20724-An Improved Method to Predict Future Ipr Curves
Transcript of 20724-An Improved Method to Predict Future Ipr Curves
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An improved Method To Predict
Future IPR Curves
M.A. Klins,
SPE, Chevrm U.S.A. Production CO. Inc., and J.w. Clark III, spEt
Chevron Petroleum Technology Co. Inc.
5P6
Q 07a9
Summaw This
paper presents a si~lcantly improved yet simple method to prdct future oilwelf deliverability and inflow per-
formance relationship (IPR) curves. For the 21 reservoirs studied, current empirical techniques overpredlcted future performance by
117%, while the new approach reduced the average error to only 9%. This new method, when coupled with nodal analysis, could
affect equipment stilng, ifr@iii6i-plarming, and properly sales economics significantly because it provides more realistic predictions.
Introduction.
An
important engineering td for
mzddziug future fmancid return
through design optimization is the abtity to develop a family of
future fPR curves for a given well or field. These curves maybe
able to provide answers to such questions as tubing and choke size,
timing of atitkikd lift, future revenue streams, and abandonment
time with some certainty.
Currently, three simple hand-held metfmds 1-3 are used to esd-
mati future absobme-open-f low (AOF) rates for wells producing
from solution-gasdrive reservoirs. After several maxiumm-ratel
mservok-pressure pairs have been established, these values nor-
mally are coupled with Vogels4 dimensionless fPR equation to
create a family of future LPR curves. However, the e methods appear
to introduce significant error into the estimation process.
First, we will describe the current methods to predict future max-
imum flow rates. Fetkovich 1 presented a relationship between oil
flow rate, average reservoir pressure, and flowing bottomhole pres-
sure (BHP) by
q. J P? Pn/)n,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(1)
where tbe flow exponent, n, is assumed to be cons~t orrOughOut
the life of the reservoir and the flow constant, J2, varies accord-
ing to
.J2=J1(P2/Pr,).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(2)
J1 =flow constant at current reservoir pressure,
P,I,
and Jz =flow
constant at a future reservoiz pressure,
pa.
Therefore, with a
three- or four-point flow test, n and J can be estimated for that test
rind that reservoir pressure, and any future maximum flow rate cwi
be projected by
dm=Jz prz2)~ . . . . . . . . . . . . . . . . . . . . . . . . . . ...(3)
fn a second approach, Eickmeier2 coupkd Feikovichs 1 work
with Vogels4 equation and set the flow exponent to a freed value
of 1..0 to arrive at
(40)m@=(qo)m1(Pfi/P,1 )3. . . . . . . . . . . . . . . . . . . . ..(4)
Instead of a multipoirx test liie that needed to implement Fet-
koviclr)s
Eqs. 1, 2, and 3, a one-point test can be coup]ed With
Vogels equation to estimate (qo)m=i. Then, for any selected
future reservoir pressure, the corresponding maximum open-flow
petentiaI, (qo)mm, can be predicted with Eq. 4.
The tbhd method is Uhri and Blounts3 pivot-point approach,
which requires two separate flow-rate tests at two different average
reservoir pressures. Their numerical solution requires that two flow
constants be determined from tie two flow-rate tests such that
(Pr, Pd
a=
[
P,l 2 _
Pr2=
. . . . . . . . . . . . . . . . . . . . . . ..(5)
(%?)mwl (%Jmm2
[
P,l
and b=j+
1.0. . . . . . . . . . . . . . . . . . . . . . . . . ..(6)
(Qlaxl
The maximum flow rate for any given resemok pressure is then
determined from
(qo)mrx=(ap?)/@ r+b). . . . . . . . . . . ... . . . . . ...0)
These three simple methods are available to esdmate timrre max-
imum open-flow rates for wells under solution-gasdrive. These
AOF values, coupled witi Vogels4 equation, can be used to esti-
mate future IPRW The Eickmeier2 approach requires a single-
point flow test to implement, the Fetkovich L method uses a muki-
point test, and the pivot-point procedure needs two single-point tests
taken at different times.
IPR Data Development
Before describing M papers new method of estimating future
AOFS and hence future IPR performance, discussion of the de-
velopment of the pressureltlow database used is appropriate. Kim
and Majcher5 give a more complete description.
