Ideal Packing Research Articles

Neutron diffraction of chlorine substituted fluorapatite

Fluorapatite, chlorapatite and a mixed apatite synthesised by a high temperature solid state reaction route were analysed using time-of-flight neutron diffraction of the series Ca 5(PO 4) 3F 1 − x Cl x , where x = 0.0, 0.5 and 1.0. Fluorapatite and the mixed apatite were found to be hexagonal in crystal structure. The chlorapatite was monoclinic in structure. The lattice parameters a and b increased with chlorine addition while c decreased. The unit cell volume increased linearly with chlorine content and the density decreased. The Ca(1)O 6 metaprism twist angle ( φ) decreased with chlorine addition indicating a tendency towards ideal hcp packing.

On contact numbers in random rod packings

Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well with experiments on granular packings. Contact numbers are also compared to caging numbers calculated for sphero-cylinders with arbitrary aspect-ratio. The caging number for rods arrested by uncorrelated point contacts asymptotes towards $${\langle \gamma \rangle = 9}$$ at high aspect ratio, strikingly close to the experimental contact number $${\langle C \rangle \approx 9.8}$$ for thin rods. These and other findings confirm that thin-rod packings are dominated by local arrest in the form of truly random neighbor cages. The ideal packing law derived for random rod–rod contacts, supplemented with a calculation for the average contact number, explains both absolute value and aspect-ratio dependence of the packing density of randomly oriented thin rods.

Rheological property of low-damage, ideal packing, film-forming amphoteric/sulfonation polymer drilling fluids

Low-permeability dense reservoirs, including micro-fractured reservoirs, are commonly characterized by high content of clay substances, high original water saturation, high sensitivity to invasive fluids, high capillary pressure, complicated structure and anisotropic, high flow-resistance and micro pore throats etc,. Generally they also have lots of natural micro fractures, probably leading to stress sensibility. Main damaging factors in such reservoirs are water-sensibility and water-blocking caused by invasive fluids during drilling and production operations. Once damaged, formation permeability can rarely recovered. Numerous studies have shown that damaging extent of water-blocking ranges from 70% to 90%. Main damaging mechanisms and influencing factors of water-blocking were systematically analyzed. Also some feasible precaution or treating approaches of water-blocking were put forward. In a laboratory setting, a new multi-functional drilling fluid composed mainly of amphion polymer, sulfonation polymer, high effectively preventive water-blocking surfactants, ideal packing temporary bridging agents (TBA) and film-forming agents, etc., were developed. New low-damage drilling fluids has many advantages, such as good rheological properties, excellent effectiveness of water-blocking prevention, good temporary plugging effect, low filtration and ultra-low permeability (API filtration⩽5 mL, HTHP filtration⩽10 mL, mud cake frictional coefficient⩽0.14, permeability recovery>81%), can efficiently prevent or minimize damage, preserve natural formation and enhance comprehensive development-investment effect in TUHA Jurassic dense sandstone reservoir formation with low-permeability, the only one developing integrated condense gas field. Some references can be provided to similar reservoir formations.

Unjamming due to local perturbations in granular packings with and without gravity

We investigate the unjamming response of disordered packings of frictional hard disks with the help of computer simulations. First, we generate jammed configurations of the disks and then force them to move again by local perturbations. We study the spatial distribution of the stress and displacement response and find long range effects of the perturbation in both cases. We record the penetration depth of the displacements and the critical force that is needed to make the system yield. These quantities are tested in two types of systems: in ideal homogeneous packings in zero gravity and in packings settled under gravity. The penetration depth and the critical force are sensitive to the interparticle friction coefficient. Qualitatively, the same nonmonotonic friction dependence is found both with and without gravity, however the location of the extrema are at different friction values. We discuss the role of the connectivity of the contact network and of the pressure gradient in the unjamming response.

Multiple Minima on the Energy Landscape of Elemental Zinc: A Wave Function BasedAb InitioStudy

Zinc crystallizes in the hcp structure, but with an anomalously large c/a ratio, indicating a strong distortion away from ideal packing. Coupled cluster calculations within the framework of the method of increments, improved by an embedding scheme for metals, were performed to explore the potential energy surface of zinc with respect to the hexagonal lattice parameters. The inclusion of the filled d shell in the correlation treatment proved to be essential. From the exceptional shape of the potential energy surface the existence of a zinc modification with a nearly ideal c/a ratio can be deduced.

