Abstract

For deep bed filtration equations, exact solutions are constructed that describe typical laboratory experiments: injection of a suspension into a porous sample. In the case of kinetic equation with an arbitrary dependence of the clogging rate on the retention (the volume of deposited particles per unit filter volume), the solution is obtained in quadratures. In the special case of linear dependence of the clogging rate on the retained particles volume, an analytical solution is given. For the axisymmetric flows of suspensions (injection into a porous bed through a well), the solution is provided in terms of the solution to a system of ordinary differential equations.

中文翻译：

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低浓度悬浮液深床过滤问题的精确解

摘要

对于深床过滤方程式，可以构建描述典型实验室实验的精确解决方案：将悬浮液注入多孔样品中。在动力学方程式中，堵塞率与保留率（每单位过滤器体积的沉积颗粒量）具有任意依赖性时，以正交方式获得溶液。在堵塞率与保留颗粒体积呈线性关系的特殊情况下，给出了一种分析解决方案。对于悬浮液的轴对称流（通过井注入多孔床中），根据解将其提供给常微分方程组。