一种新型平面组合传感器的误差建模与分析

设计了一种新型三自由度位姿测量平面组合传感器装置,用于完成对平面运动的两个移动自由度和一个转动自由度的动态测量。介绍了传感器的机构构成和测量原理,利用微分法原理建立了误差模型,对误差产生原因进行分析,得出了机构误差对测量精度的影响曲线,试验和仿真验证了新型平面组合传感器机构的合理性。新型平面组合传感器机构简单,测量精度高,适用于特定环境下的高精度平面运动位姿测量。

贝尔凹陷苏德尔特构造带古潜山构造与储层研究

With the develop ment of oil and gas exploration, the conventional struc ture exploration era has gradually been substituted by the concealed reser voir exploration technology. Hill poll becomes one of the most important areas in the future exploration. This paper is based on the three-dimensional seismic interpretation of Sudeerte structure. In terms of the overall character istics of Sudeerte structure, we use the coherent cube and the time slice to interpret the fault in plane. For the interpretation，we especially used the well to adjust the interpretation results. The results of seismic attribution analysis, spectrum decomposition and post- stack seismic inversion forecast that hill pools reservoir are dist ributed in several bands along the north-northeast to northeast-east. Xing'anling Group shows that the potential reser voirs are mainly distributed along Bei 14 –Bei 40 and De (99-212) - Bei (16-1) and Budate Group distributed along Bei 14 –Bei 40 in northwestern direction and De (99-212) - Bei (16-1) in north eastern direction. At the same time, by analyzing the structure and the reservoir, and combining with other data, three models are built. The characteristics of reservoirs dist ribution are concl uded，and potent ional favorable exploration dire ctions are predi cted.

鄂尔多斯盆地志丹地区延长组储层综合评价

Sedimentary provenance direction，sedimentary facies，reservoir geological characteristic，pore structure； physical property characteristic，reservoir classification and evaluation ，forthermore，favorable area area are forecasted of Yanchang formation in ZhiDan region， by mainly study on the data of field section observation ，core observation, well logging explaination and routine microscope slice identification，scanning Electron Microscope and reservoir analysis of lithology and physical property , Under the guidance of such advanced theories and methods as sedimentology，reservoir sedimentology，lithological oil pool and so on，in the thesis. The following fruits are mainly achieved in this paper： Yanchang formation stratum is divided and correlated in this entire region， and the characteristic of oil layer unit is detailed discussed , respectively. According to main marker bed and supplementary ones.and research result shows that the source of provenance direction during Yanchang Formation mianly is north-east. Delta and lake are mainly developed in study area ，sub-facies and micro-facies are divided，distribution of sedimentary micro-facies in plane and palaeogeographic evolution are described，and gentle slope type- shallow water delta depositional model is established. Fine-grain arkose sandstone is the main reservoir，and which have experienced such different degree diagenesis as compaction, cementation, replacement and dissolution, and in which compaction and cementation are mainly factors to reduce sandstone physical property and dissolution effectively improved physical property during burial diagenesis procedure. All reservoirs of Yanchang Formation have entered A period of late diagenetic stage according to scheme of diagenesis period division . Intergranular porosity，dissolution porosity，fissure porosity are main pore types. And porosity structure are analyse by mercury penetration capillary pressure parameter，fine-shortness type and fine- length throat type are mainly developed. as a whole，the reservoir， with the characteristic of porosity and permeability altering apparently，strong inhomogeneity ， is a medium- porosity and medium permeability one. In plane，higher- porosity and higher-permeability are corresponded well with distributary channel area， physical property and inhomogeneity are affected by both deposition and diagenesis，and distributary channel and underwater distributary channel are favorable facies . According to such characteristic as lithology，physical property，pore structure ，diagenesis and sandstone distribution, the sandy reservoir can be classified 4 types, and the main sandy in every oil layer unit are evaluated according to the standard. The analysis result of petroleum concentration rule shows that Yanchang Formation are with not only favourable oil source rock，reservoir，covering combination ，but also good entrapment condition in study area. Lithology and structure-lithology oil pool are mainly developed ，based on condition of favorable reservoir developments，accounting for deliverability and sandstone superface elevation，zone of profitabilitis are forecasted.

