TWO PHASE MIXTURE FILTRATION

This study describes new theory about filtrating of two-phase mixture passing through porous media. As a base of the two-fluid model of the two-phase flow and accepting the porous material as a media with increased resistance. The mathematical model is numerically solved using the appropriate descretization method. Some preliminary results from the numerical solution are presented – gas and admixture velocities distribution in longitudinal direction as a function of filtrating layer thickness.


INTRODUCTION
The two fluid model of the two phase flow is here could not be applied.
The first limitation means that pressure and viscous stresses are missing. However the admixture phase possesses the tensor of the turbulent stresses, respectively it has own turbulence because the turbulence is not a flow characteristic but of its behavior.
For all parameters here with subscript " " are noted the gas phase parameters, and with " " -the admixture phase parameters.
The Reynolds number ( ) also shows the impact of the relative velocity between two phases -, and also the viscosity of the carrying media.
The loss coefficient of the porous media layer after passing the solid media could be expressed as follow: (4) or based on the volume concentration : where , and are correction functions giving the impact of the respect parameters.
The polynomial expression here is proposed for function commonly used for porous layer resistance calculations.
According [3] for the friction drag coefficient of the spherical particle the following values for the independent parameters could be accepted as , , , . Therefore for we have the expression: Referring to the mass concentration the where: ho is layer thickness, -resistance coefficient for unit of thickness: where: , In relations (13) and are given with: ; The proposed correction functions (7 10 or to be avoided any kind of uncertainty for relation (17) could also be accepted: where uncertainty factor that the particle could pass through the porous media without to be kept on the entrance level.
The solid particles going through the porous media are kept from the filtrating material, and deposited. Over the time the characteristics of the media have been changed, and its porosity decreasing as a result of pore slogging. As a result the resistance coefficient has been increased over the time.
The flow rate could be calculated as number of particles to be multiplied by their volume in the porous material: (20) where: number of particles is: , -mass rate is identified with incoming mass for unit time; .
-is number of particles for unit time.
The time needed for filling-up the given volume from the porous media is calculating as follow: Trang 9 As well as the loss coefficient of the admixture phase is derivative of the last one will increase when increasing.

MATHEMATICAL MODEL
Two phase stationary turbulent flow passing over porous media is describing with Euler's type equations concerning the resistance media.
Two-fluid scheme of the flow here is accepted.
It is accepted also that two-phase flow reaching porous media as a two separate jets either with flat or symmetric initial cross section. In order to be used one system differential equation for both phases an index " " here is accepted.  Table 1.
The value of is based on numerical experiment for the flow where the generation ( ) and turbulent dissipation energy are equal.
where are reduced variables and parameters with meanings shown in Table 2.

NUMERICAL SOLUTION RESULTS
The presented mathematical model, which describes the filtration process of two-phase mixture is numerically solved by using the appropriate Duffort-Frankel discretization scheme. The scheme of discretization is If the filtrating layer thickness is higher than the "holding", from the figure is obvious that velocity profile is not changing significantly which means that increasing of the thickness above the "holding" does not influence under filtration process.