2

Special to Dr. Tarek Ahmed:

I thank you Dr. Tarek for your attention and I promise you that I will be one of

the greatest Reservoir Engineers all over the world one day, en shaa' Allah.

Please remember my name; you will hear it frequently… soon not later,

en shaa' Allah.

Kamal Shawqi

3

That’s great Kamal! You are very smart and I believe you'll be an expert who can play big

roles in industry.

Maysam Azizi, Senior Reservoir Engineer in Project Manager Position, Research & Development

Division, Petropars Company, Iran. Currently, Maysam is a leadership for 4 reservoir teams.

Luca Trombi, Regional Manager of Directional Drilling, Weatherford.

“ Your paper looks perfect from Academic point of view “

“ This paper is excellent and I recommend you to send it to Dr. Tarek Ahmed. “

Eng. Ibrahim Awny, Reservoir Engineering Manager, Egypt's Belayim Petroleum Company

(Petrobel).

“The most amazing thing is that you are still a 3rd year student. I agree with you

and I expect a great future to you. Keep going ahead."

Prof. Dr. Hamid Khattab, Reservoir Engineering Department, Suez Canal University.

4

Contents

Preface…………………………………………………….…………………..………… 4

Introduction to correlations…………….…………………………………..…… 5

Note 1 …………………………………………………………….…………………..…. 6

Correction of Ppc and Tpc to high molecular weight Gases,6.

Note 2 ……………………………………………………………….………………..…. 7

Direct calculation of the compressibility z factor (using Dranchuk-Abu-Kassem

correlation),7.

Note 3…………………………………………………………………………………… 10

Range of Dranchuk-Abu-Kassem correlation,10.

Note 4………………………………………………………………………………….…11

Coefficient ‘b’ of Glaso Bubble Point Pressure Correlation,11

Note 5…………………………………………………………………………….…….. 13

Absence of correlations’ ranges,11. Absence of correlations’ nomographs,13.

Correlations’ nomographs and ranges …………………………………...... 15

PVT LAB 2009 program,15. Correlations supported by their nomographs

and ranges, 16-27.

references………………………………………………………………………..……. 27

5

Preface

It’s honor to me to share in making Reservoir Engineering Handbook as

complete as possible by notifying Dr. Tarek about some important misprints in the

3rd edition. I only hope them to be taken into account in the next editions of this

well-known handbook. All of these misprints were found initially in the 2nd edition;

exactly in chapter of reservoir fluid properties. In addition, two of these misprints

are printed correctly in Hydrocarbon Phase Behavior, Tarek Ahmed.

All notes presented here show only my way of thinking, therefore any errors found

in this paper are related only to me.

I’m so grateful to Dr. Ahmed for this easy-to-use handbook. Many advised me to

carefully read it, if really I hope to be a professional reservoir engineer one day.

I would like to express my especial thanks to Eng. Tawfik El-Shehabi and Eng.

Omar Saad, Suez Canal University, for their honest assistances by providing me

with the desired SPE papers. Also, I thank each petroleum engineer who read this

paper and show me his encouragement. Finally, I thank my friend Amr Abdel-Aziz

for his contribution in constructing chart of Dranchuk and Abu-Kassem correlation

using Microsoft Excel.

Kamal Shawqi Kamal Mohammad,

Head of SPE Academic Committee, Suez Chapter.

3rd year student of Petroleum Engineering Faculty,

Suez Canal University, Egypt.

E-mail: Kamal-Shawqi@spemail.org

Mobile: +20.12.888.9829

Kamal Shawqi Kamal

6

Introduction to correlations:

Reservoir fluid properties form the basis of many petroleum Engineering

calculations. The evaluation of oil and gas reserves, fluid flow through porous media,

multiphase flow in pipe, surface and subsurface equipment design, and production system optimization all depend heavily upon reservoir fluid physical properties. These properties may be measured experimentally in a PVT (pressure-volume-temperature) laboratory or they may be estimated by using empirical correlations. The most accurate method for determining the behavior of these fluids is a laboratory PVT analysis; however, the evaluation of exploratory wells and the advanced design of equipments often requires an estimation of the fluid behavior prior to obtaining a representative reservoir sample. Also, experimental data is often unavailable in reservoirs which do not warrant the cost of an in depth fluid study. Empirical correlations are often used for these purposes.

