Reactor Design within Excel Enabled by Rigorous Physical Properties and an Advanced Numerical Computation Package Mordechai Shacham Department of Chemical Engineering Ben Gurion University of the Negev Beer-Sheva, Israel Michael B. Cutlip Department of Chemical Engineering University of Connecticut Storrs, CT, USA
Problem Solving in Chemical Engineering Mathematical Model Physical Properties Solution Algorithm Documentation
Chemical Engineer s Tools of Trade - 1965 Calculation Documentation Properties Graphical Solution
Chemical Engineer s Problem Solution Techniques - 1965 Analytical solutions, including Model simplification by neglecting less important terms Model manipulation to bring it into a solvable form Short-cut solution techniques Replacing the problem with a simpler one that can be solved Graphical solutions Trial and error solution techniques Numerical solution, including Computer language programming and debugging
Shortcomings of the Traditional Solution Techniques Manual and Graphical Solution Techniques Tedious, time consuming error prone process Oversimplification may lead to wrong results Highest precision is two decimal digits Time constraints prevent screening of large number of alternatives to find an optimal solution Computer Language Programming Requires experts in programming, numerical and optimization methods Tedious, time consuming error prone process
Modern Problem Solving Techniques Mathematical Model Physical Properties User Supplied Solution Algorithm Mathematical Software Package Documentation Using this approach the USER supplies the mathematical model and the physical properties and the package provides the numerical solution. Appropriate for small scale problems and when model flexibility is essential.
Modern Problem Solving Techniques Fogler H. S., An Appetizing Structure of Chemical Reaction Engineering for Undergraduates, Chem. Eng. Ed., 27(2), 110(1993)
Modern Problem Solving Techniques Mathematical Model Physical Properties Process Simulator Solution Algorithm Documentation Using this approach the USER provides only the process data. Appropriate for large scale problems.
Chemical Engineering Student s Tools of Trade - 2004 Material and Energy Balances (Prentice- Hall textbook by Himmelblau, 2003) Thermodynamics (Prentice-Hall textbook by Kyle, 1999) Chemical Reaction Engineering (Prentice-Hall textbook by Fogler, 2004, Wiley-VCH textbook by Hagen, 2004) Process Dynamics and Control, Process Modeling and Numerical Methods Product and Process Design and Simulation
The use of POLYMATH throughout the ChE curriculum Chapters Coming next year in the 2 nd edition Basic Principles and Calculations, Thermodynamics, Fluid Mechanics, Heat transfer, Mass Transfer, Chemical Reaction Engineering Regression and Correlation of Data, Advanced Techniques in Problem Solving. Additional chapters: Separation Processes, Biotechnology, Process Dynamics and Control Conversion of POLYMATH models to Excel and MATLAB
Need for Spreadsheet-Based Calculations 287 Responses http://www.cache.org/ This nonprofit Educational Corporation is headquartered at the University of Texas at Austin.
Process Simulation Programs (Flowsheeting) in Organizations None 58.2% (163) Aspen+ 20% (56) Hysys 14.3% (40) SIMSCI Pro II 7.5% (21) ChemCAD 1.8% (5) gproms 1.4% (4) WINSIM 0.7% (2) Other 6.1% (17)
Extending the Use of Numerical Problem Solving By Practicing Engineers 100% of the engineers in the industry use spreadsheets (mainly Excel) while only a very small percentage use programs as Polymath, MATLAB and Aspen. Excel is inappropriate for complex numerical problem solving because of the need to convert variable names to cell addresses, difficulties in program documentation and unavailability of an ODE solver. Polymath 6.0, due to be released this fall, enables definition of the problem using the Polymath notation and syntax and conversion of the Polymath input into a well documented Excel worksheet. A new ODE solver for Excel is also provided.
