Mathematical modeling of filtration consolidation with salt transfer in a double-relaxation system
- PDF / 107,084 Bytes
- 9 Pages / 595 x 842 pts (A4) Page_size
- 44 Downloads / 167 Views
MATHEMATICAL MODELING OF FILTRATION CONSOLIDATION WITH SALT TRANSFER IN A DOUBLE-RELAXATION SYSTEM
UDC 517.954:532.546
V. M. Bulavatskii
A mathematical model of the filtration consolidation of porous media saturated with saline solutions is developed. The filtration process is relaxed and occurs in a relaxation-compressible medium. A corresponding boundary-value problem is formulated. Asymptotic approximations of the solutions are found and an algorithm for numerical modeling of the process is proposed. Keywords: mathematical modeling, filtration consolidation, mass transfer, relaxation, nonclassical models, systems of partial differential equations, boundary-value problems, asymptotic approximations, numerical solutions. INTRODUCTION Studying filtration consolidation in deformed saturated porous media is important due to its applications in various scientific and technical domains, in particular, in determining deformations of cores and screens of earthfill dams, stability of earthwork slopes, in hydraulic, road, industrial, and civil engineering, etc. [1–3]. An analysis of the consolidation of bases of surface industrial and household sewage ponds is important because of environmental protection problems [4, 5]. These sewage ponds are often filled with industrial waste products that are concentrated saline solutions; therefore, the dynamics of consolidation of bases of these sewage ponds cannot be analyzed using the classical theory of filtration consolidation, which is based on the assumption that the filtrate in the soil mass is pure water [1–3], and it is necessary to account for saline mass transfer during the filtration of a pore solution [4–6]. During deformation, the “pore medium–saline solution” system is too complicated to be described mathematically in view of the variety of factors that influence the dynamics of consolidation. Therefore, according to the requirements of systems analysis, when constructing a mathematical model, we will take into account only the interactions and parameters that are of paramount importance for filtration consolidation in a double-relaxation system: relaxation filtration of a pore fluid in a deformed relaxation-compressible medium. Note that a mathematical model describing the consolidation of a deformable porous soil mass saturated with saline solution and considering that the filtration process alone is relaxational was studied in [7]. In the model proposed below, we additionally consider that consolidation may occur in a relaxation-compressible porous medium, which is especially important in case of sharp and considerable changes of pressure (explosions and rock bumps) since the change in porosity would be of strongly pronounced relaxation nature in this case [8]. We will use this model below to formulate a boundary-value problem to describe the consolidation (in view of the above factors) of a salt-saturated soil mass on an impermeable bed and present the results of asymptotic analysis in the case of a weakly relaxation-compressible medium. In the general case (rel
Data Loading...