Intlow performance of 21 theoretical solution-gasdrive reser-
voirs was simulated with the WeUer6 method. Table 1 shows that
these reservoirs contain a wide range ,of rock and tluid properdes,
relative permeability characteristics, and skin effects. .To constmct
the >19,000 flow-ratelpressure-point data set, WeUer describes
the pressure gradient as
ap
()
w%% r? rz
; =141.2
. . . .
(8)
rkkmh rj +,
The d saturation at any time and location can be estimated from
;=SL(,-9).,2.6_~. . . ...(9)
The fractional recovery, NP/N, is calculated with tie Muskat7
method.
Eqs. 8 and 9 allow stepwise calculation of pressure and satura-
tion profiles for a specitied flow rate from the outer boundary to
the weUbore. To conserve computer time, and because pressure
gradients get gradually steeper approaching the weUbore, a vti-
able stepping procedure was incorporate l. At any point >200 ft
from the weUbore; a 1.O-ft step was ustxl between 100 and 200
ft, a 0.5-ft stew between 10 and 100 ft, a 0.05-ft stew and within
10 ft of the wellbore, a O.01-ft step. The variable stepping proce-
dure was checked by compming its results WM those obtained with
a constant radius step of 0.01 ft results were v@ualIy identical.
Tb& prccedure produces an accurate solution wbife mark.dy reduc-
ing computation time.
Because V/eUer6 did not account for skin in his formulation, tie
method had to be adjusted to simulate the performance of damaged
or improved weUs. Hawkins8 viewed the skin effect as a zone of
ilnite widti with ~tered permeability and defined it as
(k. ) (rw)
= 11 h~ . . . . . . . . . . . . . . . . . . . . . . . . . . ....(10)
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TABLE 1RESERVOIR DATA VARIABLES FROM
21 THEORETICAL RESERVOIRS
Base-Case
Range
100 to 4,000
25 to 45
1,052.2 (2o to 80)
wpyia
2,000 1 ,0(
r., ft (acres)
7447(40) 526.6 to 1
sgc Yo 5
Otolo
so,, % 30 20
to 40
k,
md 100
10 to 1.000
&
oh
15 10
to
20
I
.
s
..s %
30
A 2
s
o
20 to 40
4 and co
-4 to +6
I
Eq. IO
was solved fork.
to
include the skio effect in the model.
A vaiue of altered perme&ility can be calctiated by specifying a
skin value aud damage radius when k and IWare known. For con-
v&ience, a
4-ft damage radius was used in the
model.
To include the desired range of PVT data, it was necessay to
use general correlations to estimate those values. The following
correlations were used to develop the rock and fluid propeties of
the reservoirs mcdeled Dranchuk et al. s9 correlation was used
for gas @repressibility; ke et al.s 10 correladon for gas viscosi~,
Vazquti and Beggs11 correlations for solution-gasloil ratio, oil
compressibility, and oil ~ and Burdines 12 correction for mla-
twe penno@ili ty.
Model Verification
Data from Vogels4 origimd work w,ere used with the model, and
the results were compared with his inflow performance curves to
verify the developed models accuracy. IPR cwves for three. stages
of mservok depletion were generated with Vogels Case A data.
The curves from the two works were virtuauY identical. ~y minor
differences in results were probably tbe&sult of commting Vogels
graphical data to workable, tabular form.
Data Generation
To develop a general equation that could b.e used to predict future
inflow performance for my solution-gas reservoir, IPR curves were
generated for wells producing from 21 theoretical reservoirs. Mid
reservoir pressure (lwbblepoint pressure), reservoir depletion, oil
API gravity, resid@ oil smuwion, critical gas saturation, rela-
tive and absolute permeabfbies, and skin effec~ on AOF were in-
vestigated. Table 1 lists each va able, the base+ase value, and the
rauze used in the study. For each case. runs were made for eieht
diff&nt skin values: 6, 4,2,0, 1, -2, 3, .&d 4. Also, ~or
each data case and sk@, curves were genemted foreight depletion
stages. These combinations of conditions resolted in the generation
of 1,344 12R curves with 19,492 total data points.
10s
EEl\
-.
