Steady State Productivity Equations for a Vertical Well in Anisotropic Sector Fault, Channel, and Rectangular Reservoirs

2009 ◽  
Vol 131 (1) ◽  
Author(s):  
Jing Lu ◽  
Djebbar Tiab ◽  
Jalal Farhan Owayed
Keyword(s):  
Steady State ◽  
Flow Rate ◽  
Mapping Method ◽  
Vertical Well ◽  
Drainage Radius ◽  
Conformal Mapping Method ◽  
Field Practice ◽  
Anisotropic Reservoir ◽  
Anisotropic Systems ◽  
New Equation

This paper presents steady state productivity equations for a fully penetrating vertical well in the following three anisotropic systems: (a) sector fault, (b) channel, and (c) rectangular reservoir using a uniform line sink model. The new equations, which are based on conformal mapping method, are simple, accurate, and easy to use in field practice. If the well is in a sector fault reservoir, the productivity is a function of the angle of the sector, wellbore location angle, off-vertex distance, and drainage radius. If the well is in a channel reservoir with two parallel impermeable lateral boundaries, well flow rate reaches a maximum value when the well is located in the middle of the channel width. If the well is in a rectangular reservoir with constant pressure lateral boundaries, a new equation is provided to calculate the productivity of the well arbitrarily located in the anisotropic reservoir for the case where the flow rate of an off-center well is bigger than that of a centered well. It is concluded that, for a vertical well, different steady state productivity equations should be used in different reservoir geometries.

scholarly journals New analytical solution for solving steady-state heat conduction problems with singularities

2013 ◽  
Vol 17 (3) ◽  
pp. 665-672 ◽  
Author(s):  
Najib Laraqi ◽  
Eric Monier-Vinard
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Thermal Resistance ◽  
Exact Expression ◽  
Mapping Method ◽  
State Heat ◽  
Conformal Mapping Method ◽  
Annular Disc ◽  
Steady State Heat ◽  
Christoffel Transformation

A problem of steady-state heat conduction which presents singularities is solved in this paper by using the conformal mapping method. The principle of this method is based on the Schwarz-Christoffel transformation. The considered problem is a semi-infinite medium with two different isothermal surfaces separated by an adiabatic annular disc. We show that the thermal resistance can be determined without solving the governing equations. We determine a simple and exact expression that provides the thermal resistance as a function of the ratio of annular disc radii.

The Model for Calculation the Hall Effect Parameter

2004 ◽  
Vol 9 (2) ◽  
pp. 129-138
Author(s):  
J. Kleiza ◽  
V. Kleiza
Keyword(s):  
Magnetic Field ◽  
Field Effect ◽  
Magnetic Field Effect ◽  
Mapping Method ◽  
Sample Thickness ◽  
System Of Nonlinear Equations ◽  
Specific Resistivity ◽  
Conformal Mapping Method ◽  
Effect Parameter ◽  
The Magnetic Field

A method for calculating the values of specific resistivity ρ as well as the product µHB of the Hall mobility and magnetic induction on a conductive sample of an arbitrary geometric configuration with two arbitrary fitted current electrodes of nonzero length and has been proposed an grounded. During the experiment, under the constant value U of voltage and in the absence of the magnetic field effect (B = 0) on the sample, the current intensities I(0), IE(0) are measured as well as the mentioned parameters under the effect of magnetic fields B1, B2 (B1 ≠ B2), i.e.: IE(β(i)), I(β(i)), i = 1, 2. It has been proved that under the constant difference of potentials U and sample thickness d, the parameters I(0), IE(0) and IE(β(i)), I(β(i)), i = 1, 2 uniquely determines the values of the product µHB and specific resistivity ρ of the sample. Basing on the conformal mapping method and Hall’s tensor properties, a relation (a system of nonlinear equations) between the above mentioned quantities has been found.

scholarly journals IMPROVEMENT OF FORECASTING METHOD OF RECESSION CHARACTERISTICS OF RIVER FLOW RATE INTO A DAM BY USING ESTIMATION OF STEADY STATE

