reservoir properties correlation

5/28/2018 Reservoir Properties Correlation

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PROJECT # 1

IPG 516: Petroleum Production

Submitted to Jose Alvarez

Group Members:

Samaneh Sadeghi

Richard Ugwu

Nyamgerel Burenmend

Niaz Hussain
http://easweb.eas.ualberta.ca/person/jalvahttp://easweb.eas.ualberta.ca/person/jalva


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SUMMARY OF THE WORKFLOW

The objective for our project is to select different hydrocarbon properties for the

correlations that have already been performed, select the datasets for heavy oil/bitumen and use

the dataset for these properties to check the efficiency, applicability, reliability and drawbacks

for different correlations.

Search engine ONE PETRO from the library database of UAlberta was utilized t o find

the correlations. All the publications used in the study are from Society of Petroleum Engineers

publications which includes both modern and old work. Key words used to access different

papers of our interest are PVT Analysis, Viscosity Correlations, Formation Volume Factor

Correlations, Bubble Point Pressure Correlations, Standings Correlations and heavy oil, bitumen

correlations. After initially scrutinizing papers, checking the available data, quality of papers and

discussion in group we decided to focus on four different parameters from hydrocarbon

properties. Every property has been assessed by different correlations. The properties that our

project focuses on are.

(i) PREDICTION OF HEAVY OIL VISCOSITY (Samaneh Sadeghi)

(ii) CORRELATION OF VISCOSITY AND SOLUTION GOR FOR GAS-FREE

ATHABASCA BITUMEN(Richard Ugwu)

(iii) FORMATION VOLUME FACTOR(Nyamgerel burenmend)

(iv) BUBBLE POINT PRESSURE CORREALTION(Niaz Hussain)

Datasets from different publications have been utilized to check the applicability and reliability

of the correlations that we choose to work on. Comparisons of these correlations have been

performed and mean values of different types of errors have been calculated to support the

results. Graphs have also been sketched to get firsthand quick information about the results as

well.


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PREDICTION OF HEAVY OIL VISCOSITY

Abstract

The evaluation of viscosity of dead oil is an important step in the design of various operations in

oilfield and refineries. Correlations can be used to estimate fluid viscosity and can provide a

useful method to provide the reservoir engineer with preliminary values for reservoir

calculations. Trevor Bennison in 1998 developed a new correlation to identify an alternative

correlation of viscosity. There are number of correlations for the estimation of fluid viscosity

based on measured fluid properties. These correlations can be divided into three categories: dead

oil viscosity (od), bubble-point viscosity (ob) and undersaturated oil viscosity (o).

I ntroduction

In overall, the correlations use oil density and temperature to determine od. Beals correlation

was developed in 1946 using data obtained from California crude oil [1, 2]. It is still widely used

throughout the oil industry and is considered to be fairly accurate. Beggs and Robinson in 1975

Glas in1980 [3]; Labedi in 1992 [4]; Kartoamodjo & Schmidt in 1994 [5]; and Petrosky &

Farshad in 1995 [6] developed their correlations for different types of crude oils. Egbogah-Jacks

proposed different correlations with respect to the type of oil (Extra heavy, heavy oil) and

without pour point [7, 8]. Several oil companies have identified heavy oil reservoirs in the North

Sea and obtained measured viscosity data for them. Viscosity data has been provided through the

offices of the DTI for oils from four reservoirs identified as Oil 1, Oil 2, Oil 3 and Oil 4. Details

of these data are listed in Table 1.

Table 1: Summary of Data Provided.

The API gravity of the dead oil has been assumed to remain near constant for the temperatures

studied. In this work dead oil viscosities have been predicted using different forms of

correlations. Mean absolute difference (MAD) is used to compare and evaluate the prediction

ability of correlations, which is defined as below:


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| |

Also root mean square error (RMSE) and correlation coefficient (r) can be used to compare and

evaluate the prediction ability of correlations too.

()

Where n is the number of data points, is the viscosity obtained experimentally and ispredicted viscosity. Table 2 summarized comparison of predicted dead oil viscosities.

Table 2: Comparison of Predicted Dead Oil Viscosities

Based on their comparison of all the predictions with the measured dead oil viscosity data, It

have been concluded that Beals equation {2} and Egbogah-Jacks {6} are perhaps the best

showing the smallest mean difference, though none of the correlations provide a reliable estimate

of the dead oil viscosity (Table 2). We check the results and calculate the Beals and Modified

Egbogah-Jacks (Heavy Oils) correlations that are shown in Table 3.

- Beals dead oil correlation

- Modified Egbogah-Jacks (Heavy Oils)correlation


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DEVELOPMENT OF NEW CORRELATION FOR od

In this paper sixteen data points have been used to develop a new correlation for od. However,

the data is fairly well spread, covering four different fluids with 3 or 5 temperatures per fluid.The supporting fluid property data available was not very extensive, therefore only the API

gravity and temperature have been utilised. The best two correlations for od (Beal {2} and

Modified Egbogah-Jacks (Heavy Oils) {6}) were used to generate a range of data between 10

and 20 API and 50 to 200F.

This form of correlation has been used , , and . By plotting these two correlations (Figure 1), it can be foundthey are reasonably well fitted with below equation. The closeness of two fits is shown in Figure

1.

Figure 1: Left side: Dependence of Viscosity (od) on API Gravity and Temperature-

Right side: Curve Fitting to Obtain Coefficients a and b.

