A numerical study of fluids with pressure dependent viscosity flowing through a rigid porous media

نویسندگان

  • K. B. Nakshatrala
  • K. R. Rajagopal
چکیده

Abstract. Much of the work on flow through porous media, especially with regard to studies on the flow of oil, are based on “Darcy’s law” or modifications to it such as Darcy-Forchheimer or Brinkman models. While many theoretical and numerical studies concerning flow through porous media have taken into account the inhomogeneity and anisotropy of the porous solid, they have not taken into account the fact that the viscosity of the fluid and drag coefficient could depend on the pressure in applications such as enhanced oil recovery. Experiments clearly indicate that the viscosity varies exponentially with respect to the pressure and the viscosity can change, in some applications, by several orders of magnitude. The fact that the viscosity depends on pressure immediately implies that the “drag coefficient” would also depend on the pressure. In this paper we consider modifications to Darcy’s equation wherein the drag coefficient is a function of pressure, which is a realistic model for technological applications like enhanced oil recovery and geological carbon sequestration. We first outline the approximations behind Darcy’s equation and the modifications that we propose to Darcy’s equation, and derive the governing equations through a systematic approach using mixture theory. We then propose a stabilized mixed finite element formulation for the modified Darcy’s equation. To solve the resulting nonlinear equations we present a solution procedure based on the consistent Newton-Raphson method. We solve representative test problems to illustrate the performance of the proposed stabilized formulation. One of the objectives of this paper is also to show that the dependence of viscosity on the pressure can have a significant effect both on the qualitative and quantitative nature of the solution.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A numerical study of fluids with pressure dependent viscosity flowing through a rigid porous medium

Abstract. Much of the work on flow through porous media, especially with regard to studies on the flow of oil, are based on “Darcy’s law” or modifications to it such as Darcy-Forchheimer or Brinkman models. While many theoretical and numerical studies concerning flow through porous media have taken into account the inhomogeneity and anisotropy of the porous solid, they have not taken into accou...

متن کامل

Global Stability for Thermal Convection in a Couple Stress Fluid Saturating a Porous Medium with Temperature-Pressure Dependent Viscosity: Galerkin Method

A global nonlinear stability analysis is performed for a couple-stress fluid layer heated from below saturating a porous medium with temperature-pressure dependent viscosity for different conducting boundary systems. Here, the global nonlinear stability threshold for convection is exactly the same as the linear instability boundary. This optimal result is important because it shows that lineari...

متن کامل

On the determination of a generalized Darcy equation for yield-stress fluid in porous media using a Lattice-Boltzmann TRT scheme.

Simulating flow of a Bingham fluid in porous media still remains a challenging task as the yield stress may significantly alter the numerical stability and precision. We present a Lattice-Boltzmann TRT scheme that allows the resolution of this type of flow in stochastically reconstructed porous media. LB methods have an intrinsic error associated to the boundary conditions. Depending on the sch...

متن کامل

Mobility and Pore-Scale Fluid Dynamics of Rate-Dependent Yield-Stress Fluids Flowing through Fibrous Porous Media

The steady ow of viscoplastic uids through brous porous media is studied numerically and theoretically. We consider uids with a plastic yield stress and a rate-dependent viscosity that can be described by the HerschelBulkley model. We rst investigate the pore-scale ow characteristics through numerical simulations for ow transverse to a square array of bers with comprehensive parametric studies ...

متن کامل

Gas-liquid Relative Permeability Estimation in 2D Porous Media by Lattice Boltzmann Method: Low Viscosity Ratio 2D LBM Relative Permeability

This work is a primary achievement in studying the CO2 and N2–oil systems. To predict gas-liquid relative permeability curves, a Shan-Chen type multicomponent multiphase lattice Boltzmann model for two-phase flow through 2D porous media is developed. Periodic and bounce back boundary conditions are applied to the model with the Guo scheme for the external body force (i.e.,...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • CoRR

دوره abs/0907.5234  شماره 

صفحات  -

تاریخ انتشار 2009