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THE BEST EQUATION OF STATE AND CORRELATION

PROPOSED FOR PREDICTION OF IRANIANCRUDE OIL

DENSITY AND VISCOSITY

INTRODUCTION

Density and viscosity are two important physical properties which are highly used in chemical engineering calculations. Fordetermination of these two physical properties two general types are applied:

1. Experimental type 2. calculation type

The experimental cost is more expensive than that of calculation type, and

preparation of the reservoir conditions in the laboratory is difficult. Further

more due to different pressures and temperatures exist in reservoir conditions,

applying the reservoir condition in laboratory causes many difficulties with more errors. The calculation methods which are based onseveral mathematical relationships may predict density and viscosity, if needed data are available. Due to the lower cost of this methodthan that of the experimental method, by computerization of the calculation method, if logical results with low errors is desired, it can be

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used insisted of experimental method.

In this work with using of some needed experimental data from the "Iranian oil field PVT reports" are prepared and needed steps are applied

to predict the oil density and viscosity, and compared with the experimental works. Finally the best calculation method which satisfies theexperimental works with the lowest

error is selected and recommended.

APPLIED STEPS

1- Searching in several equations of state and correlation for determination of

density and viscosity.

2- Preparation of required data(from the PVT reports).

3- Computerization of the defined available equations or using of the available

packages.

4- Retrieve the determined results and compare with the experimental values with

using of tables and graphs.

EQUATIONS OF STATE AND CORRELATIONS FOR

DETERMINATION OF DENSITY AND VISCOSITY




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Equations which are consisted of relations between pressure, volume, and temperature are called equations of state(EOS).

By using of these equations some fluid physical properties can be calculated.

In this work one of the wanted physical properties is density which can be calculated by "EOS". The ability of these equations fordetermination of density

differs from each other, so causes different error percentages. To decrease the

error percentages, in this work, besides the EOS, some correlation are used.

In other words, at first, some needed data are calculated from the EOS, then by

applying the calculated data and another needed data in correlation the liquid

density with lower error percentage may be calculated.

For prediction of "liquid viscosity" some required calculated data from EOS and

density correlation and the other required data are applied in the viscosity

correlation. To have a good accuracy with lower error percent by using of a

computer program "C7+" is break down in to nine pseudo components.

USED EQUATIONS OF STATE AND CORRELATIONS

In this work, it is attended to use the best known "EOS" and correlation. So,

after a literature survey about different EOS and correlation their ability for

needed calculations were studied. Finally, several available equations and



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correlation were selected. Six EOS which are tabulated as the following:

Method Type

PR EOS

SRK EOS

SRK(KD) EOS

BWRST EOS

LKP Corresponding state

GS Corresponding state

RECOMMENDATION OF THE BEST USED EOS AND

CORRELATION FOR DENSITY PREDICTION

After some studies and calculations, "API" correlation was selected as the best

equation used with EOS for density prediction.

In other words, due to the fact that the experimental densities are measured at

variable pressures and constant temperature conditions, so, by using "EOS" the



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compositions and any other required data of the liquid mixture are calculated

isothermally at any needed pressure, and then by using "API" correlation, liquid

density is calculated. Among the mentioned EOS, Peng Robinson (PR), Soave-

Redlich-Kwong(SRK), Kabadi-Danner modification of Soave-Redlich-Kwong [SRK(KD)],

and Grayson-Streed(GS) equations of state when used with "API" correlation have

good density prediction, which the best results are predicted by "SRK(KD)" and

"GS" when used with "API" correlation.

VISCOSITY PREDICTION

The studies for viscosity prediction shows that if the "C7+"content is less than

45%, it is better to break down "C7+" in to some pseudo components and calculate

their required physical properties. Then, with use of the viscosity correlation,

liquid viscosity is calculated. There are some computer programs for break down

of "C7+" in to some pseudo components. In this work the "C7+" break down package

(which is installed on the NIOC main frame) has been used. The required data for

using the package are: pressure, temperature, composition,and some data from the

"Assay Book"in NIOC south oil field. In the mentioned package the "C7+" fraction





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is broken down in to some pseudo components. The results of running this program

are "Normal Boiling Point", "Molecular Weight", and "Specific gravity" of the

determined pseudo components. There is some data about the Iranian oil fields in

the "Assay Book". In this work the effect of some parameters such as temperature

and pressure, are considered in calculations and the following methods are

studied to find the best method for prediction of oil viscosity. "Beal" method, "Beggs and Robinson" method, "Lohrenz and Bray" method,

"Abbot-Kaufmann-Domash" correlation, Internally consistent correlation, and "API" method.