10?
n
=0.Y70
,3
lO6-
~ n
7X1 *~@~
:: ::: -
,.5
.&
,,,,, .,,CJ
M.lm psis
10
%=1750@
A F+=15C4 @a
103
1 10
100 103) 10COO
% @OPD)
Fi9. IFIow constants
J
and n calculated with base-case
reservoir data.
Development of a Simplified Approach
To Estimate Future AOF
Fetkovich-type I isochronal plots were generated for each of the
J =0 cases to estimate the flow exponent, n, aod PI coefficient, J.
J and n parameters for each case were calculated with regression
techniques. Fig. 1 is an example of basecase resolts for three reser:
voir pressures. Although it is not readily apparent from the plot
that n cbaoges considerably with reservoh pressure, as pressure
declines furthe~, the values for n and J do vary significantly. Fig.
2 shows that the values for n increase with depleting reservok pres-
sure, whiIe the values for J
decrease (Fig.
3). Investigations of n
and J behavior for the ~emaiiiing 20 reservoir cases showed simi-
lar trends for a wide vaiiety of cases.
Because the absolute values for n
and
J varied greatly ftom case
to case, these relatiombips had to be comerted to a dimensionless
form before a statistically mea@r@l relationship could be d.svel-
oped. After several differeni format attempts, we decided dmt the
n and J values at any pressure could be related to the values at the
bubblepoint pressure and that a reIationsbip between dimemion-
less n/nb, dimensionless
J/Jb,
and dimensiodess pressure,
p~b,
could be made. Note that, with the 156 cases investigated, n/rab
increases with decreasing pressures @ii. 4) while Jflb (Fig. .5)
decreases. These same trends also were obserfed for cases witl
varying skin values. We determined that skin had almost no effect
when these dimensior@s relationships (F&. 6 and T) were used
to esdmate futme AOF rates.
A third-order polynomi~ fit was generated with the dimmsio@ess
tz lnb and
J/Jb vabms,
~d the quations that descnie the trends are
.
I.m
I
o
1.05
i
1,C4 j
i
iLO
500 IWO 1S00 2W4
R w)
603
484
1
200
0
a
.
o
0 500 limo 1504 Zmo
Fig. 2Base-case n with resewoir prassure decline.
Fig. 3-Base-case J with reservoir pressure decline.
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4:
1,4
1
0
1.3
4
1.
:L
.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fig. 4-Dimensionless flow exponent, nhb, a3 a function of
dimensionless pressure.
1,0-
0.9-
0.8-
0.7-
0,6-
.
0.5-
~o
LdAiilL
.0 0.1 0;2 0.3 0.4 0.5 3.6 0.7 0.8 0.9 1.0
(:) (:Y
nd 1=13.5718 1 +4.7981 l
Jb
3
2.3065 1 3
, . . . . . . . . . . . . . . . . . . . . . . . ..(12)
Fig. 5Dlm.enslordess flow constant, .VJb, as a function of
dimensionless pressure.
120-
1.15-
1.10-
1.05-
:
2
%.=0
- Skin= 6
.
w=.
k
k
ml
a,
0.0 0.1 0,2 0,3 0.4 0.5 0,6 0.7- 0.8 0.9 1.0
Fig. 6Skin effect on nhb.
( ~b) ( J
=1+0.0577 l~ 0.2459 l~
b
3
+0.5030 l~
, . . . . . . . . . . . . . . . . . . . . . . . . . ..(11)
12-
~
skin= o
1.0- 9 Skin= 6
m
A skin=4
0.8
.k ~,6-
0,4-
0,2-
.
*
k
0.0.
,
&0 0.1 0.2 02 0.4 ?5 0,6 0:7 0.8 0:9 .1.0
g
Fig. 7Skin effect on J/J~.
1CCLC4
o
marl
..*P 0
mm
d
.;.O
.%O 0
103
.;?&@
10
~o o
80
~ .
1 0
Avera~ Akdte Error 130.70%
o
Maximm Awl. . Em, 21635%
Awrw Enm
-17839?4
0.,
0.1 1 10 100 1030 Iomo Iwo
Actual (qJ,w @OPD)
Fig. 8Error analysis using the Fetkovlch t approach.
