Fundamentals of Mathematical Modeling, Simulation, and Process Control

  • Ricardo Simpson
  • Sudhir K. Sastry


Believe it or not, we have extensively, unconsciously, exposed you to, practiced, and developed mathematical models throughout this book. The first exposure to mathematical modeling was probably in  Chap. 2 (Sect.  2.4.1), where we introduced the ideal gas law. In Sect.  2.7, you were exposed to several mathematical models that are very common in chemical and bioprocess engineering. Then, in several of the subsequent chapters, we utilized mathematical models. For example, in  Chap. 6, we used different mathematical models that are frequently utilized in, for example, thermodynamics, heat transfer, and mass transfer.

First, the main purpose of this chapter is to understand and discover, through examples, the importance of mathematical modeling and to start constructing simple mathematical models. The second purpose is introduce you to process and bioprocess simulation. Again, in the case of simulation, you already have been exposed to and practiced simulation through exercises in previous chapters. For example, in  Chap. 8 (Sect.  8.6, problem 3), it was proved that two continuous bioreactors in series (total volume V) were more effective than one continuous bioreactor of volume V.

Due to the descriptive nature of this chapter, quantitative problems have not been included, but five conceptual questions are analyzed and discussed.


Bioprocess Engineer Proportional Integral Derivative Supervisory Control Simple Mathematical Model Pressure Relief Valve 
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  1. Simpson, R., Almonacid, S., and Teixeira, A. 2002. Optimization criteria for batch retort battery design and operation in food canning-plants. J. Food Proc. Eng., 25, 515–538.CrossRefGoogle Scholar

Additional Web References

  1. Teacher package: Mathematical Modeling
  2. Introduction to Modeling Lesson
  3. C Batch Process Control System
  4. PID Control - A brief introduction

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Ricardo Simpson
    • 1
  • Sudhir K. Sastry
    • 2
  1. 1.Department of Chemical and Environmental EngineeringUniversidad Técnica Federico Santa MaríaValparaísoChile
  2. 2.The Ohio State UniversityColumbusUSA

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