Static equilibrium studies

Guo, G. and Long, Y. (2001) Static equilibrium studies on separation of dichlorobenzene isomers on binder-free hydrophobic adsorlaent of MFI type zeolite. Sep. Purif. Technol,... 

STATIC EQUILIBRIUM STUDY TO DETERMINE THE RELATIVE REACTIVITY OF RESERVOIR SANDS AND BEREA SANDSTONE SAND WITH THE USE OF Cm PORE VOLUME ALKALINE CHEMICALS AT 125 F... 

It was felt that none of the experiments that had been devised thus far truly approached representing v at is happening in the reservoir. The static equilibrium study experiments were... 

Many investigators 35 have reported experimental results on the necessary conditions for the static equilibrium of a sphere. The results of all such studies may be represented by a factor Z which is proportional to the ratio of the forces due to the yield stress xY and those due to gravity. 

Guo, G.-Q., Chen, H., and Ying-Cai, L. (2000) Separation of p-xylene from C8 aromatics on binder-free hydrophobic adsorbent of MFI zeolite. I. Studies on static equilibrium. Micropor. Mesopor. Mater., 39, 149-161. 

A rate and equilibrium study of the cis/trans isomerization of tris(l,l,l-trifluoro-2,4-pentanedionato)chromium(III) in the vapour phase has been reported.761 The equilibrium constant 3.56 was independent of temperature in the range 118-144.8 °C, the same value being measured by both static and kinetic methods. The activation energies for isomerization were both less than 115 kJmol-1 the Cr—O bond energy is 210 kJ mol-1. On these grounds, a bond-rupture mechanism was rejected. A similar mechanism may operate for the isomerization in solution. 

Equilibrium studies of [Cu(chelate)2] complexes are generally determined spectrophotochem-ically using static and stopped-flow techniques.967,969 In the substitution9 of water in the five-coordinate [Cu(trenMe6)(OH2)]2+ cation by NCO-, Cl" or Br , the rate is very much slower than that reported for the [Cu(OH2)6]2+ cation (Table 58), with K values of... 

Petrie and Ito (84) used numerical methods to analyze the dynamic deformation of axisymmetric cylindrical HDPE parisons and estimate final thickness. One of the early and important contributions to parison inflation simulation came from DeLorenzi et al. (85-89), who studied thermoforming and isothermal and nonisothermal parison inflation with both two- and three-dimensional formulation, using FEM with a hyperelastic, solidlike constitutive model. Hyperelastic constitutive models (i.e., models that account for the strains that go beyond the linear elastic into the nonlinear elastic region) were also used, among others, by Charrier (90) and by Marckmann et al. (91), who developed a three-dimensional dynamic FEM procedure using a nonlinear hyperelastic Mooney-Rivlin membrane, and who also used a viscoelastic model (92). However, as was pointed out by Laroche et al. (93), hyperelastic constitutive equations do not allow for time dependence and strain-rate dependence. Thus, their assumption of quasi-static equilibrium during parison inflation, and overpredicts stresses because they cannot account for stress relaxation furthermore, the solutions are prone to numerical instabilities. Hyperelastic models like viscoplastic models do allow for strain hardening, however, which is a very important element of the actual inflation process. 

Phenol, a common priority pollutant, was extracted from two environmental matrices, soil and water, using near critical and supercritical carbon dioxide. The primary objective of this study was to determine the distribution of the contaminant between the soil or water and the supercritical phase, and the effect of soil moisture and co-solvents on the distribution coefficients. Static equilibrium extractions were performed on dry and wetted soil contaminated with 1 wt.% phenol and on water containing 6.8 wt.% phenol. Supercritical carbon dioxide (with and without en-trainers) was chosen as the solvent for the study. An appropriate entrainer for dry soil extractions (methanol) ffiffered from that found for aqueous extractions (benzene). However, soil moisture was found to have a significant impact on the effectiveness of en-trainers for soil extractions of phenol. Entrainers appropriate for extracting wetted soil were found to be the same as those advantageous for aqueous extractions. Benzene was also extracted from dry and wetted soil to investigate the extractability of a hydrophobic compound. 

