Porous Media Sorption

You can define porous media sorption using either the analytical logarithmic form or the tabulated form.

Logarithmic

The absorption and exsorption behaviors can be defined by the following analytical form:

u_{w} = \frac{1}{B} \ln [\frac{(s - s_{0})}{(1 - s_{0}) + A (1 - s)}] f o r s_{1} \leq s < 1,

u_{w} = u_{w} |_{s_{1}} - \frac{ⅆ u_{w}}{ⅆ s} |_{s_{1}} (s_{1} - s) f o r s_{0} \leq s < s_{1},

where

$u_{w}$: is the pore pressure;
$s$: is the saturation;
$A, B$: are positive material constants; and
$s_{0}, s_{1}$: are parameters used to define the lower bounds of the saturation values of interest.

If a single sorption curve is specified to describe both the absorption and exsorption behaviors:


Input Data	Description
A	Material constant $A$ in the analytical form of the absorption/exsorption behaviors. This value must be positive.
B	Material constant $B$ in the analytical form of the absorption/exsorption behaviors. This value must be positive.
S0	Parameter $s_{0}$ in the analytical form of the absorption/exsorption behaviors.
S1	Parameter $s_{1}$ in the analytical form of the absorption/exsorption behaviors. The value of $s_{1}$ cannot be the same as that of $s_{0}$ .

If separate sorption curves are specified to describe the absorption and exsorption behaviors, respectively:

Table 1. Scanning slope between Absorption and Exsorption curves
Input Data	Description
Slope	Slope of scanning line. This slope must be positive and larger than the slope of any segment of the absorption or exsorption behavior definitions.

Table 2. Absorption Data
Input Data	Description
A	Material constant $A$ in the analytical form of the absorption behavior. This value must be positive.
B	Material constant $B$ in the analytical form of the absorption behavior. This value must be positive.
S0	Parameter $s_{0}$ in the analytical form of the absorption behavior.
S1	Parameter $s_{1}$ in the analytical form of the absorption behavior. The value of $s_{1}$ cannot be the same as that of $s_{0}$ .

Table 3. Exsorption Data
Input Data	Description
A	Material constant $A$ in the analytical form of the exsorption behavior. This value must be positive.
B	Material constant $B$ in the analytical form of the exsorption behavior. This value must be positive.
S0	Parameter $s_{0}$ in the analytical form of the exsorption behavior.
S1	Parameter $s_{1}$ in the analytical form of the exsorption behavior. The value of $s_{1}$ cannot be the same as that of $s_{0}$ .

If a single sorption curve is specified to describe both the absorption and exsorption behaviors:


Input Data	Description
Pore pressure	Pore pressure $u_{w}$ with the condition $u_{w} \leq 0$ .
Saturation	Saturation, $s$ . This value must lie in the range $0.01 \leq s \leq 1.0$ .

If separate sorption curves are specified to describe the absorption and exsorption behaviors, respectively:

Table 4. Absorption Data
Input Data	Description
Pore pressure	Pore pressure $u_{w}$ with the condition $u_{w} \leq 0$ .
Saturation	Saturation, $s$ . This value must lie in the range $0.01 \leq s \leq 1.0$ .

Table 5. Exsorption data
Input Data	Description
Pore pressure	Pore pressure $u_{w}$ with the condition $u_{w} \leq 0$ .
Saturation	Saturation, $s$ . This value must lie in the range $0.01 \leq s \leq 1.0$ .

Table 6. Scanning slope between Absorption and Exsorption curves
Input Data	Description
Slope	Slope of scanning line. This slope must be positive and larger than the slope of any segment of the absorption or exsorption behavior definitions.