# Model Mass, Momentum, and Energy Transport in Porous Media with the Porous Media Flow Module

## Optimize a Variety of Industrial Processes

Analyze and optimize processes found in the pharmaceutical, biomedical, food, and other industries with the Porous Media Flow Module, an add-on to the COMSOL Multiphysics® software. Model transport phenomena in porous media using Darcy's law, including variably saturated porous media flow. More advanced models include fast flow with the Brinkman equations, multiphase transport, fracture flow, or non-Darcian flow. For the most realistic and accurate models, multiphysics capabilities include nonisothermal flows in porous media, effective properties for multicomponent systems, poroelasticity, and transport of moisture and chemical species.

## What You Can Model with the Porous Media Flow Module

Agricultural, chemical, civil, and nuclear engineers and scientists all need to simulate different types of processes in porous media, which is why the Porous Media Flow Module provides a comprehensive set of modeling tools in this area. These tools are packaged into physics interfaces, which automatically set up and solve the equations specific to the type of physics you are modeling.

### Slow Flow in Porous Media

Darcy’s law describes fluid movement through interstices in a fully saturated porous medium that is mainly 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 pressure, and the velocity field is then determined by the pressure gradient, fluid viscosity, and permeability.

### 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.

### Variably Saturated Porous Media Flow

Richards' equation describes the movement of water in partially saturated porous media, accounting for the changes in hydraulic properties as fluids move through the porous medium, filling some pores and draining 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 media effect 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.

### Heat and Moisture Transport

Thermal and moisture management in paper, wood, and other porous materials is vital to the design of building components and consumer packaging. The Laminar 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.

### 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 a built-in multiphysics interface (of the same name), which implements separate equations for the fluid and porous matrix temperature fields with a coupling to account for the heat transfer at the fluid–solid interface in pores.

### 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.

### 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. The Darcy's Law and Brinkman Equations interfaces include non-Darcian options for the permeability model, the Forchheimer and Ergun models for the Brinkman Equations interface, and the Forchheimer, Ergun, Burke–Plummer, and Klinkenberg models for the Darcy's Law and Multiphase Flow in Porous Media interfaces.

### 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, while changes in volumetric strains will in turn affect the momentum, material, and heat transport. To employ 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.

### 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.

When combined with the CFD 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.

### 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, adsorption, and volatilization of an arbitrary number of chemical species. These are easily connected to definitions of reversible, irreversible, and equilibrium reaction kinetics. With the Porous Media Flow Module, you are able to extend this functionality to porous media and fractures.

Every business and every simulation need is different.

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