_._-----'-'--,
JC.p/66:"'D3 -~2
Determination of Natural Gas Recovery Factors
By E. STOIAN and A. S. TELFORD*
,
~.
07th Annual Technical Meet·ing, The Petroleum Society of C.I.k!., Edmonton, May, 1966)
,.~.
L
ABSTRACT
.~
.
INTRODUCTION
,,
~
T
HE topic of this paper is the recovery factor! defined as:
J
RF (fraction)
.j
=
Initial Gas in Place - Ga5
Remaining in Reservoir
Initial Gas in Place
CEq. [)
The recovery factor is related to the gas remaInIng
in the reservoir which cannot be produced at economic rates, Le_, the "reservoir loss," as follows:
RF (per cent)
=
100 - Reservoir Loss (per ct:nt)
(Eq.2)
The recovery factor depends upon the type of occurrence of natural gas and the production processes,
and will be treated accordingly.
NON-ASSOCIATED GAS
;,:''''-'.
Range of Recove?'Y Factors
A preliminary recovery estimation may be based on
the recovery factors of depleted or nearly depleted
pools. Table I shows the probable ranges of recovery
factors on the assumption of normal distributions_
Whereas the averages of the estimations (Ref, 1, 2)
compare favourably with the average recoverJ.' factor
of depleted pools (Ref. 3, 4), the spread in estimations
is relatively small, especially in view of the conclusion of some water-drive reservoirs.
A.
~~~~~::
:~ .'
CONSTANT VOLUME GAS RESERVOIRS
This section is applicable to constant volume, volumetric or expansion-type gas pools.
A-I. Methods Based on Reco'Very Factors Applied to
I n;tial Gas in Place
(I) The Conventional Method.- A formula commonly
used to calculate the recovery factor may be derived
from material balance considerations (Ref. 5) :
P;!Zi - P'lO/Z"b
Pi/Z,
RF (fraction)
(Eo. 3'
In terms of the gas formation volume factor, this
equation may be expressed as:
RF(fraction)
=
BgnL-Bl':,i
(Eq.4)
B,,; lib
This method requires the initial and abandonment
pressures which may be obtained from either generalized correlations or detailed considerations.
(2; 3)-The recovery factor may be expressed also in
terms of density (Ref. 6) or pound-mole volumes
(Ref. 7) at initial and abandonment conditions_
(4) C01Telations_-Both direct and indirect correlations were evaluated_
~
..
Di1-ect Con·elCLtions. Regression analyses indicated
that it is not possible to correlate the recovery factor directly with pool and well characteristics such as
depth, gas in place, pay thickness, average absolute
open flow and initial reservoir pressure. The aggregate effect of these parameters seems to account for
less than 20 per cent of the variations in the recovery
factors.
·..rOil and Gas ConseTvation Boa/rd, Calga:ry, Alta.
TABLE I
RANGE OF RECOVERY FACTORS
Average Recovery
Factor (%)
84.8
85.4
84.6
85.1
83.7
Range fOT 68 per cent of
RecOl'U}' Factors (%)
80.5
80.4
75.7
75.8
75.8
-
89.1
90.4
93.5
94.4
91.6
Technology, July-September, 1966, Montreal
Number of
Pools
44
114
76
49
28
Remarks
Alberta gas pools
Alberta gas pools
Pools nearly depleted
Study of mature pools
Reference
I
2
3, 4
3
4
.
.:
lIS
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Theoretical and statistical methods of determining recovery factors of solution, associated and non-associated
natural gas, including gas condensate. are presented as a
set of practical tools_
The effects of recovery mechanisms and pool and gaswell performance on gas recovery are examined for conditions applying to constant \-'olume, water drive, gravit:,..
segregation and secondary recovery_ 'Val's of recognizing
such cases are indicated.
The supporting tech.niques comprise material balance
calculations, performance predictions and statistical analyses of depleted pool and predicted recovery data_ In
material balance calculations, the gas recovery is considered in terms of either: (1) initial gas in place multiplied by a recover}· factor or (2) initial gas in place leas
the gas remaining at abandonment. Performance predictions are based on geological, engineering and economic
factors. The background study dealt with explicit correlations between: (1) recovery factor, abandonment pressure
or related expressions - e_g_, (p/Z)"b - and pool depth,
pay thickness, initial reservoir pressure, flow capacity and
size of gas accumulation; and (2) equivalent residual gas
saturation and formation water saturation, porosity, permeability and specific surface area. The format for several
correlations presented is predetermined lly theoretical
considerations. Existing short-cut methods are also evaluated. Easy-to-use approximations readily yield reliable
estimations despite their simplicit}· and can be of considerable significance; however, the practicing engineer is
urged to recognize and understand their limitations.
An extensive review of methods of determining recol'ery
and an analysis of many evaluations by industry form the
foundation for the recommended guidelines to serve the
engineer. The methods of determining recovery factors
are considered according to their practicality; Le. the
al'ailability of data and the complexity of implementation.
Useful relationships are classified, important steps of the
proposed procedures are outlined and several applications
are illustrated.
TABLE
II
INDIRECT CORRELATIONS OF RECOVERY FACTORS
=
(D
R'
RegH'ssio1l Eqrtafiolls
~
=
~
(P/zl; (psial
(p/z)i (p~iaJ
([l,lz); (psia'i
- - - - ----
(P/Z)"h (psia) ~ 38.91 D
(Plz)"h (psia) ~ 56.20 D
Pi (p!'iia)
Pi (psia)
Pi (psiai
(psi a)
p:." (p:mll
= 378.11
~ 409.65
~ ~68.65
~
~
2,1
(psia)
(psia)
~
=
0.05 p;
0.12 Pi
Pnll (psia)
~
·19
mo~t
-....
115D' ..
- 0.04 AOF
D
= depth
-
D in lOOO's feel
:J.334 ± 1.6·10
.,1.796 ± 2.1G3
8.07-[ ± 2.527
2
1
M
(p/zLIo in p"ia
197 ± R3
:10~i ± 146
2
1
229
301
265
11~
29~
25~
0.59
O,li9
0.35
0.47
53
81
53
83
11~
0.93
1713
177
230
420
114
4·1
0.91
0.86
0.88
0.82
O.fiO
0.li9
0.36
0,46
~9
111
7·t
49
75
0.672
OA~9
60
61
158
D Ln 1000's feel
:Uoll ± 1.917
1.2
0675
OA50
60
61
158
Polt. in p"ia
2H1 ± lOG
1.2
OAO
60
60
11~
0.70
0.16
0,48
7~
44
Pi Ln psia
12:11:: ± 915
17,fl2 ± 91-1
2
1
0.69
0.45
7,'
76
4~
AOF in Mscf/D
2 -- 120
+ 50 D
22~
402
44
24
44
Pi In PS1~
12:18 ± G-l5
17fl2 ± 914
:{609 ± 1241
2·1
2
1
H
(1) The Cou'ventional M ethod.-The difference between the initial and terminal gas in place is readily
expressed as:
(
2
I
(2;3 )-Similarly, equations in terms or gas density
and pound-mole volumes may be developed (Ref. 6, 7l.
A-3. Methods Based on M(ll(~rial Balance Concepts
(l) The Pl'es.wrl' Decline .M et!lud.-ThC! matcrial lmlance equation may be written as:
-
III
G...
+ ..E'_
z,
tEq.7)
where
m
~
p.~
·13,560 A iJ
~
Tr
(I -
~",I
'1'••
IEq. H)
A plot of (p/z) against cumulative gas pmduction,
G p • may be extrapolated to either (p/zl =
(P/Zl~h
in
order to obtain the gas reserves, or extended to {p/zl
= 0 to determine the initial gas in place. Eq. 7 correctly applieH onl.}' to constant volume resel'voil"~ where
the fluids remain in their initial phase (Ref. 9)_
(2) The "Equal Pound. Loss" M(~t!lod.-The original
·'equal pound lo:-;s" method is a special cmie of the
pressure decline method eliminating the need for a
graphical representation:
G
~
- G
","
-
(P/z), I'
(p/zi,
(p/Z)nl,
-I P/z)-
(Eq.9)
A-4. IHiscellaueolis Methods
in lOOO'!; or feet.
43.560 T"A h ~ (I - S,,,)
T r p""
n
190 ± 77
291 ± 131
4~
(Eq.5)
A-2. Methods Based on DiffereJlce Betn'een Initial
Gas in Place QJld Gas Remaining at Abandonme,Ji
116
Ref.
227
lIseful equations is:
Pal,(psia) = 50
where
S
l\vcragc ±
Pools
0.8·1
0.B6
0.92
IlHlireet C01"l'elatio1/s. In the pursuit of a rapid tool
for recovery factol' estimation, indirect correlations
were performed between components of the basic recovery fador formula (Eq. 3) and practical reservoir parameters. The results of this analysis, using
data pertaining to pools in Alberta, are summarized
in Table II.
The average (p/Z)alJ for shallow reservoirs is 13.5
per cent (Ref. 2) and for deeper pools is 14.5 per cent
(Ref. 1) of the average (piz);. The magnitude of the
free term (77 - 120 psia) relative to the gradient
(0.05 - 0.12) would indicate that it may not be advisable to express the abandonment pressure solely as
a fraction 01' pel' cent of the initial pressure. High
well deliverability, a:-; expected, tends to reduce thc
abandonment pressure and increase the recovery, but
the magnitude of this effect appears insignificant on
the basis of the information analyzed. Because of this
and because the correlation involving depth and absolute open flow does not indicate an improvement
over the correlation vi'ith depth alone. a theoreti~al
approach seems necessar,)! to determine the effect of
well productivity on l'e~o"ery.
One of the
Sr
0.92
0.93
0.96
0.9~
+ 120
+ 77
+ 5ID
Sy
pnlo in psia
+ 50.
+ 57.50 +
=
--
+ 69.
+ 50
31;.37 D
50.36 D
Pall (psia)
Pnh
+ 68.
+ 35
D - 22.5.
D - 183
D - 175._
P.L (psia.l ~ ·15.1 D
Pnh
-- .
R'
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P~L
..
462.35 D - 77.
482.42 D - 245.
450.12 D - ~67.
I
depth on 1000 feet: AOF in MIVIscf;'day/wellJ
Ec _
Zi
P".)
