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European Journal of Scientific Research ISSN 1450-216X Vol.45
No.4 (2010), pp.552-565 EuroJournals Publishing, Inc. 2010
http://www.eurojournals.com/ejsr.htm
Correlation for Real Time Prediction of Flowing Bottom Hole
Pressure of Oil and Gas Wells
Samuel Ositadimma Onyeizugbe University of Port Harcourt,
Nigeria
E-mail: [email protected] Tel: +33-559-814486
Joseph A. Ajienka University of Port Harcourt, Nigeria
Abstract
Well performance monitoring is an important step towards
realising optimal recovery from the reservoir by any well. Quick
resolutions of wells problems will ensure that the well continues
to produce at its potential. To ensure that quick solutions are
provided to producing wells, real time monitoring of the wells
performance is very essential.
One of the key parameters in real time well performance
monitoring is the Flowing Bottom hole Pressure (FBHP). Therefore,
this study uses some of the available measured data from oil and
gas wells in Niger delta of Nigeria to develop correlations for
predicting the FBHP. The correlation obtained closely predicts the
measured FBHP for both oil and gas wells.
Using the flowing bottom hole pressure, well productivity index
is estimated in real time. Other real time evaluation includes the
well skin factor and well performance efficiency index. It is also
useful for the evaluation of the water coning problems by comparing
the critical rate with the actual well production rate.
Using the FBHP determined in real time, well surveillance
becomes more efficient and with faster remedial actions, the well
performance is enhanced.
Keywords: Correlation, Prediction, Pressure, oil, gas, well,
Real time.
1. Introduction The real time prediction of the bottom hole
pressure is one of the most important steps towards realising real
time monitoring of well performance. Porter, D. A. (1992) showed
that flowing bottom hole pressure is such an important parameter
even at very early life of the well. The major challenge has been
getting this down hole information without running tools into the
well to make this measurement. In this regard, Abdullah M.
Al-Qahtani (2003) and Boyun Guo (2001) presented different methods
of evaluating downhole data using surface parameters.
The modern technology of using clamp-on device on the well head
to record well head parameters which are later converted to down
hole parameters have been tried but needs further calibrations to
give the desired result. In most of the cases, tools need to be
introduced into the well,
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Correlation for Real Time Prediction of Flowing Bottom Hole
Pressure of Oil and Gas Wells 553
mounted as clamp-on, introduce on the well head as an intrusive
device. This means that extra personnel and resources are required
to get the well data as well as the data processing and
analysis.
Engel, R. F., Shell Oil Co., Billings, Mont (1963) showed that
permanent down gauges have been in use since 1950s. However the
permanent downhole gauges is expensive. This makes it less
attractive and it is usually deployed when it is absolutely
necessary.
There are many vertical lift equations in the text book. Some of
them were presented by Beggs, H. D. (1991), Cullender, M. H. and
Smith, R. V. (1996) and Sukkar, Y. K and Cornel D. (1955). They
apply principle of accounting for the pressure losses across
different nodes of the production tubing. However, they are not
easily applied to real time evaluation of FBHP as they involve
iterations and require detailed matching using the measured
data.
The method adopted in this project is to establish correlation
that links all the important parameters that influence the flowing
bottom hole pressure. It uses the well head parameters, well data,
fluid properties and produced well fluids volumes in the estimation
of the FBHP. The approach applied is to relate the pressure drop in
the tubing of a given length (in true vertical depth) to the well
effluent mass flow rate. The mass flow rate was used in order to
get common basis for evaluating the contribution of different
fluids to the pressure loss in the tubing without being affected by
their volumes. This is critical for the gas wells or high GOR wells
because gas volume is highly dependent on the prevailing
temperature and pressure.
The flowing bottom hole pressure is estimated as the sum of the
flowing well head pressure and the pressure loss in tubing relative
to the mass flow rate.
2. Data Analysis and Selection The available data covers
different fields in the Niger delta of Nigeria. A total of about
6500 points were selected. However, using all these points for the
correlation was difficult because the data gives wide range of
clustered points though having a trend ( Figure 1).
In order to select representative data points for the
correlation, data frequency method was adopted. In this method, the
cumulative frequency (converted to the percentile) was plotted for
every selected range (Figure 2). The data corresponding to the 50%
percentile were selected from each of the cumulative frequency
curves and then plotted for the correlations. An example of this
selection for a range is shown in Figure 3.
3. Correlation for Predicting FBHP The main focus of this
correlation is to establish relationship between the measured
pressure loss in tubing and calculated pressure drop in tubing.
