Scaled External Correlation models

Saddle optimization, 329 Scalar relativistic corrections, 209 Scaled External Correlation (SEC), Scaled All Correlation (SAC) models, 169 Scaling of different methods with basis set, 145 Schrodinger equation, 2, 53 Schwarz inequality, for integral screening, 78 Second quantization, 411 Second-order corrections, in perturbation methods, 126... 

Hydrate dissociation is of key importance in gas production from natural hydrate reservoirs and in pipeline plug remediation. Hydrate dissociation is an endothermic process in which heat must be supplied externally to break the hydrogen bonds between water molecules and the van der Waals interaction forces between the guest and water molecules of the hydrate lattice to decompose the hydrate to water and gas (e.g., the methane hydrate heat of dissociation is 500 J/gm-water). The different methods that can be used to dissociate a hydrate plug (in the pipeline) or hydrate core (in oceanic or permafrost deposits) are depressurization, thermal stimulation, thermodynamic inhibitor injection, or a combination of these methods. Thermal stimulation and depressurization have been well quantified using laboratory measurements and state-of-the-art models. Chapter 7 describes the application of hydrate dissociation to gas evolution from a hydrate reservoir, while Chapter 8 describes the industrial application of hydrate dissociation. Therefore in this section, discussion is limited to a brief review of the conceptual picture, correlations, and laboratory-scale phenomena of hydrate dissociation. 

In a kinetic investigation, the rate-determining step and, hence, the functional form of the rate model are not known a priori also unknown are the rate constants and adsorption equilibrium coefficients. Hence, the aim of data procurement and correlation is both model discrimination and parameter estimation which are completed in tandem [17]. The critical problem at this point is to obtain reliable experimental data from which kinetic models that reflect steady-state chemical activity can be extracted and evaluated. In order to measure correctly the rates of chemical events only, (i) external and internal mass and heat transport resistances at the particle scale have to be eliminated,... 

The only gross mode that is normally observed is the rotational n = 2 instability. The observed stable period before the mode onset is consistent with the FRC increasing in angular velocity until it crosses a threshold for instability predicted by a Vlasov fluid code. The angular acceleration could be due to an external torque perhaps applied by plasma outside the separatrix through viscosity.Another cause of acceleration could be net angular momentum carried by particles diffusing across the separatrix. This particle loss model predicts that the onset of the instability should occur when about half the particles are lost. This prediction is consistent with the experiment. Since the external torque or other sources of rotation are also possible, better correlation between experiment and theory is needed to properly understand this issue. However, if the FRC stable period Xg (time before mode onset) continues to scale with the time required to lose half the particles, then particle transport, not the rotational mode, will limit the reactor potential of the FRC. 

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