Z.,b
(Eq. 6)
(1) Rate Decline AnalY81s.-Gas rate decline method~
are useful in directly determinating re::'ierves after
the onset of the true productivity decline.
Lamont applied the constant rate decline method
to predict the recovery faclol· for scvel'al nearly depleted gas reservoirs (Ref. 4).
Davis used average performaIll..:e curves to predicL
the availability of natural gas (Ref. 3). The anllual
rate of production at abandonment, about 2 per cent
The Journal of Canadian Petroleum
of the initial gas in place, may serve as an end point
in reserve evaluations_
(2) The Cumulative Pressure DrOp ilfethod.-This
method consists of plotting the cumulative reservoir
pressure decline against the cumulative gas production on logarithmic paper_
Several empirical methods are discussed in the section pertaining to variable volume gas reservoirs, to
which they are more routinely applied.
Quantitative Analysis of Factors Influencing Recov","y.-In a studl' by Muller, (Ref. 5), several reservoir models ",.'ere obtained by assuming a series of
pool depths and associated initial pressures. For each
model, the abandonment rate and permeability were
varied. Simplified equations were used, e.g.
Q
~
(Eq. 10)
C (p,' _ p,')"
(Eq. 11)
According to this analysis, a generalized recovery
factor as high as 85 per cent would apply only to reservoirs deeper than 3,300 feet with initial pressures
of 1,470 psig or higher and capacities in excess of 600
md-feet.
Several conclusions regarding the gas recovery can
be drawn from an examination of these models;
(a) The higher the initial reservoir pressure the
higher the recovery factor.
(b) The effect of the wellhead flowing pressure at
abandonment is greatest for shallow reservoirs
with low initial pressures.
(c) The advantage of high permeability is substantially reduced at high initial reservoir pressure.
(d) The abandonment rate affects the recovery
factor more in low-pressure and low-flow-capacity reservoirs than in high-pressure and highflo,y-capacity reservoirs.
:~
Sim1Jlijied Analysis of Abandonment Pressu"re.The terminal pressure is an important variable in
most recovery factor expressions reviewed and it deserves special consideration.
Several rules of thumb for the estimation of the
abandonment pressure are summarized as follows
(Ref. 10) :
Fi?-st Rule. Set the abandonment pressure at 10 per
cent of the initial pressure. For a 5,OOO-foot-deep reservoir with an initial pressure of 1,865 psia, the
recovery factor would be slightly more than 90 per
cent.
Second R~lle. To obtain the terminal pressure in psia,
multiply the depth in feet by 0.05. This leads to a recO\'ery factor of about 87 per cent.
Third Rule. To find the "optimum" abandonment
pressure in psia, multiply depth in feet bl' 0.095. On
a consistent basis, this yields a recover)' factor of
about 75 per cent.
Fow·th Rule. Use an abandonment pressure of 100
psia per 1000 feet of depth. In a comparable situation,
this rule would result in a recovery factor of slightly
more than 73 per cent.
Fifth R"le. According to the studl' reported in this
paper, the abandonment pressure cannot be determined on the basis of initial pressure alone. If it is
necessary to relate the abandonment pressure to the
initial pressure, however, the following rule may be
used:
Technology, July-September, 1966, Montreal
".
p~~.
Procedu'res tOl' Determining Recovery Factors. The
recovery factor can be accurately expressed in terms
of the initial and abandonment pressures by Eq. 3.
The initial pressure is usually measured and the abandonment pressure may be estimated by methods already discussed.
If it is desirable to develop a systematic approach
for the determination of the recovery factors for constant volume gas reservoirs, the follo\'i!ing procedures
are recommended:
During the initial stages of development and production, a recover}C factor of 85 per cent may be assigned, or preferably it ma~y be determined from the
abandonment pressure:
p,," (psia)
~
50
+ 50 D
(Eq.
c.
117
..
,;.
.-c'· .
5)
At the stage when 10 to 15 per cent of the initial
gas in place has been produced, sufficient information
is usually a\'ailable for material balance calculations
and the recovery factor may be more specifically
evaluated. The abandonment pressure from Eq. 5 applies to "average" pool performance and economics
of production as qualified by: (a) lack of water and
oil in gas production; (b) average deliverability; (c)
gas processing, inclusive of removal of hydrocarbon
liquids but exclusive of special processing for gas
conditioning and sulphur production; and (d) gas
delivery using compressors.
On the basis of general considerations. statistics and
especially the fact that the spread in the actus! recover}C factors is substantially larger than that of the
estimations, the following guidelines are recommended
for modifying pab, the abandonment pressure calculated by Eq. 5.
(1) n'ate1· and Oil Production.-Because the production of oil and water at gas wells is a "nuisance"
and may result in a relatively high abandonment pressure, it is suggested that:
(a) p,,~ should be increased by 10 to 15 per cent if
the liquid production is confined to a few wells in the
pools;
(b) po. should be increased by 15 to 40 per cent if
the production of oil and water is extensive! I.e., most
of the wells in the pool are affected;
(c) conditions of widespread and progressive coning may lead to still higher pab'S.
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RF (fraction) =
"To approximate the abandonment pressure in psia,
add 100 psia to 10 per cent of the initial pressure-"
On the average, this would result in an abandonment
pressure of 15 per cent of initial pressure and a recovery factor slightly higher than 84 per cent.
Sixth Rnte. Eq. 5 may be set up as a "50-50" rule of
thumb: "To determine the abandonment pressure in
psia, multiply the depth in 1000's of feet by 50 and
add 50:' Accordingly, the recovery factor would be
84 per cent.
Extended Analysis of Abandon'ment PressuTe. The
terminal production rate is determined on the basis of
economic considerations. Individual factors which
should be considered include: well operating costs and
gas compression costs - capital, depreciation, fuel,
lubrication, maintenance and labour costs. Once the
abandonment rate and the lowest practical surface
flowing pressure have been established. the COlTesponding sand-face flowing pressure, p.., can be calculated. This sand-face flowing pressure is used in the
appropriate back-pressure flow equation to obtain
the average formation pressure, prj or in this case
.,
(2) Delivc1·abilify.-Average deliverabilities at certain reservoir pressures are assumed as follo\\'s:
500 1.000 2,000 3.000 4,000
Reservoir Pressure (psia):
"AvcriJge" AOF (MIvIscfjD):
2
7
20
35
50
and
P(ldcn,IJ is the pressure which woul~1 ex~st at the saillc recoverr
for an Ideal gas, Tbe plot representmg Ideal gas bellm'iour is i1
straight line Joining the points p = r'!2;; GI' = 0 and Jl = o.
Gp
=
G.
(2) Retrograde liquid saflll"a~ion u.~ a fmctio-n of
the hljdroca1'bon prITt volullle ·ver:jjf.~ prcssl/l·e,-Depending upon data, the following equation may ue
used:
RF (fraction)
=
P:lI, Zi (1 - S~h)
1_
Z",h
Pi
fj.233 TrP,cz,Seh V,
Pi Toe
= condensate saturation at abandonment pressure as .1
fraction of the h~!droc3rbon pore \"Olume;
V,. = vapour volume of one Imperial gallon of retrograde liquid
at standard conditions; and
Zalo is based on the propcrties of thc ~as existing at Poll,.
(3) Retrograde loss e3.·7J1·f!s:'~erl in blJls pel" MJlIscf
of initial gas in place.-If the retrograde liquid at
abandonment pressure, Se'lb, is measured during a reservoir fluid study and reported in bbls pel· Mi\'Iscf of
initial gas in place:
Sell
RF(fraction)
p,
Z"h
pur> T""
Z"h
s,.
+ 5.015 X 10-11
~ ~
= 1 Rio
- 0.000035
T r p••
S~ nh
RF
where
Z'"lo
=
~
z,
I -
(Eq. 12)
p,
two-phase deviation factor at the abandonment
pressure.
Calculation of Recm·er,., Factors
Methods Based on Resetyoir Fluid Studies
B-1.
(l) Cwmua.fi1.,e IJrodnction ?)eTSll.s IJressU1·e..-The
l"ecovery factol" for any abandonment pressure can be
obtained from the relationship between pressure and
the cumulative production expressed in per cent of
initial gas in place. The two-phase deviation factor
can be determined from laboratory measurements
conducted at reservoir tempera cure :
21
=
\' (cf)
G'(sof)
C'I'(scf)
p V T _c
(G'
----.£..E_G_'__
=
G'p)p~c T r
Pi (GI -
G\.,l
(Eq. 13)
cell volume used in the reservoir fluid studY;
initial g3S ,·olume in the cell; and
.
cumulati"e gas vo!umt' removed to pressure p
The two-phase deviation factor may also be determined from:
z'
118
P
(pu<"c)_
p("!e,,l)
(Eq. 14)
(Eq. IIi)
B-2. IVlethods Based on Material Balauce Concepts
Material balance equations for volumetric gal-! condensate resen'oirs are as follows:
G I' = G
Of extreme importance in gas-condensate pools is
the formation of a liquid phase as the pressure decline~ below the de,v point. Usually, even in extremely wet reservoirs, the maximum liquid drop-out \"I'ill
not exceed the critical liquid saturation.
The recovery factor for a constant-volume gas-condensate reservoir may be expressed as:
V,.
The effect of compressibility and temperature on
liquid volumes has been negleeted in Eqs. 15 and IG.
B. CONSTANT VOLUME GAS-CONDENSATE
RESERVOIRS
(Eq. 151
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Accordingly:
(a) P.,h should be modified by 15 to 25 per cent
when the actual AOF depart~ 25 to 50 per cent from
the "uyerage" AOF;
(b) palo should be modified by 25 to 40 per cent
when the actual AOF departs 50 to 75 per cent from
the "a'verage" AOF.
(.'3) Extent of Gas Processinu.-In cases where the
operating costs relative to o,\'er-all revenue are higher because of sulphur and acid gases, it is suggested
that Palo be increased by 15 per cenL In dry shallow
gas pools, which require processing solely to remove
water '\'apour, palo should be decreased by 15 per cent.
(4) Pre.sSII..l"B at DeliueTij Po'int. In cases of exceptionally low delivery pressure, Pab should be reduced
by 15 per cent.
