| Panel |
|---|
| borderColor | wheat |
|---|
| bgColor | mintcream |
|---|
| borderWidth | 7 |
|---|
|
| LaTeX Math Block |
|---|
| G(t) = \sum_{p=1}^{N^{\uparrow}_P} \left[
(R_O - C^{\uparrow}_{O,p}) \cdot q^{\uparrow}_{O, p} + (R_G - C^{\uparrow}_{G,p}) \cdot q^{\uparrow}_{G, p}
- C^{\uparrow}_{L,p} \cdot q^{\uparrow}_{L, p} - C^{\uparrow}_{W,p} \cdot q^{\uparrow}_{W, p}
\right]
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j}
|
| LaTeX Math Block |
|---|
| G(t) = \sum_{p=1}^{N^{\uparrow}_P} \left[
\left[ (R_O - C^{\uparrow}_{O,p}) + (R_G - C^{\uparrow}_{G,p}) \cdot Y_{g,p} \right] \cdot q^{\uparrow}_{O, p}
- C^{\uparrow}_{L,p} \cdot q^{\uparrow}_{L, p} - C^{\uparrow}_{W,p} \cdot Y_{w,p} \cdot q^{\uparrow}_{L, p}
\right]
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j}
|
| LaTeX Math Block |
|---|
| G(t) = \sum_{p=1}^{N^{\uparrow}_P} \left[
\left[ (R_O - C^{\uparrow}_{O,p}) + (R_G - C^{\uparrow}_{G,p}) \cdot Y_{g,p} \right] \cdot (1- Y_{w,p})
- C^{\uparrow}_{L,p} \cdot q^{\uparrow}_{L, p} - C^{\uparrow}_{W,p} \cdot Y_{w,p}
\right] \cdot q^{\uparrow}_{L, p}
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j}
|
Translating | LaTeX Math Inline |
|---|
| body | q^{\downarrow}_{W, i} |
|---|
|
and | LaTeX Math Inline |
|---|
| body | q^{\downarrow}_{G, j} |
|---|
|
to Sandface flowrates | LaTeX Math Inline |
|---|
| body | q^{\downarrow}_{w, i} |
|---|
|
and | LaTeX Math Inline |
|---|
| body | q^{\downarrow}_{g, j} |
|---|
|
with formation volume factor and substituting liquid production rate from | LaTeX Math Block Reference |
|---|
| anchor | qL |
|---|
| page | Liquid production rate |
|---|
|
one arrives to:| LaTeX Math Block |
|---|
| G(t) = \sum_{p=1}^{N^{\uparrow}_P} \frac{\left[ (R_O - C^{\uparrow}_{O,p}) + (R_G - C^{\uparrow}_{G,p}) \cdot Y_{g,p} \right] \cdot (1- Y_{w,p})
- C^{\uparrow}_{L,p} \cdot q^{\uparrow}_{L, p} - C^{\uparrow}_{W,p} \cdot Y_{w,p} }
{B_w Y_{w,p} + \left[ (B_o - R_s B_g) + (B_g - R_v B_o) \, Y_{g,p} \right] \cdot (1-Y_{w,p})}
\cdot q^{\uparrow}_{t, p}
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot B_w \cdot q^{\downarrow}_{w, i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot B_g \cdot q^{\downarrow}_{g, j}
|
which is equivalent to | LaTeX Math Block Reference |
|---|
|
. |
|
