Schlumberger (France)

Immiscible displacements in porous media with both capillary and viscous effects can be characterized by two dimensionless numbers, the capillary number C , which is the ratio of viscous forces to capillary forces, and the ratio M of the two viscosities. For certain values of these numbers, either viscous or capillary forces dominate and displacement takes one of the basic forms: (a) viscous fingering, (b) capillary fingering or (c) stable displacement. We present a study in the simple case of injection of a non-wetting fluid into a two-dimensional porous medium made of interconnected capillaries. The first part of this paper presents the results of network simulators (100 × 100 and 25 × 25 pores) based on the physical rules of the displacement at the pore scale. The second part describes a series of experiments performed in transparent etched networks. Both the computer simulations and the experiments cover a range of several decades in C and M . They clearly show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged. The domains of validity of the three different basic mechanisms are mapped onto the plane with axes C and M , and this mapping represents the ‘phase-diagram’ for drainage. In the final section we present three statistical models (percolation, diffusion-limited aggregation (DLA) and anti-DLA) which can be used for describing the three ‘basic’ domains of the phase-diagram.

The results of magnetoconductivity measurements in ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells are presented. The observed magnetoconductivity appears due to the quantum interference, which lead to the weak localization effect. It is established that the details of the weak localization are controlled by the spin splitting of electron spectra. A theory is developed that takes into account both linear and cubic in electron wave-vector terms in spin splitting, which arise due to the lack of inversion center in the crystal, as well as the linear terms that appear when the well itself is asymmetric. It is established that, unlike spin-relaxation rate, contributions of different terms into magnetoconductivity are not additive. It is demonstrated that in the interval of electron densities under investigation [(0.98-1.85)\ifmmode\times\else\texttimes\fi{}${10}^{12}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ ] all three contributions are comparable and have to be taken into account to achieve a good agreement between the theory and experiment. The results obtained from comparison of the experiment and the theory have allowed us to determine what mechanisms dominate the spin-relaxation in quantum wells and to improve the accuracy of determination of spin-splitting parameters in ${\mathit{A}}_{3}$${\mathit{B}}_{5}$ crystals and two-dimensional structures. \textcopyright{} 1996 The American Physical Society.

We show that fractal viscous fingers can be formed in a Hele-Shaw cell with radial symmetry, thereby permitting their study---for the first time---without the complicating effects of boundary conditions such as those present in the conventional linear cell. We find---for a wide range of shear-thinning fluids, flow rates, and plate separations---that radial viscous fingers have a fractal dimension ${\mathrm{d}}_{\mathrm{f}}$=1.70\ifmmode\pm\else\textpm\fi{}0.05, the same as diffusion-limited aggregation. We also quantitatively measure the set of growth sites and compare with diffusion-limited aggregation.

Chemical dissolution of a two-dimensional porous medium by a reactive fluid which produces fractal patterns is studied. A new model is proposed that introduces a cumulative erosion process which broadens the branches of the cluster and gives structures very similar to the experimental ones. Diffusion-limited aggregation is a limiting case of this model. An interpretation of the evolution of the injection pressure with time which yields the fractal dimension is also presented, and agrees with the experimental results.

Abstract Three-dimensional finite-element modeling was performed to investigate the response to fractures of the Formation MicroScanner (Mark of Schlumberger), which records high-resolution electrical scans of the borehole wall. It is found that the equationEquationdescribes, over two orders of magnitude of resistivity contrasts between borehole mud and the formation, the relationship between fracture width W (in mm), formation resistivity R x0 , mud resistivity R m , and the additional current flow A caused by the presence of the fracture. A is the additional current which can be injected into the formation divided by the voltage, integrated along a line perpendicular across the fracture trace. Coefficient c and exponent b are obtained numerically from forward modeling. Tool standoffs of up to 2.5 mm and fracture dips in the range from 0 degrees to 40 degrees were found to have an insignificant effect on the above relation.A three-step approach to detect, trace, and quantify fractures is used. Potential fractures in Formation MicroScanner images are detected as locations where conductivity exceeds the local matrix conductivity by a statistically significant amount. Integration over a circular area is performed around these locations to gather all excessive currents; this integral is then geometrically reduced to approximate the line integral A. Line sharpening and neighborhood connectivity tests are done to trace the fractures, and apertures are computed for all fracture locations.Results from a well into basement in Moodus (Connecticut) show that the method successfully traces fractures seen on Formation MicroScanner images. The resulting fracture apertures range from 10 mu m to 1 mm. For the wider fractures there is acceptable agreement with apertures obtained from Stoneley wave reflection measurements. This unique and novel technique for characterizing fractures in wellbores has a very low detection threshold of around 10 mu m and resolves fractures as little as 1 cm apart. Furthermore, it provides azimuthal orientation of the fractures.