Laboratory study of ideal packing approach applied to high permeability sandstones

Abstract It is difficult for conventional temporary bridging methods to seal large pore throats, which usually make the dominant contribution to permeability. The reason is that the particle size of conventional bridging agents is optimized depending on the median pore size of target formation. High-permeability sandstone reservoirs have such features as wide permeability distribution range, high porosity, argillaceous cement, and wide distribution range of pore throat sizes. The key factors of reservoir damage are invaded particles and filtrate of drilling fluids, as well as the hydrate expansion and dispersion of clay. The KPAM polymer drilling fluids are optimized, and ideal packing approach is applied to the drilling fluids, and the instrument of dynamic fluid loss test is used to evaluate return permeability. The test results indicate that the ideal packing approach can reduce the dynamic fluid loss, improve the return permeability, and reduce breakthrough pressure.

Strength, porosity, and permeability development during hydrostatic and shear loading of synthetic quartz‐clay fault gouge

The strength and permeability of fault zones must be quantified in order to accurately predict crustal strength and subsurface fluid migration. To this end, we performed experiments on mixtures of fine‐grained quartz and kaolinite incremented at 10 wt% intervals between the two end‐member components (analogues for natural fault gouge) in order to establish their strength and fluid flow properties during hydrostatic and shear loading. Hydrostatically compacted samples exhibited permeability reduction on increasing effective pressures from 5 MPa to 50 MPa, with the rate of reduction displaying strong dependency on the synthetic fault gouge composition. The permeability decreases continuously with increasing kaolinite content. Porosity exhibits a distinct minimum that evolves with increasing effective pressure according to the relative compaction of the quartz and kaolinite end‐members. Porosity evolution with increasing clay content is predicted satisfactorily by a simple ideal packing model. At the highest effective pressure (50 MPa), permeability reduced log‐linearly over 4 orders of magnitude with increasing clay content. Mechanically, sheared gouge samples showed a continuous reduction in frictional strength with increasing clay fraction. Permeability decreased further on shear loading after initial hydrostatic compaction to 50 MPa. This was most evident for the pure quartz end‐member, with two orders of magnitude additional reduction, whereas the clay‐rich samples were reduced only tenfold, mostly before a shear strain of 5. Variation of permeability with both clay content and shear deformation may be adequately described by previously published empirical predictors for fault zone permeability. Clay content has the largest effect on permeability, and shear deformation affects permeability of quartz‐rich gouges more than clay‐rich gouges.

A new laboratory method for evaluating formation damage in fractured carbonate reservoirs

Natural carbonate core samples with artificial fractures are often used to evaluate the damage of fractured carbonate formations in the laboratory. It is shown that the most frequent error for evaluation results directly from the random width characterized by the artificial fractures. To solve this problem, a series of simulated fractured core samples made of stainless steel with a given width of fracture were prepared. The relative error for the width of artificial fracture decreased to 1%. The width of natural and artificial fractures in carbonate reservoirs can be estimated by image log data. A series of tests for formation damage were conducted by using the stainless steel simulated core samples flushed with different drilling fluids, such as the sulfonate/polymer drill-in fluid and the solids-free drill-in fluid with or without ideal packing bridging materials. Based on the experimental results using this kind of simulated cores, a novel approach to the damage control of fractured carbonate reservoirs was presented. The effective temporary plugging ring on the end face of the simulated core sample can be observed clearly. The experimental results also show that the stainless steel simulated cores made it possible to visualize the solids and filtrate invasion.

