Inevitability

The rate at which the catalyst is lost or degrades has a major influence on the design. If degradation is rapid, the catalyst needs to be regenerated or replaced on a continuous basis. In addition to the cost implications, there are also environmental implications, since the lost or degraded catalyst represents waste. While it is often possible to recover useful materials from degraded catalyst and to recycle those materials in the manufacture of new catalyst, this still inevitably creates waste, since the recovery of material can never be complete. 

By considering only those raw materials which undergo reaction to undesired byproduct, only the raw materials costs which are in principle avoidable are considered. Those raw materials costs which are inevitable (i.e., the stoichiometric requirements for FEED which converts into the desired PRODUCT) are not included. Raw materials costs which are in principle avoidable are distinguished from those which are inevitable from the stoichiometric requirements of the reaction. ... 

Feed purification. Impurities that enter with the feed inevitably cause waste. If feed impurities undergo reaction, then this causes waste from the reactor, as already discussed. If the feed impurity does not undergo reaction, then it can be separated out from the process in a number of ways, as discussed in Sec. 4.1. The greatest source of waste occurs when we choose to use a purge. Impurity builds up in the recycle, and we would like it to build up to a high concentration to minimize waste of feed materials and product in the purge. However, two factors limit the extent to which the feed impurity can be allowed to build up ... 

Of this book Albert Einstein said Gives a really clear idea of the problem, especially the development of our knowledge concerning the propagation of light and the difficulties which arose from the apparently inevitable introduction of the ether. 

Fluid samples may be collected downhole at near-reservoir conditions, or at surface. Subsurface samples are more expensive to collect, since they require downhole sampling tools, but are more likely to capture a representative sample, since they are targeted at collecting a single phase fluid. A surface sample is inevitably a two phase sample which requires recombining to recreate the reservoir fluid. Both sampling techniques face the same problem of trying to capture a representative sample (i.e. the correct proportion of gas to oil) when the pressure falls below the bubble point. 

The field may enter into an economic decline when either income is falling (production decline) or costs are rising, and in many cases both are happening. Whilst there may be scope for further investment in a field in economic decline, it should not tie up funds that can be used more effectively in new projects. A mature development must continue to generate a positive cashflow and compete with other projects for funds. The options that are discussed in this section give some idea of the alternatives that may be available to manage the inevitable process of economic decline, and to extend reservoir and facility life. 

Very many types of eddy current instruments available tend to look remarkably similar in much the same way as automobiles tend to look alike. This may be an inevitable trend since developments are converging on users needs, plus PC platforms are being used more and these too are tending to look more and more alike. In the way that the DSP has changed the inside of the instrument, the PC. is changing the outside. 

More accurately, as the inverse problem process computes a quadratic error with every point of a local area around a flaw, we shall limit the sensor surface so that the quadratic error induced by the integration lets us separate two close flaws and remains negligible in comparison with other noises or errors. An inevitable noise is the electronic noise due to the coil resistance, that we can estimate from geometrical and physical properties of the sensor. Here are the main conclusions ... 

Small differences of the correlator output can be explained taking into account inevitable variations of the sheet steel thickness. 

After many decades of application, industry has completely accepted standard NDT as an inevitable but invaluable part of production and maintenance of components. Its application has been well-regulated, acceptance criteria for weld defects exist, good schemes for personnel qualification are in place and equipment has evolved to a standard of nearperfection. NDT has become a commodity. Pioneering years are over. 

The problem of correcting for inevitable, small differences between the mock-up and the process persists ... 

This is known as the Stefan-Boltzmaim law of radiation. If in this calculation of total energy U one uses the classical equipartition result = k T, one encounters the integral f da 03 which is infinite. This divergence, which is the Rayleigh-Jeans result, was one of the historical results which collectively led to the inevitability of a quantum hypothesis. This divergence is also the cause of the infinite emissivity prediction for a black body according to classical mechanics. 

Diffraction is not limited to periodic structures [1]. Non-periodic imperfections such as defects or vibrations, as well as sample-size or domain effects, are inevitable in practice but do not cause much difSculty or can be taken into account when studying the ordered part of a structure. Some other forms of disorder can also be handled quite well in their own right, such as lattice-gas disorder in which a given site in the unit cell is randomly occupied with less than 100% probability. At surfaces, lattice-gas disorder is very connnon when atoms or molecules are adsorbed on a substrate. The local adsorption structure in the given site can be studied in detail. 

A number of experimental and physical realities cloud this rosy picture. Inevitably many emitted photons are lost due to the finite solid angle over which the fluorescence is collected, losses at the various filters, lenses, windows, and other... 

In addition to their practical importance, colloidal suspensions have received much attention from chemists and physicists alike. This is an interesting research area in its own right, and it is an important aspect of what is referred to as soft condensed matter physics. This contribution is written from such a perspective, and although a balanced account is aimed for, it is inevitably biased by the author s research interests. References to the original literature are included, but within the scope of this contribution only a fraction of the vast amount of literature on colloidal suspensions can be mentioned. 

Th e calcn lation of the two-electron repulsion mtegraism ah iniiio method is inevitable and time-consuming. The computational iim e is main ly dom in alcd by th e performance of Ih e two-electron integral calcii lalion. The following item s can con trol the performance of the two-electron integrals. 

In a systematic search there is a defined endpoint to the procedure, which is reached whe all possible combinations of bond rotations have been considered. In a random search, ther is no natural endpoint one can never be absolutely sure that all of the minimum energ conformations have been found. The usual strategy is to generate conformations until n new structures can be obtained. This usually requires each structure to be generate many times and so the random methods inevitably explore each region of the conformc tional space a large number of times. 

In most engineering problems the boundary of the problem domain includes curved sections. The discretization of domains with curved boundaries using meshes that consist of elements with straight sides inevitably involves some error. This type of discretization error can obviously be reduced by mesh refinements. However, in general, it cannot be entirely eliminated unless finite elements which themselves have curved sides are used. 

All numerical computations inevitably involve round-off errors. This error increases as the number of calculations in the solution procedure is increased. Therefore, in practice, successive mesh refinements that increase the number of finite element calculations do not necessarily lead to more accurate solutions. However, one may assume a theoretical situation where the rounding error is eliminated. In this case successive reduction in size of elements in the mesh should improve the accuracy of the finite element solution. Therefore, using a P C" element with sufficient orders of interpolation and continuity, at the limit (i.e. when element dimensions tend to zero), an exact solution should be obtaiiied. This has been shown to be true for linear elliptic problems (Strang and Fix, 1973) where an optimal convergence is achieved if the following conditions are satisfied ... 

Upon boiling the alkaline ferrous salt solution, some ferric ions are inevitably produced by the action of the air upon the addition of dilute siilphurio acid, thus dissolving the ferrous and ferric hydroxides, the ferrocyanides reacts with the ferric salt producing ferric ferrocyanide (Prussian blue) ... 

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