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OILWELL TESTING                                    209

                     other words, complex boundary conditions of the differential equations implicit in the
                     analysis are required to obtain meaningful results. As fig. 7.26 clearly demonstrates,
                     varying the boundary conditions can have a profound influence on the shape and
                     position of the theoretical buildup plot. One hopeful feature in this diagram is again the
                     fact that the observed data gives an absolute buildup plot. By the appropriate choice of
                     the boundary condition it may therefore be possible to match the observed buildup as
                     demonstrated in exercise 7.7, in which the original geological interpretation was
                     confirmed. With a reasonable geological map of the reservoir the technique can be
                     diagnostic in building a model of the current drainage patterns.

                     In addition, attempting even some crude match of the observed buildup can eliminate
                     serious error. If it were assumed, for instance, that the well in exercise 7.7 was located
                     at the centre of a circle, which is the conventional boundary condition assumed in the
                     literature, then the reader can confirm by calculation, or merely by inspection of
                     fig. 7.26, that the estimated value of p calculated in this latter exercise would be about
                     100 psi too low.

                     One other feature in fig. 7.26 is of interest and that is the rather strange shape of the
                     theoretical buildup plot for the assumed 4:1 rectangular geometry. In this case there is
                     a pronounced increase of slope which is due to the proximity of the no-flow boundaries.
                     This is just a more complex manifestation of the phenomenon of "doubling of the slope"
                     due to the presence of a fault close to a well in an otherwise infinite reservoir, which
                                                           4,6
                     has repeatedly featured in the literature . References 17 and 18 of this chapter are
                     recommended to the reader who is further interested in the subject of matching
                     theoretical with actual pressure buildups.


              7.8    MULTI-RATE DRAWDOWN TESTING

                     Closing in a well for a pressure buildup survey is often inconvenient since it involves
                     loss of production and sometimes it is difficult, for a variety of reasons, to start the well
                     producing again after the survey. Therefore, multi-rate drawdown testing is sometimes
                     practised as an alternative means of measuring the basic reservoir parameters and
                     indeed, in some places the regulatory bodies insist that such surveys be conducted in
                     preference to other forms of testing. This restriction is more common in the case of gas
                     well testing which will be described separately in Chapter 8, sec. 10.

                     The basic equation for analysing a multi-rate drawdown test for liquid flow has already
                     been presented in sec. 7.5 as equ. (7.33). In field units this becomes


                                             p −
                                        kh   ( i  p wf  )  n  ∆ q j
                           7.08 10 − 3              n  =          p D  ( D  −  t  )  + S            (7.69)
                                                                       t
                                ×
                                       µ B o    q n       j1  q n       n   D − j 1
                                                          =
                     in which p wf n   is the specific value of the flowing pressure at total flowing time t n during
                          th
                     the n  production period at rate q n. It should also be noted that throughout this section t
                     is the actual rather than effective flowing time.
                     Consider the typical multi-rate test shown in fig. 7.27 for four sequential flow periods.
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