In situ SANS study of the surface and pore filling adsorption of subcritical and supercritical CO2 in porous silica as a function of pore size

We applied small-angle neutron scattering (SANS) and ultra small-angle neutron scattering (USANS) to monitor evolution of the CO2 adsorption in porous silica as a function of CO2 pressure and temperature in pores of different sizes. The range of pressures (0 < P < 345 bar) and temperatures (T=18 OC, 35 OC and 60 OC) corresponded to subcritical, near critical and supercritical conditions of bulk fluid. We observed that the adsorption behavior of CO2 is fundamentally different in large and small pores with the sizes D > 100 Å and D < 30 Å, respectively. Scattering data from large pores indicate formation of a dense adsorbed film of CO2 on pore walls with the liquid-like density (ρCO2)ads≈0.8 g/cm3. The adsorbed film coexists with unadsorbed fluid in the inner pore volume. The density of unadsorbed fluid in large pores is temperature and pressure dependent: it is initially lower than (ρCO2)ads and gradually approaches it with pressure. In small pores compressed CO2 gas completely fills the pore volume. At the lowest pressures of the order of 10 bar and T=18 OC, the fluid density in smallest pores available in the matrix with D ~ 10 Å exceeds bulk fluid density by a factor of ~ 8. As pressure increases, progressively larger pores become filled with the condensed CO2. Fluid densification is only observed in pores with sizes less than ~ 25 – 30 Å. As the density of the invading fluid reaches (ρCO2)bulk~ 0.8 g/cm3, pores of all sizes become uniformly filled with CO2 and the confinement effects disappear. At higher densities the fluid in small pores appears to follow the equation of state of bulk CO2 although there is an indication that the fluid density in the inner volume of large pores may exceed the density of the adsorbed layer. The equivalent internal pressure (Pint) in the smallest pores exceeds the external pressure (Pext) by a factor of ~ 5 for both sub- and supercritical CO2. Pint gradually approaches Pext as D → 25 – 30 Å and is independent of temperature in the studied range of 18 OC ≤ T ≤ 60 OC. The obtained results demonstrate certain similarity as well as differences between adsorption of subcritical and supercritical CO2 in disordered porous silica. High pressure small angle scattering experiments open new opportunities for in situ studies of the fluid adsorption in porous media of interest to CO2 sequestration, energy storage, and heterogeneous catalysis.

Monitoring phase behavior of sub- and supercritical CO2 confined in porous fractal silica with 85% porosity

Phase behavior of CO2 confined in porous fractal silica with volume fraction of SiO2 φs = 0.15 was investigated using small-angle neutron scattering (SANS) and ultrasmall-angle neutron scattering (USANS) techniques. The range of fluid densities (0<(FCO2)bulk<0.977 g/cm3) and temperatures (T=22 °C, 35 and 60 °C) corresponded to gaseous, liquid, near critical and supercritical conditions of the bulk fluid. The results revealed formation of a dense adsorbed phase in small pores with sizes D<40 A° at all temperatures. At low pressure (P <55 bar, (FCO2)bulk <0.2 g/cm3) the average fluid density in pores may exceed the density of bulk fluid by a factor up to 6.5 at T=22 °C. This “enrichment factor” gradually decreases with temperature, however significant fluid densification in small pores still exists at temperature T=60°C, i.e., far above the liquid-gas critical temperature of bulk CO2 (TC=31.1 °C). Larger pores are only partially filled with liquid-like adsorbed layer which coexists with unadsorbed fluid in the pore core. With increasing pressure, all pores become uniformly filled with the fluid, showing no measurable enrichment or depletion of the porous matrix with CO2.

