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The MatBal equation
| LaTeX Math Block Reference |
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can be
re-written in the following popular form:...
| LaTeX Math Block |
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| anchor | MatBal_formula |
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| alignment | left |
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p = p_i + \frac{\delta Q}{c_\phi \, V_\phi} + \delta p_i |
...
| LaTeX Math Block |
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| anchor | MatBal_formula |
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| alignment | left |
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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 |
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B_{og} = \frac{B_o - R_s \, B_g}{1- R_s \, R_v} |
...
| LaTeX Math Block |
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B_{go} = \frac{ B_g - R_v \, B_o}{1- R_s \, R_v} |
where
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The MatBal equation
| LaTeX Math Block Reference |
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can be complemented by constant
PI model of Bottom-Hole Pressure ( for
producers and
| LaTeX Math Inline |
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| body | p^{\downarrow}_{wf}(t) |
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for
injectors):...
| Low pressure dry gas |
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| LaTeX Math Inline |
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| body | --uriencoded--c_t = c_\phi + c_%7B\rm fluid%7D = %7B\rm const%7D |
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| | LaTeX Math Inline |
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| body | --uriencoded--c_g = \sim \frac%7B1%7D%7Bp%7D |
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|
| LaTeX Math Block |
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| p(t) = p_i + \frac{\Delta Q(t)}{V_\phi \cdot c_t} |
| | LaTeX Math Block |
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| p(t) = p_i \exp \left[ \frac{\Delta Q(t)}{V_\phi} \right] |
|
where
is Cumulative Voidage Replacement Balance (CVRB):| 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) |
|
The above approximations sometime allow using simple graphical methods for rough estimation of drainage volume
and associated
Hydrocarbon Reserves.
...
