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Abstract In this paper are presented new correlations to determine the dew point pressure and C7+ content of gas condensate reservoirs, based on production fields parameters usually available. To develop these correlations it were collected 146 PVT analyses of Venezuela (Anaco) fields: San Joaquin: 42 ; Santa Rosa: 26 ; El Roble: 16 ; Guario: 4 ; Santa Ana: 3 ; El Toco: 3 ; Zapatos: 15 ; Mata-R: 15 ; Aguasay: 13 ; La Ceibita: 5 ; Carisito: 4. The PVT results were validated through consistence tests: mathematical recombination and mass balance. After these steps an statistical analysis of the variables was done. For this, statistical methods were used and they were focused on multiple no linear regressions. The correlations's accuracy was the following: dew point pressure showed 5.74 % of average error with a correlation coefficient of 0.82 based on 80 PVTs data, the first C7+ content correlation showed 9.59 % of average error with a correlation coefficient of 0.98 based on 81 PVTs data, the second C7+ content correlation showed 7.85 % of average error with a correlation coefficient of 0.99 based on 90 PVTs data. The new retrograde dew point correlation obtained improves the Nemeth and Kennedy`s (10) that forecast dew points with 9.69 % of average error when it is applied on 54 Anacos PVT analyses which had all the compositional information that it requires; with the new dew point correlation the average error was 5 % for the same data. These new correlations allow to improve the characterization and exploitation plans of gas condensate reservoirs without PVT information.

Introduction Anaco area has been one of the most important venezuelan petroleum operational districts and it has a high number of gas condensate reservoirs. Due to the importance of gas exploitation in this area, it is fundamental the development of new technologies that allow their efficient characterization and exploitation. There are two basic parameters of the gas condensate reservoirs: the dew pressure and the heavy components content (C7+), since retrograde condensation occurs when the pressure reservoir falls below it. They are rather available for this kind of reservoirs, and in order to get them it was necessary to develop new correlations to estimate them based on field parameters easily and usually available. These parameters are: condensate API gravity, gas/condensate production ratio and in some cases separator gas gravity and reservoir temperature. The selected PVT analyses passed the consistent tests of mathematical recombination and the mass balance of the constant volume depletion experiment (CVD), this allowed to verify that those samples were in thermodynamic equilibrium at each pressure depletion level. Finally, a nonlinear regression software was used to fit appropriate models to the data. Data Description The collection of PVT data, included the PVT reports of the Greater Oficina Area as well as the Greater Anaco Area. The total PVT data included 146 analyses. After the process of selection and validation, it was obtained a consistent PVT data base of 114 tests. After a dispersion analyses, the final data base to develop the new correlations was reduced to 106 PVTs. Correlations Development The equations were developed through a commercial nonlinear regression software to fit appropriate models. The ones for C7+ content were developed using a matrix to connect all the independent parameters or variables. To develop the dew point correlations, it was used the multiple non linear

SPE 75686 Correlations To Determine Retrograde Dew Pressure and C7+ Percentage of Gas Condensate Reservoirs on Basis of Production Test Data of Eastern Venezuelan Fields ILsis Marruffo*, PDVSA, Jose Maita, Jesus Him*, Gonzalo Rojas*, Universidad de Oriente. *SPE

2 I. MARRUFFO, J. MAITA, J. HIM, AND G. ROJAS SPE 75686

regressions section of the program , applying statistical tools like residual analyses and cross-plots. It is important to note that the more relevant parameters to achieve this equations were the gas heavy components content (%C7+) and the gas/condensate production ratio (GCR). The following are the developed correlations: First C7+ correlation: %C7+ = (GCR).....................................................................(1)

%C7+=8207.0

70680

GCR ....................................................(2) Second C7+ correlation : %C7+ = (GCR, SSG).......................................................(3) %C7+ = 10260* ( ) 8499.0* SSGGCR ..............................(4) Dew point correlation: Pd = (GCR, %C7+, API, Tr)........................................(5)

Pd =

+

+ 77

5 *6*42

37

*8**1KK CKTrKK

K APIKCGCRK (6)

Where: K1 = 346.7764689,K2 = 0.0974139,K3 =-0.294782419.