松辽盆地南部岩性油藏成藏模式与分布规律

According to the basic geologic conditions, the paper is directed by the modem oil-gas accumulation theory and petroleum system in which typical oil pools are analyzed and the shape of lithologic trap and geologic factors are pointed out. The process during which oil and gas migrate from source rock to lithologic trap is rebuilt, and the accumulation model of oil pool is set up. With the comprehensive application of seismic geologic and log data and paying attention to the method and technology which is used to distinguish lithologic accumulation. Promising structural-lithofacies zones are got and the distribution rule of various lithologic accumulation is concluded. With making use of the biologic mark compound, different reservoirs are compared. As a result, the oil and gas in HeiDimiao come from Nenjiang Group's source rocks; in SaErTu from QingShenkou Group's and Nenjiang Group's, and in PuTaohua. GaoTaizi and FuYang from QingShankou Group's. According to the development and distribution of effective source rock, oil distribution and the comparison in the south of SongLiao basin, the characteristic of basin structure and reservoir distribution is considered, and then the middle-upper reservoir of SongLiao basin south are divided into two petroleum system and a complex petroleum system. Because of the characteristic of migration and accumulation, two petroleum systems can furtherly be divided into 6-7 sub-petroleum systems,20 sub-petroleum systems in all. As a result of the difference of the migration characteristic, accumulation conditions and the place in the petroleum system, the accumulation degree and accumulation model are different. So three accumulation mechanism and six basic accumulation model of lithologic trap are concluded. The distribution of lithologic pools is highly regular oil and gas around the generation sag distribute on favorable structural-lithofacies zones, the type of lithological pool vary regularly from the core of sandstone block to the upper zone. On the basic of regional structure and sedimentary evolution, main factors which control the form of trap are discovered, and it is the critical factor method which is used to discern the lithologic trap. After lots of exploration, 700km~2 potential trap is distinguished and 18391.86 * 10~4 tons geologic reserves is calculated. Oil-water distribution rule of pinch-out oil pool is put up on plane which is the reservoirs can be divided into four sections. This paper presented the law of distribution of oil and water in updip pinch-out reservoir, that is, hydrocarbon-bearing formation in plane can be divided into four zones: bottom edge water zone, underside oil and water zone, middle pure oil zone and above residual water zone. The site of the first well should be assigned to be middle or above pure oil zone, thus the exploration value of this type of reservoir can be recognized correctly. In accordance with the characteristics of seism and geology of low permeability thin sandstone and mudstone alternation layer, the paper applied a set of reservoir prediction technology, that is: (1)seism multi-parameter model identification; (2) using stratum's absorbing and depleting information to predict reservoir's abnormal hydrocarbon-bearing range. With the analysis of the residual resource potential and the research of two petroleum system and the accumulation model, promising objective zones are predicted scientifically. And main exploration aim is the DaRngZi bore in the west of ChangLin basin, and YingTai-SiFangZi middle-upper assembly in Honggang terrace.

河道砂油藏产能预测系统研究

Productivity prediction is a serious factor to oil reservoir management and working out economic plans so that it is paid great attention to all the time. Gudao Oil Field, which has been yielding more than 100 million tons of crude oil accumulatively since it was put into developing in 1970's as a complete set of oil field, now entering double extra high water-bearing period after productivity construction, stable production and depletion stage. It's main layer series of development is thought to be type of channel sand reservoir in east China. Form channel sand reservoir in upper Guantao Group of Shengli Oil Field, there are several large oil fields such as Gudao, Gudong and Chengdao etc. with almost one-third reserves of whole Shengli Oil Field. It is considered the common characteristics in this area would be that the layer is less developed, the sand distribution is sporadic, the connectivity is weak, the heterogeneity is strong in plane, the oil layer is unconsolidated with big porosity, high permeability and serious sanding, and the oil is heavy. Because of the restricted factors to productivity of this kind of reservoir, it is very significant to study the productivity prediction this kind of reservoir. By selecting the upstream fluvial reservoir in Guantao Group of Neogene system as researching object, the author studied the forecasting technology with heterogeneous reservoir. Firstly, the author constructed the 3D subtle geological model quantificationally through researching exploitation geology in the way of combination of dynamic and static methods. Secondly, by the aid of dynamic material obtained while producing, the author analyzed the oil distribution law and influencing factors, then finished dynamic oil reservoir description on the basis of static oil reservoir description. Thirdly, via comparing and analyzing all the forecasting methods of productivity existed, the author developed a set of method to forecast productivity of single well and oil field which fit to channel sand reservoir. At last, under the support of ORACLE database, with the advanced computer technology, the author programmed the software called 'Channel Sand Reservoir Prediction System'. Up to now, this system has been putting into use in Gudao Oil Field and very successful.