Table 3:Comparison of predicted dead Oil Viscosities

Fluid API Temp Exp. od Bealsod Bennison

od

Modified

Egbogah-

Jacks od

cp cp cp cp

Oil 1 19.5 39 1904 498.004 2117.869 9280.324

19.5 87 272 133.3983 159.656 180.3494

19.5 150 38 31.97634 27.60292 33.72113

Oil 2 14.5 106 383 511.4641 444.8022 259.5545

14.5 200 29.6 34.1475 34.63595 34.22506

14.5 300 6.4 3.582647 6.784128 13.57319

Oil 3 11 90 8396 9626.538 7615.002 1349.964


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11 120 1349 2115.756 1382.371 360.3787

11 150 357 532.6837 367.9808 152.7965

11 175 143 184.2041 147.4843 90.74137

11 200 66 68.21867 66.80052 60.22003

Oil 4 11.5 100 3369 3806.467 2952.28 703.7996

11.5 120 969 1515.731 1065.41 319.4698

11.5 150 338 422.0451 306.0333 137.7838

11.5 200 58.1 62.79988 61.28209 55.29189

11.5 250 20.1 11.69877 17.60294 30.37292

Table 4:Comparison of this work with some others correlation

Bennison

(1998)

Beal

(1946)

Modified Egbogah-

Jacks(1995)

RMSE 231.50 538.79 2653.63

MAD% 11.74% 33.16% 69.58%r 0.998 0.982 0.245

As we can see MAD% and RMSE of the developed correlation for the test data-set are 11.74%

and 231.505, respectively, which are comparable with Beals and Modified Egbogah-Jacks

results. That means, developed equation is a generalized correlation and is not over-fitted to the

data-points and has lower mean absolute difference with experimental data. Figure 2 is shown

the compares the scatter diagrams of this work(Bennison) with Beals, and Modified Egbogah-

Jacks.


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Figure 2:Scatter diagrams of experimental and predicted viscosities of dead oil at the

top left: with beal's, at the top right: with modified Egbogah-Jacks, and at the bottom: with

developed correlation (Bennison).

Comparing predicted viscosity with Beals correlation and predicted viscosity with proposed

correlation is shown in Figure 3. Also a comparison of Scatter diagrams of experimental and

predicted viscosities of dead oil with all three correlations is demonstrated in Figure 4.

Figure 3: Scatter diagrams of predicted viscosities of dead oil with Beals correlation

and predicted viscosities with Bennison correlation.

1

10

100

1000

10000

1 100 10000

PeredictedeViscosity,cP

Experimental Viscosity, cP

Beal's Correlation

od

1

10

100

1000

10000

1 10 100 1000 10000

Predicted

Viscosity,cP


Modified Egbogah-Jacks( heavy oil)

od

1

10

100

1000

10000

1 10 100 1000 10000PeredictedViscosity,cP


Bennison Correlation

od

1

10

100

1000

10000

1 10 100 1000 10000

Pre

dictedvicosity

withBennisoncorr.

Predicted viscosity with Beal's corr.

Beal's vs. Bennison

od


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Figure 4:Scatter diagrams of experimental and predicted viscosities of dead oil with

all three correlations

These curves show good agreement with the measured data and show that the results of

Bennison correlation are accurate for the North Sea data tested. It is recommended that this is

used to estimate dead oil viscosity of other heavy oils.

Estimated dead oil viscosities were compared with experiment viscosity data at different

temperatures for Bennison, Beals, Modified Egbogah-Jacks correlations by plotting them az a

function of temprature and API. Figure 5 demonestrates for log odvs. temprature. Developed

correlation is closed to the experimental data and other correlations are alittle under estimate or

over estimate the heavy oil viscosity.

Figure 5:Predicted data oil viscosity vs. temprature compared with experimenta data

with their API.

Testing proposed correlation with data bank

The reliability of the correlations has been evaluated against a set of 53 crude oil samples

collected from the Mediterranean Basin, Afrca, the Persian Gulf and the North Sea which is

related to the Ghetto et al. (1994) [9]. To assess the results that discussed in previous part and

based on the reservoir classification (Fluids) data with API


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Modified Egbogah-Jacks correlations. Figure 6 is shown the compares the scatter diagrams of

this work(Bennison) with Beals, Modified Egbogah-Jacks.

Figure 6: Scatter diagrams of experimental and predicted viscosities of dead oil at the

top left: with beal's, at the top right: with modified Egbogah-Jacks, and at the bottom: withdeveloped correlation (Bennison).

Figure 7:Scatter diagrams of predicted viscosities of dead oil with Beals correlation

and predicted viscosities with Bennison correlation.

Table 5:Comparison of this work with some others correlation

Bennison

(1998)

Beal

(1946)

Modified Egbogah-

Jacks

1

10

100

1000

10000

100000

1 10 100 1000 10000Predictedviscosity,cp

Experimental viscosity, cp

Beal's correlation-data bank

od

1

10

100

1000

1 10 100 1000 10000Predictetedviscosity,c

p


Modified Egbogah-Jacks data bank

od

1

10

100

1000

10000

1 10 100 1000 10000

PredictedViscosity,cP


Bennison Correlation-Data bank

od

1

10

100

1000

10000

1 10 100 1000 10000


withBennison

Predicteted Viscosity, cP with Beal's corr.

Beal's vs. Bennison -data bank

od


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(1995)

RMSE 117.71 394.63 145.56

MAD% 68.47 91.92 43.26

r 0.882 0.853 0.779

Table 5 reveals the superiority of the new model(Bennison), though, %MAD of Modified

Egbogah-Jacks, is lower than Bennison model. However, purely attributed to the accuracy of the

models in the entire range of oil gravity, since their RMSE and regression coefficients are not as

good. The contradiction may be clarified by referring to Figure 8, which compares the scatter

diagrams of this work with other two correlations. Using this data set Bennison correlation

predicted more accurate viscosity.

Figure 8:Scatter diagrams of experimental and predicted viscosities of dead oil with

all three correlations

In this curve shows a good agreement with the measured data with Bennison correlation and

experimental data. The results of Bennison correlation are accurate as well as previous part for

53 crude oil samples collected from the Mediterranean Basin, Afrca, the Persian Gulf and the

North Sea.