A detailed description of the experimental apparatus and procedure used for the aqueous study are given elsewhere (Roop and Akgerman, Ind. Eng. Chem. R., in review) Static equilibrium extractions were carried out in a high pressure equilibrium cell (300 mL Autoclave). After the vessel is initially charged with 150 mL of water containing 6.8 wt.% phenol and supercritical carbon dioxide (and a small amount of entrainer, if desired), the contents were mixed for one hour followed by a two hour period for phase separation. Samples from both the aqueous phase and the supercritical phase were taken for analysis and the distribution coefficient for phenol calculated. 

Static, equilibration studies indicated that a molecular association forms at the styrene/water interface in the presence of mixed emulsifiers. Interfacial layers were also observed in spinning drop experiments between various oil phases and aqueous mixed emulsifier solutions. The formation of these interfacial layers as a function of time was found to be a non-equilibrium effect that depended primarily on the chemical structure of the oil phase. Oil phase water solubility had little effect. 

It should be noted that in this study the term dynamic equilibrium applies to the situation where two components are adsorbed simultaneously on an adsorbent in a flow system. Consequently, the pore volume of the molecular sieves is occupied by both nitrogen, the less strongly adsorbed species, and SO2. The dynamic equilibrium is consequently characterized by adsorption and desorption of molecules of both species at different rates. In contrast, static equilibrium applies to adsorption of a pure gas in a non-flowing system and is attained when the adsorption and desorption rates of the single component are equal. 

We first examine the statics and dynamics of a one-dimensional macroscopic particle of mass M. Specifically, we study a relaxation process xp xp=o that takes the particle from an initial point of static equilibrium xp to a final point xp = o (Fig- 3.1). 

X HE CONFIGURATIONAL PROPERTIES OF WATER-SOLUBLE POLYMERS and their interactions with other polymers and with colloidal particles are relevant to understanding the intermolecular interactions in associative thickeners and steric stabilization of colloidal particles. We used fluorescence spectroscopy to study both the dynamic and the static equilibrium properties... 

Figure L Static equilibrium experiments to study caustic consumption of reservoir sands in the presence of large excess of NaOH solution. Key A, Aminoil LMZ sand at 165°F in 0.2% NaOH O, THUMS Ranger sand at 125°F in 0.2% NaOH X> Berea sandstone sand at 125°F...

In another set of static equilibrium tests, one pore volime (PV) of alkaline solution was mixed individually with Aminoil IMZ, THUMS Ranger and Berea sandstone sands. The volume of one PV used was calculated from the porosity of the same sand v en it was packed for sand pack flow study. After standing for a number of days, the mixtures were filtered and the filtrates were analyzed for their alkaline consurtption by titration with standard acid. As depicted in Table II, the consurapticxis were rapid in all cases and the alkaline chemicals were totally or almost totally consumed after 6 to 9 days for the THUMS Ranger and Aminoil IMZ sands. The consumption with Berea sandstone sand was slower by comparison but still quite significant. 

Poles or dipoles The state variables used in this case study are all relative to poles when the piston is at rest (static equilibrium). On the contrary, when the piston is asked to convert energy, by a displacement made at a given velocity (variable or not), it is necessary to complete the model for making two dipoles between the interior and the exterior of the piston for each of the two energy varieties. (Supplanentary conductive dipoles may be required if mechanical friction occurs or viscous fluids are used.) Recall that it is only by using dipoles that the time may be taken into account. 

Statics the study of bodies remaining at rest (equilibrium) as a result of forces acting upon them... 

Kristof, E. Orszag, I. Ratkovics, F. Static vapour-Uquid equilibrium studies on xC3H7NH2 + (1 - x)C3H70H J. Chem. Thermodyn. 1981,13, 557-562... 

Remarks. Close inspection of the nonequilibrium model outputs reveals that assumption of nonequilibrium capillary pressure in the studied range of experimental conditions was not necessary and static equilibrium described by PcxPg-Pe was sufficient to account for the interfacial forces [54], However, recourse to empirical capillary relationships, such as the Leverett /-function, is unnecessary as the nonequilibrium two-phase flow model enables access to capillary pressure via entropy-consistent constitutive expressions for the macroscopic Helmholtz free energies. Also, the role of mass exchange between bulk fluid phase holdups and gas-liquid interfacial area was shown to play a nonnegligible role in the dynamics of trickle-bed reactor [ 54]. By accounting for the production/destruction of interfacial area, they prompted much briefer response times for the system to attain steady state compared to the case without inclusion of these mass exchange rates. 

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