Designing drill-in fluids by using ideal packing technique

Selecting bridging agents properly is a critical factor in designing non-damaging or low-damaging drill-in fluids. Historically, Abrams’ rule has been used for this purpose. However, Abrams’ rule only addresses the size of particle required to initiate a bridge. The rule does not give an optimum size nor an ideal packing sequence for minimizing fluid invasion and optimizing sealing. This paper elaborates an ideal packing approach to solving the sealing problem by sealing pores with different sizes, especially those large pores which usually make dominant contribution to permeability and thereby effectively preventing the solids and filtrate of drill-in fluids from invading into formations, compared with the conventionally used techniques. Practical software has been developed to optimize the blending proportion of several bridging agents, so as to achieve ideal packing effectiveness. The method and its use in selecting the best blending proportion of several bridging agents are also discussed in this paper. A carefully designed drill-in fluid by using the ideal packing technique (named the IPT fluid) for offshore drilling operations at the Weizhou Oilfield, Nanhai West Company, CNOOC is presented. The near 100% return permeabilities from the dynamic damage tests using reservoir cores demonstrated the excellent bridging effect provided by this drill-in fluid.

Structural and electronic properties of Mg, Zn, and Cd from Hartree-Fock and density functional calculations including hybrid functionals

The crystal structures of Zn and Cd deviate from an ideal hexagonal close packing by a significantly increased $c∕a$ ratio. In order to investigate the electronic reason for this deviation, especially with regard to the nearly ideal hcp element Mg, Hartree-Fock and density functional theory calculations were performed, employing various functionals within the local density or the generalized gradient approximations as well as hybrid functionals. The cohesive energy, lattice constants optimized with respect to the energy and elastic constants were computed. The role of electronic correlation in consideration of the filled $d$-shell is emphasized, postulating different intra- and inter-layer interactions, both in Zn and Cd. On the potential energy surface in the space of varying lattice constants, a path is explored that corresponds to a uniaxial compression along the $c$ axis. In contrast to Mg, the potential energy surface of Zn and Cd is very flat along this path, and an electronic topological transition occurs, leading to a Mg-like band structure.

Cross-Linked Hydrogels for Middle Ear Packing

To develop an ideal supportive packing material for ossiculoplasty, tympanoplasty, or other otologic procedures. Several materials, namely, Carbylan-SX (P-C; Sentrx Surgical, Inc., Salt Lake City, UT), Gelfoam (P-GF; Pharmacia & Upjohn, Kalamazoo, MI), and Merogel (P-MG; Medtronics, Inc., Minneapolis, MN), were prepared and then placed into a Hartley guinea pig's (Elm Hill, Chelmsford, MA) middle ear cavities through a large myringotomy incision. The contralateral ear underwent a large myringotomy without packing material being placed. Preoperative and posteroperative auditory brainstem response studies were performed using Intelligent Hearing system software. The animals were examined weekly. Two weeks after packing placement, the animals were killed, and the temporal bones were harvested. Whole temporal bone sectioning was performed to analyze the presence of implant, surrounding inflammation, presence of osteoneogenesis and fibrosis, or adhesions. All the materials, except the P-MG, were easy to place into the middle ear cavity. The P-MG contains woven strands that are difficult to trim into the small sizes needed for placement. The P-MG group had a smaller average amount of implant present compared with the other groups at 2 weeks. The degree of osteoneogenesis was similar among the P-GF, P-C, and P-MG groups. The P-MG and P-C groups contained the lowest amount of fibrosis between the implant and surrounding middle ear structures. This study demonstrates promising results with P-C as a potential supportive packing material for otologic procedures. P-C compares favorably with P-MG and P-GF in a guinea pig model with respect to ease of placement and amount of fibrosis.

Application of biological activated carbon as a low pH biofilter medium for gas mixture treatment

Packing material is a crucial component of a bioreactor as it is the microbial population's habitat. This study assessed potential improvements to current biofiltration processes by investigating use of a novel support medium. Biological activated carbon (BAC) with microorganisms growing on granular activated carbon can produce a novel medium in which both adsorption and biodegradation contribute to pollutants removal. Investigation of carbon characteristics demonstrated that BAC was an ideal packing medium for biofiltration. The application of the novel packing medium for gas mixture treatment was evaluated in a low pH biofilter. Results demonstrated that BAC biofilter obtained high removal efficiency for both H(2)S and toluene. The removal mechanisms of BAC were investigated after the biofilter operation and it demonstrated that the performance of the BAC system was mainly controlled by the additive contributions of two removal mechanisms - adsorption and biodegradation. This study also indicated the potential for simultaneous treatment of hydrogen sulfide and toluene at low pH condition.

