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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017 Chapte - p33/743
The build-up pressure (see details in the chapter ‘Analytical models - 13.C - Superposition in
time’) is then:
   t p t t p p t t p DD p DD i p BU     ) (
In term of delta p, it is:
     
t t p t p t p t p p DD DD p DD BU      ) (
Therefore:
       t p t p and t p t p DD BU p DD BU     
Note: the build-up response will be ‘flatter’ than the drawdown response, and the pressure will
never get back above initial pressure…
2.F.3 Multirate superposition
Multi-rate superposition is the natural extension of the build-up superposition to any type of
production history. A sequence of rates q1, q2, …, qn, of respective durations T1, T2, ... Tn, with
respective starting times t 1=0, t2, .... tn.
More derivation details are given in ‘Analytical models - 13.C - Superposition in time’.
The multirate superposition general function is finally:
     
i unit
n
i
i i i t t p q q p tp      


1
1
We have shown how multirate solutions can be derived from elementary drawdown solutions.
Horner time, superposition time, etc, will be introduced in the PTA methodology chapter.