Tje XCRM modle model predicts the formation pressure
LaTeX Math Inline |
---|
body | --uriencoded--p_%7Be,n%7D |
---|
|
and
bottomobottom-hole
pressure pressure LaTeX Math Inline |
---|
body | --uriencoded--p_%7Bwf,n%7D |
---|
|
in
response to theGiven -th oil producer
in response to its production rateGiven :
LaTeX Math Block |
---|
| p_{e,n} \ (t) = p_{i,n} \ (0) + \gamma_n^{-1} \cdot \sum_m \left( Q^{\uparrow}_{nm} + Q^{\downarrow}_{nm} \ \right) |
| LaTeX Math Block |
---|
| p_{{\rm wf}, n} \ \ \ (t) = p_e \ (t) + 0.5 \cdot J_{On}^{-1} \cdot \left[ q q^{\uparrow}_{On}(t) + f^{\uparrow}_{W,nn} \cdot \frac{\mu_W}{\mu_O} \cdot \frac{k_{ro}(s_{wn})}{k_{rw}(s_{wn})} \cdot qq^{\uparrow}_{Wn}(t) \right] |
| LaTeX Math Block |
---|
| s_{wn} = \left[ 1 + \frac{B_o}{B_w} \cdot \frac{q^{q\uparrow}_{On}}{f^{\uparrow}_{W,nn} \cdot qq^{\uparrow}_{Wn}} \right]^{-1} |
|
LaTeX Math Block |
---|
| Q^{\uparrow}_{nm} \ =
\ - \ f^{\uparrow}_{O,nm} \ \cdot B_{ob} \cdot \, Q^{\uparrow}_O
\ - \ f^{\uparrow}_{G,nm} \ \cdot B_{go} \cdot Q^{\uparrow}_G
\ - \ f^{\uparrow}_{W,nm} \ \cdot B_w \cdot Q^{\uparrow}_W
|
| LaTeX Math Block |
---|
| Q^{\downarrow}_{nm} \ =
f^{\downarrow}_{G,nm} \ \cdot B_{go} \cdot Q^{\downarrow}_G
\ + \ f^{\downarrow}_{W,nm} \ \cdot B_w \cdot Q^{\downarrow}_W
\ + \ B_{go} \cdot Q^{\downarrow}_{GCAP} \
\ + \ B_w \cdot Q^{\downarrow}_{WAQ}
|
|
...