Information transfer in disordered media by broadband time-reversal: stability, resolution and capacity

We analyse rigorously the time reversal of a multiple-input-multiple-output system in a strongly fluctuating disordered medium described by the stochastic Schrödinger equation with a random potential under the sub-Gaussian assumption. We prove that in a broadband limit the conditions for stable super-resolution are the packing condition such that the spacing among the N transmitters and M receivers be more than the coherence length ℓc and the consecutive symbols in the datum streams are separated by more than the inverse of the bandwidth B−1 and the multiplexing (or stability) condition such that the number of the degrees of freedom per unit time at the transmitters (∼NB) be much larger than the number of the degrees of freedom (∼MC) per unit time in the ensemble of intended messages. Here C is the number of symbols per unit time in the datum streams intended for each receiver. When the two conditions are met, all receivers simultaneously receive streams of statistically stable, sharply focused signals intended for them, free of fading and interference. We show that an O(P/ν) information rate P/ν can be achieved with statistical stability under the condition N ≫ M ≫ P/(ν B) where P is the average total power constraint and ν the noise power per unit bandwidth. The packing condition then implies that in the optimal transfer regime where γ is the Fresnel number, βc the coherence bandwidth and d the transverse dimension. Our results should be valid for diffusive waves with βc = Thouless frequency. Therefore, under the ideal packing and multiplexing conditions time reversal communications result in a high signal-to-interference ratio and low probability of intercept and is an effective means for achieving the information capacity of disordered media in the presence of multiple users.

High-pressure x-ray and neutron powder diffraction study ofPbWO4 and BaWO4 scheelites

The room-temperature high-pressure behaviour ofPbWO4 andBaWO4 scheelites(I41/a,Z = 4) has been studied with synchrotron angle-dispersive x-ray powder diffractionin a diamond anvil cell and time-of-flight neutron powder diffraction in alarge-volume Paris–Edinburgh cell. Full profile Rietveld refinements of theneutron data provide evidence for distinct compressibility mechanisms in thesematerials. The distortion in the anionic array from the ideal fluorite packing inBaWO4 increases upon compression while it decreases inPbWO4.

On the mechanism of the P2–Na 0.70CoO 2→O2–LiCoO 2 exchange reaction—Part II: an in situ X-ray diffraction study

A model was proposed to describe the exchange reaction of sodium by lithium in P2 crystals, it was based first on the formation of nucleation centers and then on the growth of O2 domains in P2 crystals from these nucleation centers. This study has shown that depending on the ratio between the growing and nucleation speeds, O2, O6 or faulted structures are obtained and that this model allows a good analysis of the exchange process. XRD patterns simulation and their comparison with that of experimental O2–LiCoO 2 have shown that there was almost no defects in the O2–LiCoO 2 structure obtained by ion exchange in water. Therefore, this study has shown that the growth of the O2 domains in the P2–Na 0.7CoO 2 crystals is faster than the formation of nucleation centers. This P2–Na 0.7CoO 2→O2–LiCoO 2 exchange reaction was also studied in situ by X-ray diffraction; simulations of key XRD patterns by P2–O2 intergrowths were also achieved. It was shown, in good agreement with the simulations, that the growth of O2 domains was faster than the formation of the nucleation centers and kinetically activated by a P2–Na 0.70CoO 2→P2 *–Na ∼0.50CoO 2 phase transition. For those reasons, the P2–Na 0.70CoO 2→O2–LiCoO 2 exchange reaction in water leads to an O2 phase, with an almost ideal packing.

P-Decylphenyl isocyanide and p-decylbenzonitrile: isomorphous isonitrile/nitrile isomers.

p-Decylphenyl isocyanide, p-C(10)H(21)-C(6)H(4)-NC or C(17)H(25)N, and p-decylbenzonitrile, p-C(10)H(21)-C(6)H(4)-CN or C(17)H(25)N, are isomorphous. The molecules lie in mirror planes, with the C(6) rings perpendicular to the mirror. The packing of both molecules includes an aliphatic region, with close to ideal packing of the C(10)H(21) chains, and an aromatic region, with phenyl ring-CN interactions. In addition, the CN ends of the molecules are also involved in a CN.NC dipolar interaction.

