Implication that a total pressure in any point of a porous reservoir is a 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(\tau) |
In case reservoir point defines location of -well the superposition principle can be rewritten as:
p_m(t) = p_i + \sum_k \delta p_{mk}(t) = p_i + \sum_k \int_0^t p_{umk}(t-\tau) \, dq_k(\tau) = p_i + \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
specific component of -well pressure variation caused by -well flowrate history | |
bottomhole pressure response in -well to unit-rate production in the same well (DTR) | |
bottomhole pressure in -well to unit-rate production in -well (CTR), |