Nguyen model

Governing Equation

Based on experimental observations, Nguyen et al. (2006)¹ proposed to relate the relative permeability to the effective degree of saturation using the following simple cubic expressions. Instead of the original expression, we adopted a generalized exponential expression:

\[\begin{equation*} k^w = (1-k^w_{min}) (S^e)^m + k^w_{min} ~~~\mbox{and}~~~ k^a= (1-k^a_{min}) (1-S^e)^m + k^a_{min}. \end{equation*}\]

For \(m=3\) the original relation of Nguyen is recovered.

The development of relative permeability \(k^\beta\) with effective degree of saturation \(S^e\) is presented here:

Jacobian Contribution

The contributions to the Jacobian read:

\[\begin{align*} \frac{\partial k^w}{\partial S^e} &= m (S^e)^{m-1}, \\ \frac{\partial k^a}{\partial S^e} &= -m (1-S^e)^{m-1}. \end{align*}\]

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• Reference manual

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  How to use it

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1. Viet Hoai Nguyen, Adrian P. Sheppard, Mark A. Knackstedt, and W. Val Pinczewski. The effect of displacement rate on imbibition relative permeability and residual saturation. Journal of Petroleum Science and Engineering, 52(1-4):54–70, 6 2006. Reservoir Wettability. doi:10.1016/j.petrol.2006.03.020. ↩