Efficiencies estimating, example

This column requires you to indicate "Yes or "No" to whether the treatment efficiency estimate is based on actual operating data. For example, you would check Yes if the estimate is based on monitoring of influent and effluent wastes under typical operating conditions. For sequential treatment, do not indicate "Yes" or "No" in column F for a treatment step unless you have provided a treatment estimate in column E. 

Temperature Ihe temperature in a bioreactor is an important parameter in any bioprocess, because all microorganisms and enzymes have an optimal temperature at which they function most efficiently. For example, optimal temperature for cell growth is 37 °C for Escherichia coli and 30 °C for Saccharomyces sp, respectively. Although there are many types of devices for temperature measurements, metal-resistance thermometers or thermistor thermometers are used most often for bioprocess instrumentation. The data of temperature is sufficiently reliable and mainly used for the temperature control of bioreactors and for the estimation of the heat generation in a large-scale aerobic fermentor such as in yeast production or in industrial beer fermentation. 

In practice the tray efficiency is estimated from a model that combines information about the tray hydrodynamics, with a model for the point efficiency that is defined analogously to the tray efficiency but applied to a narrow vertical slice of the froth (see Fig. 12.1). The Murphree vapor-phase point efficiency, for example, is defined by... 

The new estimate of 0 is a more efficient estimator since it makes use of the variability in the data. A modification of this process is to combine Steps 2 and 3 into a single step and iterate until the GLS parameter estimates stabilize. This modification is referred to as iteratively reweighted least-squares (IRWLS) and is an option available in both WinNonlin and SAS. Early versions of WinNonlin were limited in that g(.) was limited to the form in Eq. (4.6) where is specified by the user. For example, specifying 4> = 0.5, forces weights... 

In new construction, the current requirement is often calculated from estimates such as those in Table 6. The amount of bare steel depends on the assumed quality of the coating, both to begin with and after several years of operation. A coating efficiency, for example, of 95% equals 5% bare metal. The current requirement is then the total area of the pipe, times the percent bare (as a decimal) times the current per square meter, or... 

The light source should be tuned to have an output which matches the AM 1.5 G spectrum at one sun intensity (100 mW/cm ) to most accurately estimate real-world STH efficiencies. An example is shown in Fig. 8.2 for a GalnP2/GaAs tandem cell. Note that this particular sample is not the same sample shown in Fig. 8.1. 

An approximation of the parameter distributions by a Gaussian density enables an efficient estimation of the failure probability variation which agreed very well with the results of the sample analysis in the investigated example. 

Example 13.4 Overall Efficiency Estimate Using O Connell s Correlation... 

This means that the number of samples N needed to achieve an acceptable level of accuracy is inverse proportional to pp, and therefore very large, N oc 1/ pp 1. For example, if Pf = 10 " and the c.o.v. of 10 % is desirable, then Af = 10 samples are required. Note, however, that each evaluation of Ip i= I,.., N, in Eq. 12 requires a system analysis to be performed to check whether the sample is a failure sample. As it has been already mentioned in section Engineering Reliability Problem, the computation effort for the system analysis, i.e., computation of the performance function g(x), is significant (usually involves the FEM method). As a result, the DMC method becomes excessively costly and practically inapplicable for reliability analysis. This deficiency of DMC has motivated research to develop more advanced simulation algorithms for efficient estimation of small failure probabilities in high dimensions. 

When the confidence interval is determined by unbiased and efficient estimators, we may say that the parameter is estimated accurately. It is not always possible, however, to satisfy both conditions simultaneously. In the previous example, the arithmetic mean is the unbiased and efficient estimator of the true weight (Hamilton, 1964, p. 39 Johnson and Leone, 1977, p. 214). The estimator of the sample variance, can be given by two expressions (Hamilton, 1964, p. 40) ... 

The increased use of composite materials in aireraft industry the last years has impliedagrowing need for efficient methods for nondestructive characterization of composite materials. One example is determination of porosity contents in composite specimens during manufacturing. Results have been reported [1], showing that the porosity contents can be estimated with good aceuracy by utilizing a linear relation between the frequeney dependenee of the attenuation, i.e., P = +1, where P is the porosity content, K and I are constants and where is the slope... 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

The method for estimating point efficiency, outhned here, is not the only approach available for sieve plates, and more mechanistic methods are under development. For example, Prado and Fair [Ind. Eng. Chem. Re.s., 29, 1031 (1990)] have proposed a method whereby bubbling and jetting are taken into account however the method has not been vahdated tor nonaqueous systems. Chen and Chuang [Ind. Eng. Chem. Re.s., 32, 701 (1993)] have proposed a more mechanistic model for predicting point efficiency, but it needs evaluation against a commercial scale distillation data bank. One can expect more development in this area of plate efficiency prediction. 

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