Natural Oil Depletion
The EUR during the natural oil depletion can be assessed with the following formulaequation (see NDR @model for derivation):
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{\rm EUR}_{ND}O = \frac{Q_oO}{V_oO} = \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
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| minimal flowing bottom-hole pressure |
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| initial formation pressure |
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| formation volume factor for oil, |
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| cumulative oil production |
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| initial water saturation in oil pay |
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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, the total 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} |
For the naturally flowing wells the production bottom hole pressure under flowing conditions can be roughly assed by homogeneous multiphase pipe flow model 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 defined by the production gathering system,
– is the true vertical depth at formation top,
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| body | \{ \rho_o, \, \rho_g \} |
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– oil and gas densities,
– bubble-point pressure.
Natural Gas Depletion
The Expected Ultimate Recovery during the natural gas depletion can be assessed with the following formula:
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Petroleum Industry / Upstream / Production / Field Development Plan / Recovery Methods
[ Waterflood Recovery (WF) ]
[ NDR @model ]
