Shell (Netherlands)

<p>We present a novel method for simulating hydrodynamic phenomena. This particle-based method combines features from molecular dynamics and lattice-gas automata. It is shown theoretically as well as in simulations that a quantitative description of isothermal Navier-Stokes flow is obtained with relatively few particles. Computationally, the method is much faster than molecular dynamics, and the at same time it is much more flexible than lattice-gas automata schemes.</p>

A total of 2128 calcitic and phosphatic shells, mainly brachiopods with some conodonts and belemnites, were measured for their δ18O, δ13C and 87Sr/86Sr values. The dataset covers the Cambrian to Cretaceous time interval. Where possible, these samples were collected at high temporal resolution, up to 0.7 Ma (one biozone), from the stratotype sections of all continents but Antarctica and from many sedimentary basins. Paleogeographically, the samples are mostly from paleotropical domains. The scanning electron microscopy (SEM), petrography, cathodoluminescence and trace element results of the studied calcitic shells and the conodont alteration index (CAI) data of the phosphatic shells are consistent with an excellent preservation of the ultrastructure of the analyzed material. These datasets are complemented by extensive literature compilations of Phanerozoic low-Mg calcitic, aragonitic and phosphatic isotope data for analogous skeletons. The oxygen isotope signal exhibits a long-term increase of δ18O from a mean value of about −8‰ (PDB) in the Cambrian to a present mean value of about 0‰ (PDB). Superimposed on the general trend are shorter-term oscillations with their apexes coincident with cold episodes and glaciations. The carbon isotope signal shows a similar climb during the Paleozoic, an inflexion in the Permian, followed by an abrupt drop and subsequent fluctuations around the modern value. The 87Sr/86Sr ratios differ from the earlier published curves in their greater detail and in less dispersion of the data. The means of the observed isotope signals for 87Sr/86Sr, δ18O, δ13C and the less complete δ34S (sulfate) are strongly interrelated at any geologically reasonable (1 to 40 Ma) time resolution. All correlations are valid at the 95% level of confidence, with the most valid at the 99% level. Factor analysis indicates that the 87Sr/86Sr, δ18O, δ13C and δ34S isotope systems are driven by three factors. The first factor links oxygen and strontium isotopic evolution, the second 87Sr/86Sr and δ34S, and the third one the δ13C and δ34S. These three factors explain up to 79% of the total variance. We tentatively identify the first two factors as tectonic, and the third one as a (biologically mediated) redox linkage of the sulfur and carbon cycles. On geological timescales (≥1 Ma), we are therefore dealing with a unified exogenic (litho-, hydro-, atmo-, biosphere) system driven by tectonics via its control of (bio)geochemical cycles.

Abstract The splitting of globules is an important phenomenon during the final stages of disintegration processes. Three basic types of deformation of globules and six types of flow patterns causing them are distinguished. The forces controlling deformation and breakup comprise two dimensionless groups: a Weber group N We and a viscosity group N Vi . Breakup occurs when N We exceeds a critical value ( N We ) crit . Three cases are studied in greater detail: (a) Taylor's experiments on the breakup of a drop in simple types of viscous flow, (b) breakup of a drop in an air stream, (c) emulsification in a turbulent flow. It is shown that ( N We ) crit depends on the type of deformation and on the flow pattern around the globule. For case (a) ( N We ) crit shows a minimum value ∼ 0.5 at a certain value of ( N Vi ) and seems to increase indefinitely with either decreasing or increasing ratio between the viscosites of the two phases. For case (b) ( N We ) crit varies between 13 and ∞, depending on N Vi and on the way in which the relative air velocity varies with time, the lowest value refers to the true shock case and N vi →0. For case (c) ( N We ) crit , which determines the maximum drop size in the emulsion, amounts to ∼1, and the corresponding values of N Vi appear to be small. A formula is derived for the maximum drop size.

