Batch scale factors

For every atom in the model that is located on a general position in the unit cell, there are three atomic coordinates and one or six atomic displacement parameters (one for isotropic, six for anisotropic models) to be refined. In addition there is one overall scale factor per structure (osf, or the first free variable in SHELXL see Section 2.7) and possibly several additional scale factors, like tbe batch scale factors in the refinement of twirmed structures, the Flack-x parameter for non-centrosymmetric structures, one parameter for extinction, etc. In addition to the overall scale factor, SHELXL allows for up to 98 additional free variables to be refined independently. These variables can be tied to site occupancy factors (see Chapter 5) and a variety of other parameters such as interatomic distances. 

A value of 0.5 for the Flack-x parameter points to a 50 50 twin, corresponding to a value of 0.5 for the BASF. Frequently, however, a starting value of 0.5 for free variables or batch scale factors corresponds to a pseudo-minimum. It is better to start with values slightly above or below 0.5, for example 0.4 or 0.6. 

The matrix rij is the twin law and n the number of twin domains. The batch scale factor BAS F is followed by n — 1 starting values for the fractional contributions. The default value for n is 2, which corresponds to a twin with two domains. 

Scale Up of Process. The scale up of fluidized bed coating processes has received little attention in the literature. Current practices in the pharmaceutical industry are reviewed by Mehta (1988). The basic approach described by Mehta (1988) is to scale the airflow and liquid spray rates based on the cross-sectional area for gas flow. This seems reasonable except for the fact that in the scaling of the equipment, the height of the bed increases with increasing batch size. For this reason, a time scale factor is also required. 

Equation 4.4.4 is die dimensionless, reaction-based design equation of an ideal batch reactor, written for die mth-independent reaction. The factor ( / Co) is a scaling factor that converts die design equation to dimensionless form. Its physical significance is discussed below (Eqs. 4.4.13-4.4.15). 

The scaling factor itself is expressed in this case as a mass ration of DSC sample amount and material per plant batch. 

The. hkl file consists of one line per reflection in FORMAT (3I4,2F8.2,I4) for h, k, 1, Fl, a (Fq), and (optionally) a batch number. This file should be terminated by a record with all items zero individual data sets within the file should not be separated from one another—the batch numbers serve to distinguish among groups of reflections for which separate scale factors are to be refined. The reflection order and the batch number order are unimportant. The. hkl file is read when the hklf instruction (which terminates the. ins file) is encountered. The HKLF instruction specifies the format of the. hkl file, and allows scale factors and a reorientation matrix to be applied. Lorentz, polarization and absorption corrections are assumed to have been applied to the data in the. hkl file. Note that there are special extensions to the. hkl format for Laue and powder data, as well as for twinned crystals that cannot be handled by a TWIN instruction alone. 

Figure 4.18c plots the cumulative distribution function, P x), for the minimum case while Fig. 4.18d plots the Gumbel cumulative distribution function, P(x), for the maximum case. To infer the value of both /j. and / of a batch of data we can proceed as for the assessment of the exponent m and the scale factor x, of a WeibuU distribution (see Eq. 4.38). Using the P(x) expression (4.64) for the maximum case, it is... 

Hydrothermal Synthesis Systems. Of the unit operations depicted in Figure 1, the pressurized sections from reactor inlet to pressure letdown ate key to hydrothermal process design. In consideration of scale-up of a hydrothermal process for high performance materials, several criteria must be considered. First, the mode of operation, which can be either continuous, semicontinuous, or batch, must be determined. Factors to consider ate the operating conditions, the manufacturing demand, the composition of the product mix (single or multiple products), the amount of waste that can be tolerated, and the materials of constmction requirements. Criteria for the selection of hydrothermal reactor design maybe summarized as... 

Esterification is generally carried out by refluxing the reaction mixture until the carboxyHc acid has reacted with the alcohol and the water has been spHt off. The water or the ester is removed from the equiUbrium by distillation. The choice of the esterification process to obtain a maximum yield is dependent on many factors, ie, no single process has universal appHcabiUty. Although extensive preparative techniques have been reviewed elsewhere (7,68), the methods given ia this section are representative of both laboratory and plant-scale techniques used ia batch esterifications. 

Scaling Up Test Results The results of small-scale tests are determined as dry weight of sohds or volume of filtrate per unit of area per cycle. This quantity multiplied by the number of cycles per day permits the calculation of either the filter area reqiiired for a stipulated daily capacity or the daily capacity of a specified plant filter. The scaled-up filtration area should be increased by 25 percent as a factor of uncertainty. In the calculation of cycle length, proper account must be made of the downtime of a batch filter. 

Where activated carbon is a potential treatment technology, the first evaluation step is generally to run simple isotherms to determine feasibility. Isotherms are based on batch treatment where impurities reach equilibrium on available carbon surface. While such tests provide an indication of the maximum amount of impurity a GAC can adsorb, it cannot give definite scale up data for a GAC operation due to several factors ... 

As far as industrial applications are concerned, the easy scale-up of two-phase catalysis can be illustrated by the first oxo aqeous biphasic commercial unit with an initial annual capacity of 100,000 tons extrapolated by a factor of 1 24,000 (batch-wise laboratory development production reactor) after a development period of 2 years [4]. 

Similar observations can be made on other installation factors - for example, stractures and building. While traditionally (large) continuous plants are built outdoors and (small) batch plants indoors, it may not necessarily imply that small and intermediate-scale continuous plants should follow this mle. Product containment and contamination requirements may dictate the need for an enclosed manufacturing environment, meaning that little saving in capital may be realized. 

Establishing the process sensitivity with respect to the above-mentioned factors is crucial for further scale-up considerations. If the sensitivity is low, a direct volume scale-up is allowed and the use of standard batch reactor configurations is permitted. However, many reactions are characterized by a large thermal effect and many molecules are very sensitive to process conditions on molecular scale (pH, temperature, concentrations, etc.). Such processes are much more difficult to scale up. Mixing can then become a very important factor influencing reactor performance for reactions where mixing times and reaction times are comparable, micromixing also becomes important. 

Factors re.sponsible for the occurrence of scale-up effects can be either material factors or size/shape factors. In addition, differences in the mode of operation (batch or semibatch reactor in the laboratory and continuous reactor on the full scale), or the type of equipment (e.g. stirred-tank reactor in the laboratory and packed- or plate- column reactor in commercial unit) can be causes of unexpected scale-up effects. A simple misuse of available tools and information also can lead to wrong effects. 

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