
Publication History:
This article is based on
"Crain's Petrophysical
Pocket Pal" by E. R. (Ross) Crain, P.Eng., first
published in 1987, and updated annually until 2016.
This
webpage version is the copyrighted intellectual
property of the author.
Do not copy or distribute in any form without explicit
permission. 
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.
DECline 
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)
COMMENTS:
None.
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.
