The two-cycle drill stem test, consisting of an initial flow period, an initial shut-in period, a second flow period and a second shut-in period, remains the most common type of test run in the field. Unfortunately, the most widely used method of analyzing data for these tests can result in significant errors. By far the most widely used method for DST analysis is a Horner plot prepared using Tp=t1F+t2F. In this method, an average flow rate is used in the calculation. Earlougher1 suggests that plots can be based on TP =t2F or Tp=t1F+t2F but is decidedly vague on when one is preferable to the other. Actually, the selection of TP is not nearly as significant as is the selection of the flow rate to be used in the calculations.
In practice it seems that most tests are analyzed with Tp=t1F+t2F, presumably because it generates a straighter line on the Horner plot. Unfortunately, the slope of this straight line can be very misleading. This is not to say that this slope is "wrong" since Horner slope in and of itself is not the parameter we are seeking. Only when combined with a flow rate does the Horner slope take on any physical significance. Thus while a Horner slope itself cannot be "wrong," the combination of a Horner slope with an inappropriate flow rate can result in a "wrong" answer. Conversely any slope can be the right slope if it is combined with the appropriate flow rate. Thus we must remember that any discussion of Horner slopes must be rate-specific.
Fig. 1 is a schematic of an idealized two-cycle test periods of constant rate flow alternating with shut-in periods. (Since DST behavior is actually governed by slug flow, there can be tests where the rate variation within a flow period will be large enough to make the assumption of constant rate invalid, but we shall ignore them here. Correa and Ramey2 propose a method by which such tests may be analyzed.)
Figure (1) (Available in full paper)
The principle of superposition allows us to consider this as the sum of two separate buildup tests as shown in Figs. 2a and 2b.
Figure (2a) (Available in full paper)
Figure (2b) (Available in full paper)
During the second shut-in period, the transient radial flow pressure response attributable to the two separate tests has been previously defined through superposition by Horner3 as:
from Fig 2a:
Equation (from Fig 2a) (Available in full paper)
From Fig 2b:
Equation (from Fig 2b) (Available in full paper)
The total pressure response is then:
Equation (Available in full paper) recognizing that Equation (Available in full paper)
Equation (1) (Available in full paper)
Equation 1 is the recognized multi-rate equation for a two-cycle test, and if q1B1 and q2B2 can be independently verified, a plot of PRESSURE vs
Equation (Available in full paper)
Should yield a straight line of slope
Equation (Available in full paper)
