Radial dissociation

Figure 3.35 (See color insert following page 390.) X-ray CT imaging shows radial dissociation of a hydrate core. Image number 1 -8 (top number on each image) recorded over 0-245 min (bottom number on each image). The cell pressure was decreased from 4.65 to 3.0 MPa over 248 min. The hydrate core temperature decreased from 277 to 274 K with time, following the three-phase methane hydrate equilibrium line. (From Gupta, A., Methane Hydrate Dissociation Measurements andModeling The Role of Heat Transfer and Reaction Kinetics, Ph.D. Thesis Colorado School of Mines, Golden, CO (2007). With permission.)...

More importantly, the result of Booth et al. also suggests that only massive hydrate samples can survive the trip from the bottom of the ocean to ship deck. For example, if the massive MAT Guatemala 2 sample (topmost in Figure 7.7) were recovered at constant pressure, the temperature would need to rise more than 16°C before the sample reached the three-phase line, where dissociation would begin. This result is consistent not only with laboratory determinations for dispersed hydrates (Kumar et al., 2004 Pauli et al., 2005 Wright and Dallimore, 2005) but also shows the parallel of recovered core dissociation with radial dissociation due to depressurization in pipelines, modified for sediment content (Davies and Sloan, 2006). 

Hydrate plug radial dissociation in three experiments. 

Two-sided dissociation eliminates the Joule-Thomson cooling that may stabilize the downstream end of the plug. With radial dissociation along the plug, two-sided dissociation is more than twice as fast as single-sided dissociation. 

The flow can be radial, that is, in or out through a hole in the center of one of the plates [75] the relationship between E and f (Eq. V-46) is independent of geometry. As an example, a streaming potential of 8 mV was measured for 2-cm-radius mica disks (one with a 3-mm exit hole) under an applied pressure of 20 cm H2 on QT M KCl at 21°C [75]. The i potentials of mica measured from the streaming potential correspond well to those obtained from force balance measurements (see Section V-6 and Chapter VI) for some univalent electrolytes however, important discrepancies arise for some monovalent and all multivalent ions. The streaming potential results generally support a single-site dissociation model for mica with Oo, Uff, and at defined by the surface site equilibrium [76]. 

For these reasons, in the MCSCF method the number of CSFs is usually kept to a small to moderate number (e.g. a few to several thousand) chosen to describe essential correlations (i.e. configuration crossings, near degeneracies, proper dissociation, etc, all of which are often tenned non-dynamicaI correlations) and important dynamical correlations (those electron-pair correlations of angular, radial, left-right, etc nature that are important when low-lying virtual orbitals are present). 

According to these data, which structural features provide stabilization of radial centers Determine the level of agreement between these data and the radical stabilization energies given in Table 12.7 if the standard C—H bond dissociation energy is taken to be 98.8 kcal/mol. (Compare the calculated and observed bond dissociation energies for the benzyl, allyl, and vinyl systems.)... 

Smoluchowski, who worked on the rate of coagulation of colloidal particles, was a pioneer in the development of the theory of diffusion-controlled reactions. His theory is based on the assumption that the probability of reaction is equal to 1 when A and B are at the distance of closest approach (Rc) ( absorbing boundary condition ), which corresponds to an infinite value of the intrinsic rate constant kR. The rate constant k for the dissociation of the encounter pair can thus be ignored. As a result of this boundary condition, the concentration of B is equal to zero on the surface of a sphere of radius Rc, and consequently, there is a concentration gradient of B. The rate constant for reaction k (t) can be obtained from the flux of B, in the concentration gradient, through the surface of contact with A. This flux depends on the radial distribution function of B, p(r, t), which is a solution of Fick s equation... 

We report MCSCF calculations of the dipole and quadmpole polarizability tensor radial functions of LiH and HF for internuclear distance reaching from almost the unified atom to the dissociation limit. Large one-electron basis sets and MCSCF wavefunctions of the CAS type with large active spaces were employed in the calculations. 

Capture cf electron This process is also ionization. Electrons with yet lower energy can be captured by molecules. The resulting ion can dissociate into a free radical and a radial ion ... 

The calculations of g(r) and C(t) are performed for a variety of temperatures ranging from the very low temperatures where the atoms oscillate around the ground state minimum to temperatures where the average energy is above the dissociation limit and the cluster fragments. In the course of these calculations the students explore both the distinctions between solid-like and liquid-like behavior. Typical radial distribution functions and velocity autocorrelation functions are plotted in Figure 6 for a van der Waals cluster at two different temperatures. Evaluation of the structure in the radial distribution functions allows for discussion of the transition from solid-like to liquid-like behavior. The velocity autocorrelation function leads to insight into diffusion processes and into atomic motion in different systems as a function of temperature. 

The y>Ee(R) are the radial free-state wavefunctions (see Chapter 5 for details). The free state energies E are positive and the bound state energies E(v,S) are negative v and ( are vibrational and rotational dimer quantum numbers t is also the angular momentum quantum number of the fth partial wave. The g( are nuclear weights. We will occasionally refer to a third partition sum, that of pre-dissociating (sometimes called metastable ) dimer states,... 

Tubular and radial Parabolic flow Dissociation rate coefficient treated as a parameter 73... 

The modern conceptual picture of dissociation of a hydrate core/plug typically involves radial hydrate dissociation rather than the previously suggested axial... 

A hydrate plug or core dissociates radially, not axially. 

CSMPlug can predict the total dissociation time by two-sided depressurisation, and by evenly applied radial heat input to an accuracy of 10%, provided accurate plug properties are known. Predictions from the one-sided depressurisation module are less accurate than those of the other modules, but are within an order of magnitude of those observed dissociation times for laboratory scale hydrates are typically over predicted but industrial hydrates are under predicted. 

---