Digital simulation

Elliott s digital simulation program (EDSCAN) was developed to assist eustomers in designing reliable and eeonomie FCC systems. The program is used for analyzing any type of Elliott equipment, assoeiated... 

Safriet, B, E., Analysis of Pressure Pulsation in Reciprocating Piping Systems by Analog and Digital Simulation, ASME 76-WA/DGP-3, New York, NY American Society of Mechanical Engineers, 1976. 

Brunot, W.K., 1970, Reliability of a Complex Safety injection System from Digital Simulation, ANS Trans 12 p 169, June. 

Scott, K. Reaction Engineering and Digital Simulation in Electrochemical Processes 27... 

Detailed kinetic studies in connection with digital simulations do confirm the RR coupling mechanism postulated in older publications as well as the oxidation of the resulting dimer D to the dication D. But the surprising drop in the height of the reduction wave for the redox pair as the concentration... 

In the theoretical treatment of ion exchange polymers the roles of charge propagation and of migration of ions were further studied by digital simulation. Another example of proven 3-dimensional redox catalysis of the oxidation of Ks[Fe(CN)5] at a ruthenium modified polyvinylpyridine coated electrode was reported... 

Figure 4, Differential pulse voltammetry of a freshly polished, activated glassy carbon surface (a) and a digital simulation of the DPV (b). The pulse frequency vas2 Hz with an amplitude of 10 mV. The DC scan rate was 2 mV s...

Brltz, D. "Digital Simulation In Electrochemistry", Springer Verlag Berlin, 1981. 

T.A.H.M. Janse, G. Kateman, Enhancement of the performance of analytical laboratories by a digital simulation approach. Anal. Chim. Acta, 159 (1984), 181-189. 

B.G.M. Vandeginste, Strategies in molecular spectroscopic analysis with application of queueing theory and digital simulation. Anal. Chim. Acta, 112 (1979) 253-275. 

B. Van de Wijdeven, J. Lakeman, J. Klaessens, B. Vandeginste and G. Kateman, Digital simulation as an aid to sample scheduling in a routine laboratory for liquid chromatography. Anal. Chim. Acta, 184 (1986) 151-164. 

Full details of the ISlM digital simulation programming language can be found in the appendix, and by reference to the ISIM programs associated with the simulation examples of Chapter 5. 

All the above changes are easily implementable in dynamic simulations, using ISIM and other digital simulation languages. The forms of response obtained differ in form, depending upon the system characteristics and can be demonstrated in the various ISIM simulation examples. The response characteristics of real systems are, however, more complex. In order to be able to explain such phenomena, it is necessary to first examine the responses of simple systems, using the concept of the simple, step-change disturbance. 

Dynamic models expressed in terms of transform functions can be solved by digital simulation by transposing the transfer function into an equivalent set of differential equations, as shown by Ord-Smith and Stephenson (1975) and by Matko et al. (1992). Also some languages include special transfer function subroutines. 

Process control is highly dynamic in nature, and its modelling leads usually to sets of differential equations which can be conveniently solved by digital simulation. A short introduction to the basic principles of process control, as employed in the simulation examples of Sec. 5.7, is presented. 

In the solution of mathematical models by digital simulation, the numerical integration routine is usually required to achieve the solution of sets of simultaneous, first-order differential equations in the form... 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

This analysis is limited, since it is based on a steady-state criterion. The linearisation approach, outlined above, also fails in that its analysis is restricted to variations, which are very close to the steady state. While this provides excellent information on the dynamic stability, it cannot predict the actual trajectory of the reaction, once this departs from the near steady state. A full dynamic analysis is, therefore, best considered in terms of the full dynamic model equations and this is easily effected, using digital simulation. The above case of the single CSTR, with a single exothermic reaction, is covered by the simulation examples, THERMPLOT and THERM. Other simulation examples, covering aspects of stirred-tank reactor stability are COOL, OSCIL, REFRIG and STABIL. 

Compared to this a solution approach based on digital simulation is much more realistic. 

The main process variables in differential contacting devices vary continuously with respect to distance. Dynamic simulations therefore involve variations with respect to both time and position. Thus two independent variables, time and position, are now involved. Although the basic principles remain the same, the mathematical formulation, for the dynamic system, now results in the form of partial differential equations. As most digital simulation languages permit the use of only one independent variable, the second independent variable, either time or distance is normally eliminated by the use of a finite-differencing procedure. In this chapter, the approach is based very largely on that of Franks (1967), and the distance coordinate is treated by finite differencing. 

The coupling of the component and energy balance equations in the modelling of non-isothermal tubular reactors can often lead to numerical difficulties, especially in solutions of steady-state behaviour. In these cases, a dynamic digital simulation approach can often be advantageous as a method of determining the steady-state variations in concentration and temperature, with respect to reactor length. The full form of the dynamic model equations are used in this approach, and these are solved up to the final steady-state condition, at which condition... 

Axial and radial dispersion or non-ideal flow in tubular reactors is usually characterised by analogy to molecular diffusion, in which the molecular diffusivity is replaced by eddy dispersion coefficients, characterising both radial and longitudinal dispersion effects. In this text, however, the discussion will be limited to that of tubular reactors with axial dispersion only. Otherwise the model equations become too complicated and beyond the capability of a simple digital simulation language. 

Using the digital simulation approach to steady-state design, the design calculation is shown to proceed naturally from the defining component balance and energy balance equations, giving a considerable simplification to conventional text book approaches. 

Here the nomenclature is the same as in Sec. 4.4.2 and in addition, Dq is the effective eddy dispersion coefficient for the organic or extract phase (m / s) and Dl is the effective eddy dispersion coefficient for the aqueous or feed phase (m / s). The above equations are difficult to solve analytically (Lo et al., 1983) but are solved with ease, using digital simulation. 

Assuming constant coefficients, both the dynamic and steady-state equations describing this system can be solved analytically, but the case of varying coefficients requires solution by digital simulation. 

Chu, Y. (1969) Digital Simulation of Continuous Systems, McGraw-Hill. 

Ingham, J. and Dunn, I. J. (1974) Digital Simulation of Stagewise Processes with Backmixing. The Chem. Eng., June, 354-365. 

Prenosil, J. E. (1976) Multicomponent Steam Distillation A Comparison between Digital Simulation and Experiment. Chem. Eng. J., 12, 59-68. 

Smith, J. M. (1987) Mathematical Modelling and Digital Simulation for Engineers and Scientists, 2nd edition, Wiley-Interscience. 

For solution by digital simulation, the depth of filter cake is divided into nine segments, each of which has an equivalent dimensionless thickness Ax. For any element n, the form of the resulting difference differential equation is given by... 

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