Nonequilibrium consolidation model for pressured shale layers

2001 ◽  
Vol 38 (2) ◽  
pp. 422-426
Author(s):  
Zekai Sen
Keyword(s):  
Mathematical Model ◽  
Fluid Migration ◽  
Mass Balance Equation ◽  
Dimensionless Length ◽  
Consolidation Process ◽  
Type Curves ◽  
Consolidation Model ◽  
Pressure Increment ◽  
The Finite Difference Method ◽  
Simplified Mathematical Model

A simplified mathematical model is developed for fluid migration as a separate phase in the consolidation process due to sedimentation. The consolidation mechanism is presented and the sedimentation ratio is related to the consolidation of shales. The model is composed of simple differential equations which relate the mass balance equation to the linear fluid flow law and pressure increment. In the derivation of equations the fluid and shale compressibilities are taken into consideration. In addition, the shale porosity decrease with depth is included in the consolidation equations. These equations are converted into dimensionless standard forms, which are universally valid for any fluid migration or shale consolidation calculations. The equations are solved numerically by the finite difference method, and the results are presented as graphs referred to as type curves. These type curves are simple tools for those who do not want to be concerned with the mathematical aspects but are interested particularly in quantitative answers concerning the fluid-migration and consolidation processes.Key words: consolidation, dimensionless length, fluid migration, nonequilibrium, shale.

Research on Flux Damping Control Strategy of DFIG during Grid Voltage Dips

2015 ◽  
Vol 713-715 ◽  
pp. 756-759
Author(s):  
Xu Guang Zhang ◽  
Zhen Xie
Keyword(s):  
Mathematical Model ◽  
Control Strategy ◽  
Grid Voltage ◽  
Damping Control ◽  
Simulink Simulation ◽  
Voltage Dips ◽  
Simulation Results ◽  
Stator Flux ◽  
Natural Component ◽  
Simplified Mathematical Model

A flux damping control strategy was proposed to accelerate the decay of stator flux and restrain stator, rotor current and torque oscillation caused by grid voltage dips. Firstly, this paper analyzes the simplified mathematical model of DFIG during symmetrical voltage dips. Then, the mechanism of flux damping control strategy to restrain stator, rotor current oscillation and increase flux damping was analyzed. The flux damping control strategy can increase the damping of stator side, which accelerates the decay of the stator flux natural component and improve the dynamic LVRT performance of DFIG. The correctness and effectiveness of this method is verified by MATLAB/Simulink simulation results.

scholarly journals Mathematical model to estimate of the deterioration of wooden poles in contact with soil used in rural areas

2011 ◽  
Vol 31 (5) ◽  
pp. 1015-1026
Author(s):  
Julio C. Molina ◽  
Carlito Calil Júnior ◽  
Roberto R. de Freitas
Keyword(s):  
Mathematical Model ◽  
Rural Areas ◽  
Sao Paulo ◽  
São Paulo ◽  
Climatological Data ◽  
Paulo State ◽  
São Paulo State ◽  
Useful Life ◽  
Wooden Structures ◽  
Simplified Mathematical Model

In São Paulo State, mainly in rural areas, the utilization of wooden poles is observed for different purposes. In this context, wood in contact with the ground presents faster deterioration, which is generally associated to environmental factors and, especially to the presence of fungi and insects. With the use of mathematical models, the useful life of wooden structures can be predicted by obtaining "climatic indexes" to indicate, comparatively among the areas studied, which have more or less tendency to fungi and insects attacks. In this work, by using climatological data of several cities at São Paulo State, a simplified mathematical model was obtained to measure the aggressiveness of the wood in contact with the soil.

scholarly journals About Two-dimensional Mathematical Model of Contaminant Migration in Unsaturated Catalytic Porous Media with Traps

2020 ◽  
pp. 25-28
Author(s):  
Anatolyy Vlasyuk ◽  
Viktor Zhukovskyy ◽  
Nataliia Zhukovska ◽  
Serhiy Kraychuk
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Moisture Transfer ◽  
Physical Problem ◽  
Two Dimensional ◽  
Contaminant Migration ◽  
Nonlinear Case ◽  
The Finite Difference Method ◽  
Saline Solutions ◽  
Assessment Strategies

This paper proposes an approach for the computer simulation of complex physical problem of contaminant migration through unsaturated catalytic porous media to the filter-trap. The corresponding mathematical model in the two-dimensional nonlinear case is presented. The model includes detailed considerations of the moisture transfer of saline solutions under the generalized Darcy’s and Cluta’s laws in different subregions of soil. The numerical solution of the boundary value problem was found by the finite difference method and proposed the algorithm for computer implementation. The proposed algorithm may be used for creating software with effective risk assessment strategies and predicting the cleaning and further useful use of the soil massifs.

scholarly journals A SIMPLIFIED MATHEMATICAL MODEL OF THE EFFECT OF GAZ HYDRATES ON INTRA-TUBE CORROSION

2017 ◽  
Vol 27 (6) ◽  
pp. 150-153
Author(s):  
L. Ya. Poberezhnyi ◽  
A. V. Hrytsanchuk ◽  
S. M. Petrushchak
Keyword(s):  
Mathematical Model ◽  
Simplified Mathematical Model

scholarly journals Tail-Actuator Propulsion Device for Aquatic Robot

2006 ◽  
Vol 18 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Andrea Manuello Bertetto ◽  
◽  
Maurizio Ruggiu
Keyword(s):  
Mathematical Model ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Operating Principle ◽  
The Other ◽  
Kinematics And Dynamics ◽  
Experimental Characterization ◽  
Fish Propulsion ◽  
Geometrical Dimensions ◽  
Simplified Mathematical Model

In this paper an aquatic device inspired to the fish propulsion is proposed. At the first, the operating principle of the fluidic actuator and its experimental characterization are presented. Then, the results of numerous tests carried out on the integrated tail-actuator device are shown either in terms of thrust exerted or as biomorphism of its kinematics. The tests were run at several driven frequencies with different fins depending on their geometrical dimensions and compliances. On the other hand, a simplified mathematical model of the propulsion system, based on the calculation of the instantaneous tail kinematics and dynamics by means of a numerical procedure, is proposed with the aim of simulating performances either in terms of thrust exerted or kinematics behavior. Finally a discussion about the results obtained and a comparison between experimental and numerical data are presented.

scholarly journals Analysis and Simulation about a Simplified Model for Modulation and Demodulation of Ship-borne Single Channel Monopulse Radar

2018 ◽  
Vol 232 ◽  
pp. 04043
Author(s):  
Xudong Zhang ◽  
Haiyu Ji
Keyword(s):  
Mathematical Model ◽  
Single Channel ◽  
Simplified Model ◽  
Modulation And Demodulation ◽  
Pulse Radar ◽  
Factors Influencing ◽  
Simplified Mathematical Model

A simplified mathematical model for modulation and demodulation of a single channel monopulse (SCM) system is proposed, which is based on a ship-borne pulse radar S-band guided receiver. Using the proposed mathematical model, the modulation and demodulation of single-channel and multi-channel signals were simulated respectively, and the factors influencing the modulation and demodulation of the SCM system were analysed.

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