(5) Sltmmation of EffBcts.-Siml1ltaneoL1~ effects
should be accounted for as follo\o,.'s:
(a) individual effects of gas processing, deliverability and delivery pressure should be added;
(b) only a fraction of the modifications for deliverability and deli'\·ery pressure should be added to that
for liquid production.
During the advanced stages of production, the
"tail-end" gas recover:,! should be determined from a
rate decline analysis provided that trends reflect productivity limitations.
p(eum) is the pressure on the. depletion curve (i,c. cumulillivc
production vs. pressure) corresponding to a particular rccovcrr;
( 1 -
IJ" )
B~
(Eq.17)
A plot of G~ against liB'" will be a straight line intersecting the absci!::sa at the ,gas in place, G or GIr.
A second equation IS:
p
Z'
=~
z,
(Eq. lR)
A plot of plz' against G1, represents a straight line
with the intercept on the abscissa being the gas in
place, G 01" GIP.
In thp absence of measurements, the initial gas
deviation factor may be llsed instead of tv.'o-phase
deviation factors.
Ga.s Cycling. The recovery factor fol' cycling operations is difficult to determine. A simplified assumption is that the recovery factm' fOI" a c.\'cled pool flllls
beh...· een a minimum obtained by pressure depletion
(e.g., 80 per cent) and a maximum attained at zero
retrograde loss (e.g., 88 per cent) and that within
these limits it is proportional to the condensate recovery {e.g., if the retrograde 108s decreases from
10 to J per cent by cycling, the gas recovery factor
will be 84 per cent).
Procedures for Determining fhe Abandonment Pl'esSll.rc. The procedures for determining the abandonment pressures are identical to those for constant
volume gas reservoirs.
C. WATER DRIVE GAS RESERVOIRS
As pressure reduction causes water influx, the gassaturated reservoir volume shrinks with production.
During this procegs, the water advances. either uniformly or through coning, fingering or channelling.
The Journal of Canadial"l Pefroleum
','
In the case of uniform water encroachment ill a homogeneous reservoir, the gas flow practically ceases
as SOon as the water enters the well (Ref. 11).
The abandonment of wells in a water drive reservoir is usually governed by the economics of the
j
j-
(2) Effect of Rate of Produetion.-The pressure
at abandonment will depend primarily on the relative
size of the aquifer, the permeabilit;)r of the aquiferreservoir system and the production rate (Ref. 13,
21). On the basis of reservoir pressure alone, the recovery factor improves with an increase in the production rate, because the reservoir loss is smaller at
lower pressures. Actually, the producing rate is often
limited because of contract commitments and sometimes controlled in an attempt to prevent water entr;)'.
(3) Methods of Dete>-mining Water Influx.-There
are several methods for the determination of water
influx and the pressure performance of water drive
reservoirs; e.g.; digital, analog, graphical (Ref. 14).
A few useful equations are summarized in Table III.
(4) Sweep Efficienc1J.-Certain concepts, not necessarily accurate in all aspects, are useful in the prediction of reserves of water drive gas reservoirs: (a)
areal s\\'eep, (b) conformance or vertical sweep and
(c) displacement efficiencies.
A reduction in recovery because of water b:~r-passing
a group of pores may be accounted for through a reduction in either the sweep efficiency or the average
TechnoloC"', July-September, 1966, Montreal
Rock Invaded lacre-feet)
W. - (W, - W;)
= 7758 (1
S"i
Sl:fw)
(Eq. 19)
The current position of the gaS-\lirater interface
may then be determined from the relationship between rock volume and height above the original interface, as determined by geological studies.
(a) Areal Sweep Efficiency. For mobility ratios
smaller than 0.05, areal sweep efficiencies higher than
95 per cent may be expected (Ref. 11). As typical
gas pools have mobility ratios of about 0.001, areal
sweep efficiencies should approach 100 per cent.
(b) Vertical Sweep EfficienC1j. In stratified water
drive reservoirs, the limiting water-gas ratio (e.g.
30 bbls per MMcf) will correspond to a vertical sweep
efficiency that may be calculated on the basis of the
formation stratification (Ref. 12). Figure 1 shows a
relationship between vertical sweep efficiency and
permeability variation at several water-gas ratios,
calculated from published data (Ref. 16).
(c) Volumetric Sweep Efficiency_ Cross-flow, capi)larity, diffusion, high density contrasts and low mobility ratios tend to establish high volumetric sweep
efficiencies. Experience elsewhere has indicated that
a distance of 5 to 20 feet from the gas-water interface to the base of perforations is necessary to pre'lent flooding-out of a gas welL Information in Alberta indicates a wide range; however, in the absence of definite information, a value of 15 feet may
be used to position the gas-water interface at abandonment.
In blanket-type reservoirs, sweep efficienci.es may
be extremely low. In the case of bottom water drive
reservoirs having substantial relief, the volumetric
sweep efficiency may approach unity_In the case of
edge water drive reservoirs, both pay thickness and
T.'SLE
III
WATER INFLUX AND MATERIAL BALANCE
EQUATIONS
(1) Steady Slate and Afodz]ied Stead)' State Flow.t
W. (bbls) ~ CONSTANT E (p,-p) <l. t/F (t); where:
o
F(t) ~ I - Standard steady state; F(t) - log t - Simplified Hurst formula;
F(l) = (A + log t) - Simplified Hurst with time con-
version; F(t)
= t""n.tBlit -
Empirical-statistical method_
(2) Unsteady Stale Radial Flow Jl,tlodel:
Wo (bbls)~B E QD <l. P ~ B(<l.po Qvo
Ap2' QnIl-D2 ... .uP"_l QOn-D(n-l) J
+ <l.p,
(3) Slraigllt Line A1alerial Balam:e Equation:
G,B.+(W,-W;) ~ B E<l.PQv
Bg
81;;
(Ba: BEl)
QD_D.
+
+G
119
-,'.
,.
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,
;,
pl-O-
duction of gas and removal of water; the reservoir
pressure plays a secondary role, in that it may prolongthe flow against increasing back pressure.
Wells in pools with substantial relief would be successively flooded out, and the recovery would be dictated by the economics of producing the last wells high
on the structure.
In homogeneous edge water drive reservoirs, depending upon the proximity of water and the severity
of pressure drawdowns, water may form tongues or
fingers and cause premature abandonment of wells_
In stratified edge water drive reservoirs, water will
preferentially invade layers of higher permeability.
In this case, the vertical sweep efficiency at economic water-gas ratios is important and may be calculated by waterflood prediction techniques (Ref. 12).
The volume of rock invaded at the time bottom water first enters the well is dependent upon the relative
size of the horizontal and vertical permeabilities (including shale breaks, impermeable barriers), the gaswater density contrast, pay thickness and well penetration, well spacing and pressure drawdowns.
The recovery factor of water drive gas pools may be
as low as a few per cent for a blanket-type reservoir
and as high as 90 per cent for a partial water drive.
(1) Identification. of TVater Drive.-Several static
and dynamic conditions and factors are indicative of
actual or potential \vater drives:
(a) Relative size of the aquifer as determined by
geological and geophysical data; potentiometric surfaces.
(b) ""Vater produ.ction, its sensitivity with rate and
relation to cumulative production; distribution
and position of wet wells with respect to structure.
(c) Ratio of fractional pressure depletion, {(p/z),
- (p/z)} I (p/z)" to fractional recover;', G,/G.
(d) Experience in similar but more mature pools
is lIsefui.
displacement efficiency. According to Gorring (Ref.
15), a pore is either flushed of all its gas contents
or by-passed by the water. Thus, the displacement
efficiency at the pore level may be viewed to be 100
per cent. In practice, the concept of a statistical average pore is frequentl;' used. This pore, when flushed
by water, will contain a residual saturation, 8 g .......
expressed as a fraction of the pore volume. Consequently, the rock volume contacted by the advancing
water may be related to the net water influx and the
residual gas saturation as follows:
•
:~ ~
that gas in excess of the initially trapped gas saturation is recovered, then:
K~
RF(fractiunJ
,
,
\:~,-• ,
'" '\
•,
k=l
~
I~ ~
~
30
10
.
~O
0
V.llneAl
60
.. ..
,.
JW~~" ~"'CI~Nr:::V l'~.
,
CENT!
Fi,qw'c t.-Relationship Bei!L.·celL Permeability
and Ve1'tical Sweep Effidcm;y_
l'ariatiol~
reservoir dip are significant. The actual yalue of the
volumetric sweep efficiency depends primarily upon
structure, and thus each pool requires individual consideration.
The water influx, \V~, and the volumetric ~weep
efficiency, E..,., can be calculated from the following
equations:
and
W.. (hbls)
=
E,., (fraction)
G(B g ,
-
Eo;'
+
GI' BJ:
+ WI'
- Wi
We + Wi - \V p
7758 Vp (l-S",-So:r~)
(Eq.20)
(Eq. 21)
where
Vp
=
reservoir pore volume ill3cre-feeL
As Wells are successively flooded out, obser"ation~
of the water-gas interface should be made to determine the extent of agreement between predicted and
actual volumetric sweep efficiencies. Large \'ariations
in well performance are to be expected \\·heL·e fracture
networks exist. The application of the method of Perrotti et rzl. (Ref.17) to gas reservoirs demonstrates
that, for practical producing rates, the gas water interface advances uniformly O\'er the entire resen'oir.
The analysis, however, neglects localized pressure
drawdowns.
(5) Effect oj Residual Ga~~ SatuHl.-tion 01/. Rcco've1'Y_
-Generally, the gas in excess of the residual gas entrapped during period m. calculated at time n following expansion, equals:
(Pn,
L
([10-1
This gas
maJo~
+ Pm)
+ [Jo)
- l ] S"" CEq. 22)
or may not be reco\'erable.
Case 1: Gas in Excess of Residual is Fully Recovered.
Assuming that the gas in the pores behind the waterflood expands to the abandonment pressure, pUb, and
120
CEq 23)
p,
Z,t.
( ~ + ~)
2
ZI.._I
z;
z;
1 - (1 - En') ~
k=n
SI;<l,.!l E",-I..
