Natural Oil Depletion
The EUR during the natural oil depletion can be assessed with the following formula:
| LaTeX Math Block |
|---|
|
{\rm EUR}_{\rm NDR} = \frac{Q_o}{V_o} = \frac{ (p_i - p_{wf}) \, c_t}{(1-s_{wi})\, B_o} =
\frac{ (p_i - p_{wf}) }{(1-s_{wi})\, B_o} \, \big( c_r + s_{wi} c_w + (1-s_{wi})c_o \big) |
where
is flowing bottom-hole pressure,
– initial formation pressure,
– formation volume factor for oil,
– cumulative oil production,
– STOIIP,
– initial water saturation in oil pay.
| Expand |
|---|
|
The total compressibility of oil saturated formation | LaTeX Math Block |
|---|
| c_t = \frac{1}{V_{\phi}} \frac{\partial V_{\phi}}{\partial p} = c_r + s_{wi} c_w + (1-s_{wi})c_o |
The STOIIP can be written as:| LaTeX Math Block |
|---|
| V_O = V_o/B_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi |
The pore volume reduction due to offtakes is: | LaTeX Math Block |
|---|
| \delta V_\phi = Q_o \, 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:| LaTeX Math Block |
|---|
| \frac{\delta V_\phi}{V_\phi} = c_t \, \delta p = c_t \, (p_i - p_{wf \, min}) |
The volume reducation is
and hence | LaTeX Math Block |
|---|
| \frac{Q_o \, B_o \, (1-s_{wi})}{V_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} |
|
For the naturally flowing wells the bottom hole pressure under flowing conditions can be roughly assed by homogeneous multiphase pipe flow model assessed as:
| LaTeX Math Block |
|---|
|
p_{wf} = p_s + \rho_g \, g\, h + \bigg( 1- \frac{\rho_g}{\rho_o} \bigg) \, p_b |
where
– tubing-head pressure defined by the production gathering system,
– is the true vertical depth at formation top,
| LaTeX Math Inline |
|---|
| body | \{ \rho_o, \, \rho_g \} |
|---|
|
– oil and gas densities,
– bubble-point pressure.
Natural Gas Depletion
The Expected Ultimate Recovery during the natural gas depletion can be assessed with the following formula:
| LaTeX Math Block |
|---|
|
EUR_{GD} = \frac{Q_g}{V_g} = 1- \frac{p_{wf}}{p_i} |
See also
Petroleum Industry / Upstream / Production / Field Development Plan / Recovery Methods
