Journal articles on the topic 'Guinier approximation'

In the field of small-angle X-ray scattering (SAXS), the task of estimating the size of particles in solution is usually synonymous with the Guinier plot. The approximation behind this plot, developed by Guinier in 1939, provides a simple yet accurate characterization of the scattering behavior of particles at low scattering angle or momentum transfer q, together with a computationally efficient way of inferring their radii of gyration R G. Moreover, this approximation is valid beyond spherical scatterers, making its use ubiquitous in the SAXS world. However, when it is important to estimate further particle characteristics, such as the anisotropy of the scatterer's shape, no similar or extended approximations are available. Existing tools to characterize the shape of scatterers rely either on prior knowledge of the scatterers' geometry or on iterative procedures to infer the particle shape ab initio. In this work, a low-angle approximation of the scattering intensity I(q) for ellipsoids of revolution is developed and it is shown how the size and anisotropy information can be extracted from the parameters of that approximation. The goal of the approximation is not to estimate a particle's full structure in detail, and thus this approach will be less accurate than well known iterative and ab initio reconstruction tools available in the literature. However, it can be considered as an extension of the Guinier approximation and used to generate initial estimates for the aforementioned iterative techniques, which usually rely on R G and D max for initialization. This formulation also demonstrates that nonlinearity in the Guinier plot can arise from anisotropy in the scattering particles. Beyond ideal ellipsoids of revolution, it is shown that this approximation can be used to estimate the size and shape of molecules in solution, in both computational and experimental scenarios. The limits of the approach are discussed and the impact of a particle's anisotropy in the Guinier estimate of R G is assessed.

Small-angle scattering of X-rays and neutrons is a routine method for the determination of nanoparticle sizes. The so-called Guinier law represents the low-q approximation for the small-angle scattering curve from an assembly of particles. The Guinier law has originally been derived for nonmagnetic particle-matrix-type systems and it is successfully employed for the estimation of particle sizes in various scientific domains (e.g. soft-matter physics, biology, colloidal chemistry, materials science). An important prerequisite for it to apply is the presence of a discontinuous interface separating particles and matrix. Here, the Guinier law is introduced for the case of magnetic small-angle neutron scattering and its applicability is experimentally demonstrated for the example of nanocrystalline cobalt. It is well known that the magnetic microstructure of nanocrystalline ferromagnets is highly nonuniform on the nanometre length scale and characterized by a spectrum of continuously varying long-wavelength magnetization fluctuations, i.e. these systems do not manifest sharp interfaces in their magnetization profile. The magnetic Guinier radius depends on the applied magnetic field, on the magnetic interactions (exchange, magnetostatics) and on the magnetic anisotropy-field radius, which characterizes the size over which the magnetic anisotropy field is coherently aligned into the same direction. In contrast to the nonmagnetic conventional Guinier law, the magnetic version can be applied to fully dense random-anisotropy-type ferromagnets.

The structure and optical properties of soot were studied in the fuel-rich (underfire) region of buoyant laminar diffusion flames of ethylene and acetylene burning in coflowing air. The objective was to evaluate scattering predictions based on the Rayleigh–Debye–Gans (RDG) approximation for polydisperse fractal aggregates of spherical primary soot particles having constant diameters, for conditions where the Guinier (small angle) regime, and the transition between the Guinier and the power-law (large-angle) regimes, were dominant, in order to supplement earlier work for conditions where the power-law regime was dominant. Soot structure was measured using thermophoretic sampling and analysis by transmission electron microscopy (TEM) to yield primary particle diameters, distributions of the number of primary particles per aggregate, and the aggregate mass fractal dimensions. Soot optical property measurements included vv, hh, hv, and vh differential scattering cross sections, total scattering cross sections, and the albedo at 514.5 nm, as well as several soot structure parameters inferred from these measurements using the approximate theory. The approximate RDG theory generally provided an acceptable basis to treat the optical properties of the present soot aggregates over a range of conditions spanning the Guinier and power-law regimes. Other scattering approximations were less satisfactory with performance progressively becoming less satisfactory in the order: RDG polydisperse fractal aggregate scattering using a single mean squared radius of gyration (from the Guinier regime), Mie scattering for an equivalent sphere, and Rayleigh scattering—the last underestimating differential scattering levels by a factor of roughly 100 for the present test conditions.

In this article, a practical procedure for absolute intensity calibration for small-angle scattering (SAXS) studies on liquid microjets is established. A gold nanoparticle suspension is used as standard so that the intercept at Q = 0 of the SAXS scattering curve provides a scaling reference. In order to obtain the most precise extrapolation at Q = 0, an extension of the Guinier approximation has been used, with a second-order term in the fit that adapts to a larger Q range.

