Mathematical simulation

The above example is a simple one, and it can be seen that the individual items form part of the chain in the production system, in which the items are dependent on each other. For example, the operating pressure and temperature of the separators will determine the inlet conditions for the export pump. System modelling may be performed to determine the impact of a change of conditions in one part of the process to the overall system performance. This involves linking together the mathematical simulation of the components, e.g. the reservoir simulation, tubing performance, process simulation, and pipeline behaviour programmes. In this way the dependencies can be modelled, and sensitivities can be performed as calculations prior to implementation. 

We used the concept of sound velocity dispersion for explanation of the shift of pulse energy spectrum maximum, transmitted through the medium, and correlation of the shift value with function of medium heterogeneity. This approach gives the possibility of mathematical simulation of the influence of both medium parameters and ultrasonic field parameters on the nature of acoustic waves propagation in a given medium. 

Occidental Petroleum Coal Conversion Process. Garrett R D Co. (now the Occidental Research Co.) developed the Oxy Coal Conversion process based on mathematical simulation for heating coal particles in the pyrolysis unit. It was estimated that coal particles of 100-mm diameter could be heated throughout their volumes to decomposition temperature (450—540°C) within 0.1 s. A large pilot faciUty was constmcted at LaVeme, California, in 1971. This unit was reported to operate successfully at feed rates up to 136 kg/h (3.2 t/d). 

A discussion of retention time in rotary Idlns is given in Brit. Chem. Eng., 27-29 (Januaiy 1966). Rotary-ldln heat control is discussed in detail by Bauer [Chem. Eng., 193-200 (May 1954)] and Zubrzycki [Chem. Can., 33-37 (Februaiy 1957)]. Reduction of iron ore in rotaiy Idlns is described by Stewart [Min. Congr J., 34—38 (December 1958)]. The use of balls to improve solids flow is discussed in [Chem. Eng., 120-222 (March 1956)]. Brisbane examined problems of shell deformation [ Min. Eng., 210-212 (Februaiy 1956)]. Instrumentation is discussed by Dixon [Ind. Eng. Chem. Process Des. Dev., 1436-1441 (July 1954)], and a mathematical simulation of a rotaiy Idln was developed by Sass [Ind. Eng. Chem. Process Des. Dev., 532-535 (October 1967)]. This last paper employed the empirical convection heat-transfer coefficient given previously, and its use is discussed in later correspondence [ibid., 318-319 (April 1968)]. 

The algorithm is based both on a mathematical simulation of a spectmm of secondary radiation emitted by a sample to be studied and the detector response function. The detection limit is given by criteria 3s ... 

Mathematical A mathematical simulation of the emission, dispersion, and chemical process relating to the concentration of pollutants. 

Mathematical simulation of C, E curves shows that the shape of the diffuse-layer capacitance minimum depends on the difference of Eamo in individual faces and their fractions, as well as on the shape of partial Cj, E curves (Fig. 9). 

Collins, M.J., Riley, M.S., Child, A.M. and Turner-Walker, G. 1995 A basic mathematical simulation of the chemical degradation of ancient collagen. Journal of Archaeological Science 22 175-183. 

Topaz was used to calculate the time response of the model to step changes in the heater output values. One of the advantages of mathematical simulation over experimentation is the ease of starting the experiment from an initial steady state. The parameter estimation routines to follow require a value for the initial state of the system, and it is often difficult to hold the extruder conditions constant long enough to approach steady state and be assured that the temperature gradients within the barrel are known. The values from the Topaz simulation, were used as data for fitting a reduced order model of the dynamic system. 

Shimao, K, Mathematical Simulation of Isotachophoresis Boundary Between Protein and Weak Acid, Electrophoresis 7, 297, 1986. 

