Schlumberger (United States)

We consider the response of a Newtonian fluid, saturating the pore space of a rigid isotropic porous medium, subjected to an infinitesimal oscillatory pressure gradient across the sample. We derive the analytic properties of the linear response function as well as the high- and low-frequency limits. In so doing we present a new and well-defined parameter Λ, which enters the high-frequency limit, characteristic of dynamically connected pore sizes. Using these results we construct a simple model for the response in terms of the exact high- and low-frequency parameters; the model is very successful when compared with direct numerical simulations on large lattices with randomly varying tube radii. We demonstrate the relevance of these results to the acoustic properties of non-rigid porous media, and we show how the dynamic permeability/tortuosity can be measured using superfluid 4 He as the pore fluid. We derive the expected response in the case that the internal walls of the pore space are fractal in character.

Abstract A class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors. Previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices. In contrast, the methods presented here are based on the recently developed theory of wavelets and are applicable to all Calderon‐Zygmund and pseudo‐differential operators. The algorithms of this paper require order O ( N ) or O ( N log N ) operations to apply an N × N matrix to a vector (depending on the particular operator and the version of the algorithm being used), and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here.

The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible metals. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces, constraints, ambient media, and impenetrable obstacles. The models are fundamentally dynamic and realistic animation is created by numerically solving their underlying differential equations. Thus, the description of shape and the description of motion are unified.

A new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system. The model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces, but in principle it may be applied to any kind of invasion process which proceeds along a path at least resistance. The name invasion percolation is proposed for this new process. Similarities to, and differences from, ordinary percolation theory are discussed.

The failure detection and identification (FDI) process is viewed as consisting of two stages: residual generation and decision making. It is argued that a robust FDI system can be achieved by designing a robust residual generation process. Analytical redundancy, the basis for residual generation, is characterized in terms of a parity space. Using the concept of parity relations, residuals can be generated in a number of ways and the design of a robust residual generation process can be formulated as a minimax optimization problem. An example is included to illustrate this design methodology.

ABSTRACT A means of relating geochemical concentrations to existing sandstone classification schemes is based on three chemical parameters: the SiO2/Al2O3 ratio, the Fe2O3/K2O ratio, and the Ca content. In terrigenous sands and shales, the SiO2/Al2O3 ratio separates Si-rich quartzarenites from Al-rich shales, with other sand types showing intermediate values. The ratio of total iron (as Fe2O3) to K2O separates lithic sands (litharenites and sublitharenites) from feldspathic sands (arkoses and subarkoses). In addition, very high Fe2O3/K2O ratios indicate Fe-rich shales (e.g., pyritic, sideritic, hematitic) or Fe-rich sands (e.g., gl uconitic) depending on the silica/alumina ratio. The Ca content is used to differentiate noncalcareous from calcareous sandstones and shales and to separate siliciclastic from carbonate rocks. Sandstones are classified the same by this scheme as by petrographic analysis about 84% of the time, and shales are effectively discriminated from sandstones. The requisite input data can be accurately supplied by geochemical well-logging measurements, enabling unbiased sandstone classification to be displayed on a continuous basis with depth.

No abstract available.

A model for an imperfectly bonded interface between two elastic media is proposed. Displacement across this surface is not required to be continuous. The displacement discontinuity, or slip, is taken to be linearly related to the stress traction which is continuous across the interface. For isotropic interface behavior, there are two complex frequency dependent interface compliances, ηN and ηT, where the component of the slip normal to the interface is given by ηN times the normal stress and the component tangential to the interface is given by ηT times the shear stress and is in the same direction. Reflection and transmission coefficients for harmonic plane waves incident at arbitrary angles upon a plane linear slip interface are computed in terms of the interface compliances. These coefficients are frequency dependent even when the compliances are real and frequency independent. Examples of the effects of buried slip interfaces on reflection coefficient spectra and on Love-wave dispersion relations are presented.

Asphaltenes, the most aromatic of the heaviest components of crude oil, are critical to all aspects of petroleum use, including production, transportation, refining, upgrading, and heavy-end use in paving and coating materials. As such, efficiency in these diverse disciplines mandates proper chemical accounting of structure−function relations of crude oils and asphaltenes, the vision of petroleomics (Asphaltenes, Heavy Oils and Petroleomics; Mullins, O. C., Sheu, E. Y., Hammami, A., Marshall, A. G., Eds.; Springer: New York, 2007). Indeed, the molecular characterization of asphaltenes is required as well as the detailed understanding of the hierarchical colloidal structures of asphaltenes and petroleum. With great prescience, Professor Teh Fu Yen and co-workers proposed a hierarchical model of asphaltenes to account for many of their characteristics known at that time (Dickie, J. P.; Yen, T. F. Macrostrucutres of asphaltic fractions by various instrumental methods. Anal. Chem. 1967, 39, 1847−1852). This model is rightfully known as the Yen model. Nevertheless, at the time the Yen model was formulated, there were many order-of-magnitude uncertainties in asphaltene science that precluded establishing structure−function relations and causality, thereby rendering the Yen model somewhat phenomenological. Petroleum science has advanced greatly in recent years enabling development of a much more specific model yet still based on precepts of the Yen model; we call this the “modified Yen model”. The modified Yen model is shown to account for wide ranging, myriad properties of asphaltenes, including their dynamics. In addition, the modified Yen model has even proven successful for understanding interfacial phenomena involving asphaltenes. Moreover, the modified Yen model accounts for fundamental observations in oil reservoirs and is now propelling significantly improved efficiency in oil production. The modified Yen model is a simple, yet powerful construct that provides the foundation to test future developments in asphaltene and petroleum science; refinement of the modified Yen model is an expected outcome of this process.

