Simulation column, mathematical model

Digital simulation based on an appropriate mathematical model is the best tool in order to understand the dynamic behaviour of the column We used a set of equations which models every stage as an heterogeneous two-phase system consisting of the two totally mixed homogeneous phases vapour and liquid (Figure 2). 

Cybulski et al. [39] have studied the performance of a commercial-scale monolith reactor for liquid-phase methanol synthesis by computer simulations. The authors developed a mathematical model of the monolith reactor and investigated the influence of several design parameters for the actual process. Optimal process conditions were derived for the three-phase methanol synthesis. The optimum catalyst thickness for the monolith was found to be of the same order as the particle size for negligible intraparticle diffusion (50-75 p.m). Recirculation of the solvent with decompression was shown to result in higher CO conversion. It was concluded that the performance of a monolith reactor is fully commensurable with slurry columns, autoclaves, and trickle-bed reactors. 

Chapter 4 starts with some basic equations, which relate the molecular-kinetic picture of gas-solid chromatography and the experimental data. Next come some common mathematical properties of the chromatographic peak profiles. The existing attempts to find analytical formulae for the shapes of TC peaks are subject to analysis. A mathematical model of migration of molecules down the column and its Monte Carlo realization are discussed. The zone position and profile in vacuum thermochromatography are treated as chromatographic, diffusional and simulation problems. 

So-called plant dispersion" or extra column effects" have to be taken into account by additional mathematical models rather than including them indirectly in the model parameters of the column, e.g. by altering the dispersion coefficient. The combination of peripheral and column models is easily implemented in a modular simulation approach. In a flowsheeting approach the boundary conditions of different models are connected by streams (node balances) and all material balances are solved simultaneously. 

The determination of kinetic parameter values from column experiments is predicated upon the ability of the mathematical model to successfully simulate the experimental data. Confidence in the robustness of the parameter values so determined is attained only with a unique solution (i.e., when one suite of parameter values provides a solution that is significantly better than all others). For cases wherein a system is near equilibrium or under extreme nonequilibrium, attainment of a unique solution may prove difficult. A modified miscible-displacement technique, involving flow interruption, that enhances the potential for achieving unique solutions, and thus increases the robustness of optimized values of kinetic parameters, was presented by Brusseau et al. (1989a). In addition, the method has increased sensitivity to nonequilibrium, making it useful for process-level investigation of sorption kinetics. This method would appear to be especially useful for systems com-... 

Park [74] studied the efficiency of the ELM with non-Newtonian hquids in the removal of Zn, Pb, Ni and Cd from a simulated industrial wastewater using the Taylor-vortex column. The author adapted the shrinking core mathematical model of Liu and Liu [86] for quantitative description of the mass-transfer kinetics of the process [74]. The LM was prepared by the dissolution of 5 g dm of polyisobutylene in Soltrol 220 (see above). After complete dissolution of the polymer, the membrane phase... 

Before reviewing larger-scale studies and applications, we briefly discuss the modes of operation possible in fonm flotation and the corresponding details of column desiga to optimize results. Although mathematical models currently provide excellent simulations of column design and operation,1 that discussion is beyond the scope of lhis chapter. The discussion herein is qualitative. 

Nowadays, several process simulators such as Aspen Plus and Aspen HYSYS are commercially available for simulating complete chemical processes. Common process units and a property database for numerous chemicals are available in such simulators. However, models for less common and/or new process units (for example, membrane separation) are not readily available in the simulators, but they may be available in the literature or can be developed from first principles. Mathematical model for a new process unit can be implemented in Aspen Custom Modeler (ACM), and then it can be exported to (included in) Aspen Plus or Aspen HYSYS for simulating processes having a new process unit besides common process units such as heat exchangers, compressors, reactors and columns. Process simulators for simulation and ACM for implementing models of new process units are... 

The mathematical model was successfiilly used for the computation of the performance of the industrial cadmium column at Metaleurop Nord, Noyelles Godault and also for the trials on a laboratory scale. The Murphree efficiency and also the heat contribution along the height of the column are very sensitive parameters for the simulation program. 

The mathematical modelling of chemical processes in chemical plants, e.g. the dynamical simulation of complex chemical and physical processes in heat- and current-coupled distillation columns, leads to initial value problems for large scale systems of differential algebraic equations (DAE)... 

The numerical methods were tested by means of two examples delivered with the chemical process simulator SPEEDUP [1, 6]. The example DYNEVAP consisting of 87 equations within 13 subsystems represents a double effect evaporator. The second example BTX, a mathematical model of a Benzene-Toluene-Xylene distillation column, is made of 52 subsystems containing 1089 equations. It has been written a code which is able to create automatically an interface for our codes out of the data supplied by SPEEDUP when simulating a process. The interface contains the DAE system in a structured representation. It is used for subsystem-wise function and Jacobian matrix evaluation. 

Balzli, M.W. Liapis. A.I.. and Rippin, D.W.T., Applications of mathematical modelling to simulation of multicomponent adsorption in activated carbon columns, Trans. IChemE, 56, T145-T156 (1978) Chem. Eng. Res. Des., 61,393 (1983). 

A column with a number of trays may be represented by a mathematical model such as shown in Figure 13.3. This may be simulated readily on a large digital computer. For a mathematical analysis, however, or for hand calculations, we need a simpler model. 

Our miscible-displacement modeling approach was modified in order to describe S04 effluent from the BS (as well as BC) layers. We adjusted the computer code to account for a variable concentration of the input pulse rather than a constant one as is commonly accepted in most column experiments and mathematical solutions. In all our simulations presented here, for each soil column, the S04 input concentrations from our experimental results were incorporated as inputs to the model. In addition, presentations of relative concentrations (C/C0) were based on the respective C0 of the applied solution to the top layer (E). 

Computer simulation models have been formulated for cascade and Stratco sulfuric acid alkylation units. These complete models incorporate mathematical descriptions of all the interacting parts of the units, including reactors, distillation columns, compressors, condensers, and heat exchangers. Examples illus-strate diverse model applications. These Include identifying profitable unit modifications, comparing cascade to Stratco performance, evaluating optimal unit capacity and determining optimal deisobutanizer operation. 

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