沾化凹陷泥质岩油气藏成藏特征研究

Mudstone reservoir is a subtle reservoir with extremely inhomogeneous, whose formation is greatly related to the existence of fracture. For this kind of reservoir, mudstone is oil source rock, cover rock and reservoir strata, reservoir type is various, attitude of oil layer changes greatly, and the distribution of oil and gas is different from igneous or clastic rock reservoir as well as from carbonate reservoir of self-producing and self-containing of oil and gas. No mature experience has been obtained in the description, exploration and development of the reservoir by far. Taking Zhanhua depression as an example, we studied in this thesis the tectonic evolution, deposit characteristics, diagenesis, hydrocarbon formation, abnormal formation pressure, forming of fissure in mudstone reservoir, etc. on the basis of core analysis, physical simulation, numerical simulation, integrated study of well logging and geophysical data, and systematically analyzed the developing and distributing of mudstone fissure reservoir and set up a geological model for the formation of mudstone fissure reservoir, and predicted possible fractural zone in studied area. Mudstone reservoir mainly distributed on the thrown side of sedimentary fault along the sloping area of the petroleum generatiion depression in Zhanhua depression. Growing fault controlled subsidence and sedimentation. Both the rate of subsidence and thickness of mudstone are great on the thrown side of growing fault, which result in the formation of surpressure in the area. The unlocking of fault which leads to the pressure discharges and the upward conduct of below stratum, also makes for the surpressure in mudstone. In Zhanhua depression, mudstone reservior mainly developed in sub-compacted stratum in the third segment of Shahejie formation, which is the best oil source rock because of its wide spread in distribution, great in thickness, and rich in organic matter, and rock types of which are oil source mudstone and shale of deep water or semi-deep water sediment in lacustrine facies. It revealed from core analysis that the stratum is rich in limestone, and consists of lamina of dark mudstone and that of light grey limestone alternately, such rock assemblage is in favor of high pressure and fracture in the process of hydrocarbon generation. Fracture of mudstone in the third segment of Shahejie formation was divided into structure fracture, hydrocarbon generation fracture and compound fracture and six secondary types of fracture for the fist time according to the cause of their formation in the thesis. Structural fracture is formed by tectonic movement such as fold or fault, which develops mainly near the faults, especially in the protrude area and the edge of faults, such fracture has obvious directivity, and tend to have more width and extension in length and obvious direction, and was developed periodically, discontinuously in time and successively as the result of multi-tectonic movement in studied area. Hydrocarbon generation fracture was formed in the process of hydrocarbon generation, the fracture is numerous in number and extensively in distribution, but the scale of it is always small and belongs to microfracture. The compound fracture is the result of both tectonic movement and hydrocarbon forming process. The combination of above fractures in time and space forms the three dimension reservoir space network of mudstone, which satellites with abnormal pressure zone in plane distribution and relates to sedimentary faces, rock combination, organic content, structural evolution, and high pressure, etc.. In Zhanhua depression, the mudstone of third segment in shahejie formation corresponds with a set of seismic reflection with better continuous. When mudstone containing oil and gas of abnormal high pressure, the seismic waveform would change as a result of absorb of oil and gas to the high-frequency composition of seismic reflection, and decrease of seismic reflection frequency resulted from the breakage of mudstone structure. The author solved the problem of mudstone reservoir predicting to some degree through the use of coherent data analysis in Zhanhua depression. Numerical modeling of basin has been used to simulate the ancient liquid pressure field in Zhanhua depression, to quantitative analysis the main controlling factor (such as uncompaction, tectonic movement, hydrocarbon generation) to surpressure in mudstone. Combined with factual geologic information and references, we analyzed the characteristic of basin evolution and factors influence the pressure field, and employed numerical modeling of liquid pressure evolution in 1-D and 2-D section, modeled and analyzed the forming and evolution of pressure in plane for main position in different periods, and made a conclusion that the main factors for surpressure in studied area are tectonic movement, uncompaction and hydrocarbon generation process. In Zhanhua depression, the valid fracture zone in mudstone was mainly formed in the last stage of Dongying movement, the mudstone in the third segment of Shahejie formation turn into fastigium for oil generation and migration in Guantao stage, and oil and gas were preserved since the end of the stage. Tectonic movement was weak after oil and gas to be preserved, and such made for the preserve of oil and gas. The forming of fractured mudstone reservoir can be divided into four different stages, i.e. deposition of muddy oil source rock, draining off water by compacting to producing hydrocarbon, forming of valid fracture and collecting of oil, forming of fracture reservoir. Combined with other regional geologic information, we predicted four prior mudstone fracture reservoirs, which measured 18km2 in area and 1200 X 104t in geological reserves.

