Natural Depletion

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

EUR =  \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.

c_t = \frac{1}{V_{\phi}} \frac{\partial V_{phi}}{\partial p} = c_r + s_{wi} c_w + (1-s_{wi})c_o \big

c_t = c_r + s_{wi} c_w + (1-s_{wi})c_o \big

\frac{\delta V_\phi}{V_\phi} = c_t \, \delta p = c_t \, (p_i - p_{wf \, min})

\delta V_\phi = Q_o \, B_o

V_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi

\frac{Q_o \, B_o \, (1-s_{wi})}{V_o} = c_t \, (p_i - p_{wf \, min})

EUR =  \frac{Q_o}{V_o} =  \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})\, B_o}

For the naturally flowing wells the production bottom hole pressure can be assessed as:

p_{wf} = p_s + \rho_g \, g\, h + \bigg( 1- \frac{\rho_g}{\rho_o} \bigg) \, p_b

where  – tubing-head pressure defind by the production athering system,  – is the true vertical deoth at formation top,  – oil and gas densities,  – bubble-point pressure.

Water flooding

Motivation = maintain formation pressure at sweep interface

EUR =  E_S \, E_D = E_{SV} \, E_{SH} \, E_D

Sweep effciency

E_S = \frac{V_{sweep}}{V_\phi}

E_{SH} = \frac{A_{sweep}}{A_\phi}

E_{SV} = \frac{h_{sweep}}{h_\phi}

Water displacement efficiency

E_D = \frac{1-s_{wi}-s_{orw}}{1-s_{wi})}

Gas flooding

Motivation = maintain formation pressure at sweep interface with gas in case of high water mobility  which makes watrflood inefficient.

Gas displacement efficiency

E_D = \frac{1-s_{wi}-s_{org}}{1-s_{wi})}

WAG flooding

Motivation =  maintain formation pressure at sweep interface with alternating inejction of water and gas  in case of high residual oil to water sweep is high   and gas sweep is less than to water sweep .

E_D = \frac{1-s_{wi}-s_{org}}{1-s_{wi})}

Chemical EOR

Motivation =  maintain formation pressure at sweep interface with chemical injection and reduce residual oil to EOR sweep  .

E_D = \frac{1-s_{wi}-s_{or \, eor}}{1-s_{wi})}

CО2 injection

Reference

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