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Modelling facility for field-average formation pressure 

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bodyp(t)
 at any time moment 
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bodyt
 as response to production flowrates history:

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anchorMatBal
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\phi_n(p) = \frac{B_o - R_s \, B_g}{1- R_s \, R_v} \cdot G_O 
+\frac{ B_g - R_v \, B_o}{1- R_s \, R_v} \cdot G_G 
+B_w  \, G_W 
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anchorphin
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\phi_n = \exp \left[ c_\phi \, (p-p_i)  \right] \approx 1 + c_\phi \, (p-p_i)  + 0.5 \, c^2_\phi \, (p-p_i)^2 
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anchorGO
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G_O = V_e^{-1} \, \delta \, Q_O + \left[ \frac{s_{oi}}{B_{oi}}  + \frac{R_{vi}\, s_{gi}}{B_{gi}}\right] 
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\delta \, Q_O = - Q^{\uparrow}_O
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anchorGG
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G_G = V_e^{-1} \, \delta \, Q_G + \left[ \frac{R_{si}\, s_{oi}}{B_{oi}}  + \frac{ s_{gi}}{B_{gi}}\right] 
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anchordGG
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\delta \, Q_G = Q^{\downarrow}_G - Q^{\uparrow}_G + Q^{\downarrow}_{GCAP}
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anchorGW
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G_W = V_e^{-1} \, \delta \, Q_W +  \frac{ s_{wi}}{B_{wi}} 
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anchordGW
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\delta \, Q_W = Q^{\downarrow}_W - Q^{\uparrow}_W + Q^{\downarrow}_{WAQ}
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anchorphin
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\phi_n = \exp \left[ c_\phi \, (p-p_i) \right] \approx 1 + c_\phi \, (p-p_i) + 0.5 \, c^2_\phi \, (p-p_i)^2

where

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bodyp_i

initial formation pressure:

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bodyp_i = p(0)

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body--uriencoded--Q%5e%7B\uparrow%7D_O(t)

Cumulative oil production by the time moment

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bodyt

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bodyV_e = V \cdot \phi_i

initial drainage volume of Main Pay (excluding the aquifer and gas cap)

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body--uriencoded--Q%5e%7B\uparrow%7D_G(t)

Cumulative gas production by the time moment

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bodyt

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body\phi_i = \phi(p_i)

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body--uriencoded--Q%5e%7B\uparrow%7D_W(t)

Cumulative water production by the time moment

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bodyt

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bodyc_\phi

pore compressibility 

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body--uriencoded--Q%5e%7B\downarrow%7D_W(t)

Cumulative water injection by the time moment

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bodyt

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body--uriencoded--s_%7Bwi%7D

initial water saturation

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body--uriencoded--Q%5e%7B\downarrow%7D_G(t)

Cumulative gas injection by the time moment

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bodyt

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body--uriencoded--s_%7Bgi%7D

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body--uriencoded--Q%5e%7B\downarrow%7D_%7BWAQ%7D(t)

Cumulative water influx from Aquifer Expansion by the time moment

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bodyt

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body--uriencoded--s_%7Boi%7D

initial oil saturation:

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body--uriencoded--s_%7Boi%7D = 1 - s_%7Bwi%7D - s_%7Bgi%7D

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body--uriencoded--Q%5e%7B\downarrow%7D_%7BGCAP%7Dt)

Cumulative gas influx from Gas Cap expansion by the time moment

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bodyt





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bodyB_o(p)

Oil formation volume factor as functions of reservoir pressure

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bodyp

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bodyR_s(p)

Solution GOR as functions of reservoir pressure

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bodyp

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bodyB_g(p)

Gas formation volume factor as functions of reservoir pressure

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bodyp

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bodyR_v(p)

Vaporized Oil Ratio as functions of reservoir pressure

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bodyp

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bodyB_w(p)

Water formation volume factor as functions of reservoir pressure

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bodyp
 



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The above approximations sometime allow using simple graphical methods for rough estimation of drainage volume 

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bodyV_e
and associated Hydrocarbon Reserves.


See Also

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Petroleum Industry / Upstream /  Production / Subsurface Production / Field Study & Modelling / Production Analysis / Material Balance Analysis (MatBal)

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