Chemical Engineering Model Research Articles

The mathematical modelling of transient systems using differential-algebraic equations

The mathematical difficulties associated with a class of mixed systems of differential and algebraic equations are presented and an algorithm for dealing with them is described. Two classes of chemical engineering models which give rise to such systems, are identified. Also some problems arising from rigorous dynamic distillation models are analysed.

Application of digital simulation languages with personal computers in chemical and biochemical engineering education

Dynamic models in chemical and biochemical engineering are usually non-linear, and the resulting differential equations require numerical solution. Recently it became possible to run simulation software on microcomputers such as the IBM-PC or Apple-Macintosh. Comparison is made for three languages: ISIM and ACSL for the IBM-PC and STELLA for the Macintosh. For ISIM and ACSL model equations have to be set up and directly typed in. Output may be in a tabular or graphic form. With ISIM interactive variation of parameters (pump on/off; stirrer speed etc.) during the run is possible. The graphic capabilities are limited. STELLA is programmed using an interactive graphical model procedure. The model can be presented either graphically or as a list of equations. Graphic output possibilities are excellent. These methods were used both at the ETH and Bradford University in both university and short professional courses. Based on this experience it was found that computer simulation modelling methods greatly enhance the learning process.

A SOLUTION METHOD FOR A CLASS OF NONLINEAR BOUNDARY VALUE PROBLEMS

An approximation formula for finite Sturm-Liouville integral transforms of nonlinear functions allows determination of approximate analytical solutions to a certain class of nonlinear boundary value problems. The proposed method is extremely powerful in analysis of a variety of chemical engineering models. The influence of the degree of nonlinearity of the nonlinear term on results obtained using the approximate transform formula is investigated numerically. An iterative procedure in transform space is described for improving solution accuracy, and fast convergence is observed in three illustrative examples. The technique yields solutions which can be related to bounds on the exact solution derived by Kalaba. The asymptotic solution for the mode error, which is the error in approximating the nonlinear function in transform space, is obtained analytically.

On the equations of facilitated diffusion

THE PROCESS in which a permeant molecule crosses a solution barrier both by means of passive diffusion and by being carried on a molecular carrier which itself diffuses passively is called facilitated diffusion. The process has been invoked as a model in chemical engineering [l, 7, 191, and in biology [20, 211. We are interested in the mathematics of the facilitated diffusion of oxygen and carbon monoxide with the carriers hemoglobin and myoglobin. The mathematical equations governing the simultaneous chemical reaction and diffusion of several molecular species have been known for a long time [3], and are commonly referred to as reaction-diffusion equations. When applied to the steady-state facilitated diffusion of a substrate reacting reversibly with and diffusing in a solution slab of carrier molecules, they may be reduced to a single nonlinear ordinary differential equation for one molecular species [l]. We shall call such an equation a Wyman’s Equation [24]. Consider the reaction

Application of the method of weighted residuals to mixed boundary value problems: Dual-series relations

Mixed boundary value problems arise in a number of chemical engineering models for heat conduction, simultaneous diffusion and reaction, and fluid flow whenever there is a change in the type of boundary condition along the same boundary. In this paper a general computer algorithm based on the method of weighted residuals (MWR) is developed for determining approximate solutions of all problems of the above type which lead to dual series equations. The solution procedure reduces the determination of the series coefficients to the solution of a large system of algebraic equations. This technique offers advantages over finite difference or artificial interface methods in the accuracy which can be obtained, the type of problem which may be treated, and the simplicity of calculations to be performed. Solutions obtained by the application of MWR are compared and analysed for three example problems which are of interest in diffusion, reaction and conduction.

Modeling and Simulation in Chemical Engineering

Modeling and Simulation in Chemical Engineering

Modeling and Simulation in Chemical Engineering

Modeling and Simulation in Chemical Engineering

Variational optimization in control and time domains

AbstractThe study has established, with the help of two typical chemical engineering models, the superiority and versatility of the functional conjugate gradient method in computing optimal control policies for continuous systems. An algorithm named as Difference Method has been developed and tested for optimization in the secondary domain of time. A computationally sound and stable scheme is presented to compute simultaneously optimum duration of time and optimal control policy for a process.

Modeling and simulatioin in chemical engineering, R. G. E. Franks, Wiley‐Interscience, London, 1972. No. of pages: 285. Price: £7.75

Modeling and simulatioin in chemical engineering, R. G. E. Franks, Wiley‐Interscience, London, 1972. No. of pages: 285. Price: £7.75

Mathematical modeling in chemical engineering, Roger G. E. Franks, John Wiley and Sons, Inc., New York, 285 pages, $1 0.95

Mathematical modeling in chemical engineering, Roger G. E. Franks, John Wiley and Sons, Inc., New York, 285 pages, $1 0.95