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.

scholarly journals Pressure Drop Equations for a Partially Penetrating Vertical Well in a Circular Cylinder Drainage Volume

2009 ◽  
Vol 2009 ◽  
pp. 1-33
Author(s):  
Jalal Farhan Owayed ◽  
Jing Lu
Keyword(s):  
Pressure Drop ◽  
Circular Cylinder ◽  
Constant Pressure ◽  
Dimensional Space ◽  
Outer Boundary ◽  
Superposition Principle ◽  
Vertical Well ◽  
Drainage Volume ◽  
Partial Penetration ◽  
Line Sink

Taking a partially penetrating vertical well as a uniform line sink in three-dimensional space, by developing necessary mathematical analysis, this paper presents unsteady-state pressure drop equations for an off-center partially penetrating vertical well in a circular cylinder drainage volume with constant pressure at outer boundary. First, the point sink solution to the diffusivity equation is derived, then using superposition principle, pressure drop equations for a uniform line sink model are obtained. This paper also gives an equation to calculate pseudoskin factor due to partial penetration. The proposed equations provide fast analytical tools to evaluate the performance of a vertical well which is located arbitrarily in a circular cylinder drainage volume. It is concluded that the well off-center distance has significant effect on well pressure drop behavior, but it does not have any effect on pseudoskin factor due to partial penetration. Because the outer boundary is at constant pressure, when producing time is sufficiently long, steady-state is definitely reached. When well producing length is equal to payzone thickness, the pressure drop equations for a fully penetrating well are obtained.

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.

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.

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