2017 ◽  
Vol 73 (1) ◽  
pp. 12-21
Author(s):  
Tomonari KAWAI ◽  
Katsuhiro ICHIYANAGI ◽  
Takuo KOYASU ◽  
Kazuto YUKITA ◽  
Yasuyuki GOTO
Keyword(s):  
Steady State ◽  
Flow Rate ◽  
River Flow ◽  
Forecasting Method

scholarly journals Determination of Permeability and Inertial Coefficients of Sintered Metal Porous Media Using an Isothermal Chamber

2018 ◽  
Vol 8 (9) ◽  
pp. 1670 ◽  
Author(s):  
Wei Zhong ◽  
Xiang Ji ◽  
Chong Li ◽  
Jiwen Fang ◽  
Fanghua Liu
Keyword(s):  
Porous Media ◽  
Steady State ◽  
Flow Rate ◽  
Pressure Difference ◽  
Testing Time ◽  
Sintered Metal ◽  
Steady State Method ◽  
Volume Limit ◽  
Inertial Coefficient

Sintered metal porous media are widely used in a broad range of industrial equipment. Generally, the flow properties in porous media are represented by an incompressible Darcy‒Forchheimer regime. This study uses a modified Forchheimer equation to represent the flow rate characteristics, which are then experimentally and theoretically investigated using a few samples of sintered metal porous media. The traditional steady-state method has a long testing time and considerable air consumption. With this in mind, a discharge method based on an isothermal chamber filled with copper wires is proposed to simultaneously determine the permeability and inertial coefficient. The flow rate discharged from the isothermal chamber is calculated by differentiating the measured pressure, and a paired dataset of pressure difference and flow rate is available. The theoretical representations of pressure difference versus flow rate show good agreement with the steady-state results. Finally, the volume limit of the isothermal chamber is addressed to ensure sufficient accuracy.

Pitfalls for Accurate Steady-State Port Flow Simulations

2012 ◽  
Author(s):  
Xiaofeng Yang ◽  
Zhaohui Chen ◽  
Tang-Wei Kuo
Keyword(s):  
Steady State ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Measured Data ◽  
Steady State Flow ◽  
Bench Tests ◽  
Flow Simulations ◽  
Mesh Topology ◽  
State Flow

Steady-state port flow simulations were carried out with a commercial three dimensional (3D) Computational Fluid Dynamics (CFD) code using Cartesian mesh with cut cells to study the prediction accuracy. The accuracy is assessed by comparing predicted and measured mass-flow rate and swirl and tumble torques at various valve lifts using different boundary condition setup and mesh topology relative to port orientation. The measured data is taken from standard steady-state flow bench tests of a production intake port. The predicted mass-flow rates agree to within 1% with the measured data between the intermediate and high valve lifts. At low valve lifts, slight over prediction in mass-flow rate can be observed. The predicted swirl and tumble torques are within 25% of the flow bench measurements. Several meshing parameters were examined in this study. These include: inlet plenum shape and outlet plenum/extension size, embedded sphere with varying minimum mesh size, finer meshes on port and valve surface, orientation of valve and port centerline relative to the mesh lines. For all model orientations examined, only the mesh topology with the valve axis aligned closely with the mesh lines can capture the mass-flow rate drop for very high valve lifts due to flow separation. This study further demonstrated that it is possible to perform 3D CFD flow analyses to adequately simulate steady-state flow bench tests.

A conformal-mapping method for predicting the thermal properties of U-shaped borehole heat-exchangers

Geothermics ◽  
2014 ◽  
Vol 50 ◽  
pp. 66-75 ◽  
Author(s):  
Nai-Wen Liang ◽  
Ching-Hsien Lai ◽  
Chien-Yeh Hsu ◽  
Yuan-Ching Chiang ◽  
Chih-Chung Chang ◽  
...  
Keyword(s):  
Thermal Properties ◽  
Conformal Mapping ◽  
Heat Exchangers ◽  
Mapping Method ◽  
Conformal Mapping Method ◽  
Borehole Heat Exchangers
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