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.
The definition of total compressibility
and can be split into rock, water, oil components:
For low compressible oil compressibility can be assumed constant and the volume reduction can be related to pressure decline as:
and
hence
and
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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.
Motivation = maintain formation pressure at sweep interface
The Expected Ultimate Recovery during the waterflood sweep can be assessed with the following formula:
EUR = E_S \, E_D = E_{SV} \, E_{SA} \, E_D |
where – displacement efficiency, – sweep efficiency, – areal sweep efficiency, – vertical sweep efficiency (see below).
Total sweep | Areal sweep | Vertical sweep | |||
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– sweep volume – pore volume | – sweep area – pore area | – sweep thickness – pore thickness |
E_D = \frac{1-s_{wi}-s_{orw}}{1-s_{wi}} |
where – inititial water in oil pay, – residual oil to water sweep.
Motivation = maintain formation pressure at sweep interface with gas in case of high water mobility which makes watrflood inefficient.
E_D = \frac{1-s_{wi}-s_{org}}{1-s_{wi}} |
where – inititial water in oil pay, – residual oil to gas sweep.
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}} |
Motivation = maintain formation pressure at sweep interface with chemical injection and reduce residual oil to EOR sweep .
E_D = \frac{1-s_{wi}-s_{ori}}{1-s_{wi})} |
where – inititial water in oil pay, – residual oil to injection sweep.
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