ANALYSIS OF A COMPRESSIBLE GAS-LIQUID MODEL MOTIVATED BY OIL WELL CONTROL OPERATIONS Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

We are interested in a viscous two-phase gas-liquid mixture model relevant for modeling of well control operations within the petroleum industry.We focus on a simplified mixture model and provide an existence result within an appropriate class of weak solutions.We demonstrate that upper and lower limits can be obtained for the gas and liquid masses which ensure that transition to single-phase regions do not occur.This is used together with appropriate a prior estimates to obtain convergence to a weak solution for a sequence of approximate solutions corresponding to mollified initial data.Moreover,by imposing an additional regularity condition on the initial masses,a uniqueness result is obtained.The framework herein seems useful for further investigations of more realistic versions of the gas-liquid model that take into account different flow regimes.     

RECENT DEVELOPMENTS ON THE STRUCTURAL CHEMISTRY OF COMPLEXES OF SELENIUM AND TELLURIUM WITH SULFUR-AND SELENIUM CONTAINING LIGANDS

Abstract

The stereochemistry of selenium and tellurium and the role of lone electron pairs will be discussed on the basis of recent X-ray diffraction studies appearing in the literature. Some of the studies represent new types of structures.     

Global weak solutions for a viscous liquid–gas model with transition to single-phase gas flow and vacuum

This work deals with a viscous two-phase liquid–gas model relevant to the flow in wells and pipelines. The liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic. The model is rewritten in terms of Lagrangian coordinates and is studied in a free boundary setting where the liquid and gas masses are of compact support initially, and continuous at the boundary. Consequently, the initial masses involve a transition to single-phase gas flow and vacuum at the boundary. An appropriate balance between pressure and viscous forces is identified which allows obtaining pointwise upper and lower estimates of masses. These estimates rely on the assumption of a certain relation between the rate of degeneracy of the viscosity coefficient and the rate that determines how fast the initial masses are vanishing at the boundary. By combining these estimates with basic energy type of estimates, higher order regularity estimates are obtained. The existence of global weak solutions is then proved by showing compactness for a class of semi-discrete approximations.     

Global weak solutions for a compressible gas-liquid model with well-formation interaction

The objective of this work is to explore a compressible gas-liquid model designed for modeling of well flow processes. We build into the model well-reservoir interaction by allowing flow of gas between well and formation (surrounding reservoir). Inflow of gas and subsequent expansion of gas as it ascends towards the top of the well (a so-called gas kick) represents a major concern for various well operations in the context of petroleum engineering. We obtain a global existence result under suitable assumptions on the regularity of initial data and the rate function that controls the flow of gas between well and formation. Uniqueness is also obtained by imposing more regularity on the initial data. The key estimates are to obtain appropriate lower and upper bounds on the gas and liquid masses. For that purpose we introduce a transformed version of the original model that is highly convenient for analysis of the original model. In particular, in the analysis of the transformed model additional terms, representing well-formation interaction, can be treated by natural extensions of arguments that previously have been employed for the single-phase Navier-Stokes model. The analysis ensures that transition to single-phase regions do not appear when the initial state is a true gas-liquid mixture.     

Thermal desorption of carbon monoxide from Mo(110)

Adsorption and desorption of carbon monoxide (CO) from Mo(110) have been investigated by temperature programmed desorption (TPD). The TPD spectra exhibit peaks in two temperature regions: 250-400 and 850-1100 K. The first region correspond to adsorption in molecular form, whereas the latter region corresponds to desorption of CO that has been dissociatively adsorbed. When the surface was saturated by CO, about 35% of the desorption intensity originates from the high-temperature region (recombinative desorption) and the remaining desorption signal is from the low-temperature region (molecular adsorption). Desorption parameters for molecular adsorbed CO were obtained using several different heating rates. Desorption energies were estimated to range from 0.9 eV for low coverages of CO to about 0.65 eV for high coverages. Corresponding prefactors were estimated to be in the range from 1 210¹¹ to 1 210⁹ s^{m 1}. The experimental data have been compared with Monte Carlo simulations of first-order TPD from a bcc (110) lattice, in which partial poisoning of adsorption sites by dissociated carbon and oxygen was modelled. Repulsive near-neighbour interactions were used.     

Surface alloy formation after deposition of Ce on Rh(1 1 0)

Vapour deposition of Ce onto a Rh(1 1 0) single crystal at room temperature is studied by X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS) and low energy electron diffraction (LEED). The thicknesses of the deposited Ce layers are estimated to be between 2 and 9 Å. To study the changes in the Ce-Rh surface layer, the samples are annealed at temperatures between 500 and 1000 °C after Ce deposition.After heating, a c(2 × 2) LEED pattern appears for the sample with the thinnest deposited Ce layer (2.4 Å). For samples with thicker Ce-films, the LEED pattern co-exists of a c(2 × 2) structure and a more diffuse 6% contracted (2 × 1) structure. This appears at the same temperature as the Ce 3d and Rh 3d core levels exhibit sharp intensity changes and binding energy shifts.The intensity of the f⁰, f¹ and f² multiplets in the Ce 3d core level spectra change when the annealing temperature is increased. The relative intensity of the Ce 3d f⁰ and f² features compared to the Ce 3d f¹ features is largest after annealing to 500 °C. This is below the temperature at which the ordered surface alloy is formed. When the sample is heated above the formation temperature of the surface alloy, the relative intensity of the Ce 3d f⁰ and f² features decrease.     

Formation of the porous structure during the polymerization of meta-divinylbenzene and para-divinylbenzene with toluene and 2-ethylhexanoic acid (2-EHA) as porogens

Macroporous polymers of pure meta-divinylbenzene (meta-DVB) and pure para-divinylbenzene (para-DVB) have been prepared in the presence of toluene and 2-EHA as pore forming agents. The formation of the pore structure has been studied during the polymerization by pore-size distribution measurements, together with determination of the specific surface area from nitrogen sorption isotherms using the BET treatment. In addition, the morphology and texture have been characterized by SEM during the polymerization process. Large differences in the pore-size distribution among all the polymer samples are found. The polymers prepared in toluene as porogen have a pore-size distribution, which mainly consists of small pores, while large pores appear with 2-EHA as porogen. In the presence of 2-EHA, a major change in the pore-size distribution is also observed when the monomer is shifted from para-DVB to meta-DVB, leading to a bimodal distribution. The texture characterization by SEM shows details and discriminates the samples in consistency with what may be expected from pore-size distribution measurements. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3973–3990, 1999