This correlation takes into account the key parameters that affect
the flowing bottom pressure of a well. The parameters are basically
the well head parameters (well head pressure and temperature), well
data (Well depths), fluid data (oil density, gas density, water
density, gas deviation factor) and produced well fluids (oil rate,
BSW, GOR).
The equivalent well effluent fluid density is calculated in
order to calculate the pressure drop in the tubing.
For eruptive wells (natural flow): TVDgP
equivalentcalculatedtubing =
Where
gwo
gwoequivalent QQQ
MMM++
++= (1)
Considering field units, the pressure drop is calculated as
follows
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554 Samuel Ositadimma Onyeizugbe and Joseph A. Ajienka
=
144TVD
P equivalentcalculatedtubing
(2) For wells on gas lift:
+
= +
144)(
144mallmgasliftall
calculatedtubingTVDTVDTVD
P
(3)
Where: all+lift gas = Equivalent density of oil, water, gas and
lift gas (lbm/ft3)
gwo
gwogasliftall QQQ
MMM++
++=+
all = Equivalent density of oil, water and gas (lbm/ft3) TVDm =
Mandrel depth (ftTVDMSL) TVD = Reference depth for the pressure
(ftTVDMSL) P = Pressure drawdown in tubing (psia) The gas volume
needs to be converted to the prevailing temperature and pressure
condition in
the tubing. The volume of gas is converted from standard
condition to the tubing condition using the
equation below.
2/)(*****
)( FTHPFBHPTSBHTZPGORQQ
assumedsc
assumedscocondwellg
+=
(4) Note: Temperature in the gas volume conversion equation is
in degree Rankine (R).
The assumed FBHP and SBHT could be taken from the previous
measurement in the well with downhole gauges where the data is
available. Where the previous gauge data is not available, assumed
FBHP and SBHT are obtained from the correlation developed in this
study using measured well data. The processes for these
correlations are the same as the one described in the data analysis
and selection section.
The assumed FBHP obtained from the correlation of FBHP and the
FTHP (Figure 4) is given as:
2642)104(732.0 25 += FTHPFTHPFBHPassumed (5) Similarly, the SBHT
is also estimated using correlation developed to predict the
temperature
using the well true vertical depth (Figure 5). )102(34.87049.0
26 TVDTVDSBHTassumed = (6)
The reliability of Equation-6 was found to be limited to maximum
depth of 12,000ftTVDss because of quadratic effect. For depths less
than 7000ft TVDSS or more than 12,000ftTVDSS, it is recommended to
use the power law equation or the logarithmic equation. The power
law and logarithmic correlations are shown in Figure 6 and the
corresponding equations are given as
Logarithmic: ( ) 669ln29.93 = TVDSBHTassumed (7)
Power law: ( ) 532.0409.1 TVDSBHTassumed = (8)
The calculated pressure loss is the tubing was correlated
against the measured pressure drop in the tubing. This was done to
get a better estimate of the pressure in the tubing by correcting
for other pressure losses (friction, deviation, etc). The plot of
the measured pressure loss in tubing against the calculated
pressure drop is shown in Figure 7.
4364.0.
)(34.91 calculatedtubcorrectedtubing PP = (9)
correctedPtubingFTHPFBHP +=
(10) The general equation for the developed correlation is given
as follows:
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Correlation for Real Time Prediction of Flowing Bottom Hole
Pressure of Oil and Gas Wells 555
4364.0.
144)(
14434.91
+
+=
+ mandrelreffluidsallmandrelliftgasfluidsall
TVDTVDDensityTVDDensityFTHPFBHP (11)
where ( ) ( )( )( )
( )( ))2/)((
)460()100/(1(
)100/(615.5
)100/(1()100/()615.5(615.5
.
.
FTHPPTTZPQGORQ
BSWBSWQQ
QGORQBSW
BSWQQDensity
asssc
assscliftgasoiloiloil
liftgasoilairgasoilwaterwateroilwateroil
liftgasfluidsall
+
+++
+
++
+
=+
(12)
2642)054(732.0 2.
+= FTHPEFTHPFBHPass (13) 532.0.
409.1 refTVDTass = (14) Replacing oil density with API gravity,
considering the density of water = 62.4 lbs/ft and that
FTHP relates to choke size as in Gilberts equation as presented
by Beggs (1991),
5.1315.141
+=
APIooil (15)
89.1
546.031086.3C
RqFTHP l =
(16) The FBHP equations above become
4364.0.
