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The plot of. of WOR (along y-axis) against the inverse oil production rate

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bodyq_O
 (along x-axis) (see Fig. 1).


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Fig. 1. WOR (logarithmic vertical axis) vs inverse oil production rate (linear horizontal axis)

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anchorqOW
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WOR = \frac{q_W}{q_O} = a  + b \, \cdot q^{-1}_O
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anchora
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a = J^{-1}_{1O} \cdot ( J_{1W} + J_{2W})
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anchorb
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b = J_{2W} \cdot (p^*_2 - p^*_1)

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anchor<qOW>
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<WOR>\langle WOR \rangle =\frac{\langle <q_W>/<q_O>q_W \rangle}{\langle q_O \rangle}  = a  + b \cdot \,langle /<q_O>q_O^{-1} \rangle

where

LaTeX Math Inline
body<q_W>\langle q_W \rangle, \ <q_O>\langle q_O \rangle

are weighted average of

LaTeX Math Inline
bodyq_W
 and
LaTeX Math Inline
bodyq_O

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LaTeX Math Block
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<\langle A >\rangle_t \ = \frac{1}{t} \int_o^t A(t) \, dt
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<A>\langle A\rangle_q \ = \frac{1}{Q(t)} \int_o^t A(t) \, q(t) \, dt

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