Robust design and optimisation of a radial turbine within a supercritical CO2 solar Brayton Cycle

The generation of solar thermal power is dependent upon the amount of sunlight exposure,as influenced by the day-night cycle and seasonal variations. In this paper, robust optimisation is applied to the design of a power block and turbine, which is generating 30 MWe from a concentrated solar resource of 560oC. The robust approach is important to attain a high average performance (minimum efficiency change) over the expected operating ranges of temperature, speed and mass flow. The final objective function combines the turbine performance and efficiency weighted by the off-design performance. The resulting robust optimisation methodology as presented in the paper gives further information that greatly aids in the design of non-classical power blocks through considering off-design conditions and resultant performance.

Tris[4,4,4-trifluoro-1-(2-thienyl)butane-1,3-dionato]aluminium(III)-tris[4,4,4-trifluoro-1-(2-thienyl)butane-1,3-dionato]iron(III) (3/1)

In the title compound, [Al(C8H4F3O2S)3]3[Fe(C8H4F3O2S)3], the metal centre is statistically occupied by AlIII and FeIII cations in a 3:1 ratio. The metal centre is within an octahedral O6 donor set defined by three chelating substituted acetoacetonate anions. The ligands are arranged around the periphery of the molecule with a mer geometry of the S atoms.

Bow and stern flows with constant vorticity

Free surface flows of a rotational fluid past a two-dimensional semi-infinite body are considered. The fluid is assumed to be inviscid, incompressible, and of finite depth. A boundary integral method is used to solve the problem for the case where the free surface meets the body at a stagnation point. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterized by a train of waves upstream. It is shown numerically that the amplitude of these waves increases as each of the Froude number, vorticity and height of the body above the bottom increases.

Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

Smoothly attaching bow flows with constant vorticity

The free surface flow of a finite depth fluid past a semi-infinite body is considered. The fluid is assumed to have constant vorticity throughout and the free surface is assumed to attach smoothly to the front face of the body. Numerical solutions are found using a boundary integral method in the physical plane and it is shown that solutions exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Vorticity is included in the flow and it is shown that the behaviour of the solutions is qualitatively the same as that found in the problem described above.

Pulse dynamics in a three-component system : existence analysis

In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.

Pulse dynamics in a three-component system : stability and bifurcations

In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.

Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.

Pore accessibility by methane and carbon dioxide in coal as determined by neutron scattering

Contrast-matching ultrasmall-angle neutron scattering (USANS) and small-angle neutron scattering (SANS) techniques were used for the first time to determine both the total pore volume and the fraction of the pore volume that is inaccessible to deuterated methane, CD4, in four bituminous coals in the range of pore sizes between ∼10 Å and ∼5 μm. Two samples originated from the Illinois Basin in the U.S.A., and the other two samples were commercial Australian bituminous coals from the Bowen Basin. The total and inaccessible porosity were determined in each coal using both Porod invariant and the polydisperse spherical particle (PDSP) model analysis of the scattering data acquired from coals both in vacuum and at the pressure of CD4, at which the scattering length density of the pore-saturating fluid is equal to that of the solid coal matrix (zero average contrast pressure). The total porosity of the coals studied ranged from 7 to 13%, and the volume of pores inaccessible to CD4 varied from ∼13 to ∼36% of the total pore volume. The volume fraction of inaccessible pores shows no correlation with the maceral composition; however, it increases with a decreasing total pore volume. In situ measurements of the structure of one coal saturated with CO2 and CD4 were conducted as a function of the pressure in the range of 1−400 bar. The neutron scattering intensity from small pores with radii less than 35 Å in this coal increased sharply immediately after the fluid injection for both gases, which demonstrates strong condensation and densification of the invading subcritical CO2 and supercritical methane in small pores.