89.1
546.03
144)(
14434.911086.3
+
+
=
+
mandrelreffluidsallmandrelliftgasfluidsalll
TVDTVDDensityTVDDensityC
RqFBHP (17)
( )( )( )( )( )
+
+++
+
++
+
+
=
+
2/1086.3
)460()100/(1(
)100/(615.5
)100/(1()100/()376.350(
5.1315.141376.350
89.1
546.03
.
.
CRqPT
TZPQGORQBSW
BSWQQ
QGORQBSW
BSWQQAPI
Density
lasssc
assscliftgasoiloiloil
liftgasoilairgasoilwateroilo
liftgasfluidsall
(18) 26421086.3)054(1086.3732.0
2
89.1
546.03
89.1
546.03
.
+
=
CRqE
CRqFBHP llass
(19)
Equation-11 is retained as the best estimate while equation-17
could be used where the flowing well THP is not available.
Figure 1: Raw data points of FBHP versus FTHP
0
2000
4000
6000
8000
10000
0 1000 2000 3000 4000 5000
FBH
P (ps
ia)
FTHP (psia)
Raw data: FBHP vs FTHP
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556 Samuel Ositadimma Onyeizugbe and Joseph A. Ajienka
Figure 2: The cumulative Frequency plots for given data set
0
0.25
0.5
0.75
1
1000
1500
2000
2500
3000
3500
4000
Cum
ula
tive
frequ
ency
FBHP (psia)
Cumulative Frequency Curves for diff. ranges of FTHP
52.9 - 105.8105.8 - 158.7158.7 - 211.6211.6 - 264.5264.5 -
317.4317.4 - 370.3370.3 - 423.2423.2 - 476.1476.1 - 529529 -
581.9581.9 - 634.8634.8 - 687.7687.7 - 740.6740.6 - 793.5793.5 -
846.4846.4 - 899.3899.3 - 952.2952.2 - 1005.11005.1 - 10581058 -
1110.91110.9 - 1163.8
Figure 3: The cumulative Frequency plots for a given range in
the data set.
0
12.5
25
37.5
50
0
0.25
0.5
0.75
1
500
900
1300
1700
2100
2500
2900
3300
3700
Da
ta di
str
ibu
tion
Cum
ula
tive fr
equ
ency
FTHP (psia)
Data Selection for FTHP correlation
FBHP range : 212 - 265
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Correlation for Real Time Prediction of Flowing Bottom Hole
Pressure of Oil and Gas Wells 557
Figure 4: FBHP versus FTHP correlation
R = 0.9755
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 500 1000 1500 2000 2500 3000
FB
HP
FTHP (psia)
FBHP vs FTHP
Q50
Poly. (Q50)
Figure 5: Static BHT versus depth correlation (Polynomial)
R = 0.88
0
50
100
150
200
250
0 5000 10000 15000
Sta
tic B
HT
(de
g C)
Depth (ftss)
Static BHT versus Depth
Q50Poly. (Q50)
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558 Samuel Ositadimma Onyeizugbe and Joseph A. Ajienka
Figure 6: Static BHT versus depth correlation (Power law and
Log)
Static BHT versus Depth
R2 = 0.8401
R2 = 0.8386
0
50
100
150
200
250
0 2000 4000 6000 8000 10000 12000 14000 16000
Depth (ftss)
Sta
tic BH
T (de
g C)
Q50
Power Law
Logarithmic Law
Figure 7: Ptubing measured and P tubing calculated
correlation
R = 0.9891
0
500
1000
1500
2000
2500
3000
3500
0 1000 2000 3000 4000
Ptu
bin
g m
ea
sure
d (
psi
a)
Ptubing calculated (psia)
Ptubing measured vs Ptubing calculated
Q50
Power Law (Q50)
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Correlation for Real Time Prediction of Flowing Bottom Hole
Pressure of Oil and Gas Wells 559
Figure 8: Ptubing corrected for different rates for the same P
tubing calculated
1500
2000
2500
3000
3500
4000
0 1000 2000 3000 4000 5000
P
tubi
ng
co
rre
cte
d (p
sia
)
P tubing calculated (psia)
Ptubing correction for rates
501-750
751-1000
1001-1500
2001-2500
2501-3000
3001-4000
All-Power law
Liquid rate (stb/d)
Figure 9: FBHP correlation evaluation using Well-A
0500
1000150020002500300035004000
31/10/1992 31/10/1998 31/10/2004
FBH
P (p
sia
)
Date
Measured FBHP vs Predicted FBHP using the correlation
Measured FBHPPredicted FBHP
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560 Samuel Ositadimma Onyeizugbe and Joseph A. Ajienka
Figure 10: FBHP correlation evaluation using Well-B
0500
1000150020002500300035004000
30/04/1986 30/04/1994 30/04/2002
FBH
P (p
sia
)
Date
Measured FBHP vs Predicted FBHP using the correlation
Measured FBHPPredicted FBHP
Figure 11 : Cross plot of oil wells FBHP points analysed
