Mathematical modeling of nonlinear displacement processes in oil LEF-layer by methods of complex analysis and summary representations
Journal Title: Геофизический журнал - Year 2019, Vol 41, Issue 2
Abstract
The approach to the modeling of nonlinear displacement processes (one and two-phase filtration) in heterogeneous oil deformable layers is developed, taking into account the inverse effect of the potential of the velocity field and the flow function on the conductivity of the medium. We constructed a method and computational technology for solving the corresponding boundary value problems for nonlinear-layered triple-connected curvilinear domains, bounded by equipotential lines and flow lines, on the basis of the synthesis of numerical methods of quasiconformal mappings and summary representations for differential equations with discontinuous coefficients in combination with domain decomposition by Schwartz method. Quasi-ideal processes in nonlinearly double-layered horizontal LEF-layers, whose geometry of heterogeneity zones is unknown in advance, is described by the corresponding boundary value problems obtained on the basis of the Darcy law and the continuity equation with the coefficient of layer permeability, which is given by a piecewise-constant function with ruptures along the searched equipotentials and lines of flow. The coefficient of conductivity the medium is given as a piecewise-constant function, that is dependent on the searched quasipotential and function of flow, with unknown line dividing layers (lines gap conductance coefficient) that is along the searched equipotential lines and flow lines and that is finding in the process of solving the problem. The proposed algorithms automatically solve the problem of choice of nodes and building a dynamic grid, finding of the unknown dividing lines of areas constancy coefficient of conductivity the medium, the calculation of the velocity field and calculate other characteristic parameters of the process. The decomposition of the domain on the layers of the constancy of permeability coefficient allows us to solve problems in more «comfortable» subdomain than the original problem the whole domain, and allows make in parallel the computational process, since calculations in the subdomain at each iterative step are independent of each other and can be done in parallel with the use of modern computer technology.
Authors and Affiliations
O. М. Hladka
Keywords
Related Articles
- EP ID EP526278
- DOI 10.24028/gzh.0203-3100.v41i2.2019.164465
- Views 57
- Downloads 0
Occurrence of metal iron inside the planets
Comparison of thermomagnetic and microprobe data on metal iron in terrestrial rocks (xeno- lithes, Siberian trap and oceanic basalt) has been conducted with the data on extraterrestrial metal iron (in sediments, lunar ba...
Analysis of results of interpretation of elastic parameters of solid core of the Earth from the standpoint of current geomechanics
It follows from the basic principles of mechanics of deformable solids relating to the strength, stability and propagation of elastic waves that the inner core of the Earth cannot exist in the form of a spherical structu...
Definition of the death of seismic events by using digital channel data of the Main center of special control and foreign seismic stations
Among the main parameters of the source of the seismic event, the depth of the hypocentre is of greatest interest, which, as a rule, is determined with the least accuracy. The knowledge of the exact spatial position of t...
Influence of resonance and nonlinear properties of soils on seismic hazards of construction areas
The article discusses the need to take into account the resonance and nonlinear phenomena in soils for the seismic micro zoning of building and operating sites. Resonance and nonlinear phe¬nomena are closely related to e...
Modern gravimeters of aviation gravimetric system
The expediency of using aviation gravimetric systems for gravimetric measurements and receiving information about the Earth's gravitational field is proved. An analysis of existing gravimeters of aviation gravimetric sys...