The error is investigated which results from the employment of tangential approximation in the calculation of line shift caused by specimen displacement from the recording circle in focusing systems (Guinier, Seemann–Bohlin). After an exact expression has been deduced and compared with the approximate formula in a numerical example, it is concluded that the error caused by the approximate formula may be important only in exceptional cases. The deduced exact formula is also compared with that given by Rafaja and Valvoda [Powder Diffr. 6, 200–203 (1991)] with the conclusion that both formulas are mathematically equivalent and complementary with respect to the theoretical and measured values of the diffraction angle 2θ.

A computational evaluation of an approximate theory for the optical properties of soot is described, emphasizing the small-angle (Guinier) regime. The approximate theory (denoted RDG-FA theory) is based on the Rayleigh–Debye–Gans scattering approximation while treating soot as mass-fractal aggregates of spherical primary particles that have constant diameters and refractive indices. The approximate theory was evaluated by more exact predictions from the solution of the volume integral equation formulation of the governing equations, using the method of moments, and based on the ICP algorithm of Iskander et al. (1989). Numerical simulations were used to construct statistically significant populations of soot aggregates having appropriate fractal properties and prescribed numbers of primary particles per aggregate. Optical properties considered included absorption, differential scattering, and total scattering cross sections for conditions typical of soot within flame environments at wavelengths in the visible and the infrared. Specific ranges of aggregate properties were as follows: primary particle optical size parameters up to 0.4, numbers of primary particles per aggregate up to 512, mean fractal dimensions of 1.75, mean fractal prefactors of 8.0, and refractive indices typical of soot. Over the range of the evaluation, ICP and RDG-FA predictions generally agreed within numerical uncertainties (ca. 10 percent) within the Guinier regime, complementing similar performance of RDG-FA theory in the power-law regime based on recent experiments. Thus, the use of approximate RDG-FA theory to estimate the optical properties of soot appears to be acceptable—particularly in view of the significant uncertainties about soot optical properties due to current uncertainties about soot refractive indices.

A family of stochastic models of disordered particles is proposed, obtained by clipping a Gaussian random field with a function that is space dependent. Depending on the shape of the clipping function, dense or hollow particles can be modelled. General expressions are derived for the form factor of the particles, for their average volume and surface area, and for their density and surface-area distributions against the distance to the particle centre. A general approximation for the form factor is also introduced, based on the density and surface-area distributions, which coincides with the Guinier and Porod expressions in the limits of low and high scattering vector magnitude q. The models are illustrated with the fitting of small-angle X-ray scattering (SAXS) data measured on Pt/Ni hollow nanoparticles. The SAXS analysis and modelling notably capture the collapse of the particles' porosity after being used as oxygen-reduction catalysts.

The theory of small-angle neutron or X-ray scattering from a solution consisting of rods that are uncorrelated in position and orientation and its use in determining the mass per unit length and cross-sectional radius of gyration is extended to rods of finite length and non-uniform cross-sectional structure. The case of a rod made up of identical motifs spaced in a regularly repeating axial structure is considered first. Analysis of the small-angle scatter by a modified Guinier plot gives the mean mass per unit length of the motifs. The apparent squared cross-sectional radius of gyration is the weight average. These results are then generalized to the case where variable randomly distributed structural elements are present including variable spacing between the motifs making up the rod. In this way expressions are obtained that describe the scatter from rods with structural contributions from random thermal fluctuations, bound ligands and intrinsic structural heterogeneity. It is shown that, in general, systematic errors are introduced in the analysis of rods of finite length having variable structural components. However, if all the motifs have the same mass, and if the variance in their spacing is small, such errors are not important provided that the rods are of sufficient length.

The optical properties of soot were studied for the fuel-lean (overfire) region of buoyant turbulent diffusion flames in still air. Results were limited to the long residence time regime where soot structure is independent of position in the overfire region and residence time for a particular fuel. Measurements included scattering, absorption, and extinction cross sections at 514.5 nm and extinction cross sections at 632.8 and 1152 nm for flames fueled with acetylene, propylene, ethylene, and propane. The measurements were used to evaluate scattering predictions based on the Rayleigh-Debye-Gans (RDG) approximation for randomly oriented poly disperse fractal aggregates of spherical primary soot particles having constant diameters. The present soot aggregates exhibited significant departures from Rayleigh-scattering behavior at 514.5 nm, with forward scattering roughly 100 times larger than wide-angle scattering and ratios of scattering to absorption cross sections in the range 0.22–0.41, increasing with increasing propensity of the fuel to soot. The approximate RDG theory generally provided an acceptable basis to treat the optical properties of the present overfire soot aggregates, although additional measurements in the Guinier (small angle) regime are needed for a definitive evaluation of model performance.

