Porous Media Model
Flow through porous materials governs some of the most important processes in engineering and the natural sciences. Groundwater moves through aquifers and embankments. Resins infiltrate fiber preforms in composite manufacturing. Fuel cells transport gases through porous electrodes. Filtration systems separate particles from fluids. Geological formations store and transmit oil, gas, and water over vast distances. In all of these systems, the resistance of the porous structure to flow, the capillary forces at the fluid-solid interface, and the degree of saturation all interact to determine how the fluid moves.
The Porous Media Model is available across the FLOW-3D product family and simulates both saturated and unsaturated flows within porous structures, fully coupled to the free surface flow solver. Porosity, permeability, and wettability can be specified independently for each component in the model, giving engineers precise control over how different regions of the domain resist and transmit flow. Permeability can be isotropic or anisotropic, and several drag law formulations are available to cover the full range of flow regimes from slow Darcian creep to higher velocity inertial flow.
A droplet source moves in a circular pattern while ejecting droplets downward into a porous medium, creating a ring-shaped deposition pattern.
Saturated Porous Media
Saturated flow occurs when the pores of the material are fully occupied by liquid, with a relatively sharp interface between the saturated and unsaturated zones. This is the relevant regime for groundwater flow, flow through filter media, and most pressure-driven infiltration applications. The FLOW-3Dproduct family provides two drag law formulations for saturated porous flow: Darcian Drag and Forcheimer Drag.
Darcian Drag
The resistance to flow is modeled using Darcy’s Law in which the flow rate through a porous medium is proportional to the applied pressure gradient, with the proportionality determined by the permeability of the material. This relationship holds in the low-velocity regime where viscous forces dominate and inertia is negligible.
Forchheimer Drag
At higher flow velocities, inertial effects become significant and the linear Darcy relationship underestimates the true pressure drop. The Forchheimer model extends Darcy’s Law by adding a quadratic drag term that accounts for inertial losses at the pore scale.
Capillary Pressure in Saturated Media
When a wetting fluid is in contact with a porous material, surface tension at the fluid-gas interface inside the pores generates a capillary pressure that drives absorption. For saturated porous media, this capillary pressure is a fixed value determined by the average pore diameter, the surface tension of the fluid, and the contact angle of the fluid on the solid. A positive capillary pressure drives absorption into a wetting material; a negative capillary pressure (non-wetting) means that external pressure must be applied to force the fluid into the pores.
Unsaturated Porous Media
Unsaturated flow occurs when both liquid and gas are present within the pore space, with a gradual transition between the fully saturated and dry zones. There is no fixed capillary pressure; instead, capillary pressure varies continuously with local saturation. This regime describes wicking, drainage, and moisture transport in porous materials where the saturation history matters.
FLOW-3D uses the Volume of Fluid method to track the local fluid fraction throughout the porous domain, which acts as the saturation variable. Both the drag coefficient and the capillary pressure are functions of the local saturation, and both filling and draining curves can be specified independently to capture the hysteresis that is characteristic of real porous materials.
Three unsaturated drag models are available:
- Power law model: drag is related to saturation through a power-law relationship, the simplest and most commonly used approach
- Exponential model: drag is related to saturation through an exponential relationship, more physically descriptive than the power law model
- Mualem’s drag model for relative permeability: drag is related to the saturation through an additional relationship based on a relative permeability, strong experimental basis
Two unsaturated capillary pressure models are available:
- Simplified model: assumes a linear scanning curve between wetting and draining capillary pressure versus local saturation curves
- Van Genuchten model: a smooth, differentiable saturation-permeability relationship that provides a better fit to many real soil types, particularly for fine-grained materials
Anisotropic Permeability
In many real porous materials, flow resistance is not the same in all directions. Layered sediments, fiber-reinforced composites, and directionally compacted filter media all exhibit different permeabilities depending on the flow direction. The FLOW-3D product family supports fully anisotropic permeability specification, where independent permeability values can be assigned for each of the three coordinate directions. This allows accurate representation of materials such as carbon fiber preforms, where permeability along the fiber direction can be orders of magnitude higher than the transverse permeability.
Porous Baffle Plates
In addition to volumetric porous media regions, the FLOW-3D product family supports thin porous baffles: surfaces that impose a flow resistance without occupying a finite volume in the mesh. Porous baffles are useful for modeling perforated plates, screen meshes, filter membranes, and other thin resistive elements where the physical thickness is much smaller than the mesh cell size. The pressure drop across a baffle is defined by linear and quadratic resistance coefficients, consistent with the Forchheimer formulation for volumetric porous media.
Moisture Drying Model
Building on the unsaturated porous media framework, the Moisture Drying Model simulates the evaporation of moisture from porous materials as heat is applied. This is relevant to drying processes in food manufacturing, pharmaceutical production, construction materials, and any application where the thermal and moisture transport in a porous solid are coupled. The model tracks the distribution of moisture within the porous component and computes the evaporation rate as a function of local temperature and saturation.
Applications
The Porous Media Model is used across the FLOW-3D product family for:
- Resin transfer molding and liquid composite molding: tracking resin infiltration through fiber preforms
- Absorbent product design: fluid absorption and wicking through nonwoven fabrics and superabsorbent materials, used in hygiene and medical product development
- Fuel cell modeling: gas transport through porous electrodes and diffusion layers
- Filter and membrane performance analysis: pressure drop and flow distribution in filtration equipment
- Oil and gas reservoir simulation: multiphase flow through porous rock formations
- Soil moisture transport and irrigation system design
- Inkjet and coating processes: fluid absorption into paper, fabric, and other porous substrates
- Heat exchanger design with porous inserts for flow distribution and heat transfer enhancement
- Drying processes in food, pharmaceutical, and construction material manufacturing
- Packed bed reactor design and flow distribution analysis