Abstract
The article is devoted to the determination of the parameters of impurity transport in a porous medium, the hydrodynamic resistance of which changes due to the settling of impurity particles on the pore walls (blockages). In most cases, experimental measurement of the parameters of such transport is not possible. When finding such parameters for the transport model under study, the inverse problem can be solved. The inverse problem is solved, for a certain set of experimental data, which can be correlated with the results obtained in modeling, using the BFGS method in combination with the adjoint function method. This paper simulates the pumping of a fixed volume of impurities through a working area filled with a porous medium at a constant pressure drop at its ends. As an "experimental" data set, the flow rate and concentration of impurities at the exit from the working area, obtained for the investigated model with the given parameters, are taken. The main approach for describing such transport is the MIM (mobile / immobile media) approach, which consists in dividing the total concentration of an impurity into a concentration of mobile and nonmobile. For small impurity concentrations, a nonlinear MIM model can be applied, the kinetic equation of which contains the saturation concentration of the immobile component, upon reaching which the adsorption of particles stops. Blockage in the model is taken into account by a change in the permeability of a porous medium due to a change in its porosity, which in turn decreases linearly with an increase in the concentration of the immobile component. For the model under consideration, the inverse problem of finding a given set of parameters was solved. The results of the test operation of the algorithm for solving the inverse problem are presented. It is shown that the algorithm converges to the specified parameters in a small number of iterations. It is assumed that this algorithm will be used to process the experimental data with a cylindrical working area filled with glass granulate as a porous medium.
Highlights
Статья посвящена определению параметров транспорта примеси в пористой среде, гидродинамическое сопротивление которой меняется вследствие оседания частиц примеси на стенках пор
The article is devoted to the determination of the parameters of impurity transport in a porous medium, the hydrodynamic resistance of which changes due to the settling of impurity particles on the pore walls
The inverse problem is solved, for a certain set of experimental data, which can be correlated with the results obtained in modeling, using the BFGS method in combination with the adjoint function method
Summary
Работа посвящена определению параметров модели, описывающей транспорт примеси в пористой среде. Экспериментальная верификация модели, применяемой для описания транспорта примеси в пористой среде, осложнена тем, что экспериментальное измерение параметров транспорта, входящих в модель, либо затруднено, либо не является возможным. Последний класс методов является наиболее точным и быстросходящимся, однако существует проблема при вычислении градиента целевой функции в пространстве параметров модели. Не происходит механической закупорки пор, связанной с «затыканием» поры достаточно большой частицей или агломератом таких частиц), то уменьшение порового пространства приводит к снижению проницаемости среды. Закупорка становится заметной только при достаточно больших значениях концентрации примеси в немобильной фазе, что подразумевает использование нелинейной MIM модели с учетом насыщения неподвижной фазы [15]. Чтобы для переноса примеси течением в пористой среде определить параметры нелинейной MIM модели на основе экспериментальных данных
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