This article presents new procedures for multisite spatiotemporal neuronal data analysis. A new statistical model—the diffusion model—is considered, whose parameters can be estimated from experimental data thanks to mean-field approximations. This work has been applied to optical recording of the guinea pig's auditory cortex (layers II—III). The rates of innovation and internal diffusion inside the stimulated area have been estimated. The results suggest that the activity of the layer balances between the alternate predominance of its innovation process and its internal process.

A program suite for one-dimensional small-angle scattering data processing running on IBM-compatible PCs under Windows 9x/NT/2000/XP is presented. The main program,PRIMUS, has a menu-driven graphical user interface calling computational modules to perform data manipulation and analysis. Experimental data in binary OTOKO format can be reduced by calling the programSAPOKO, which includes statistical analysis of time frames, averaging and scaling. Tools to generate the angular axis and detector response files from diffraction patterns of calibration samples, as well as binary to ASCII transformation programs, are available. Several types of ASCII files can be directly imported intoPRIMUS, in particular, sasCIF or ILL-type files are read without modification.PRIMUSprovides basic data manipulation functions (averaging, background subtraction, merging of data measured in different angular ranges, extrapolation to zero sample concentration,etc.) and computes invariants from Guinier and Porod plots. Several external modules coupled withPRIMUSviapop-up menus enable the user to evaluate the characteristic functions by indirect Fourier transformation, to perform peak analysis for partially ordered systems and to find shape approximations in terms of three-parametric geometrical bodies. For the analysis of mixtures,PRIMUSenables model-independent singular value decomposition or linear fitting if the scattering from the components is known. An interface is also provided to the general non-linear fitting programMIXTURE, which is designed for quantitative analysis of multicomponent systems represented by simple geometrical bodies, taking shape and size polydispersity as well as interparticle interference effects into account.

Regulation of muscarinic receptors in cultured guinea pig pancreatic acini was investigated by assessing the effects of cholinergic agonists on binding of [N-methyl-3H]scopolamine [( 3H]NMS) and on amylase release. Freshly dispersed acini bound [3H]NMS with a Kd of 74 pM and a maximal binding level (Bmax) of 908 fmol/mg DNA. Carbachol (CCh) stimulated amylase secretion and inhibited [3H]NMS binding. Incubation of acini for 30 min with 0.1 mM CCh decreased the subsequent efficacy of CCh in stimulating amylase release by threefold but had no effect on its potency. In contrast, amylase release in response to cholecystokinin octapeptide (CCK-8) was not altered by CCh preincubation. [3H]NMS binding to acini was decreased only 15–20% after 30-min incubation with CCh. However, culture of acini with 0.1 mM CCh decreased [3H]NMS binding by 50% at 3–4 h and by 85–90% at 24 h. This decrease was attributable primarily to a reduction in Bmax. [3H]NMS binding also was decreased to a similar extent by the cholinergic agonists bethanechol and methacholine but not by other secretagogues. The decrease in antagonist binding induced by CCh was dose dependent, with the IC50, 5.8 microM, approximating the EC50 for amylase release, 4.3 microM. Culture of acini for 24 h with CCh abolished subsequent amylase release in response to CCh but not to CCK-8. When CCh was removed from the culture medium after 24 h and acini recultured in its absence, [3H]NMS binding increased with a half-time for recovery of 20–24 h; this recovery was blocked by cycloheximide.(ABSTRACT TRUNCATED AT 250 WORDS)

In order to further understand the shape memory mechanism of a silicon dioxide/shape memory polyurethane (SiO2/SMPU) composite, the thermodynamic properties and shape memory behaviors of prepared SiO2/SMPU were characterized. Dynamic changes in the molecular orientation and interphase structures of SiO2/SMPU during a shape memory cycle were then discussed according to the small angle X-ray scattering theory, Guinier’s law, Porod approximation, and fractal dimension theorem. In this paper, a dynamic mechanical analyzer (DMA) helped to determine the glass transition start temperature (Tg) by taking the onset point of the sigmoidal change in the storage modulus, while transition temperature (Ttrans) was defined by the peak of tan δ, then the test and the calculated results indicated that the Tg of SiO2/SMPU was 50.4 °C, and the Ttrans of SiO2/SMPU was 72.18 °C. SiO2/SMPU showed good shape memory performance. The programmed SiO2/SMPU showed quite obvious microphase separation and molecular orientation. Large-size sheets and long-period structures were formed in the programmed SiO2/SMPU, which increases the electron density difference. Furthermore, some hard segments had been rearranged, and their gyration radii decreased. In addition, several defects formed at the interfaces of SiO2/SMPU, which caused the generation of space charges, thus leading to local electron density fluctuations. The blurred interphase structure and the intermediate layer formed in the programmed SiO2/SMPU and there was evident crystal damage and chemical bond breakage in the recovered SiO2/SMPU. Finally, the original and recovered SiO2/SMPU samples belong to the surface fractal system, but the programmed sample belongs to the mass fractal and reforms two-phase structures. This study provides an insight into the shape memory mechanism of the SiO2/SMPU composite.

