Exponential Decay Permeability Model

Overview

This stress-dependent permeability model assumes a simple exponential law for the fracture permeability as function of the effective normal stress acting on the fracture surface (Gutierrez et al., 2000):

\[k = k_{i} \text{exp} (- C {\sigma_n}')\]

where \(k_{i}\) is the initial unstressed fracture permeability; \(C\) is an empirical constant; \({\sigma_n}'\) is the effective normal stress.

Parameters

The Exponential Decay Permeability model can be called in the <Constitutive> block of the input XML file. This permeability model must be assigned a unique name via the name attribute. This name is used to assign the model to regions of the physical domain via a permeabilityModelName attribute in the <CompressibleSolidExponentialDecayPermeability> block.

The following attributes are supported:

Name	Type	Default	Description
empiricalConstant	real64	required	an empirical constant.
initialPermeability	R1Tensor	required	initial permeability of the fracture.
name	string	required	A name is required for any non-unique nodes

Example

<Constitutive>
   ...
   <ExponentialDecayPermeability
     name="fracturePerm"
     empiricalConstant="0.27"
     initialPermeability="{1e-15, 1e-15, 1e-15}"/>
   ...
</Constitutive>