K4 =-0.047833243,K5 =0.281255219,K6 =0.00068358.

K7 =1.906328237,K8 =8.417626216.

This equation has the same form of Gulf of Mxico correlation for bubble point (Ref. 5)

Number of PVT PVT Properties Minimum Maximum

C7+ FirstCorrelation

81 Gas CondensateRatio (SCF/STB)

3084 253130

C7+ SecondCorrelation

90Gas CondensateRatio (SCF/STB) 2577 253130

Specific gasseparator gravity

(SSG).0,655 0,904

Dew pointCorrelation

80 Gas CondensateRatio (SCF/STB)

2000 200.000

Percentage of C 7+ 0,37 15,15API 39 61

Temperature F 160 352

TABLE 1-DESCRIPTION OF THE DATA USED FOR THE CORRELATIONS

Results: Discussion and Evaluation During the development of all kind of correlations it is always necessary to validate the models using statistical techniques like residual analyses and cross-plots, to get confidence in those correlations. The correlations accuracy was the following: dew point pressure showed 5.74 % of average error with a correlation coefficient of 0.82 based on 80 PVTs data; the first C7+ content correlation showed 9.59 % of average error with a correlation coefficient of 0.98 based on 81 PVTs data; the second C7+ content correlation showed 7.85 % of average error with a correlation coefficient of 0.99 based on 90 PVTs data. Figure 1 shows that the GCR and the C7+ are inversely proportional. Figure 2 shows the Cross-plot for this correlation. (%C7+ calculated vs. %C7+ observed). Figure 3 shows the behavior of the variation %C7+ vs. GCR*SSG. Figure 4 shows the cross-plot for this correlation. It is important clarify that although this correlation is better that the previous one, any of them may be used because the difference between their average errors is not so considerable. Dew Point Correlation After finishing the elimination of dispersed points through residuals analysis, 80 PVT analyses were used to obtain the dew point correlation. The independent variables were: %C7+ (C7+ percentage , obtained from equations 2 and 4 ), GCR ( Gas Condensate Ratio , SCF/STB), API ( API Gravity) and Tr ( Reservoir Temperature, F). For the data used (80 PVTs) it was obtained a correlation coefficient of 0.82 and an average error of 5.74%. Figures 5 and 6 show the final residuals and the cross-plot for the dew point correlation , respectively. Reviewing the petroleum literature it was found the Nemeth and Kennedy ( NK ) correlation (10) for gas condensate dew point. This correlation requires the knowledge of the gas condensate composition which is very difficult to have without a PVT analysis. The NK correlation was applied to 54 PVT`s that had the information required by it yielding an average error of 9.69% which is higher, for this 54 PVTs, than the average error of 5% obtained with the new correlation presented in this paper (eq.6). Besides of calculating the dew point pressure with less error than the NKs , the new correlation only requires information from the production tests.

Figures 7 and 8 show the cross-plots of the NK and the new correlations, respectively , and Figure 9 shows a comparison between both. It is observed that the new correlation shows less dispersion ( the points fall closer to the 45 line). Also Table 2 illustrates the results obtained with both correlations applied to 54 PVT analyses.

CORRELATIONS TO DETERMINE RETROGRADE DEW PRESSURE AND C7+ PERCENTAGE OF GAS SPE 75686 CONDENSATE RESERVOIRS ON BASIS OF PRODUCTION TEST DATA OF EASTERN VENEZUELAN FIELDS 3

Table 2.Results of Dew Point Correlations Applied to 54 PVTs

SCRSCTR2R

AVERAGEOF

RESIDUALS AVERAGE

ERROR

CORRELATION OF NEMETHAND KENNEDY NEW CORRELATION

33,9*10 6 3*106

30,3*10 6 27,9*10 6

0.12 0.891

9.69 5

0.34 0.95

399.75 201

0

2

4

6

8

10

12

14

0 50000 100000 150000 200000 250000 300000GCR(SCF/STB)

%C

7+

%C 7 + = (GCR/70680) -0,8207

R 2 = 0,9604; R = 0,98

Fig 1-First Correlation of C7+ ( 81 PVTs)

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14%C7+ observed

%C

7+ c

alcu

late

d

R 2 =0.9725,R=0.98

Fig.2-Crossplot for the First Correlation of C7+.