Im
.@
10333
. ..OOO .
. . .90%0
H
.oom 0
Km:
0 0.
0 00
0 0?0 ., ~
103 ?
o .s
.o@
10
~oo.. o
o
.0
1
Avaa@ Ah dute Era 189.08%
Maximum Absolute Em 297.41%
o
+vcrw Em,
-1785s%
0.1
0.1 1 10
iwl ICal Icmo Icaoo
Add (W., (?OPD1
Fig. 9Error analysis using the Eickmeier2 approach.
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Im
o
moo
s
~
Km
8
%F +P
.3
~ ~w
g
0 d%
E
&o&
10
.0
~
.OO
0
1
0
Avcra@ .4bsdu,c En., 124 5%
o
Maximum AWW Emw 176,27%
AvePw Em, 44.36%
0.1
0.1 1 10 1C4 1000 1r3m
Icmoo
AmJd (q.)= @OPD)
Fig. 10Error analysis
using the
pivot-points approach.
Im
o
Im
~
Icm
g
~ @@O
%
Q 1~
.3
3
g h
10
:&
..O.
1:
.
Average Absolute Error 30.70%
a Maxim. &dute Error 37,35%
.
AWW Em, .9.29%
0.1.
.
0.1 1 10 100 lam 10W4 lCQCOJI
Ati
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I
TABLE 3CALCULATION RESULTS FROM BASE-CASE DATA
E
(P%)
1,990
i ,750
1,500
1,250
1,000
750
500
nln ~ n
J/Jb
1.00030,8507 0.9823
1,0044 0.8542 0.6240
1.0069 0,8564 0.3709
1.0136 0.8621 0.2137
1.0303 0.8762 0,1253
1.0628 0.9039 0,0786
1.1172 0.9502 0,0470
(STS/~-psia2)
0.0048
0.0031
0.0018
0.0010
0.0006
0.0004
0.0002
Calculated
(qO)mU
(STBID)
1,974
1,061
500
229
111
61
31
Actual
(q.)mw
(STBID)
2,001
i , 082
449
215
117
63
31
Step 3. Using the known flow point, the AOF, and Fetkovichs 1
equation, solve for n and J.
l?=J(P; -PwJ+,
where n= O.8508 and J= O.0048.
Step 4. Use Eqs. 11 and 12 to solve for nlnb and J/Jb:
2=+0(--)-+--7
b
()
1,990 3
+0.5030 l
=1
.CO03
2,000
J
( :;) ( ;gY
and =1-3.5718 1 +4.7981 l
Jb
()
1,990 3
2.3066 1 =0.9823.
2,000
Step 5. From Steps 3 and 4, solve for constants nb and Jb:
0.8508
~b=L=
=0.8505
nhtb
1.0003
J 0.0048
and Jb=-= =0.0049.
J/Jb 0.9823
Step 6. Use l+?+. 11 and 12 to solve for n
andJ at future
pressures.
The deliverability at reservoir pressures below bubblepoint can
be estimated with the nb and Jb constants and an estimate of the
IIJnb and J/Jb ratios for any pressure. At a 1,750-psi reservoir
pressure, estimates for n and J aIe derived fmm
n=nb(n/nb)
=0.8505 X 1.0044=0;8542,
and J=Jb (J/Jb)
=0.0049x0.6240=0.0031.
Stsp 7. Use Eq. 1 to solve for the new (qo)m .
With these values and assuming pWf=O pm, the maximum
deliverability
at the new reservoir
pressure can be calculated by
( j)max 0.0031 (1,702)08542 =1,061 BOPD.
Steps 6 and 7 can be repeated to estimate deliverability at other
pressures. Table 3 shows results of calculations with the base-case
dat6.
Conclusions
Inflow performance curves were generated for 21 ihwretical
solution-gasdrive reservoirs. These reservoirs encompassed a wide
rage of depletion, reservoir, PVT, and relative penmability char-
acteristics
The data then were evdwiied to examine tie ibtluence of 10 prop
erties on future AOF potential. Of these variables, only pressore.
depletion was found to 6ffect future flow rates significantly and
measurable.
