Implication that pressure
at any point of a porous reservoir is a linear sum of pressure responses LaTeX Math Inline |
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body | \delta p_k(t, {\bf r}) |
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to individual rate variations in all wells connected to this reservoir:Equation, expressing that total pressure in any point of a reservoir is a sum of pressure responses to individual pressure responses from all offset wells:
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p(t, {\bf r}) = p_i + \sum_k \delta p_k(t, {\bf r}) = p_i + \sum_k \int_0^t p_{uk}(t-\tau, {\bf r}) \, dq_k(\tau) |
In case reservoir point
defines location of -well the superposition principle can be rewritten as: LaTeX Math Block |
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p_m(t) = p_{mi} + \sum_k \delta p_{mk}(t) = p_{mi} + \sum_k \int_0^t p_{umk}(t-\tau) \, dq_k(\tau) = p_{mi} + \int_0^t p_{umm}(t-\tau) \, dq_m(\tau) + \sum_{k \bfneq r}) m} \int_0^t p_{umk}(t-\tau) \delta q(\tau), dq_k(\tau) |
where