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LaTeX Math Block
anchorQ6XP7
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p(t)  = p_i + \frac{\Delta Q(t)}{V_e\phi \cdot c_t}

where

LaTeX Math Inline
body\Delta Q(t)

Cumulative Voidage Replacement Balance (CVRB) over time 

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyV_e \phi = V \cdot \phi_i

initial drainage volume of the main pay (excluding the aquifer and gas cap)

LaTeX Math Inline
body\phi_i = \phi(p_i)

initial porosity

LaTeX Math Inline
body--uriencoded--c_t = c_\phi + c_o \, s_%7Boi%7D + c_g \, s_%7Bgi%7D + c_w \, s_%7Bwi%7D

total compressibility

LaTeX Math Inline
bodyc_\phi

pore compressibility 

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

initial water saturation

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

initial gas saturation

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

LaTeX Math Inline
bodyc_o, \, c_g, \, c_w

fluid compressibility of water phaseoil phase and gas phase
Show If
grouparax
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titleARAX

The MatBal equation 

LaTeX Math Block Reference
pageMaterial Balance Pressure @model
can be re-written as following:

LaTeX Math Block
anchorMatBal_formula
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p = p_i + \frac{\delta Q}{c_\phi \, V_\phi} + \delta p_i
LaTeX Math Block
anchorMatBal_formula
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\delta p_i =  \frac{ B_{og} \, F_{Oi} + B_{go} \, F_{Gi} + B_w \, F_W -1}{c_\phi}
LaTeX Math Block
anchor1
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B_{og} = \frac{B_o - R_s \, B_g}{1- R_s \, R_v}
LaTeX Math Block
anchor1
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B_{go} = \frac{ B_g - R_v \, B_o}{1- R_s \, R_v}

where

LaTeX Math Inline
body\delta Q

Cumulative Voidage Replacement Balance (CVRB) 

See Also

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

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