(Predicted versus Measured)
1000
1500
2000
2500
3000
3500
1000 1500 2000 2500 3000 3500
Pre
dic
ted
FB
HP
Measured FBHP
Predicted versus measured
FBHPProj_TW1Proj_TW10Proj_TW11Proj_TW12Proj_TW13Proj_TW14Proj_TW15Proj_TW16Proj_TW17Proj_TW18Proj_TW19Proj_TW2Proj_TW20Proj_TW21Proj_TW22Proj_TW23Proj_TW24Proj_TW25Proj_TW26Proj_TW3Proj_TW4Proj_TW5Proj_TW6Proj_TW7Proj_TW8Proj_TW9
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Correlation for Real Time Prediction of Flowing Bottom Hole
Pressure of Oil and Gas Wells 561
Figure 12 : Well GW1 - Predicted and Measured FBHP (Gas
well)
0
1000
2000
3000
4000
5000
6000
06/04/2000 05/06/2000 08/02/2003
FBH
P (ps
ia)
Date
GW1: Measured and Predicted FBHP
Measured FBHPPredicted FBHP
Apr-2000 Jun-2000 Feb-2003
Figure 13 : Well GW2 - Predicted versus Measured FBHP (Gas
well)
3000
3500
4000
4500
5000
5500
6000
3000 3500 4000 4500 5000 5500 6000
Pre
dic
ted
FB
HP
Measured FBHP
GW2: Measured vs Predicted FBHP
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562 Samuel Ositadimma Onyeizugbe and Joseph A. Ajienka
4. Sensitivity of Liquid Rate on P Correction The P correction
is applied to the correlation to compensate for other pressure
losses. Since pressure loss due to friction is the dominant factor
in the other pressure losses, sensitivity on rate is performed to
see if variable correction could be applied to different rate
ranges. Sensitivity of liquid rate on the pressure loss correction
shows that different correction could be applied to different rates
(Figure 8).
5. Correlation Evaluation / Application The evaluation covers
the reconciled production data and well production test data. The
objective of performing the evaluation using the reconciled
production data is to see how close the correlation matches the
reconciled monthly average production so as to use it to estimated
well performance in the absence of well production test data.
Figure 9 and Figure 10 show that the correlation prediction using
reconciled production data matches closely the measured FBHP.
Generally, prediction using production test data gives better
results for both oil wells (Figure 11) and gas wells (Figure 12)
and Figure 13). Figure 12 shows that the trend of FBHP measured at
different times on the same well could be predicted and thus the
correlation developed in this study could be relied upon for
performance well production monitoring.
The reservoir pressure could be estimated using the FBHP from
the correlation. The Vogel equation (Equation-20) which gives the
relation between rate, flowing bottom hole pressure and the
reservoir pressure was used as the basic equation for estimating
the reservoir pressure. Two sets of valid surface production test
data (i.e. two estimated flowing bottom hole pressures) measured
consecutively without delay that would have resulted to change in
pressure is required. The closer the two test data the better. The
flowing bottom hole pressure (Pwf) could be estimated using the
correlation developed in this study.
2
max
0 8.02.01
+
=
r
wf
r
wf
o PP
PP
qq
(20) Using the two sets of data, two equations with two unknowns
(Pressure and qomax), the
unknowns are determined by solving the resulting simultaneous
equation. 2
11
max
01 8.02.01
+
=
r
wf
r
wf
o PP
PP
qq
first set of data (21) 2
22
max
02 8.02.01
+
=
r
wf
r
wf
o PP
PP
qq
second set of data (22)
+
+
=
222
211
012 8.02.01
8.02.01r
wf
r
wf
r
wf
r
wfo P
PP
P
PP
PP
qq (23)
Equation-23 above could be solved iteratively to get the
reservoir pressure that matches the measured oil rate.
With the reservoir pressure known, the productivity index, the
skin factor, performance efficiency and coning in high BSW wells
could be evaluated in real time.
The Productivity index and skin factor are calculated using
Darcy equation (Equation-24).