REQUIRED DATA PREPARATION

Due to the fact that the prediction of "Oil density and viscosity of the Iranian

oil fields" are to be considered, so, the existing "PVT" reports have been used.

The required data are retrieved from the Ahwaz, Aghajari, Gach saran, and Marun

reservoirs PVT Wells Reports. The under saturated reservoir oil composition and

the density and viscosity at variable pressures and constant temperature can be

retrieved from the PVT Reports. In PVT reports for identification of "C7+", it's molecular weight and specific gravity are given. As anexample for viscosity and density prediction, the retrieved data from "Well AZ - 34" are as follows:





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Component Composition Mole %

C1 39.389

C2 7.595

C3 5.322

iC4 1.030

nC4 2.835

iC5 1.182

nC5 1.571

C6 2.155

C7+ 33.476

CO2 4.549

H2S 0.897

The "C7+ required existing data are

Molecular Weight of C7+ = 265

Specific Gravity of C7+ = 0.8959, So the density of C7+ = 55.879 lb/Ft^3

COMPUTERIZING USED EQUATIONS

There are some suitable packages for prediction of the fluid physical properties





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that have been used in this work. Among available packages the most perfect one

is "Pro2 Package". For prediction of "density and viscosity", the selected EOS

and correlation have been used to apply on this package. For calculation of

the viscosity, as previously mentioned, the "C7+" component is broken in to nine pseudo components by using the " C7+ break downpackage".

For comparison of the calculated data with the experimental data, they have been

tabulated and graphed by using the "Quatroporo Package (QP)".

The recommended type and its errors are given in the last columns.

DISCUSSION AND RECOMMENDATIONS

Due to the difference in the compositions of the oil fields and the formations

(Asmary and Bangestan formations)from which oil is produced,the data are divided

in to four groups based on the ratio of the amount of "C1","C2",and "C3" to that

of "C7+". The ratio may be written as the following:

X M +X M +X M

C1 C1 C2 C2 C3 C3

R = --------------------

X M





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C7+ C7+

Where:

R=Ratio, Xi=Mole fraction of component "i", Mi=Molecular weight of component "i"

The groups can be classified as follows:

1 - R < 10

=

2 - 10 < R < 12

=

3 - 12 < R < 14

=

4 - R > 14

GROUP 1 R < 10

=

In this case "C7+" content is higher than that of light components. So, the

dependence of the oil density to the light component physical properties is

decreased,and all of the selected equations predict the liquid density with good

accuracy. Among these equations, SRK(KD) is the best and is recommended for

prediction of liquid density of this group.





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GROUP 2 10 < R < 12

=

In this case, the light components of the oil are a little higher than that of

the previous cases, This causes that the calculated physical properties by some

of the selected equations differs from the experimental values. For example the

"LKP" equation doesn't predict logical results, because of a calculated "bubble

point much higher than that of experimental values. The other equations predict

good results up to the bubble point. But after matching the bubble point "BWRST"

method is failed. The liquid density prediction by the "SRK" "PR", "SRK(KD)",and

"GS" methods are good. Among these methods "SRK(KD)" is the best. To have the

best results a combination of "SRK(KD)" and "GS" (after the bubble point for the

pressure lower than 3000 PSI)is recommended.

GROUP 3 12 < R < 14

=

In this case the oil light components are more than that of the 2nd group. So,

the calculated physical properties by some of the equations is far from the

experimental values. In this case the "LKP" and "BWRST" methods, theoretically

flash the oil at a pressure much higher than that of the experimental values.

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The difference is about 2000 PSI. So, the predicted density by these equations

cannot be accepted(even though the results match experimental density values).

