Spreadsheet Techniques and Problem Solving for ChEs
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1 AIChE Webinar Presentation co-sponsored by the Associação Brasileira de Engenharia Química (ABEQ) Problem Solving for ChEs David E. Clough Professor Dept. of Chemical & Biological Engineering University of Colorado Boulder, CO :00 p.m. EST, 5:00 p.m. BRST, 3 December
2 Problem Solving for ChEs Outline of Presentation Part I: Creating engineering spreadsheets efficiently setting up Excel a couple suggestions selection, copying and moving rapid techniques creating formulas using cell and range names suggestions on creating engineering graphs Part II: ChE problem-solving scenarios case studies using Data Table targeting calculations using Goal Seek optimizing with constraints using Solver curve-fitting with Data Analysis Regression 2
3 Part I: Creating engineering spreadsheets efficiently setting up Excel a couple suggestions o one worksheet in a new workbook o move selection after enter cancel it o make sure you have Solver and Data Analysis add-ins else Problem Solving for ChEs 3
4 Part I: Creating engineering spreadsheets efficiently selection, copying and moving rapid techniques o making jumps around the spreadsheet o selecting blocks of data quickly o copying make selection o moving double -click Ctrl-c Ctrl- select destination Enter also also F5 key adjoin Shift key also Ctrl-a or Ctrl-* for entire block to jump technique hold down Ctrl for selections that are not contiguous edge with Ctrl drag and drop make selection Ctrl-x select destination Enter also 4 Problem Solving for ChEs
5 Part I: Creating engineering spreadsheets efficiently selection, copying and moving rapid techniques o using Autofill for an adjacent index column double -click the Fill Handle can drag it out, but not useful for long columns o creating a free-standing index column starting index Problem Solving for ChEs 5
6 Part I: Creating engineering spreadsheets efficiently creating formulas using cell and range names o build formulas using pointing more reliable start formula with = point to n and click build rest of formula using pointing status bar o Enter mode and Edit mode double-click cell or F2 In Edit mode, can use End and Home also arrow keys to move within formula. In Enter mode, those keys point to cells. toggle between and with F2 Problem Solving for ChEs 6
7 Part I: Creating engineering spreadsheets efficiently creating formulas using cell and range names o cell addressing relative, absolute and mixed A1 relative $A$1 absolute A$1 relative column/absolute row $A1 absolute column/relative row fill a table with single formula result in single cell A1 $A1 F4 $A$1 note use of addressing copy to entire table A$1 use the F4 key to cycle through the addressing modes see how addressing translated to reference the appropriate cells Problem Solving for ChEs 7
8 Part I: Creating engineering spreadsheets efficiently creating formulas using cell and range names o creating names for cells and ranges of cells formula references cell addresses have to back-trace to cells to see meaning of formula references enter n in Name Box to create name n for cell B2 formula with names much easier to decipher (and debug) use names wherever possible! When not to use names? When you need to take advantage of cell addresses in copying formulas. Problem Solving for ChEs 8
9 Part I: Creating engineering spreadsheets efficiently creating formulas using cell and range names o introducing built-in functions (there are 100 s) use the Insert Function button just to the left of the Formula Bar to find and insert functions if we want to find out whether Excel has a built-in gamma function, type it in and click Go we find that Excel 2013 has the gamma function built in, so we proceed to use it with the argument 2.3, as an example Problem Solving for ChEs 9
10 Part I: Creating engineering spreadsheets efficiently creating formulas using cell and range names o using array formulas one-stop shopping press Ctrl-Shift-Enter these ranges named V and T Array formulas also allow for matrix calculations (multiplication, inverse, transpose, determinant) select destination range and type in single formula making reference to V and T 10 Problem Solving for ChEs
