Implication that pressure at any point
of a porous reservoir is a linear sum of pressure responses
to individual rate variations
in all wells connected to this reservoir:
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:
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 \neq m} \int_0^t p_{umk}(t-\tau) \, dq_k(\tau) |
where
initial formation pressure in | |
specific component of | |
bottomhole pressure response in | |
bottomhole pressure in |