Page 271 - Introduction to Petroleum Engineering

258 PRODUCTION PERFORMANCE
The value of N is determined by using production data and assuming a water influx
model for water influx W . By contrast, solving Equation 13.11 for W gives
e e
WB w NB oi B o N B o W B w (13.13)
p
p
e
The value of W can be estimated using production data and a value of N from volu-
e
metric analysis.

Example 13.5 Water Influx
Calculate water influx W using the material balance equation for an oil–
e
(
water system: WB w NB oi B ) N B o W B . We have the estimate
e
p
w
p
o
.
OOIP N N 85 MMSTB where N is from volumetric analysis. Initial
vol vol
.
/
/
.
oil FVF is B oi 1 347 RB STB. Oil FVF B o 1 348 RB STB when 46
MSTB oil has been produced. Water FVF is approximately constant and has
.
/
the value B 10 RB STB. No water production has been reported.
w
Answer
(
No reported water production implies W = 0 so that WB w NB oi B ) N B .
p
o
o
e
p
.
(
Substituting values into WB w NB oi B ) N B gives WB w 765
p
e
e
o
o
.
MSTB 62 02 MSTB so that W 54.37 MSTB.
e
13.4.2 Schilthuis Material Balance Equation
Schilthuis (1936) presented a general material balance equation that accounted for
oil, water, and gas in the system. The general material balance equation is derived
by assuming that the system is an isothermal system in pressure equilibrium. It is
also based on the assumption that the distribution of oil, water, and gas phases does
not affect tank model results. Following the discussion by Fanchi (2010b), we write
the general material balance equation as
B B BS B B
N B t B ti NmB ti gc gi N tiwio tw twi
B gi 1 S wio B twwi
mB S B 1 m
iwig B
N t t w t wi N Bc p (13.14)
if
t
1 S wig B t wi 1 S wio 1 S wiig
NB NR B G B G B G B W W W W B
p o p so g ps g pc gc i g e i p w
The terms in Equation 13.7 and associated units are specified in Table 13.2.
Application of the general material balance equation presumes that fluid property
data from fluid samples are representative of reservoir fluids and that production,
injection, and pressure data are reliable.