11 Part I: Creating engineering spreadsheets efficiently suggestions on creating engineering graphs o options with scatter plots avoid artificial smoothing options use markers only for experimental data use markers and straight lines for pattern recognition use straight lines only for analytical functions or hundreds of data o moving charts to their own sheet data data whenever feasible, move charts to their own sheet formatting and presentation is much better avoid data avoid scatter plots are the best choice for engineering graphs Problem Solving for ChEs 11
12 Part I: Creating engineering spreadsheets efficiently suggestions on creating engineering graphs o adding a data series to the graph many users don t realize that you can select a new data series on the spreadsheet, copy and paste it onto the chart, and it is added automatically o using a secondary y-axis if one or more series on the plot don t work well with the scale required on the left, assign them to a secondary scale on the right Problem Solving for ChEs 12
13 Part I: Creating engineering spreadsheets efficiently suggestions on creating engineering graphs o annotating graphs add text boxes, arrows pointing to features of the graph, shapes such as ellipses reformat these to suit 4.5 Heat Capacity of Nitric Acid Solutions Notice the inflection in the curve here Heat Capacity (kj/(kg*k) %HNO 3 by wt 13 Problem Solving for ChEs
14 case studies using Data Table Input cell Spreadsheet calculation involving one to many cells Result cell Set of input values Corresponding result values typically create graph of result vs input Problem Solving for ChEs 14
15 case studies using Data Table o identifying the input cell(s) and output cell input cell output cell one-way case study o creating the range(s) of input values o entering the study pointer formula Problem Solving for ChEs 15
16 case studies using Data Table o selecting the study range, invoking Data Table the Data Table is live -- change the temperature and the values will update notice the range selected includes F2 Problem Solving for ChEs 16
17 case studies using Data Table o graphical interpretation of the case study 2.5 Case Study of Ideal Gas Law -- Pressure versus Volume 2 Temperature = 32 degf Pressure (atm) Note: two-way case studies are possible and can be depicted in a surface or contour plot Volume (L) Problem Solving for ChEs 17
18 targeting calculations using Goal Seek o the back-solving scenario input cell spreadsheet calculation involving one or more cells output cell adjust Goal Seek compare target value Problem Solving for ChEs 18
19 targeting calculations using Goal Seek o putting Goal Seek to work adjust V to get a pressure of 2 atm 2 19 Problem Solving for ChEs
20 targeting calculations using Goal Seek o using Goal Seek for equation solving f x = 0 ( ) target value is zero o Solver as an alternative 2 Problem Solving for ChEs 20
21 optimizing with constraints using Solver o adjusting multiple cells to achieve an objective n input cells performance calculation performance result n-1 constraints o constraint-free optimization n = 1 Problem Solving for ChEs 21
22 V optimizing with constraints using Solver V 2 cyl 1 = = π rh 1 rh 3 π 2 cone 2 Minimize total cost A = 2π rh cyl 1 Cost cyl = $1000/m 2 Total Volume = 25 m 3 A = π r r + h 2 2 cone 2 Cost cone = $1500/m 2 Total Height = 5 m Three inputs: r, h 1 and h 2 Two constraints: total volume and total height One performance objective: total cost r h 1 h 2 Problem Solving for ChEs 22
23 optimizing with constraints using Solver Adjust h 1, h 2 and r to minimize TotalCost while keeping TotalHt = 5 and Volume = 25 Problem Solving for ChEs 23
24 optimizing with constraints using Solver o setting Solver parameters o adding constraints Problem Solving for ChEs 24
25 optimizing with constraints using Solver Click Solve Optimized design Problem Solving for ChEs 25
26 curve-fitting with Data Analysis Regression o using Trendline its limitations and pitfalls to add a Trendline, right-click a data point and click Add Trendline Problem Solving for ChEs 26
27 curve-fitting with Data Analysis Regression o using Trendline its limitations and pitfalls Here, pick a polynomial fit and adjust the order until the fitted curve looks good. Check to display the model equation on the chart. We advise against displaying R 2, since it is a misleading statistic for goodness of fit. Problem Solving for ChEs 27
