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Consider a pressure convolution equation for the above 2-wells system with constant BHP: LaTeX Math Block |
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anchor | Case2_PSS_p11 |
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alignment | left |
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| p_1(t) = p_i - \int_0^t p_{u,\rm 11}(t-\tau) dq_1(\tau) - \int_0^t p_{u,\rm 21}(t-\tau) dq_2(\tau) = \rm const |
The time derivative is going to be LaTeX Math Block |
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anchor | Case2_PSS_p11 |
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alignment | left |
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| \dot p_1(t) = - \left( \int_0^t p_{u,\rm 11}(t-\tau) dq_1(\tau) \right)^{\cdot} - \left( \int_0^t p_{u,\rm 21}(t-\tau) dq_2(\tau) \right)^{\cdot} = 0 |
LaTeX Math Block |
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anchor | Case2_PSS_p11 |
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alignment | left |
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| p_{u,\rm 11}(0) \cdot q_1(0) + \int_0^t \dot p_{u,\rm 11}(t-\tau) dq_1(\tau) = - p_{u,\rm 21}(0) \cdot q_2(0) - \int_0^t \dot p_{u,\rm 21}(t-\tau) dq_2(\tau) |
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For the finite-volume drain
LaTeX Math Inline |
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body | V_{\phi,1} \leq V_{\phi,2} < \infty |
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the flowrate response factor
LaTeX Math Inline |
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body | \delta q_1 / \delta q_2 |
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is getting stabilised over time as:
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