"GS" method, theoretically flashes the oil at a pressure about "600 - 1000" PSI

higher than the that of the experimental values. So, the "GS" method density

results cannot be accepted, but if it is used after the bubble point, predicts

good results. "PR","SRK",and "SRK(KD)prediction is good and among these methods

"SRK(KD)" is the best. To have the best results a combination of "SRK(KD)" and

"GS"(after the bubble point for the pressure lower than 3000 PSI)is recommended.

GROUP 4 R > 14

In this case because of high content of light components, the dependence of the

oil density to the light components physical properties plays an important role.

As previously described, if the content of the oil light components is increased

the accuracy of the equations for density prediction is decreased. In this case

the "BWRST","LKP", and "GS" methods don't have a logical prediction because of

calculating the bubble point much higher than that of experimental values, but

"PR", "SRK", and "SRK(KD)" equations of state predict acceptable bubble point.

Among these EOS "SRK(KD)" is the best, but for the best results a combination of

"SRK(KD)" and "GS" (after the bubble point for the pressure lower than 3000 PSI)




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is recommended. It is important to know that with the equations mentioned in the all discussed groups the "API" density correlation is used.

RECOMMENDED VISCOSITY METHOD

Reservoir oil is consisted of hydrocarbon components ranges from "C1" to heavy

hydrocarbon components. Since there are high contents of "C1"and"C2"in reservoir

oil, (especially at high pressure reservoir conditions) and individual viscosity

determination of these two components isnt available, so, the methods based on

the data of individual component viscosity cannot predict the reservoir oil

viscosity with good accuracy. In addition, the presence of the high contents of

the heavy components causes an approaching to the real oil viscosity prediction.

Especially, if "C7+" is broken down to several pseudo components the approaching

to the real oil viscosity would be increased. In the other hand one of the most

important parameter for prediction of oil viscosity is density. So, by using the

mentioned equations for density prediction, the oil viscosity is calculated.

Inspite of logical approaching oil viscosity predicted by "Lohrenz and Bray"

method to the real oil viscosity, due to the fact that this method is based on

individual components viscosity, it cannot predict accurate viscosity.

Viscosity determination by "Beal method" which is based on graphs, cannot be

computerized with good accuracy for viscosity determination,because of different




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ranges. Viscosity prediction by "Beggs and Robinson"which is based on the liquid

"API gravity"is not more accurate than the similar methods. The method of "Abott

-Kaufmann-Domashm", TWU", and "API" which are the same, predict liquid viscosity

with good accuracy but "API" method prediction is better than the others.

The calculated viscosity without broken down of the "C7+" have an average error

of 20%. So, for the best prediction of the oil viscosity, a "C7+" broken down in

to nine pseudo components applied in the "SRK(KD)"and"GS" EOS with the mentioned

condition, and finally use of the "API" viscosity correlation is recommended.




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PRESSUREVISC(L)

VISC(L)

VISC(L)

VISC(L)

VISC (L)VISC(L)

VISC(L)

VISC(L)

VISC (L)

PSIA C.P. C.P. C.P. C.P. C.P.%

ERROR

%

ERROR

%

ERROR

%ERROR

V-130 LAB PR SRK(KD)

GS REC.TYPE PR SRK(KD)

GS REC.TYPE

5015 1.219 0.91474 0.91474 0.91474 1.2068 24.9598 24.9598 24.9598 1.00082

4555 1.1778 0.88502 0.88502 0.88502 1.1666 24.8582 24.8582 24.8582 0.950925

4040 1.1318 0.8495 0.8495 0.8495 1.1184 24.9426 24.9426 24.9426 1.183955

3540 1.0867 0.81335 0.81335 0.81335 1.069 25.1541 25.1541 25.1541 1.628784

3040 1.047 0.7761 0.7761 0.7761 1.0178 25.8739 25.8739 25.8739 2.7889212590 1.0021 0.742 0.742 0.742 0.97072 25.9555 25.9555 25.9555 3.131424

