Natural Oil Depletion

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

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

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 STOIIP $\begin{array}{l}V_O\end{array}$ is related to reservoir oil volume $\begin{array}{l}V_o\end{array}$ as:

(2)	$\begin{array}{l}\displaystyle V_O = V_o/B_o\end{array}$

and to the reservoir pore volume $\begin{array}{l}V_\phi\end{array}$ as:

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

so that

(4)	$\begin{array}{l}\displaystyle B_o \, V_O = (1-s_{wi}) \, V_\phi \quad \Rightarrow \quad V_\phi = \frac{B_o \, V_O}{(1-s_{wi})}\end{array}$

The pore volume reduction due to offtakes is:

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

thus leading to

(6)	$\begin{array}{l}\displaystyle c_t = \frac{1}{V_{\phi}} \frac{\partial V_{\phi}}{\partial p} = \frac{1-s_{wi}}{B_o \, V_O} \frac{B_o \, Q_O}{\delta p} =\frac{1-s_{wi}}{\delta p} \frac{Q_O}{V_O} = \frac{1-s_{wi}}{\delta p} \cdot {\rm EUR_O}\end{array}$

where

(7)	$\begin{array}{l}\displaystyle c_t = c_r + s_{wi} c_w + (1-s_{wi})c_o\end{array}$

is total compressibility of oil saturated formation and

(8)	$\begin{array}{l}\displaystyle \delta p = p_i - p_{wf}\end{array}$

pressure reduction due to pore volume reduction caused by offtakes.

For low compressible oil, the total compressibility can be assumed constant $\begin{array}{l}c_t = \rm const\end{array}$ and (6) becomes:

(9)	$\begin{array}{l}\displaystyle \frac{1-s_{wi}}{(p_i - p_{wf \, min})} \cdot {\rm EUR_O} = c_t = \rm const\end{array}$

and

(10)	$\begin{array}{l}\displaystyle {\rm EUR}_O = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})}\end{array}$

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

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

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:

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

Page tree

Natural Oil Depletion

Natural Gas Depletion

See also

Page tree

Natural Depletion Recovery (NDR)

Natural Oil Depletion

Natural Gas Depletion

See also