Subsurface Flow Module Physics Interfaces
The Subsurface Flow Module contains a number of physics interfaces that predefine equations or sets of equations adapted to earth-science applications. 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.
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 Subsurface 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 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.
Fluid Flow
Subsurface flows usually 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 Laminar Flow interface () describes fluid motion when the Reynolds number is less than approximately 1000, and turbulences are not present. The physics interface solves the Navier-Stokes equations, for incompressible or weakly compressible flows, where the Mach number (Ma), given by Ma=U/c, where c is the velocity of sound in the fluid, is less than 0.3.
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 is appropriate for use when viscous flow is dominant.
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, and does not track the interface between the different phases.
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.
Porous Media Flow
The Darcy’s Law interface () describes fluid movement through interstices in a porous medium. Because the fluid loses considerable energy to frictional resistance within the pores, flow velocities in porous media are very low. Darcy’s Law applies to water moving in an aquifer or stream bank, oil migrating to a well, and even magma rising through the earth to a chamber in a volcano. You can also set up multiple Darcy’s Law interfaces to model multiphase flows involving more than one mobile phase.
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.
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, hydraulic properties change 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. Nonlinearities arise because the material and hydraulic properties vary from unsaturated to saturated conditions. The analytic formulas of van Genuchten and Brooks and Corey are frequently employed with variably saturated flow modeling. With Darcy’s law or Richards’ equation, COMSOL Multiphysics solves for pressure and has physics interfaces for pressure head and hydraulic head.
The Two-Phase Darcy's Law interface () is used to simulate fluid flow through interstices in a porous medium. It solves Darcy's law for the total pressure and the transport of the fluid content for one fluid phase. The physics interface can be used to model low velocity flows or media where the permeability and porosity are very small, for which the pressure gradient is the major driving force and the flow is mostly influenced by the frictional resistance within the pores.
The Phase Transport in Porous Media interface () is used to simulate the transport of multiple immiscible phases through a porous medium. The interface solves for the averaged volume fractions (saturations) of the phases, and it does not track the interface between the different phases, although microscopic interfacial effects are taken into account in the macroscopic equations through capillary pressure functions.
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 Brinkman Equations interface () is used to model compressible flow at moderate speeds, given by a Mach number less than 0.3. You can also choose to model incompressible flow and simplify the equations to be solved. Furthermore, 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. Consequently, they are well-suited to transitions between slow flow in porous media, governed by Darcy’s law, and fast flow in channels described by the Navier-Stokes equations. Interesting uses of the Brinkman to Navier-Stokes coupling include modeling of the hyporheic zone near a river, or the flow of oil through a reservoir into a well. The equations and boundary conditions that describe these types of phenomena are in the Free and Porous Media Flow interface. The Brinkman Equations interface can also add a Forchheimer drag term, which is a viscous drag on the porous matrix proportional to the square of the flow velocity.
The Free and Porous Media Flow interface () is useful for modeling problems where free flow is connected to porous media. It should be noted that if the porous region is large in comparison to the free fluid region, and you are not primarily interested in results in the region of the interface, then you can always couple a Fluid Flow interface to the Darcy’s Law interface, to make your overall application computationally cheaper.
The Free and Porous Media Flow 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.
As always, the physics interface gives 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 characterize temperature distributions for geological phenomena and can be freely coupled to other physics interfaces in an application. These physics 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.
The Heat Transfer in Fluids interface () accounts for conduction and convection as the main heat transfer mechanisms. The coupling to the flow field in the convection term may be entered manually, or it may be selected from a list that couples the heat transfer to an existing Fluid Flow interface. The Heat Transfer in Fluids interface can be solved simultaneously with the Laminar Flow interface, or when the flow field has already been calculated and the heat transfer problem is solved afterward, typically for simulations of forced convection.
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, as well as including geothermal heating. 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.
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 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 will affect the mass transport.
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 basic license.
Chemical Species Transport
Reacting Flow
Reacting Flow in Porous Media
Fluid Flow
Single-Phase Flow
Phase Transport
Porous Media and Subsurface Flow
Heat Transfer
Structural Mechanics
1 This physics interface is included with the core COMSOL package but has added functionality for this module.