Magnetic interpretations are usually carried out either by assuming induced magnetization and estimating the model geometry, or by presuming a known source spatial orientation to estimate the total magnetization. We present a 3-D magnetic interpretation method that estimates simultaneously the total magnetization direction and the spatial orientation of the source. It is based on the approximation of the anomaly by the series derived from expanding the magnetic potential into multipoles and retaining source moments up to second order. The moments and linear combinations of moments appearing in the series are then inverted from the magnetic anomaly. The total magnetization is assumed constant in direction but not in magnitude. It is also presumed implicitly that the anomalous distribution of magnetization intensity has nonzero values in a finite‐volume region, is far from the observation points, and presents three othogonal planes of symmetry intersecting at the center of the dipole moment. The method is essentially linear and requires no a priori explicit assumption of a fixed geometry for the sources. The method is particularly suited to interpret compact, isolated or disjoint, but spatially correlated sources. If the source satisfies all assumptions presumed by the method, it is possible to obtain accurate, stable estimates of the total dipole moment vector, the position of the center of dipole moment, and the directions of all three principal axes of symmetry. If the source is not far from the observation plane and/or if the total magnetization direction is not constant, it is still possible to obtain accurate and stable estimates of the direction of the mean total magnetization and the projection, on the observation plane, of the center of dipole moment. The method is applied to magnetic data from the Gulf of Guinea Seamount. The estimated magnetic palaeopole is at 50°48′S and 74°54′E which is in good agreement with estimates published by other authors.

Lungs from near-term fetal guinea-pigs were supported in vitro for 3 h; lung liquid production was measured by a dye-dilution method using Blue Dextran 2000 [fetuses 63 +/- 2 days of gestation, 97.6 +/- 19.8 (SD) g body weight]. Preparations were incubated in pairs taken from the same mother. Twenty lungs incubated in pairs without treatment (controls) showed no significant changes in fluid production throughout incubation (analysis of variance; regression analysis); rates in successive hours were: first lung, 1.36 +/- 0.39, 1.09 +/- 0.34 and 1.27 +/- 0.42 ml/kg body weight per h; second lung, 1.46 +/- 0.52, 1.09 +/- 0.41 and 1.18 +/- 0.43 ml/kg body weight per h. Twenty lungs were incubated similarly in pairs, but after one hour one lung from each pair was expanded with Krebs-Henseleit saline in volumes approximating those of the first breath (68 +/- 10% of lung volume). The expanded lungs began to reabsorb fluid immediately after expansion; the untreated lungs also stopped production or reached reabsorption by the final hour. Rates in successive hours were: expanded lungs; before expansion, 1.00 +/- 0.21, after expansion, -0.23 +/- 0.17 and 0.14 +/- 0.09 ml/kg body weight per h; unexpanded lungs, 1.27 +/- 0.49, 0.02 +/- 0.01 and -0.01 +/- 0.004 ml/kg body weight per h. The decrease in production was significant for each type of lung. The effects persisted in both expanded and unexpanded lungs in the presence of 1.78 x 10(-5) M phentolamine (n = 12; 70 +/- 2% expansion). The results suggest that expansion of the lungs at birth may release an unknown inhibitory factor, provisionally termed Expansion Factor (EF), within the lungs; this agent, probably not a catecholamine, can change lung fluid production into reabsorption and may partly account for the failure of beta-antagonists to prevent fluid reabsorption at delivery.

