Understanding Matrix Diffusion Zones

Matrix diffusion is the process by which solutes diffuse from a mobile zone (e.g., a fracture) into surrounding porous matrix material. In GoldSim, it is assumed that this diffusive process is one-dimensional and orthogonal to the flow direction.

The figure below illustrates the effect of matrix diffusion on the breakthrough of a slug input. Note that as the degree of matrix diffusion increases (implemented in this case by increasing the perimeter, and hence the diffusive area), the breakthrough is retarded and the tail is extended far to the right.

GoldSim allows up to three separate matrix diffusion zones to be specified for each Pipe. The fraction of the pathway’s perimeter associated with each zone is specified by the user. Each matrix diffusion zone is also assigned a thickness (which can be defined to vary over the pathway perimeter). For each zone, one of three possible one-dimensional diffusive geometries can be assumed:

• slab (in which the diffusive area remains constant with distance into the matrix). Such a model could be appropriate, for example, for representing uniform, parallel fracture sets, in which the thickness of the zone was defined as half the thickness of the rock block (assuming that a similar fracture exists on the other side of the rock block).

• sphere (in which the diffusive area decreases with distance into the matrix according to a spherical geometry). Such a model could be appropriate, for example, to represent intact blocks in highly fractured zones.

• slot (in which the diffusive area increases exponentially with distance into the matrix). Such a model could be appropriate, for example, to represent a long, “thin” (width << length) pathway.

Each matrix diffusion zone is assigned a porous material type (a Solid), and the properties of this medium impact the transport properties (diffusivity, partitioning) within the zone.

A skin zone can also be defined for the Pipe. The skin zone is defined in a similar manner to that of the matrix diffusion zones (although its geometry is always assumed to be slab). While the three matrix diffusion zones exist in parallel, the skin zone, if present, is assumed to exist in front of all matrix diffusion zones (i.e., between the matrix diffusion zones and the mobile zone). Hence, if a skin zone is present, species must first diffuse through the skin before reaching the underlying diffusive zones (forming a two-layer diffusive system).