~
•,
,•
if':'.:;" ]
(1
(Eq.24)
Zk
The residual gas is thermodynamically lInlitable
and tends to diffuse through the water_ The rate uf
diffusion is expected to be low and should not play u
sub~tantial role in economic g-as recoverJor t Ref. 18).
(6) Determination of Residl'nJ Gas Safu1"atiml.The displacement of gas by water is an imbibition
process. Therefore. a specific gas saturation is ap~
pro<lr;hed from above; that iE;, the reservoir rock is
first saturated with the "displaced" fluid, ill this case
gas, and the gas satul"ation is reduced by the displacing fluid, waler. This ::;pecific gas saturation i,g
the "residual" gas saturation existing when the relative permeability to the displaeed fluid, i.e., gas, is
zero.
Re~idual gas saturations are equivalent to residllul
oil saturations for corresponding wettahility conditions I Ref. 18).
According to Naar and Henderson, the maximum
residual ga1i saturation in a mathematical model representing the trapping of the non-wetting phase dul'ing an imbibition process i.s equal to !)O per cellt of
the initial hydrocarbon pore volume (Ref. 1:~)_
The residual gas .saturation data from 251 tests
on small samples were analyzed b.r Chierici ef at and
none of the attempted correlatil)f1S proved to be SUl.'cessful for unconsolidated sand~i. s~llldstones or lime,tones (Ref. 19l.
Based on a careful analysis of fluid and rock daLa
pertaining to sixty frontal displacement experiments,
Gorring found that, "to a good firsL order of appl"oximation," the non-wetting phase saturation, e.g'. gas,
was a function of porosity only (Ref. 15. 20). The
relation ~uggested is:
Sl':r,'
t ('~ t =
62 -
1.3~,
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•,
·•
=
RF (fraction)
~
·
+
Case :2: Gas in Excess of In-itz-al Residual is Not Recovered. Assuming the gas that remained in the pores
at the time they were contacted bJor the invading water
is not recovered, then:
. .
.~
•
Z,
Pi
[ 1 - E"
~G'~·o~o~...~
•
PaL
Z"L
'"
'"0 ~
••
1
=
IEq.2ri)
The equation applies to sandstones and uncomiolidated
porou.,; media.
Residual oil :mturations obLained from waterfloocl
studies for principal oil-producing pools in Alberln
were analyzed using a digital computer. A summary
of regression equations is shown in Table IV. In practice, the follo\''t'ing selected equations for Sur" may be
used for Sgrw in the order listed, depending upon data:
Sandstone Resei"'/}oirs
~
~
~
~
50.5 - 0.5l S,,, ·18.3 - 0.68 S",
51 - ~
33.5
om"
(Eq. 26)
t E q.27)
(Eq. 28)
(Eq. 29)
L-imestone Reservoirs
In the absence of any reservoir information fOI'
limestone formations, it is suggested that a value of
S.-:r" = 35 per cent be used.
The JDurnal of Canadian PCl'roleum
The regression analysis failed to provide a satisfactory correlation; however, there appears to be some
merit in using an equation of the form:
S,~
(%)
~
40 (1 - 5.-;)
(Eq.30)
01'
(b) gas in excess of initial residual is not recovered,
(RF,) .
Figure 8 shows the effect of the residual gas saturation on the recovery factor for various permeabilities at a constant volumetric sweep efficiency.
Figw"e 4 illustrates the effect of the aquifer permeability on the recovery factor for several volumetric sweep efficiencies.
Figure 5 illustrates the effect of production rate,
as reflected by the producing life, on the recovery
factor for several volumetric sweep efficiencies.
,
r\..
-- '"~I": ::::::
1
~
u
~
~ ~oo
5.. (%) ~ 483 - 0.685.;
5.. (%) ~ 37.5 - 0.14 S.,
So, (%) ~ 43.2 - 0.·17 S",
So, (%) ~ 51 - q,
So, (%) ~ 24.9 + 1.3 q,
So, (%) ~ 39.7 - 043q,
So, (%) ~ 56.5 - 0.51 s"., 0.69q,
So, (%) ~ 20.7 + 0.14 So·, +
1.54 q,
So, (%) ~ 45.0 - 0.41 So; 0.25 q,
So, (%) ~ 45.0 - 0.23 q, -
are as follows:
S,
°
')
\f1.
('
·'"•
o
Q
.. " • a~eov!.l' , ... elO. A~~UMINa
.~51DU"'l
Figu?"r~
carbonate
0.21 5.6
18
unclassified 0.33 6.2
31
,.
0.33 6.2
31
0.81 3.8
13
s."
Sandstone
335
Carbonate
35.3
Unclassified 34.5
••
,.
.!CDV~lfD
IS NDI
:10
:10
..
••
.0
••
~
••
I!COVlI,Y ....Cl0 •• 1'1 ... ND I"~ ('11 CINlI
,~
f.-Relations/tip Between plz and Recovel·Y Factor
- Producing Life as a Parameter.
17
~'i'" I'-...
"',
••
"'" '- '\.
"\
""
" "'"""
'"
\.
"-
10
U
:
'-
.0
~
~
• ••
31
31
VD\U""n.IC 5W!!' I,"CUNCT
7.=1 'fa erNT
~J_)
'.
:r:
0.46 5.5 30
'.,.1
'.,••I
~
'\.
q,
l%) k(mdl
21.7
16.1
18.5
17.5 236
7.9 41'
11.9 335
"-
••
••
'0
~o
anlD\J"'l O ... ~
m
\
,- -
'\.
••
s",
"Ptchnology, July-September, 1966, Montreal
.15IDU"'~
INITI"'l
Pools
••
(%) (%)
IN I.CIU 0'
IN UCU5 0'
•• •
13
0.35 6.1
OA~
I' 'ULW AlCOVIUD
A'~I Areovfu fA.CIO" ""~U""INO 0""
0.81 3.9
0.35 6.1
...
10 .... 11.
~
sandstone
0.26 5.1
'\.
, ~'
0.60 5,7 13
0.02 6.3 18
0.29 6.4 31
0.53 6.1 13
0.19 5.7 18
0.14 7.0 31
unclassified
- 14q,'/k (100 - q,l'
So, (%) ~ 58.4 + 0.0118 k sandstone
0.88 q,
- 0.202 (k/q,' - 0.455.,
So, (%) ~ 23.0 - 0.0105 k +
carbonate
1.73 q,
+ 0.080 (k/q,l - 0.03 5.;
So, (%) ~ 50.3 + 0.0027 k
unclassified
- 036q,
- 0.069 (k/q,l - 0.525,,,
So, (%) ~ 47,3 - 0216 q, unclassified
0,033 (k/q,)
- 0,47 Sw' - 67 q,'/k (100·q,)'
So, (%) ~ 47.3 - 0.21q,·0.032
unclassified
(k/q,)
-475., - 69 q,' Ik (100-4»'
- 0.006 kJ1
graphic parameters Fonnation
'-' '.
0-.:
\
•
U
sandstone
carbonate
unclassified
sandstone
carbonate
unclassified
0.41 S..-~
Note: Average petro-
R'
~~
" " ~~
,:: ~'OCI
••
Formation
RegressioJl Equations
~
•
:
TABLE IV
RESIDUAL OIL SATURATION CORRELATIONS
.
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(c) Laboratory Tests. The residual gas saturation
can be determined experimentally by conducting imbibition, relative permeability and flood tests. Eperimental residual gas saturations var~r from 15 to 50
per cent of pore volume. An analysis of core and log
data in watered out gas sands showed agreement between field and laboratory residuals (Ref. 18).
(7) Recovery Factor Relatio'nships, Calculations
based on information contained in Ref, 9 and 21 illustrate significant recovery factor relationships.
Figure 2 represents associated p/zJ s and recover}'
factors for a particular set of conditions assuming
either that:
(a) gas in excess of residual is fully recovered, (RF 1 ) ,
Figure 6 shows the relationship between water influx and .cumulative gas production for a set of permeability values.
Calculations indicated that the recovery factor decreases rapidly with increasing ratio of aquifer to
reservoir radii below r,Jrw = 5.
.0
'"
\.
..',.
\.
~o
~
...
..~ ~
..
'
. ;....
~:.: '
t- .,.
_
~
5 ..,U ....,IDN ( , n CI'NT 0' 'DAr: VDlUM!1
Figure 8:-Relationship Bet1fJ6en RecoveJ·y Factor, RFJo
Gas Satm'atton Permeability as a
Parameter.
and Reszdual
121
,
.
(8) Procedw'es ;01' Detennining Recovery Factors.
-The following guidelines are recommended:
Prior to production, the pro~edure is the same as
that proposed for constant volume reservoirs, except
that where edge 01' bottom water is present, the abandonment pressure is increased by 15 to 25 per cent.
·
·
,.
•
.! ,. ~
u
i\.""
,.
'"
'"""
,.
""""-~
......
............
,.
............
~'110 "t"1I Cr"",
.... ~.
1
1tI "EII CtN ,
""'"- ~f..!~60Ptt
en... ,
..........-.~ • .sa n-!II .eH.Ir
~
~
r...... ' ..opr.. 1ch.lr
r.... !(Jpr.li!
•
,.
l
CrN,
I
a •• ~o Pl'1l
.. ,. ..
~
~
Ce-Nr
-
,~
".
FigllJ"C 4.-Relationship Betwcen Recovery Fa.ctol', RF..
and Pcrmeability - Volumctric Sweep Efficiency as a
Pll/'amettr.
..•
21.
6, Determine the areal sweep efficiency. En. and the
vertical sweep efficiency, E., or the volumetric sweep
efficiency K •• , at abandonment conditions, Find the
"•
....
....
·
·
·"
·,
0
3
u
.....
.....
"
~ ~~
•
t':
~Ellel!"""
~I
Cr"",
"
,
• ,
1'-....""- ~~N' I
• Cl!1V'
•
0
" ~ ~I
:-.............
r----~ I
'0.
0
...............
0
f,1 Cl!N
~I'''C'N)
.~
• i
<
.. cr..... '
I
/
..
,.
,.
Figure 5.--Rclationslrip Between Recovery Factor and
Producing Life Volll.metric S1veep Efficiency as a.
Parameter.
