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The Volatile Oil flow dynamics is defined by the following set of equations.:
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| \partial_t \bigg [ \phi \ \rho_W \bigg ] + \nabla \bigg ( \rho_{Ww} \ \mathbf{u}_w \bigg ) = q_{mW}(\mathbf{r}) |
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| \partial_t \bigg [ \phi \ \rho_O \bigg ] + \nabla \bigg ( \rho_{Oo} \ \mathbf{u}_o
+ \rho_{Og} \ \mathbf{u}_g \bigg ) = q_{mO}(\mathbf{r}) |
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| \partial_t \bigg [ \phi \ \rho_G \bigg ] + \nabla \bigg ( \rho_{Go} \ \mathbf{u}_o
+ \rho_{Gg} \ \mathbf{u}_g \bigg ) = q_{mG}(\mathbf{r}) |
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anchor | DarcyW1 |
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alignment | left |
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| \mathbf{u}_w = - k_a \ \frac{k_{rw}(s_w, s_g)}{\mu_w} \ ( \nabla P_w - \rho_w \mathbf{g} ) |
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anchor | DarcyO1 |
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alignment | left |
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| \mathbf{u}_o = - k_a \ \frac{k_{ro}(s_w, s_g)}{\mu_o} \ ( \nabla P_o - \rho_o \mathbf{g} ) |
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anchor | DarcyG1 |
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alignment | left |
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| \mathbf{u}_g = - k_a \ \frac{k_{rg}(s_w, s_g)}{\mu_g} \ ( \nabla P_g - \rho_g \mathbf{g} ) |
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anchor | CapilarOW1 |
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alignment | left |
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| P_o - P_w = P_{cow}(s_w) |
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anchor | CapilarOG1 |
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alignment | left |
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| P_o - P_g = P_{cog}(s_g) |
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anchor | swsosg1 |
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alignment | left |
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| s_w + s_o + s_g = 1 |
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