Chemical Engineering Dynamics: An Introduction to Modelling by Dr. John Ingham, Dr. Irving J. Dunn, Prof. Dr. Elmar

By Dr. John Ingham, Dr. Irving J. Dunn, Prof. Dr. Elmar Heinzle, Dr. Jiri E. Prenosil, Dr. Jonathan B. Snape(auth.)

During this e-book, the modelling of dynamic chemical engineering approaches is gifted in a hugely comprehensible method utilizing the original blend of simplified basic concept and direct hands-on computing device simulation. the math is saved to a minimal, and but the approximately a hundred examples provided on a CD-ROM illustrate nearly each point of chemical engineering technology. every one instance is defined intimately, together with the version equations. they're written within the smooth straight forward simulation language Berkeley Madonna, which might be run on either home windows computer and Power-Macintosh computers.

Madonna solves types comprising many traditional differential equations utilizing extremely simple programming, together with arrays. it's so strong that the version parameters can be outlined as "sliders", which permit the impact in their switch at the version habit to be obvious shortly. information can be integrated for curve becoming, and sensitivity or a number of runs can be played. the consequences could be noticeable concurrently on multiple-graph home windows or through the use of overlays. the consequent studying impact of this is often large. The examples should be diverse to slot any actual scenario, and the recommended workouts offer sensible guidance.

The vast event of the authors, either in college instructing and foreign classes, is mirrored during this well-balanced presentation, that's appropriate for the trainer, the scholar, the chemist or the engineer. This booklet presents a better knowing of the formula and use of mass and effort balances for chemical engineering, in a such a lot stimulating manner.
This ebook is a 3rd version, which additionally contains organic, environmental and nutrition approach examples.

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Extra info for Chemical Engineering Dynamics: An Introduction to Modelling and Computer Simulation, Third Edition

Example text

A total material balance is required to model the changing liquid volume and this is combined with a dynamic heat balance equation. Assuming constant density, the material balance equation is dV ˆ F0 À F1 dt where for time t less than the filling time, V/F0, the outlet flow, F1, equals zero, and for time t greater than V/F0, F1 equals F0. 2 Formulation of Dynamic Models The heat balance is expressed by Vqcp dT ˆ F0 qcp …T0 À T† ‡ UA…TS À T† dt Assuming A0 is the total heating surface in the full tank, with volume V0, and assuming a linear variation in heating area with respect to liquid depth, the heat transfer area may vary according to the simple relationship A ˆ A0 V V0 More complex relationships can of course be derived, depending on the particular tank geometry concerned.

6 Microbial Growth Kinetics Under ideal batch growth conditions, the quantity of biomass, and therefore the biomass concentration will increase exponentially with respect to time and in accordance with all cells having the same probability to multiply. Thus the overall rate of biomass formation is proportional to the biomass itself where rX ˆ kX Here rX is the rate of cell growth (kg cell m–3 s–1), X is the cell concentration (kg cell m–3) and k is a kinetic growth constant (s–1). For a batch system, this is equivalent to dX ˆ kX dt where dX/dt is the rate of change of cell concentration with respect to time (kg cell m–3s–1).

Thus dividing by CA0 and multiplying by s gives  A1 dC  A1  A1 À …ks†C ˆ1ÀC dt The parameter term (ks), which is called the Damköhler Number Da, is dimensionless and is now the single governing parameter in the model. This results in a considerable model simplification because originally the three parameters, s, k and CA0, all appeared in the model equation. The significance of this dimensionless equation form is now that only the parameter (ks) is important; and this alone determines the system dynamics and the resultant steady state.

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