In some jurisdictions, initial flow rate may be restricted by market demand or legislative control, or by good engineering judgment, common sense, or facilities restrictions. If this kind of production occurs, we assume the initial production rate (Qi) to be constant until this rate equals the well's ability to produce. Thereafter, production will decline at the exponential rate.
The production rate on decline is defined as Qa = Qd * exp (XTd). Thus solving for (XTd): 1: (XTd) = ln (Qf / Qd) The instantaneous decline rate (E) is found by. 2: E = -365 * Qd (1 - exp (XTd)) / R The annual decline rate is. 3: D = exp (E) - 1 Life of well on decline is found as follows. 4: IF Qi >= Qd 5: THEN Td = (XTd) / E If the well is restricted to a constant rate. 6: IF Qi < Qd 7: THEN (XTd) = ln (Qf / Qi) 8: AND Td = (XTd) / E The reserves produced on decline are. 9: Rd = -365 * Qi * (1 - exp (XTd)) / E The reserves produced at constant rate are. 10: Rc = R - Rd The life at constant rate is. 11: Tcon = Rc / Qi / 365 The total economic life is. 12: Tec = Tc + Td Where:
Reserves: Roil = 2.2*10^6 bbl/section Deliverability: QI = 1800 bopd Economic Limit: QF = 10 bopd (XTd) = ln (10 / 1800) = -5.193 E = -365 * 1800 * (1 - exp (-5.193)) / 2.2*10^6) = -0.297 D = exp (-0.297) - 1 = -0.257 Td = -5.194 / (-0.297) = 17.5 years = 210 months Rd = -365 * 1800 * (1 - exp (-5.193)) / (-0.297) = 2.2*10^6 bbl Rc = (2.2 - 2.2)*10^6 = 0.0 bbl Tcon = 0 / 1800 / 365 = 0.0 years Tec = 0 + 17.5 = 17.5 years = 210 months 2.
If the initial flow rate was restricted to 1000 bopd: The
constant rate lengthens the life and reduces the profitability
of the well, as will be seen in the next section. |
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