Some versions of limit and Dieudonné-type theorems with respect to filter convergence for (<Emphasis Type="Italic">ℓ</Emphasis>)-group-valued measures

Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results.     

Kinetics of dissolution of powdered Pentelic marble in under-saturated solutions: the role of particle characteristics

In the present study, the effect of mesopore and particle size distributions on the kinetics of dissolution of powdered Pentelic marble was investigated. Powders obtained by grinding marble slabs in an agate mortar with a pestle (1-3.5 min) were found to be non-porous by nitrogen absorption measurements. These powders, upon dissolution under conditions of constant under-saturation, 25 degrees C, pH 8.25, showed that the kinetics in the absence of mesopores depended on the number of active sites on the exposed surface. Thus, powders consisting of smaller particles, having higher specific surface areas, yielded higher rates of dissolution. Powders, however, which were prepared by grinding marble slabs in a cylinder mill for time periods between 2.0 and 30.0 min, and which exhibited considerable mesoporosity, showed the opposite trend. The rates of dissolution measured for these powders in under-saturated solutions increased with increasing mean particle size and decreased with increasing specific surface area. This finding suggested that the presence of mesopores resulted in lower dissolution rates even though the exposed total surface area was larger. Furthermore, the larger the number of mesopores in a powder sample the slower the corresponding dissolution rates in under-saturated solutions.     

Principles of demineralization: modern strategies for the isolation of organic frameworks. Part II. Decalcification

This is the second paper on principles of demineralization. The initial paper is dedicated to the common definitions and the history of demineralization. In present work we review the principles and mechanisms of decalcification, i.e., removing the mineral Ca-containing compounds (phosphates and carbonates) from the organic matrix in its two main aspects: natural and artificial. Natural chemical erosion of biominerals (cavitation of biogenic calcareous substrata by bacteria, fungi, algae, foraminifera, sponges, polychaetes, and mollusks) is driven by production of mineral and organic acids, acidic polysaccharides, and enzymes (cabonic anhydrase, alkaline and phosphoprotein phosphataes, and H(+)-ATPase). Examples of artifical decalcification includes demineralization of bone, dentin and enamel, and skeletal formations of corals and crustacean. The mechanism and kinetics of Ca-containing biomineral dissolution is analyzed within the framework of (i) diffusion-reaction theory; (ii) surface-reaction controlled, morphology-based theories, and (iii) phenomenological surface coordination models. The application of surface complexation model for describing and predicting the effect of organic ligands on calcium and magnesium dissolution kinetics is also described. Use of the electron microscopy-based methods for observation and visualization of the decalcification phenomenon is discussed.     

Spontaneous precipitation of calcium silicate hydrate in aqueous solutions

Calcium silicate hydrates (C‐S‐H) are very important not only for their contribution to the development of cement and concrete properties but also for use as fillers and in silicate glasses. In the present work, the thermodynamics and the kinetics of the spontaneous precipitation of C‐S‐H from aqueous solutions were investigated over the pH range 10‐12 at 25 °C. The thermodynamic driving force was calculated taking into consideration all equilibria involved in the supersaturated solutions. In the range of the solution supersaturation values examined the precipitation occurred spontaneously, with the exception of the series of experiments done at pH 12.0, where induction times preceded the appearance of the precipitate. The rates were measured at constant pH as a function of the solution supersaturation and were found to depend strongly on the solution supersaturation, pH and on the total calcium to total silicate molar ratio in solution. Fit of the kinetics results in a power law relating rates of precipitation with respect to C‐S‐H precipitated, suggested a surface diffusion controlled mechanism for the formation of C‐S‐H. The precipitated solids did not show significant morphological differences at different pH values. From the induction times preceding the spontaneous precipitation at pH 12.0, a value of 30 mJm^‐2 was calculated for the surface energy of C‐S‐H. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modular filter convergence theorems for Urysohn integral operators and applications

We prove some versions of modular convergence theorems for nonlinear Urysohn-type integral operators with respect to filter convergence. We consider pointwise filter convergence of functions giving also some applications to linear and nonlinear Mellin operators. We show that our results are strict extensions of the classical ones.     

Precipitation of sparingly soluble salts in packed sandbeds in the presence of miscible and immiscible organic substances

Sparingly soluble salts precipitation, e.g. calcium carbonate or calcium sulfate, results in pore clogging in rock formations and in the concomitant reduction of the local permeability of oil wells during the oil extraction processes. On the other hand, in situ controlled salt precipitation is desirable in various applications e.g. waterproofing of concrete constructions suffering from leakages, etc. In the present study, calcium carbonate (CaCO₃) precipitation in sandbeds was investigated, in the presence of organic solvents simulating the conditions prevalent in oil‐well zones. CaCO₃ precipitation was investigated from supersaturated solutions prepared by in‐situ mixing of NaHCO₃ and CaCl₂.2H₂O solutions before the inlet of sandbeds. The solution resulting from the mixing of the two solutions was supersaturated with respect to all calcium carbonate polymorphs. Three types of experiments were performed depending on the supersaturated solutions: a) aqueous solutions b) aqueous supersaturated solutions in contact with sandbeds pre‐saturated with n‐dodecane c) aqueous solutions containing monoethylene glycol (MEG). Results showed that oil–water interfaces enhanced the heterogeneity of the supersaturated solutions and accelerated crystal growth of calcium carbonate at the inlet of the sandbed, resulting in early pore clogging and limitation of local permeability. Maximum sandbed consolidation was obtained with the solutions containing MEG.     