Correlations are also needed for the calculation of multiphase flowing pressure gradients which occur in pipe. These calculations require the prediction of fluid properties at various pressures and temperatures. Even though laboratory measurements of these properties may be available as a function of pressure, they are usually measured under isothermal conditions. The behavior of these properties as a function of temperature is usually predicted by using empirical correlations. The accuracy of empirical PVT correlations is often limited because reservoir fluids consist of varied and complex multi component systems. It is also difficult to describe these complex systems with simple parameters such as gas gravity, oil gravity and gas-oil ratio because these parameters depend upon the process by which the oil and gas are separated. New empirical PVT correlations for estimating bubble point pressure, solution gas-oil ratio, bubble point oil formation volume factor and under saturated isothermal oil compressibility have been developed as a function of commonly available field data.

The results of material balance calculations on a typical Gulf of Mexico, water-drive,

saturated oil reservoir indicate that the estimated original oil in place can vary by over 35% depending on the PVT correlation chosen to generate PVT properties.

7

Note 1, page 50:

Correction of Tpc to High Molecular Weight Reservoir Gases.

Sutton’s approach for the determination of Tpc of high M.wt gases is1:

Formula of the adjustment parameter,Ek , includes a misprint. That’s the first

term of heptanes plus, Tc

M. pc

C7+

, must be: Tc

𝐩𝐜

C7+

.

This is also clear from the dimensional homogeneity analysis:

𝐾′ = k = Ek = Ro / Psia0.5.

Both Kay’s mixing rules and gravity relationships for calculating Pseudo

critical Pressure and Temperature aren’t applicable to gases whose specific

gravities are greater than 0.75 (namely, for whose apparent molecular

weight are greater than 21.67). This usually obtained in real situations since

gas mixtures usually contain appreciable amount of the heptanes plus

fraction.

Studies showed that Key’s mixing rules has a general trend of increasing

the error in Z-factor as the heptanes plus fraction is increased2.

1 Along this paper, formulas contained in red-borders boxes are snapshots from either the 3

rd edition of the Handbook or from a

SPE paper. 2 Compressibility Factor for Gas Condensates, Adel M. ELsharkawy, Yousef Hashem and Abbas Alikhan, SPE No. 59702

8

Note 2, page 56:

Direct calculation of the compressibility Z-factor, DAK Model.

Dranchuk and Abu-Kassem fitted an 11-parameters EOS to Standing and

Katz (SK) general compressibility factor chart and they extrapolated it to

higher reduced pressures. This famous EOS duplicates the Standing and

Katz chart with an Average Absolute Error of only 0.486%. Formula, whose

solution is the reduced density; expressed by ρr = 0.27 PPr

Z TPr , is:

However, The 5th term of this formula must be multiplied by the square of

reduced density. Mathematically, the correct term is:

(R5 ) 1 + A11 ρr2 . 𝛒𝐫

𝟐 . exp −A11 ρr2

TaKacs reviewed the performance of five Z-factor correlations and

concluded that DAK correlation is the best one to fit SK chart3. Also, Adel

ELsharkawy, after his studies on the current 144 methods for estimating Z-

factor, concluded that DAK correlation resulted in the lowest error and

standard deviation4.

I noticed some references referred only to this correlation when speaking

about direct determination of z-factor such reference 3, 4 and 5. This

reflects DAK correlation importance.

3 Compressibility Factor for Gas Condensates, Adel M. ELsharkawy, Yousef Hashem and Abbas Alikhan, SPE No. 59702 4 The same above paper.

9

Z-factor based on this EOS is accurate within usual engineering standards:

0.2 ≤ 𝑃𝑟 < 30 and 1.0 < 𝑇𝑟 ≤ 3.0, and 𝑃𝑟 < 1.0 and 0.7 < 𝑇𝑟 ≤ 1.0 .

However, it gives poor results for 𝑇𝑟 = 1.0 and 𝑃𝑟 > 1.0 .

Below is DAK Model chart5 after correcting this misprint. It’s comparable

well to Katz and Standing compressibility factor chart on the next page.

5 Constructed using MS Excel 2007 with contribution of student: Amr Abdel-Aziz Essa, third year, Suez University. This work was under direct supervision of Prof. Dr. Attia Mahmud Attia.

