Steady-state data

A real-time optimization (RTO) system determines set point changes and implements them via the computer control system without intervention from unit operators. The RTO system completes all data transfer, optimization c culations, and set point implementation before unit conditions change and invahdate the computed optimum. In addition, the RTO system should perform all tasks without upsetting plant operations. Several steps are necessaiy for implementation of RTO, including determination of the plant steady state, data gathering and vahdation, updating of model parameters (if necessaiy) to match current operations, calculation of the new (optimized) set points, and the implementation of these set points. 

Sikdar, S.K., 1977. Size-dependent growth rate from curved log n(L) vs. L steady-state data. Industrial and Engineering Chemistry Fundamentals, 16, 390. 

Most vibration programs that use microprocessor-based analyzers are limited to steady-state data. Steady-state vibration data assumes the machine-train or process system operates in a constant, or steady-state, condition. In other words, the machine is free of dynamic variables such as load, flow, etc. This approach further assumes that all vibration frequencies are repeatable and maintain a constant relationship to the rotating speed of the machine s shaft. 

While steady-state data provide a snapshot of the machine, dynamic or real-time data provide a motion picture. This approach provides a better picture of the dynamics of both the machine-train and its vibration profile. Data acquired using steady-state methods would suggest that vibration profiles and amplitudes are constant. However, this is not tme. All dynamic forces, including mnning speed, vary constantly in all machine-trains. When real-time data acquisition methods are used, these variations are captured and displayed for analysis. 

Most of the microprocessor-based vibration monitoring systems collect single-channel, steady-state data that cannot be used for all applications. Single-channel data are limited to the analysis of simple machinery that operates at relatively constant speed. 

Dynamic simulations for an isothermal, continuous, well-mixed tank reactor start-up were compared to experimental moments of the polymer distribution, reactant concentrations, population density distributions and media viscosity. The model devloped from steady-state data correlates with experimental, transient observations. Initially the reactor was void of initiator and polymer. 

Nal concentration, up to 1 X 10 They also obtained steady-state data using a potential step method. The applied potential was initially set at -0.9 V, where no iodide absorption occurs. The electrode was stepped to various positive potentials and A/(ad) was recorded until equilibrium values were obtained. Similar measurements were done in an electrolyte without Nal, and A/(no-ad) was recorded as a reference. The net change in frequency was determined as IAA/I = A/(ad) -A/(no-ad). Figure 27.22 shows I AA/I vs. E plots for various Nal concentrations. Analysis of the data showed that iodide adsorption occurred in accordance with the Temkin isotherm. 

Timm, Gilbert, Ko, and Simmons O) presented a dynamic model for an isothermal, continuous, well-mixed polystyrene reactor. This model was in turn based upon the kinetic model developed by Timm and co-workers (2-4) based on steady state data. The process was simulated using the model and a simple steady state optimization and decoupling algorithm was tested. The results showed that steady state decoupling was adequate for molecular weight control, but not for the control of production rate. In the latter case the transient fluctuations were excessive. 

Barrer (19) has developed another widely used nonsteady-state technique for measuring effective diffusivities in porous catalysts. In this approach, an apparatus configuration similar to the steady-state apparatus is used. One side of the pellet is first evacuated and then the increase in the downstream pressure is recorded as a function of time, the upstream pressure being held constant. The pressure drop across the pellet during the experiment is also held relatively constant. There is a time lag before a steady-state flux develops, and effective diffusion coefficients can be determined from either the transient or steady-state data. For the transient analysis, one must allow for accumulation or depletion of material by adsorption if this occurs. 

Any model which can explain all such complicated results is bound to be nearer the truth than one based on steady state data alone. 

Especially for the low temperature water gas shift reaction the mechanistic scheme, proposed here, seems to correspond to the three different adsorbed oxygen species, proposed by Kobaya-shi (13) for the ethylene oxidation on silver, whereas the importance of some surface complexes of CO - 1 0 type has been revealed (14) by analysing steady state data. 