Sanchez, Russell M., Alisa Surkis, and Christopher S. Leonard. Voltage-clamp analysis and computer simulation of a novel cesium-resistant A-current in guinea pig laterodorsal tegmental neurons. J. Neurophysiol. 79: 3111–3126, 1998. Increased firing of cholinergic neurons of the laterodorsal tegmental nucleus (LDT) plays a critical role in generating the behavioral states of arousal and rapid eye movement sleep. The majority of these neurons exhibit a prominent transient potassium current ( I A) that shapes firing but the properties of which have not been examined in detail. Although I A has been reported to be blocked by intracellular cesium, the I A in LDT neurons appeared resistant to intracellular cesium. The present study compared the properties of this cesium-resistant current to those typically ascribed to I A. Whole cell recordings were obtained from LDT neurons ( n = 67) in brain slices with potassium- or cesium-containing pipette solutions. A transient current was observed in cells dialyzed with each solution (KGluc-85%; CsGluc-79%). However, in cesium-dialyzed neurons, the transient current was inward at test potentials negative to about −35 mV. Extracellular 4-aminopyridine (4-AP; 2–5 mM) blocked both inward and outward current, suggesting the inward current was reversed I A rather than an unmasked transient calcium current as previously suggested. This conclusion was supported by increasing [K]o from 5 to 15 mM, which shifted the reversal potential positively for both inward and outward current (+17.89 ± 0.41 mV; mean ± SE). Moreover, recovery from inactivation was rapid (τ = 15.5 ± 4 ms; n = 4), as reported for I A, and both inward and outward transient current persisted in calcium-free solution [0 calcium/4 mM ethylene glycol-bis(β-aminoethyl ether)- N,N,N′,N′-tetraacetic acid; n = 4] and during cadmium-blockade of calcium currents ( n = 3). Finally, the transient current was blocked by intracellular 4-AP indicating that adequate dialysis occurred during the recordings. Thus the Cs-resistant current is a subthreshold I A. We also estimated the voltage-dependence of activation ( V 1/2 = −45.8 ± 2 mV, k = 5.21 ± 0.62 mV, n = 6) and inactivation ( V 1/2 = −59.0 ± 2.38 mV, k = −5.4 ± 0.49 mV, n = 3) of this current. Computer simulations using a morphologically accurate model cell indicated that except for the extreme case of only distal A-channels and a high intracellular resistivity, our parameter estimates were good approximations. In conclusion, guinea pig LDT neurons express subthreshold A-channels that are resistant to intracellular cesium ions. This suggests that these channels differ fundamentally in their ion permeation mechanism from those previously studied. It remains to be determined if Cs+ resistance is common among brain A-channels or if this property is conferred by known A-channel subunits.

Lungs from near-term fetal guinea-pigs were supported in vitro for 3 h; lung liquid production was measured by a dye-dilution method using Blue Dextran 2000 (fetuses 62 +/- 2 days of gestation, 97.6 +/- 19.0 (SD) g body weight; n = 134). Untreated control preparations produced fluid at 1.30 +/- 0.22 ml/kg body weight per h, and showed no significant changes during incubation (n = 30). After 1 h of incubation, experimental lungs were expanded with Krebs-Henseleit saline in volumes estimated to be below or approximating those of the first breath (n = 30; first breath, 0.6-1.2 ml). Expansions were graded at 18 +/- 4%, 31 +/- 4%, 43 +/- 3%, 50 +/- 3% and 72 +/- 2% of lung volume (volumes used for expansion at the maximal level, 0.64 +/- 0.25 ml). All expansions of 31% or above produced reductions in fluid production significant by analysis of variance (P < 0.01-0.001); production halted at 50% expansion, and there was strong reabsorption at 72% expansion (-0.87 +/- 0.45 ml/kg body weight per h by the final hour). There was an exponential relationship between percentage expansion and percentage fall in production (r = 1.00). There was no evidence for excessive pressure, and no evidence for lung damage as judged by electron microscopy or entry of intracellular materials into the fluid (lactic dehydrogenase, protein, K+). In studies based on 36 preparations, 10(-6) M amiloride present in the lung lumen (apically) abolished the reabsorptions seen at 70 +/- 3% expansion, but not the arrest of production; it had no effect on control preparations. Studies based on 24 preparations showed that responses to 72 +/- 2% expansion were not affected by 10(-7) M propranolol placed in the outer saline. In studies of 14 fetuses of widely different body weights (68.3-124.9 g), responses to 74 +/- 2% expansion showed an exponential increase with increasing body weight (r = 0.96). Although caution is needed, the results suggest that expansion of the lungs at birth may induce fluid reabsorption by an action independent of tissues outside the lungs, probably involving both activation of a Na(+)-based reabsorptive system and arrest of production, but not requiring beta-receptor activation. The probability that the responses are maximal at birth is discussed, and it is suggested that the effect of expansion may be a specialization of the perinatal lung.

