A model for analyzing tests under the spherical flow condition has been developed and applied to sequential formation testing. This technique involves plotting change in pressure (from original reservoir pressure) versus time (from start of drawdown) on logarithmic scale. The buildup part of the test should follow a straight line whose slope can be used to determine flow regime. In a spherical flow the slope is -1.5. The paper also presents application of the radial flow model to surge tests. Several field examples are presented in the paper.
Surge tests and sequential formation tests are basically buildup tests preceded by very short producing time. However, because of this very shott producing time, application of conventional techniques may not produce satisfactory results. For example, the use of the Agarwal1 equivalent time concept would compress the buildup data into a very narrow range of equivalent time that may imply unanalyzable data. Consequently the log-log graph cannot be used to indicate the validity of a semi-log interpretation.
In a paper dealing with a buildup test preceded by short producing time. Soliman2 formulated this problem differently. He combined the shut-in period with the drawdown period by modifying the boundary condition at the wellbore. In solving the newly formulated problem, Soliman recognized a pattern of behavior not described earlier in literature. His work produced a new technique for plotting buildup data which Can be used to identify flow regime and to calculate formation permeability. Skin factor can be obtained using a curve matching technique. However, this procedure is not recommended because the match may lack uniqueness.
This technique showed that plotting change in pressure versus time on a log-log scale for late time data yields a straight line. Soliman2 found that the slope of the straight line depends on the type of flow regime. The slope is -1, -3/4, and -1/2 for radial, bilinear, and linear flow, respectively.
The technique was later expanded to include buildup tests preceded by 2 drawdown under constant pressure3. Cinco4 used the instantaneous source concept to prove that the plot Soliman developed is equivalent to a derivative plot.
In this paper. the spherical flov model is investigated and the slope of the late time data on a log-log scale is found to be -1.5. As will be shown later investigation of the spherical flow model was necessary to explain some of the observed behavior of surge and sequential testing.
The technique developed in Reference expanded in this paper is applied to both tests and a sequential formation test (also as a repeated formation test).
A surge test generally uses an assembly of two remote or pressure controlled valves, a temporary packer and one or more pressure gauges. The assembly is run into the wellbore with the chamber between the two valves usually occupied by air or nitrogen at or above atmospheric pressure. As the packer is set., the overbalance pressure is relieved and pressure below the packer becomes equal to static reservoir pressure.