10

11

Note 3, page 586:

Ranges on Dranchuk-Abou Kassem correlation.

Ranges of DAK correlation as present on the book:

In many reservoir engineering calculations, it’s necessary to use the

assistance of a computer. Therefore, using any chart, as SK chart, becomes

difficult. The original SK chart covered pressures to Pr = 15 and it was

extended to Pr = 30. So, there

is need to use correlations to

fit it throughout large range

as possible.

Hall and Yarborough ,for

example, used high-pressure

data and an equation of state

to extend the original Z-factor

chart to Pr = 24. However,

one great advantage of DAK

correlation is that it was

extrapolated to be valid in

range of 0.2< Ppr <30.

Error of using Dranchuk- Abu

Kassem correlation is about

1% in range of 0.2< Ppr <15.

While it increases to 3% in range of 15< Ppr < 30. All other books show its

range to be 0.2< Ppr <30.

6 This note is added to my paper later and no one checked it yet.

12

Note 4, page 90:

Coefficient ‘b’ of Glaso Bubble Point Pressure Correlation.

Coefficients of Glaso Pb correlation as presented in the handbook are:

However, the ‘b’ coefficient is divided into two parts, one for black oil and

the other is for volatile oil systems:

a 0.816

b 0.172 For black oil.

0.13 For volatile oil.

C -0.989

Using b= 0.172 , for example, for a volatile oil system deviates the results

more from the expected values of Pb, and vice versa.

For example, Rebort P. Sutton and F. Farshad7 studied 31 different crude-

oil/natural-gas systems data which were gathered from PVT samples taken

along the Louisiana and Texas gulf coast. They mentioned also that those

samples were typical of the crude oil systems found in the Gulf of Mexico

and the majority of the data came from oils were of low to moderate

volatility and two of the oil had a highly volatile nature. Hence, we must

take the volatility nature of oil systems into account.

On the other hand, most Egyptian oils can be classified as conventional

black oil which has the following characteristics8:

7 Review SPE Paper No. 13172. 8 From SPE Paper No. 15721, A.M. Saleh, I.S. Mahgoub and Y. Assad.

13

One useful use of Glaso Pb correlation is that it’s the most accurate one in

determining the Bubble Point Pressure of the Egyptian oils9.

The samples considered in that study to determine the most accurate

correlations for the Egyptian oil systems were taken from different reservoir

zones and from different oil fields. Also the laboratory analyses for those

samples were not conducted in the same laboratory. Some of the analyzed

samples were not in complete agreement with the approximate range of

black oil properties. They showed a slight deviation as to one or two

properties, however, other properties do agree. The samples used in that

evaluation were almost free of hydrogen sulfide and contain a very small

mole percent of nitrogen and carbon dioxide, (0 - 0.3) and (0 - 2.71) mole %,

respectively.

The results from that study were as the following:

Comparing in Glaso Standing Lasater Vasquez and Beggs

Average error -3.61 -30.17 -26.37 -31.35 Standard deviation 8.9 30.16 27.56 24

Average Absolute error 7.34 30.17 26.68 31.35 Standard Deviation 5.77 30.16 27.23 24

CHI- Square 118.21 1003.2 867.28 1355.2

It’s believable that each correlation has its own benefits and applications

and I hope this great handbook to be the most comprehensive handbook

that collects all about correlations in one place.

9 From SPE Paper No. 15721, A.M. Saleh, I.S. Mahgoub and Y. Assad.

characteristics from to

Stock tank oil color ranges brown dark green

The stock tank oil gravity, API 15 40

Gas Oil Ratio, SCF/BBL zero 700

Typical reservoir temperature, F 100 200

Typical reservoir Pressure, Psia 300 5000

14

Note 5:

Absence of correlations’ ranges and Nomographs.

1) Absence of correlations’ ranges:

Nearly each correlation has its own nomograph and ranges for its

correlating parameters. We, from my point of view, can’t ignore listing either

their ranges or their nomographs. Researchers use the correlations to

determine samples properties and they must take ranges of them into their

considerations. Taking such consideration may make some correlations to

be not applicable to an oil system, according to its conditions.

For example, authors of SPE Paper No. 15721 concluded that:

If these authors used correlations without taking their ranges into account,

their results may be differ and Standing’s correlation, for example, may not

be the most accurate in determining Egyptian Oil FVF.