Empiric~ equations were developed tlzt related Fetiovichs I PI
to be auo icable to the wide range of solution-gas-drive reserioits
.,
imfesti~ated.
Comparison of the new approach with three tmditiond approaches
of estimating future maximum flow rates showed that eiisting em-
pirical procedures for predicting future performance were in sub-
stantial error (> 110%) and tie new approach introduced average
errors of < 10%.
These analyses verify the increased accuracy of predicting fu-
ture AOFs and LPR curves with the procedures in this study. More
accurate esdmatm of foture well perfonnqm for recove~ timing,
ardtlcial-lii selection, and production-equipment sizing should
resuk.
STB/D-psia,
b = Ubri and BIounts3 flow constant, m/Lt2, psia
B. = oil FVF, dimensionless, bbl/STB
B; = initial o~ FVF, dimen~onkss, bb fSTB
Coi = 01 compressibility at initial conditions, Lt2/m,
psil
d = polynomial exponent, dimensionless
h = reservoir thickness, L, ft
J = Fetkovich PI coefficient, LZ3fm2, STBID-psia2
J~ =
Fetkovich PI cceffkient at bubblepoint, L5t3/m2,
sTB/D-psia2
k = absolute reservoir permeability, L2, md
koi = permeability to oil at initial conditions, L2, md
km = relative permeabili~ to oil, dimensionless
k, = altered permeabfity tlom skin effwt, L2, md
n = Fetkovich flow exponent, dimensionless
nb = Fetkovich flow exponent at bubblepoint,
dimemionkss
N = original oil in place, L3, STB
NP = cuumfative oil production, L3, STB
Np, = cumulative oil producdon during transient period,
L3 s~
p = pressure, mlLt2, psia
Pb = bubblepoint pressure, m/Lt2, psia
p. = reservoir pressure, mJLt2 psia
pwf = flowing BHP, ro/L.t2, psia
q. = oil flow rate, L3/t, STB/D
(qJ_ = ofl flOW mte at
P~j=o, AOR L3k STBD
r = radial distance Ilom qenter of well, L, h
rd = external
drainage radim, L, II
r, = d~age Iafis, L, fl
rW = we~bOre radi~, L, H
s = sh .q=&t
S8, = criticzl gaz saturation, dimensionless, fraction
SO = Oil saturation, dimerisioidess, fraction
SOi = oil saturation at initial conditions, dimemionk.ss,
fmction
SW =
connat+water saturation, dimensionless, IYaction
h = pore size distribution iodex, diroeosionkzs
P. = 03 viscosity, m/Lt, cp
Y.i = ofi Viscosiv at initial conditions, m/Lt, cp
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Mark A. Kilns is a
district engineer for
Chevron U.S.A.
Production Co. In
Lost Hills, .CA,
whers his responsl-
bllitles include d8-
slgn and lmplemen-
tat[on of a Lost Hills
dlatomite water-
flood and direction
Kilns
Clark of the new district
well-development
program. He previously was a petroleum engineering profes-
sor at Penn8ylv8nia St8te U. and a consultant, and he worked
in drilling, produ.zfion, and reservoir engineering for chevron
on the U.S. gulf cdast and In the Permian Sash and San Joa-
quin valley. Kilns holds MS and PhD degrees in petroleum
and n8tural gas engineering from Pennsylvania State U. He
was 1983-S4 Pittsburgh Petroleum Section chairman, Hobbs
Section 1989-90 membership chairman, a 7984-88 Technical
Editor, a 19s4-67 Career Guidance Committee member, 1988-
91 member and 1991-92 chairman of the Distinguished Leo-
turer Committee, and the 1982-83 chairman of the Education
and Professionalism Technical Committee. Klins received the
19S6 SPE Outstanding Young Member Award.
Jame8 W.
Clark Ill is a ga8- and
waterdrive engineer for Chevron Pe-
troleum Techtiology Co. Inc. in L8 Habr8, CA. His responsi-
bilities include ressrvoir consulting and simulation of U.S. and
international fields for Chevron affiliates. He previously held
various reservoir and production engineering assignments
in Louisiana, Arkansas, New Mexico, and Texas. Clark holds
SS and MS degrees in petroleum engineering from Texas A&L
U. He was the Permian Basin Sstion 1980-91 continuing edu-
cation director and 1636-90 Hobbs Section publicily chalnqan.