Historically, treatment of measurement noise has been addressed through two distinct avenues. For steady-state data and processes, Kuehn and Davidson (1961) presented the seminal paper describing the data reconciliation problem based on least squares optimization. For dynamic data and processes, Kalman filtering (Gelb, 1974) has been successfully used to recursively smooth measurement data and estimate parameters. Both techniques were developed for linear systems and weighted least squares objective functions. 

Chapter 5 deals with steady-state data reconciliation problem, from both a linear and a nonlinear point of view. Special consideration is given, in Chapter 6, to the problem of sequential processing of information. This has several advantages when compared with classical batch processing. 

In this chapter we concentrate on the statement and further solution of the general steady-state data reconciliation problem. Initially, we analyze its resolution for linear plant models, and then the nonlinear case is discussed. 

As in the classical steady-state data reconciliation formulation, the optimal estimates are those that are as close as possible (in the least squares sense) to the measurements, such that the model equations are satisfied exactly. 

This chapter discusses some recent approaches for dealing with different aspects of the data reconciliation problem. A more general formulation in terms of a probabilistic framework is first introduced, and its use in dealing with gross error is discussed in particular. Robust estimation approaches are then considered, in which the estimators are designed so that they are insensitive to outliers. Finally, a strategy that combines principal component analysis and steady-state data reconciliation will be discussed. 

Correlations are inherent in chemical processes even where it can be assumed that there is no correlation among the data. Principal component analysis (PCA) transforms a set of correlated variables into a new set of uncorrelated ones, known as principal components, and is an effective tool in multivariate data analysis. In the last section we describe a method that combines PCA and the steady-state data reconciliation model to provide sharper, and less confounding, statistical tests for gross errors. 

The key idea of this section is to combine PCA and the steady-state data reconciliation model to provide sharper and less confounding statistical tests for gross errors, through exploiting the correlation. 

Since steady-state data are much easier to obtain, some effort has been directed to methods for deriving time-resolved anisotropy parameters from the steady-state anisotropy/2 4549-1 A number of relationships have been described, some of which require knowledge of r0 and the fluorescence lifetime (see, e.g., Ref. 48). An example(50) of such an empirical relationship is... 

Vatcha reports that the rate expression given by Eq. (1) describes the global rate, thus allowing gas phase concentrations to be used in the reaction analysis. Global reaction kinetics will be used in the analysis to follow. Consequently, these kinetics must account for microscopic processes such as adsorption/desorption on the catalyst surface and intraparticle diffusion. Since most available kinetic information is based on steady-state data, a major... 

The presence of a thermodynamically favourable interaction between protein and polysaccharide is commonly associated with a marked decrease in protein surface activity at the air-water or oil-water interface (see Figures 7.5b and 7.15). There is a slower decay in the surface tension for complexes in comparison with the pure protein, and also higher values of the tension in the steady state. Data establishing these trends have been reported for the following biopolymer pairs in aqueous media legumin + dextran and legumin + maltodextrin (Antipova and Semenova,... 

The enzyme has been shown to be specific for the (3 form by rapid reaction measurements on a time scale faster than that for the interconversion of the anomers, and also by determination of the activity toward model substrates that are locked in either of the configurations. By using sufficient enzyme to phos-phorylate all the active anomer of the substrate before the two forms can reequilibrate, it is found that 80% of the substrate reacts rapidly, and that the remaining 20% reacts at the rate constant for the anomerization. The kinetics were followed both by quenched flow using [y-32P]ATP10 and by the coupled spectrophotometric assay of equation 6.4.11 The other evidence comes from the steady state data on the following substrates 12... 

Table III. Steady-State Data Arranged According to Pressure Level...

Although V)/ ss is a steady-state parameter, it can be calculated using non-steady-state data as... 

As noted k3 cannot be found from the steady state data. 

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