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| q_t(\mathbf{r}) = q_w + q_o + q_g = B_w \, q_W + (B_o - R_v \, B_g) \, q_O + (B_g - R_s \, B_o) \, q_G |
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| B_w = B_w(p_{\rm ref}, T_{\rm ref}), \ B_o = B_o(p_{\rm ref}, T_{\rm ref}), \ B_g = B_g(p_{\rm ref}, T_{\rm ref}) |
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| \phi(\mathbf{r}, \ p_{\rm ref}) |
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| s(\mathbf{r}) = \{ s_w(\mathbf{r}), \ s_o(\mathbf{r}), \ s_g(\mathbf{r}) \} |
| reservoir saturation as a function of location
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| c_t(s,p, T) = c_r + c_w s_w + c_o s_o + c_g s_g + s_o [ R_{sp} + (c_r + c_o) R_{sn} ] + s_g [ R_{vp} + R_{vn}(c_r + c_g) ] |
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| с_w(p, T), \ с_o(p, T), \ с_g(p, T) |
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| M(s, p, T) = M_w + M_o \big( 1 + R_{sn} \big) + M_g \big( 1 + R_{vn} \big) |
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| M_w(s,p, T) = k_a \cdot M_{rw}(s,p, T) |
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| M_o(s,p, T) = k_a \cdot M_{ro}(s,p, T) |
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| M_g(s,p, T) = k_a \cdot M_{rg}(s,p, T) |
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| M_{rw}(s, p, T) = \frac{k_{rw}(s)}{\mu_w(p, T)} |
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| M_{ro}(s,p, T) = \frac{k_{ro}(s)}{\mu_o(p, T)} |
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| M_{rg}(s,p, T) = \frac{k_{rg}(s)}{\mu_g(p, T)} |
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| k_a(\mathbf{r}, \ p_{\rm ref}) |
| absolute permeability as a function of location at reference pressure
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| \mu_w(p, T), \ \mu_o(p, T), \ \mu_g(p, T) |
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| R_{sn}(p, T) = \frac{R_s B_g}{B_o} \ , \quad R_{vn}(p, T) = \frac{R_v B_o}{B_g} |
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| R_{sp}(p, T) = \frac{\dot R_s B_g}{B_o} \ , \quad R_{vp}(p, T) = \frac{\dot R_v B_o}{B_g} |
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| \rho(p, T) = \frac{ M_{rw} \rho_w + M_{ro} (1 + R_{sn}) \rho_o + M_{rg} (1+R_{vn}) \rho_g }{ M_{rw} + M_{ro} (1 + R_{sn}) + M_{rg} (1+R_{vn}) }
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| g = 9.81 \ \textrm{m} / \textrm{s}^2 |
| standard gravity |
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| \big ( \big)^{\LARGE \cdot} = \frac{d}{dp} |
| differentiation with respect to the pressure
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