Sequential experimental procedure

Hosten, L. H.. A sequential experimental procedure for precise parameter estimation based on the shape of the joint confidence region, Chem. Eng. Sci.. 29, 2247-2252 (1974). 

As an example for precise parameter estimation of dynamic systems we consider the simple consecutive chemical reactions in a batch reactor used by Hosten and Emig (1975) and Kalogerakis and Luus (1984) for the evaluation of sequential experimental design procedures of dynamic systems. The reactions are... 

Buzzi-Ferraris, G. and P. Forzatti, "A New Sequential Experimental Design Procedure for Discriminating Among Rival Models", Chem. Eng. Sci., 38, 225-232(1983). 

Hosten, L.H. and G. Emig, "Sequential Experimental Design Procedures for Precise Parameter Estimation in Ordinary Differential Equations", Chem. Eng. Sci., 30, 1357 (1975)... 

Procedures on how to make inferences on the parameters and the response variables are introduced in Chapter 11. The design of experiments has a direct impact on the quality of the estimated parameters and is presented in Chapter 12. The emphasis is on sequential experimental design for parameter estimation and for model discrimination. Recursive least squares estimation, used for on-line data analysis, is briefly covered in Chapter 13. 

The text reviews the methodology of kinetic analysis for simple as well as complex reactions. Attention is focused on the differential and integral methods of kinetic modelling. The statistical testing of the model and the parameter estimates required by the stochastic character of experimental data is described in detail and illustrated by several practical examples. Sequential experimental design procedures for discrimination between rival models and for obtaining parameter estimates with the greatest attainable precision are developed and applied to real cases. 

In this paper, a new computer-aided technique was presented, with which the experimental procedure of developing catalysts is scheduled sequentially. In each sequential step the neural networks model and multi-objective optimization are used to determine optimal design for the next experiment. The sequential method proved very efficient in developing catalysts for propane ammoxidation to acrylonitrile. And the yield of acrylonitrile corresponding to the best catalyst was up to 58.9%. 

The experimental procedure presented above involves a number of sequential steps that utilize relatively small volumes and weights of material. This contributed to scatter of the experimental data. Since there was no clear justification for rejecting a specific data point, all points obtained were included in the final graphs regardless of how markedly they deviated from an observed trend. The effect of data scatter on interpretation of results was minimized by assaying a number of samples for each coacervate system characterized. 

Sequential applications of iprodione were made in both laboratory and field experiments and changes in rate of degradation were monitored. Similar experiments were made with the related compound vinclozolin. A full description of the experimental procedures can be found in Walker, Brown and Entwistle (11). The results gave a clear indication that both iprodione and vinclozolin are susceptible to enhanced degradation and those from the laboratory experiments are reproduced in Figure 1. In soil treated at time 0, the time for 50% loss of iprodione was about 23 days and less than 2% of the applied dose was recovered after 49 days. In soil treated for the second time (50 days), the time for 50% loss was reduced to 5 days. When treated for the third time (100 days), only 10% of the applied dose remained 2 days later, and none was recovered after 7 days. The results for vinclozolin were similar to those for iprodione (Figure 1). 

In Chapter 3.4 a method has been presented for long-term prognosis of metal pollutant mobility, which combines column circulation leaching experiments at variable pH/E -conditions with sequential extraction procedures on the solid waste material before and after these experiments (Schoer FSrstner, 1987). Temporal release patterns are different for the individual elements (Figure 6-5) While at pH 5/400 mV release of cadmium seems to be completed within the experimental period mobilization of copper is still going on and the end point cannot be estimated from the data of the "kinetic" experiments. The same effect has been found for the examples of thallium and vanadium. For the other elements, the endpoint of release can be determined as approximately 10 mg cobalt, 0.6 mg cadmium, 600 mg zinc and 0.3 mg chromium, 2 mg barium and 20 mg lead (per 100 g of solid substrate treated with 140 L solu-... 

An experimental procedure for the direct measurement of self diffusion is the radiotracer technique. Here, molecules are marked with radioactive atoms, e.g. with C, and deposited onto the surface of the crystal at a time t = 0. Thereafter, layers are sUced off the crystal surface sequentially at times t > 0 using a microtome. A typical layer thickness is 5 /rm. The crystal is thus dissected layer by layer and the quantity of tracer molecules in each layer is analysed with a spatial resolution given by the layer thicknesses [31, 32]. 

Dumez and Froment studied the dehydrogenation of 1-butene into butadiene on a chromium-aluminium oxide catalyst in a differential reactor [57]. This work is probably the first in which the experimental program was actually and uniquely based on a sequential discrimination procedure. The reader is also referred to a more detailed treatment, Dumez, Hosten, and Froment [58]. The following mechanisms were considered to be plausible ... 

Growing interest in detailed information related to particular locations at an electrochemical interface (e.g. steps on a single crystal surface or particular features at a modified electrode surface) combined with instrumental developments have resulted in experimental methods providing localized information. In cases where this information is obtained point-by-point (sequentially), the procedure is called a scanning one and the method may be called mapping. In some cases (e.g. with focal plane... 

In the sequential procedure, the combination of experiments A and B is the same as the experiment in the first reactor in the parallel procedure. The c t) dependence is given by the same equation, Eq. (11.82) (or Eq. 11.85) and the steady-state concentration for both experimental procedures is given by Eq. (11.86). 

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