Another example is from SPE paper No.13718 by Al-Marhoun, at which he

concluded the following results for the Middle East crude oils:

15

Al-Marhoun considered the ranges of each of these correlations before

saying that his own correlation is more accurate than Glaso correlation, for

example, in determining the Total FVF of Middle East crude oils.

2) Absence of the nomographs:

Nomographs initially were constructed by the original authors of the

correlations such Standing, Glaso, Lasater … etc. depending on

experimental data. While an empirical correlation is just a mathematical try

to fit a nomograph with small deviation as possible to be programmed using

computer routines. Deviation between the nomographs and the empirical

correlations lies in accepted range for nearly all engineering purposes.

Although the empirical correlations are used constantly in lieu of laboratory

data for determining reservoir fluid properties necessary for calculating

reserves, reservoir performance, equipment design ….,etc., it’ll be more

accurate to digitize these nomographs. This may be achieved using

modern computer software.

An imagination of programming procedures of

such software, for example, in case of Katz and

Standing chart is:

according to the calculated Tpr, the imagined

software shows the digitized line of it from

Katz and Standing chart. (If the calculated Tpr

line lies between two Tpr lines, the program

creates it by interpolation).

Finally, the software locates a point on this line depending on the predetermined

Ppr, and then read the most accurate Z-factor value from Y-axis.

I hope to be able to program such software although it requires high level of

programming skills.

4 0.99

16

Correlations’ nomographs and ranges:

PVT LAB. 2009

I have collected some of correlations with their ranges and nomographs in a

simple computer program. It’s programmed using VBA under Microsoft

Excel 2007 environment. The next section contains the used correlations.

17

Bubble Point Correlation:

Standing:

From PVT correlations published until now, Standing’s work is perhaps the most widely used.

His correlations were developed for California oils and made no corrections for oil type or

non-hydrocarbon content. In 1947, Standing published correlations for determining the bubble

point pressure and Oil FVF from known values of temperature, solution GOR, gas relative

density, and oil API gravity. A total of 105 experimentally determined data points on 22

different crude oil and gas mixtures from California were used in deriving the correlations.

Standing reported an average relative error of 4.8% for the bubble point pressure correlation.

𝑃𝑏=18.2 𝑅𝑠𝑏𝛾𝑔

.83

10.00091 𝑇−460 −.0125∗𝐴𝑃𝐼

− 1.4

Ranges and Nomo Graph:

Physical Property, Unit Lower Limit Upper Limit

Pb , Psia 130 7000 Temp , F 100 258 Rsb , SCF/STB 20 1425 API 16.5 63.8 γg ( air = 1.0 ) .59 .95

18

The Vasquez-Beggs Correlation:

In 1976, Vazquez and Beggs presented relationships for determining the solution GOR and

FVF of a gas saturated crude oil. In total, 6004 data points were used in the development of

these correlations. The data were separated into two groups because of variations in the

volatility of crude oil. The first group contained oils with gravities > 30 API, second group

contained oils with gravities < 30.

=

𝑅𝑠𝑏𝐶1∗𝛾𝑔∗𝑒𝑥𝑝 𝐶3∗𝐴𝑃𝐼 𝑇

1𝐶2

The gas gravity used to develop all the correlations reported by Vasquez and Beggs was that

which would result from a two-stage separation. The first-stage pressure was chosen as 100

psig and the second stage was the stock tank. If the known gas gravity resulted from a first-

stage separation at a pressure other than 100 psig, the corrected gas gravity to be used in the

correlations can be obtained from :

𝛾𝑔𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 = 𝛾𝑔 1.0 + 5.912𝐸 − 5 ∗ 𝐴𝑃𝐼 ∗ 𝑇𝑠𝑒𝑝 ∗ log(𝑃𝑠 114.7)

Ranges:

Physical Property, Unit Lower Limit Upper Limit

Pb , Psia 50 5250 Temp , F 70 295 Rsb , SCF/STB 20 2070 API 16 58 γg ( air = 1.0 ) .56 1.18

Constant API≼ 30 API≻ 30

C1 .0362 .0178 C2 1.0937 1.187 C3 25.724 23.931

19

Lasater:

Lasater presented a bubble point pressure correlation in 1958. A total of 158 experimentally

measured bubble point pressure from 137 independent crude oil system from Canada,

western and mid continental U.S. and south America was used in its development. The natural

gases associated with these crudes were essentially free of non hydrocarbon. Lasater used

Henry’s law to derive a Bubble Point Pressure Factor, BPPF.

