Determination of the filtration properties and stresses in a coal seam by solving the inverse problem

2000 ◽  
Vol 36 (2) ◽  
pp. 106-113 ◽  
Author(s):  
L. A. Nazarov ◽  
L. A. Nazarova
Keyword(s):  
Inverse Problem ◽  
Coal Seam ◽  
Filtration Properties

scholarly journals Determination of stress state in coal seam based on inverse problem solution using acoustic sounding data

Mining Scince ◽  
2019 ◽  
Vol 26 ◽  
Author(s):  
Mels Kudaibergenovich Kudaibergenov ◽  
Kazizat Takuadinovich Iskakov ◽  
Bakytzhan Serikzhanovna Kudaibergenova
Keyword(s):  
Inverse Problem ◽  
Coal Seam ◽  
Biharmonic Equation ◽  
Second Step ◽  
Problem Solution ◽  
Acoustic Sounding ◽  
Tangential Stresses ◽  
Residual Functional ◽  
Uniqueness Of The Solution

The paper presents an algorithm for calculating the horizontal, vertical and tangential stresses in a horizontal coal seam lying between galleries. These stresses are expressed in terms of the Airy function, which satisfies a homogeneous biharmonic equation. For its numerical solution it is necessary to set boundary conditions. Practical limitations do not allow us to determine the tangential stresses on horizontal boundaries of the coal seam. Calculations of stresses are proposed to be carried out in two steps. The first step is to solve the inverse problem for the biharmonic equation to find unknown tangential stresses on horizontal boundaries of the coal seam. The inverse problem is solved by minimizing the residual functional. Its strong convexity is proved, which implies the existence and uniqueness of the solution of the inverse problem. The second step is to solve the boundary value problem for the biharmonic equation to calculate stresses in the coal seam. The result of a numerical experiment is presented.

Precipitation and filtration of zinc, magnesium, copper and aluminium hydroxides

1982 ◽  
Vol 47 (12) ◽  
pp. 3362-3370
Author(s):  
Otakar Söhnel ◽  
Eva Matějčková
Keyword(s):  
Residence Time ◽  
Mean Residence Time ◽  
Filtration Resistance ◽  
Filtration Pressure ◽  
Bed Porosity ◽  
The Mean ◽  
Filtration Properties

Filtration properties of batchwise precipitated suspensions of Zn(OH)2, Mg(OH)2 and Cu(OH)2 and continuously precipitated Al(OH)3 were studied. For batchwise precipitated suspensions was verified the theoretically predicted dependence of specific filtration resistance on initial supersaturation and for the continuously precipitated Al(OH)3 the relation between the specific filtration resistance and the mean residence time of suspension in the reactor. Dependences were also recorded between the bed porosity and concentration of precipitated solutions, specific filtration resistance and used filtration pressure and the effect of aging of the batchwise precipitated suspension of Mg(OH)2on its filtration properties. The used CST method for determination of filtration characteristics of Zn(OH)2 suspension was also studied.

Determination of an impulsive diffusion operator from interior spectral data

Analysis ◽  
2020 ◽  
Vol 40 (1) ◽  
pp. 39-45
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Potential Functions ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Impulsive Diffusion

AbstractIn the present work, the interior spectral data is used to investigate the inverse problem for a diffusion operator with an impulse on the half line. We show that the potential functions {q_{0}(x)} and {q_{1}(x)} can be uniquely established by taking a set of values of the eigenfunctions at some internal point and one spectrum.

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