1

10

100

1000

10000

1 10 100 1000 10000



Bennison

Corr.

Beal's Corr.

Modified

Egbogah-

Jacks Corr.


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NEW VISCOSITY CORRELATIONS FOR DEAD CRUDE OILS

A new comprehensive correlation for prediction of viscosity of the Iranian heavy and light dead

crude oils was developed with Sattarina et al. in 2007 [10]. They found absolute average

deviation (%AAD) of 19.5% for the heavy (API=17~28). The new models correlate viscosity,

API gravity and temperature for a quite wide range, i.e. 2-570 cP for viscosity and 17-45 forAPI gravity. Table 6 shows data used for dead crude oil viscosity correlation:

A comprehensive dead oil viscosity correlations for off-shore and onshore Iranian crude oils

with respect to their nature is proposed. For this correlation API are between 17 and 28 and

temperature of 10 C, 20 C, and 40 C.

Coefficients a and b were regressed against temperature and the following equations were

derived:

Figure 9 is showing the comparison of Beals correlation and developed correlation as a function

of temperature and stock- F F).

Figure 9:comparison of Beals correlation and developed correlationas a function of

temperature and API.

As it can be seen there is a fairly difference between the results of proposed correlation and

Beals correlation. One reason could be that the Beals correlation is applicable to crude oil

viscosity with temperatures between 100- F.

1

1000

1000000

17 22 27 32

Absoulteviscosityofgasfree

cruidoil,cp

Cruid Oil API at 60 F and atmospheric pressure

T=68 F(new)

T=105 F(new)

T=68 F(Beal)

T=105 F(Beal)


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References:

1. The Viscosity of Air, Water, Natural Gas, Crude Oil and Its Associated Gases at Oil Field Temperatures and

Pressures. C Beal -SPE Reprint Series No 3. Oil and Gas Property Evaluation and Reserves Estimates.

Society of Petroleum Engineers of AIME, Dallas, TX (1970) pp114-127.

2. Volumetric and Phase Behaviour of Oil Field Hydrocarbon Systems M B Standing Society of Petroleum

Engineers of AIME, Dallas, TX (1981).

3. Estimating the Viscosity of Crude Oil Systems H D Beggs and J R Robinson JPT, September 1975, pp 1140-

1141.

4. Improved Correlations for Predicting the Viscosity of Light Crudes R Labedi Journal of Petroleum Science

and Engineering, 8, (1992) pp221-234.

5. Large Data Bank Improves Crude Physical Property Correlations T Kartoatmodjo and Z Schmidt Oil & Gas

Journal, July 4, 1994, pp51-55.

6. Correlations for Fluid Physical Property Prediction M Vazquez and H D Beggs JPT, 1980, 6, pp 968-970.

7. An Improved Temperature-Viscosity Correlation for Crude Oil Systems E O Egbogah and J T Ng Journal of

Petroleum Science and Engineering, 5, (1990) pp197-200.

8. Pressure-Volume-Temperature Correlations for Heavy and Extra Heavy Oils G De Ghetto, F Paone and MVilla. SPE 30316, International Heavy Oil Symposium, Calgary, Canada, 19-21 June 1995.

9. Reliability Analysis on PVT Correlations Giambattista De Ghetto, Francesco Paone, and Marco Villa, AGIP

SpA. SPE 28904. European Petroleum Conference hefd In Londen, U.K., 25-27 Octcber 1994.

10. NEW VISCOSITY CORRELATIONS FOR DEAD CRUDE OILS, M. Sattarina, H. Modarresi*b, M. Bayata, M.

Teymoria. Petroleum & Coal, ISSN 1335-3055, 2007.


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Appendix

Table 6:Comparison of predicted dead Oil Viscosities-collected from the Mediterranean Basin, Afrca, the

Persian Gulf and the North Sea.

API Temp Bennison

od

Beals

od

Modified

Egbogah-Jack od

API Temp Bennison

od

Beals od Modified

Egbogah-Jack od

F cp cp cp F cp cp cp cp

7.5 153.5 1133 1216.55 305.0043 19 238.3 11.6 7.079417 12.68408

7.9 208.9 236 74.24132 92.17332 19 163.4 50.9 23.67739 29.26593

7.9 165.2 443.7 552.593 208.9664 19 217.4 23.9 9.49622 15.28809

8 215.6 264.9 56.30582 81.83061 19.2 165.2 43.4 21.76352 27.67736

8 210.2 230 69.77313 88.67387 19.2 158 49.3 25.10569 30.90602

8.2 215.6 233.2 55.5478 78.88104 19.3 154.4 55.5 26.38457 32.27559

8.3 212 262 63.28862 81.63340 19.4 172.4 41 18.06742 24.28765

8.6 217.4 186 50.52902 71.51734 19.5 240.8 7.7 6.006589 11.73246

8.9 212 219.2 59.89723 73.18674 19.5 177.8 33 15.96035 22.291789 210 160.7 63.70196 74.00209 19.5 178.7 43.1 15.7028 22.03369

