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Equation, expressing that total pressure
in any point of a reservoir
is a sum of pressure responses
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body | \delta p_k(t, {\bf r}) |
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to individual rate variations
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(\tau) |
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p_m(t) = p_i + \sum_k \delta p_{mk}(t) = p_i + \int_0^t p_{umk}(t-\tau) \, dq_k(\tau) = p_i + \int_0^t p_{umm}(t-\tau) \, dq_k(\tau) + \sum_{k \neq m} \int_0^t p_{umk}(t-\tau) \, dq_k(\tau) |
where
| specific component of -well pressure variation caused by -well flowrate history |
| pressure response in -well to unit-rate drawdown in the same well (DTR) |
| pressure response in -well to unit-rate drawdown in -well (CTR) |
The super
Applies to single-layer linear diffusion model