Natural Depletion
The Expected Ultimate Recovery during the natural depletion can be assessed with the following formula:
(1) | 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 p_{wf} is flowing bottom-hole pressure, p_i – initial formation pressure, B_o – formation volume factor for oil, Q_o – cumulative oil production, V_o – STOIIP, s_{wi} – initial water saturation in oil pay.
For the naturally flowing wells the production bottom hole pressure can be assessed as:
(9) | p_{wf} = p_s + \rho_g \, g\, h + \bigg( 1- \frac{\rho_g}{\rho_o} \bigg) \, p_b |
where p_s – tubing-head pressure defind by the production athering system, h – is the true vertical deoth at formation top, \{ \rho_o, \, \rho_g \} – oil and gas densities, p_b – bubble-point pressure.
Water flooding
Motivation = maintain formation pressure at sweep interface
The Expected Ultimate Recovery during the waterflood sweep can be assessed with the following formula:
(10) | EUR = E_S \, E_D = E_{SV} \, E_{SA} \, E_D |
where E_D – displacement efficiency, E_S – sweep efficiency, E_{SA} – areal sweep efficiency, E_{SV} – vertical sweep efficiency (see below).
Sweep effciency
Total sweep | Areal sweep | Vertical sweep | ||||||
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V_{sweep} – sweep volume V_\phi – pore volume | A_{sweep} – sweep area A_\phi – pore area | h_{sweep} – sweep thickness h_\phi – pore thickness |
Water displacement efficiency
(14) | E_D = \frac{1-s_{wi}-s_{orw}}{1-s_{wi}} |
where s_{wi} – inititial water in oil pay, s_{orw} – residual oil to water sweep.
Gas flooding
Motivation = maintain formation pressure at sweep interface with gas in case of high water mobility \frac{k_{rw}}{\mu_w} \gg \frac{k_{ro}}{\mu_o} which makes watrflood inefficient.
Gas displacement efficiency
(15) | E_D = \frac{1-s_{wi}-s_{org}}{1-s_{wi}} |
where s_{wi} – inititial water in oil pay, s_{org} – residual oil to gas sweep.
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 s_{orw} and gas sweep is less than to water sweep s_{org} < s_{orw}.
(16) | 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 s_{or \, eor} < s_{orw}.
(17) | E_D = \frac{1-s_{wi}-s_{ori}}{1-s_{wi})} |
where s_{wi} – inititial water in oil pay, s_{ori} – residual oil to injection sweep.
CО2 injection
Reference
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