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Correlation for Real Time Prediction of Flowing Bottom Hole
Pressure of Oil and Gas Wells 563
( )
+
=
Sr
rB
PPKhq
w
eoo
wfro
75.0ln
00708.0
(24)
In coning evaluation, the Craft and Hawkins coning equation as
was given by Joshi, S. D. (1991) was used in evaluating the
possible coning of some wells in an oil rim reservoir. The
equations are given as follows: ( )
=
w
e
oo
wfwsooc
r
rB
PRPPhKq
ln
00708.0 '
(25)
PR is given by:
+= )90cos(
271 '
'
' bhb
rbPR w (26)
Limitation The main limitation of this correlation is that it
applies only to producer wells (oil, gas and water).
6. Conclusions 1. The correlation closely predicts the measured
flowing bottom-hole pressure. 2. With this correlation the well
productivity index, flow efficiency and skin could be derived
in
real time. 3. It is very useful where field measurement is
difficult and could also save the cost of well
intervention to acquire downhole pressure. 4. Real time
evaluation using the correlation ensures that wells produce at
their potentials through
timely problem diagnosis and remedial action.
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564 Samuel Ositadimma Onyeizugbe and Joseph A. Ajienka
Nomenclature b = penetration ratio = hp/h Bo = oil formation
volume factor rate (RB/STB). BSW = basic sediment water (%) C =
choke size (inches) FBHP = flowing flowing bottom hole pressure
(psia) FTHP = flowing tubing head pressure (psia) GOR = gas / oil
ratio (scf/stb) h = oil column thickness (ft) hp = thickness of
perforated interval (ft) Mg = gas mass flowrate (lbm/d) Mo = oil
mass flowrate (lbm/d) Mw = water mass flowrate (lbm/d) Pws = Static
well pressure corrected to the middle of the producing interval
(psia) Pass = assumed FBHP from correlation (psia) Pr = reservoir
pressure at refrence depth (psia) PR = productivity ratio Psc =
standard pressure (psia) Pwf = flowing well pressure at the middle
of the producing interval (psi) Qg (or qg) = gas volumetric rate
(scf/d) Qgaslift = lift gasrate(scf/d) ql = liquidrate (stb/d) Qo
(or qo) = oil volumetric rate (stb/d) qoc = critical rate (maximum
oil rate without coning, stb,day) qomax = maximum oil rate
(stb,day) Qw (or qw) = water volumetric rate (stb/d) R = gas/liquid
ratio (scf/stb) SBHT = Static Bottom Hole Temperature (oC) Tass =
assumed bottom hole temperature from correlation (o F) Tsc =
standard temperature (oC) Tsc = standard pressure (o F) TVD = well
vertical depth (mid perf, ft) TVD mandrel = true vertical depth of
gas lift mandrel (ft ss) TVDref = true vertical depth for pressure
reference (ft ss) Z = gas deviation factor gas = gas specific
gravity (fraction) oil = oil specific gravity (fraction) water =
water specific gravity (fraction) air = air density (lbs/ft3) water
= water density (lbs/ft3) P = pressure drop between the reservoir
sand face and the wellbore (psia) o = oil viscosity (cp)
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Correlation for Real Time Prediction of Flowing Bottom Hole
Pressure of Oil and Gas Wells 565
References [1] Abdullah M. Al-Qahtani, 2003 A new approach for
estimating well productivity and reservoir
pressure using surface performance data. SPE 81520. [2] Beggs,
H. D., 1991, Production Optimization Using Nodal Analysis, OGCI
Publications,
Tulsa. [3] Beggs, H. D. and Brill J. P., 2001, "Two phase flow
in pipes, University of Tulsa, UK, 1978. [4] Boyun Guo, 2001, Use
of Wellhead-Pressure Data to Establish Well-Inflow Performance
Relationship, SPE 72372. [5] Cullender, M. H. and Smith, R. V.,
1996, Practical Solution of Gas-Flow Equations for Wells
and Pipelines with Large Temperature Gradients, Phillips
Petroleum Co. Dartlesville, Okla. [6] Engel, R. F., Shell Oil Co.,
Billings, Mont., 1963, "Remote Reading Bottom-Hole Pressure
Gauges- An Evaluation of Installation Techniques And Practical
Applications" JPT P. 1303, (Paper 662-PA).
[7] Joshi, S. D., 1991, Horizontal Well Technology, PennWell
Books, U.S.A., 1991, Pages 46, 73.
[8] Porter, D. A., 1992, "Acquisition And Application Of
Early-Life Well Performance Data", Society of Petroleum Engineers,
Inc. (Paper 23725), P. 233.
[9] Sukkar, Y. K and Cornel D., 1955, Direct Calculation of
Bottom Hole Pressures in Natural Gas Wells, Paper SPE T. P. 4010,
SPE 439-G, Vol 204.