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SPE 16798 PRAMOD K. SINGH, RAM G. AGARWAL AND LOREN D. KRASE 3 Pi pwf ° (qj qj-1) vs L -Log (t-t. ) qj 91_1 qn j_1 qn �-1 ( ) n-1 tn_1 - t. 1 qn-1 _ qn is made of the SRT data. Note that the rates are j11 (Et + tt o-1 - j-1) At considered negative for injection. Theoretically, this should provide a single straight line of slope m' and intercept b' for all data below parting pres- sure, where: Multirate analysis has found limited applica- tion in the analysis of actual SRT data due to the lack of continuously measured pressure-time data, M. = 162kh NB .............(2) large sensitivity to the value of initial pressure used for superposition2,3 and Lack of stability of rate and pressure data. These limitations are dis- and cussed in the later sections of this paper. It will also be shown that with the excellent rate control and pressure measurement devices now available, mul- tirate analysis is a powerful analysis tool for det- b, = 162.6 8 [Log k 2 _ 3.23 ermining the FPP from SRT data. kh �Pctrw FACTORS AFFECTING SRT ANALYSIS + 0.87s] ..• .. .......(3) As with any other pressure transient test, SRTs are also affected by wellbore storage, skin damage, reservoir fracturing, etc. In addition, other con- Formation flow capacity, kh, and wellbore skin, s, siderations such as time step size, rate increment before fracturing can therefore be determined from and changing wellbore storage are important factors this line using Eqs. 2 and 3, respectively. The to consider for SRT design and/or analysis and will method breaks down above parting pressure. Data be discussed next. points above the parting pressure should no Longer fall on the previous straight line, indicating that 1. Time Step Size fracturing has occurred and early time data are no Longer in a radial flow regime. The pressure corre- The linear relationship between p and q below sponding to the point where this occurs should the parting pressure for a SRT can also be explained relate to the FPP. by the transient radial flow equation: Fig. 3 is the Odeh and Jones plot for the simu- lated case. As expected, data for the first three Pi - Pwf kh= q 16kh [log kL1t preparting steps fall on a single straight line. 4c r 2 The slope and intercept yield the correct kh and t w skin, respectively. A downward shift of data points is observed for each successive step when the frac- - 3.23 + 0.87s] .............(4) ture length is increased. The plot indicates that the data from the fourth step onward are above the parting pressure. The same general trend has been Ignoring the effect of superposition, a linear rela- consistently observed with field SRT data. Field tionship between injection pressure (p) at the end data for steps above the FPP, however, usually show of each step and rate (q) should exist below the a continued flattening trend. This is because the parting pressure if a constant time step size (At) fracture Lengths are probably longer and extend con- is used. tinuously during each step above the FPP. For the simulated case, it was possible to calculate the To demonstrate the impact of changing the time fracture length values from the equivalent wellbore step size within a SRT, a preparting (radial flow) radius concept.4 This was done using the skin values six-step SRT with equal rate increments and no well- calculated from the radial flow semilog straight bore storage or skin was simulated. Time steps of line data obtained for each step above the FPP. 12 hours were used for the first three steps and Such a calculation may not be possible on actual SRT then reduced to 1 hour for the remaining three data if the data are not in the pseudo-radial flow steps. Fig. 4 is the p vs. q plot for this case. A regime. change (reduction) in slope is observed when the duration of the injection step is reduced within the Although not shown, Agarwal's multirate equiva- test. This indicates that a false parting pressure lent times can also be applied for the analysis of may be interpreted by decreasing the time step size. SRT data. This requires making a plot of: Conversely, an increase in slope should be observed if the duration of the injection step is increased during the test. pwfn pwfn-1(tn-1) V5 qn-1 q The above discussion emphasizes the necessity of maintaining equal step time lengths during a SRT. Further, from our earlier discussion, it should be evident that ideally the duration steps should be 493