Scale Properties of a One-Dimensional Lattice Model for Blood Vessel with a Heterogeneous Part
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The scale properties of a one-dimensional lattice model for the blood vessel with a heterogeneous part (an extended Sakanishi model) have been investigated. In the present study, from the viewpoint of mechanics, a part of the blood vessel, which has the different mechanical properties of the vessel wall, that is, a part of arteriosclerosis, prosthesis and so on, is regarded as the heterogeneous part by a generalization for the one-dimensional lattice model. The stability of the solitary wave is applied in order to obtain the reliable results by the numerical analysis of the pulse wave which propagates through the heterogeneous part in the blood vessel. As a result, we show the behaviors of the pulse wave through the blood vessel with the heterogeneous part under the condition that the scale of the pulse wave, the length of the heterogeneous part and the mechanical properties of the vessel wall are changed.Keywords:
Lattice (music)
Arteriosclerosis
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This paper presents a scale-model relationship for the similarity between large and small scale-models in two-dimensional equilibrium beach profiles. Taking large scale-models using large scale equipment as prototypes, the experimental scale of a medium-sized model was gradually varied keeping the grain size ratio of model to prototype constant. A similarity-comparison between large and small scale beach profiles is made by considering the degree of experimental errors. Judgement results are graphically shown, and a scale-model relationship is proposed. It is found that the scale-model relationship proposed agrees with the ones derived from the empirical formulae expressing the properties of beach profiles. Additionally, the applicability of this scale-model relationship to the reproduction test of natural beaches is examined.
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Similarity (geometry)
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Constant (computer programming)
Degree (music)
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The wave model regime, in the given bay of the arbitrary outline, have been studing at the three scales 1:150, 1:300 and 1:450. The models had the fixed bed. The model of the scale 1:1^0 had been conditionally admitted as the prototype at the investigation. As a result of the study the scale effect for the present case have been found* The correction scale factors depend on the relative water depth.
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This paper presents a scale-model relationship for the similarity between large and small scale-models in two-dimensional equilibrium beach profiles. Taking large scale-models using large scale equipment as prototypes, the experimental scale of a medium-sized model was gradually varied keeping the grain size ratio of model to prototype constant. A similarity-comparison between large and small scale beach profiles is made by considering the degree of experimental errors. Judgement results are graphically shown, and a scale-model relationship is proposed. It is found that the scale-model relationship proposed agrees with the ones derived from the empirical formulae expressing the properties of beach profiles. Additionally, the applicability of this scale-model relationship to the reproduction test of natural beaches is examined.
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Similarity (geometry)
Constant (computer programming)
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Abstract The objective of this study is to derive the time scale to be applied to bed‐load transport in movable‐bed experiments. Based on the model similitude law, the hydraulic time scale and the sedimentation time scales, which were derived from nine selected empirical formulas, were compared in detail. The hydraulic time scale is found to usually be smaller than the sedimentation time scale in a length‐scale distorted model. The time‐scale distortion problem can only be solved using a model that employs heavy (more dense) sediment, which is contrary to the general movablebed models that employ light (less dense) sediment. The analytical results show that the deviation between these two time scales increases as the model length‐scale distortion ratio increases. The time‐scale distortion problem may only be negligible when the model has a small length‐scale distortion ratio.
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A time scale for preserving the similarity of beach change processes between prototype and model under the unsteady condition is studied using a series of small- and large-scale experiments. The time scale is proposed as a function of experimental scale. By appling the time scale and the scale-model relationship to model experiments, the temporal beach change such as shoreline change and relative breaker point were well reproduced within the allowable range of experimental errors. Also, time scale is derived theoretically from the continuty equation of sediments and so on. The correspondence between the experimental and the theoretical time scales is discussed. The reliability of the proposed time scale and the scale-model relationship is checked by the movable bed model of beach change in the Ogata coast during a storm.
