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LaTeX Math Block
anchorMatBal
alignmentleft
(B_o - R_s \, B_g) \, G_O +(B_g - R_V \, B_o) \, G_G + (B_w  \, G_W - \phi_n )\, (1- R_s \, R_v)  = 0
LaTeX Math Block
anchorGO
alignmentleft
G_O = V_e^{-1} \, \delta \, Q_O + \left[ \frac{s_{oi}}{B_{oi}}  + \frac{R_{vi}\, s_{gi}}{B_{gi}}\right]
LaTeX Math Block
anchordQO
alignmentleft
\delta \, Q_O = - Q^{\uparrow}_O
LaTeX Math Block
anchorGG
alignmentleft
G_G = V_e^{-1} \, \delta \, Q_G + \left[ \frac{R_{si}\, s_{oi}}{B_{oi}}  + \frac{ s_{gi}}{B_{gi}}\right]
LaTeX Math Block
anchordGG
alignmentleft
\delta \, Q_G = Q^{\downarrow}_G - Q^{\uparrow}_G + Q^{\downarrow}_{GCAP}
LaTeX Math Block
anchorGW
alignmentleft
G_W = V_e^{-1} \, \delta \, Q_W +  \frac{ s_{wi}}{B_{wi}}
LaTeX Math Block
anchordGW
alignmentleft
\delta \, Q_W = Q^{\downarrow}_W - Q^{\uparrow}_W + Q^{\downarrow}_{WAQ}
LaTeX Math Block
anchorphin
alignmentleft
\phi_n = 1 + c_\phi \, (p-p_i)  + 0.5 \, c^2_\phi \, (p-p_i)^2

where

LaTeX Math Inline
bodyp

(t)

_i

initial formation pressure

at  time moment

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

Cumulative oil production by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inlinebody

:

LaTeX Math Inline
body

t 

p_i = p(0)

initial formation pressure


LaTeX Math Inline
body--uriencoded--Q%5e%7B\uparrow%7D_
G
O(t)

Cumulative

gas

oil production by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyV_e

initial oil+gas pay drainage volume (excluding the aquifer and gas cap)


LaTeX Math Inline
body--uriencoded--Q%5e%7B\uparrow%7D_
W
G(t)

Cumulative

water

gas production by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyc_\phi

pore compressibility 


LaTeX Math Inline
body--uriencoded--Q%5e%7B\
downarrow%7D
uparrow%7D_W(t)

Cumulative water

injection

production by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
body--uriencoded--s_%7Bwi%7D

initial water saturation


LaTeX Math Inline
body--uriencoded--Q%5e%7B\downarrow%7D_
G
W(t)

Cumulative

gas

water injection by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
body--uriencoded--s_%7Bgi%7D

initial gas saturation


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

Cumulative

water influx from Aquifer Expansion

gas injection by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
body--uriencoded--s_%7Boi%7D

initial oil saturation:

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

initial oil saturation


LaTeX Math Inline
body--uriencoded--Q%5e%7B\downarrow%7D_
%7BGCAP%7Dt
%7BWAQ%7D(t)

Cumulative

gas

water influx from

Gas Cap expansion

Aquifer Expansion by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyB_o(p)

Oil formation volume factor as functions of reservoir pressure

LaTeX Math Inline
bodyp

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

Cumulative gas influx from Gas Cap expansion by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyB_g(p)

Gas formation volume factor as functions of reservoir pressure

LaTeX Math Inline
bodyp



LaTeX Math Inline
bodyB_w(p)

Water formation volume factor as functions of reservoir pressure

LaTeX Math Inline
bodyp



LaTeX Math Inline
bodyR_s(p), \, R_v(p)

 Solution GOR and Vaporized Oil Ratio as functions of reservoir pressure

LaTeX Math Inline
bodyp










The MatBal equation 

LaTeX Math Block Reference
anchorMatBal
 is often complemented by constant PI model of Bottom-Hole Pressure (
LaTeX Math Inline
bodyp^{\uparrow}_{wf}(t)
 for producers and 
LaTeX Math Inline
bodyp^{\downarrow}_{wf}(t)
 for injectors):

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