The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible metals. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces, constraints, ambient media, and impenetrable obstacles. The models are fundamentally dynamic and realistic animation is created by numerically solving their underlying differential equations. Thus, the description of shape and the description of motion are unified.

Abstract We develop a theory for dielectric response of water-saturated rocks based on a realistic model of the pore space. The absence of a percolation threshold manifest in Archie’s law, porecasts, electron-micrographs, and general theories of formation of detrital sedimentary rocks indicates that the pore spaces within such rocks remain interconnected to very low values of the porosity ϕ. In the simplest geometric model for which the conducting paths remain interconnected, each grain is envisioned to be coated with water. The dielectric constant of the assembly of water-coated grains is obtained by a self-consistent effective medium theory. In the dc limit, this gives Maxwell's relation for conductivity σ of the rock σ = 2σωφ/(3 − φ), where σω is the conductivity of water. In order to include the local environmental effects around a grain, a self-similar model is generated by envisioning that each rock grain itself is coated with a skin made of other coated spheres; the coating at each level consists of other coated spheres. The self-consistent complex dielectric constant ɛ* is given in this model in terms of that of water ɛω* and of rock ɛm*, by [(ɛm*−ɛ*)/(ɛm*−ɛω*)][ɛω*/ɛ*]1/3=φ for spherical particles. This gives, in the dc limit, σ = σωφ3/2. For nonspherical particles, the exponent m in Archie's law σ = σωφm is greater than 3/2 for the plate-like grains or cylinders with axis perpendicular to the external field and smaller than 3/2 for plates or cylindrical particles with axis parallel to the external field. Artificial rocks with a wide range of porosities were made from glass beads. We present data on the glass bead rocks for dc conductivity and the dielectric constant at 1.1 GHz. The data follow the conductivity and the dielectric responses given by the self-similar model. The present theory fails to explain the salinity dependence of ɛ* at lower frequencies.

The Yen–Mullins model, also known as the modified Yen model, specifies the predominant molecular and colloidal structure of asphaltenes in crude oils and laboratory solvents and consists of the following: The most probable asphaltene molecular weight is ∼750 g/mol, with the island molecular architecture dominant. At sufficient concentration, asphaltene molecules form nanoaggregates with an aggregation number less than 10. At higher concentrations, nanoaggregates form clusters again with small aggregation numbers. The Yen–Mullins model is consistent with numerous molecular and colloidal studies employing a broad array of methodologies. Moreover, the Yen–Mullins model provides a foundation for the development of the first asphaltene equation of state for predicting asphaltene gradients in oil reservoirs, the Flory–Huggins–Zuo equation of state (FHZ EoS). In turn, the FHZ EoS has proven applicability in oil reservoirs containing condensates, black oils, and heavy oils. While the development of the Yen–Mullins model was founded on a very large number of studies, it nevertheless remains essential to validate consistency of this model with important new data streams in asphaltene science. In this paper, we review recent advances in asphaltene science that address all critical aspects of the Yen–Mullins model, especially molecular architecture and characteristics of asphaltene nanoaggregates and clusters. Important new studies are shown to be consistent with the Yen–Mullins model. Wide ranging studies with direct interrogation of the Yen–Mullins model include detailed molecular decomposition analyses, optical measurements coupled with molecular orbital calculations, nuclear magnetic resonance (NMR) spectroscopy, centrifugation, direct-current (DC) conductivity, interfacial studies, small-angle neutron scattering (SANS), and small-angle X-ray scattering (SAXS), as well as oilfield studies. In all cases, the Yen–Mullins model is proven to be at least consistent if not valid. In addition, several studies previously viewed as potentially inconsistent with the Yen–Mullins model are now largely resolved. Moreover, oilfield studies using the Yen–Mullins model in the FHZ EoS are greatly improving the understanding of many reservoir concerns, such as reservoir connectivity, heavy oil gradients, tar mat formation, and disequilibrium. The simple yet powerful advances codified in the Yen–Mullins model especially with the FHZ EoS provide a framework for future studies in asphaltene science, petroleum science, and reservoir studies.

