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