A 2L-dimensional multiple phase-shift keyed (L*MPSK) signal set is obtained by forming the Cartesian product of L two-dimensional MPSK signal sets. A systematic approach to partitioning L*MPSK signal sets that is based on block coding is used. An encoder system approach is developed. It incorporates the design of a differential precoder, a systematic convolutional encoder, and a signal set mapper. Trellis-coded L*4PSK, L*8PSK, and L*16PSK modulation schemes are found for 1<or=L<or=4 and a variety of code rates and decoder complexities, many of which are fully transparent to discrete phase rotations of the signal set. The new codes achieve asymptotic coding gains up to 5.85 dB.<<ETX>>

Nearly 70 years old, hydraulic fracturing is a core technique for stimulating hydrocarbon production in a majority of oil and gas reservoirs. Complex fluids are implemented in nearly every step of the fracturing process, most significantly to generate and sustain fractures and transport and distribute proppant particles during and following fluid injection. An extremely wide range of complex fluids are used: naturally occurring polysaccharide and synthetic polymer solutions, aqueous physical and chemical gels, organic gels, micellar surfactant solutions, emulsions, and foams. These fluids are loaded over a wide range of concentrations with particles of varying sizes and aspect ratios and are subjected to extreme mechanical and environmental conditions. We describe the settings of hydraulic fracturing (framed by geology), fracturing mechanics and physics, and the critical role that non-Newtonian fluid dynamics and complex fluids play in the hydraulic fracturing process.

The propagation of acoustic waves in waveguides with variable cross section is considered using multimodal decomposition. The approach adopted is to construct two infinite first-order differential equations for the components of the pressure and the velocity projected over the normal modes. From these an infinite matricial Riccati equation is derived for the impedance matrix. These equations are ordinary differential equations that can be integrated after truncation at a sufficient number of modes and take into account the coupling between modes. The stiffness of the pressure-velocity equations induced by the presence of evanescent modes is avoided by first calculating the impedance matrix along the guide. The method is checked using different examples where the solutions of the plane-wave approximation or the finite element method are known. Results show the method provides simple and accurate means to obtain the acoustic field with correct boundary conditions in a nonuniform guide with no restriction on the flare.

Storing carbon dioxide (CO2) underground is considered the most effective way for long-term safe and low-cost CO2 sequestration. This recent application requires long-term wellbore integrity. A CO2 leakage through the annulus may occur much more rapidly than geologic leakage through the formation rock, leading to economic loss, reduction of CO2 storage efficiency, and potential compromise of the field for storage. The possibility of such leaks raises considerable concern about the long-term wellbore isolation and the durability of hydrated cement that is used to isolate the annulus across the producing/injection intervals in CO2-storage wells. We propose a new experimental procedure and methodology to study reactivity of CO2-Water-Cement systems in simulating the interaction of the set cement with injected supercritical CO2 under downhole conditions. The conditions of experiments are 90°C under 280 bars. The evolution of mechanical, physical and chemical properties of Portland cement with time is studied up to 6 months. The results are compared to equivalent studies on a new CO2-resistant material; the comparison shows significant promise for this new material.

Smart structural health monitoring (SHM) for large-scale infrastructure is an intriguing subject for engineering communities thanks to its significant advantages such as timely damage detection, optimal maintenance strategy, and reduced resource requirement. Yet, it is a challenging topic as it requires handling a large amount of collected sensors data continuously, which is inevitably contaminated by random noises. Therefore, this study developed a practical end-to-end framework that makes use of physical features embedded in raw data and an elaborated hybrid deep learning model, namely 1-DCNN-LSTM, featuring two algorithms—convolutional neural network (CNN) and long-short term memory (LSTM). In order to extract relevant features from sensory data, the method combines various signal processing techniques such as the autoregressive model, discrete wavelet transform, and empirical mode decomposition. The hybrid deep learning 1-DCNN-LSTM is designed based on the CNN’s capacity of capturing local information and the LSTM network’s prominent ability to learn long-term dependencies. Through three case studies involving both experimental and synthetic data sets, it is demonstrated that the proposed approach achieves highly accurate damage detection, as accurate as the powerful 2-D CNN, but with a lower time and memory complexity, making it suitable for real-time SHM. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article aims to develop a practical data-driven method for automatically monitoring the operational state of structures. In order to achieve consistently and highly accurate results in performing different tasks for diverse structures, we combine underlying features in both time and frequency domains extracted from measured signal vibration data. Three popular data featuring methods are combined to achieve the diversity gain which would not be possible with each individual method. As the vibration is usually measured by long time-series signals, the most efficient deep learning architecture for time-series signal, namely long-short term memory (LSTM), is considered for this work. Besides, each structure has its own dynamic properties, i.e., eigenfrequencies, around which the most relevant information is in the frequency domain, thus convolutional neural network specifically designed for capturing local information is used in combination with LSTM, forming a hybrid deep learning architecture. The applicability and effectiveness of the proposed approach are supported by three case studies with different types of structures, showing highly accurate damage detection with reduced resource requirements. These advantages can be valuable for developing a model for live monitoring of structural health in the future life-line infrastructures.

