Replacing annual shut-in well tests by analysis of regular injection data: Field-case feasibility study Page: 2 of 11
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The procedure consists of several steps. First, a data set has to be selected. Each
data point has three components: time of measurement, injection pressure, and injection
rate. The data set must include transient changes in the pressures and flow rates. If the
flow rates are not very high and the injected fluid is practically incompressible, the
bottomhole pressure can be calculated from the instantaneous wellhead pressure. In fact,
if an average reservoir pressure estimate is not required, the wellhead injection pressures
can be used without any adjustments.
A distinctive feature of the method is that an effective injection rate, denoted by
Q.1, is introduced to account for the pre-test pumping. This parameter plays an
intermediate role in the fitting procedure. If some information about the flow rates before
the test interval is available, the magnitude of the discrepancy between these actual rates
and Q.1 can be used as an additional measure of the quality of analysis. A small
discrepancy confirms a good quality of fitting, whereas a large discrepancy indicates that
either some minimization parameters need to be changed or a different data interval has
to be selected for the test.
The selected data interval is split into two parts: the beginning phase and the test
phase. The test-phase data points of the pressure curve are used in a best-fitting
procedure to estimate formation parameters, whereas the beginning-phase data interval is
used for intermediate calculations only. Let us denote by to and t2, respectively, the
beginning and the end times of the whole selected interval, and denote by ti the splitting
time. Then the modified radial flow solution has the following form (Silin and Tsang,
p(t)= p(to)+AQ E i B A Jt- Q(T)dT+sAQ(t), t1 <t st2 (1)
t -to 0 t - z
Here p and Q are the injection pressures and rates, respectively. We adopt the convention
that the pumping rate is positive if the fluid is injected. The skin factor s, pre-test
pumping rate Q.1, and coefficients A and B are the fitting parameters. Skin factor is an
optional parameter and can be excluded from the fitting procedure by setting it at zero. If
the pressures and rates were measured between ti and t2 at points 01, 02,..., 0N , then the
quality of fitting can be estimated using criterion
J = p(0)-Pp.(9,)] (2)
where data is the measured injection pressure. An effective minimization algorithm for
the functional (2) was proposed in Silin and Tsang (2002, 2003). This algorithm has
been implemented in the code ODA, which was used as the main tool in this study. The
coefficients of transmissivity T and storativity S are related to A and B as follows:
T = , S = 2B (3)
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Silin, Dmitry; Tsang, Chin-Fu & Gerrish, Harlan. Replacing annual shut-in well tests by analysis of regular injection data: Field-case feasibility study, article, May 21, 2003; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc739823/m1/2/: accessed March 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.