Correlation for Real Time Prediction of Flowing Bottom

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,

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

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:


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


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


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)


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)


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


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


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


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


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


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).


( )

+

=

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.


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)


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.

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Correlation for Real Time Prediction of Flowing Bottom