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Tidal range
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Multiphase flow
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Abstract Linking a fine-scale geologic description to a coarse-scale reservoir simulation model requires accurate and efficient scale-up. Advanced techniques are necessary to construct reservoir models that incorporate geologic and production data gathered at different scales. In this paper, we present a new global scale-up technology for calculating effective permeability and/or transmissibility and its applications to reservoir modeling. This technology involves using global flow solutions on the fine-scale model to improve scale-up accuracy and reusing them to improve scale-up efficiency for re-gridded coarser models. Global scale-up was initially proposed about 20 years ago [1]. Its potential benefits have been demonstrated for simple models in the literature. Until now, significant technical challenges associated with applying global scale-up to real reservoir models have prevented its adoption by the industry. Real reservoir models are often characterized by complex geometry and connectivity, caused by faults, pinch-outs, and flow barriers. Here, we present industry's first commercial global scale-up technology that overcomes these difficulties. Our studies show that the new global scale-up technology leads to significant improvements in scale-up accuracy. Our global scale-up method preserves complex fine-scale connectivity much more accurately than the industry-standard, local scale-up methods. Moreover, the reuse of flow solutions makes it very efficient to scale-up a fine-scale reservoir model to different coarse-scale models. These advantages enable us to build more accurate reservoir models at different scales and optimize these models for different business objectives. Several applications of global scale-up to the reservoir modeling are presented. Introduction Reservoir modeling involves integrating all available geologic and engineering information that are known to or believed to affect the flow behavior in a reservoir. Static reservoir models, i.e., rock property models, are constructed using data measured at different resolutions and covering different vertical and lateral extents. For example, core analysis describes rock property at centimeter scale and covers a large vertical extent of a reservoir. Seismic data provides indirect rock property measures and covers large lateral and vertical extents; however, it lacks vertical resolution. In addition to measured data, geologic concepts at multiple scales are used in building reservoir models. These concepts are required to interpolate the sparse, measured data to fill the 3D model space. In most reservoirs, rock properties are heterogeneous over many spatial scales and therefore, they are scale dependent. This makes it difficult to consistently incorporate rock property data measured at 0.01~1 meter scale into reservoir models with cell sizes of 50 to 100s of meters. Therefore, an accurate scale-up is required to bridge this wide gap. Often, scale-up needs to be performed recursively at intermediate scales before fine-scale data can be brought into coarse-scale models (see e.g., [2–4]). Permeability, a key rock property which directly affects the flow, is particularly challenging to model since coarse-scale permeability relates to fine-scale permeability through Darcy's flow and cannot be accurately calculated using simple averages of the fine-scale permeability. Therefore, flow-based scale-up has been widely used in the industry for modeling permeability at different scales. Simply put, the procedure entails solving flows in a volume of interest, e.g., a gridblock, and using the flow solutions to calculate the "effective" permeability of that volume, see [5] for a recent review of development in this area. In the following, we present an overview of a global scale-up technology, we recently developed [4], and its applications to reservoir modeling. Global Scale-up Different from standard flow-based scale-up, global scale-up uses flow solutions obtained in the entire model domain to calculate effective permeability on a set of volumes of interest (e.g., gridblocks) in the domain. In contrast, standard local scale-up methods use flow solutions calculated from local boundary conditions imposed on each individual volume of interest. In this section, we explain the rationale behind global scale-up, then we review our global scale-up procedure and the technology required for its commercial applications.
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Reservoir Simulation
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This paper presents a scale-model relationship for the similarity between large and small scale-models in two-dimensional equilibrium beach profiles. Taking large scale-models using large scale equipment as prototypes, the experimental scale of a medium-sized model was gradually varied keeping the grain size ratio of model to prototype constant. A similarity-comparison between large and small scale beach profiles is made by considering the degree of experimental errors. Judgement results are graphically shown, and a scale-model relationship is proposed. It is found that the scale-model relationship proposed agrees with the ones derived from the empirical formulae expressing the properties of beach profiles. Additionally, the applicability of this scale-model relationship to the reproduction test of natural beaches is examined.
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Similarity (geometry)
Degree (music)
Constant (computer programming)
Scale Effects
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