| LaTeX Math Block |
|---|
| q_O = q_{Oo} + q_{Og} |
|
| LaTeX Math Block |
|---|
| q_G = q_{Gg} + q_{Go} |
|
| LaTeX Math Block |
|---|
| q_W = q_{Ww} |
| LaTeX Math Block |
|---|
| q_O = q_{Oo} + q_{Og} |
| LaTeX Math Block |
|---|
| q_G = q_{Gg} + q_{Go} |
| LaTeX Math Block |
|---|
| q_W = q_{Ww} |
|
| LaTeX Math Block |
|---|
|
\begin{cases}
q_O = q_{Oo} + q_{Og}
\\
q_G = q_{Gg} + q_{Go}
\\
q_W = q_{Ww}
\end{cases} |
Following the definition of Solution GOR (Rs) and Vaporized Oil Ratio (Rv) :
...
...
|
| LaTeX Math Block |
|---|
| R_v = q_{Og}/q_{Gg} |
|
...
so that:
...
...
q_O = q_{Oo} + R_v \, q_{Gg} |
|
...
|
| LaTeX Math Block |
|---|
| q_G = q_{Gg} + R_s \, q_{Oo} |
|
...
|
| LaTeX Math Block |
|---|
| q_W = q_{Ww} |
|
...
Following the definition of Oil formation volume factor (Bo) , Gas formation volume factor (Bg) and Water formation volume factor (Bw):
...
...
...
|
| LaTeX Math Block |
|---|
| q_{Gg} = \frac{q_g}{B_g} |
|
...
|
| LaTeX Math Block |
|---|
| q_{Ww} = \frac{q_w}{B_w |
|
...
so that:
...
...
q_O = \frac{q_o}{B_o} + R_v \,\frac{q_g}{B_g} |
|
...
|
| LaTeX Math Block |
|---|
| q_G = \frac{q_g}{B_g} + R_s \, \frac{q_o}{B_o} |
|
...
|
| LaTeX Math Block |
|---|
| q_W = \frac{q_w}{B_w} |
|
...
and solving the above system of equations leads to:
...
...
q_o = \frac{B_o \cdot (q_O - R_v \, q_G)}{1- R_v \, R_s} |
|
...
|
| LaTeX Math Block |
|---|
| q_o = \frac{B_o \cdot (q_G - R_s \, q_O)}{1- R_v \, R_s} |
|
...
|
| LaTeX Math Block |
|---|
| q_w = B_w \cdot q_w |
|
...