28 curve-fitting with Data Analysis Regression o using Trendline its limitations and pitfalls Visual fit appears good for 5 th -order polynomial. Be cautious in manually copying model equation to use in calculations precision of display will cause (big!) round-off errors. Statistical information on regression is not available. Flexibility in specifying model structure is very limited. Problem Solving for ChEs 28
29 curve-fitting with Data Analysis Regression o Data Analysis Regression allowable models Models must be linear in the parameters being fitted. Generally, y = a f x,x,,x + a f x,x,,x + + a f x,x,,x Example allowable linear models: n Polynomials: y= a0 + ax ax n Response surface: y= a0 + ax ax a12xx 1 2 (multilinear) Models nonlinear in parameters can t be handled: ( ) ( ) ( ) m m n n 1 2 m e.g., Antoine s Eqn (can by Solver) ( ) B A T C P T 10 + = Problem Solving for ChEs 29
30 curve-fitting with Data Analysis Regression o step-wise regression using Data Analysis Create an array of the X-input variable (%HNO3) to powers 1 through 6 Set up the Regression dialog as shown Include Labels and Residuals Problem Solving for ChEs 30
31 curve-fitting with Data Analysis Regression o step-wise regression using Data Analysis From Regression output, find term with highest P-value (2 nd -order term) Run Regression again, eliminating the 2 nd -order column from the X-input range. Continue eliminating the highest P-value until all are less than, for example, 5%. Notice result has intercept, first-order, 4 th,5 th, and 6 th order not a conventional polynomial fit. This model would not have been found using Trendline. Problem Solving for ChEs 31
32 curve-fitting with Data Analysis Regression o step-wise regression using Data Analysis Heat Capacity (kj/(kg*k) Heat Capacity of Nitric Acid Solutions y = x x x x %HNO 3 by wt Data Model Residuals 2.0E E E E E E E E E-02 Residual Values Model curve shown with data and residuals plotted on secondary axis Model equation embedded on graph using equation typesetter Problem Solving for ChEs 32
33 curve-fitting with Data Analysis Regression o nonlinear regression use of Solver Start by creating a graph to test models Log10 Vapor Pressure vs Temperature Problem Solving for ChEs 33
34 curve-fitting with Data Analysis Regression o nonlinear regression use of Solver Choose an initial set of parameters and compute model predictions Add this curve to the graph Log10 Vapor Pressure vs Temperature Make sure the initial estimates are such that the model curve is in the ballpark of the data, as shown here. Problem Solving for ChEs 34
35 curve-fitting with Data Analysis Regression o nonlinear regression use of Solver Compute the differences between the predictions and data in the Error column sum the squares of this column in SSE Set up Solver Parameters to minimize SSE by adjusting Antoine parameters. Problem Solving for ChEs 35
36 curve-fitting with Data Analysis Regression o nonlinear regression use of Solver Solver s minimization of SEE performs a nonlinear regression resulting in a snapping of the model curve onto the data. Problem Solving for ChEs 36
37 Problem Solving for ChEs Windup: A Few Key Points use names instead of cell addresses wherever possible take the time to learn efficient techniques try array formulas they improve reliability recognize the problem-solving scenarios -- especially case studies, targeting and optimization we have left out many topics especially VBA 37
38 Want to go more in depth on spreadsheets? Consider enrolling in the AIChE E-learning courses Spreadsheet Problem-Solving for ChEs Spreadsheet Programming for ChEs Excel s VBA or attend the AIChE in-person versions available as 1-day offerings or a 2-day combo package public offerings at major city locations in the U.S. and abroad as arranged with AIChE in-house, private offerings for your organization Thanks for your attention. Now, questions?? 38
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AIChE Webinar Presentation Problem Solving for ChEs David E. Clough Professor Dept. of Chemical & Biological Engineering University of Colorado Boulder, CO 80309 Email: David.Clough@Colorado.edu 2:00 p.m.
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