Decline Rate and Economic Life
In order to determine the economic potential of a well, it is necessary to predict the production profile and economic life of a well from the reserves and flow capacity established by log data. Some assumptions must be made, as usual. These are the final production rate (Qa) below which it is uneconomic to produce the well, the annual exponential decline rate (D) and the initial deliverability (Qd).

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.

Exponential Decline Rate Calculation
This routine presumes that recoverable reserves are known from some other source, such as volumetric analysis from log data, decline curve analysis, or material balance calculations. Set R in the equations below to equal Roil or Rgas, then proceed.

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:
D = annual decline rate (fractional)
E = instantaneous decline rate (fractional)
Qd = initial well deliverability (bopd, mcf/d or m3/d)
Qa = economic limit or abandonment flow rate (bopd, mcf/d or m3/d)
Qi = initial production rate (bopd, mcf/d or m3 /d)
R = recoverable reserves of well (bbl, mcf or m3)
Rc = reserves produced during constant rate (bbl, mcf or m3)
Rd = reserves produced during decline (bbl, mcf or m3)
Tcon = constant rate life (years)
Td = decline life (years)
Tec = total economic life of well (years)
X = instantaneous decline rate (fractional)
(XTd) = decline factor (fractional)

RECOMMENDED PARAMETERS:
None.

NUMERICAL EXAMPLE:
1. Assume data as follows:
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:
(XTd) = ln (10 / 1000) = -4.605
Td = -4.605 / (-0.297) = 15.5 years = 186 months
Rd = -365 * 1000 * (1 - exp (-4.605)) / (-0.297) = 1.2 * 10 ^ 6 bbl
Rc = (2.2 - 1.2)*10^6 = 1.0*10^6 bbl
Tcon = 1.0*10^6 / 1000 / 365 = 2.7 years = 32 months
Tec = 15.5 + 2.7 = 18.2 years = 218 months

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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