Natural Depletion

Oil Depletion

The EUR during the natural oil depletion can be assessed with the following formula:

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.

c_t = \frac{1}{V_{\phi}} \frac{\partial V_{\phi}}{\partial p} = c_r + s_{wi} c_w + (1-s_{wi})c_o

c_t = c_r + s_{wi} c_w + (1-s_{wi})c_o 

\frac{\delta V_\phi}{V_\phi} = c_t \, \delta p = c_t \, (p_i - p_{wf \, min})

\delta V_\phi = Q_o \, B_o

V_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi

\frac{Q_o \, B_o \, (1-s_{wi})}{V_o} = c_t \, (p_i - p_{wf \, min})

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 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 defined by the production gathering system,  – is the true vertical depth at formation top,  – 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:

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:

EUR_{WF} =  E_S \, E_D + (1-E_S) EUR_{ND} 

where  – displacement efficiency,   – sweep efficiency.

Sweep efficiency

Water-Oil displacement efficiency

Gas flooding

Motivation = maintain formation pressure at sweep interface with gas in case of high water mobility  which makes waterflood inefficient.

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 .

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  .

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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