Summary We present a new approach to solve the problem of complex wells located in layered reservoirs with crossflow. First, the well path is discretized into a carefully chosen series of source points. Second, pressure solution for each source point is obtained in the Laplace domain anywhere in a rectangular reservoir, where crossflow is permitted between layers and with possibly mixed boundary conditions (no-flow or constant pressure). We used the Fourier transforms in the space variables after removing the time variable by the Laplace transformation. The problem is reduced to a matrix product to solve in the transformed domain. The above method is validated through comparisons with known line source solutions and numerical simulations. It can be used to compute the pressure distribution within a well with complex geometry in a stratified bounded reservoir under the assumption of infinite well conductivity. The well can be located anywhere in the reservoir. Boundaries can be no-flow or constant pressure. Last, variable skins along the well path can be imposed. An application on a field located in the deep offshore of the Gulf of Guinea demonstrates the great value for well design optimization in the context of complex heterogeneous reservoirs where classical analytical approaches are typically inappropriate. Introduction Recent drilling technology advances have led the oil industry to use wells with complex geometry (e.g., multilaterals) for performance improvement, particularly in the context of low-productivity reservoirs or in adverse reservoir conditions such as deep-offshore. At present, evaluating productivity of such complex wells remains a difficult task. Indeed, available analytical approaches do not allow modeling complex well geometry in heterogeneous reservoirs. An extensive literature deals with horizontal wells 1–6 in a single, homogeneous layer. Recently, several authors have considered horizontal wells in multilayered reservoirs. For this type of problem it is almost impossible to obtain a single pressure point that approximates the infinite-conductivity solution for all times. Kuchuk 7 presented a new general method to solve transient-pressure problems in a lateral composite reservoir allowing crossflow between layers. This method is based on the principles of reflection and transmission. To determine an approximate infinite-conductivity solution (constant pressure) at the wellbore, the point-source solution is integrated along the well, and the uniform flux line source so obtained is averaged over the length of the well. The wellbore pressure for a horizontal well in a layered and bounded system is developed by Kuchuk8 using the image method (in the x and y direction) applied to the transient solution. Cinco9,10 investigated steady flow in reservoirs producing through a fully slanted well in an infinite slab reservoir. He obtained the analytical solution by representing the well as an infinite-conductivity source so that the pressure transient is the same along the well. Later, Gommard11 and Lu 12 concentrated on the pressure-transient behavior of slanted wells crossing several layers in multilayered reservoirs with crossflow. Gommard particularly studied an optimum subdivision of the well to calculate the pressure-drop response. Larsen13 proposed a slanted well model in multilayer reservoirs based on the multiple permeability concept. The first limitation of the approach is due to the fact that the perforated zone of the well in each layer is represented by a uniform flux fracture solution. Besides, this model does not allow accounting for the early time radial flow period because of the integration of the governing equation along the z axis. At present, the solutions mentioned above cannot solve the general problem of a complex (nonlinear) well located anywhere in a bounded, multilayered reservoir with crossflow. To attempt solving this general problem, we propose in the following a point-source approach where we keep all the points describing the entire well path in order to obtain a good approximation of transient or pseudo-steady-state (PSS) productivity. A new point-source solution is proposed to solve the pressure-diffusion equation. This method is based on:Fourier transforms together with solutions of transcendental equations, to take into account lateral boundaries,the "quadripole" method to represent the crossflow between layers as well as the top and bottom boundary conditions. This method has been used by several authors14,15 for solving heat-conduction problems, for example, to calculate heat transfer across a two-dimensional plane crack. The paper is organized as follows:recall of the governing equations,description of the point-source solution,description of the complete solution for a complex well,validations against known analytical and numerical solutions,case study on real data, andconclusions. Governing Equations We consider a well with complex geometry in an anisotropic medium bounded, above and below, by horizontal layers with crossflow and laterally by limits with constant pressure or no-flow conditions (respectively, Hk=8 or Hk=0 in Eqs. 2a-2d). The more appropriate coordinate system, due to the boundary surface is a Cartesian one (Fig. 1).

