MATHEMATICAL MODELS OF GEOFILTRRATION AND GEOMIGRATION IN POROUS MEDIA WITH FRACTAL STRUCTURE

2020 ◽  
Vol 6 (3) ◽  
pp. 21-27
Author(s):  
R.A. Yusupov ◽  
◽  
Sh.S. Axrolov ◽  
N.M. Mirzanova ◽  
A.N. Nasiriddinov ◽  
...  

In this study 2-D linear models are coming from generalised, Boussinesq eqution describing geofiltration in soils with fractal structures are presented. In this study are presented too mathematical models geomigration of contaminations with groundwater in classical way and in soils with fractal structures.

2020 ◽  
Vol 5 (3) ◽  
pp. 39-45
Author(s):  
R.A. Yusupov ◽  
◽  
Sh.S. Axrolov ◽  
N.M. Mirzanova ◽  
A.N. Nasiriddinov

In this study 2-D linear models are coming from generalised, Boussinesq eqution describing geofiltration in soils with fractal structures are presented. In this study are presented too mathematical models geomigration of contaminations with groundwater in classical way and in soils with fractal structures


2020 ◽  
Vol 4 (1) ◽  
pp. 40-46
Author(s):  
R. A. Yusupov ◽  
◽  
S. Axrolov ◽  
N. M. Mirzanova ◽  
A. N. Nasiriddinov ◽  
...  

In this study 2-D linear models are coming from generalised, Boussinesq eqution describing geofiltration in soils with fractal structures are presented. In this study are presented too mathematical models geomigration of contaminations with groundwater in classical way and in soils with fractal structures


1988 ◽  
Vol 127 ◽  
Author(s):  
P. J. Bourke ◽  
D. Gilling ◽  
N. L. Jefferies ◽  
D. A. Lever ◽  
T. R. Lineham

ABSTRACTAqueous phase mass transfer through the rocks surrounding a radioactive waste repository will take place by diffusion and convection. This paper presents a comprehensive set of measurements of the mass transfer characteristics for a single, naturally occurring, clay. These data have been compared with the results predicted by mathematical models of mass transport in porous media, in order to build confidence in these models.


2014 ◽  
Vol 68 (6) ◽  
pp. 781-791 ◽  
Author(s):  
Radivoj Petronijevic ◽  
Vesna Matekalo-Sverak ◽  
Aurelija Spiric ◽  
Ilija Vukovic ◽  
Jelena Babic ◽  
...  

The aim of this research was to develop a novel colorimetric method based on mathematical models, by multiple linear regression (MLR), from the CIE L*a*b* measurements and data of the HPLC determination of food colorants. Calibration set of 10 production batches of finely grinded cooked sausage with food colorants added was manufactured in industrial conditions as follows: one control batch and 9 products with various quantities of added food colorants: E120 (3.4, 7.5 and 12.5 mg/kg), E 124 (5.0, 15.0, 25.0 mg/kg) and E 129 (5.0, 15.0, 25.0 mg/kg). The estimation of the added food colorants was assessed by measuring L*, a*, b* parameters of cross-section. The quantification of food colorants was achieved by HPLC-PDA. Food colorants were extracted from meat products using Accelerated Solvent Extraction (ASE). Quantification of food colorants was achieved in the range from 1 to 100 mg / kg, and recovery values were from 76.15% to 107.04%, for E 120, from 97.61% to 101.03%, for E 124 and from 99.91% to 101.67%, for E 129. Correlation of the results obtained using HPLC and colorimetric measuring data was assessed by Multiple Linear Regression (MLR). The results from colorimetric and chromatographic determinations in four experimental batches (three batches with different quantities of food colorants and one control batch) were used for calibration. Coefficients of determination (R2) for linear models in experimental batches were 0.954, for E 124, 0.987, for E 120 and 0.993, for E 129. Correlation functions of food colorant quantities and corresponding L*a*b* values were established. The obtained mathematical models were tested for the estimation of the content of dyes in 21 samples of finely grinded cooked sausages purchased in retail stores. Food colorants were confirmed in 20 samples (95.24 %), and one sample (4.76 %) did not contain any of these compounds. Out of the positive samples, sixteen samples (80.00 %) contained E 120, while four samples (20.00 %) contained E 129. Food colorant E124 was not established in any of the analyzed samples. Colorimetric CIE L*a*b* method might be used during sensory evaluation of meat products for the assessment of the added food colorants.


2021 ◽  
Author(s):  
Qili Wang ◽  
Jiarui Sun ◽  
Yuehu Chen ◽  
Yuyan Qian ◽  
Shengcheng Fei ◽  
...  

