The slopes of the initial and final shut-in periods of a drillstem test (DST) are used to calculate the corresponding flow rates knowing the recorded flow times and the total liquid recovery and assuming constant transmissibility. Examples of the calculation are included for a closed-chamber test and a conventional test from Earlougher.1
Calculations
" If the shut-in period is long enough, and if wellbore storage is not dominant, a Horner plot of buildup data should have a straight-line section with slope -m." 1 The value of the slope of the Horner plot may be used to calculate the transmissibility:
Equation 1
The value of the constant 162.6 is 2121 for the corresponding SI units listed in the Nomenclature. The following derivation is based on the assumption of constant transmissibility and a flow regime in which the Horner analysis is valid (see Discussion):
Equation 2, 3, and 4
Substituting Eqs. 3 and 4 into Eq. 2 and rearranging yields
Equation 5
where
Equation 6
Substituting
Equation 7
into Eq. 5 yields
Equation
Rearranging results in
Equation 8
Eqs. 7 and 8 used to allocate recovered liquid volumes between the initial and final flow periods.
Example 1: A Closed-Chamber DST
A northwest Alberta well, Well 6–4-65–20W5, had a straddle-packer DST run at a depth of 5,653 ft [1720 m] in 7 7/8-in. [200-mm] hole with 442 ft [134.7 m] of 2.875-in.- [73-mm]-ID drill collars. A 9.1-lbm/gal [1090-kg/m3] gel chemical mud resulted in an initial and final hydrostatic mud pressure of 2,736 psi [18 864 kPa]. The preflow was 10 minutes with corresponding final pressure of 161 psi [1110 kPa]. The initial shut-in time and pressure were 90 minutes and 2,153 psi [14 844 kPa]. The pressure at the beginning of the second flow was 106 psi [730 kPa], building to 561 psi [3868 kPa] over 90 minutes, and the final shut-in pressure was recorded as 2,121 psi [14 624 kPa]. The slopes of the Horner plot for the initial and final shut-in periods were 107.6 and 127.4 psi/cycle [741.9 and 878.4 kPa/cycle], respectively. The formation temperature was 119°F [48.3°C] and the net pay was 7 ft [2.1 m]. The operator (Mobil Oil Canada) calculated a total fluid recovery of 400 ft [122 m], composed of 340 ft [103.7 m] of 26°API [898.4-kg/m3] oil with a viscosity of 4.05 cp [4.05 mPa·s], and 60 ft [18.3 m] of oil-cut mud from closed-chamber calculations and a production rate of 46 B/D [7.4 m3/d].
