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LaTeX Math Block
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\Delta Q_N = \frac{\Delta Q}

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{V_e

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LaTeX Math Block
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\Delta Q = -  \frac{B_o - R_s \, B_g}{1- R_s \, R_v} \cdot  \, Q^{\uparrow}_O + \frac{ B_g - R_v \, B_o}{1- R_s \, R_v} \cdot \, \left( Q^{\downarrow}_G - Q^{\uparrow}_G + Q^{\downarrow}_{GCAP} \right) + B_w \, \left( Q^{\downarrow}_W - Q^{\uparrow}_W + Q^{\downarrow}_{WAQ} \right)

where

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body\Delta Q(t)

Cumulative Voidage Replacement Balance (CVRB) over time 

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bodyt

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bodyV_e = V \cdot \phi_i

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

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body\phi_i = \phi(p_i)

initial porosity


If Aquifer Expansion and/or Gas Cap expansionare unknown they are simply ignored for the first pressure modelling run: 

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body--uriencoded--Q%5e%7B\downarrow%7D_%7BGCAP%7D = 0, \ Q%5e%7B\downarrow%7D_%7BWAQ%7D = 0
.

They can be adjusted at the next model runs by fitting formation pressure response (see Material Balance Pressure @model).

See Also

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Petroleum Industry / Upstream /  Production / Subsurface Production / Field Study & Modelling / Production Analysis / Voidage Replacement Balance (VRB)

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