The New Paradigm in Problem Solving Mathematical Model Physical Properties Aspen Properties Solution Algorithm Excel Polymath 6.0 Documentation
POLYMATH 6.0 Allows Easy Entry and Solution of Mathematical Problems using Numerical Analysis Capabilities Linear Equations - up to 264 simultaneous equations. Nonlinear Equations - up to 300 simultaneous nonlinear and 300 explicit algebraic equations Differential Equations - up to 300 simultaneous ordinary differential and 300 explicit algebraic equations Data analysis and Regression - up to 1200 data points with capabilities for linear, multiple linear, and nonlinear regressions with extensive statistics plus polynomial and spline fitting with interpolation and graphing capabilities NEW Automatic Migration of All Problems to Excel
POLYMATH A Long History in Engineering Computations
Aspen Properties Excel Calculator Pure component constants (MW, Normal boiling point). Vapor pressure at a specified temperature Pure component property at specified temperature and pressure Mixture properties for a specified mixture at given temperature and pressure Two and three phase flash, bubble and dew point calculations (enables solving simultaneous differential and algebraic equations, DAE)
Non-isothermal Reactor Design Problem Adiabatic operation will be modeled. 1 Fogler, H. S., Example 8-7, Elements of Chemical Reaction Engineering, 3rd Edition, Prentice-Hall, Upper Saddle River, NJ (1999)
Reactor Design Problem Model Equations Let A = acetone, B = ketene and C = methane, thus A B + C Mole Balances df dv A df dv B = ra; = ra and df C dv = r A Rate Law r = A kc A Stoichiometry C Energy Balance (Adiabatic Operation) A y P A = ; RT dt dv = y F A A = C F pa A + F F ( H + F B A B R C + pb F C )( r + A ) F C C pc
Reactor Design - Polymath Model Entry Physical properties are needed Note notation and syntax as in problem definition No need to reorder equations Model serves as documentation
Physical Properties The Traditional Approach
Physical Properties The Traditional Approach (2) Data and part of the calculations
Creation of a Physical Property Data File in Aspen Properties Physical Properties The New Approach
Specification of Components in Aspen Properties Physical Properties The New Approach
Specification of Property Method in Aspen Properties Physical Properties The New Approach
Saving Data File within Aspen Properties for Use in Excel
Provision of Physical Property Data in Excel by Aspen Properties Add-In Feed temperature and mole fractions CPA CPB CPC Copy to Polymath
Connection of Property Data to Polymath Program within Excel The variables T, P, ya (mole fraction of A), yb, and yc must be sent to the corresponding variable locations with the Aspen Properties area of the Excel worksheet. Additionally, the variables deltah (heat of reaction calculated from the enthalpies), CpA (heat capacity of A), CpB, and CpC must be made available in the Polymath coding for the solution of the differential equations.
Polymath Model With Aspen Properties Data
Export of Polymath Program to Excel (A single key press automatically migrates the problem.) Excel Formulas Documentation Documentation
Excel Formulas for the Reactor Problem Initial model set-up with Excel is a tedious and error prone process because of the need to convert variable names to cell addresses. This is practically impossible for a complex problem.
Connecting Data Information between Polymath and Aspen Properties Constant values are replaced by cell addresses from Aspen Properties
The Polymath ODE_Solver can then be used to solve the system of differential and explicit algebraic equations.
Note that as the temperature changes in the reactor, this new temperature is used in Aspen Properties to update the heat of reaction and the heat capacities within the equations used to solve the differential and algebraic equations. During the integration of the differential equations, the property values change with the temperature as the independent variable goes from 0 to 4.
The Polymath ODE_Solver automatically presents the results in a new sheet in the Excel workbook.
Columns of intermediate data can be identified for plotting in Excel.
These data columns can then be plotted with Excel. 40 Fogler Example Problem 8-7 35 30 Molar Flow Rates, mol/s 25 20 15 10 FA FB FC FB and FC coincide in this graph. 5 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Reactor Volume, m3
Figure E8-7.1 from the Fogler textbook can also be generated from the intermediate data by using Excel. Fogler Example 8-7 1050 0.3 1030 0.25 Temperature, K 1010 990 970 950 0.2 0.15 0.1 Conversion Excel Plot 930 910 0.05 890 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Volume, m3 Fogler Text Plot
Additional Typical Examples that Have Been Solved Utilizing the New Approach 1. Reactor Design Conversion of Nitrobenzene to Aniline in a Tubular Reactor Oxidation of O-Xylene to Phthalic Anhydride in a Tubular Reactor Batch Decomposition of Acetylated Castor Oil Semi-Batch Manufacture of Hexamethylenetriamine 2. Batch Distillation Separation of Methanol from Water in a Four Stage Column Multicomponent, Semi-Batch Steam Distillation 3. Steady State Absorption Column Design 4. Rigorous Heat Exchanger Design
SUMMARY This paper highlights the highlights the concepts necessary for advanced problem solving with Excel as enabled by Polymath and Aspen Properties. These are: Entry of basic problem in Polymath 6 with constant physical properties followed by export to Excel. Creation of a physical property data base within Aspen Properties followed by export to Excel via Aspen Properties Excel Add-In. Formulation of the problem within Excel that links the physical properties from Aspen Properties to the equations from Polymath. Use of the Polymath ODE_Solver Add-In to solve the problem within Excel. Generation of tabular and graphical outputs within Excel.
CONCLUSIONS Polymath and Aspen Properties now allow the solution of real-life, process design and related problems in a short time and with high precision, using Excel. Chemical engineering professionals can start using the combined Polymath -> Excel <- Aspen Properties capability immediately in solving real problems on the personal computer desktop.
CONCLUSIONS (Cont.) Chemical engineering students can begin using the combined Polymath -> Excel <- Aspen Properties capability for problem solving in their first engineering course of Material and Energy Balances. Students can continue to use the same approach throughout their CHEG curriculum and will carry this capability into their industrial practice.
Software References Aspen Properties is a product of AspenTech http://www.aspentech.com/ Excel is a product of Microsoft Corporation http://www.microsoft.com/ Polymath is a product of Polymath Software http:// www.polymath-software.com/