Subsurface Flow Module

Slow Flow in Porous Media

Darcy’s law describes fluid movement through interstices in a fully saturated porous medium that is driven by a pressure gradient, and the transport of momentum due to shear stresses in the fluid is negligible. The Darcy’s Law interface computes the pressure, and the velocity field is then determined by the pressure gradient, fluid viscosity, and permeability.

Variably Saturated Porous Media Flow

Richards' equation describes fluid flow through a partially saturated porous medium, accounting for the changes in hydraulic properties as the fluid fills some pores and drains from others. The Richards' Equation interface includes built-in fluid retention models to select from, such as the van Genuchten or Brooks–Corey models. Similar to the Darcy’s Law interface, only the pressure is computed. Richards' equation is nonlinear due to the fact that the hydraulic properties vary based on saturation.

Heat Transfer in Porous Media

Heat transfer in porous media occurs through conduction, convection, and dispersion. Dispersion is caused by the tortuous path of the liquid in the porous medium and is described by including additional effects beyond that of mean convection. In many cases, the solid phase can be made up of multiple materials with differing conductivity, and there can also be a number of differing fluids. The Heat Transfer in Porous Media interface automatically accounts for these factors, and mixing rules are provided for calculating the effective heat transfer properties.

The fluid inside the pore space can also undergo one or more phase transitions, which is of interest when modeling the process of freezing soil. A specialized Phase Change Material feature enables you to model this and similar processes by specifying two materials and the phase change properties (phase change temperature, transition interval, and latent heat).

Laminar and Creeping Flow

For maximum flexibility, the Subsurface Flow Module includes the ability to simulate flow in free media as well as porous media. Modeling transient and steady flows at relatively low Reynolds numbers is possible with the Laminar Flow and Creeping Flow interfaces. A fluid viscosity may be dependent on the local composition and temperature or any other field that is modeled in combination with fluid flow.

Poroelasticity

Compaction and swelling can be modeled with a dedicated physics interface for poroelasticity, which combines a transient formulation of Darcy’s law with a linear elastic material model of the porous matrix. The fluid flow affects the compressibility of the porous medium, and changes in volumetric strains will in turn affect the mass transport. To enable these effects, the Poroelasticity multiphysics interface includes an expression of the stress tensor, as a function of the volumetric strain, and the Biot–Willis coefficient.

Fast Flow in Porous Media

The Brinkman equations account for fast-moving fluids in porous media, with the kinetic potential from fluid velocity, pressure, and gravity driving the flow. The Brinkman Equations interface generalizes Darcy’s law to compute the dissipation of the kinetic energy by viscous shear, similar to the Navier–Stokes equations. Additionally, with the CFD Module, you can combine fast flow in porous media with turbulent flow.

Non-Darcian Flow

Darcy's law and Brinkman's correction to Darcy's law only apply when the interstitial velocity in the pores is low enough that the creeping flow approximation holds. For higher interstitial velocities, an additional nonlinear correction can be included in the momentum equation. There are multiple permeability models available in the Subsurface Flow Module for modeling non-Darcian flow in porous media: The Brinkman Equations interface includes the Forchheimer and Ergun models, and the Darcy's Law and Multiphase Flow in Porous Media interfaces include the Forchheimer, Ergun, Burke–Plummer, and Klinkenberg models.

Fracture Flow

Fractures within a porous medium affect the flow properties through the porous matrix. The Fracture Flow interface solves for pressure on internal (2D) boundaries within a 3D matrix, based on a user-defined aperture. The computed pressure is automatically coupled with the physics that describes the porous media flow in the surrounding matrix — an approximation that saves time and computational resources involved in meshing the fractures.

Multiphase Flow in Porous Media

Functionality for phase transport can be combined with the Darcy's Law interface to simulate multiphase flow in porous media with an arbitrary number of phases. Users can specify porous media properties such as relative permeabilities and capillary pressures between phases. These properties are passed between phases with a multiphysics coupling that connects the Phase Transport in Porous Media interface with the Darcy's Law interface.

Transport of Chemical Species in Porous Media and Fractures

The COMSOL Multiphysics^® simulation software provides intuitive-to-use features for defining material transport in dilute solutions or mixtures through convection, diffusion, dispersion, adsorption, and volatilization of an arbitrary number of chemical species. These features can easily be connected to definitions of reversible, irreversible, and equilibrium reaction kinetics by combining the Subsurface Flow Module with the Chemical Reaction Engineering Module. With the Subsurface Flow Module, this functionality can be extended to porous media and fractures.