### TK Solver for Chemical Engineers

**Overview**

TK Solver is frequently used for
calculations involving mass balances, fluid flow, distillation,
agitation/mixing, combustion, heat transfer, dust/mist collection, and reactor
design. The program includes built-in
thermodynamic and transport property functions based on the NIST Standard
Reference Database 23. Additional material
property tables and curves can be integrated into TK models. TK’s unique backsolving capability allows
engineers to optimize designs according to their process/performance
requirements. The versatile TK library
of mathematical and statistical tools handles critical number crunching tasks
such as nonlinear curve-fitting, simulation, and solutions of differential
equations.

Chemical engineering educators also find TK
useful because of its structured approach to model building and its powerful
equation solving and unit conversion abilities.
Students can progressively build on previously learned concepts. TK’s List Solve feature empowers students to
explore the sensitivity of the variables in their models, generating tables and
plots of important relationships -- even those involving large sets of
nonlinear equations. Engineering
textbooks are available which integrate TK into the teaching of chemical
engineering.

**Glimpses of the History of TK Solver in Chemical Engineering**

Since its initial release in 1983, TK
Solver has proven to be a very powerful and practical tool for chemical
engineers. It has also been favorably
reviewed many times from a variety of perspectives. Here are some examples:

Mark Jennings, Digital Kinetics -- Mr.
Jennings used TK Solver to develop and publish PCOST, an extensive collection
of process and pollution control equipment costing models based on a series of
articles published in Chemical Engineering magazine.

Vijay Singh, Schering-Plough, for Chemical
Engineering Magazine -- Mr. Singh presented material balance and flash
calculation examples, concluding that “TK reduces the time spent on problems by
allowing the engineer to concentrate on defining the solution rather than
working out the mechanics of the computer program required. It allows for the formulation of design
models in a natural equation form... It
greatly facilitates the exploration of “what-if” situations.”

D.W. Pepper and A.H. Weber, DuPont, for the
Journal of the Air Pollution Control Association -- Pepper and Weber discussed
calculations involving accidental atmospheric dispersions and reported that TK
Solver is easy to program and, because it can backsolve problems, can yield
quick, reasonable estimate of the source term.

Allan L. Smith, Drexel University
Department of Chemistry -- “Every student said that TK Solver was easier to use
than the programming languages they knew.”
Professor Smith has used TK Solver to model the composition of “acid
rain”.

Gerald Rich for Pollution Engineering
Magazine -- Mr. Rich reviewed TK Solver and summarized, “This is a simple,
fun-to-use program for solving equations.”

Edward M. Rosen, Monsanto Co. -- Mr. Rosen
investigated TK Solver’s equation solving capabilities as applied to four
chemical engineering problems:
fractional conversion in a chemical reactor; energy and material
balances; plug flow reactor equilibrium conversion and temperature;
kinetics. Successfully solving all four
problems with TK Solver, he concuded that TK is a useful tool for chemical
engineers.

Curt Arnold, M.W. Kellogg, quoted in
Digital News -- “Although we have promoted TK inside the company primarily for
relatively simple calculations, we have some very large models with 800 to
1,000 rules. These systems handle
complicated problems such as modeling steam systems for process plants, very
difficult and very important calculations.”

Ali Cinar, Illinois Institute of Technology
-- Volume II of the HAWK MANUAL, published by IIT to assist engineering
students in learning to use computers, features 22 engineering case studies and
corresponding TK Solver models. Mr. Cinar’s
case study models an ammonia reactor operation and the effects of inerts
molefraction level on recycle streams.

Amoco Production Company and the American
Petroleum Institute teamed up with UTS to develop TK Solver applications for
the API Gas Measurement Manual.

Z.Z. Zhang, Donald L. Sparks, and Noel
Scrivner;

*Characterization and Modeling of the Al-Oxide/Aqueous Solution Interface*, published in the Journal of Colloid and Interface Science -- The authors, from DuPont and the University of Delaware, successfully used TK Solver to build their mathematical model and study the sensitivity of the variables involved.
Dan Deitz, Mechanical Engineering
Magazine -- To determine the
specifications for a combustor in a high-speed civil transport plane, Pratt
& Whitney engineers are using TK Solver to solve hundreds of complex
equations. The article focuses on TK’s
many unique features put to use in solving heat transfer problems.

