Approximation of Material Balance Pressure @model for slightly compressibility flow:

p(t)  = p_i + \frac{\Delta Q(t)}{V_\phi \cdot c_t}

\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

	Cumulative Voidage Replacement Balance (CVRB) over time
	initial drainage volume of the main pay (excluding the aquifer and gas cap)
	initial porosity
	total compressibility
	pore compressibility
	initial water saturation
	initial gas saturation
	initial oil saturation:
	fluid compressibility of water phase, oil phase and gas phase

The equations and are often used in express assessment of thief water production share and thief water injection share :

p_i - p(t) = \alpha \cdot Q^{\uparrow}_O(t) + \beta \cdot Q^{\uparrow}_W(t) - \gamma \cdot Q^{\downarrow}_W(t)

\alpha > 0, \quad \beta > 0, \quad \gamma > 0

V_\phi = \frac{ 1 }{ \alpha \cdot c_t}  \cdot \frac{B_o - R_s \, B_g}{1- R_s \, R_v}

\Omega^{\uparrow}_W = \frac{Q^{\uparrow}_{W,{\rm true}}}{Q^{\uparrow}_W} = \frac{\beta}{\alpha}  \cdot \frac{1}{B_w} \cdot \frac{B_o - R_s \, B_g}{1- R_s \, R_v}

\Omega^{\downarrow}_W = \frac{Q^{\downarrow}_{W, {\rm true}}}{Q^{\downarrow}_W} =\frac{\gamma}{\alpha}  \cdot \frac{1}{B_w} \cdot \frac{B_o - R_s \, B_g}{1- R_s \, R_v}

The MatBal equation can be re-written as following:

p = p_i + \frac{\delta Q}{c_\phi \, V_\phi} + \delta p_i

\delta p_i =  \frac{ B_{og} \, F_{Oi} + B_{go} \, F_{Gi} + B_w \, F_W -1}{c_\phi}

B_{og} = \frac{B_o - R_s \, B_g}{1- R_s \, R_v}

B_{go} = \frac{ B_g - R_v \, B_o}{1- R_s \, R_v}

where

Cumulative Voidage Replacement Balance (CVRB)

See Also