Implication that a total pressure in any point of a reservoir
is a sum of pressure responses
to individual rate variations
in all wells
:
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) |
For a given -well location this can be rewritten as:
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 | |
pressure response in | |
pressure response in |