ICP=10 Modified Brooks-Corey Model

A modified version of the Brooks-Corey model (Brooks and Corey, 1964) has been implemented. In order to prevent the capillary pressure from decreasing towards negative infinity as the effective saturation approaches zero, a linear function is used for saturations $S_l$ below a certain value $S_{lrc}+\varepsilon$, where $\varepsilon$ is a small number. The slope of the linear extrapolation is identical with the slope of the capillary pressure curve at $S_l=S_{lrc}+\varepsilon$. Alternatively, the capillary pressure is prevented from becoming more negative than $-p_{c,max}$. The modified Brooks-Corey model is invoked by setting both IRP and ICP to 10.

$p_c=\left\{\begin{matrix}-p_e\left(S_{ec}\right)^{-1/\lambda}\mathrm{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ for\ }\ S_l>(S_{lrc}+\varepsilon)\\-p_e\left(\frac{\varepsilon}{1-S_{lrc}}\right)^{-1/\lambda}+\frac{p_e}{\lambda}\frac{1}{1-S_{lrc}}\left(\frac{\varepsilon}{1-S_{lrc}}\right)^{-\frac{1+\lambda}{\lambda}}\left(S_l-S_{lrc}-\varepsilon\right)\mathrm{\ \ \ \ for\ }\ S_l<(S_{lrc}+\varepsilon)\\\end{matrix}\right.$

$p_c\geq-p_{c,max}$

where

$S_{ec}=\frac{S_l-S_{lrc}}{1-S_{lrc}}$

Parameters:

CP(1): λ (pore size distribution index)

CP(2): Pe (gas entry pressure [Pa])

if CP(2) is negative and USERX(1,N) is non-zero, apply Leverett’s rule:

$P_e=-\mathrm{\mathrm{CP}}(2)\sqrt{\mathrm{USERX}(\mathrm{1,N})\mathrm{/PER}(\mathrm{NMAT})}$

if USERX(2,N) is positive, Pe = USERX(2,N)

if USERX(2,N) is negative, Pe = -USERX(2,N)∙CP(2)

CP(3): ε or Pc,max

if CP(3) = 0, ${p}_{c,max}=10^{50}$, $\varepsilon=-1$

if 0 < CP(3) < 1, use linear model for $S_l<S_{lrc}+\varepsilon$

if CP(3) $\geq 1$ , $p_{c,max}$= CP(3), $\varepsilon=-1$

CP(6): $S_{lrc}$