and catalysts We will discuss various types of reactors that could be chosen to obtain the kinetic parameters for the specific reaction system

Criteria Used To Evaluate Laboratory Reactor 1.Ease of sampling and product analysis 2.Degree of isothermality 3.Effectiveness of contract between catalyst and reactant 4.Handling of catalyst decay 5.Reactor cost and ease of construction

Types of Reactors Integral (Fixed-Bed) Reactor

Stirred-Batch Reactor

Stirred Contained-Solids Reactor (SCSR)

Continuous-Stirred Tank Reactor (CSTR)

Straight-Through Transport Reactor

Recirculating Transport Reactor

1.From this table one notes that the CSTR and recirculating transport reactor appear to be the best choice because they are satisfactory in every category except for construction. 2.If the catalyst under study does not decay, the stirred batch and contained solids reactors appear to be the best choices 3.If the system is not limited by internal diffusion in the catalyst pellet, larger pellets could be used, and the stirred-contained solids is the best choice. 4.If the catalyst is nondecaying and heat effects are negligible, the fixed-bed (integral) reactor 5.would be the top choice, owing to its ease of construction and operation. In practice, usually more than one reactor type is used in determining the reaction rate law parameters. Summary of Reactor Ratings

Closure After studying this section, the student should be able to analyze data to determine the rate law and rate law parameters using the graphical and numerical technique. Nonlinear regression is the easiest method to analyze rate- concentration data to determine the parameters, but the other techniques such as graphical differentiation help one get a feel for the disparities in the data. The student should be able to describe the care that needs to be taken in using nonlinear regression to ensure you do not arrive on a false minimum for  2. It is advisable to use more than one method to analyze the data. The student should be able to carry out a meaningful discussion on reactor selection to determine the reaction kinetics along with how to efficiently plan experiments.