Page History

q_t = q_w + q_o (1+R_{sn})  + q_g (1 + R_{vn})

\phi(\mathbf{r}, \ P) = \phi_0(\mathbf{r}) \exp \bigg[ - \int_{P_i}^P c_r(P) dP \bigg]

s(\mathbf{r}) = \{ s_w(\mathbf{r}), \ s_o(\mathbf{r}), \ s_g(\mathbf{r})  \}

c_t(s,P) = c_r (1 + R_{sn} s_o + R_{vn} s_g) + c_w s_w + c_o s_o (1+R_{sn}) + c_g s_g (1 + R_{vn}) + R_{sp} s_o + R_{vp} s_g

с_r(P), \ с_w(P), \ с_o(P), \ с_g(P) 

\alpha(s, P) = \alpha_w + \alpha_o \big( 1 + R_{sn} \big) + \alpha_g \big( 1 + R_{vn} \big)

\alpha_w(P) = k_a \alpha_{rw}(P), \quad \alpha_o(P) = k_a \alpha_{ro}(P), \quad \alpha_g(P) = k_a \alpha_{rg}(P)

k_a(\mathbf{r}, \ P, \ | \nabla P|)  = k_a^{\LARGE \circ} (\mathbf{r}) \cdot k_P (P, \ |\nabla P|)

k_a^{\LARGE \circ} (\mathbf{r})

k_P(P, \ | \nabla P|)

\alpha_{rw}(s, \ P) = \frac{k_{rw}(s)}{\mu_w(P)}, \quad \alpha_{ro}(s, \ P) = \frac{k_{ro}(s)}{\mu_o(P)}, \quad \alpha_{rg}(s, \ P) = \frac{k_{rg}(s)}{\mu_g(P)}

\mu_w(P), \ \mu_o(P), \ \mu_g(P)

R_{vn}(P) = \frac{R_v B_o}{B_g} \ , \quad R_{sn}(P) = \frac{R_s B_g}{B_o} \ , \quad
R_{vp}(P) = \frac{\dot R_v B_o}{B_g} \ , \quad R_{sp}(P) = \frac{\dot R_s B_g}{B_o}

\rho_{\alpha} = \frac{ \alpha_{rw} \rho_w + \alpha_{ro} \rho_o (1 + R_{sn})  + \alpha_{rg} \rho_g (1+R_{vn}) }{ \alpha_{rw}  + \alpha_{ro}  (1 + R_{sn})  + \alpha_{rg}  (1+R_{vn}) }

 g = 9.81 \ \textrm{m} / \textrm{s}^2

 \big (   \big)^{\LARGE \cdot} = \frac{d}{dP}