Ingmanson Simplified

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Description

The Ingmanson Simplified relationship (Ingmanson et al., 1959) is a simplified version of the Davies-Ingmanson (after Davies (1952) and Ingmanson et al. (1959)) for high porosity. For porosity values above 0.9 the two relationships are nearly the same.

Application

Ingmanson Simplified leads to approximately same permeability values as Davies-Ingmanson for porosity values above 0.9, which is the region it is best suited for.

Background

The Davies-Ingmason relationship is given by:

$\displaystyle K \left(\phi_\mathit{ext}\right) = \frac{\phi_\mathit{ext}^3}{k_0 S_v^2(1-\phi_\mathit{ext})^2},$    

where $ k_0$ is the Kozeny constant:

$\displaystyle k_0 = \begin{cases}5.50 & \text{if $\phi_{ext} < 0.7$} \\ \frac{k... ...hi_{ext}^3))}{\sqrt{1-\phi_{ext}}} & \text{if $\phi_{ext} \ge 0.7$} \end{cases}$    

and $ S_v$ is the specific surface area, $ \phi_\mathit{ext}$is the external porosity and $ k_1$ and $ k_2$ are parameters.

Ingmanson et al. realised that:

$\displaystyle 1 + 57(1-\phi_{ext}^3) \sim 1$    

for porosity values above 0.9. Thus, making this simplification, permeability can be expressed as:

$\displaystyle K \left(\phi_\mathit{ext}\right) = \frac{1}{k_1 S_v^2(1-\phi_\mathit{ext})^{1.5}},$    

where the constant $ k_1$ is the same as in the Davies-Ingmanson relationship, i.e. 3.5.

Bibliography

Davies, C. N., 1952, Proc. Inst. Mech. Engrs. .

Ingmanson, W. L., B. D. Andrews, and R. C. Johnson, 1959, Tappi Journal 42(10), 840.

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