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- its current oil/water production rate
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body | --uriencoded--\left( q%5e%7B\uparrow%7D_%7BOn%7D, \ q%5e%7B\uparrow%7D_%7BWn%7D \right) |
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- its cumulative oil/water production rate
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body | --uriencoded--\left( Q%5e%7B\uparrow%7D_%7BOn%7D, \ Q%5e%7B\uparrow%7D_%7BWn%7D \right) |
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- cumulative oil/water production from the offset wells
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body | --uriencoded--\left( Q%5e%7B\uparrow%7D_%7BOm%7D, \ Q%5e%7B\uparrow%7D_%7BWm%7D \right)_%7Bm \neq n \, \in \uparrow%7D |
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- cumulative water injection in the offset wells
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body | --uriencoded--\left( Q%5e%7B\downarrow%7D_%7BOm%7D, \ Q%5e%7B\downarrow%7D_%7BWm%7D \right)_%7Bm \in \downarrow%7D |
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using the following equations:
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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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