Conceptualization

Douglas, J. M., Conceptual Design of Chemical Processes, McGraw-Hill, New York, 1988. 

The composite curves are useful in providing conceptual understanding of the process, but the problem table algorithm is a more convenient calculation tool. 

In 1990, at the request of the Director of the Center for Refining, Petrochemistry and Engineering at the Ecole Nationale Superieure du Petrole et des Moteurs, the late Jean Durandet initiated the conceptual foundations for the new series that he was unable to complete. We would like to pay a tribute to him here. 

The field development plan s prime purpose is to serve as a conceptual project specification for subsurface and surface facilities, and the operational and maintenance philosophy required to support a proposal for the required investments. It should give management and shareholders confidence that all aspects of the project have been... 

At each phase of a project cost information is required to enable decisions to be taken. In the conceptual phase these estimates may be very approximate (e.g. + 35% accuracy), reflecting the degree of uncertainty regarding both reservoir development and surface options. As the project becomes better defined the accuracy of estimates should improve. 

Quality management in NDT is a fairly new trend and can be approached by two different conceptual routes (Figure 4). 

In several generating banks inspected, a number of tubes have been found with eccentricity exceeding 1,0 mm and in one extreme case 2,0 mm, or 40 % of the nominal wall thickness was noted. A conceptual diagram of tire cross section of a concentric tube and a simulated plot of the wall thickness scan is presented in figure 3. The scan presented in figure 2 is a relatively concentric tube less than 0,2 mm of wall variation. 

The calculation involved here is conceptually a complex one, and for the necessarily detailed discussion needed to do it justice, the reader is referred to Verwey and Overbeek [5] and Kruyt [6] or to Hamed and Owen [10]. Qualitatively, what must be done is to calculate the reversible electrostatic work for the process ... 

Various kinds of potentials have been referred to in the course of this and the preceding chapter, and their interrelation is the subject of the present section. The chief problem is that certain types of potential differences are physically meaningful in the sense that they are operationally defined, whereas others that may be spoken of more vaguely are really conceptual in nature and may not be definable experimentally. 

Infrared Spectroscopy. The infrared spectroscopy of adsorbates has been studied for many years, especially for chemisorbed species (see Section XVIII-2C). In the case of physisorption, where the molecule remains intact, one is interested in how the molecular symmetry is altered on adsorption. Perhaps the conceptually simplest case is that of H2 on NaCl(lOO). Being homo-polar, Ha by itself has no allowed vibrational absorption (except for some weak collision-induced transitions) but when adsorbed, the reduced symmetry allows a vibrational spectrum to be observed. Fig. XVII-16 shows the infrared spectrum at 30 K for various degrees of monolayer coverage [96] (the adsorption is Langmuirian with half-coverage at about 10 atm). The bands labeled sf are for transitions of H2 on a smooth face and are from the 7 = 0 and J = 1 rotational states Q /fR) is assigned as a combination band. The bands labeled... 

The preceding treatments are based on the concept of localized rather than mobile adsorption. The distinction may be difficult experimentally note Ref. 109 and the discussion in connection with Fig. XVII-25. There are also conceptual subtleties see Section XVIII-5. 

The corresponding fiinctions i-, Xj etc. then define what are known as the normal coordinates of vibration, and the Hamiltonian can be written in tenns of these in precisely the fonn given by equation (AT 1.69). witli the caveat that each tenn refers not to the coordinates of a single particle, but rather to independent coordinates that involve the collective motion of many particles. An additional distinction is that treatment of the vibrational problem does not involve the complications of antisymmetry associated with identical fennions and the Pauli exclusion prmciple. Products of the nonnal coordinate fiinctions neveitlieless describe all vibrational states of the molecule (both ground and excited) in very much the same way that the product states of single-electron fiinctions describe the electronic states, although it must be emphasized that one model is based on independent motion and the other on collective motion, which are qualitatively very different. Neither model faithfully represents reality, but each serves as an extremely usefiil conceptual model and a basis for more accurate calculations. 

It turns out that there is another branch of mathematics, closely related to tire calculus of variations, although historically the two fields grew up somewhat separately, known as optimal control theory (OCT). Although the boundary between these two fields is somewhat blurred, in practice one may view optimal control theory as the application of the calculus of variations to problems with differential equation constraints. OCT is used in chemical, electrical, and aeronautical engineering where the differential equation constraints may be chemical kinetic equations, electrical circuit equations, the Navier-Stokes equations for air flow, or Newton s equations. In our case, the differential equation constraint is the TDSE in the presence of the control, which is the electric field interacting with the dipole (pemianent or transition dipole moment) of the molecule [53, 54, 55 and 56]. From the point of view of control theory, this application presents many new features relative to conventional applications perhaps most interesting mathematically is the admission of a complex state variable and a complex control conceptually, the application of control teclmiques to steer the microscopic equations of motion is both a novel and potentially very important new direction. 

