Process Yield Uncertainty

Variations in star formation history should be imprinted on the s- and r-process ratios as well, however their interpretation can be more complicated because of uncertainties in their exact sources (and thus yields). Y and Ba trace the first and second peak in neutron magic number, respectively, and can be used to examine r-process yields in very metal-poor stars. However, they also have a significant contribution from the s-process in AGB stars, which dominates their production with increasing metallicity. Since AGB s-process yields are thought... 

This chapter addresses the planning, design and optimization of a network of petrochemical processes under uncertainty and robust considerations. Similar to the previous chapter, robustness is analyzed based on both model robustness and solution robustness. Parameter uncertainty includes process yield, raw material and product prices, and lower product market demand. The expected value of perfect information (EVPI) and the value of the stochastic solution (VSS) are also investigated to illustrate numerically the value of including the randomness of the different model parameters. 

Since the randomness in the profit uncertainty term is a product of two random parameters, process yield 6cp,m,fc and chemical prices Pr, its variance can be written based on the variance of a product of two variables x and y (J ohnson and Tetley, 1955), that is ... 

Table 8.1 shows the stochastic model solution for the petrochemical system. The solution indicated the selection of 22 processes with a slightly different configuration and production capacities from the deterministic case, Table 4.2 in Chapter 4. For example, acetic acid was produced by direct oxidation of n-butylenes instead of the air oxidation of acetaldehyde. Furthermore, ethylene was produced by pyrolysis of ethane instead of steam cracking of ethane-propane (50-50 wt%). These changes, as well as the different production capacities obtained, illustrate the effect of the uncertainty in process yield, raw material and product prices, and lower product... 

The results of the model considered in this Chapter under uncertainty and with risk consideration, as one can intuitively anticipate, yielded different petrochemical network configurations and plant capacities when compared to the deterministic model results. The concepts of EVPI and VSS were introduced and numerically illustrated. The stochastic model provided good results as the objective function value was not too far from the results obtained using the wait-and-see approach. Furthermore, the results in this Chapter showed that the final petrochemical network was more sensitive to variations in product prices than to variation in market demand and process yields when the values of 0i and 02 were selected to maintain the final petrochemical structure. 

For some experiments, the solar neutrino flux and the rate of decay of the proton being extreme examples, tire count rate is so small that observation times of months or even years are required to yield rates of sufficiently small relative uncertainty to be significant. For high count rate experiments, the limitation is the speed with which the electronics can process and record the incoming infomiation. 

We take a Bayesian approach to research process modeling, which encourages explicit statements about the prior degree of uncertainty, expressed as a probability distribution over possible outcomes. Simulation that builds in such uncertainty will be of a what-if nature, helping managers to explore different scenarios, to understand problem structure, and to see where the future is likely to be most sensitive to current choices, or indeed where outcomes are relatively indifferent to such choices. This determines where better information could best help improve decisions and how much to invest in internal research (research about process performance, and in particular, prediction reliability) that yields such information. 

The production of the agrochemical 6 (Scheme 5.7) is carried out batchwise via a three-step protocol. Mass balancing has been conducted for three stages of development Laboratory-, pilot- and operation scale. An LCA was available for the operation stage only. A description of this LCA including data sources and data acquisition methods was published by Geisler et al. (product A in reference [9] corresponds to product 6 here). Many parameters in the Life-Cycle Inventory (LCI) are estimated, especially utihty demands and yields of processes for the production of precursors. Uncertainty in these estimations was illustrated in a... 

Modern dynamical calculations of the r-process are described by Cowan, Thielemann and Truran (1991ab), Takahashi, Witti and Janka (1994) and Woosley et al. (1994). Chen el al. (1995), Langanke and Wiescher (2001), Thielemann et al. (2001) and Kratz (2001) discuss the nuclear physics issues. Goriely and Arnould (2001) discuss the estimation of yields and their uncertainties. 

The strong global competition has been increasing the pressure to an efficient operation of chemical batch plants. Flexible batch plants are used to react quickly to changes in customers demands. The variations in the demands as well as, e.g., the prices of raw materials, or the yields ofthe production process are not exactly known at the time of scheduling. When these uncertainties are not sufficiently considered in the scheduling, the operations will lead to lower profits or even losses. 

Collection of multiple data sets for each time span, with frequent alternation of the polarization, is an essential feature of our protocol. This provides some protection against the effects of drifts in laser power, photomultiplier quantum yield, and absolute calibration of the TAC, photochemical decomposition of the dye, and any other long-term processes that may alter the measured fluorescence response curves. Separate analysis of each data set is necessary to provide an indication of the uncertainty in run-to-run reproducibility and to detect and delete the rare spurious data set. 

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