Page 288 - Fundamentals of Reservoir Engineering
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OILWELL TESTING                                    225

                     if no packer is used and the afterflow effects will be of less significance. Afterflow
                     distorts the early part of the Horner buildup plot, as shown in fig. 7.37.


                                    p ws
                                                Buildup dominated
                                                by afterflow                            p*












                                              1000         100            10           1
                                                           t +∆ t
                                                              t ∆

                     Fig. 7.37  Pressure buildup plot dominated by afterflow

                     Several theoretical methods have been presented for analysing the pressure response
                     during the afterflow period in order to determine kh and S. Due to the basic complexity
                     of the problem, it should be stated from the outset that the results obtained from any of
                     the various techniques are liable to be less accurate than those from the simple Horner
                     analysis of the straight line part of the buildup, once the afterflow has ceased.


                     In some cases, however, afterflow analysis provides a valuable means of obtaining
                     information about the reservoir. For instance, in several areas in the Middle East, wells
                     are capable of producing in excess of 50000b/d from limestone reservoirs. Because of
                     the very high kh values, which leads to very rapid pressure buildups, and the fact that
                     in many cases the wells produce through the casing, the afterflow period can
                     completely dominate the pressure buildup and afterflow analysis is the only method of
                     determining the essential reservoir parameters. The analysis methods which will be
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                     described in this section are those of Russell  and McKinley .
                     a) Russell Analysis

                     Russell developed a theoretical equation describing how the bottom hole pressure
                     should increase as fluid accumulates in the wellbore during the buildup. As a result of
                     this, he determined that the correct way of plotting the pressures during the part of the
                     buildup influenced by the afterflow was as

                              ∆ p
                                     versus log t ∆                                                 (7.77)
                                1
                           1−
                              Ct
                                ∆
                     in which ∆p = p ws(∆t) − p wf(t) (psi),and ∆t is the closed in time (hrs). The denominator of
                     the left hand side contains a correction factor C to allow for the gradually decreasing
                     flow into the wellbore. This constant C must be selected by trial and error so that the
                     resulting plot is linear. This is illustrated in fig. 7.38. For very small values of ∆t the
                     buildup is dominated by the skin factor rather than afterflow. Therefore, not all the
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