Acknowledgments
We thank Chevron 7J.S .A. Produ&on Co. hc. for permission
publish this paper. Special thanks go to Phoebe Frisbie for typing
the manuscript md to Becky Davis for figure preparation.
References
1. Fetkovich, M.K.: The Isochronal Testing of Oil Wells, paper SPE
4529 presented at tie 1973 SPE Annual Meeting, Las Vegas, Sept. 30
Ott. 3.
2. Eickmeier,
J.R.: HOW to Accurately Predict
Fume Well Prcdnctivi-
ties, World Oil (l&y 1968) 99,
3. U&i, D.C. and Blount, E. M.: Pivot Point Method Quickly Predicts
Well Pecfmmance,s,
Wo,fd Oil (My
S982) 153.
4. Vogel, J. V.: gInOow Performance Relatiombips for 2cduti0n-GasDive
Wells,,> JPT.(Jan. 1968) 83; Trans., AOvfE, 243.
5. Klim, MA. and M+ichm, M. W.: Tntlow Performance Relationships
for Dammd or Immoved Wells Frcducine Under Si.tion-Gas Dtie.
JPT (Dc: 1992) i357.
6. Weller, W.T.: Reservok Performance Dining IW@Phase Flow, JPT
(Feb. 19661 2Q Trans., A3ME, 237.
7. hkkat. M.: The Prodcdm Histories of Oil Pm&wing Gas-Drive
Reservoirs,, J.
Applied Physics (1943) 16, 147.
8.
Haw dns. M. F.: A Note on the Skin Effect.,, Trans.. A3ME (1956)
207, 356.
9.
Dranchuk, P.M., Fmrvis, R.A., and Robinson, D.B.:
Computer Cd-
cul.ati.ms of Natural Gas Compressibility Factors Using the N@ing
and Katz Correlation, Jam of Petroleum Technical Series, No. f
74-0C08, Edmonton (1974) 1.
10. k. A.L.. Gonzalez. M. H.. and E&in. B. E.: The Viscosifv of Na
& Gases, JPT
(April 1966) 9n Trans., AIME, 237. .
11. Vazquez, M. and Beggs, H.D.: Correlation for Fluid PhysicaI PmP
erty pmdicdon,
JPT
(June 1980) 968.
12. Bmdim. N.T.: Relative Permeabiiiw Calculations From Pore Size
DNrib&n Data,,, Tram., - (i953) 196, 71
S1
Metric Conversion Factors
acre X 4.046 S73
E01 = ha
API 141.5/(131.5+ API) = gk?ms
bbl X 1.5S9 S73 E01 = ms
Cp x 1.0*
E03 = Pas
II X 3.048* E01 = m
ma
x 9.S69 233 E04 = pmz
psi x 6.S94 757 E+OO = Wa
.Covwsron Wt., is ,=. . SP33R33
original SPE manuwlpt mewed for review Sm. 2,1990. Revised manuscript mcdved
Jan. 22, 1993. Paper accepled (0, pubbcatim March 4, 1993, Pwer (SPE 20724] IIrs
w-em at the 1990 SPE Am.a Tech.rca C.nfe~.@ a.d ~fib[fi.. held i. N.w
Orleans sem 23-26.
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c
l.lo -
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1.00 1 1 1 1 I t 1
I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Pr/Pb
PrlPb
PIGIJRE 6
EffectONSkmon IhcDnncmmnk.x Fh>wExpnmnt, nlnr,,
FJGIJRE 5
Dimcmimfss F lmvCon.want.CfCP~ m aFuntxrnnof ~mnlm Fnmnc.
1.2
~n
Skin = O
1.0
= Sxjn = 6
A Skin=-4
0.8
8
4
0.6
0.4
1
i-sL---
0
Average Absolute Error
1
o
Maximum Absolute Error 2
Average Error
-12
.1 i 10
100
1000 IOooo
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Actual Qomax (BOPD)
Pr/Pb
FIGURE 7
EfkuofSkinon hc~
Jmticmslam,acpb
FIGIJRE 8
&rnr Adyss UsingIJKFdkovich Appmxh,
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