C 7 + = 10260*(GCR*SSG) -0,8499

R 2 = 0,9874; R=0,99

0

2

4

6

8

10

12

14

16

18

0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000

GCRXSSG

%C 7

+

Fig.3-Second Correlation of C7+ ( 90 PVTs )

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16C7+ observed

C7+

cal

cula

ted

R 2 =0.9727,R=0.98

Fig.4-Crossplot for the Second Correlation of C7+

(90 PVTs )

Fig.5-Residuals Analysis for the Dew Point Correlation

4 I. MARRUFFO, J. MAITA, J. HIM, AND G. ROJAS SPE 75686

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000Pd. Observed (lpcm)

Pd.C

alcu

late

d(lp

cm) R 2=0.6735,R=0.82

Fig.6-Crossplot for the Dew Point Correlation(80 PVTs)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000Pd.Observed

Pd.C

alcu

late

d

R 2 =0.2099,R=0.45

Fig.7-Crossplot for the NK Correlation ( 54 PVTs )

1000

2000

3000

4000

5000

6000

1000 2000 3000 4000 5000 6000Pd. Observed

Pd. C

alcu

late

d

R 2=0.731,R=0.85

Fig.8-Crossplot for the New Dew Point Correlation

(54 PVTs)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000Pd.observed

Pd.c

alcu

late

d

Serie1 Serie2 New Correlation of PdCorrelation of Nemeth and Kennedy

Fig.9-Comparison of NK and New Correlations

Conclusions 1- The key parameters for the determination of the Dew point Pressure are: the C7+ content and the gas condensate ratio (GCR) 2-The C7+ content and the GCR, of eastern venezuelan gas condensates are inversely proportional. 3-It was obtained a new correlation to determine the Dew point Pressure of gas condensates reservoirs on basis of production test data., usually available. It does not require the knowledge of the gas condensate composition which is very difficult to get without a PVT analysis.

4- It were obtained two new correlation to estimate the C7+ content on gas condensate reservoirs, at dew point conditions , on basis of production test data., usually available; one of them does not require the knowledge of the gas condensate composition only the GCR and the other one requires additionally the SSG.

5-A resume of the new correlations is the following: Correlation Variables PVT Analyses Average To Calculate Correlated No. Error ( %) C7+(first) GCR 81 9.595 C7+(second) GCR,SSG 90 7.85 Dew Point GCR,%C7+,API,Tr 80 5.74

6-The correlation obtained in this work to determine the gas condensate Dew point Pressure improves in four percentiles the Nemeth and Kennedys (one which has been used extensively by the petroleum industry), when it was applied to Eastern Venezuelan Anacos fields.

CORRELATIONS TO DETERMINE RETROGRADE DEW PRESSURE AND C7+ PERCENTAGE OF GAS SPE 75686 CONDENSATE RESERVOIRS ON BASIS OF PRODUCTION TEST DATA OF EASTERN VENEZUELAN FIELDS 5

Nomenclature % C7+ Percentage of heptane plus Pd Dew point pressure, psia GCR Gas Condensate Ratio, SCF/STB SSG Specific gas separator gravity ( air=1) API API condensate gravity Tr Reservoir temperature,F R Correlation Coefficient among variables R2 Determination Coefficient among variables % Error Average error, % Yi Observed or experimental value( available data) y Estimated or calculated value by a correlation ei residual SCR Sum of regression squares SCT Sum of total squares SCE Sum of squares for error ( nor explained by the regression) Ki Regression coefficients of the correlations Ei Relative error percentage Ea Absolute average error percentage N Number of values corresponding to certain data

Acknowledgments The authors want to thank to PDVSA-Puerto La Cruz Exploration and Production to allow us to develop this work, and to Dr. Jaime Almeida (PDVSA-Intevep) for his help in results discussion.

