scholarly journals Pseudo-Steady-State Productivity Formula for a Partially Penetrating Vertical Well in a Box-Shaped Reservoir

2010 ◽  
Vol 2010 ◽  
pp. 1-35 ◽  
Author(s):  
Jing Lu ◽  
Djebbar Tiab
Keyword(s):  
Steady State ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Neumann Boundary ◽  
Vertical Well ◽  
Homogeneous Neumann Boundary Condition ◽  
Arbitrary Position ◽  
Dirac Function ◽  
Flow Boundaries ◽  
Three Dimensional Space

For a bounded reservoir with no flow boundaries, the pseudo-steady-state flow regime is common at long-producing times. Taking a partially penetrating well as a uniform line sink in three dimensional space, by the orthogonal decomposition of Dirac function and using Green's function to three-dimensional Laplace equation with homogeneous Neumann boundary condition, this paper presents step-by-step derivations of a pseudo-steady-state productivity formula for a partially penetrating vertical well arbitrarily located in a closed anisotropic box-shaped drainage volume. A formula for calculating pseudo skin factor due to partial penetration is derived in detailed steps. A convenient expression is presented for calculating the shape factor of an isotropic rectangle reservoir with a single fully penetrating vertical well, for arbitrary aspect ratio of the rectangle, and for arbitrary position of the well within the rectangle.

scholarly journals Productivity Formulas for a Partially Penetrating Vertical Well in a Circular Cylinder Drainage Volume

2009 ◽  
Vol 2009 ◽  
pp. 1-34 ◽  
Author(s):  
Jing Lu ◽  
Tao Zhu ◽  
Djebbar Tiab ◽  
Jalal Owayed
Keyword(s):  
Circular Cylinder ◽  
Dimensional Space ◽  
Outer Boundary ◽  
Three Dimensional ◽  
Vertical Well ◽  
Drainage Volume ◽  
Cylindrical System ◽  
Center Distance ◽  
Bottom Reservoir ◽  
Three Dimensional Space

Taking a partially penetrating vertical well as a uniform line sink in three-dimensional space, by developing necessary mathematical analysis, this paper presents steady state productivity formulas for an off-center partially penetrating vertical well in a circular cylinder drainage volume with constant pressure at outer boundary. This paper also gives formulas for calculating the pseudo-skin factor due to partial penetration. If top and bottom reservoir boundaries are impermeable, the radius of the cylindrical system and off-center distance appears in the productivity formulas. If the reservoir has a gas cap or bottom water, the effects of the radius and off-center distance on productivity can be ignored. It is concluded that, for a partially penetrating vertical well, different productivity equations should be used under different reservoir boundary conditions.

Virtual Audio Systems

2008 ◽  
Vol 17 (6) ◽  
pp. 527-549 ◽  
Author(s):  
B. Kapralos ◽  
M. R. Jenkin ◽  
E. Milios
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Fixed Number ◽  
Technical Literature ◽  
Auditory Cues ◽  
Advantages And Disadvantages ◽  
Arbitrary Position ◽  
Environment Simulation ◽  
Three Dimensional Space ◽  
Virtual Audio

To be immersed in a virtual environment, the user must be presented with plausible sensory input including auditory cues. A virtual (three-dimensional) audio display aims to allow the user to perceive the position of a sound source at an arbitrary position in three-dimensional space despite the fact that the generated sound may be emanating from a fixed number of loudspeakers at fixed positions in space or a pair of headphones. The foundation of virtual audio rests on the development of technology to present auditory signals to the listener's ears so that these signals are perceptually equivalent to those the listener would receive in the environment being simulated. This paper reviews the human perceptual and technical literature relevant to the modeling and generation of accurate audio displays for virtual environments. Approaches to acoustical environment simulation are summarized and the advantages and disadvantages of the various approaches are presented.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

scholarly journals Quantitative image analysis of microbial communities with BiofilmQ

2021 ◽  
Author(s):  
Raimo Hartmann ◽  
Hannah Jeckel ◽  
Eric Jelli ◽  
Praveen K. Singh ◽  
Sanika Vaidya ◽  
...  
Keyword(s):  
Image Analysis ◽  
Microbial Communities ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Software Tool ◽  
Image Cytometry ◽  
Quantitative Image Analysis ◽  
Space And Time ◽  
Quantitative Image ◽  
Three Dimensional Space

AbstractBiofilms are microbial communities that represent a highly abundant form of microbial life on Earth. Inside biofilms, phenotypic and genotypic variations occur in three-dimensional space and time; microscopy and quantitative image analysis are therefore crucial for elucidating their functions. Here, we present BiofilmQ—a comprehensive image cytometry software tool for the automated and high-throughput quantification, analysis and visualization of numerous biofilm-internal and whole-biofilm properties in three-dimensional space and time.

scholarly journals How Can I Grab That?

i-com ◽  
2020 ◽  
Vol 19 (2) ◽  
pp. 67-85
Author(s):  
Matthias Weise ◽  
Raphael Zender ◽  
Ulrike Lucke
Keyword(s):  
Virtual Reality ◽  
User Experience ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Advantages And Disadvantages ◽  
Multiple Dimensions ◽  
Application Developers ◽  
Three Dimensional Space

AbstractThe selection and manipulation of objects in Virtual Reality face application developers with a substantial challenge as they need to ensure a seamless interaction in three-dimensional space. Assessing the advantages and disadvantages of selection and manipulation techniques in specific scenarios and regarding usability and user experience is a mandatory task to find suitable forms of interaction. In this article, we take a look at the most common issues arising in the interaction with objects in VR. We present a taxonomy allowing the classification of techniques regarding multiple dimensions. The issues are then associated with these dimensions. Furthermore, we analyze the results of a study comparing multiple selection techniques and present a tool allowing developers of VR applications to search for appropriate selection and manipulation techniques and to get scenario dependent suggestions based on the data of the executed study.

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