Reactor Design within Excel Enabled by Rigorous Physical Properties and an Advanced

Numerical Computation Package

Mordechai ShachamDepartment of Chemical Engineering Ben Gurion University of the Negev

Beer-Sheva, Israel

Michael B. CutlipDepartment of Chemical Engineering

University of ConnecticutStorrs, CT, USA

Problem Solving in Chemical Engineering

MathematicalModel

Physical Properties

Solution Algorithm

Documentation

Chemical Engineer’s Tools of Trade - 1965

CalculationDocumentation

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 TechniquesManual 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

MathematicalModel

Physical Properties

Solution Algorithm

Documentation

Mathematical Software Package

User Supplied

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

MathematicalModel

Physical Properties

Solution Algorithm

Process Simulator

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 curriculumChapters

Basic Principles and Calculations, Thermodynamics, Fluid Mechanics, Heat transfer, Mass Transfer, Chemical Reaction Engineering

Regression and Correlation of Data, Advanced Techniques in Problem Solving.

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 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

MathematicalModel

Physical Properties

Solution Algorithm

Documentation

Excel

Aspen Properties

Polymath 6.0

POLYMATH 6.0 – Allows Easy Entry and Solution of Mathematical Problems using

Numerical Analysis CapabilitiesLinear 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

1Fogler, H. S., Example 8-7, “Elements of Chemical Reaction Engineering,” 3rd Edition, Prentice-Hall, Upper Saddle River, NJ (1999)

Adiabatic operation will be modeled.

Reactor Design Problem – Model Equations

Let A = acetone, B = ketene and C = methane, thus

A → B + C

AC

AB

AA r

dVdFr

dVdFr

dVdF

−=−== and;Mole Balances

AA kCr −=Rate Law

CBA

AA

AA FFF

FyRT

PyC++

== ;Stoichiometry

Energy Balance (Adiabatic Operation)

pCCpBBpAA

AR

CFCFCFrH

dVdT

++−∆−

=))((

Reactor Design - Polymath Model Entry

Note – notation and syntax as in problem definition

No need to reorder equations

Model serves as documentation

Physical properties are needed

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 inAspen 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.Fogler Example Problem 8-7

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3 3.5 4

Reactor Volume, m3

Mol

ar F

low

Rat

es, m

ol/s

FAFBFC

FB and FC coincide in this graph.

Figure E8-7.1 from the Fogler textbook can also be generated from the intermediate data by using Excel.

Fogler Example 8-7

890

910

930

950

970

990

1010

1030

1050

0 0.5 1 1.5 2 2.5 3 3.5 4

Volume, m3

Tem

pera

ture

, K

0

0.05

0.1

0.15

0.2

0.25

0.3

Con

vers

ion

Excel Plot

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

SUMMARYThis 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 AspenTechhttp://www.aspentech.com/

• Excel is a product of Microsoft Corporationhttp://www.microsoft.com/

• Polymath is a product of Polymath Softwarehttp:// www.polymath-software.com/