A Study of Free Boundary Problems of Fluid Flow in Porous Media by Mixed Methods
نویسندگان
چکیده
In this article, the ow of uids in porous media is studied as a free or moving boundary problem by the mixed method. In particular, a new weak formulation for the problem of seepage of uids through a porous media is discussed and analyzed mathematically and numerically. The new formulation is in a mixed form and is suitable for the use of mixed nite element methods in the numerical approximation. It is proved that the weak formulation and its nite element discretization has a solution which can be approximated by a sequence of regularized problems. 1. Introduction In this paper, we are concerned with the free or moving boundary value problem in the study of the ow of uids through a heterogeneous porous media. Such problems are important in many branches of science and engineering. For example, in the areas of soil science, agricultural engineering , and groundwater hydrology, the movement of uids and their dissolved components in both saturated and unsaturated soils is an important environmental consideration. In petroleum engineering, improved recovery of oil and gas is based on simulation of multiphase and multicomponent uid transport in deep rocks. In both application areas, mass transfer across phase boundaries is an important consideration which can be discussed in the context of free or moving boundary problems. Another important application of the free or moving boundary problem is water seepage through a dam, or rain water creeping through an unsatu-rated zone. The underlying physics of the petroleum and seepage problems are very similar. For comparison, assume that there are two uids owing simultaneously in the porous medium. In unsaturated ow, these uids are water and air, while in the petroleum problem, the uids are assumed to be water and oil. Relevant material properties, including the capillary pressure and relative permeability are assumed to be known. Free boundary problems are also seen in other areas of petroleum industry such as basin simulation. The research of basin simulation is important
منابع مشابه
Axisymmetric Magnetohydrodynamic Squeezing flow of Nanofluid in Porous Media under the influence of Slip Boundary Condition
The various industrial, biological and engineering applications of flow of squeezing flow of fluid between parallel plates have been the impetus for the continued interest and generation renewed interests on the subject. As a part of the renewed interests, this paper presents the study of axisymmetric magnetohydrodynamic squeezing flow of nanofluid in porous media under the influence of slip bo...
متن کاملFree connective flow of a micropolar fluid a long an elliptic cylinder in porous media using the thermal non-equilibrium model
متن کامل
Capillary Effects on Surface Enhancement in a Non-Homogeneous Fibrous Porous Medium
The evaluation of a free fluid surface in a porous medium has several mathematical applications that are important in industries using molds, particularly in the fluid injection process. The vacuum-assisted resin transfer molding (VARTM) process is a promising technology in the primary composite industry. An accurate computational simulation of the VARTM process would be a cost-effective tool i...
متن کاملExperimental Investigation of the Permeability and Inertial Effect on Fluid Flow through Homogeneous Porous Media
The value of the permeability in fluid flow through porous media is important for process investigation. In low Reynolds number, the classic Darcy’s law is suitable for simulation of fluid flow. In this paper, an experimental study for evaluation of preformed fiber permeability has been done. Also, the deviations from the classical Darcy law by experimental and numerical simulation of the N...
متن کاملImplementation of D3Q19 Lattice Boltzmann Method with a Curved Wall Boundary Condition for Simulation of Practical Flow Problems
In this paper, implementation of an extended form of a no-slip wall boundary condition is presented for the three-dimensional (3-D) lattice Boltzmann method (LBM) for solving the incompressible fluid flows with complex geometries. The boundary condition is based on the off-lattice scheme with a polynomial interpolation which is used to reconstruct the curved or irregular wall boundary on the ne...
متن کاملConjugate Heat Transfer of MHD non-Darcy Mixed Convection Flow of a Nanofluid over a Vertical Slender Hollow Cylinder Embedded in Porous Media
In this paper, conjugate heat transfer of magneto hydrodynamic mixed convection of nanofluid about a vertical slender hollow cylinder embedded in a porous medium with high porosity have been numerically studied. The Forchheimer’s modification of Darcy’s law was used in representing the nanofluid motion inside the porous media. The governing boundary layer equations were transformed to non-dimen...
متن کامل