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OILWELL TESTING                                    208

                     and subtracting equ. (7.66), the equation of the linear buildup, from this equation gives

                                                                    t +∆ t
                                            −
                           0.0288 = (p ws (LIN )  p ws  =  In t -In  t ∆  DA  − ln  + p D (MBH )  ( t ∆  DA )
                                                      DA
                                                                       t ∆
                     which can be simplified as

                                                                   t +∆ t
                           0.0288 ∆  p ws  =  p DMBH )  (∆ t DA )  −  ln                            (7.68)
                                              (
                                                                      t ∆
                     in which ∆p ws = p ws(LIN) − p ws, the pressure deviation below the linear buildup trend.
                     Values of ∆p ws as a function of ∆t are listed in table 7.9 for the three geometrical
                     configurations presented in table 7.8. The actual pressure buildups for these three
                     cases are included in fig. 7.26 by plotting the deviations ∆p ws below the linear buildups.




                                                       2                                     4
                     t = 4464 hrs
                                                             1                                     1


                      ∆t     ∆t DA   ln   t +∆ t  p D(MBH)  ∆p ws  p D(MBH)    ∆p ws   p D(MBH)    ∆p ws
                     (hrs)                t ∆             (psi)                (psi)               (psi)
                        5    .005     .001       .063      2.1       .063       2.1      .063       2.1
                       10    .009     .002       .106      3.6       .113       3.8      .113       3.8
                       20    .019     .004       .176      6.0       .232       7.9      .224       7.6

                       50    .047     .011       .205      6.7       .591      20.1      .334      11.2
                     100     .095     .022       .133      3.9      1.163      39.6      .305       9.8
                     250     .237     .054       .100      1.6      2.013      68.0     −.081      −4.7
                     500     .473     .106       .224      4.1      2.744      91.6     −.634     −25.7

                     1000    .947     .202       .757     19.3      3.442     112.5    −1.030     −42.8
                     2500   2.367     .455      1.648     41.4      4.363     135.7     −.563     −35.3
                     5000   4.735     .751      2.324     54.6      5.032     148.6      .134     −21.4

                                                          TABLE 7.9

                     Exercises 7.6 and 7.7 illustrate the common techniques applied in pressure buildup
                     analysis. One of the most reliable features of the analysis is that the Horner plot of
                                                    t +∆ t
                     observed pressures p ws versus      can be drawn without a knowledge of the p D
                                                       t ∆
                     function at the start of the survey. Furthermore, if a linear section of the plot can be
                     defined for small values of the closed in time this can be analysed to determine the kh
                     value and skin factor.

                     In partially depleted reservoirs, in which the aim is also to determine the average
                     pressure p, the analysis is necessarily more complex. The difficulty lies in the fact that
                     to determine p requires a knowledge of the magnitude of the area drained and the
                     geometrical configuration, including the well position with respect to the boundary. In
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