Published in Petroleum Transactions, AIME, Vol. 210, 1957, pages 153–168. Paper presented at Petroleum Branch Fall Meeting in Los Angeles, Oct. 14–17, 1956. Abstract A theoretical examination of the fracturing or rocks by means of pressures applied in boreholes leads to the conclusion that, regardless of whether the fracturing fluid be of the penetrating or non-penetrating type, the fractures produced should be approximately perpendicular to the axis of least stress. The general state of stress underground is that in which the three principal stresses are unequal. For tectonically relaxed areas characterized by normal faulting, the least stress should be horizontal; the fractures produced should be vertical with the injection pressure less than that of the overburden. In areas of active tectonic compression, the least stress should be vertical and equal to the pressure of the overburden; the fractures should behorizontal with injection pressures equal to or greater than the pressure of the overburden. Horizontal fractures cannot be produced by hydraulic pressures less than the total pressure of the overburden. These conclusions are compatible with field experience in fracturing and with the results of laboratory experimentation. Introduction The hydraulic-fracturing technique of well stimulation is one of the major developments in petroleum engineering of the last decade. The technique was introduced to the Petroleum Industry in a paper by J. B. Clark, of the Stanolind Oil and Gas Co. in 1918, and since then its use has progressively expanded so that by the end of 1955 more than 100,000 individual treatments had been performed.

Abstract The theory of the deformation of a porous elastic solid containing a compressible fluid has been established by Biot. In this paper, methods of measurement are described for the determination of the elastic coefficients of the theory. The physical interpretation of the coefficients in various alternate forms is also discussed. Any combination of measurements which is sufficient to fix the properties of the system may be used to determine the coefficients. For an isotropic system, in which there are four coefficients, the four measurements of shear modulus, jacketed and unjacketed compressibility, and coefficient of fluid content, together with a measurement of porosity appear to be the most convenient. The porosity is not required if the variables and coefficients are expressed in the proper way. The coefficient of fluid content is a measure of the volume of fluid entering the pores of a solid sample during an unjacketed compressibility test. The stress-strain relations may be expressed in terms of the stresses and strains produced during the various measurements, to give four expressions relating the measured coefficients to the original coefficients of the consolidation theory. The same method is easily extended to cases of anisotropy. The theory is directly applicable to linear systems but also may be applied to incremental variations in nonlinear systems provided the stresses are defined properly.

Estimating the model parameters from measured data generally consists of minimizing an error functional. A classic technique to solve a minimization problem is to successively determine the minimum of a series of linearized problems. This formulation requires the Frchet derivatives (the Jacobian matrix), which can be expensive to compute. If the minimization is viewed as a non-linear optimization problem, only the gradient of the error functional is needed. This gradient can be computed without the Frchet derivatives. In the 1970s, the adjoint-state method was developed to efficiently compute the gradient. It is now a well-known method in the numerical community for computing the gradient of a functional with respect to the model parameters when this functional depends on those model parameters through state variables, which are solutions of the forward problem. However, this method is less well understood in the geophysical community. The goal of this paper is to review the adjoint-state method. The idea is to define some adjoint-state variables that are solutions of a linear system. The adjointstate variables are independent of the model parameter perturbations and in a way gather the perturbations with respect to the state variables. The adjoint-state method is efficient because only one extra linear system needs to be solved.

ABSTRACT A simple physical model was used to develop an equation that relates the electrical conductivity of a water-saturated shaly sand to the water conductivity and the cation- exchange capacity per unit pore volume of the rock. This equation fits both the experimental data of Hill and Milburn and data obtained recently on selected shaly sands with a wide range of cation-exchange capacities. This model was extended to cases where both oil and water are present in the shaly sand. This results in an additional expression, relating the resistivity ratio to water saturation, water conductivity and cation-exchange capacity per unit pore volume. The effect of shale content on the resistivity index- water saturation function is demonstrated by several numerical examples. INTRODUCTION A principal aim of well logging is to provide quantitative information concerning porosity and oil saturation of the permeable formations penetrated by the borehole. For clean sands, the relationships between measured physical quantities and porosity or saturation are well known. However, the presence of clay minerals greatly complicates log interpretation, particularly the electrical resistivity and SP logs, and considerably affects evaluation of hydrocarbon-bearing formations. The conductance and electrochemical behavior of shaly sands and their relation to log interpretation have been studied by many workers. Wyllie and Lynch reviewed this work in some detail. Virtually all laboratory measurements of electrical resistivity and electrochemical potential of shaly sands published to date are the work of Hill and Milburn.

We address the problem of finding interatomic force fields for silicas from ab initio calculations on small clusters. It is shown that the force field cannot be determined from cluster data alone; incorporation of bulk-system information into the force field remains essential. Bearing this in mind, we derive a force field based on both microscopic (ab initio) and macroscopic (experimental) data. This force field combines accuracy with transferability to other polymorphs. The possibility of parametrizing other elements is also demonstrated.