Summary Thermally induced fracturing (TIF) during water injection is a well-established phenomenon. TIF modeling implies solving equations simultaneously that conventional petroleum engineering applications deal with separately. Combining these equations leads to very complex computer programs. This has led to the need for a simple model, which we present in this paper. Coupling analytical expressions representing each of these phenomena, rather than the basic physical equations, has led to a computer program that can be run on a modern desk-top computer. This program has successfully matched the daily wellhead pressure and injection rate during a period of 3 to 5 years for injection wells in complex sandstone/dolomite reservoirs. The model can be used for injection-well monitoring as well as in a predictive mode when planning new water-injection projects. The algorithm is sufficiently simple to be implemented in a conventional reservoir simulator. Introduction The concept of a constant productivity index, extrapolated below bubble point by use of Vogel's curve, is one of the fundamental tools of petroleum engineering. One of its most interesting features is that it depends on reservoir and reservoir properties alone. It is independent of downstream wellbore equipment and surface facilities. One would like to be able to use a similar concept for water injection wells, but, unfortunately, calculating an injectivity index, turns out to be much more complex. Water available for injection is often much colder than the reservoir, and numerous temperature-induced phenomena often having opposite effects occur within the first few days or weeks of injection. From the beginning of injection, the bottomhole flowing temperature decreases and finally reaches a stabilized value depending on surface and reservoir temperature, injection rate, depth, and well completion. During that time, matrix flows will have a reducing effect on injectivity. This is because, in such conditions, the bottom-hole viscosity can often increase two- to four-fold. Also, when water displaces oil, there is a relative-permeability effect tied to the growth of the zone from which oil has been displaced. At the same time, mechanical effects will tend to decrease injectivity inversely. The reservoir stress near the well is reduced when the reservoir is cooled, and fracturing will occur if the reservoir stress falls below bottomhole flowing pressure. This phenomena is called TIF.1–6 It leads to a continuous increase in injectivity when fracture develops. In fact, the final reduced stress is the result of a thermal reducing effect (thermoelasticity) and a fluid-pressure increasing effect (poroelasticity) at the injector. In general, however, the latter is much smaller. As we have shown, the injectivity index cannot be calculated without taking into account the wellbore pressure and temperature performance. Injectivity therefore depends on the situation both upstream (wellbore equipment and surface facilities) and downstream (reservoir properties). Modeling water injectivity therefore leads to very large computer programs in which the complexities of both reservoir models and fracturing simulators are intermingled. The pioneering work of Hagoort7 and Perkins and Gonzalez8 on thermo-poroelasticity were followed by more refined models, such as that published by Dikken and Niko.9 More recently, Settari10,11 and Clifford12 presented three-dimensional (3D) fracturing calculations. This paper presents a model that uses simple analytical formulas representing all these intermingled physical processes that influence the injectivity index. The model has been programmed on a PC and used to match the performance of wells injecting into a complex sandstone/dolomite reservoir in the Gulf of Guinea. Well behavior is modeled as a sequence of timesteps. The basic assumption is that steady-state equilibrium is reached at the end of each timestep. This is a good approximation for long-term well behavior. We do not aim to simulate short-term phenomena such as those encountered during well tests; in our model, reservoir pressure transients are ignored, as are the mechanics of fracture propagation. Our model starts at the wellhead, with a given injection rate and wellhead temperature. The model calculates a wellhead pressure, which can be compared to measurements. The least known parameters are adjusted within their plausible range of values until a satisfactory match is obtained. The algorithm also has been programmed so that when wellhead pressure and temperature are given as data, the model calculates the injection rate. This calculation mode is of particular interest when planning waterfloods. Part 1: The Model Wellbore Temperature Profile. The first task is to calculate bottomhole flowing temperature, ?wf, from surface temperature, injection rate, and wellbore equipment. A linear geothermal gradient is assumed. Bottomhole flowing temperature is calculated from wellhead temperature by dividing the tubing into 25 segments. We use the transient heat-exchange solution13 between each segment and the surrounding earth to calculate the quantity of heat that reaches the water in the tubing. This solution assumes that the well rate is constant. To cope with rate-varying behavior, an effective injection time has been defined with the cumulative injection Wi and the current injection rate i : As long as injection rate does not decrease too abruptly, this simple algorithm gives satisfactory results. The reason that such a simple algorithm works is that most of the heat exchange between an injection well and the surrounding earth takes place at depth, where the well geometry is simplest: a tubing and one casing. On the contrary, such a simple calculation is impossible on a production well because, in this case, the biggest temperature contrast and therefore most of the heat exchange are close to the surface where well geometry and its surroundings are most variable. This algorithm does not give realistic results when the injection rate is reduced abruptly (for instance, when the well is shut in). A smoothing function has therefore been introduced to limit the change in ?wf during any one timestep. Calculation Assuming Radial Injection. We use the term radial injection when flow is radially outwards from the well; the alternative, when the reservoir is fractured by the water injection process, is called fractured injection.