122
V/
/
V
/
1
V
/
/
1/
0
••
V
/ / V
/
0
/
/
-
0
0
If
f
,
· . ,,
" ce-..... r
./
0
"'fOil Cr""'r
0
~
.J
••
p
0
'0
.:10 PI!
u
~
~
r-......
.........
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t\:
........
Following production, procedureH depend on whether
water drive is indicated:
Ca.se 1: Production and pressure date do not yet
ascertain that the reservoir is ~ubject to a water
drive.
The pool performance. particularly the water production, ~hould be examined t(J determine the amount
by which the abandonment preSSl1 re should be modi~
fi~d, The abandonment pressure may be illcrea~ed by
25 to 100 per cent Ol' more, depending upon the performance of wells.
Case Z.- Production and pre::>sure data confirm a water drive.
(a) In the presence of a small water influx, the procedures outlined in Ca:;e 1 apply,
(b) In the presence of an active water drive. the following procedures are recommended:
L Determine the \\,~,ter influx constant and the initial
gas-in-place by extended material bal::t.nce calculntiomi
or determine the water influx c:onstant only by matching the pressure-production hi."tor:-r u~ing appropriate
steady 01' unsteady state flow E'quations (Ref. 22, 14).
2. Predict the performance ful' probable production
rates and obtain a plot of reservoir pressure, 1'.
again.::5t cumulative gas production, G...
3. Determine the cumulative water influx. \V... at ~e­
vel'al "alues of cumulative ga:-:; production, G I ,. using
the p VS, G I, plot and Eq_ 20.
4, A~sign a residual gas saturation, 81:...... either from
measurements or from Eqs. 26, 27, 28, 29 or 30,
5. Calculate the volumetric sweep efficiency. En,. for
various \'alues of cumulative water influx uHing E(I.
o
"
V
.~
,.
.~
/
...
,~
".
,~
".
_.
Figlll'c a.-Relationship Bctween IV/act· Influx and CIlItllllatiL'c Gas P/'oduclioJl - Permeability as a Paraml'tf.'1'.
The Journal of Canadian Petroleum
·
-
._- -
...
--
... --'--~
.appropl·iate abandonment pressure from the predict-
ed performance and calculate the recovery factor using
Eq. 23 01' preferably Eq. 24.
7. Assume the abandonment pressure and estimate
;~
,
.;
RF (fraction)
1 _
Pi T ae
the volumetric sweep efficiency if a performance pre-
diction cannot be made and determine the recovery
factor from Eq. 23.
(S., V,.)" -
6.233 T r P8U z! (Seh V~')8h
z,
Pill
A recovery factor evaluation is presented in Appen-
(1 - Eo,) - (1 - S.b).b
6.233 ~r p8e Zi n ~ n
Pi 1..
n = 1
S"i)
~
n = 1
~EII"'II
dix III.
'.'~.~'
n = n
ISh~w -
Seh (1 - SRi) III
( .E...
z )"
(Eq.35)
The subscript "n" refers to the pressure level and
production interval considered.
D.
WATER DRIVE GAS-CONDENSATE
RESERVOIRS
In water drive reservoirs, the recovery of condensate will normally be improved, but the gross fluid
recovery will be less than in constant volume gascondensate reservoirs.
For simplicitJ', retrograde liquid saturation and
c.ompressibility factors are assumed to be identical
to those obtained from a laboratory constant-volume
depletion stud}'.
(1) RecoveTy Fa.eto',- Expressions.-Two limiting
conditions will be considered.
Case 1: Gas in Excess of Residual is Fully Recovered.
The residual saturation, expressed in terms of pore
volume, contains gas at the abandonment reservoir
pressure.
Method (a.).- Proper substitutions in Eq. 1 result in:
RF (fraction) = 1 _ 0.233 T r Poe Zi Sell V...
p. T~e
-
[ E""IS'm· - So', (1 - S,,;)I
+ (1
- Eo") (1 - So',) (1 - S.i) ]
,
.j
\~
..
j
1
Note: If Pub =
n"
Pi
then z"" =
Zi
(Eq.3I)
(1 Po's".).
~
and Seh =
0,
PI
ZRb
Eq. 31 reduces to
RF (fractl·on) _ (1 - S"i - S,,,,) Eo,·
(1
5",.)
(Eq.32)
lliethod (b): The total gas recovered in terms of initial gas in place is the sum of the gas recovered by
depletion down to the abandonment pressure plus the
gas recovered by water displacement at this presBure:
RF (Iraction)
~
RF (1)
+ RF (2)
(Eq.33)
The recovery by pressure depletion for constant volume gas condensate reservoirs, RF (1). has already
been discussed.
P1-ocedu,Tes fo}· Determining ReC01JeTY FactaJ"s.
-The procedures for determining pressures, water
influx, volumetric sweep efficiency and residual saturation are similar to those recommended for water
drive gas reservoirs_
(2)
II,
ASSOCIATED GAS
Because of mixing in the reservoir, gas produced
from either the gas cap or the oil zone may contain
both solution and associated gas in undetermined proportions. For this reason, it is not practical to attempt to discriminate between associated and solution gas in production_ The remaining gas at any
time is simply the combined initial solution and associated gas minus the cumulative aggregate gas production.
Proced'ures for Determining Recovery Factors. Procedures for determining the recovery factors for constant volume and water drive gas and gas-condensate
reservoirs are applicable to associated· gas in corresponding situations. The underlying oil and water are
appraised in terms of the effect they have on volumetric sweep and displacement efficiencies in the gas
cap (e.g., oil influx). The recovery mechanisms include pressure depletion and displacement by oil and
water. In the absence of measured residual gas saturations after displacement by oil, Sgr<>J the following
approximations may be useful:
(a) If the reservoir rack is preferentially waterwet:
S.~(fraction) ~
(S... or S",,)
+ 0.10
(Eq.36)
(b) If the reservoir rock is preferentially oil-wet,
Sg"" may be assumed equal to the residual oil saturation, Sn....... determined from Eqs_ 26 or 30. If measured values of Sn......, and Sgrw are available for preferentially oil-wet rocks, S&rn could be approximated by:
Sara (fraction) = (So,,, or Sgr",) - 0.10
(Eq. 37)
The additional recovery resulting from water displaoement, RF (2). may be approximated as follows:
RF(2\ ~ 1(1 -5.i -S'm)!(I-S.i)1 EO'. p.bZi
Pi
(Eq.34)
Znb
Case 2: Gas in Excess of Initial Residual is Not Recove1-ed. The amount of gas remaining in the reservoir at abandonment c.an be approximated by the
summation of the gas volumes "trapped" over a series
of pressure levels_ The recovery factor becomes a
function of the incremental water influx and the
con'esponding entrapment pressures:
TechnDlogy, Julv-September, 1966, Montreal
III.
SOLUTION GAS
Recovery of solution gas or "oil-well gas" depends
on fluid and reservoir properties, as well as on the
methods used to produce the oiL
A.
Primary Operations
The soJubility of gas in oil, the saturation pressurQ
and the formation volume factors are determined from
either measurements or correlations_
123
~/~:::
,.~X,':.;:~
'.
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The recoverJ~ factor depends on the composition of
the reservoir fluid, the pressure at which the hydrocarbon is trapped, the rock volume invaded by water
and residual hydrocarbon saturation.
A similar equation can be developed by expressing
the retrograde loss in barrels per MMscf of initial gasin-place.
Production pressure data are useful in many ways:
(a) identifying the predominant recovery mechanisms, (b) confirming the initial solution gas-oil ratio and bubble point pressure, (c) checking the l·eliability of existing performance predictions, (d) forecasting gas-oil ratio and pre~sure trends and (e)
evaluating reserves b.y empirical methods,
Particular attention should be directed to gas lJroduction statistics, as the unawareness of the presence
of gas cap gas in the production will result in misleading solution gas-oil ratios and erroneous reserve
estimations.
(6) Specific ProcedU.1"es fol' Determining RecavcTY
Facto-l"s.Sol1ttion Gas Dri'ue - Jlla..tenal Balance Calf:luations.
Case 1: Using the Ultimate Oil Recovery, The expression [01' lh~ recuvel·Y fadm', Eq_ I, becomes
RF (fr3ction)
(N -N p ) fin
Ca."ie 2:
(N - N v) B~ ,,1,1 5.615 T. r [l.. 11
T r Jl~r Znh
-
(Eq. :i9>
Using the Residual Gas Saturation.
RF(fraction)
=
1
-~'_
[ ' II
'a' ""II
([ - 5.,,1
(I
C
'
l
- oJ",
- SlH
5.615 To. Bm S.-:t P"10
(1-5,,,) H... T r p,r Z"h
In cumplete water c1riye pooLs" the ga::;-oil ratio
will u:5ually remain low. In solution gas drive pools.
the gas-oil ratio will increase gradually to a maximum and then decrease rapidly_ Gravity segregation
lends to low producing gas-oil ratios.
The gas recovery fador may range from 40 per cent
in complete water drive reservoirs to more than 75
per cent in the solution drive reservoirs.
\I::q. ·10,
Sol1(tioll
Ga..~
DTiN' and Gra.vity Sf.gr·cgfi.firttL - PerPredictiolls, The total gas recovery in terms
of original gas in place is the .sum of the recover,}' to
the limiting oil rate, RFI' as obtained by performance
predictions and the blowdown recovel'.", RF!. as determined from material balance calculations.
;uJ"maflee
:::(~:~~:I~)al:U[at(e:1~r~~'1I~8)'aI(l~~l~i:~
N
5.615 T.. PII'
+
T, p.: H
II'_,II -
Zm
II ,
5.615 T•• p",
1'1 p.c R.: z.. "
~:--r"
". )
([ -
(l --N,
N,. '"
I B,,,-
fiR
Il"
ll,;
"I,)
B~",I
II0."1,,'
)
,Eq.oI[,
Subscript "m" in Eq. 41 refers to condition." existing
at the end of the period of economic nil production.
H'uter D,.ire - J[ulerial Balal/ce Crrlculntioll:'. Eq, 1
may be expressed as follows:
Ui. l Matel-iai BalClrllce Calculation.J3.-The recovery
factor for any type of drive can be expressed b~r Eq.
llF'"
{traction/ = I -
( [ -
N,.)
N·
----U:--
Il...,.
