Porous Media Flow Module Interfaces
The Porous Media Flow Module contains a number of physics interfaces that predefine equations or sets of equations adapted to mass, momentum, and energy transport in porous media. You can take the equations in these physics interfaces and their variables and then modify them, link them together, and couple them to physics interfaces represented elsewhere in COMSOL Multiphysics.
The physics interfaces are based on the laws for conservation of mass, momentum, and energy in porous media. The flow models contain different combinations and formulations of the conservation laws that apply to the physics of the fields. These laws of physics are translated into partial differential equations and are solved together with the specified initial and boundary conditions.
A physics interface defines a number of features. These features are used to specify the fluid properties, initial conditions, boundary conditions, and possible constraints. Each feature represents an operation describing a term or condition in the conservation equations. Such a term or condition can be defined on a geometric entity of the component, such as a domain, boundary, edge (for 3D components), or point.
Another useful tool in these physics interfaces is the ability to describe material properties such as density and viscosity by entering expressions that describe them as a function of other parameters, such as species concentration, pressure, or temperature. Many materials in the material libraries use temperature- and pressure-dependent property values.
Figure 1 shows the group of physics interfaces available with this module in addition to the COMSOL Multiphysics basic license. Use these interfaces to model chemical species transport, fluid flow, heat transfer and solid mechanics, to make modeling easier, something that is briefly discussed next. See also Physics Interface Guide by Space Dimension and Study Type.
Figure 1: The physics interfaces for the Porous Media Flow Module as shown in the Model Wizard for a 3D application.
The module handles time-dependent and stationary problems for 1D, 2D, and 3D geometries with axisymmetry for 1D and 2D. The predefined physics interfaces cover four main categories: Chemical Species Transport (), Fluid Flow (), Heat Transfer (), and Structural Mechanics (), as discussed in the next pages.
Chemical Reaction and Mass Transport
The Transport of Diluted Species interface () simulates chemical species transport through convection (when coupled to fluid flow), diffusion, and reactions, for mixtures where one component, a solvent, is present in excess.
The Transport of Diluted Species in Porous Media interface () is tailored to model solute transport in saturated and partially saturated porous media. This physics interface characterizes the rate and transport of individual or multiple and interacting chemical species for systems containing fluids, solids, and gases. The equations supply predefined options to describe mass transfer by convection, adsorption, dispersion, diffusion, volatilization, and reactions. You define the convective velocity from either of the included physics interfaces, or you set it to a predefined velocity profile.
The Laminar Flow, Diluted Species interface () under the Reacting Flow branch combines the functionality of the Single-Phase Flow and Transport of Diluted Species interfaces. This multiphysics interface is primarily applied to model flow at low to intermediate Reynolds numbers in situations where the mass transport and flow fields are coupled.
The Transport of Diluted Species interface () under the Reacting Flow in Porous Media branch combines the Brinkman Equations and the Transport of Diluted Species in Porous Media interfaces. This multiphysics interface is primarily applied to model the transport of diluted reacting mixtures in porous media.
The Transport of Diluted Species in Fractures interface () is used to model the transport of a solutes along thin porous fractures, taking into account diffusion, dispersion, convection, and chemical reactions. The fractures are defined by boundaries in 2D and 3D, and the solutes are diluted in a solvent. The mass transport equation solved along the fractures is the tangential differential form of the convection–diffusion–reaction equation. Different effective diffusivity models are available.
The Moisture Transport in Air interface () is used to compute the relative humidity distribution in air. It simulates moisture transport by vapor convection and diffusion in moist air and the evaporation or condensation on walls.
The Equilibrium Moisture Transport in Porous Media interface () is used to compute the relative humidity field in porous media. It simulates moisture transport by vapor convection and diffusion in the gas phase, liquid water transport by convection and capillarity in the pores of the media. A Hygroscopic Porous Medium feature with an equilibrium formulation is active by default on all domains.
