Natural Depletion
Oil Depletion
The EUR during the natural oil depletion can be assessed with the following formula:
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EUR_{ND} = \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.
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The total compressibility of oil saturated formation LaTeX Math Block |
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| c_t = \frac{1}{V_{\phi}} \frac{\partial V_{\phi}}{\partial p} = c_r + s_{wi} c_w + (1-s_{wi})c_o |
and can be split into rock, water, oil components: LaTeX Math Block |
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| c_t = c_r + s_{wi} c_w + (1-s_{wi})c_o |
For low compressible oil compressibility can be assumed constant and the volume reduction can be related to pressure decline as: LaTeX Math Block |
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| \frac{\delta V_\phi}{V_\phi} = c_t \, \delta p = c_t \, (p_i - p_{wf \, min}) |
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| \delta V_\phi = Q_o \, B_o |
and LaTeX Math Block |
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| V_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi |
hence LaTeX Math Block |
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| \frac{Q_o \, B_o \, (1-s_{wi})}{V_o} = c_t \, (p_i - p_{wf \, min}) |
and LaTeX Math Block |
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| EUR = \frac{Q_o}{V_o} = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})\, B_o} |
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For the naturally flowing wells the production bottom hole pressure can be assessed as:
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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,
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body | \{ \rho_o, \, \rho_g \} |
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– oil and gas densities,
– bubble-point pressure.
Gas Depletion
The Expected Ultimate Recovery during the natural gas depletion can be assessed with the following formula:
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EUR_{GD} = \frac{Q_g}{V_g} = 1- \frac{p_{wf}}{p_i} |
Water flooding
Motivation = maintain formation pressure at sweep interface
The Expected Ultimate Recovery during the waterflood sweep can be assessed with the following formula:
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EUR_{WF} = E_S \, E_D + (1-E_S) EUR_{ND} |
where
–
displacement efficiency,
–
sweep efficiency.
Sweep efficiency
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| Sweep Efficiency |
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| Sweep Efficiency |
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nopanel | true |
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Water-Oil displacement efficiency
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| Displacement Efficiency (ED) |
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| Displacement Efficiency (ED) |
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nopanel | true |
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Gas flooding
Motivation = maintain formation pressure at sweep interface with gas in case of high water mobility
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body | \frac{k_{rw}}{\mu_w} \gg \frac{k_{ro}}{\mu_o} |
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which makes watrflood inefficient.
Gas displacement efficiency
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E_D = \frac{1-s_{wi}-s_{org}}{1-s_{wi}} |
where
– inititial water in oil pay,
– 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
and gas sweep is less than to water sweep
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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
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body | s_{or \, eor} < s_{orw} |
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E_D = \frac{1-s_{wi}-s_{ori}}{1-s_{wi}} |
where
– inititial water in oil pay,
– residual oil to injection sweep.
CО2 injection
Reference
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