Abstract A variety of non-equilibrium growth processes are characterized by phase boundaries consisting of moving fingers, often with interesting secondary structures such as sidebranches. Familiar examples are dendrites, as seen in snowflake growth, and fluid fingers often formed in immiscible displacement. Such processes are characterized by a morphological instability which renders planar or circular shapes unstable, and by the competing stabilizing effect of surface tension. We survey recent theoretical work which elucidates how such systems arrive at their observed patterns. Emphasis is placed upon dendritic solidification, simple local models thereof, and the Saffman-Taylor finger in two-dimensional fluid flow, and relate these systems to their more complicated variants. We review the arguments that a general procedure for the analysis of such problems is to first find finger solutions of the governing equations without surface tension, then to incorporate surface tension in a non-perturbative manner, and lastly to examine possible secondary instabilities and the effects of noise.

We incorporate information flow between a supplier and a retailer in a two-echelon model that captures the capacitated setting of a typical supply chain. We consider three situations: (1) a traditional model where there is no information to the supplier prior to a demand to him except for past data; (2) the supplier knows the (s, S) policy used by the retailer as well as the end-item demand distribution; and (3) the supplier has full information about the state of the retailer. Order up-to policies continue to be optimal for models with information flow for the finite horizon, the infinite horizon discounted and the infinite horizon average cost cases. Study of these three models enables us to understand the relationships between capacity, inventory, and information at the supplier level, as well as how they are affected by the retailer’s (S − s) values and end-item demand distribution. We estimate the savings at the supplier due to information flow and study when information is most beneficial.

Fluorescence depolarization measurements are used to determine the size of asphaltene molecules and of model compounds for comparison. Mean molecular weights of roughly 750 amu with a range of roughly 500−1000 amu are found for petroleum asphaltenes. A strong correlation is established between the size of an individual fused ring system in an asphaltene molecule and the overall size of this corresponding molecule, showing that asphaltene molecules have one or perhaps two fused ring systems per molecule. Subtle differences in molecular size are found for different virgin crude oil asphaltenes and for a vacuum resid asphaltene. Coal asphaltene molecules are found to be much smaller than petroleum asphaltenes. The molecular sizes of resins and asphaltenes are found to form a continuous distribution.

The authors discuss a single-crystal inorganic scintillator, cerium-doped lutetium oxyorthosilicate (Lu/sub 2(1-x)/Ce/sub 2x/(SiO/sub 4/) or LSO). It has a scintillation emission intensity which is approximately 75% of NaI(Tl) with a decay time of approximately 40 ns. The peak emission wavelength is 420 nm. It has a very high gamma-ray detection efficiency due to its density of 7.4 g/cm/sup 3/ and its effective atomic number of 66. Its radiation length of 1.14 cm is only slightly longer than bismuth germanate (BGO). The scintillation properties of Ce-doped LSO are compared to NaI(Tl), BGO, and cerium-doped gadolinium oxyorthosilicate (GSO). In addition to desirable physical properties such as high density and high atomic number, LSO also processes a combination of high emission intensity and fast decay which together are superior to any other known single crystal scintillator.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Scale-space filtering constructs hierarchic symbolic signal descriptions by transforming the signal into a continuum of versions of the original signal convolved with a kernal containing a scale or bandwidth parameter. It is shown that the Gaussian probability density function is the only kernel in a broad class for which first-order maxima and minima, respectively, increase and decrease when the bandwidth of the filter is increased. The consequences of this result are explored when the signal¿or its image by a linear differential operator¿is analyzed in terms of zero-crossing contours of the transform in scale-space.

Inverse problems, such as the reconstruction problems that arise in early vision, tend to be mathematically ill-posed. Through regularization, they may be reformulated as well-posed variational principles whose solutions are computable. Standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions. Discontinuities present serious difficulties to standard regularization, however, since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers. This paper proposes a general class of controlled-continuity stabilizers which provide the necessary control over smoothness. These nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with (noncontinuous) continuity control functions. In the context of computational vision, they may be thought of as controlled-continuity constraints. These generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities, for which global smoothness constraints fail.

A reconstruction algorithm is derived for parallel beam transmission computed tomography through two-dimensional structures in which diffraction of the insonifying beam must be taken into account. The algorithm is found to be completely analogous to the filtered backprojection algorithm of conventional transmission tomography with the exception that the backprojection operation has to be replaced by a back propagation process whereby the complex phase of a field measured over a line outside the object is made to propagate back through the object space. The algorithm is applicable to diffraction tomography within either the first Born or Rytov approximations. Application of the algorithm to three-dimensional structures is also discussed.

Spacetime constraints are a new method for creating character animation. The animator specifies what the character has to do, for instance, "jump from here to there, clearing a hurdle in between;" how the motion should be performed, for instance "don't waste energy," or "come down hard enough to splatter whatever you land on;" the character's physical structure ---the geometry, mass, connectivity, etc. of the parts; and the physical resources' available to the character to accomplish the motion, for instance the character's muscles, a floor to push off from, etc. The requirements contained in this description, together with Newton's laws, comprise a problem of constrained optimization. The solution to this problem is a physically valid motion satisfying the "what" constraints and optimizing the "how" criteria. We present as examples a Luxo lamp performing a variety of coordinated motions. These realistic motions conform to such principles of traditional animation as anticipation, squash-and-stretch, follow-through, and timing.