Natural Oil Depletion

The EUR during the natural oil depletion can be assessed with the following formula:

(1)	$\begin{array}{l}\displaystyle {\rm EUR}_{\rm NDR} = \frac{Q_o}{V_o} = \frac{ (p_i - p_{wf}) \, c_t}{(1-s_{wi})\, B_o} = \frac{ (p_i - p_{wf}) }{(1-s_{wi})\, B_o} \, \big( c_r + s_{wi} c_w + (1-s_{wi})c_o \big)\end{array}$

where $\begin{array}{l}p_{wf}\end{array}$ is flowing bottom-hole pressure, $\begin{array}{l}p_i\end{array}$ – initial formation pressure, $\begin{array}{l}B_o\end{array}$ – formation volume factor for oil, $\begin{array}{l}Q_o\end{array}$ – cumulative oil production, $\begin{array}{l}V_o\end{array}$ – STOIIP, $\begin{array}{l}s_{wi}\end{array}$ – initial water saturation in oil pay.

EUR Deduction

The total compressibility of oil saturated formation

(2)	$\begin{array}{l}\displaystyle c_t = \frac{1}{V_{\phi}} \frac{\partial V_{\phi}}{\partial p} = c_r + s_{wi} c_w + (1-s_{wi})c_o\end{array}$

The STOIIP $\begin{array}{l}V_O\end{array}$ can be written as:

(3)	$\begin{array}{l}\displaystyle V_O = V_o/B_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi\end{array}$

The pore volume reduction due to offtakes is:

(4)	$\begin{array}{l}\displaystyle \delta V_\phi = Q_o \, B_o\end{array}$

For low compressible oil, the total compressibility can be assumed constant $\begin{array}{l}c_t = \rm const\end{array}$ and the pore volume reduction to due to offtakes can be related to pressure decline as:

(5)	$\begin{array}{l}\displaystyle \frac{\delta V_\phi}{V_\phi} = c_t \, \delta p = c_t \, (p_i - p_{wf \, min})\end{array}$

The volume reducation is

and

hence

(6)	$\begin{array}{l}\displaystyle \frac{Q_o \, B_o \, (1-s_{wi})}{V_o} = c_t \, (p_i - p_{wf \, min})\end{array}$

and

(7)	$\begin{array}{l}\displaystyle {\rm EUR}_{\rm NDR} = \frac{Q_o}{V_o} = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})\, B_o}\end{array}$

For the naturally flowing wells the bottom hole pressure under flowing conditions can be roughly assed by homogeneous multiphase pipe flow model assessed as:

(8)	$\begin{array}{l}\displaystyle p_{wf} = p_s + \rho_g \, g\, h + \bigg( 1- \frac{\rho_g}{\rho_o} \bigg) \, p_b\end{array}$

where $\begin{array}{l}p_s\end{array}$ – tubing-head pressure defined by the production gathering system, $\begin{array}{l}h\end{array}$ – is the true vertical depth at formation top, $\begin{array}{l}\{ \rho_o, \, \rho_g \}\end{array}$ – oil and gas densities, $\begin{array}{l}p_b\end{array}$ – bubble-point pressure.

Natural Gas Depletion

The Expected Ultimate Recovery during the natural gas depletion can be assessed with the following formula:

(9)	$\begin{array}{l}\displaystyle EUR_{GD} = \frac{Q_g}{V_g} = 1- \frac{p_{wf}}{p_i}\end{array}$

Page tree

Natural Oil Depletion

Natural Gas Depletion

See also

Page tree

Natural Depletion Recovery (NDR)

Natural Oil Depletion

Natural Gas Depletion

See also