References 1. Marruffo, I; Cabrera, J; Contreras N., Fonseca ;: Estudio

Integrado Carisito-Aguasay Central. PDVSA. Junio. (2000). Inventario de PVTs, Tomos de PVTsValidacin de Informes PVT. Campo Carisito, Aguasay C y Zapatos. CDG-Produccin Puerto la Cruz.

2. Rojas, G.: Anlisis PVT de Gas Condensado.

PDVSA, CIED, Universidad Corporativa. Puerto la Cruz. Septiembre. (1999).

3. Almeida, J.: Recomendaciones para la Evaluacin de

Informes PVT y Muestreo de Fluidos en Yacimientos de Gas Condensado. INTEVEP, S.A. Los Teques. (1989).

4. McCain, W.: The Properties of Petroleum Fluids.

Segunda Edicin. PennWell Publishing Company. Tulsa, Oklahoma.(1989).

5. Petrosky, G y Farshad, F.: Pressure Volume

Temperature Correlations for Gulf of Mexico Crude Oils. SPE, Chevron U.S.A. Production. (1998).

6. Kazmier, L. y Daz, A.: Estadstica aplicada a la administracin y a la economa. Segunda edicin. McGraw Hill. Serie Schaum. Madrid. (1989).

7. Neter, J. y Wasserman, W.: Fundamentos de

estadstica. Nueva edicin. C.E.C.S.A. Compaa Editoriales Continental, S.A. Mexico. (1973).

8. Hamke, E. y Reitcsh, G.: Estadsticas para negocios.

Segunda Edicin. McGraw-Hill. Madrid, Espaa. (1997). 9. Visauta, B.: Anlisis estadstico con SPSS para

Windows. McGraw Hill. Madrid. Espaa. (1997). 10. Nemeth,L.K. y Kennedy, H.T.: A Correlation of

Dewpoint Pressure with Fluid Composition and Temperature. SPE Paper Number 1477. Junio. Texas. (1979).

Appendix-Statistical Parameters The following statistical equations were used for the correlation development: 1-Determination coefficient(R2) is defined by the ratio of the sum of regression squares and the sum of the total squares. SCR SCE R2 = -------- = 1 - -------- ..................(A-1) SCT SCT 0 R2 1 2-The correlation coefficient ( R) is given by the square root of the determination coefficient (R2)1/2 . This criteria allows to measure the level of association that exists between two variables : Dependent - independent or independent independent.

R =iationtotaliationlained

varvarexp

=SCTSCR

......................(A-2)

3-The analysis of residuals is based on the difference between the observed and adjusted values of a population or data.

ei= iYYi ...............................................................(A-3) On the whole , the analysis of residuals means to make an analysis of residual graphs

4-The relative error percentage is the difference between observed and calculated or estimated values divided by the observed value and multiply by 100. That is

Ei = 100*Yi

YiYi

......................................(A-4)

6 I. MARRUFFO, J. MAITA, J. HIM, AND G. ROJAS SPE 75686

5-The absolute average error percentage is given by the sum of all relative error percentages divided by the number of values used in the calculation of the average error.

Ea = =

n

iEi

n 11

................................................................(A-5)

6-The cross-plots are the graphic representation of the calculated values by the correlation vs. the experimental or observed values. When both values are equals ( Zero error), all the points fall on a 45 line and R2=1 . Points far from the 45 line indicate low accuracy of the correlation. SI Metric Conversion Factors 1 pound mole 379.63 standard cubic feet 1 barrel 5.615 cubic feet Water density at 60F and 14.7 Asia = 62.4 pound/cubic feet.