hw4q1b_non_linear_regression2

Hw4q1b_non_linear_re - 6 Input initial guesses(Green Arrow 7 Check “Graph” and “Residual”(Violet Arrow 8 Click “Pink Arrow button”(Sky

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Ca (mol/cm^3) t (min) 62.5 0 50.0 10 41.7 20 35.7 30 31.3 40 27.0 50 23.8 60 ECH146 Winter 2008 Solution for HW4Q1b with Polymath Non Linear Regression Tutorial Problem Setting Characteristics of Reaction A 2B + C Isothermal no volume change rate equation known to follow A A r kC α - = Experimental condition: Bach reactor C A0 = 62.5 mol/cm^3 (pure) Design Spec/objectives PFR C A0 = 62.5 mol/cm^3 (pure) Volumetric flow rate =100cm^3/sec X = 0.55 C A,outlet = 28.125 mol/cm^3 Find α and k Calculate the residence time
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A. Data Input (See “HW3Q1 solution X 0.7”) 1. Open “Polymath”, choose “Regress and Analyze Data” 2. Input data in spread sheet (or copy and paste from excel) 3. The spread sheet looks like B. Non Linear Regression 1. Click “Regression” tab at the right side of screen (Red arrow.) 2. Click “Nonlinear” tab (Blue arrow.) 3. Let’s try 1 α . That is ( 29 ( 29 (1 ) (1 ) (1 ) (1 ) 0 1 1 62.5 (1 ) (1 ) A A A t C C C k k - - - - = - = - - -
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4. Input the equation into “model” window. (Red Arrow) 5. Chose function. Usually, L-M works better. (Blue Arrow)
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Unformatted text preview: 6. Input initial guesses. (Green Arrow) 7. Check “Graph” and “Residual” (Violet Arrow) 8. Click “Pink Arrow button” (Sky Blue Arrow) 9. Check Value and 95%CI 10. Check quality of fitting with R^2, residual, and graphs. 11. The results are ( 29 1.69 3 3 95% 95% 0.0013 0.0008 mol/cm -min mol/cm 1.7 0.2 CI CI k α-= ± ⋅ = ± *Notice 95%CI for k is large. 10 20 30 40 50 60 70 20 40 60 80 time (min) Ca (mol/cm^3) Experimental alpha = 1.7 alpha = 2 C. Find the residence time 1. from the equation and determined parameters, ( 29 0.7 0.7 1 62.5 28.125 0.0013( 0.7) 46min t--=--= D. Comparison with 2 nd order 1. The result of 2 nd order fitting is 2. The value of R^2 and Variance are worse than the corresponding values in part C. 3. The residence time is ( 29 1 1 1 62.5 28.125 0.00042( 1) 47min t--=--= *Pretty much the same. 4. Lt’s plot the models *Pretty much the same....
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This note was uploaded on 02/13/2011 for the course ECH 146 taught by Professor Faller during the Winter '08 term at UC Davis.

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Hw4q1b_non_linear_re - 6 Input initial guesses(Green Arrow 7 Check “Graph” and “Residual”(Violet Arrow 8 Click “Pink Arrow button”(Sky

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