AbstractThis paper correlates the interlaminar shear strength of 7 different carbon fiber/epoxy composite with structural characteristics determined by Small Angle X-ray Scattering (SAXS) measurements. The carbon fibers were all of the same type but had different surface treatments. The SAXS patterns of the fibers and of the composites showed a highly nonlinear Guinier region which could not be approximated by traditional linear regression. A new approach to the Guinier approximation was developed to treat this nonlinear curve using a polynomial of second order. The radius of gyration (RG) of the fibers, as determined by this new method, correlated clearly with both the extent of the surface treatment and the interlaminar shear strength of the composite. Also the difference in scattering between a dry fiber and a glycerine soaked fiber provides a way to characterize the changes obtained by surface treatments. These methods provide new ways to estimate the efficiency of a surface treatment and its effect on the interlaminar shear strength by analyzing the SAXS patterns of the fibers.

AbstractThe presented work follows the theme of applied chemistry toward nanomaterials and multiphase functional systems of practical importance. Structural studies of nanocomposite materials are important due to the correlation between physicochemical/structural properties and their application potential. In this work, we report the fabrication and structural characterization of nanocomposite materials constituting noble metal (plasmonic) nanoparticles (AgNP and AuNP) dispersed on selected types of nanostructured solid hosts (nonporous silica, microporous activated carbon, chitosan biopolymer, and ordered mesoporous silica). The ability to maintain a dispersed state of colloidal precursors throughout their deposition on solid hosts was assessed. The influence of the carrier role in the formation and stabilization of nanometallic phases was evaluated taking into account the physicochemical and textural properties of the support surfaces. The size and shape of nanoobjects, clustering effects, interfacial properties, and stability of the immobilized nanophase were implemented by analyzing relevant parameters of SAXS analysis. The dimensional characteristic of the scatterers was evaluated by volume-weighted particle size distribution Dv(R). The detailed overall shape and maximal particle dimension were described by the analysis of pair distance distribution functions (PDDFs). The radius of gyration (Rg) from PDDF and Guinier approximation was calculated for illustrating the dimension of scattered heterogeneities in the investigated solids. The asymptotic behavior of a scattering curve and Porod theory were applied for determining the diffusion and quality of the interfacial surfaces. The size and morphology of nanoparticles in colloidal precursor solutions have been defined as spherical and bimodal in size (~ 6 nm and 20 nm). It was observed that the spherical shape and dispersed state of nanoparticles were achieved for all systems after deposition. However, the morphology of their final form was conditioned by the solid matrices. The particle properties from SAXS were correlated with properties determined by TEM and low-temperature nitrogen sorption analysis. Obtained results suggest good compatibility and correctness of SAXS data reading of nanocomposite systems and can be successfully applied for quick, nondestructive, and effective evaluation of structural properties of complex systems. Graphical abstract

AbstractSmall angle light scattering has been used to quantitatively study microvoids in polycrystalline CVD diamond. Guinier's approximation was used to calculate the average radius of gyration of these defects for diamond films made by both DC arc-jet and microwave CVD assuming a spherical defect geometry. Values of the radius of gyration varied between approximately 1 and 5 μm and were found to correlate with the thickness, relative transmission and thermal conductivity measured for the films. Some inconsistencies were observed between microwave and DC arc-jet materials which may be related to fundamental differences in the growth processes. This represents the first quantitative analysis of such defects in polycrystalline films and holds great promise for improving our understanding of the diamond CVD processing and properties.

p-Hydroxyanisole is used as an antioxidant in cosmetic products at concentrations of up to 1.0 percent. The acute oral LD50 of p-Hydroxyanisole in rats was estimated as 1630 mg/kg. Undiluted p-Hydroxyanisole is a severe skin and ocular irritant in rabbits but produced minimal eye irritation at 0.1 percent and minimal rabbit skin irritation at 5 percent. Skin sensitization to p-Hydroxyanisole occurred when guinea pigs were treated at 0.5 M. p-Hydroxyanisole is a skin-depigmenting agent at concentrations approximating those used in cosmetic products. p-Hydroxyanisole was nonmutagenic in the Ames assay. No local toxic changes or tumors were observed following long-term application of 5 and 10 percent p-Hydroxyanisole. The antioxidant was inactive as a tumor promoter. Solutions of p-Hydroxyanisole produced embryotoxicity but not teratogenicity. The function of p-Hydroxyanisole in cosmetics is that of an antioxidant; it is not intended for use as a skin lightener or skin-depigmenting agent. Because of the depigmenting action of p-Hydroxyanisole in black guinea pigs at reported concentrations approaching those used in cosmetics, it is concluded that p-Hydroxyanisole is unsafe for use as a cosmetic ingredient.