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• The superposition time function accounts for variable rate conditions preceding the <br /> falloff. <br /> 1. It is the most rigorous of all the time functions and is usually calculated using <br /> welltest software. <br /> 2. The use of the superposition time function requires the operator to accurately <br /> track the rate history. As a rule of thumb, at a minimum, the rate history for twice <br /> the length of the falloff test should be included in the analysis. <br /> The determination of which time function is appropriate for the plotting the welltest on semilog <br /> and log-log plots depends on available rate information, injection period length, and software: <br /> 1. If there is not a rate history other than a single rate and cumulative injection, use a Horner <br /> time function <br /> 2. If the injection period is shorter than the falloff test and only a single rate is available, use <br /> the Agarwal equivalent time function <br /> 3. If you have a variable rate history use superposition when possible. As an alternative to <br /> superposition, use Agarwal equivalent time on the log-log plot to identify radial flow. <br /> The semilog plot can be plotted in either Horner or Agarwal time if radial flow is <br /> observed on the log-log plot. <br /> Parameter Calculations and Considerations <br /> • Transmissibility- The slope of the semilog straight line,in, is used to determine the <br /> transmissibility(kh/µ) parameter group from the following equation: <br /> k-h 162.6•q-B <br /> ,u m <br /> where, q= injection rate, bpd (negative for injection) <br /> B = formation volume factor, rvb/stb(Assumed to be 1 for formation <br /> fluid) <br /> m = slope of the semilog straight line through the radial flow portion of <br /> the plot in psi/log cycle <br /> k=permeability, and <br /> h=thickness, ft(See Appendix, page A-15) <br /> µ =viscosity, cp <br /> • The viscosity, µ , is usually that of the formation fluid. However, if the waste plume size <br /> is massive, the radial flow portion of the test may remain within the waste plume. (See <br /> Appendix, page A-14) <br /> 1. The waste and formation fluid viscosity values usually are similar, however, if the <br /> wastestream has a significant viscosity difference, the size of the waste plume and <br /> distance to the radial flow period should be calculated. <br /> 2. The mobility, k/µ, differences between the fluids may be observed on the <br /> derivative curve. <br /> • The permeability, k, can be obtained from the calculated transmissibility (kh/µ) by <br /> A-10 <br />