The first well known publication on this topic is “The Behavior of Naturally Fractured Reservoirs” by J.E.Warren and P.J. Root from 1963. Since then the researchers further developed the idea of a dual porosity/permeability type of a porous medium. One of the well established models is based on the findings of H. Gerke and M. van Genuchten (Ref. 9). Basically the idea behind is to solve for each part of the porous medium (macro- and micropores) the relevant equations and connect them via an exchange term.

Darcy's Law is solved for the macropores and taking into account their volume fraction θM the equation reads:

The term Qip describes the mass source from the Interporosity Flow which is the mass transfer from the macropores to the micropores system. An additional ODE for the (passive) micropores is solved which only act as additional storage volume:

The indices M and m stand for macropores and micropores, respectively.

θM is the volume fraction of the macropores, Qip denotes the interporosity flow, signifying the mass transfer from the macropores (identified by index M) to the micropores (identified by index m).

Solving Darcy’s law for both systems entails solving two equations, each associated with dependent pressure variables pm and pM. These equations are coupled via Qip. From this, average quantities for the dual permeability medium as a whole are computed. The average pressure of the dual permeability medium is defined as:

Use the Unsaturated Dual Permeability Medium feature to model the transport in an unsaturated dual permeability medium where the Richards’ Equation (Equation 4-26) describes the transport in each system.

θM is the volume fraction of the macropores, Qip is the interporosity flow which is the mass transfer from the macroscale to the microscale system. The indices M and m stand for macropores and micropores, respectively.

Specify the Fluid Transfer Function αw which is used to calculate the interporosity flow, which is the mass exchange between macro- and microscale system:

with pM being the pressure within the macroscale system and pm the pressure within the microscale system