Page 97 - Fundamentals of Reservoir Engineering

SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 36
−bt
Q = Q e
o

where Q o is the rate at t = 0, i.e. 100 MMscf/d, and b is the exponential decline
factor of 0.2 p.a. Therefore, the time required for the rate to fall to 20 MMscf/d will
be

1 Q 1 100
t = ln o = ln = 8.05 yrs
b Q 0.2 20

If g p is the cumulative gas production at time t, measured from the start of the
decline, then

t t
g = Qdt = Q e − bt dt
p
o
o o
i.e.

Q − bt
g = o (1 e )
−
p
b
and when t = 8.05 yrs.

6
100 10 × 365 − 0.2 8.05
×
×
9
g p (8.05) = 0.2 (1 e ) 146.02 10 scf
−
×
=
Therefore, the total cumulative recovery at abandonment will be
9
9
G p 3 = G p 2 + g p (8.05) = (491.04 146.02) 10 = 637.06 10 scf
×
×
+
and the recovery factor
G p 637.06 10 9
×
RF = 3 = = 0.91 or 91% GIIP
G 699.70 10 9
×
which will be recovered after a total period of
t 1 + t 2 + t 3 = 2 + 12.45 + 8.05 = 22.5 years.

This simple exercise covers the spectrum of reservoir engineering activity,
namely, estimating the hydrocarbons in place, calculating a recovery factor and
attaching a time scale to the recovery. The latter is imposed by the overall market
rate required of the field, i.e.

cumulative production
time =
field rate

Later in the book, in Chapters 4, 6 and 8, the method of calculating individual well
rates is described, which means that the time scale can be fixed by the more
usual type of expression.