板北断块油藏储层均质特征与剩余油分布研究

With the growing development and perfection of reservoir describing technology, its research achievements have played an increasingly important role in old oilfields in recent years. Reservoir description quantitatively describes, characterizes and predicts every kind of reservoir characters in 3D space. The paper takes Banbei block reservoir as an object, studies the reservoir characters and residual oil distributing characteristics of gravity flow genetic reservoir, and definitudes potential adjustment direction of reservoir development. Main achievements are gained as follows. Through fine correlation of strati graphic sequence, the classification of layers and single sands of main payzones in Banbei block is ascertained, the classifying methods of sedimentary unit in gravity flow reservoir characterized with picked cyclical marker bed are formed. On the basis of comprehensive logging evaluation, depositional characters of Banbei block are studied, and classifying methods of sedimentary microfacies in gravity flow reservoir are described. The sedimentary background of main oil layers in Banbei block is open lake with shallow water, and belongs to lacustrine underwater gravity flow- lacustrine phase depositional system. Main microfacies types are underwater water course^ water course side-wing, underwater floodplain, between two water courses, and lacustrine mud, etc. Reservoir sands mainly are underwater water course sands. Influenced by distributing characters of gravity flow underwater water course, sand shapes in plane mainly are stripe, finger-shape, tongue-shape. Sand distribution shows obvious split property. Sands overlap each other. According to comprehensive analysis of lithologic data, logging parameters, and dynamic production data, the researching threads and methods of reservoir heterogeneous characters are perfected. The depositional characters of gravity flow underwater water course in Banbei block determine its high reservoir heterogeneity. Macroscopic heterogeneity is studied in many aspects such as the scale of layers, the scale of single sands, in-situ scale, the distribution of interlayer types, the interlayer scale, and heterogeneity in plane. Thus, heterogeneous characters of reservoir are thoroughly analyzed. Through microscopic research of reservoir, the types of porous structure and related parameters are determined. According to the analysis of dynamic production data, the reaction and inner influential factors of reservoir heterogeneity in waterflood development are further revealed. Started with the concept and classifying methods of flow unit, clustering classification which can better meet the requirements of production is formed. The flow unit of Banbei block can be classified into four types. According to comprehensive evaluation, the first and second type of flow unit have better percolating capability and reserving capability. Research thread of 3D model-building and reservoir numerical simulation combined as an integral is adopted. The types and characters of residual oil distribution are determined. Residual oil of Banbei block mainly distributes in the boundary of sands, near the faults, areas with non-perfect injection-production well pattern , undeveloped sands, vertically poor developed layers. On the basis of comprehensive reservoir study, the threads and methods of improving development effect towards reservoir with high water cut, high recovery percent, serious heterogeneity are ascertained. The whole waterflood development effect of Banbei block reservoir is good. Although its water cut and recovery percent is relatively high, there is still some potential to develop. According to depositional characters of gravity flow and actual production situation? effective means of further improving development level are as follows. We should drill new wells in every kind of areas abounding with residual oil, implement comprehensive measures such as increasing liquid discharge, cyclic waterflood, changing fluid direction when injection-production well pattern is perfected, improve water quality, enhance displacement efficiency in flooding.