(·ll
RF (fraction) =
~I'
=
f
N"
a
Rl'dN[,
N R"
(I::q 38,
Eq. 38 may be applied to oil pools subject to any type
of drive mechanism.
(5) Statistical Metlwds.-Empirical methods have
praetical significance, particularly in the latter stages
of depletion. Useful plots are: (i) log G p ·vs.log N p or N p ;
(ii) log \V I' vs. log G I,; (iii) \vater-gas ratio vs. G v ;
(iv) log N p vs, log \-VI'; (v) per cent oil in liquid pruduction vs. NT'; (vi) fluid interface positions vs. G I,
or NT'; (vii) cumulative gas-oil ratios vs. N p or pel'
cent recovery; and (viii) rate decline methods: (a)
constant "lo~s ratio," (b) exponential or constant percentage; (c) hyperbolic. (d) harmonic. (e) antilog
N I, vs. time. and (f) general statistical decline. e.g'.
polynomial.
The rate decline cun'es are applicable onl)r to wells
producing at capacity_ A basic assLlmption in empirical methods is that future performance obeys past
performance trends. Oil recovery may be determined
using correlations with pres::;ure, production and petrographic pat·Hmeters.
124
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Sirnilal'ly, the recovery factor may be represented in
terms of SO'. This may be done b~r replacing S"t in Eq.
40 by 1 - S., - So,.
l2) C·riterla. for ldentijviua TY1JCS of Dri·ves.The method.s for identifying potential and actual recovery mechanisms are based on: (a) experience with
similar pools, (b) structural and regional geological
data, including pregSUI'e, zone continuity and permeability, interface and outcrop information, (Cl drilling. coring, completion ~md test data, (d) pressure
and solution, gravity segregation and "'ater dri\'e indices and (e 1 manner of productivity and rate declines.
I-'el'jonnance Prcd.icticn1s.-These usually include the average gas-oil ratio as a function of oil
production. Therefore, the gas recovery factor can be
expressed as:
-IN B 01
"L
N R"
(1) Dh1Je f.'IechQ11i.cnn and .tlssociatcd Recovery.The gas recovery is dependent on the amount of oil
produced and the gas-oil ratio, :uul these are goYerned
by the resenroir drive mechanisms.
L The gas remaining in the reservoir at abandonment
",ill consist of the gas dissolved in the unrecovered oil
in the reservoir as well as free gas.
1 -
=
l ' rP
I
5.615 T,e p.[,
5 .~,) I'. . 6i
Z,'h ( 1 -
8C
I
I'
~
, - '".1 - ..
+ "."
I:"
C'
0"",
I
~
2
,o>q.·r)
where S~r.. is the l·esidllal gas entrapped by water in
per c:~nt of pore volume.
Note:
5..., + 5",.• ~ 5,,,.
rI::q. ·13)
\...· hel'e S"r~ i~ the residual oil M .. soc-iated with the residual gas. In developillg' Eq. 42, the pressurefl in the
inyaded and uninwlded portions of the reservoir were
assumed to be identical.
For a water dri\'e pool whel'e the pressure is maintained above the saturation pressure: R~ "" = R. I ; Slit
and S"t~ = 0; and the gas recovery factor, Eq. 42, reduces to: RF (fraction) = NI.jN, identical to the oil
recoyery factor.
Watc7' Drive and Gravity Segregalion Malcj~ial
Balance CalCHlClrti()11i~. An equation for the recovery
factor can be developed assuming that: (a) no gal;! is
trapped by the encroaching water and (b) the oil in
the water-inv~-Ided portion of the reservoir is treated as
if it had been trapped at the abandonment pressure:
RF (traction)
l
=
1 -
( 1 -
~n.) ~:1~
5.6 [5 T., p", lB'
E)
'
n
g; {I -"". f
p.c Znl' 1.... 6;
B
0""
+
(I -
E", ll,,; ~I
(I-S",)
~,,)
(I::q. ·1·1)
The Journal of Canadian PctrolCl.lm
The recovery factors obtained from Eqs. 38, 39, 40,
41, 42. and 44 apply to tbe initial solution gas in place.
B.
Secondary Operations
As secondary and enhanced oil recovery operations
can considerably reduce the gas recovery, it is importa.nt to know whether an oil pool will be affected.
Economics and reservoir and fluid properties will dictate the type and size of secondary operations. The
change in gas recovery for a solution gas pool caused
by conversion to a gas or miscible flood will be small,
but where ,vater is injected there may be a substantial
reduction (e.g., 30 per cent).
In most cases it is necessary to consider separately
the recovery during secondary operations_ For practical reasons, the gas produced is equated with the
i,
CONCLUSIONS
There is a need for a good understanding of the
processes influencing recovery (e.g_ \vater entry in
individual wells), additional experimental data (e.g.
residual gas saturations that may be cheaply determined b:~r imbibition tests) and effective lise of information disclosed by actual performance. The proper consideration of theory, laboratory measurements
and performance feed-back should substantially improve the reliability of gas recovery factor evaluations_ In this endeavour, the recover}' should be determined by a method which is consistent with the
amount and quality of the reservoir information and
the economics of the over-all gas production operation.
The application of either the simplified or comprehensive procedures proposed in this paper should be
beneficial in this regard.
NOMENCLATURE
Symbols are AIME standard) as indicated in the
text and additionally as follows:
PEl·
PE
R2y
R2
Sy
Sy
probable error of estimate of y - population
probable error of estitnate of y - sample
coefficient or index of determination; fractionofyvariation accounted for by the regression equation
sample
coefficient or index of correlation - population
standard error of estimate of}' - sample
standard error of estimate of y - population_
ACKNOWLEDGMENTS
The authors express their apprec.iation to the Oil
and Gas Conservation Board, Calgary, fOl" permission
to publisb this paper.
Technoloc " July-September, 1966, Montreal
(I) "Recovery Data for Alberta Natural Gas Pools,"
Company SUbmissions, OU and Gas GonseJ·vation
BOQ1·d Records, Calgary.
(2) DeGolycT and MacNaughtrm, "Natural Gas Reserve
Estimates for Trans-Canada Pipelines," Oil and
GaB Conservation Board Records, Calgary.
(3) R. Davis and L. H. ll'Ieltzer, "A Method of Predicting the Availability of Nat.ural Gas Based on Average Reservoir Performance/' T?·ans. AIl\1E (1953),
198, p. 249.
(4) N. Lamont, "Gas Reservoir Study Promises Accurate Recovery Estimate," The Oil and Gas JOll?"nal.
January 14, 1963.
(5) IC. 111uUe?·, "Recovery Factors of Gas Reservoirs
with Gas Expansion," ETdol u. Kohle, November,
(6)
1961, p. 900.
W_ H. Jllensch, "Calculation of Gas Reserves from
Gas Density Data:' The Petl·oleu1n Engineer, Sep-
tember, 1959, p. B-49_
(7) H. J. GTUy and J. A. Crichton, "A Critical Review
of Methods Used in the Estimation of Natural Gas
Reserves," T?·a71s. AHdE (1949), 179, p_ 249_
(8) R. E. Davis, "Natural Gas Reserve Estimates fo!."
Alberta and Southern Gas Company/' Oil and Gas
Conse1"1Jaticrn BoaTd Reco?·ds, Calgary.
(9) J. R. Bntn8, M. J. Ketkoviclr" and V. C. ilIeitzen,
"The Effect of 'Yater Influx on p/z Cumulative
Gas Production Curves," Journal of PetToleulll Tech_
nology, March, 1965, p. 287.
(10) R. P. Schoemake1', "Gas Appraisal, A Graphical
Short-Cut for Geologists," Alberta Society of PetToleltm Gcologists) 1957 - 1958, 5 and 6. p. 200.
(11) A. B. Dyes, B. H. Caudle and R. A. E1·ickso71, "Oil
ProducUon After Breakthrough - as Influenced by
Mobility Ratio," Petrolelt1n T?·ans. AIME (1954),
201, p. 81
(12) Jf. E. Stiles, HUse of Permeability Distribution in
'Yaterflood Calculations," Trans. AIME (1949),186,
Downloaded from http://onepetro.org/JCPT/article-pdf/5/03/115/2165663/petsoc-66-03-02.pdf by guest on 04 March 2022
,~
"
initial gas in place less the gas remaining in the reservoir. regardless of its origin.
(1) Pressu're IIJaintenance by Gas. Eq. 39 may be used,
or Eq. 38 ma~y be applied to primary pressure maintenance and blowdown operations.
(2) PTessuTe 111aintenance by ~Vate1' and Flooding.
Eq. 42. mal' be used where S". '" 0, and Eq. 44 may be
used where S~r~ --= 0_
(3) Miscible Floods. Eq. 39 may be used.
(4) llIiscellaneous, Secondary, Tertiary and Exotic Recovery P1"ocesse,~. As there are many different types
and combinations of enhanced oil recover~' operations,
it is impractical to predict orders of implementation
and set up specific rules for determining gas reCOver}'
factors.
REFERENCES
p. 9.
(13) R. G. Aganval, R. Al-Hu8sainy and H_ J. Ra1ney.
Jr., "The Impol'tance of v;.rater Influx in Gas Reservoirs," Jow·nal of Pet?'oleum Technology, Novem_
ber, 1965, p. 1336.
(14) D. L. [(atz, M. R. Tck, [(. H. CoatB, M. L. [Catz, S.
C. Jones and M. C. Mille?·, "1lovement of Underground 'Yater in Contact ,'lith Natural Gas," The
Ame?·ican Gas Association, February, 1963
(15) R. L. Gon'i11g, "Multiphase Flow of 'Immiscible
Fluids in POl"OUS l\'Iedia," Ph.D. thesis, The University of Michigan, Ann Arbor, 1952.
(16) H. Dyksbou and R. L. PUTSOn8) "The Prediction of
Oil Recovery by '\Vaterflood," Secondary Recovel!.1
of Oil in the United States, Second Edition, New
York, AmeTican Pet?·oZeum Institute, 1950, p. 160.
(17) G. Perl'otti, T. van GoldfTacht, D. Gal{etti and L
Pcytchev, "Predicting Fract.ured Water-Drive Reservoir Performance," Pet1'oleum Engineer. November and December 1963, p. 54.
