RTD Functions for CSTRs Where N Is Not an Integer

It is often difficult to use Equations 8-101 or 8-103 to represent die response curve of an actual reactor where N is not an integer. Stokes and Nauman [16] have considered tills simation, which is reviewed below. 

If die equivalent number of perfectly mixed stages N is not an integer, let i be an integer slightly smaller dian N. A fraction 0 h 1 is defined as 

The model consists of i -i- 1 stirred tanks in series, i of which have a common volume, and one of which has a smaller volume 

Equations 8-109, 8-110, 8-111, and 8-112 are redueed to an ordinary tanks-in-series model when N = i and h = 0. For the equivalent number of ideal CSTRs, N is obtained by minimizing the residual sum of squares of the deviation between the experimental F-eurve and that predieted by Equation 8-109. The objeetive funetion is minimized from the expression 

A one-dimensional seareh optimization teehnique, sueh as the Fibonaeei seareh, is employed to miniiTtize Equation 8-113. A eomputer program (PROG81) was developed to estimate the equivalent number of ideal tanks N for the given effluent traeer response versus time data. Additionally, the program ealeulates the mean residenee time, varianee, dimensionless varianee, dispersion number, and the Peelet number. 

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