The Nonequilibrium Moisture Transport in Porous Media interface () is used to compute the relative humidity and liquid water saturation fields in porous media. It simulates moisture transport by vapor convection and diffusion in the gas phase, liquid water transport by convection and capillarity in the pores of the media. A Hygroscopic Porous Medium feature with a nonequilibrium formulation is active by default on all domains.
The Moisture Transport in Building Materials interface () is used to compute the relative humidity field in building materials. It simulates moisture transport by taking into account moisture storage, liquid transport by capillary suction forces.
The Moisture Transport in Free and Porous Media interface () is used to compute the relative humidity field in all domains, and additionally the liquid water saturation in porous media. It simulates moisture transport by vapor convection and diffusion in the gas phase, liquid water transport by convection and capillarity in the pores of the media. A Moist Air feature is active by default on all domains, and a Hygroscopic porous Medium is added by default with no selection. This interface handles all types of interface between free and porous media, and between two porous media.
The Moisture Transport in Solids interface () is used to compute the relative humidity and moist air pressure in porous media. It simulates moisture transport by vapor convection and diffusion in the gas phase and liquid water transport by convection and capillarity in the pores of the medium.
The Laminar Flow interface () under the Moisture Flow branch combines all features from the Moisture Transport in Air and Single-Phase Flow interfaces. The Moisture Flow multiphysics coupling is automatically added. The fluid properties may depend on vapor concentration. The physics interface supports low Mach numbers (typically less than 0.3). Similarly to Conjugate Heat Transfer coupling, the moisture transport interface can be coupled with additional turbulence models for the free flow with the use of the CFD Module.
The Porous Media Flow interface () under the Moisture Flow branch combines all features from the Equilibrium Moisture Transport in Porous Media and Brinkman Equations interfaces. The Moisture Flow multiphysics coupling is automatically added. The transport properties can depend on vapor concentration in air. Models can also include moisture transport in building materials.
Fluid Flow
Flow in porous media normally occur at low Reynolds numbers. The Reynolds number (Re) is a measure of the ratio of the fluid viscous to the inertial forces acting on the fluid and is given by: Re=ρUL/μ, where ρ is the fluid density, U is a characteristic velocity, L is a characteristic length scale, and μ is the dynamic viscosity.
The Creeping Flow interface () approximates the Navier–Stokes equations for the case when the Reynolds number is significantly less than 1. This is often referred to as Stokes flow and it is appropriate for use when viscous flow is dominant.
The Laminar Flow interface () describes fluid motion when turbulences are not present, and the Reynolds number is less than approximately 1000. The physics interface solves the Navier–Stokes equations for incompressible, weakly compressible, or compressible flows where the Mach number (Ma) is less than 0.3.
The Two-Phase Flow, Level Set interfaces () under the Multiphase Flow branch are used to model two fluids separated by a fluid-fluid interface in a free or a porous medium. The moving interface is tracked in detail using the level set method. The level set method solves additional equations to track the interface location.
The Phase Transport interface ()under the Multiphase Flow branch is used to simulate the transport of multiple immiscible phases in free flow. This interface solves for the averaged volume fractions of the phases.
The Phase Transport in Porous Media() interface is used to simulate the transport of multiple immiscible phases through a porous medium. This interface solves for the averaged volume fractions (also called saturations in a porous medium) of the phases.
The Phase Transport in Free and Porous Media Flow interface () can be used to model transport of an arbitrary number of phases in coupled free and porous media flow. An absolute pressure must be supplied in the porous region and a velocity must be supplied in the free-flow region. Both can be obtained from one of the momentum conservation interfaces or be specified manually.
Porous Media Flow
The Darcy’s Law interface () describes fluid movement through interstices in a porous medium. This physics interface can be used to model low velocity flows, for which the pressure gradient is the major driving force, and the flow is mostly influenced by the frictional resistance within the pores. Its use is within very low flows, or media where the permeability and porosity are very small. You can also set up multiple Darcy’s Law interfaces to model multiphase flows involving more than one mobile phase. The Darcy’s Law interface can also add non-Darcian effects such as Ergun or Forchheimer drag terms, which are important for Reynolds numbers bigger than 100.