2025 1.0442 0.69889 0.69889 0.73992 1.06 33.0693 33.0693 29.14 -1.51312

1505 1.2738 0.82712 0.8375 0.8439 1.2247 35.0667 34.2518 33.7494 3.854608

1000 1.4187 1.0054 1.0126 1.0017 1.4946 29.1323 28.6248 29.3931 -5.34997

480 1.7644 1.27 1.2727 1.267 1.9706 28.0209 27.8678 28.1909 -11.6867

AVERAGE

%ERROR 27.7033 27.5617 27.2218 3.30892

COMPARISON OF THE EXPERIMENTAL WITH PREDICTED VISCOSITY(FAJR-44)




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PRESSURE DENSITY DENSITY DENSITY DENSITY DENSITY DENSITY DENSITY DENSITY DENSITY DENSITY DENSITY DE

PSIA LB/FT3 LB/FT3 LB/FT3 LB/FT3 LB/FT3 LB/FT3 LB/FT3 %ERROR %ERROR %ERROR %ERROR %E

D - 400 LAB PR SRK SRK

(KD) GS BWRST LKP PR SRK

SRK

(KD) GS BW

5035 44.3465 44.345 44.345 44.345 44.432 44.486 44.727 0.00338 0.00338 0.00338 -0.1928 -0.3

4531 44.1095 44.165 44.165 44.165 44.328 44.507 45.287 -0.1258 -0.1258 -0.1258 -0.4954 -0.9

4332 43.9535 44.01 44.01 44.01 44.276 44.488 45.573 -0.1285 -0.1285 -0.1285 -0.7337 -1.2

4032 43.8475 43.887 43.887 43.887 44.252 44.468 45.749 -0.0901 -0.0901 -0.0901 -0.9225 -1.4

3836 43.7415 43.75 43.75 43.75 44.239 44.442 45.911 -0.0194 -0.0194 -0.0194 -1.1374 -1.6

3736 43.6853 43.675 43.675 43.675 44.239 44.437 45.991 0.02358 0.02358 0.02358 -1.2675 -1.7

3636 43.6292 43.595 43.595 43.595 44.243 44.408 46.069 0.07839 0.07839 0.07839 -1.4069 -1.7

3536 43.574 43.511 43.511 43.511 44.252 44.388 46.145 0.14458 0.14458 0.14458 -1.556 -1.8

3436 43.5169 43.423 43.423 43.423 44.267 44.366 46.22 0.21578 0.21578 0.21578 -1.7237 -1.9

3363 43.4733 43.356 43.356 43.356 44.282 44.298 46.273 0.26982 0.26982 0.26982 -1.8602 -1.8

3027 44.0471 43.021 43.021 43.021 44.397 44.249 46.514 2.32955 2.32955 2.32955 -0.7944 -0.4

2726 44.571 42.874 42.961 43.006 44.583 44.228 46.726 3.80741 3.61221 3.51125 -0.0269 0.76

2424 45.1012 43.57 43.636 43.677 44.862 44.222 46.943 3.39503 3.24869 3.15779 0.53036 1.942124 45.6251 44.316 44.364 44.4 45.244 44.244 47.169 2.86925 2.76405 2.68514 0.83529 3.02

1820 46.1553 45.122 45.155 45.185 45.743 44.356 47.413 2.23875 2.16725 2.10225 0.89329 3.89

1521 46.673 45.961 45.98 46.005 46.384 44.552 47.676 1.52551 1.4848 1.43123 0.6192 4.54

1222 47.1719 46.837 46.847 46.865 47.061 44.909 47.968 0.70996 0.68876 0.6506 0.2351 4.79

918 47.7339 47.765 47.765 47.778 47.89 45.491 48.306 -0.0652 -0.0652 -0.0924 -0.327 4.69

618 48.3009 48.725 48.717 48.723 48.807 46.544 48.701 -0.878 -0.8615 -0.8739 -1.0478 3.63

319 48.9745 49.79 49.776 49.777 49.872 47.644 49.23 -1.6652 -1.6366 -1.6386 -1.8326 2.71153 49.436 50.527 50.514 50.513 50.516 48.021 49.698 -2.2069 -2.1806 -2.1786 -2.1846 2.86

AVERAGE %ERROR 1.08525 1.05422 1.03575 0.98201 2.28

COMPARISON OF THE EXPERIMENTAL WITH THE PREDICTED CRUDE OIL DENSITY IN DIFFERENT P


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