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SYSTEMATIC DESIGN AND ANALYSIS OF STEP RATE TESTS TO 6 DETERMINE FORMATION PARTING PRESSURE SPE 16798 not surprising since the basic assumption of a stabilized shut-in (zero rate) condition prior to 1/2 the SRT is not correct for this case. Reworking the _ 4.064 q8t superposition for the case of a stabilized low Pi _ Pwf x h [—Ocpk] ............'(7) injection rate (q ) prior to the SRT will result in f t the pressure funcFion to be (p - p )/(q - q r ) instead of just q in the denominator.Thentime function is also adjusted to account for a finite which, when superposed, yields rate (q ) prior to the SRT. Data for all the steps now fa1F on a single straight line with the correct semiLog slope as shown in Fig. 18. If the reduced Pi Pwf _ 4.064 B injection rate period is not long enough for pss/ss qn xfh [�ctk to be achieved, it should be accounted for as a transient step in calculating the multirate superpo- sition time similar to the 3 hour shut-in case dis- cussed earlier. n (qj _ qj_1) )1/2 .............(8) The above cases indicate that for the multirate j-I q j-1 analysis: (i) a knowledge of p. is not required, and (ii) multirate test data can be analyzed using any pressure point as p f at the beginning of a The resulting plot is presented in Fig. 21. Data rate change, and by inc Fe the appropriate rate- for the first three preparting steps fall together. time history starting from the last pss/ss period to Fracture extension can be noted by a definite shift in data for each subsequent step. This technique the time corresponding to Pref' provides a powerful tool to determine the propaga- SRT ON A FRACTURED WELL tion pressure for fractured wells where linear flow is occurring. This also suggests that the SRT for a The analysis techniques discussed in the fractured well can be designed with shorter time preceding sections assume transient radial flow steps corresponding to the duration of the linear during the preparting steps of a SRT. For a frac- flow period. Although not shown here, Agarwal's tured well, if the time steps are not long enough, multirate equivalent time type superposition can the radial flow assumption is obviously violated. also be applied to the Linear flow equation. To investigate the proper analysis method for such a Similar requirements and limitations for the appli- test on a fractured well, a six-step SRT with no cability of linear flow muLtirate analysis are wellbore storage was simulated. A fracture half expected to apply as was discussed earlier for the Length, xf, of 130 Et was kept constant for the radial flow multirate analysis. first three steps representing steps below the frac- For wells with low Finite conductivity frac- ture propagation pressure. The xE was then Y increased to 140 ft, 160 ft and 175 ft at the begin- tures, a plot of the Linear flow superposition ning of the fourth, fifth and sixth steps, respec- method applied to SAT data, may also exhibit a shift tively, to approximately simulate fracture in data corresponding to an increase in fracture extension. The fracture was of infinite conduc- width (fracture opening). This is due to the tivity (F >500) throughout the simulation run. The increased fracture conductivity. In this situation, time step Csize was just long enough for data to be it may not be possible to distinguish the fracture in a linear-pseudo radial transition flow regime. width effects (fracture opening above closure pres- sure) from the fracture propagation effects (frac- Fig. 19 is the p vs. q plot of the simulated ture propagation above FPP). It appears that a SRT. A reduction in slope, corresponding to frac- bilinear flow13 superposition method may be prefer- ture extension from the fourth step onward, is not able to use for wells with loo finite conductivity clearly evident on this plot. This suggests that fractures. However, this aspect has not been the conventional p vs. q analysis may not be ade- included in this paper. quate for determining the true parting (propagation) FIELD EXAMPLES for wells with long preexisting fractures. Fig. 20 is the conventional Odeh and Jones plot 1. Field Example A for the simulated case. Data for each step have the This illustrates the analysis of a SRT influ- characteristic concave upward loshape enced by wellbore storage and changing storage. The resulting from early time lineaarr flow. . Late time well was shut-in prior to the SRT and the bottomhole data for the first four steps £tens together. There pressure was allowed to stabilize. Wellbore fillu is some evidence of fracture extension far steps P five and six, reflected by a slight shift in data occurred during the third step. A Log-log plot of points for these steps. However, it appears that AP vs cumulative water injected (Fig. 22) indicates the muLtirate analysis using radial flow superposi- that all data points until the middle of the third tion also may not be adequate for determining the step are dominated by wellbore storage. The rapid parting pressure in such cases. rise in pressure during the third step is simulta- neous with wellbore fillup and is caused by a The data was reanalyzed by performing an Odeh changing wellbore storage. and Jones typemultiple rate superposition using the linear flow equation: Data for the initial storage and changing storage dominated steps 1, 2 and 3 show a concave upward curvature on the p vs. q plot (Fig. 23). A 496