The influence of cobalt particle size in the range of 2.6-27 nm on the performance in Fischer-Tropsch synthesis has been investigated for the first time using well-defined catalysts based on an inert carbon nanofibers support material. X-ray absorption spectroscopy revealed that cobalt was metallic, even for small particle sizes, after the in situ reduction treatment, which is a prerequisite for catalytic operation and is difficult to achieve using traditional oxidic supports. The turnover frequency (TOF) for CO hydrogenation was independent of cobalt particle size for catalysts with sizes larger than 6 nm (1 bar) or 8 nm (35 bar), while both the selectivity and the activity changed for catalysts with smaller particles. At 35 bar, the TOF decreased from 23 x 10(-3) to 1.4 x 10(-3) s(-1), while the C5+ selectivity decreased from 85 to 51 wt % when the cobalt particle size was reduced from 16 to 2.6 nm. This demonstrates that the minimal required cobalt particle size for Fischer-Tropsch catalysis is larger (6-8 nm) than can be explained by classical structure sensitivity. Other explanations raised in the literature, such as formation of CoO or Co carbide species on small particles during catalytic testing, were not substantiated by experimental evidence from X-ray absorption spectroscopy. Interestingly, we found with EXAFS a decrease of the cobalt coordination number under reaction conditions, which points to reconstruction of the cobalt particles. It is argued that the cobalt particle size effects can be attributed to nonclassical structure sensitivity in combination with CO-induced surface reconstruction. The profound influences of particle size may be important for the design of new Fischer-Tropsch catalysts.

Furfural offers a promising, rich platform for lignocellulosic biofuels. These include methylfuran and methyltetrahydrofuran, valerate esters, ethylfurfuryl and ethyltetrahydrofurfuryl ethers as well as various C(10)-C(15) coupling products. The various production routes are critically reviewed, and the needs for improvements are identified. Their relative industrial potential is analysed by defining an investment index and CO(2) emissions as well as determining the fuel properties for the resulting products. Finally, the most promising candidate, 2-methylfuran, was subjected to a road trial of 90,000 km in a gasoline blend. Importantly, the potential of the furfural platform relies heavily on the cost-competitive production of furfural from lignocellulosic feedstock. Conventional standalone and emerging coproduct processes-for example, as a coproduct of cellulosic ethanol, levulinic acid or hydroxymethyl furfural-are expensive and energetically demanding. Challenges and areas that need improvement are highlighted. In addition to providing a critical review of the literature, this paper also presents new results and analysis in this area.

With the design charts presented here, and nothing more elaborate than aslide rule, it is possible to predict the dimensions of either a linearly or aradially propagating, hydraulically induced fracture around a wellbore. Introduction During the hydraulic fracturing treatment of an oil or gas well the liquidpressure in the borehole is increased until tensile stress in the surroundingrock exceeds tensile strength. Once a tensile fracture is initiated, it ispenetrated by liquid from the borehole and fracture propagation undercontinuous hydraulic action takes place. The fracturing liquid carries apropping agent to ensure a highly permeable flow propping agent to ensure ahighly permeable flow channel after pressure release. Field results range fromfailure to obtain increased production to outstanding success. In all cases, production to outstanding success. In all cases, however, it unfortunatelyremains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact theideal ones. Though experience provides a lead, a more satisfactory way topredict results would seem to be the subject the fracture propagation processto a theoretical analysis that (1) makes the maximum use of the relevantphysical information and (2) so simplifies the resulting calculations that thefield engineer gets practical data that he can handle comfortably. We areattempting here to do this in connection with the prediction of fracture widthand areal extent before pressure release. What remains of the fractureafterwards depends on the distribution of the propping agent between thefracture walls, and that is a propping agent between the fracture walls, andthat is a separate story. Idealization of the Problem To keep the problem tractable, a number of simplifying assumptions have hadto be made:The formation is homogeneous and isotropic as regards those ofits properties that influence the fracture-propagation process.Thedeformations of the formation during fracture propagation can be derived fromlinear elastic stress-strain relations.The fracturing fluid behaves like apurely viscous liquid; i.e., any peculiar flow behavior due to the addition ofgelling agents or other additives is neglected. Moreover, the effect of thepropping agent distribution on the distribution of fluid viscosity in thefracture is not taken into account.Fluid flow in the fracture is everywherelaminar.Simple geometric fracture-extension patterns are assumed - eitherradially symmetrical propagation from a point source (Fig. 1A) or rectilinearpropagation originating from a line source (Fig. 1B). In the first case theperiphery of the fracture is circular, in the second case it is rectangular.A rectilinear propagation mode can be accomplished only by injection over alarge perforated interval, thus forming a line source. Such a rectilinearfracture must therefore be located in the vertical plane. A circularpropagation mode might be expected from injection through propagation modemight be expected from injection through a narrow band of perforations. Thisforms a point source. JPT P. 1571

