Physical processes and governing equations

Physical processes

Flow and transport of substances in porous media can be subdivided in advective transport (due to the groundwater flow) and diffusive/dispersive transport. The storage of substances is strongly influenced by sorption of the substance to the porous medium. This is often quantified by sorption coefficients.

Flow in fractured limestone can be very complex. Fractured limestone has usually strongly contrasting flow conditions between fractures and matrix. The fractures can have very high flow velocities , whereas the limestone matrix has usually a very low hydraulic conductivity and thus low flow velocities. However, for the fate of contaminants in fractured limestone aquifer, the matrix is important, since it usually has a high porosity and can store substantial amounts of contaminants, once they have diffused into the matrix.

The hydraulic conductivity of the fractures is mainly depending on their aperture (width). For an estimation of the flow velocity in fractures, the cubic law is often used as approximation. With that, the velocity scales with the third power of the fracture aperture.

Governing equations

Flow

Groundwater flow in porous media is usually described by Darcy's law, giving a relation between hydraulic head gradient and groundwater flow. The fracture conductivity is usually determined via the fracture aperture using the cubic law.

Flow equation.

Contaminant transport

To describe the transport of a substance in a porous medium, the advection-dispersion equation is usually employed. The first term describes storage (here including retardation due to linear sorption), the second and third terms describe advective and dispersive transport of a substance. Degradation can be included as additional term.

Variables are:

n	porosity
rho_b	bulk density
k_d	sorption coefficient
c	concentration
v	flow velocity
D_m	dispersion coefficient

Properties of limestone

Borehole cores from the Akacievej field site.

Limestone can be heavily fractured and include almost impermeable chert layers and nodules. The limestone found at the Akacievej site (Copenhagen kalk and bryozoan limestone) has a strongly varying hardness.

The sorption behavior for chlorinated solvents on limestone was examined in Salzer (2013). For chlorinated solvents like PCE, sorption to limestone can be strong (kd values of 0.5-1 L/kg were observed).

Determined hydraulic proporties for the Akacievej field site

The following table gives an overview of values that were determined for the Akacievej site: Include table with typical values for Akacievej

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