| time |
LaTeX Math Inline |
---|
body | \{ {--uriencoded--%7B\rm r} r%7D = (x,y,z) \} |
---|
|
| reservoir location |
LaTeX Math Inline |
---|
body | --uriencoded--\mathbf%7Br%7D_k |
---|
|
| |
LaTeX Math Block |
---|
| p = \frac{1}{3} \cdot \left( p_w + p_o + p_g \right) |
|
3-phase average reservoir pressure |
LaTeX Math Block |
---|
| q_t(\mathbf{r}) = q_w + q_o + q_g = B_w \, q_W + (B_o - R_s \, B_g) \, q_O + (B_g - R_v \, B_o) \, q_G |
| |
LaTeX Math Block |
---|
| B_w, \ B_o, \ B_g |
| |
LaTeX Math Block |
---|
| \phi(\mathbf{r}) |
| |
LaTeX Math Block |
---|
| s(\mathbf{r}) = \{ s_w(\mathbf{r}), \ s_o(\mathbf{r}), \ s_g(\mathbf{r}) \} |
| reservoir saturation as a function of location
|
LaTeX Math Block |
---|
| c_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) ] |
| |
| |
LaTeX Math Block |
---|
| с_w, \ с_o, \ с_g |
| |
LaTeX Math Block |
---|
| M = M_w + M_o \big( 1 + R_{sn} \big) + M_g \big( 1 + R_{vn} \big) |
| |
LaTeX Math Block |
---|
| M_w = k_a \cdot M_{rw} |
| |
LaTeX Math Block |
---|
| M_o = k_a \cdot M_{ro} |
| |
LaTeX Math Block |
---|
| M_g = k_a \cdot M_{rg} |
| |
LaTeX Math Block |
---|
| M_{rw} = \frac{k_{rw}(s)}{\mu_w} |
| |
LaTeX Math Block |
---|
| M_{ro} = \frac{k_{ro}(s)}{\mu_o} |
| |
LaTeX Math Block |
---|
| M_{rg} = \frac{k_{rg}(s)}{\mu_g} |
| |
LaTeX Math Block |
---|
| k_a(\mathbf{r}) |
| absolute permeability as a function of location at reference pressure
|
LaTeX Math Block |
---|
| \mu_w, \ \mu_o, \ \mu_g |
| |
LaTeX Math Block |
---|
| R_{sn} = \frac{R_s B_g}{B_o} \ , \quad R_{vn} = \frac{R_v B_o}{B_g} |
| |
LaTeX Math Block |
---|
| R_{sp} = \frac{\dot R_s B_g}{B_o} \ , \quad R_{vp} = \frac{\dot R_v B_o}{B_g} |
| |
LaTeX Math Block |
---|
| \rho = \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}) }
|
| |
LaTeX Math Block |
---|
| g = 9.81 \ \textrm{m} / \textrm{s}^2 |
| standard gravity |
LaTeX Math Block |
---|
| \big ( \big)^{\LARGE \cdot} = \frac{d}{dp} |
| differentiation with respect to the pressure
|