Abstract This paper treats the propagation of hydraulic fractures of limited vertical extent and elliptic cross-section with the effect of fluid loss included. Numerical and asymptotic approximate solutions in dimensionless form give the fracture length and width at any value of time or any set of physical parameters. The insight provided by The dimensionless parameters. The insight provided by The dimensionless results and approximate solutions should be useful in the design of fracture treatments. Introduction The theory and practice of hydraulic fracturing has been reviewed by Howard and Fast. Therefore, we confine our discussion of previous investigations to those pertinent to the present study of the propagation of vertical fractures. propagation of vertical fractures. An important theoretical result is Carter's formula for the area of a fracture of constant width formed by injection at constant rate with fluid lost to the formation. For a vertical fracture of constant height, Carter's formula gives fracture length as a function of time. In general, Carter's assumption of constant width is not realistic. However, at large values of time the effect of this assumption becomes insignificant since the effect of fluid loss dominates. The width of a vertical fracture was first investigated by Khristianovic and Zheltov under the assumption that the width does not vary in the vertical direction. Thus, a state of plane strain prevails in horizontal planes and the width can be prevails in horizontal planes and the width can be determined as the solution of a plane elasticity problem. An approximate solution is found in Ref. 3 problem. An approximate solution is found in Ref. 3 upon neglect of fluid loss, fracture volume change, and pressure variation along the fracture. The fracture length is determined by the condition of finite stress at the fracture tip. Baron et al. and Geertsma and de Klerk have included the effect of fluid loss in the approach of Ref. 3. Geertsma and de Klerk give simple approximate formulas for fracture length and width. A different approach to the determination of fracture width was taken by Perkins and Kern. They considered a vertically limited fracture under the assumption of plane strain in vertical planes perpendicular to the fracture plane. The perpendicular to the fracture plane. The cross-section of the fracture is found to be elliptical, and the maximum width decreases along the fracture according to a simple formula that contains the fracture length. In the derivation of this formula, fluid loss and fracture volume change are neglected in the continuity equation and the fracture length is not determined. In a subsequent application, a "reasonable" fracture length was assumed. Carter's formula for length and the width formula of Perkins and Kern are both cited by Howard and Fast, and combined use of the two formulas is believed to be common practice. The present theoretical investigation is concerned with vertically limited fractures of the type studied by Perkins and Kern. However, we include the effects of fluid loss and fracture volume change in the continuity equation. Consequently, fracture length is determined as part of the solution. General results for the variation of fracture width and length with time are obtained in dimensionless form by a numerical method. In addition, asymptotic solutions are derived for large and small values of time. The small-time solution is also the exact solution for the case of no fluid loss to the formation. For large values of time our asymptotic formula for fracture length is identical with Carter's formula at large time. Our large-time formula for fracture width differs from the formula of Perkins and Kern by a numerical factor that varies along the fracture. In comparison with our formula, this formulas overestimates the width by 12 percent at the well and 24 percent at the midlength of the fracture. At early times Perkins and Kern's formulas for width in terms of length is again a fair approximation to our result. However, our formula for length differs from Carter's formula, which is not applicable since the neglected width variation is important at early times. The results for the width of a vertically limited fracture as obtained here and in Ref. 6 differ from the results for vertically constant fractures.

A new method for the elimination of uninformative variables in multivariate data sets is proposed. To achieve this, artificial (noise) variables are added and a closed form of the PLS or PCR model is obtained for the data set containing the experimental and the artificial variables. The experimental variables that do not have more importance than the artificial variables, as judged from a criterion based on the b coefficients, are eliminated. The performance of the method is evaluated on simulated data. Practical aspects are discussed on experimentally obtained near-IR data sets. It is concluded that the elimination of uninformative variables can improve predictive ability.