9.6 217.4 117.2 46.76365 59.99864 19.5 167 28.1 19.53123 25.83573

10 154.5 116.3 441.9512 169.6665 19.6 231.8 11.1 6.611848 12.49585

10.5 152.6 112 398.6908 159.5841 19.7 170.6 44.5 17.36222 23.88396

10.9 154.2 115 323.6381 141.4959 19.8 244 14.7 5.30259 11.05767

11 167 438.1 194.6608 105.6907 19.8 163.4 47.2 19.48883 26.09685

11 152.6 125.2 332.3215 143.7813 19.8 150.8 55.5 25.28835 31.80865

11.2 154.8 105 284.6818 131.2942 19.9 231.8 9.7 6.093824 12.07108

11.4 153.1 110.6 282.7405 130.9790

12.4 210.2 98.7 40.58975 41.54031

12.4 152.6 133 203.4579 108.537312.6 208 88.1 41.42605 41.40425

12.8 215.6 42.2 33.7233 36.48700

13.5 211.6 53.9 32.92283 34.42939

14 183.2 47.4 55.53885 46.79855

14.6 205.9 158 30.22027 31.31141

14.9 207.9 152.7 27.43616 29.24975

15.1 207.7 152 26.47159 28.48214

15.2 214 107.3 23.1823 26.10962

15.4 203 163.6 27.13113 28.85518

15.6 131.4 161.3 127.2503 95.72179

16 211.3 37.4 20.71057 24.0645016.5 188.1 43.7 27.77419 29.70153

16.8 140 112.6 69.9699 63.18363

17 250.7 10.1 9.445837 14.51192

17.6 194 23.4 19.27097 23.58938

18.8 244.4 11.7 6.867783 12.34950


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Summary/Correlation of Viscosity and Solution GOR for gas-free Athabasca bitumen

A paper written by M.A.B. Khan, A.K.Mehrotra and W.Y.Svrcek in 1984 & and a paper on Pressure-

Volume-Temperature Correlations for Heavy and Extra Heavy Oils

Giambattista De Ghetto*, Francesco Paone, and Marco ViIla*, AGIP S.p.A.

* SPE MemberSPE 30316

The viscosity models for the correlation of bitumen, example gas-free Athabasca bitumen is

different from the correlation models applied to conventional oils. This is as a result of the complex

nature of the chemical composition of bitumen.The molecular formular for Athabsca bitumen is C36.7H55.6

N0.19 S0.82 O0.51. Athabsca bitumen consists of about 20% asphaltenes, distributed in about 80% of a

dispersing medium known as the maltenes and the maltenes itself is subdivided into two components: the

light phase ( saturates and aromatics) and the heavy phase known as the resins. This shows that bitumen

has different structural, molecular and physical properties from normal crude oil. Of all the correlation

models employed at correlating the bitumen, only two models produced reasonable correlations within

allowable error margin. They are the linear and the non-linear viscosity models that employ double-

logarithmic viscosity functions. The linear produced results with an average deviation of 8.2% while the

non-linear produced results with an average deviation of 7.1%. Hoever, the two models are applied within

temperature range of 200C to1300C.

Prior to the development of the linear and the non-linear viscosity models, there were two equations by

Eyring viscosity model and Hildebrands viscosity Molar-Volume relationship that were employed at

correlating the viscosity of Athabasca gas-free bitumen.

Eyring viscosity model: This model prposes that for a molecule in a viscous liquid to flow, its neighbours

must give way or that a hole must be created. The molecule must be activated to enable it to move.This

energy he called it free energy for activation, F. The free energy is related to the amount of energy

which a molecule must possess, H and the degree of disorder, S created as a result of the

rearrangement due to the movement. Eyring stated that F, H and S are different from the Gibbs free

energy, enthalpy and entropy.

Eyring gave the equation for correlating viscosity of Athbasca gas-free bitumen as, Khan et al noted that this equation is only applicable for liquids that behave like monoatomic ideal gas.

So Athabasca gas free bitumen highly deviate from this type of liquid in the following respects:Large

molecules with high molecular weight; at temperatures below 600C, slight associative effects may exist


15/33

between molecules thus causing extremely high viscosities and the bitumen is highly varied in size and

shape, Khan et al.

To account for all these deviations, Eyrings equation as stated above is a modified form from the original

equation. h= Planks constant, N=Avogadros number, M=Molecular weight, g/gmol, R=Universal gas

constant, =viscosity in mPa.s, T= absolute temperature in Kelvin and d=density, g/cm 3. With the

average molecular weight of bitumen taken as 617g/gmol, and substituting the numerical values for the

various constants, . To use this equation to correlate the viscosity of

Athabasca bitumen at various temperatures, the density and the activation free energy would be known.

Khan et al. noted that for simple liquids with spherical molecules in cubic packing, F is one -third the

heat of vapourization and for a number of normal liquids, Fvapourization/F is about 2.46. However, for

bitumen, there is no data on the value of F, making the correlations more complicated. However, F

was calculated using , and then correlation was attempted for F using: F=f(density,B.P.) and F=f(Temperature).

To estimate the density of bitumen at temperature range of 20 to 1300C, the correlation of Goldhammer

was used, and then the correlation of F with the density and the boilingpoint. Overall, using this correlation did not produce worthwhile viscosity values for the gas free

Athabasca bitumen.

To obtain and predict the viscosity of gas free Athabasca bitumen, double logarithmic function model of

viscosity was developed, ie a plot of the double-log of viscosity (in mP.s) versus temperature in

logarithmic scale. The equation is stated as n n() = { }, b1 and b2 areconstants. The linear model, n n() =C1 nT+C2, where C1 and C2 are constants. The two equations

provide satisfactory correlations for the viscosity of Athabasca gas free bitumen with error margin of

between 3.6% to 10.7%. In the equations, temperature is in kelvin. The correlation of the viscosity of gas

free Athabasca bitumen could be achieved graphically or by using equation. For example, at 347K, the

viscosity of the bitumen is read from the graph as { n n() =2}. See graph below. Converting to mPa.s

yields 1618mPa.s or 1618cP. However, if you use correlating equation such as the linear equation, n

n() =C1 nT+C2with parameters C1=-3.62722 and C2 =23.22, T=347K, you get the same result.


16/33

Different bitumen samples use different parameters for correlation. Sample 1 is the bitumen sample used

by Jacobs et al. See table 3. Sample 2 is a bitumen sample before N2and synthetic combustion gas run.

Sample 3 is the bitumen before C02gas run while sample 4 is the bitumen sample before NH 4gas run.

