Luyben

W. L. Luyben, Process Modeling, Simulation, and Controlfor Chemical Engineers, McGraw-HiU, Book Co., Inc., New York, 1973. 

P. S. Buckley, W. L. Luyben, andj. P. Shunta, Design of Distillation Control Sjstems, Instmment Society of America, Research Triangle Park, N.C., 1985. 

Luyben, W. L. Frocess Modeling, Simulation and Control for Chemical Engineers, 2d ed., McGraw-HiU, New York (1990). 

These differential equations are readily solved, as shown by Luyben (op. cit.), by simple Euler numerical integration, starling from an initial steady state, as determined, e.g., by the McCabe-Thiele method, followed by some prescribed disturbance such as a step change in feed composition. Typical results for the initial steady-state conditions, fixed conditions, controller and hydraulic parameters, and disturbance given in Table 13-32 are listed in Table 13-33. 

Meijer JJ, ten Hoopen HJG, Luyben KChAM, Libbenga KR (1993) Enzyme Microb Technol 15 234... 

Caulet PJC, van der Lans RGJM, Luyben KChAM (1996) Chem Eng J 62 193... 

Complex systems can often be represented by linear time-dependent differential equations. These can conveniently be converted to algebraic form using Laplace transformation and have found use in the analysis of dynamic systems (e.g., Coughanowr and Koppel, 1965, Stephanopolous, 1984 and Luyben, 1990). 

In some cases, where the wall of the reactor has an appreciable thermal capacity, the dynamics of the wall can be of importance (Luyben, 1973). The simplest approach is to assume the whole wall material has a uniform temperature and therefore can be treated as a single lumped parameter system or, in effect, as a single, well-stirred tank. 

Luyben (1973) (see simulation example RELUY) also demonstrates a reactor simulation including the separate effects of the measuring element, measurement transmitter, pneumatic controller and valve characteristics which may in some circumstances be preferable to the use of an overall controller gain term. 

Consider the binary batch distillation column, represented in Fig. 3.58, and based on that of Luyben (1973, 1990). The still contains Mb moles with liquid mole fraction composition xg. The liquid holdup on each plate n of the column is M with liquid composition x and a corresponding vapour phase composition y,. The liquid flow from plate to plate varies along the column with consequent variations in M . Overhead vapours are condensed in a total condenser and the condensate collected in a reflux drum with a liquid holdup volume Mg and liquid composition xq. From here part of the condensate is returned to the top plate of the column as reflux at the rate Lq and composition xq. Product is removed from the reflux drum at a composition xd and rate D which is controlled by a simple proportional controller acting on the reflux drum level and is proportional to Md-... 

Figure 3.58. Model representation of a batch distillation column and typical plate n, as per Luyben (1973).

The conlinuous binary distillation column of Fig. 3.60 follows the same general representation as that used previously in Fig. 3.58. The modelling approach again follows closely that of Luyben (1973, 1990). 

Sweere, A. P. J., Luyben, K. Ch. A. M. and Kossen, N. W. F. (1987) Regime Analysis and Scale-Down Tools to Investigate the Performance of Bioreactors. Enzyme Microb. TechnoL, 9, 386-398. 

Luyben, W.L. (1973) Process Modelling, Simulation and Control, McGraw-Hill. Marroquin and Luyben, W.L. (1973) Chem. Eng. Sci. 28, 993. 

In the auto-refrigerated reactor shown below, an exothermic reaction A —> B is carried out using a low boiling solvent C. The heat of reaction is removed from the reactor by vapourising the solvent, condensing the vapour in the reflux condenser and returning the condensate as saturated liquid to the reactor. The total holdup of liquid in the reactor is maintained constant, but the temperature of the reactor is controlled by regulating the mass flow of vapour to the condenser. The example is taken from the paper of Luyben (1960). 

AUTOREFRIGERATED REACTOR OF LUYBEN DYNAMIC STABILITY ANALYSIS... 

This distillation equipment is as described in Sec. 3.3.3.2. For convenience a column containing seven theoretical plates and reboiler is assumed, together with constant volume conditions in the reflux drum. The example is based on that of Luyben (1973, 1990). 

For convenience, only four stages were used in this model. An iterative solution is required for the bubble point calculations and this is based on the half-interval method. A FORTRAN subroutine EQUIL, incorporated in the ISIM program, estimates the equilibrium conditions for each plate. The iteration routine was taken from Luyben and Wenzel (1988). The program runs very slowly. 

Luyben, W.L. Wenzel, L.A. (1988) Chemical Process Analysis, Prentice-Hall. 

A major acknowledgement should be made to the pioneering texts of Franks (1966, 1973), Smith, Pike and Murrill (1970), Luyben (1973), Robinson (1975), and Ramirez (1976) for inspiring our interest in digital simulation. The textbook of Russell and Denn (1972) also applied an excellent and disciplined approach to mass balancing, which we have attempted to follow. 

Plantwide Dynamic Simulators in Chemical Processing and Control, William L. Luyben... 

Luyben WL, Tyreus BD and Luyben ML (1999) Plant-wide Process Control, McGraw Hill. 

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