Sand consolidation with calcium phosphate-polyelectrolyte composites

A new method for the consolidation of loose sand formations has been developed. The method involves in situ precipitation of a composite calcium phosphate-polyelectrolyte salt that binds together with loose sand grains, thus resulting to their consolidation. Three different polyelectrolytes (PE) were tested, i.e., polyacrylic acid (PAA), polyallylamine hydrochloride (PAH), and polyethylenimine (PEI). The effect of PE tested on the thermodynamics and the kinetics of precipitation of calcium phosphate salts was investigated. Three types of experiments were done. Investigation of the adsorption of PE on either hydroxyapatite (Ca(5)(PO(4))(3)OH, HAP) crystals or on sand grains. Measurement of the kinetics of heterogeneous nucleation of HAP on the solid substrates and the mechanical properties of the obtained crystals in batch experiments of low and high supersaturation solutions, respectively. Evaluation of the consolidation in sand packs in order to investigate the effectiveness of the method. The crystallization rates, R(p), on HAP crystals in the presence of the PE tested were found in the order R(p)(PAA)>R(p)(PEI)>R(p)(PAH), while nucleation and crystal growth on silicate sand took place only in the absence of adsorbed PE. PAH favored strongly the consolidation process, whereas PEI and PAA resulted in the formation of poorly consolidated grain agglomerates.     

Probabilistic verification of a biodiesel production system using statistical model checking

Biochemical system designers are increasingly using formal modelling, simulation, and verification methods to improve the understanding of complex systems. Probabilistic models can incorporate realistic stochastic dynamics, but creating and analysing probabilistic models in a formal way is challenging. In this work, we present a stochastic model of biodiesel production that incorporates an inexpensive test of fuel quality, and we validate the model using statistical model checking, which can be used to evaluate simple or complex temporal properties efficiently. We also describe probabilistic simulation and analysis techniques for stochastic hybrid system (SHS) models to demonstrate the properties of our model. We introduce a variety of properties for various configurations of the reactor as well as results of testing our model against the properties.     

Incorporation of Mg<Superscript>2+</Superscript>, Sr<Superscript>2+</Superscript>, Ba<Superscript>2+</Superscript> and Zn<Superscript>2+</Superscript> into aragonite and comparison with calcite

We have investigated the presence of foreign ions into the bulk structure and the external surfaces of aragonite using periodic ab-initio methods. Four cations isovalent to Ca²⁺ were studied: Mg²⁺, Sr²⁺, Ba²⁺ and Zn²⁺. The calculations were performed at structures (bulk, surface) that contain four and eight CaCO₃ units. Our results, at the Hartree-Fock level, show that the incorporation of those ions into aragonite depends strongly on their size. Mg²⁺ and Zn²⁺, due to their smaller size, can substitute Ca²⁺ ions in the crystal lattice while the incorporation of Sr²⁺ and Ba²⁺ into aragonite is energetically less favoured. Examination of the [011], [110] and [001] surfaces of aragonite revealed that the surface incorporation reduces the energetic cost for the larger ions. These systems provide challenging examples for most shape analysis methods applied in Mathematical Chemistry.     

Sandbed Consolidation with Mineral Precipitation

A new method has been developed to prevent sand reentrainment during oil production from unconsolidated or poorly consolidated reservoir formations. Consolidation of the zformation around the well is achieved through in situ precipitation of a sparingly soluble salt, namely, calcium phosphate. Control of the depth of salt formation is achieved by alternating injection, mixing, and reaction of two aqueous solutions of calcium chloride and potassium phosphate. Calcium phosphate crystals precipitate and grow on the grain surfaces, forming sufficiently uniform coatings. The formation of relatively uniform coatings on the grains causes an acceptably small decrease of the permeability, which is a feature of primary importance for oil production. The grains are gradually "cemented" with bridges of calcium phosphate crystallites and form a consolidated and still porous structure. As a result, the rate of hydrocarbon production for the problematic reservoir can be increased considerably without undesirable reentrainment of sand. The proposed method for consolidation has been successfully tested in sandbeds. Several series of experiments have been carried out under diverse conditions to establish the optimum parameter values for the implementation of this method. A set of optimum conditions at 25 degrees C were determined and these conditions gave satisfactory consolidation with permeability loss of ca. 60% of the initial value. The conditions of precipitation were chosen so that the precipitated phase was octacalcium phosphate [Ca(4)H(PO(4))(3).2.5H(2)O], along with its byproduct hydroxyapatite [Ca(5)(PO(4))(3)OH]. Experiments were also carried out at 70 degrees C and have shown that it is feasible to consolidate loose sandpacks at oil reservoir conditions. Copyright 2000 Academic Press.