SOLUTION GOR CORRELATION FOR EXTRA HEAVY OIL

RESULTS

MODIFIED STANDING CORRELATION

DATA BANK FROM WHERE PVT VALUES WERE TAKEN AND PLUGGED INTO CORRELATION EQUATIONS FOR GOR CORRELATION. Values are taken

from 1-10, i.e. for extra heavy oil


17/33

Table 1: PVT values including calculated GOR

Calculated GOR Measured

GOR API T (0F) P (Psia) gg

114.025321 224.74 6 147.9 2503.39 0.679

158.7156767 295.42 6.3 165.2 4021.96 0.624

52.30514548 84.83 6.5 210.2 697.64 1.403

13.76117823 14.43 7.3 221.7 249.47 1.044

107.5941728 202.37 7.5 153.5 2082.77 0.738

27.40897904 16.1 7.9 208.9 342.29 1.403

122.8925751 202.31 7.9 165.2 2902.25 0.623

48.00737652 46.03 8 215.6 619.32 1.389

56.08715113 90.05 8 210.2 668.63 1.47151.9682492 69.57 8.2 215.6 725.2 1.273

=752.7658 =245.85

STANDING CORRELATIOM

=0.00091(T)-0.0125yAPI

R = 0.9775

-50

0

50

100

150200

250

300

350

0 50 100 150 200

MeasuredGOR

Calculated GOR, using modified standing correlation

plot of measured vs calculated GOR for heavy oil. API


18/33

Table 2: PVT values including calculated GOR

CalculatedGOR

MeasuredGOR API T (0F) P (Psia) gg

304.8562926 224.74 6 147.9 2503.39 0.679

512.5830831 295.42 6.3 165.2 4021.96 0.624

155.5680029 84.83 6.5 210.2 697.64 1.403

33.6047645 14.43 7.3 221.7 249.47 1.044

255.6572701 202.37 7.5 153.5 2082.77 0.738

62.67645165 16.1 7.9 208.9 342.29 1.403

326.8717601 202.31 7.9 165.2 2902.25 0.623128.4222164 46.03 8 215.6 619.32 1.389

147.1269118 90.05 8 210.2 668.63 1.471

141.3453343 69.57 8.2 215.6 725.2 1.273

=2068.72 =245.85

R = 0.938

0

50

100

150

200

250

300

350

0 200 400 600

MeasuredGOR

calculated GOR using standing correlation equation

plot of calculated and measured GOR

Meassured GOR

Linear (Meassured GOR)

Figure 3: comparing calculated vs measured solution GOR using modified Standing Correlation


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Comparing modified Standing and Standing correlation

Modified Standing correlation Standing correlation

%MAD 3.95 -6.6

R2 0.9775 0.938

DISCUSSIONS

The use of double logarithm model to correlate the viscosity of heavy oil has some limitations. The main

limitation lies in the fact that correlation is not done on any type of heavy oil, the sample type would have

to be defined so that the various parameters to be applied would be known.

Correlation of viscosity for conventional oil takes into account the following factors: temperature, RS,

pressure, bubblepoint pressure, see figure 5, meanwhile, to correlate

bitumen viscosity using double logarithmic function model, one needs to know the sample type and the

temperature in absolute kelvin, see figure 4. So viscosity correlation for conventional oil is different from

the correlation of bitumen viscosity.

By using both standing and the modified form of standing equation for solubility GOR correlation, I

calculated GOR values which I plotted against measured values in each case. In the two correlations, the

Figure 4: Graphical viscosity correlation as proposed byJacobs et al., 1984 Figure 5: conventional oil viscosity correlation


20/33

modified form of standing correlations yielded a better result with R2=0.9775 (see table 1 & fig. 2) while

the un-modified standing correlation yielded result with R2=0.938, (see table 2 & fig 3).

In summary, the best solubility GOR correlation for extra heavy oil is provided by modified

standing correlation.

The use of doudle logarithm model for the correlation of extra heavy oil seems to have less

applicability because the parameters would need to be defined for it to be applied.

References

Khan, M. A. B., Mehrotra, A. X., & Svrcek, W. Y. (1984, May 1). Viscosity Models For Gas-Free Athabasca Bitumen.

Petroleum Society of Canada. doi:10.2118/84-03-05

De Ghetto, G., Paone, F., & Villa, M. (1995, January 1). Pressure-Volume-Temperature Correlations for Heavy and Extra

Heavy Oils. Society of Petroleum Engineers. doi:10.2118/30316-MS


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TECHNICAL NOTE 2009 SPE 957-G (MAY 1958)

BUBBLE POINT PRESSIRECORRELATION

J.A.LASTER (MAGNOLIA PETROLEUM CO. DALLAS TEXAS)

1. ABSTRACT

158 bubble point pressures were measured from 137 independent systems across North to

South America. Correlation of bubble point pressure for black oil systems is based on set of

standard physical and chemical equations. (Laster et.al, 1958)

1.1 INTRODUCTION

In absence of actual data from reservoir, a correlation parameter was required to

estimate the reservoir properties. Previously Standing came up with the correlation for bubble

point pressure, which had a short come that it was solely based upon data from the Californian

Crude oils. The correlation in this paper is based on data from whole across the North to South

America. (Laster et.al, 1958)

1.2 DEVELOPMENT OF CORRELATION

Working principle for the correlation is same as Standings which states that(Laster et.al,

1958).

Pb =f( R, rg, t, T) ..( 1 )

According to Henrys Law some parameters were combined to come up with the

relationship (Laster et.al, 1958).

Pb = Yg H(2)

Equation 2 defines single phase system and H is a function of gas phase composition

and temperature (Laster et.al, 1958).

Correlation suggests that bubble point is a direct function of absolute temperature since

the ratios for bubble point pressure to absolute pressure (R) obtained from the experiment


22/33

were identical. The correlation doesnt work well for the temperatures close to the critical

temperatures (Laster et.al, 1958).