Mechanisms of glycerol dehydration

Dehydration of neutral and protonated glycerol was investigated using quantum mechanical calculations (CBS-QB3). Calculations on neutral glycerol show that there is a high barrier for simple 1,2-dehydration, E-a = 70.9 kcal mol(-1), which is lowered to 65.2 kcal mol(-1) for pericyclic 1,3-dehydration. In contrast, the barriers for dehydration of protonated glycerol are much lower. Dehydration mechanisms involving hydride transfer, pinacol rearrangement, or substitution reactions have barriers between 20 and 25 kcal mol(-1). Loss of water from glycerol via substitution results in either oxirane or oxetane intermediates, which can interconvert over a low barrier. Subsequent decomposition of these intermediates proceeds via either a second dehydration step or loss of formaldehyde. The computed mechanisms for decomposition of protonated glycerol are supported by the gas-phase fragmentation of protonated glycerol observed using a triple-quadrupole mass spectrometer.

Two-dimensional bow and stern flows in a finite-depth fluid with constant vorticity

This thesis is concerned with two-dimensional free surface flows past semi-infinite surface-piercing bodies in a fluid of finite-depth. Throughout the study, it is assumed that the fluid in question is incompressible, and that the effects of viscosity and surface tension are negligible. The problems considered are physically important, since they can be used to model the flow of water near the bow or stern of a wide, blunt ship. Alternatively, the solutions can be interpreted as describing the flow into, or out of, a horizontal slot. In the past, all research conducted on this topic has been dedicated to the situation where the flow is irrotational. The results from such studies are extended here, by allowing the fluid to have constant vorticity throughout the flow domain. In addition, new results for irrotational flow are also presented. When studying the flow of a fluid past a surface-piercing body, it is important to stipulate in advance the nature of the free surface as it intersects the body. Three different possibilities are considered in this thesis. In the first of these possibilities, it is assumed that the free surface rises up and meets the body at a stagnation point. For this configuration, the nonlinear problem is solved numerically with the use of a boundary integral method in the physical plane. Here the semi-infinite body is assumed to be rectangular in shape, with a rounded corner. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterised by a train of waves upstream. In the limit that the height of the body above the horizontal bottom vanishes, the flow approaches that due to a submerged line sink in a $90^\circ$ corner. This limiting problem is also examined as a special case. The second configuration considered in this thesis involves the free surface attaching smoothly to the front face of the rectangular shaped body. For this configuration, nonlinear solutions are computed using a similar numerical scheme to that used in the stagnant attachment case. It is found that these solution exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Finally, the flow of a fluid emerging from beneath a semi-infinite flat plate is examined. Here the free surface is assumed to detach from the trailing edge of the plate horizontally. A linear problem is formulated under the assumption that the elevation of the plate is close to the undisturbed free surface level. This problem is solved exactly using the Wiener-Hopf technique, and subcritical solutions are found which are characterised by a train of sinusoidal waves in the far field. The nonlinear problem is also considered. Exact relations between certain parameters for supercritical flow are derived using conservation of mass and momentum arguments, and these are confirmed numerically. Nonlinear subcritical solutions are computed, and the results are compared to those predicted by the linear theory.

Advances in solid-catalytic and non-catalytic technologies for biodiesel production

The insecure supply of fossil fuel coerces the scientific society to keep a vision to boost investments in the renewable energy sector. Among the many renewable fuels currently available around the world, biodiesel offers an immediate impact in our energy. In fact, a huge interest in related research indicates a promising future for the biodiesel technology. Heterogeneous catalyzed production of biodiesel has emerged as a preferred route as it is environmentally benign needs no water washing and product separation is much easier. The number of well-defined catalyst complexes that are able to catalyze transesterification reactions efficiently has been significantly expanded in recent years. The activity of catalysts, specifically in application to solid acid/base catalyst in transesterification reaction depends on their structure, strength of basicity/acidity, surface area as well as the stability of catalyst. There are various process intensification technologies based on the use of alternate energy sources such as ultrasound and microwave. The latest advances in research and development related to biodiesel production is represented by non-catalytic supercritical method and focussed exclusively on these processes as forthcoming transesterification processes. The latest developments in this field featuring highly active catalyst complexes are outlined in this review. The knowledge of more extensive research on advances in biofuels will allow a deeper insight into the mechanism of these technologies toward meeting the critical energy challenges in future.