After the introduction of the concept of lattice graph and a brief discussion of its role in the theory of the Ising model, a related combinatorial problem is discussed, namely that of the statistics of non-overlapping dimers, each occupying two neighboring sites of a lattice graph. It is shown that the configurational partition function of this system can be expressed in terms of a Pfaffian, and hence calculated explicitly, if the lattice graph is planar and if the dimers occupy all lattice sites. By the examples of the quadratic and the hexagonal lattice, it is found that the dimer system may show a phase transition similar to that of a two-dimensional Ising model, or one of a different nature, or no transition at all, depending on the activities of various classes of bonds. The Ising problem is then shown to be equivalent to a generalized dimer problem, and a rederivation, of Onsager's expression for the Ising partition function of a rectangular lattice graph is sketched on the basis of this equivalence.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTPalladium-Catalyzed Alternating Copolymerization of Alkenes and Carbon MonoxideEite Drent and Peter H. M. BudzelaarView Author Information Koninklijke/Shell Laboratorium Amsterdam (Shell Research B.V.), P.O. Box 38000, 1030 BN Amsterdam, The Netherlands Cite this: Chem. Rev. 1996, 96, 2, 663–682Publication Date (Web):March 28, 1996Publication History Received13 July 1995Revised2 October 1995Published online28 March 1996Published inissue 1 January 1996https://pubs.acs.org/doi/10.1021/cr940282jhttps://doi.org/10.1021/cr940282jresearch-articleACS PublicationsCopyright © 1996 American Chemical SocietyRequest reuse permissionsArticle Views6912Altmetric-Citations842LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose SUBJECTS:Catalysts,Copolymerization,Hydrocarbons,Ligands,Palladium Get e-Alerts

The formation of a single product from terminal functionalization of linear alkanes from a transition metal-catalyzed reaction is reported. The rhodium complex Cp*Rh(eta(4)-C(6)Me(6)) (Cp*, C(5)Me(5); Me, methyl) catalyzes the high-yield formation of linear alkylboranes from commercially available borane reagents under thermal conditions. These reactions now allow catalytic, regiospecific functionalization of alkanes under thermal conditions. The organoborane products are among the most versatile synthetic intermediates in chemistry and serve as convenient precursors to alcohols, amines, and other common classes of functionalized molecules.

Abstract Equations of elasticity and consolidation for a porous elastic material containing a fluid have been previously established (1, 5). General solutions of these equations for the isotropic case are developed, giving directly the displacement field or the stress field in analogy with the Boussinesq-Papkovitch solution and the stress functions of the theory of elasticity. General properties of the solutions also are examined and the viewpoint of eigenfunctions in consolidation problems is introduced.

We have studied the flow of suspensions of solid spheres under steady shear using a newly developed flow simulator. For the first time, the complicated interplay between hydrodynamic interactions and solids' variable configuration under flow conditions in which large departures from equilibrium configurations occur can be simulated in full 3D. For volume fractions up to 35%, viscosities have been obtained that are in excellent agreement with experiments reported in the literature.

Abstract A thermodynamic liquid model has been developed to describe the behavior of asphalt and asphaltenes in reservoir crudes upon changes in pressure, temperature, or composition. Asphaltene solubility properties used as input to the model may be obtained from titration experiments on tank oil. High-pressure flocculation experiments confirm the potential of the model. The model appears to be well applicable to conditions at which asphaltenes are associated with resins. The model may be used to identify field conditions where asphalt or asphaltene precipitation will occur.

Selective partial oxidation of methane to methanol suffers from low efficiency. Here, we report a heterogeneous catalyst system for enhanced methanol productivity in methane oxidation by in situ generated hydrogen peroxide at mild temperature (70°C). The catalyst was synthesized by fixation of AuPd alloy nanoparticles within aluminosilicate zeolite crystals, followed by modification of the external surface of the zeolite with organosilanes. The silanes appear to allow diffusion of hydrogen, oxygen, and methane to the catalyst active sites, while confining the generated peroxide there to enhance its reaction probability. At 17.3% conversion of methane, methanol selectivity reached 92%, corresponding to methanol productivity up to 91.6 millimoles per gram of AuPd per hour.