Porous Media Flow Module

Slow Flow in Porous Media

Darcy’s law describes fluid movement driven by a pressure gradient through interstices in a fully saturated porous medium, where 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. The Layered Darcy’s Law interface can be used for simulating fluid flow through interstices in layered porous media, such as paperboard, composites, or plywood.

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, which can make it challenging to solve without computational software.

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 to the physics describing 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 to the Darcy's Law interface.

Poroelasticity

Compaction and swelling of porous media can be modeled with a dedicated multiphysics coupling for Poroelasticity. This bidirectional coupling links the deformation of the porous matrix to the pressurization of the pore fluid, while fluid flow affects the volumetric strain, causing swelling or shrinkage. Two formulations are available: the Biot formulation, which is suitable for most geotechnical applications where the compressibility of both the solid and the fluid needs to be accounted for, and the biphasic formulation, which is relevant for soft porous materials, like biological tissues and hydrogels where the solid and fluid constituents can be assumed as materially incompressible.

By combining the Porous Media Flow Module with the Structural Mechanics Module or the Composite Materials Module, more advanced functionality for poroelasticity becomes available. When combined with the Structural Mechanics Module, the Unsaturated Poroelasticity multiphysics interface facilitates modeling moisture transport, swelling, and shrinkage in anisotropic porous materials. When combined with the Composite Materials Module, the Poroelasticity, Layered Shell multiphysics interface is available, which enables the modeling of multilayered domains (paperboards, composites, etc.) that have different material properties per layer.

Transport of Chemical Species in Porous Media and Fractures

The COMSOL Multiphysics^® simulation software contains intuitive functionality for defining material transport in dilute solutions or mixtures through convection, diffusion, dispersion, adsorption, and volatilization of an arbitrary number of chemical species. These are easily connected to definitions of reversible, irreversible, and equilibrium reaction kinetics by combining the Porous Media Flow Module with the Chemical Reaction Engineering Module. With the Porous Media Flow Module, you are able to extend this functionality to porous media and fractures.

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.

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 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.

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, which would not be described if only the mean convective term was taken into account. 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.

To model local thermal nonequilibrium, you can use built-in technology that couples separate equations for the fluid and porous matrix temperature fields to account for the heat transfer at the fluid–solid interface in pores.

Heat and Moisture Transport

Heat and moisture management in paper, wood, and other porous materials is vital to the design of building components and consumer packaging. The Heat and Moisture Flow multiphysics interface is used to simulate heat transfer and moisture transport where fluid properties may depend on vapor concentration.

Additionally, there are tools to analyze water condensation and evaporation on surfaces, as well as specialized features for analyzing heat and moisture storage, latent heat effects, as well as diffusion and transport of moisture.

Laminar and Creeping Flow

For maximum flexibility, the Porous Media 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.

Advanced Free Flow Options

When combining the Porous Media Flow Module with the CFD Module or Polymer Flow Module, it is possible to include non-Newtonian fluids, such as Power Law, Carreau, and Bingham. In general, density, viscosity, and momentum sources can be arbitrary functions of temperature, composition, shear rate, and any other dependent variable, as well as derivatives of dependent variables.

Additionally, with the CFD Module, you can combine fast flow in porous media with free turbulent flow.