The problem of scale

Biological systems vary tremendously in size, from unicellular organisms ( 1/r.m) to sequoias ( 100 m), and in mass, they range from microbes 

Allometric scaling is commonly used to account for variations in biologic systems. If X is the variable of interest, the allometric equation assumes that this variable scales with a power of the mass M  

Correlation between total metabolic rate and body mass across species. The total metabolic rate varies with body mass according to Equation 7-45 with an exponent of.  

Welling, P.G., Pharmacokinetics processes, mathematics, and applications. ACS Professional Reference Book. Washington, DC American Chemical Society, 1997. 

Creasey, W.A., Drug Disposition in Humans The Basis of Clinical Pharmacology. New York Oxford University Press, 1979. 

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The first example involves flammability issues that are not specifically covered in this Guidelines book. However, the discussion here is highly important for safe process design considerations and represents a good example of the problems of scale-up from test data. Runaway reactions may indeed result in the production of flammable gases so an understanding of the scale-up problems is critical. 

The problems of scale-up generally arise from the transfer of heat through the walls of a vessel, or the egress of gases and vapours through a hole in the wall. Rates of both of these, being surface phenomena, increase as the square of the linear dimensions of similar vessels. However, the contents, and associated potential energies, increase as the cube. It is also the case that the pressure a... 

Leuenberger H. New trends in the production of pharmaceutical granules the classical batch concept and the problem of scale-up. Eur J Pharm 2001 52 279. Leuenberger H. New trends in the production of pharmaceutical granules batch versus continuous processing. Eur J Pharm 2001 52 289. 

The problems of scale-up generally arise from the transfer of heat through the walls of a vessel, or the egress of gases and vapours through a hole in the wall. Rates of both... 

One of the most challenging aspects of chemical engineering is the problem of scaling up a process unit from a small laboratory or pilot plant to a large commercial size. Reactors are perhaps one of the more difficult to deal with. In this section we show quantitatively what the heat transfer scaleup problem is for a CSTR. 

It must be observed again that the mixing times depend on the particular experimental techniques used to evaluate them. It is probably the different definitions of mixing time that are responsible for the differences in scale relations seen in Table V, although the limited range of some of the studies can also be a factor. The engineer faced with the problem of scale-up must decide if any of the studies outlined above are based on a mixing time definition which is especially appropriate to the situation with which he is concerned. 

The problem of scale-down may occur also, in which the geometry of the full-scale system is fixed by reasons beyond the experimenter s control. In such cases it is equally important to maintain geometric simi-... 

The full-world hypothesis, combined with the desire to design sustainable economic systems, confronts ecological economists with three economic problems - scale, distribution, and allocation. The problems of scale and distribution have traditionally been ignored by economists. 

In defining the harmonic oscillator basis by Eqs. (5.23)—(5.25) the problem of scaling was postponed. Equation (5.27) shows that the three yet undefined parameters, D, E° and a, are interrelated so that they are all determined when anyone has been given a value. A reasonable estimate is most easily obtained for the spacing E°, which should be close to the mean spacing of the levels considered, in order to minimize the dimensions of the Hamilton matrix. Thus, in the present example it was found that with E° = 80 cm-1 the basis could safely be truncated at n = 39 corresponding to matrix dimensions 20 x 20 for the diagonal blocks of H. ... 

JTY Cheung and G Stephanopoulos. Representation of process trend-s, Part II. The problem of scale and qualitative scaling. Comp. Chem. Engg., 14 511-539, 1990. 

FIGURE 3-1 Dimensions of integration and the problem of scale as illustrated for atmospheric chemical calculation. 

Moreover, there is the problem of scale. In the kitchen, apple sauce can be made from a few apples using kitchen tools such as a knife, a spoon, and a pan. The apple peels and cores can simply be thrown away. The sauce is usually eaten the same day. In an apple sauce factory on the other hand, machines have to he used to prepare the apples and the factory is expected to find a proper solution for the growing amount of apple peels and cores because they can not just he thrown away . Also, measures have to be taken to store and distribute the sauce, since production and consumption are separated in time and place (Van Aalsvoort, 2000). 

In summary, flash pyrolysis can be extremely valuable if the objective is to isolate and study the rt-quinodimethanes at low temperature or if intramolecular cyclisations are required. For intermolectilar reactions, methods producing the species in situ in solution at low standing concentration are much better. Also such methods do not suffer from the problems of. scale inherent with the flash pyrolysis technique where there is nonnally an upper limit of ca. 0.5 g. 

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