Journal: Volume 21, No. 1, 2016
Pages: 12 – 19
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Mathematical model of rheology of fractal-heterogeneous multicomponent stratal systems

Serhii Polozhaenko, Hasan Muhialdin

Abstract

Filtration processes within the reservoir fluids are highly dependent on biological characteristics of the "skeleton" of porous medium. Qualitative specificity thus has the shape of the boundary (front) of the filter flow, depending on which areas may be formed with a "zero" speed of filtration – "stagnant" zones. One possible and efficient by examining complex filtration flows with substantial heterogeneity of their boundaries is the assumption of fractal structure of porous medium and heterogeneous structure of filtered liquid. In this paper, in contrast to the available studies carried out on the basis of field experiments, mathematical model of the rheology of fractal heterogeneous porous media is considered. This gives the opportunity for multivariate experiments without a rigid peg to the characteristics of porous medium. The condition of «smoothness» of the front of components division in multicomponent (heterogeneous) systems is investigated on the basis of the analysis of saturation «jump» in the function of Bacley-Leverett. It is shown that saturation «jump» is absent, and the front of division moves up steadily and saves «a smoothness», if the mobility of ousting component does not exceed the mobility of ousted one. It is also shown that the failure of «smoothness» of the front of division brings to fractalheterogeneous structure of rheology process. The numeral values of fractal dimension of the front of division are got for rheology process, developing in real geological terms. Mathematical model of fractal-heterogeneous multicomponent system in the class of variation inequalities is offered. Mathematical formalization of rheology process of multicomponent (heterogeneous) system in the form of variation inequalities allows to adequately describe the features of the test process, in particular, its one-sided ones

Keywords

multicomponent system, heterogeneous system, rheology process, fractalheterogeneous structure, fractal cluster, mathematical model, variation inequality

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Suggested citation

Polozhaenko, S., & Muhialdin, H. (2016). Mathematical model of rheology of fractal-heterogeneous multicomponent stratal systems. Bulletin of Cherkasy State Technological University, 21(1), 12-19.