Order of magnitude estimations

In the absence of pKA data for the individual amine protons in these substitutionally labile complexes it is not possible to evaluate k2 and thereby measure precisely the amount by which deprotonation increases the lability of the complex. Even if such data were available it would be difficult, in complexes containing more than one type of amine proton, to be sure whether the two quantities related to the same proton. In spite of this major drawback it is possible to estimate orders of magnitude. The evidence suggests that in Co111 complexes the amido conjugate base can be between 105 and 1013 times more labile than the amine complex from which it was derived.301 The effect is far less marked in equivalent complexes of Crm, Ru111 and Rh111352-353 and, so far, there... 

Due to these points, and especially the last one, the applicability of Eq. (27) to measurement results appears quite restricted. Nevertheless, it allows to outline qualitative trends and to provide an estimated order of magnitude for the particle intrinsic nonlinear susceptibility. We now focus on results selected from the literature which appear to be relevant following the preceding clarification. 

To estimate orders of magnitude, assume the simple condition B = B2, let their common value be B. Then the interface velocity becomes... 

The existence of transverse gradients is associated with external mass transfer limitation. The lack of gradients in a CFD simulation is associated with kinetically limited processes. A more quantitative measure of transport or kinetic limitations can be done using an estimate (order of magnitude) of the second Damkholer... 

Preliminary feasibility estimates (order-of-magnitude or study estimates) are made to compare... 

Efficient utilization of the olefin feedstock is critical in ether production because of the limited suppfy and cost of the olefin feedstock [133], The estimated order of magnitude cost of a 12,500 bpsd MTBE complex is about 200 million (1992 dollars), of which 3550% of the cost is associated with dehydrogenation costs for isobutylene synthesis from isobutane [130]. The source of olefins is a major issue in ether production [134136], and the interest in TAME and other ethers for fuel oxygenates stems from the fact that they can be produced from methanol and olefins other than isobutylene [134]. 

Estimate (order of magnitude) the light power reaching the floor of the room where you are. Your answer is likely to be below 1W cm . On the other hand, nowadays we will not think of 10 W cm as truly high-power. Table-top lasers with output reaching all the way to 10 W cm are available. 

Calculate the weighted network area Anetwork from Eq. (7.22). When the weighted h values i4>h) vary appreciably, say, by more than one order of magnitude, an improved estimate of Anetwork can be evaluated by linear programming. ... 

These terms are analogous to those on p. 265 of [7], It will be noted that the symbol c has been reinstated as in Section VI.F, so as to facilitate the order of magnitude estimation in the nearly nonrelativistic limit. We now proceed based on Eq. (168) as it stands, since the transformation of Eq. (168) to modulus and phase variables and functional derivation gives rather involved expressions and will not be set out here. 

In spite of the three methods of estimating open question that needs to be investigated further in the future. The above expressions are order of magnitude estimates and not exact formulas. 

Usually, the denominator, if present in a similarity measure, is just a normalizet it is the numerator that is indicative of whether similarity or dissimilarity is being estimated, or both. The characteristics chosen for the description of the objects being compared are interchangeably called descriptors, properties, features, attributes, qualities, observations, measurements, calculations, etc. In the formiilations above, the terms matches and mismatches" refer to qualitative characteristics, e.g., binary ones (those which take one of two values 1 (present) or 0 (absent)), while the terms overlap and difference" refer to quantitative characteristics, e.g., those whose values can be arranged in order of magnitude along a one-dimensional axis. 

Let us make an estimate of the order of magnitude of these effects. Referring to equation (9,23), the coefficient of the term relating the micropore contribution to and grad p is larger by a factor... 

Diffusion in flowing fluids can be orders of magnitude faster than in nonfiowing fluids. This is generally estimated from continuum fluid dynamics simulations. 

The degree of uncertainty of 10 per cent or more, inseparable from estimates of specific surface from adsorption isotherms, even those of nitrogen, may seem disappointing. In fact, however, attainment of this level of accuracy is a notable achievement in a field where, prior to the development of the BET method, even the order of magnitude of the specific surface of highly disperse solids was in doubt. The adsorption method still provides the only means of determining the specific surface of a mass of non-... 