The Fracture Flow interface () is a variant of Darcy’s law that defines the flow along interior boundaries representing fractures within a porous (or solid) medium.
The Richards’ Equation interface () analyzes flow in variably saturated porous media. With variably saturated flow, the permeability changes as fluids move through the medium, filling some pores and draining others. Richards’ equation appears similar to the saturated flow equation set out in Darcy’s Law, but it is notoriously nonlinear due to changes in material properties from unsaturated to saturated conditions. The analytic formulas of van Genuchten and Brooks and Corey are frequently employed with variably saturated flow modeling.
The Brinkman Equations interface () is used to model incompressible, weakly compressible, or compressible flows where the Mach number (Ma) is less than 0.3. You can select the Stokes-Brinkman flow feature to reduce the equations’ dependence on inertial effects, when the Reynolds number is significantly less than one. The Brinkman Equations interface extends Darcy’s law to describe the dissipation of the kinetic energy by viscous shear, similar to the Navier–Stokes equation. The Brinkman Equations interface can also add an Ergun or Forchheimer drag term, which are viscous drags proportional to the square of the velocity. These non-Darcian effects are important for Reynolds numbers bigger than 100.
The Multiphase Flow in Porous Media interface () combines the functionality of the Darcy’s Law and Phase Transport in Porous Media interfaces. This multiphysics interface is intended to model flow and transport of multiple immiscible phases in a porous medium.
The Free and Porous Media Flow, Brinkman interface () is useful for modeling problems where free flow is connected to porous media, such as in fixed-bed reactors and catalytic converters. The Free and Porous Media Flow, Brinkman interface is used over at least two different domains, a free channel and a porous medium. The physics interface adds functionality that allows the equations to be optimized according to the flow properties of the relevant domain. For example, you can select the Stokes-Brinkman flow feature to reduce the equations’ dependence on inertial effects in the porous domain, or just the Stokes’ flow feature to reduce the equations’ dependence on inertial effects in the free channel.
The Free and Porous Media Flow, Darcy interface () models porous media flow connected to free flow domains. This multiphysics interface couples the Laminar Flow interface with the Darcy’s Law interface over their common boundary.
As always, the physics interfaces give you direct access to defining, with either constants or expressions, the material properties that describe the porous media flow. This includes the density, dynamic viscosity, permeability, and porosity.
Heat Transfer
The Heat Transfer interfaces apply to systems consisting of solids, fluids, and fluid-solid mixtures, and are able to calculate effective properties for porous media consisting of several fluids, gases, and solid components, such as a rock formation with different mineral proportions.
The Heat Transfer in Solids interface () describes, by default, heat transfer by conduction. The physics interface is also able to account for the heat flux due to translation in solids as well as for solid deformation, including volume or surface changes.
The Heat Transfer in Fluids interface () accounts for conduction and convection in gases and liquids as the default heat transfer mechanisms. The coupling to the flow field in the convection term is automatically set when the Nonisothermal Flow multiphysics coupling is used. Otherwise, it may be entered manually in the physics interface, or it may be selected from a list that couples heat transfer to an existing fluid flow interface.
The Heat Transfer in Solids and Fluids interface () contains solids and fluids domains by default. It is aimed to simplify the setup of models where capabilities of Heat Transfer in Solids interface () and Heat Transfer in Fluids interface () are used, in particular in conjugate heat transfer applications.
The Conjugate Heat Transfer branch () combine features from the Heat Transfer and Single-Phase Flow interfaces to describe heat transfer in solids and fluids and nonisothermal flow in fluids. The heat transfer process is tightly coupled with the fluid flow problem via a predefined multiphysics coupling. Additional turbulence models for the free flow are available with the use of the CFD Module.