Under this electrochemical configuration, it is commonly accepted that the system can be expressed by the Randles-type equivalent circuit (Fig. 6, inset) [23]. For reactions on the bare Au electrode, mathematical simsulations based on the equivalent circuit satisfactorily reproduced the experimental data. The parameters used for the simulation are as follows solution resistance, = 40 kS2 cm double-layer capacitance, C = 28 /xF cm equivalent resistance of Warburg element, W — R = 1.1 x 10 cm equivalent capacitance of Warburg element, IF—7 =l.lxl0 F cm (

charge-transfer resistance, R = 80 kf2 cm. Note that these equivalent parameters are normalized to the electrode geometrical area. On the other hand, results of the mathematical simulation were unsatisfactory due to the nonideal impedance behavior of the DNA adlayer. This should... 

Soil compartment chemical fate modeling has been traditionally performed for three distinct subcompartments the land surface (or watershed) the unsaturated soil (or soil) zone and the saturated (or groundwater) zone of a region. In general, the mathematical simulation is structured around two major cycles the hydrologic cycle and the pollutant cycle, each cycle being associated with a number of physicochemical processes. Watershed models account for a third cycle sedimentation. 

Mathematical Simulation of Single Catalyst Batch Reactions. 74... 

The method of mathematical simulation has many advantages, and is very close to the physical experiment. However the further development of this approach /a consideration of volume effects, reversible reactions and so onj can be rather difficult because it will reau.ire too much computer time, therefore it is expedient to search some simple analytical or semianalytical approximate approaches to the calculation of cross-linking kinetics and conformational properties of cross-linked macromolecules. The results obtained bv the Fonte Carlo calculation can serve as criteria of the accuracy of such approximation. 

Lupi M, Matera G, Branduardi D, D Incalci M, Ubezio P. Cytostatic and cytotoxic effects of topotecan decoded by a novel mathematical simulation approach. Cancer Res. 2004 Apr 15 64(8) 2825-32. 

A radical tandem cyclization, consisting of two radical carbocyclizations and a heterocoupling reaction, has been achieved by electrolysis of unsaturated carboxylic acids with different coacids. This provides a short synthetic sequence to tricyclic products, for example, triquinanes, starting from carboxylic acids which are accessible in few steps (Scheme 6) [123]. The selectivity for the formation of the tricyclic, bi-cyclic, and monocyclic product depending on the current density could be predicted by applying a mathematical simulation based on the proposed mechanism. 

Improvements in deterministic (photochemical/diffusion) methods are based largely on accounting for more physicochemical effects in the structure of the model. Specific research subjects for improved models include photochemical aerosol formation and the effects of turbulence on chemical reaction rates. The challenge to the researcher is to incorporate the study of these subjects without needlessly complicating already complex models. How accurate a mathematical simulation is required What, roughly, will be the effect of omitting some particular chemical or physical component What is the sensitivity of model outputs to inaccuracies in the inputs ... 

To be able to mathematically simulate and really understand the thermochemical conversion process of a packed bed both a single particle model and a bed model must be included in the overall bed model (CFSD code ... 

The emerging concept of developing experimental mini-ecosystems — focused on controlled-exposure environments for testing and for developing mathematical simulations of ecosystem impact based on limited, specific tests—should be supported. 

Figure 6. Experimentally observed and mathematically simulated regression lines of foam capacity of different percentages of glandless cottonseed flour in suspensions at various pH values. Experimental 4%, 10%, and 16% suspensions were run at pH 3.5, 6.5, and 9.5 to test the reliability of the multiple linear regression analysis. Quantitative data used in this analysis are in Figures 2 and 4.

Figure 7. Experimentally observed and mathematically simulated regression lines of foam stability at different percentages of glandless cottonseed flour in suspensions at various pH values. See Figure 6 for further explanation of the data.

Thus, the only way to study the early radiolysis stages is to study them theoretically, especially with mathematical simulation. The correctness of our theoretical conceptions is determined by how well all the consequences of the theory agree with the available experimental data... 

To analyze the temperature distribution in any real situation, it is necessary to consider mold filling and solidification simultaneously. An example illustrating temperature distributions at various times along the length of a polymeric layer at the surface of a solid wall is shown in Fig. 4.18. The initial temperature and conversion distributions are not constant but reflect mathematical simulations of various conditions at the mold filling stage. 

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