Comparison of this result with Example 3.1 shows that T AS and AH are of the same order of magnitude. Example 3.1 stressed that the value of AH estimated there was an upper limit. Experimental results show that the assumption of ideality-while a slight oversimplification-generally introduces an error of less than 10%. Comparison of the two examples shows how much more difficult it... 

The capillary retention forces in the pores of the filter cake are affected by the size and size range of the particles forming the cake, and by the way the particles have been deposited when the cake was formed. There is no fundamental relation to allow the prediction of cake permeabiUty but, for the sake of the order-of-magnitude estimates, the pore size in the cake may be taken loosely as though it were a cylinder which would just pass between three touching, monosized spheres. If dis the diameter of the spherical particles, the cylinder radius would be 0.0825 d. The capillary pressure of 100 kPa (1 bar) corresponds to d of 17.6 pm, given that the surface tension of water at 20°C is 12.1 b mN /m (= dyn/cm). 

For most hydrardic pressure-driven processes (eg, reverse osmosis), dense membranes in hoUow-fiber configuration can be employed only if the internal diameters of the fibers are kept within the order of magnitude of the fiber-wall thickness. The asymmetric hoUow fiber has to have a high elastic modulus to prevent catastrophic coUapse of the filament. The yield-stress CJy of the fiber material, operating under hydrardic pressure, can be related to the fiber coUapse pressure to yield a more reaUstic estimate of plastic coUapse ... 

The accuracy of a fixed capital estimate tends to be a function of the design effort involved. As the project definition is refined, the estimates evolve from the various preliminary phases, ie, order of magnitude, predesign, factor estimates, etc, into the more detailed estimates used for budget authorization, project control, and contracts. At the same time, the uncertainty in the estimate decreases from 50% to as Htfle as 5%. 

Order-of-Magnitude Estimates. Unit capital cost data (dollars per aimual ton of product) are occasionally reported for chemical plants. These data can be multiphed by a selected plant capacity to estimate a capital cost. This is, however, feasible only if the reference process, conditions, and capacity are similar. 

Diffusion within the largest cavities of a porous medium is assumed to be similar to ordinary or bulk diffusion except that it is hindered by the pore walls (see Eq. 5-236). The tortuosity T that expresses this hindrance has been estimated from geometric arguments. Unfortunately, measured values are often an order of magnitude greater than those estimates. Thus, the effective diffusivity D f (and hence t) is normally determined by comparing a diffusion model to experimental measurements. The normal range of tortuosities for sihca gel, alumina, and other porous solids is 2 < T < 6, but for activated carbon, 5 < T < 65. 

Order-of-magnitude estimate (ratio estimate). Rule-of-thumb method based on cost data for previous similar types of plant probable error within 10 to 50 percent. 

Study estimate (factored estimate). Better than order-of-magnitude requires knowledge of major items of equipment used for feasibihty surveys probable error up to 30 percent. 

Step Count Methods These methods, used for order-of-magnitude estimates, are based on the definition of the functional units required to carry out the process. A functional unit is a signifi-... 

Complete Plant Costs It is difficult to compare costs of domestic and overseas plants owing to the wide variation in types of plants and sizes and the rapid changes in technology. Useful data are scarce, and the following comparisons must be used with caution and then only for order-of-magnitude estimates of fixed-capital costs. 

Contrac tors bids offer the most rehable information on cost. Order-of-magnitude costs, however, may be required for preliminary studies. One way of estimating them is to obtain cost information from similar facihties and scale it to the proposed installation. Costs of steel storage tanks and vessels have been found to vaiy approximately as the 0.6 to 0.7 power of their weight [see Happel, Chemical Process Economics, Wiley, 1958, p. 267 also Williams, Chem. Eng., 54(12), 124 (1947)]. AU estimates cased on the costs of existing eqiiipment must be corrected for changes in the price index from the date when the equipment was built. Considerable uncertainty is involved in adjusting data more than a few years old. 

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