鄂尔多斯盆地上古生界包裹体研究及天然气成藏特征分析

Based on the study of types, even temperature, the character of age-old fluid and fluid pressure of the reservoir fluid-inclusion in the Upper Paleozoic of Ordos Basin , combining with the diagenesis and character of gas geochemistry, reservoir sequence, cause of the low pressure reservoir formation and formation environment have been studied, the following knows are acquired: Abundant fluid-conclusions have developed in sandstone reservoir in Upper Paleozoic of Ordos Basin,and its kinds is numerous , also taking place some changes such as shrinking rock, cracking, stretching after formation. According to formation cause, fluid inclusion is divided into two types:successive and nonsuccessive inclusion. Nonsuccessive inclusion is further divided into brine inclusion, containing salt crystal inclusion, gaseity hydrocarbon conclusion and liquid hydrocarbon conclusion and so on. The gaseity hydrocarbon conclusion distributes at all the Basin, the liquid hydrocarbon conclusion mainly distributes at the East of Basin, and its two kinds of fluorescence color: blue and buff reflects at least two periods of oil filling and oil source of the different maturity. The study of diagenesis has indicated that five periods of diagenesis correspond to five periods inclusion's growth.The first and second period conclusions mainly distribute at the increasing margin of quartz, little amount and low even temperature, containing little gaseity hydrocarbon conclusion; The third and fourth conclusions are very rich, and having multiplicity forms, gaseity hydrocarbon conclusion of different facies, distributing at the increasing margin and crevice of quartz, its even temperature is between 85℃and 135℃;The fifth inclusion is relatively few ,mainly distributing at vein quartz and calcite, and developing few gaseity hydrocarbon conclusion. The fluid in the inclusion is mainly NaCl brine:low and high salinity brine fluid(containing salt crystal).The former salinity is between 0.18% and 18.55%,and mainly centralized distributing at three sectongs: from 0% to 4%, from 6% to 8%, from 10% to 14%, expressing that the alternation of the underground fluid was not intense, the conservation condition was good in different periods. The trapping pressure of the gaseity hydrocarbon conclusion calculated by PVTsim(V10)simulation is between 21.39 MPa and 42.58MPa,the average is 28.99MPa,mainlydistributes at between 24 MPa and 34MPa,and having a character of gradually lower from early to late time. The pressure of SuLiGe and WuShenQi dropped quickly in early time, and YuLin, ShenMu-MIZhi gas area dropped slowly in early and quickly in late time, ha portrait the change of trapping pressure can be divided into three old-age pressure systems: TaiYuan-ShanXi formation, low ShiHeZi formation and high ShiHeZi-ShiQianFeng formation. In plane, the trapping pressure dropped lowly from south to north in main reservoir period, and this reflects the gas migrating direction in the geohistory period. The analysis of gas component and monnmer hydrocarbon isotope indicates that the gas in Upper Paleozoic of Ordos Basin is coal-seam gas. The gas C_1-C_4 rnonnmer hydrocarbon isotopes has distinct differences in different stratums of different areas, and forming YuLin, SuLiGe and ShenMu-MIZhi three different distributing types. To sum up, gas reservoir combination in Upper Paleozoic of Ordos Basin can be divided into three sets of combination of reservoir formation: endogenesis type, near source type and farther source type,and near source gas combinations of reservoir formation is the main gas exploration area for its high gas filling intensity, large reservoir size.

