The total compressibility of oil saturated formationSTOIIP can be written as:| LaTeX Math Block |
|---|
| cV_tO = \frac{1}{V_{\phi}} \frac{\partialV_o/B_o = s_o \, V_{\phi}}{\partial p} = c_r + s_{wi} c_w + (1-s_{wi})c_o \, V_\phi |
so thatThe STOIIP can be written as:| LaTeX Math Block |
|---|
| V_O\phi = V_o/\frac{B_o = s_o \, V_\phi = Q_O}{(1-s_{wi}) \, V_\phi} |
The pore volume reduction due to offtakes is: | LaTeX Math Block |
|---|
| \delta V_\phi = Q_oO \, B_o |
For low compressible oil, the total compressibility can be assumed constant and the pore volume reduction to due to offtakes can be related to pressure decline as:thus leading to| LaTeX Math Block |
|---|
| c_t = \frac{1}{\delta V_{\phi}} \frac{\partial V_{\phi}}{\partial p} = c_t \, \delta p = c_t \, (
\frac{1-s_{wi}}{B_o \, V_O} \frac{B_o \, Q_O}{\delta p} =\frac{1-s_{wi}}{\delta p} \frac{Q_O}{V_O} = \frac{1-s_{wi}}{\delta p} \cdot {\rm EUR_O} |
where | LaTeX Math Block |
|---|
| c_t = c_r + s_{wi} c_w + (1-s_{wi})c_o |
is total compressibility of oil saturated formation and | LaTeX Math Block |
|---|
| \delta p = p_i - p_{wf |
\, min)The volume reducation is and hencepressure reduction due to pore volume reduction caused by offtakes. For low compressible oil, the total compressibility can be assumed constant and | LaTeX Math Block Reference |
|---|
|
becomes:| LaTeX Math Block |
|---|
| \frac{Q_o \, B_o \, (1-s_{wi})}{V_o}{\delta p} \cdot {\rm EUR_O} = c_t \, (p_i - p_{wf \, min}) |
and | LaTeX Math Block |
|---|
| {\rm EUR}_{\rm NDR} = \frac{Q_o}{V_o} = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})\, B_o} |
| 