The Heat Transfer in Fractures interface () under the Thin Structures branch () describes heat transfer in fractures and thin porous media. It provides efficient models defined at the boundaries level representing thin three-dimensional domains. The simplest model assumes that the temperature changes through the fracture thickness can be neglected, while the general model computes the temperature variation across the fracture.
The Moist Air interface () under the Heat and Moisture Transport branch combines the Heat Transfer in Moist Air interface () with the Moisture Transport in Air interface (). It is used to simulate the coupling between heat transfer and vapor transport in air and the evaporation and condensation on walls.
The Moist Porous Media interface () combines the Heat Transfer in Moist Porous Media and Equilibrium Moisture Transport in Porous Media interfaces. It is used to simulate the coupling between heat transfer and moisture transport in liquid and gas phases in the pores of the medium.
The Building Materials interface () combines the Heat Transfer in Building interface () with the Moisture Transport in Building Materials interface (). It can be used to model different moisture variations phenomena in building components such as drying of initial construction moisture, condensation due to migration of moisture from outside to inside, or moisture accumulation by interstitial condensation due to diffusion.
The Heat Transfer in Porous Media interface () combines the heat conduction and convection in a solid-fluid system. This physics interface provides mixing rules for calculating the effective heat transfer properties, expressions for heat dispersion in porous media. 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. This physics interface may be used for a wide range of porous materials, from porous structures to the simulation of heat transfer in soils and rocks, and also to model heat transfer in fractures.
The Local Thermal Nonequilibrium (LTNE) interface () implements a macroscale model designed to simulate heat transfer in porous media where the temperatures in the porous matrix and the fluid are not in equilibrium. It differs from simpler macroscale models for heat transfer in porous media where the temperature difference of the solid and fluid are neglected. The absence of thermal equilibrium can result from fast transient changes, but it can also be observed in stationary cases. Typical applications are rapid heating or cooling of a porous medium using a hot fluid or internal heat generation in one of the phases (due to inductive or microwave heating, exothermic reactions, and so on). This is observed in nuclear devices, electronics systems, or fuel cells for example.
The Heat Transfer in Packed Beds interface () provides a multiscale model for heat transfer in a porous medium where the local thermal equilibrium is not assumed between the pellets of a packed bed and the fluid phase, and where the temperature variation inside the pellets is taken into account. A temperature field is defined for each phase, pellets and fluid of the porous medium, and the heat transfer between them is accounted for. The microscale pellets temperature field depends on the radial coordinate of each pellet.
These features interact seamlessly and can be used in combination in a single application. Surface-to-surface radiation can also be included in the energy equation, although this requires a license for the Heat Transfer Module.
Structural Mechanics
The Poroelasticity multiphysics interface () combines a transient formulation of Darcy’s law with a linear elastic material included in the Solid Mechanics interface. The poroelasticity coupling means that the pore fluid affects the compressibility of the porous medium, as well as changes in volumetric strains affect the porosity and the fluid flow.
Physics Interface Guide by Space Dimension and Study Type
The table lists the physics interfaces available with this module in addition to those included with the COMSOL Multiphysics basic license.
Chemical Species Transport
Moisture Transport
Moisture Flow
Reacting Flow
Reacting Flow in Porous Media
Fluid Flow
Single-Phase Flow
Multiphase Flow
Two-Phase Flow, Level Set
Phase Transport
Porous Media and Subsurface Flow
Nonisothermal Flow
Heat Transfer
Thin Structures
Heat and Moisture Transport
Heat and Moisture Flow
Porous Media
Structural Mechanics
Poroelasticity
Mathematics
1 This physics interface is included with the core COMSOL Multiphysics software but has added functionality for this module.
2 This physics interface is a predefined multiphysics coupling that automatically adds all the physics interfaces and coupling features required.
3 Requires the addition of the Structural Mechanics Module.
4 Requires the addition of the Composite Materials Module and the Structural Mechanics Module.