Quantification of the deviations from closest sphere packings

In order to quantify the deviation of the anion arrangement in a crystal structure from a closest sphere packing two parameters are introduced: Δ d rel is the relative difference between the longest and the shortest distance to neighbouring atoms within a distorted closest-packed arrangement and s is the standard deviation of the normalized distances to all neighbouring atoms. The applicability of these parameters is compared with that of the distortion parameter U cp introduced by Thompson & Downs (2001). Deviations from ideal sphere packings in pyroxenes, staurolite, kyanite, and olivine- and spinel-type structures are considered.

Geomechanical Models for Clastic Grain Packing

This study proposes a classification of sphere models for grain packing types of coarse grained clastic soft and hard rocks with special emphasis on Permocarboniferous red-beds. The classification covers the range of principal packing types and different cements. Random sphere packing models are derived from ideal symmetric packing models. The study comprises both homogeneous models with equal single grain properties and heterogeneous models with different single grain properties. For each packing type geomechanically relevant parameters like the packing density or coordination numbers are calculated and discussed. The models are correlated with results of image analysing and standard rock engineering experiments that were carried out on a variety of grain mixtures and sedimentary rocks of Permocarboniferous age. The discussion is concerned with the principles of grain packing models and the particular effects of distinct packing types on the petrophysical rock properties and the geomechanical behaviour of the examples presented.

Jamming in hard sphere and disk packings

Hard-particle packings have provided a rich source of outstanding theoretical problems and served as useful starting points to model the structure of granular media, liquids, living cells, glasses, and random media. The nature of “jammed” hard-particle packings is a current subject of keen interest. Elsewhere, we introduced rigorous and efficient linear-programming algorithms to assess whether a hard-sphere packing is locally, collectively, or strictly jammed, as defined by Torquato and Stillinger [J. Phys. Chem. B 105, 11849 (2001)]. One algorithm applies to ideal packings in which particles form perfect contacts. Another algorithm treats the case of jamming in packings with significant interparticle gaps. We have applied these algorithms to test jamming categories of ordered lattices as well as random packings of circular disks and spheres under periodic boundary conditions. The random packings were produced computationally with a variety of packing generation algorithms, all of which should, in principle, produce at least collectively jammed packings. Our results highlight the importance of jamming categories in characterizing particle packings. One important and interesting conclusion is that the amorphous monodisperse sphere packings with density φ≈0.64 were for practical purposes strictly jammed in three dimensions, but in two dimensions the monodisperse disk packings at previously reported “random close packed” densities of φ≈0.83 were not even collectively jammed. On the other hand, amorphous bidisperse disk packings with density of φ≈0.84 were virtually strictly jammed. This clearly demonstrates one cannot judge “stability” in packings based solely on local criteria. Numerous interactive visualization models are provided on the authors’ webpage.

A linear programming algorithm to test for jamming in hard-sphere packings

Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B 105 (2001)], a classification scheme of jammed packings into hierarchical categories of locally, collectively and strictly jammed configurations has been proposed. They suggest that these jamming categories can be tested using numerical algorithms that analyze an equivalent contact network of the packing under applied displacements, but leave the design of such algorithms as a future task. In this work, we present a rigorous and practical algorithm to assess whether an ideal hard-sphere packing in two or three dimensions is jammed according to the aforementioned categories. The algorithm is based on linear programming and is applicable to regular as well as random packings of finite size with hard-wall and periodic boundary conditions. If the packing is not jammed, the algorithm yields representative multi-particle unjamming motions. Furthermore, we extend the jamming categories and the testing algorithm to packings with significant interparticle gaps. We describe in detail two variants of the proposed randomized linear programming approach to test for jamming in hard-sphere packings. The first algorithm treats ideal packings in which particles form perfect contacts. Another algorithm treats the case of jamming in packings with significant interparticle gaps. This extended algorithm allows one to explore more fully the nature of the feasible particle displacements. We have implemented the algorithms and applied them to ordered as well as random packings of circular disks and spheres with periodic boundary conditions. Some representative results for large disordered disk and sphere packings are given, but more robust and efficient implementations as well as further applications (e.g., non-spherical particles) are anticipated for the future.