We show that---over a range of length scales r---the shapes of quasi-two-dimensional retinal neurons are fractal objects, and hence may be quantitatively characterized in part by their fractal dimension ${\mathrm{d}}_{\mathrm{f}}$. We analyze the shapes of numerous retinal neurons, both in vivo and in vitro. The neurons in vivo are found to have a fractal dimension ${\mathrm{d}}_{\mathrm{f}}$ of 1.68\ifmmode\pm\else\textpm\fi{}0.15. We also propose an explanation of certain stages of neuronal shape development in terms of a diffusion-limited-aggregation model, which predicts ${\mathrm{d}}_{\mathrm{f}}$=1.70\ifmmode\pm\else\textpm\fi{}0.1.

Fluid-displacement experiments in Hele-Shaw cells filled with a viscoelastic fluid show a novel transition between a viscous fingering (VF) regime producing fractal patterns of ``fingers'' and a viscoelastic facturing (VEF) regime producing fractal patterns of ``cracks.'' VEF patterns are characterized by branching angles of 90\ifmmode^\circ\else\textdegree\fi{} with respect to the main crack, behind the tip, and by a lower fractal dimension than VF. The transition is controlled by several parameters, including the Deborah number and the system deformability.

The natural vibrational modes of axially symmetric piezoelectric ceramic disks have been calculated by the finite-element method. The disks are of the type used as active elements in compressional wave ultrasonic transducers, and are electrically polarized in thickness with full electrodes on the disk's major faces. To optimize disk geometry for ultrasonic transducer application, the dependence of the vibrational modes on the disk diameter-to-thickness ratio for ratios from 0.2 (a tall cylinder) to 10.0 (a thin disk) has been studied. Series and parallel resonance frequencies for each of the modes are determined through an eigenfrequency analysis, and effective electromechanical coupling coefficients are calculated. The modal displacement fields in the disk are calculated to determine the physical nature of each mode. An analysis of the complete spectrum of piezoelectrically active modes as a function of diameter-thickness ratio is presented for the ceramic PZT-5H, including and identification of radial, edge, length expander, thickness shear, and thickness extensional vibrations. From this analysis, optimal diameter-to-thickness ratios for good transducer performance are discussed.

In a plane-channel displacement flow of two visco-plastic fluids, it is possible for there to be a static residual layer of the displaced fluid left stuck to the walls of the channel. This phenomenon provides an idealized model for the formation of a wet micro-annulus , due to poor mud removal, during the primary cementing of an oil well. Using a lubrication approximation, it is shown that sufficient conditions for the non-existence of a static wall layer can be computed simply in terms of two dimensionless parameters: the Bingham number for the displacing fluid ( B 1 ) and the ratio of the yield stresses of the two fluids (ϕ Y ). When these conditions are not met, it is possible to compute the maximum possible static wall layer thickness h max , which depends on B 1 , ϕ Y and on a third dimensionless parameter ϕ B , a buoyancy to yield stress ratio. On computing displacements using the lubrication approximation, the interface is observed to asymptotically approach the maximum static layer thickness as t → ∞. Results from fully two-dimensional displacement computations are also presented. These indicate that the displacement front propagates at a steady speed along the channel, leaving behind a static layer which is significantly thinner than h max . Surprisingly, the computed static layer thickness is observed to decrease with a parametric increase in the dimensionless yield stress of the displaced fluid. To explain these results we analyse the streamline configuration close to a steadily advancing displacement front. We demonstrate heuristically that the local visco-plastic dissipation functional will be approximately minimized by a critical layer thickness at which the displaced fluid begins to recirculate ahead of the displacement front. Comparison of the critical recirculation limit with the static layer thickness computed from the fully transient model gives a very close agreement, suggesting that a form of energy minimization is responsible in this case for selecting the static layer thickness.

