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Theory and equations

Dual-permeability model

The dual-permeability model of Gerke and van Genuchten (1993a) assumes that the porous medium consists of two overlapping domains, both of which conduct water: the fracture (macropore, inter-aggregate) domain and the matrix (micropore, intra-aggregate) domain. Each domain has its own Richards equation, coupled by a water transfer term.

Governing equations

∂θf/∂t = ∂/∂x [ Kf(hf) (∂hf/∂x + cos α) ] − Sf − Γw/w
∂θm/∂t = ∂/∂x [ Km(hm) (∂hm/∂x + cos α) ] − Sm + Γw/(1 − w)
θ = w θf + (1 − w) θm

The subscripts f and m refer to the fracture and the matrix domain, and w is the ratio of the volume of the fracture domain to the total soil volume. Each domain has its own van Genuchten–Mualem functions: in the parameter table of Materials & parameters the primary columns describe the fractures and the extra columns θr,m, θs,m, αm, nm, Ks,m the matrix.

Water transfer

The water transfer is proportional to the difference of the pressure heads Gerke and van Genuchten (1993a); Gerke and van Genuchten (1993b):

Γw = αw (hf − hm)
αw = (β / a2) γw Ka, Ka = [Ka(hf) + Ka(hm)] / 2, Ka(h) = Ka,s Kr,m(h)

with the shape factor β of the matrix blocks (3 for rectangular slabs, 15 for spheres Gerke and van Genuchten (1996)), the effective diffusion path length a (the half width of the blocks), the empirical scaling coefficient γw = 0.4 Gerke and van Genuchten (1993b), and the conductivity Ka of the fracture–matrix interface (Ka,s = 0 uses the matrix Ks). A positive Γw moves water from the fractures into the matrix.

Boundary fluxes

A prescribed flux at a boundary is distributed between the two domains, in proportion to their volumes (f = w) or with a given fraction entering the fractures (soil hydraulic model).

Dual porosity inside the matrix

Optionally the matrix itself has a mobile and an immobile region, with a water-content or pressure-head driven transfer as in the dual-porosity models.

Solute transport

The advection–dispersion equation is solved in both domains, coupled by the solute transfer

Γs = αs (1 − w) θm (cf − cm) + Γw c

with the solute transfer coefficient αs [1/T] and the concentration c of the transferred water (cf for flow into the matrix, cm otherwise) Gerke and van Genuchten (1993a); Šimůnek and van Genuchten (2008).

The interface parameters of the dual-permeability model cannot be stored in HYDRUS-1D project files. Non-equilibrium water flow, the centrifuge and density-dependent flow are not available with this model.

Literature cited in this topic

  • Gerke, H. H., and M. Th. van Genuchten (1993a). A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resources Research 29(2): 305–319. doi:10.1029/92WR02339
  • Gerke, H. H., and M. Th. van Genuchten (1993b). Evaluation of a first-order water transfer term for variably saturated dual-porosity flow models. Water Resources Research 29(4): 1225–1238. doi:10.1029/92WR02467
  • Gerke, H. H., and M. Th. van Genuchten (1996). Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media. Advances in Water Resources 19(6): 343–357. doi:10.1016/0309-1708(96)00012-7
  • Šimůnek, J., and M. Th. van Genuchten (2008). Modeling nonequilibrium flow and transport processes using HYDRUS. Vadose Zone Journal 7(2): 782–797. doi:10.2136/vzj2007.0074

All sources: References.