Abstract In order to distinguish the difference in the heterogeneous fractal structure of porous graphite used for filtration and impregnation, the fractal dimensions obtained through the mercury intrusion porosimetry (MIP) along with the fractal theory were used to calculate the volumetric FD of the graphite samples. The FD expression of the tortuosity along with all parameters from MIP test was optimized to simplify the calculation. In addition, the percolation evolution process of mercury in the porous media was analyzed in combination with the experimental data. As indicated in the analysis, the FDs in the backbone formation regions of sample vary from 2.695 to 2.984, with 2.923 to 2.991 in the percolation regions and 1.224 to 1.544 in the tortuosity. According to the MIP test, the mercury distribution in porous graphite manifested a transitional process from local aggregation, gradual expansion, and infinite cluster connection to global connection.


Author(s):  
Alla A. Mussina

The article defines the basic concepts of filtration theory and provides an overview of the existing mathematical models of inhomogeneous liquids in porous media. The paper considers the Stefan problem. The number of scientific papers devoted to the study of porous structures has recently increased. This is primarily due to the fact that the prob-lems of oil and uranium production have been identified, and the solution of environmental problems is overdue. Therefore, a new device is needed to develop models of liquid filtration. With the advent and development of computer technology, it has become easier to solve problems that require numerical methods for their solution. Understanding the movement of fluids and the mechanism of dissolution of rocks under the action of acids in heterogeneous porous media is of great importance for the extraction and production of oil and the effective management of these processes. The article examines the mathematical model of the theory of isothermal filtration. Possible variants of the solva-bility of the model are shown. The research scheme consists of the output of a mathematical model, the formulation of the problem, one variant of the solution of the problem, the algorithm of the numerical method of solving the problem.


2014 ◽  
Vol 977 ◽  
pp. 399-403
Author(s):  
Jia Hang Wang ◽  
Lei Wang ◽  
Duo Kai Zhou

Dimensionless mathematical models of the fluid flow in the semi-infinite long porous media with constant production pressure on the inner boundary conditions are built, which include the effect of threshold pressure gradient (TPG). The analytical solutions of these dimensionless mathematical models are derived through new definitions of dimensionless variables. Comparison curves of the dimensionless moving boundary under different values of dimensionless TPG are plotted from the proposed analytical solutions. For the case of constant production pressure, a maximum moving boundary exists, beyond which the fluid flow will not occur. The value of maximum boundary distance decreases with increasing TPG. However, the velocity of pressure propagation decreases with time. The larger the TPG is, the steeper the curve of pressure depression cone is and the shorter the distance of the pressure propagation is.


Author(s):  
M. V. Budyansky ◽  
S. V. Prants

We investigate typical mixing and fractal properties of chaotic scattering of passive particles in open hydrodynamic flows taking as an example a model two-dimensional incompressible flow composed of a fixed point vortex and a background current with a periodic component, the model inspired by the phenomenon of topographic eddies over mountains in the ocean and atmosphere. We have found, described and visualized a non-attracting invariant chaotic set defining chaotic scattering, fractality, and trapping of incoming particles. Geometry and topology of chaotic scattering have been studied and visualized. Scattering functions in the mixing zone have been found to have a fractal structure with a complicated hierarchy that has been described in terms of strophes and epistrophes. Mixing, trapping, and fractal properties of passive particles have been studied under the influence of a white noise with different amplitudes and frequency ranges. A new effect of clustering the particles in a noised flow has been demonstrated in numerical experiments.


Author(s):  
Jinya Liu ◽  
Vijaya Chalivendra ◽  
Charles L. Goldsmith ◽  
Wenzhen Huang

Regular-fractal topography on RF-switch MEMS surface is reported over different scale ranges. Surface topography is crucial in understanding underling physics associated with the surface contacts, switch working performance, and reliability. The complexity of these structures requires new techniques to characterize topography and then replicate the multi-scale regular-fractal structure for analysis. Topography on RF-switch contacting surfaces are scanned by atomic force microscopy (AFM) at different length scales (e.g. 1×1, 10×10 and 60×60 μm2). A sample allocation plan is designed to maximize the spatial representative of the AFM scanning patches with different resolutions and uniformly distributed sample patches. The scanning data are used for characterizing and model estimation. Hexagonal patterns are found on at coarser scales (e.g. 10×10 and 60×60 μm2). They were formed by the remnant (polymer) of etching process. Random irregularity is observed and the fractal structure at finer scales (e.g. 1×1 μm2) is identified. A regular-fractal model is proposed to decompose and characterize the regular and fractal structures with two model components: one for the regular geometric pattern and the other for fractal irregularity. The former uses a 2D cosine functions to characterize dominant modes in the regular (larger scale) patterns. The later summarizes random irregularity in finer scales with a statistical fractal model estimated from the data on the scattered sample patches. The model validation is made through the comparisons of topography and conventional roughness parameters between the results of simulation from the proposed model and that derived from AFM scanned data.


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