Increase in molecular weight results in an increase in solubility of hydrocarbon

components in gas phase and therefore saturation pressure is inversely proportional to gas

gravity (Laster et.al, 1958).

.(3)Variables on left side are considered as bubble point pressure factor (Laster et.al, 1958).

) (4)

Number of moles for tank oil relates to molecular weight of the tank oil. Correlation

assumes a unique molecular weight, known as Effective Molecular Weight (M) despite the fact

that stock tank of oil is a complex mixture. M correlation with oil gravity is as follows (Laster

et.al, 1958).

M = f (T) .. (5)

Smooth curves for both, the correlation and effective molecular weight are developed

with help of empirical relationship by assuming values of M. Figure 1 represents the

relationship between oil gravity and effective molecular weight (Laster et.al, 1958).

Due to higher values of effective molecular weight compared with C7+fractions, we get

high differences of effective molecular weight for low gravity systems. These values correspond

closely for crude oils with UOP characterization (Laster et.al, 1958).

Figure 2 shows relationship developed from the experimental data between bubble

point pressure factor and gas mole fraction and the values for curve are shown in table 1. H is

not a constant due to non-linear relationship between values. Due to non-development of a

mathematical relationship, we need to obtain values of Pf and Yg from figure 2 (Laster et.al,

1958).


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We can calculate bubble point pressure from fig. 1, 2 while effective molecular weight from fig.

1 when we are having a for gas oil system. Gas mole fraction can be calculated from (Laster

et.al, 1958).

To obtain bubble point pressure factor, we apply the obtained value of Yg is in fig.2. Than

bubble point pressure is calculated from the following equation (Laster et.al, 1958).

Values measured from correlation when compared with experimentally obtained values

displayed an algebraic deviation of 3.8 %. A deviation of less than 0.5 % and 6.5 % is observed

for 21 % and 80% data points respectively. Maximum obtained error was 14.7 % (Laster et.al,

1958).

The correlation deals with systems free of non-hydrocarbon component which includes

gases such as N2, Co2, HS2. Presence of these gases results in lowering of the value of bubble

point. Error associated with presence of the gases is shown in Table 2 (Laster et.al, 1958).

A correlation chart has also been prepared with graphical evaluation to calculate the

bubble point shown in fig.3 (Laster et.al, 1958).

1.3 CONCLUSION

The correlation has applicability to large number of producing fields and is a quick

method to estimate bubble point pressure for crude oil with an appropriate accuracy (Laster

et.al, 1958).

NOMENCLATURE

f = function


24/33

rg= total gas gravity (Air = 1.0)

r = tank oil specific gravity

H = General Henrys Law

H = Specific Henrys Law constant (Independent of gas composition and temperature)

M = Effective Molecular Weight of Tank Oil

ng= moles of gas

n = moles of tank oil

yg= mole fraction of gas

Pb= bubble point pressure (psia)

Pf = bubble point pressure factor

R = total flash separation gas oil ration ( cu ft/bbl ) ( Measured at 60F )r = tank oil gravity API ( corrected at 60F)

t = temperature F

T = absolute temperature, R

Table -1 Smoothed Bubble Point Factor Function. (Laster et.al, 1958)

Gas Mole Fraction Bubble Point Pressure Factor

0.05 0.17

0.100 0.30

0.150 0.43

0.200 0.58

0.250 0.75

0.300 0.94

0.3500 1.19

0.400 1.47

0.450 1.74

0.500 2.10

0.550 2.70

0.600 3.29

0.650 3.80

0.700 4.30

0.750 4.90

0.800 5.70

0.850 6.70

Table2 Guide to effect of presence of non-hydrocarbon materials.(Laster et.al, 1958)


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Component % Gas Error in predicted Pb

Carbon Dioxide 9.1 5.0

Hydrogen Sulfide 3.1 1.1

Carbon dioxide 3.1 1.1

Nitrogen 2.5 2.7

Carbon Dioxide 0.3 2.7

Figure 1. Effective molecular weight related to tank oil gravity (Laster et.al, 1958).


26/33

Figure.2. Correlation of bubble point pressure factor (Laster et.al, 1958).

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

4.4

4.8

5.25.6

6

6.4

0 0.2 0.4 0.6 0.8 1

BubblePointPressureFactor

Gas Mole Fraction

Correlation of Bubble Point Pressure Factor

Correlation of Bubble

Point Pressure Factor

Poly. (Correlation of

Bubble Point Pressure

Factor)


27/33

Figure.3 Chart for calculation of bubble point pressure (Laster et.al, 1958).


28/33

DATA, RESULTS AND DISCUSSION

Different datasets have been utilized to check the reliability of correlation provided by the LaThe 1

stdata set was used was based on optimum range. A valid range of parameters was selected, ap

on Lasater Correlation, graphs were generated and figure 1 and figure 2 were used and computed r

are shown in table.1. Results show a good validation of the data computed. The results obtained fro

correlation had values greater than the Standing Correlation when applied to the standing Correl

Graphs.

Table.1 Dataset used for the computation of bubble point pressure using Lasaters Correlation.

R T (F) (R) rg r ro Mo Yg Pf Pb

20 130 590 0.79 17.9 0.95 457 0.07 0.37 276.3

100 180 640 0.82 21.9 0.92 423 0.26 0.77 600.98

1000 230 690 0.85 29.9 0.88 345 0.75 4.55 3693.5

1400 258 718 0.89 39.9 0.83 240 0.75 4.55 3670.7

Figure.1 Computation of Mole fraction from tank oil gravity.


29/33

Figure.2 Computation of Bubble point pressure factor.

The second dataset which has been utilized for Lasaters correlation is from the paper SPE

Reliability Analysis on PVT Analysis Correlation by GiambattistaDe Ghetto. First the correlatio

performed on a set of values below 30API as shown in table 2 and compared with the already calc

experimental values.

