natural_logarithm#

natural_logarithm(phase, X, A1=0.0, A2=1.0, A3=1.0, A4=0.0, A5=0.0)[source]#

Calculates the rate, as well as slope and intercept of the following function at the given value of X:

\[r = A_{1} Ln( A_{2} x^{ A_{3} }+ A_{4})+ A_{5}\]
Parameters:

  • phase (OpenPNM Phase object) – The phase object to which this model is associated (i.e. attached). This controls the length of the calculated array(s), and also provides access to other necessary properties.

  • X (str) – The dictionary key on the phase object containing the the quantity of interest

  • A5 (A1 ->) – The dictionary keys on the phase object containing the coefficients values to be used in the source term model

Returns:

A dictionary containing the following three items:

’rate’

The value of the source term function at the given X.

’S1’

The slope of the source term function at the given X.

’S2’

The intercept of the source term function at the given X.

Return type:

dict

Notes

The slope and intercept provide a linearized source term equation about the current value of X as follow:

\[rate = S_{1} X + S_{2}\]
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