Experimental Study on Vortex-Induced Vibrations of a Pipeline Near a Plane Boundary in Steady Flow

对单向水流作用下近壁管道横向涡激振动进行了实验模拟,重点探讨了管道与壁面间隙比(e/D)对管道涡激振动幅值和涡激振动频率响应特性的影响规律.实验结果表明,管道与壁面间隙宽度对管道涡激振动特性有较明显影响.在较大间隙比(e/D＞0.66)下,管道振幅随着Vr数的增大先快速增长到最大值,然后平缓下降;在振动初期(即Vr数较小时),管道振动频率变化基本符合Strouhal规律;在振动中后期(即Vr数较大时),管道振动频率变化不符合Strouhal规律,而在管道固有频率附近缓慢增长.在较小间隙比(e/D＜0.30)下,管道振幅随Vr数的增大先平缓上升到最大值,随后较快速下降;在振动初期,管道振动频率变化不遵循Strouhal规律;在整个振动范围内,与较大间隙比情况相比,随着Vr数增加,管道振动频率增长幅度明显较大.

Instability Of Plane Poiseuille Flow In A Fluid-Porous System

The instability of Poiseuille flow in a fluid-porous system is investigated. The system consists of a fluid layer overlying porous media and is subjected to a horizontal plane Poiseuille flow. We use Brinkman's model instead of Darcy's law to describe the porous layer. The eigenvalue problem is solved by means of a Chebyshev collocation method. We study the influence of the depth ratio (d) over cap and the Darcy number delta on the instability of the system. We compare systematically the instability of Brinkman's model with the results of Darcy's model. Our results show that no satisfactory agreement between Brinkman's model and Darcy's model is obtained for the instability of a fluid-porous system. We also examine the instability of Darcy's model. A particular comparison with early work is made. We find that a multivalued region may present in the (k, Re) plane, which was neglected in previous work. Here k is the dimensionless wavenumber and Re is the Reynolds number. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3000643]

Asymptotic analysis of plane-strain mode I steady-state crack growth in transformation toughening ceramics (II)

Based on a constitutive law which includes the shear components of transformation plasticity, the asymptotic solutions to near-tip fields of plane-strain mode I steadity propagating cracks in transformed ceramics are obtained for the case of linear isotropic hardening. The stress singularity, the distributions of stresses and velocities at the crack tip are determined for various material parameters. The factors influencing the near-tip fields are discussed in detail.

Stress intensity factors calculation in anti-plane fracture problem by orthogonal integral extraction method based on femol

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions (or between the derivatives of eigenfunctions) of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors (SIFs), so any order SIF can be extracted based on a certain known solution of displacement (an analytic result or a numerical result). Many numerical examples based on the finite element method of lines (FEMOL) show that the present method is very powerful and efficient.

Unloading characteristics of anti-plane shear crack in softening materials

The local characteristics of the anti-plane shear stress and strain field are determined for a material where the stress increases linearly with strain up to a limit and then softens nonlinearly. Two unloading models are considered such that the unloading path always returns to the origin while the other assumes the unloading modulus to be that of the initial shear modulus. As the applied shear increases, an unloading zone is found to prevail between a zone in which the material softens and another zone in which the material is linear-elastic even though the crack does not propagate. The divisions of these zones are displayed graphically.

An asymptotic solution of hydrodynamic equations at the mid-plane of a plume in the earths mantle

From the partial differential equations of hydrodynamics governing the movements in the Earth's mantle of a Newtonian fluid with a pressure- and temperature-dependent viscosity, considering the bilateral symmetry of velocity and temperature distributions at the mid-plane of the plume, an analytical solution of the governing equations near the mid-plane of the plume was found by the method of asymptotic analysis. The vertical distribution of the upward velocity, viscosity and temperature at the mid-plane, and the temperature excess at the centre of the plume above the ambient mantle temperature were then calculated for two sets of Newtonian rheological parameters. The results obtained show that the temperature at the mid-plane and the temperature excess are nearly independent of the rheological parameters. The upward velocity at the mid-plane, however, is strongly dependent on the rheological parameters.

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.