UTS released Heat and Mass Transfer on TK,
a collection of TK Solver models co-authored with Professor David DeWitt of
Purdue University.

UTS and BHR Group Ltd. produced an on-line
electronic information system called Intermix, based on the FMP and HILINE
Design Guides for fluid mixing. The
following topics are covered -- motionless mixers as liquid-phase and
gas-liquid reactors, ejectors as gas-liquid reactors, rotor stator mixers as
liquid phase reactors, and centrifugal pumps as liquid phase reactors.

**A Case Study:**

DuPont’s Chemical Process Design Standards are an excellent example of web-based smart standards. DuPont engineers have accumulated four volumes of chemical process design standards. There are well over one thousand pages of formulas, figures, and descriptions. DuPont worked with Universal Technical Systems, Inc. to produce the web-based version of these standards.

Many topics are covered:

· fluid flow through pipes and orifices

· heat transfer

· agitation and mixing

· distillation

· dust and mist collection

· physical properties of materials

Many of the paper standards required the users to refer to figures for use in intermediate calculations. Many of these figures required users to visually interpolate within families of curves. The TK Solver software was used to process the data within these curves numerically, interpolating automatically where necessary.

Unit conversions were also handled using TK Solver. The equations were all entered using the established nomenclature for each variable. Conversion factors are automatically applied if the user wishes to view a variable in a different unit.

Perhaps the most important use of TK Solver is for backsolving problems. Once the equations are set up in TK, they can be solved in any direction depending on which variables are known and unknown. For example, a standard which computes the pressure drop from turbulent flow through a pipe can also be used to size a pipe for an allowable pressure drop. A single standard easily solves many combinations of problems.

Another major enhancement to the standards was to incorporate a database of physical properties into the calculations. DuPont has a license for the DIPPR physical properties database. That information is now used during the calculations from the standards. Users specify the substances they are working with and properties such as viscosity, density, and vapor pressure are applied at various temperatures. The integration with TK Solver means that these material property calculations can also backsolved. The result is that users can backsolve for temperatures at which to operate various processes for desired performance. Users gain a better understanding of the relationships between variables.

**A Summary of TK’s Competitive Advantages for Chemical Engineers**

TK Solver has many great features but the following ones really make TK stand out as the preferred tool.

• TK is easy to program. -- TK’s rule-based approach to model building allows engineers to enter equations just as they know them, without the need for algebra. Other programs require assignment statements where an unknown must be isolated.

• TK can backsolve. -- TK can solve problems for many combinations of inputs and outputs without any additional programming or rearranging of variables or equations. Backsolving facilitates better designs.

• TK can list solve. -- TK can solve problems repeatedly over a range of inputs to generate data for tables and plots. This feature works for models involving simultaneous nonlinear equations as easily as for simpler problems. This feature can easily be used for filtering random numbers through math models for Monte Carlo simulations.

• TK can optimize -- TK can solve problems repeatedly within given constraints to determine the optimal configuration of inputs.

• TK does table look-ups. -- TK can access material property tables and charts during model resolution and can interpolate within them as well. TK also backsolves table look-ups to find necessary inputs producing the desired properties.

• TK is uniquely programmable. -- TK combines both rule-based and procedural languages for the best of both worlds. Users can implement their own algorithms and use the resulting functions within TK as they would any of the built-in functions. Even backsolve them! It’s easy to save these functions and merge them into other models as necessary.

• The TK Library. -- Engineers with math and statistical requirements such as solving differential equations, fitting curves to experimental data, or even a combination of these two, will find a treasury of pre-programmed tools in the TK Library, all at no extra cost.

**TK Solver Library Highlights:**

List/array manipulation

Matrix manipulation

Root finders

Numerical differentiation

Numerical integration

Differential equation integrators

Optimization algorithms

Geometry and CAD functions

Functions of complex variables

Data analysis and statistical testing

Linear and nonlinear curve-fitting

Curve-fitting of differential equations

Probability distributions

Maximum likelihood estimation

Monte Carlo simulation analysis

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