Abstract By using experiments on micromodels and computer simulations, we have demonstrated the existence of three types of basic displacements when a non-wetting fluid invades a two-dimensional porous medium: capillary fingering when capillary forces are very strong compared to viscous forces, viscous fingering when a less viscous fluid is displacing a more viscous one, and stable displacement in the opposite case. These displacements are described by statistical models: invasion percolation, diffusion-limited aggregation (DLA) and anti-DLA. The domains of validity of the basic displacements are mapped onto the plane with axes Ca (capillary number) and M (viscosity ratio). The boundaries of these domains are calculated either by using theoretical laws describing transport properties of fractal patterns or by the interpretation of physical mechanisms at the pore scale. In addition, the prefactors that are not available from scaling theories are obtained by computer simulations on a network of capillaries, in which the flow equations are solved at each node.

Schlumberger RPS (Retail Petroleum Systems) integrated the Goal/Question/Metric approach into their existing measurement programs to improve their program performance. Key to their success was the use of feedback sessions as a forum to analyze and interpret measurement data. The paper discusses the elements of the GQM approach and fitting GQM to a measurement program.

Numerical simulations of wake flow behind an equilateral triangular obstacle are presented. The form of global modes and their dependence on the Reynolds number found in this study are in accordance with recent experimental results of Goujon–Durand et al. [Phys. Rev. E 50, 308 (1994)]. A scaling law of the amplitude oscillating with the fundamental frequency corresponding to the maximum of the global mode is found to agree with the Landau model in a range of Reynolds Re numbers larger than in previous studies. The position of the maximum amplitude of the fundamental modes scales as (Re−Rec)−1/2. The amplitude of the second harmonic of the longitudinal component of the velocity as well as the correction to the mean flow have different critical behavior than the velocity components oscillating with fundamental frequency. During linear growth the position of the maximum of the global modes is constant and moves only in the nonlinear regime. The effects of the blockage and the boundary conditions on the side walls on the form of the global modes are discussed.

Following the great success of traditional microfluidic devices across many disciplines, a new class of microfluidic systems emerged in recent years, which features finely tuned, localized surface modifications within the microstructures in order to keep up with the demand for devices of ever increasing complexity (lab on chip, assay on chip, etc.). Graft photopolymerization has become a powerful tool for such localized surface modifications particularly in combination with poly(dimethylsiloxane) (PDMS) devices, as it is compatible with many functional monomers and allows for high spatial resolution. However, application within enclosed PDMS microstructures and in particular well-controlled surface-directed polymerization remains challenging. Detailed understanding of the interaction between photoinitiator, benzophenone (BP), and polymer matrix is needed. We have developed a visualization technique, which allows for observation of reacted BP in situ within the PDMS matrix. We present a detailed study on solvent-driven BP diffusion providing results essential to successful surface treatment. We also identified and investigated photoinitiator inhibition by oxygen and provide appropriate mitigation strategies.

DOI: 10.2514/1.50270Aggressive motions are often discouraged when a system has flexible dynamics. Common practice suggests thatsmooth commands, such as S-curves, should be used to drive the system. However, smooth commands cannot beimplementedonsomeactuators,suchastheon/offthrustersusedonspacecraftoron/offvalvesusedwithhydraulicsand pneumatics. Furthermore, smooth commands can lead to sluggish response. A rigorous comparison of smoothand nonsmooth reference commands is presented in this paper. The evaluation is performed by treating smoothcommandprofilesasinput-shapedfunctions.Inputshapingisamethodofreducingresidualvibrationbyconvolvinga sequence of impulses with a baseline reference command. By interpreting smooth commands as input-shapedfunctions, a common criterion for comparing smooth and nonsmooth commands is developed. The results of thiscomprehensive comparison indicate that input-shaped step functions are usually more efficient for reducingvibration than commonly used smooth commands. A portable tower crane is used to experimentally verify thecomparison between input-shaped and smooth commands.

Many microfluidic applications require modified surface wettability of the microchannels. Patterning of wettability within enclosed microfluidic structures at high spatial resolution has been challenging in the past. In this paper, we report an improved method for altering the surface wettability in poly(dimethylsiloxane) (PDMS) microchannels by UV-induced graft polymerization of poly(acrylic acid). Our method presents significant improvements in terms of wettability contrast and spatial resolution of the patterned structures as compared to recent literature and is in particular applicable to complex microfluidic structures with a broad range of channel sizes and aspect ratios. A key part of our work is the clear description of the surface treatment process with the identification of key parameters, some of which have been overlooked, neglected, or misinterpreted in previous works. We have studied these key parameters in detail and provide recommended values for each parameter supported by experimental results. This detailed understanding of the treatment process and the effects of the critical parameters on it allowed us to significantly improve quality and reliability of the treatment process.