The data shows huge deviation from the experimentally measured values contrary to the

owned by the paper that the correlation can be utilized for large number of data sets. This 1stset of v

includes data for bitumen and heavy oil which doesnt bear good results because of the reaso

Lasaters correlation has been developed for the crude oil which does not give some good results f

data employed for the heavy oil. Table 2 shows the set of values measured for the Lasters Correla

compared with the end results.

We also come to the conclusion that there are different parameters which needs to be considere

developing a correlation and a statistical variation needs to be calculated and adjusted according


30/33

required parameters being used for getting more reliable results and making this correlation as a u

correlation.

Table.1 Data set and the measured values for the Lasters Correlation

T Rs rg API p a1 a2 a3 rgs PbMeasured

Pb

(Exper)

147.9 231.46 0.696 6 3428.75 27.64 1.0937 11.172 0.056459 135.241 2503.39

165.2 323.62 0.675 6.3 5391.14 27.64 1.0937 11.172 0.072772 151.0594 4021.96

210.2 93.77 1.429 6.5 4808.08 27.64 1.0937 11.172 0.196236 192.2046 697.64

221.7 18.82 1.134 7.3 4732.66 27.64 1.0937 11.172 0.18368 202.7209 249.47

153.5 208.7 0.756 7.5 3563.63 27.64 1.0937 11.172 0.080463 140.3642 2082.77

208.9 25.48 1.477 7.9 4148.14 27.64 1.0937 11.172 0.235307 191.0187 342.29

165.2 250.5 0.768 7.9 5518.77 27.64 1.0937 11.172 0.104457 151.0626 2902.25215.6 51.13 1.415 8 4494.79 27.64 1.0937 11.172 0.240875 197.1449 619.32

210.2 103.1 1.491 8 4708 27.64 1.0937 11.172 0.250582 192.2075 668.63

215.6 84.06 1.334 8.2 4851.59 27.64 1.0937 11.172 0.237611 197.1453 725.2

212 89.27 1.47 8.3 4883.5 27.64 1.0937 11.172 0.261059 193.8539 639.63

217.4 86.55 1.479 8.6 4996.63 27.64 1.0937 11.172 0.280787 198.7919 626.57

212 69.57 8.9 4908.15 27.64 1.0937 11.172 0 597.56

210 89.83 9 4908.08 27.64 1.0937 11.172 0 654.13

217.4 108.54 1.129 9.6 4895.1 27.64 1.0937 11.172 0.237961 198.7939 967.42

154.8 486.9 1.236 10 2850.04 27.64 1.0937 11.172 0.165384 141.5578 2665.84

152.6 260 0.815 10.5 2916.75 27.64 1.0937 11.172 0.11369 139.5472 2076.97154.2 31.34 0.81 10.9 2893.55 27.64 1.0937 11.172 0.118234 141.011 2802.7

167 234.18 0.735 11 5739.23 27.64 1.0937 11.172 0.142136 152.7146 2588.96

152.6 586.67 1.253 11 2916.75 27.64 1.0937 11.172 0.183113 139.5482 2916.75

154.8 316.51 0.812 11.2 2850.04 27.64 1.0937 11.172 0.121689 141.5602 2546.9

153.1 305.8 0.776 11.4 2858.74 27.64 1.0937 11.172 0.117181 140.0062 2622.32

210.2 152.18 12.4 4813.88 27.64 1.0937 11.172 0 1763.69

152.6 169.99 0.714 12.4 2916.75 27.64 1.0937 11.172 0.117624 139.551 2432.32

208 186.16 12.6 4805.18 27.64 1.0937 11.172 0 2233.62

215.6 17.21 1.323 12.8 4519.45 27.64 1.0937 11.172 0.36088 197.1545 227.71

211.6 201.53 13.5 4410.67 27.64 1.0937 11.172 0 1736.13183.2 40.97 1.295 14 2552.7 27.64 1.0937 11.172 0.277251 167.5326 1180.63

205.9 41.92 1.178 14.6 3684.02 27.64 1.0937 11.172 0.330552 188.2891 337.94

207.9 25.04 1.307 14.9 3727.53 27.64 1.0937 11.172 0.3792 190.1183 208.86

207.7 25.21 1.344 15.1 3727.53 27.64 1.0937 11.172 0.394789 189.9358 227.71

214 54.13 1.064 15.2 3784.09 27.64 1.0937 11.172 0.325556 195.6963 570.01

203 21.49 1.276 15.4 3665.16 27.64 1.0937 11.172 0.3718 185.6391 355.35

131.4 102.82 0.788 15.6 1038.49 27.64 1.0937 11.172 0.095747 120.1736 754.21


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211.3 338 0.784 16 4281.58 27.64 1.0937 11.172 0.258131 193.2292 3769.59

