Reactor Design within Excel Enabled by Rigorous Physical

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					   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                 Physical
        Model                    Properties


      Chemical Engineer’s Tools of Trade - 1965

                                       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                     Physical
                   Model                       Properties

                               User Supplied


                     Mathematical Software Package


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),
        Modern Problem Solving Techniques

              Mathematical                    Physical
                  Model                      Properties

                           Process Simulator



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
                      Basic Principles and Calculations,
                      Thermodynamics, Fluid Mechanics,
                      Heat transfer, Mass Transfer, Chemical
                      Reaction Engineering
                      Regression and Correlation of Data,
                      Advanced Techniques in Problem
Coming next year in the 2nd edition
Additional chapters: Separation Processes, Biotechnology,
Process Dynamics and Control
Conversion of POLYMATH models to Excel and MATLAB
Need for Spreadsheet-Based

        287 Responses
This nonprofit Educational Corporation is headquartered at the
University of Texas at Austin.
    Process Simulation Programs (Flowsheeting) in

•   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                Physical
       Model                   Properties

                             Aspen Properties

     Algorithm                      Excel

     Polymath 6.0

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
Aspen Properties Excel Calculator

 Pure component constants (MW, Normal boiling point).
 Vapor pressure at a specified temperature
 Pure component property at specified temperature and
 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.

1Fogler, H. S., Example 8-7, “Elements of Chemical Reaction Engineering,”
3rd Edition, Prentice-Hall, Upper Saddle River, NJ (1999)
      Reactor Design Problem – Model
       Let A = acetone, B = ketene and C = methane, thus

Mole Balances      dFA          dFB              dFC
                       = rA ;       = − rA and       = − rA
                   dV           dV               dV

Rate Law                rA = −kC A
Stoichiometry           yAP                 FA
                   CA =     ;     yA =
                        RT             FA + FB + FC
Energy Balance             dT      (−∆H R )(−rA )
(Adiabatic Operation)         =
                           dV FAC pA + FB C pB + FC C pC
Reactor Design - Polymath Model Entry

                             Physical properties are

                     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
Creation of a Physical Property Data File in Aspen

    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
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


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
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.
                                                           Fogler Example Problem 8-7



Molar Flow Rates, mol/s


                          20              FA
                                   FB and FC
                                   coincide in
                                   this graph.


                               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



Temperature, K


                 970                                                                   0.15




                 890                                                                   0
                        0   0.5   1     1.5           2            2.5   3   3.5   4
                                                  Volume, m3

                                      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
•       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
This paper highlights the highlights the concepts
necessary for advanced problem solving with Excel as
enabled by Polymath and Aspen Properties. These
• 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

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
        Software References
• Aspen Properties is a product of AspenTech

• Excel is a product of Microsoft Corporation

• Polymath is a product of Polymath Software