(18) T. Jl1. Geffen, D. R. Pm-riJ;h, G. lV_ Haynes and R.
A. Morse, "Efficiency of Gas Displacement from
Porous l\'1edia by Liquid Flooding," T7·ans. AIME
(1952), 195, p. 37.
(19) G. L. Chierici, G. M. Ciucci and G. Long, "Experimental Research of Gas .saturation Behind the Water Front in Gas Reservoirs Subjected to Water
Drive," Sixth IVo1·ld Pet1'olemn Cong~·ess, June 25,
1963; T?·ansacti07l.s, SecUon II, Paper 17-P D 6, p_
483.
(20) M. W. Legatski, D. L. Katz, llI. R. Tek, R. L. Gor_
ring and R. L. Nielsen, HDisplacement of Gas from
Porous Media by Water," AnnuaL Fait l}[eeting of
SPE, Houston, Texas, October 11 - 14, 1964; The
Oil and Gas Journal, January 10, 1966, p_ 55_
(21) K. Mulie?·, Erdol 1£. [[ohle, "Production Rates and
Ultimate Recovery Factors in Gas Fields with Edge
Water Drive," September, 1961, p. 695.
(22) D_ Havlena. and A. S. Odeh, "The Material Balance
as an Equation of a Straight Line," J~urnal of
Peb·oleum Teclmology. August, 1953, p. 896.
125
,...
,.
-,
'..
..
APPENDICES
ApPENDIX I: RECOVERY FACTOR CALCULATIONS
FOR CONSTANT VOLUME GAS RESERVOIRS
.4.n Ecollomic Allalysis of Abandonnwnt
Cond1:tions and Dcterrninat'ion of Tenninal
Reset"voit· PreSS'UTe_
Data: Gas gravit)· = 0.71; 1', = 685 psia: T c = 393 R
Ratio of specific heats, cp/c~. = 1.24
Depth = -1-,6.,10 feet: P, = 1,519 psia.
Plant capacit)' = 5,000 Mscf per dar.
Number of wells = -1..
Average back pressure test: Q = 0.. 0091 (Pf:! - p,:!)
where: Q in fvlscfjday and (Pr:! -- p,?) in psia:!
Assumptions :
1. Compressor inlet pressure = 100 psig.
2. Average compressor inlet temperature = 50"F.
3. Line or plant pressure = 900 psig..
4. Back pressure test equation will not change during
depletion.
5. Friction losses in well bore are neg"lectcd - annular flo .......
+ 1"6"
" ~;
1.250
0.0091
K
365
Pr
=
K
~
0.15 $/year
54.S q $/Year.
Expressing shrinkage (5 per cent), I~ase fuel (5
per cent) and royalty <16.67 per cent\ in terms of
gross prod lIction :
.
Raw gas production Q
=qx
100
[1)0
100
95 x -gs x 8333
.
=
1.3~ q
J\,'lscf/day.
The income from liquid producb; is as follows:
Using a unit recovery of6.0 cu_ feet per J\,·lscf of raw ,l!;<lS:
Condensate recovery = q x 1.33 x 6.0 !icf/day.
Assuming that 33 sd of condensate vapour equals one
Imperial gallon of liquid and the stabilized condem-mtl!
sells for $2.50 per bbl, then condensate saleH equal:
qxl.33x6.0x365x2.50
33 x35
~
0.0091 (Pr' - P.')
Flowing pressure at. wellhead = 113 psia, and P. = 126 psia.
=
q
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Deliverability and 'Vellhead Flowing Pressures:
Calculation of minimum formation pre.s~ure to maintain plant capacit;,',' rate. Le. 5,000 M5cf/da~!, assuming wel!head pressure of 100 p~ig:
Th us: PI-"
1. Plant. operating costs = $lO,OOO/}'ear.
2. Well and gatherlng s~'stem operating costs = $13,600/y~:J.r.
3. Compressor operat.ing and fuel cosLs = $11.300/ycar.
The income is as follows: Let the eronomic residue
gas rate equal q :i.'l'lscf/day, th(~n residue gas sales =
Q
5000/4
Operating costs are as follows:
=
630
.
$1
q,
~'~ar.
The minimum economic residue gas rate, q, is calculated from a balance throughout the system:
391'
pSia,
The production rates for formation pressures less than
391 psia can be calculated: e.g. at PI = 300 psia,
Q ~ 0.0091 (90,000 - 15,880) ~ 674 Mscf/dayIwell.
The ~mndface pressure required to maintain a rate of
1,250 Mscfjda,r/well, above PI = 391 psia, is now calculated.
e.g. at. Dr = 1000 psia: 1,2.50 = 0.0091 (1,000,000 - PA~)
Thus: DB = 929 psia, that. result.s in a wellhead flowing pressure,
pl(, of about 825 psia.
Pool production rates and compressor horsepower requirements for varil1us formation pressures are shown
in Yi(l/trc 7. Possibly 400 hp or less will be installed.
Two 150-hp compressors will be assumed.
,
Income $h'ear
54.8 q
6.30 Q
q
Operat.ing costs $;year.
10,000
13,600
11,300
571 Mscf/day.
+
+
+
Therefore, limiting raw gas production equals: 571
1.33 ~ 759 Mgcf/da)'.
Incorporating an over-all load factor of 0.90, the
deliverability required equals: 759/0.90 = 8-13 Msd/
dayIpool or 211 Msd/day lweI!.
A corresponding abandonment formation pi·eHSUl'C
of 198 p~ia is obL.'\ined from Pigure 7,
The recovery factor can nO\\' be calculated using
Eq,3.
K
RF (I
p,," z;
.)
I
raction =
-
Pi Znb
=
I
198
(181
0.97 "( 1519
= 0.89 or 89 per o~nt.
Note: If two wells instead of four remain pruducing,
then the abandonment pressure equals 230 psia and
the corresponding recovery faecal' 0,87. The effect of
different wellhead flowing pressure:" on recovery ig
indicated as follows:
·
•• •
•
•
...og~~
I
I
..0......,.
~
~
!
"lKl
I
I
5
·
~
·~
·~
\
1\
~(pprn
'IiQPUCTIQN !AU
'\
I
•
..I
,
•••'OU",.. IION
.~
126
The AOF at 1500 psia = 0.0091 x 2.25 x lOG
Ml\:fscf/day/wdl.
'\.
~.
~
,
""-
.~
0
,unuu lpo ... l
Figu1"e 7.-Delivc1"ability and
lOO
89
200
84
300
79
·100
72
Liquid production, extent of gas processing and
pressure at deliver.~! are ·'average" ~ however. the
productivity mllst be considered a~ follows:
\
/;
50
91
Applications of P1'Oposed P,.occd",.es of
Calcula.ting Reeo'very Factors for Consta"t
l' ol.urne Gas Rese7·voirs.
From EQ. 5:
Pnl' = 50 + 50 D = 50 + 50 x ·1.64 = 282 psia.
\
1/
0
~
Wellhead Pressure (psig):
Recovery Factor (% 1:
HOl"SCpOWcr
Requil·clI1rmts.
= 20.'1
The "average" deliverability for pr = 1500 psia
is 12.5 MMscf/day/well. Therefore, the average well
in this pool has an AOF which is GO per cent above
the "average" AOF and the "formula" abandonment
pressure. is reduced by 30 per cent:
P~b =
282 (1 - 0.30)
=
197 psia.
The recovery factor calculated from Eq_ 3 equals
~-!) pel' cent.
The Journq! of Canadian Petroleum
-{"_._--~
~ ".'
ApPENDIX II: RECOVERY FACTOR CALCULATIONS
FOR CONSTANT VOLUME GAS-CONDENSATE
RESERVOIRS
4700 psia
z,
~ 0.95
500 psia
Z"h
= 0.94
650'R.
V" ~ 21 sd lImp, gal.
= 0.13 per cent of hydrocarbon pore volume at
500 psia.
= 86 bbls per wlMscf of initial gas in place at 500
psia.
Data: Pi
Pob
T,
5,b
So: Jlh
The recovery factor at various pressures from a
depletion studl':
Pool Pressure
.~
(psi.)
Reco,'ery (%)
4700 4200 3600 2900 2100 1300 705
0
0 6.51 15.33 28.64 46.56 65.48 79.27 94.80
According to Method B-1 (1), the reoo"er}" factor
i
•
~
.-..
u"
:I ~IOOO
~
""
~
...........
.....
.~
~
..."",,
'0
~l
~~
8:;;000
/
',:
,,.
VI
t::--"...
~~
~ ...........
0
I':~...
""
~
........
RF ([ f ) ~ I _ 500 x 0.95 x (1-0.13)
rae Ion
0.94 x 4700
~
" ....
,•• •
6.233 x 650 x 14.65 x 0.95 x 0.13 x 21
4700 x 5.20
RF
84 per cent
Using Eq. 16:
RF(f
••
,.
"
0 .... 5 PIiCClUCTlClN 115C'1
..
••
••
Figu1"f3 B.-Plot of PreS8U?·C and P7·essure/Ccnnpressibitity
vs. Cumulative Gas Production.
.)
I
500 x 0.95
ractlon = - 0.94 x 4700
+
. .
,
•
5.615 x 10-0 x 500 x 520 x 86
0.94 x 650 x 14.65
- 0.000035 x 86 x 21
RF = 84percent
I ,"
,!;Xi!
ApPENDIX III: RECOVERY FACTOR CALCULATIONS
FOR WATER DRIVE GAS RESERVOIRS
Data: A
h
1054 acres
32.81 feet
13.4 per cent
10 md.
15.0 per cent
636 'R.
7 x lO-ii voljvoljpsia
45.0 MMscf/day lweI!
4Jo
k
...
5 wi
.~
T,
.'
e
AOF
p,
z;
po
T,
GfP
D
U''C
3670 psia
0.877
668 psia
390 'R.
40.1 Bscf
10.200 feet
0.8 cpo
Geological information indicates that the aquifer
is 100 times larger than the gas reservoir, therefore
l"c/r.. . equals 10. The equivalent radius of the gas reservoir, rw, is about 3,800 feet.
There are four wells with pay thicknesses of 55.
45, 40 and 21 feet. The last two wells are underlain
by ''irater and completed 28 and 14 feet above the gaswater interface.