188.1 97.32 1.188 16.5 3328.67 27.64 1.0937 11.172 0.334109 172.0178 697.64

140 320.34 1.517 16.8 1153.07 27.64 1.0937 11.172 0.221543 128.0392 1074.74

250.7 146.4 1.232 17 7411.54 27.64 1.0937 11.172 0.588866 229.2557 1082

194 429.16 0.934 17.6 4873.34 27.64 1.0937 11.172 0.321682 177.4145 2236.52

244.4 111.76 1.206 18.8 7411.54 27.64 1.0937 11.172 0.621454 223.499 999.33

238.3 113.7 1.172 19 7047.49 27.64 1.0937 11.172 0.587934 217.922 1047.19

163.4 188.82 1.292 19 1806.47 27.64 1.0937 11.172 0.297509 149.4389 952.91

217.4 330.12 0.914 19 6557.26 27.64 1.0937 11.172 0.410971 198.8126 2319.99

165.2 166.33 1.402 19.2 1792.26 27.64 1.0937 11.172 0.328886 151.0851 796.27

158 109.93 1.412 19.2 1593.12 27.64 1.0937 11.172 0.303222 144.5019 469.93

154.4 175.44 1.406 19.3 1877.54 27.64 1.0937 11.172 0.315108 141.2105 796.27

172.4 177.83 1.411 19.4 1649.98 27.64 1.0937 11.172 0.33852 157.6686 825.28

240.8 115.98 1.059 19.5 7211.3 27.64 1.0937 11.172 0.554022 220.2088 1038.49

177.8 145.18 1.417 19.5 1934.4 27.64 1.0937 11.172 0.373436 162.6062 796.27

178.7 332.61 1.169 19.5 5305.56 27.64 1.0937 11.172 0.420216 163.4291 1322.76

167 25.37 1.105 19.5 4238.07 27.64 1.0937 11.172 0.349455 152.7315 256.72

231.8 140.52 1.092 19.6 6927.11 27.64 1.0937 11.172 0.547387 211.9801 1209.63

170.6 186.54 1.336 19.7 1877.54 27.64 1.0937 11.172 0.337692 156.0234 967.42

244 135.47 1.347 19.8 7137.42 27.64 1.0937 11.172 0.723238 223.1353 1124.06

163.4 167.89 1.133 19.8 1806.47 27.64 1.0937 11.172 0.271881 149.4405 896.35

150.8 147.96 1.256 19.8 1749.47 27.64 1.0937 11.172 0.274921 137.9199 839.78

231.8 121.64 1.005 19.9 6856.04 27.64 1.0937 11.172 0.510201 211.9807 1067.49

185.5 500.23 0.965 21 4873.34 27.64 1.0937 11.172 0.37919 169.6495 2369.95

183.2 404.01 1.062 21.2 3721.73 27.64 1.0937 11.172 0.386139 167.5469 2432

190.4 27.76 1.421 21.2 1209.63 27.64 1.0937 11.172 0.36354 174.1301 213.12

188.8 142.35 21.3 3598.44 27.64 1.0937 11.172 0 1009.48

179.6 100.93 1.035 21.3 6272.98 27.64 1.0937 11.172 0.42628 164.2556 654.13

134.6 640.25 1.263 22 1749.18 27.64 1.0937 11.172 0.274155 123.1122 1749.18

112.3 141.02 0.83 23.1 1315.51 27.64 1.0937 11.172 0.141327 102.7249 796.27

267.8 396.41 1.218 23.3 3740.58 27.64 1.0937 11.172 0.712528 244.9032 2674.54

176 120.09 0.864 23.7 4216.31 27.64 1.0937 11.172 0.349488 160.9687 768.71

Once the correlation was tested, than I picked a third set of data points of variable API i.e. from 17

API. This time four different correlations were performed to measure the continuity and reliabil

different correlations and how do they behave when compared with the experimental results. For

purpose I have used 4 correlations i.e. Standings Correlation 974, Laster Correlation 958, Vas

and Beggs correlation 989, and Al-Shamsi Correlation 1999. Dataset used for the correlations an

computed values of bubble point are shown in table 3. A comparison has been performed in a grap


32/33

form for different correlations in figure 4.

Table.3 Computed values of bubble point for different correlations.

API Tr Rs rg Standing

(1974)

Lasater

(1958)

Vazquez

& Beggs(1989)

Al-

Shamsi(1999)

Expe

Resu

Oil1 21 185.2 500.23 0.965 2596.915 1308.95 2426.779 2616.888 2363

Oil2 23.3 276.8 396.41 1.218 2001.167 2583.038 2277.103 1796.656 267

25 117.5 133.8 0.933 691.2805 1120.676 426.0426 797.7916 73

Oil3 30.7 141.4 289.14 0.949 1152.883 1175.824 1089.271 1301.324 141

33 219.2 477.24 1.051 1768.747 1677.505 2516.266 1853.321 248

35.1 154.4 120.7 1.27 396.9049 2424.739 371.0268 458.8392 52

40 158 217.47 1.349 538.4979 2735.575 593.4317 617.6286 511

Oil4 42.5 150.1 641.47 1.113 1418.989 1714.441 2015.656 1668.015 151

45 276.8 1664.63 0.85 4752.657 1081.227 25610.66 4628.555 569

50.9 183.9 376.48 1.408 632.262 3102.114 1145.696 761.3168 661

Figure.2 Comparison of the results measured from different correlations.

On comparison of all the correlations from the data set used Standing Correlation developed in 1974 works b

for the computed results and shows minimum error amongst all the correlation and shows a close approxim

to the experimentally values. Different errors computed for this purpose are shown in table 5

0

10000

20000

30000

40000

50000

1 2 3 4 5 6 7 8 9 10

CorrelationsUsed

Comparison of the Results for Used

Correlations

ExperimentalAl-Shamsi

V & B

Lasters

Standing


33/33

Table 4. Comparison of different errors for the correlation.

Standing

Correlation

Laster

Correlation

V azquez

& Beggs

(1980)

Al-

Shamsi

(1999)

r 3.623 2.307 1.91 3.62

RMSE 0.66352 7061.68 6078.19 6648.08

MAD 0.44026 -36.9037 6078.19 -1.511

REFERENCES

EL-SEBAKHY, E., & MEDAI, I. (2009). DATA MINING IN FORECASTING PVT CORRELATIONS OF CRUDE OIL SYST

BASED ON TYPE 1 FUZZY LOGIC INFERENCE SYSTEMS. Computers & Geosciences, 35(9), 1817-1826.

Lasateret, J.A. (1958). Bubble Point pressure correlation

Moradi.B. (2010) Bubble Point Pressure Empirical Correlations, Islamic Azad University, Omidieh,

Petroleum university of Technology

reservoir properties correlation

Documents

viscosity correlations

standings correlations

number of correlations

fluid viscosity

viscosity ob

undersaturated oil viscosity

deadoil viscosity

dead oil