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Tje XCRM model predicts the formation pressure
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| body | --uriencoded--p_%7Be,n%7D |
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and bottom-hole pressure
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| body | --uriencoded--p_%7Bwf,n%7D |
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in
-th oil producer in response to its
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| body | --uriencoded--(q%5e%7B\uparrow%7D_%7BOn%7D, \ q%5e%7B\uparrow%7D_%7BWn%7D) |
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its cumulative production rate
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| body | --uriencoded--Q%5e%7B\uparrow%7D_%7BOn%7D |
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| body | --uriencoded--Q%5e%7B\uparrow%7D_%7BWn%7D |
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), cumulative production of the offset wells ( | LaTeX Math Inline |
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| body | --uriencoded--Q%5e%7B\uparrow%7D_%7BOm%7D |
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| body | --uriencoded--Q%5e%7B\uparrow%7D_%7BWm%7D |
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)Given
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| p_{e,n} \ (t) = p_{i,n} \ (0) + \gamma_n^{-1} \cdot \sum_m \left( Q^{\uparrow}_{nm} + Q^{\downarrow}_{nm} \ \right) |
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| p_{{\rm wf}, n} \ \ \ (t) = p_e \ (t) + 0.5 \cdot J_{On}^{-1} \cdot \left[ 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 q^{\uparrow}_{Wn}(t) \right] |
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| s_{wn} = \left[ 1 + \frac{B_o}{B_w} \cdot \frac{q^{\uparrow}_{On}}{f^{\uparrow}_{W,nn} \cdot q^{\uparrow}_{Wn}} \right]^{-1} |
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