(1) Recovery factm· estin-wtion p'tior to pl"odu,ct'ion.
-The abandonment pressure is calculated from Eq.
5:
p••
~
50
+ 50 D
~
50
+ 50 x 10.2
~
p~" =
560
+ 140
=
700 psia.
Using Eq. 3:
RF (fr.ction) - I -
700 x 0877
3670 K 0.927
=
,
.,
'1'
iY
0.82 or 82 per cent
(2) Recove'ry factor estimation afteT five yea.rs of
production_-Figure 8 consists of six points and indicates that either a water drive is present or the initial
TechnologYI July-Septemberl 1966, Montreol
.:lY,""
"I'
o .'
ma-
:Iv.......
/'
V
~"
,"r--
;;V:-~
V
Y,,/
D7
UI'oII!'Ob"-V
" ' - 5lClPl!'WolloTI!:R INI'LIJK CON5TANT
11-:11.5 8bl/p.;
IP .....
·/
DIP·]''i'.:II1C'
,
560 psi•.
To account for the effect of the expected water influx on recovery, pab will be increased b}' 25 per cent.
Thus.
•
u
•
,-
.-
lOp CD.
1I 1l1 -1l 1l,
6000
~_"
"" ~ . '
'.
I'...
.,.
t·;.:: -.
u .... l! ".'
/
~
84 per oent
Using Eq. 15:
RF
"""- .....
III:I:la
IQOCIO
10,,' IUc,/BbIJ
Figlln 9.-Straight-Linc Jllatel-in-l Balance Plot.
pressure is slightl:~r in error and the volume of initial
gas in place, GIP = 72 Bscf, is mueh larger than the
volumetric. estimation of 40.1 Bscf_
Evaluating the pressure-production data for the
first five years using r./rw = 9.0 and tD = 6 t. and
straight-line material balance techniques, one obtains
the first five points in FigU1·e 9.
127
~
..
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is obtained by interpolating in the above table:
•
',.-.
'.
A straight line through these points, line "b", extrapolates to a GIP of about 49,0 Bsd.
The well completed closest to the gas-water interface commenced to produce water in the third year
and was suspended within five months. The water
production is believed tu be caused b;V water coning.
G"
[1"
+ (WI'
\V,)
-
=
G
+
(13,; - B,::i)
W" =
515~...l PQD
Repeat steps (C) thruugh (f) using p = 2895 and
so forth, (e,g. 2896), until the difference between
consecutive pressures faUs within acceptable limits
,
0
IJ
I
0
z,
.
~
0
J
~. 0
-~
z
0
-.l'
J
/
J
f7
,
If
•3
~
·•
~
/
•
1//
..
.
•
CUMUlAIIVI!
FiYUJ"{' 1O.-PlfJl
0..,5
..•
PROOUCTION 1.5crl
oj Wnt,,1' Iujlwr
P1'ouuction.
128
•
!
/ 1/
J
us. C1lnwlativc
56.5 - 0.51 (IS) - 0.69 0:1.-1)
=
39.lj per cent of
According to imbibition tests, thi.s value should be
increased. Thus:
S.:;,,, = 42 pC'r rent.
The yulumetric sweep efficiency can now be determined from Eq. 21;
"·1'
w.. + W, _.
7758(1054) 132,81) 10.13-11 (LUO -1l.tS -
U.·I~1
\V~
15..W :>.lij'ii
Thll~. the volumetric sweep efficiency Lan be La 1culated for yarious amount.s of water influx (F;[JI/I'f~
10) .
The vertical .sweep efficienty i~ dl!tel'mined [rolll
Fl.qw·c 1 using a permeability variation of \' = 0_7~
and a water cut at abandonment of 40 bbl.s/i\Il\'l.sd.
For 2700 psia. z equals 0.831 ;
[J
.:;
~
3,1911, 10', 0,831
2700
~ 98"1 . lO'
..'
~
'{
res. bbls/.M.Msd, and the ;-iurface water-ga.s ratio may
be converted to re~en'oir condition.s using:
WGR (res. bbl/bbl) = "·CR Ibbl').,[\Iscfl B,.IIl'S. bbls/r.IlV[:icfl
= '10;9.821 x 1O~ = 0.041.
In Figure 1, a vertical swer::-p efficienl'Y of ·12 pel'
cent correspond:i to \' = 0,72 and \VG R --=: 0.0-11. '-\'8.sumillg that the ~ll'eal sweep effiLiency i~ 100 PCI' cent.
the vlJlumetric sweep efficienc)' equal.s ·12 pel' cent,
The water influx call be determined from 811- 21:
Moreover, the gas production rOlTespon<ling to il
water influx of 6.49 x 10'; bbls is 1:3.4 Bsd (Fi!Jul't'
10). As~uming that gas in exce:iS of residual is t'ecovered, the reco'very factor equals el.·I/'1O.1 01" 33,·1
per cent.
,
0
0
=
W•. = 7758 (0.'12100541 (32.81) ,0.13...() 11.00 - U.15 - 0.·121
- 0 = 6.'19 x lOu bbls.
1- +1/ 1
~
Sor"
=
7.2852 X lOll bbls.
(f) HI: =
7.2852 X lOG - 0 - 39.2 (7.625 x 10.';)
(1·1.696 - 39.2.1
= 9.225 X 10 5 res. bb!/Bscf.
Because plz equals lO D P". T r/5.ftI5 T dC B g • rjz = 3.1911 x lO\lj
9.2~5 X 10 5 = 3459 and z = 0.837; p = 2895 [JSi:L
/
1/
=
pore volume.
up Qo
(Bll: - BII:,1
=
0
S..-:r"
515~
The future performance of the l'eservoir may now be
predicted as illustrated below for the eleventh year;
(a) Selccted time intcn'al is one )'ear, 10th to 11th year.s.
(b) Assumed withdrawal: fiG I , = 1.336 Bscf; !l(W p - Wi) =0.
Current Gp = 13.360 + 1.336 = 14.696 BscL
(e) Firs[ estimation of reservoir pressure is 2.900 p,;;ia, and therefore p/z = 3,465 psia and 311: = 9.2095 X 10 5 res. bbls/Bscf.
(d) Pressure dechne during mLerval. ~p. equals: 2950 - 2900
= 50 psia.
(c)
The residual gas saturation determined from Eq,
26 is:
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On the basis of current performance. the estimation of the recovery factor remains unchanged at 82
per cent,
(3) Re('overy facto?' estimation after ten yeCL1"S of
pl'odudion.-At the end of the tenth year, the pressure
decline plot in FigUT6 8 curves upward, indicating
water influx into the resen.Toir. Points 5 - 10 in Figu.l'e
rJ extrapolate to a GIP of 39.2 Bscf. B equals 515 bbl.5
per psi. These points were obtained using a radial unsteady-~tate flow model and trial-and-error solutions
of 1',/1'.. = 9.0 and tn = 6 t.
Therefore, \V... = 515~.6p Qil and the material balance equation becomes:
This process is repeated for succeeding time intervals to what may be expected to be the abandonment.
Different production rates mar be used. The pool performance for a rate of 1,336 Bscf per year (i,e. 30year life) is shown in Figure S,
The water influx is plotted against cumulative ga::l
production in Fig. 10.
Gas
As the current recovery already equal,!-; the ultimate
reLO\·ery from stratifiLation cnnsideration.s, it would
appear that the \...· ater encroaehes uniformly. Depending upon economics, it may be further assumed that
the gas-water interface will d.se to within 15 feet of
the perforation of the well located hi~he~t on the reservoir structure. [n this case, the water will be within 20 feet of the crest of the pool at abandonment.
Calc:ulations on this bash; indicate thai the volumetric
s\...·eep- efficiency will equal E.5 pet' cent.
The water influx from Eq. :.!1 iti:
We = 7758 (O.RS) ( 1054, (32.81) (0.13-1 I (1.00 - 0.15 - 0.·121
- 0 ~ [3.14 X 10" bbls.
The cumulative gas production corresponding til a
water influx of 13.14 x 10( hbls in Figlll"l! 10 is 23.2
Bscf. This results in a recovery factor of 23.2/·10,1 or
58 per cent.
Nott,: The recovenr factor calculated fol' the ca!;l! whcl'e
gas in excess of irlitiai residual j,:; not recovered. using
Eq. 2·1, 1:-; 54 per cen t.
The Journol of Conadian Petroleum
-'--',-
(4) Recovery factol' estim.ation after fifteen yea-1°S of
p1"oduction_-No\v the plot includes 16 points and the
cumulative production is 20,04 Bsd. Three wells have
been suspended because of high ,'I,rater production, but
the fourth well ha~ not produced any water.
has confirmed the predicted performance_ On this
basis the recovery factor will remain unchanged:
j
RF = 58 per cent.
Using a GIP of 39.2 Bscf: Initial reserves
=
39.2 x 0.58
=
22,7 Bsc£.
Remaining reserves: 22.7 - 20.0 =
2,7 Bsc£.
The actual pool performance over the last five years
STOIAN
TELFORD
Alan S. Telford received his B.Sc. degree in chemical engineering in 1955 from the University of Manchester, England.
He was employed by Canadian Industries Limited in Edmonton until 1957. Since then, he has worked for the Oil and
Gas Conservation Boord.
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Elicdor (DareD Stoian, at time of writing, was manager,
data processing, at the Oil and Gas Conservation Board in
Calgary, Alberta. Pre.... iously, he worked os a special studies
and reservoir engineer for the same organization, as an instructor at the University of Alberto in Edmonton, and in
various capacities in France, Germany, Austria and his native country, Roumania. He holds a B.s. degree in mechanical
and petroleum engineering from the Technical University of
Hanover, Germany, and is active in several engineering, computer and data processing societies.
Effective September 15, 1966, Mr. Stoian is in the employ
of the Notional Energy Boord, Ottowa.
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i
.,
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,
REPRINTS OF TECHNICAL PAPERS
EADERS of The Journal oj Canadian Petroleum Technology are reminded that reprints of 'most
of the tec.hnical papers that have been published in these pages are available from the Journal
Business office_ The price is fifty cents each to the membership of The Canadian Institute of
Mining and Metallurgy and one dollar each to non-members.
R
Technology, Julv-September, 1966, Montreal
129
,