The alternative simulation approaches are based on molecular dynamics calculations. This is conceptually simpler that the Monte Carlo method the equations of motion are solved for a system of A molecules, and periodic boundary conditions are again imposed. This method pennits both the equilibrium and transport properties of the system to be evaluated, essentially by numerically solvmg the equations of motion... 

Conceptually similar studies have since been carried out for the reaction of Ft atoms with Cl/Aii(l 11). More recently, quantum-state distributions have been obtamed for both the Ft + Cl/Aii(l 11)[, and M and Ft(D) + D (Ft)/Cii(l 11) systems. The results of these studies are in good qualitative agreement widi calculations. Even for the Ft(D) + D (Ft)/Cii(l 11) system [89], where we know that the incident atom caimot be significantly accommodated prior to reaction, reaction may not be direct. Detailed calculations yield much smaller cross sections for direct reaction than the overall experimental cross section, indicating that reaction may occur only after trapping of the incident atom [90]. 

Modem photochemistry (IR, UV or VIS) is induced by coherent or incoherent radiative excitation processes [4, 5, 6 and 7]. The first step within a photochemical process is of course a preparation step within our conceptual framework, in which time-dependent states are generated that possibly show IVR. In an ideal scenario, energy from a laser would be deposited in a spatially localized, large amplitude vibrational motion of the reacting molecular system, which would then possibly lead to the cleavage of selected chemical bonds. This is basically the central idea behind the concepts for a mode selective chemistry , introduced in the late 1970s [127], and has continuously received much attention [10, 117. 122. 128. 129. 130. 131. 132. 133. 134... 

Secondary ion mass spectrometry (SIMS) is by far the most sensitive surface teclmique, but also the most difficult one to quantify. SIMS is very popular in materials research for making concentration depth profiles and chemical maps of the surface. For a more extensive treatment of SIMS the reader is referred to [3] and [14. 15 and 16]. The principle of SIMS is conceptually simple When a surface is exposed to a beam of ions... 

To improve upon die mean-field picture of electronic structure, one must move beyond the singleconfiguration approximation. It is essential to do so to achieve higher accuracy, but it is also important to do so to achieve a conceptually correct view of the chemical electronic structure. Although the picture of configurations in which A electrons occupy A spin orbitals may be familiar and usefiil for systematizing the electronic states of atoms and molecules, these constructs are approximations to the true states of the system. They were introduced when the mean-field approximation was made, and neither orbitals nor configurations can be claimed to describe the proper eigenstates T, . It is thus inconsistent to insist that the carbon atom... 

More advanced teclmiques take into account quasiparticle corrections to the DFT-LDA eigenvalues. Quasiparticles are a way of conceptualizing the elementary excitations in electronic systems. They can be detennined in band stmcture calculations that properly include the effects of exchange and correlation. In the... 

The conceptually simplest approach to solve for the -matrix elements is to require the wavefimction to have the fonn of equation (B3.4.4). supplemented by a bound function which vanishes in the asymptote [32, 33, 34 and 35] This approach is analogous to the fiill configuration-mteraction (Cl) expansion in electronic structure calculations, except that now one is expanding the nuclear wavefimction. While successfiti for intennediate size problems, the resulting matrices are not very sparse because of the use of multiple coordinate systems, so that this type of method is prohibitively expensive for diatom-diatom reactions at high energies. 

The approaches discussed so far are generally called time-independent methods, since they start from the time-independent Scln-ddinger equation, (//-E)l f(t. An alternative is to use the time-dependent Scln-ddinger equation [28, 29, 59, and M. Conceptually, tlie time-dependent approach is... 

The conceptually simplest approach towards controlling systems by laser field is by teaching the field [188. 191. 192 and 193]. Typically, tire field is experimentally prepared as, for example, a sum of Gaussian pulses with variable height and positions. Each experiment gives an outcome which can be quantified. Consider, for example, an A + BC reaction where the possible products are AB + C and AC + B if the AB + C product is preferred one would seek to optimize the branching ratio... 

---