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Oil Depletion
The EUR during the natural oil depletion can be assessed with the following formula:
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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 total compressibility of oil saturated formation
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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:
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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
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V_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi |
hence
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\frac{Q_o \, B_o \, (1-s_{wi})}{V_o} = c_t \, (p_i - p_{wf \, min}) |
and
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EUR = \frac{Q_o}{V_o} = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})\, B_o} |
See also
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Petroleum Industry / Upstream / Production / Subsurface Production / Reserves Depletion
Physics / Fluid Dynamics / Percolation / Reservoir flow / Reservoir flow drive mechanisms
[ Field Development Plan ]
Reference
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| title | ARAX |
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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, | LaTeX Math Inline |
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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 = \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 = E_S \, E_D = E_{SV} \, E_{SA} \, E_D |
where
– displacement efficiency, – sweep efficiency, – areal sweep efficiency, – vertical sweep efficiency (see below).Sweep effciency
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E_S = \frac{V_{sweep}}{V_\phi} |
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E_{SA} = \frac{A_{sweep}}{A_\phi} |
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E_{SV} = \frac{h_{sweep}}{h_\phi} |
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– sweep volume – pore volume ...
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– sweep thickness – pore thickness Water displacement efficiency
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E_D = \frac{1-s_{wi}-s_{orw}}{1-s_{wi}} |
where
– inititial water in oil pay, – residual oil to water sweep. 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 .| LaTeX Math Block |
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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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