Here is how to use Lasater correlation.

1) Find the effective molecular weight (Mo) as the following:

These data can be obtained graphically from chart in right.

2) Calculating the mole fraction of the gas in the system (Yg) :

Yg = 𝑅𝑠𝑏 379.3

𝑅𝑠𝑏 379.3 + 350∗ 𝛾𝑜 𝑀𝑜

3) Calculating Bubble Point Pressure Factor, Pb * Yg/TR , :

Or use chart in right to determine BPPF graphically :

4) Finally, Bubble Point Pressure = BPPF * (TR

γg)

Ranges:

Physical Properties From To

Pb , Psia 48 5780 Tf , F 82 272

API , API 17.9 51.1 Gas Gravity .574 1.223

Rsb , SCF/STB 3 2905

For API ≤ 40 Mo = 630 – 10 * API

Or if API > 40 Mo = 73110 * 𝐴𝑃𝐼−1.562

If API ≤ 60 BPPF = .679 * exp ( 2.786 * Yg ) - .323

Or if API > 60 BPPF = 8.26* Yg 3.56 + 1.95

20

Fig. 1 and Fig. 2 can be combined in a single nomograph to determine Bubble point Pressure.

Comparison of the accuracy with which the measured bubble point pressures used in each

correlation agreed with values determined from the final correlation shows that the Vasquez

and Beggs correlation is the most accurate, followed by Lasater and then by Standing.

Comparing in: Standing Lasater Vasquez-Beggs

No. of points in correlations 105 158 5008 Data points within 10% of correlation , % 87 87 85

Data points more than 200 psi in error 27 Mean error, % 4.8 3.8 - 0.7

21

Glaso correlation 1980:

In 1980, Glaso presented correlations for calculating bubble point pressure, oil FVF and total

FVF from known values of temperature, solution GOR, gas relative density and oil API gravity

as correlating parameters. A total of 45 oil samples, mostly from the North Sea region, were

used in obtaining the correlations. Glaso pointed out average relative errors of 1.28%, -0.43%,

and -4.56% for the bubble point pressure, the bubble point oil FVF and the total FVF

correlations, respectively. Parameters a, b and c are mentioned previously in note 3.

Pb= 10𝑥

X= 1.7669 + 1.7447 * log ( M ) – 0.30218 * log( 𝑀 ) 2

M = 𝑅𝑠𝑏 𝛾𝑔 𝑎∗ ( 𝑇𝐹)𝑏 ∗ ( 𝐴𝑃𝐼)𝑐

This nomograph is used to determine the bubble point pressure. Begin with GOR from most-

left side then directing to temperature vertical scale. This line intersects with the second

vertical line from the left. From this intersection point direct toward crude Oil Gravity, finally

extend this line to intersect the most-right vertical scale to read the value of bubble point

pressure.

22

Muhammad Ali Al-Marhoun (1988) :

The PVT analyses of 69 bottom hole fluid samples from 69 Middle East oil reservoirs were

made available for this study. The experimentally obtained data points were 160 each for the

bubble point pressure and bubble point oil FVF correlations, and 1,556 for the total FVF

correlation. The correlation for bubble point pressure, bubble point Oil FVF and two-phase

total FVF were developed by use of the linear and nonlinear multiple regression analyses.

Average Absolute Error of 3.66% is noted.

Pb= a * 𝑅𝑠𝑏𝑏 ∗ 𝛾𝑔

𝑐 ∗ 𝛾𝑜𝑑 ∗ 𝑇𝑒

a 5.38088E-3

b 0.715082 c -1.87784 d 3.1437 e 1.32657

Ranges:

Phyiscal Properties From To Bubble point pressure, Psia 130 3573

Pressure, psia 20 3573

Reservoir Temp. , F 74 240

Bubble point oil FVF, Res.BBl /STB 1032 1997

Total Formation FVF below Pb, Res.BBl/STB 1032 6982

Solution GOR , SCF/STB 26 1602

Average Gas Relative Density, air=1 .752 1.367

Stock Tank Oil Gravity, API 19.4 44.6

CO2 in Surface gases, mol% 0.00 16.38

Nitrogen in surface gases, mol% 0.00 3.89

H2S in surface gases, mol% 0.00 16.13

Statistical Accuracy of bubble point pressure correlation based on Al-Marhoun oil systems:

Al-Marhoun Standing Glaso

Average Relative error, % 0.03 6.6 17.76 Average absolute relative error, % 3.66 12.08 25.22

Minimum absolute relative error, % 10.4 48.89 79.52 Standard Deviation, % 4.536 16.020 29.983 Correlation coefficient 0.997 0.979 0.891

23

This study’s correlation has a mean almost equal to zero, while the peak height of the normal-

distribution curve for the Standing and Glaso correlations are at about 7 and 18% error.

24

Gas Solubility:

Standing :

He (1947) proposed a graphical correlation for determining the gas solubility as a function of

pressure, gas specific gravity, API gravity, and system temperature. The correlation was

developed from a total of 105 experimentally determined data points on 22 hydrocarbon

mixtures from California crude oils and natural gases. The proposed correlation has an

average of 4.8%. Standing (1981) expressed his proposed graphical correlation in the

following more convenient mathematical form:

Rs= 𝑃

18∗10𝑦𝑔 1.204

yg= .00091*Tf -.0125*API

Physical Property, Unit Lower Limit Upper Limit

Pb , Psia 130 7000 Temp , F 100 258

Rsb , SCF/STB 20 1425 API 16.5 63.8

γg ( air = 1.0 ) .59 .95

25

Glaso:

Glaso (1980) proposed a correlation for estimating the gas solubility as a function of the API

gravity, pressure, temperature, and gas specific gravity. The correlation was developed from

studying 45 North Sea crude oil samples. Glaso reported an average error of 1.28% with a

standard deviation of 6.98%.

X = 2.8869 – ( 14.1811 – 3.3093 * log ( P ) )0.5

M = 10X

Rs = 𝜸𝒈 𝑨𝑷𝑰𝟎.𝟗𝟖𝟗

(𝑻−𝟒𝟔𝟎)𝟎.𝟏𝟕𝟐 ∗ 𝑴 𝟏.𝟐𝟐𝟓𝟓

You can use Glaso’s nomograph , which is used to determine the bubble point pressure

previously , in the backward direction to determine the solubility at any pressure. Let’s see

how it’s done…

From the most-right line, begin with Pb value. Direct toward the second vertical line from the

left passing through API value. Finally, draw a straight line beginning from the reservoir

temperature directing to previous intersection point and extend it to the most-left line to

determine the solubility.

26

Lasater:

In 1958, Lasater presented his correlations for bubble point pressure and gas oil ratio. A total

of 158 samples from 137 independent crude oil systems from Canada, Western, Mid-

continental United States, and South America were used in their development. The natural

gases associated with these crudes were essentially free of non hydrocarbons. The data used

by Lasater in deriving his correlations ranged from heavy oils and tars to volatile oil.

1) Determine Mo as mentioned before:

2) Calculate Bubble Point pressure Factor:

BPPF = 𝑃∗ 𝛾𝑔

𝑇

3) To determine Yg :

If BPPF < 3.29 Yg =0 .359 * ln (𝟏.𝟒𝟕𝟑∗𝑷∗𝜸𝒈

𝑻+ 𝟎.𝟒𝟕𝟔)

Of if BPPf ≥ 3.29 Yg = 0.121∗𝑃∗𝛾𝑔

𝑇− 0.236

0.281

4) Finally,

Rs = 132755∗ 𝛾𝑜∗𝑌𝑔

𝑀𝑜 1−𝑌𝑔

Ranges:

Also Lasater nomograph that used to predict the Bubble point pressure can

be used in backward direction to predict the solubility at any pressure :

If API ≤ 40 Mo = 630 – 10 * API

Or if API > 40 Mo = 73110 * 𝐴𝑃𝐼−1.562

Physical Properties From To

Pb , Psia 48 5780 Tf , F 82 272

API , API 17.9 51.1 Gas Gravity .574 1.223

Rsb , SCF/STB 3 2905

27

Vasquez and Beggs:

Vasquez and Beggs (1980) presented an improved empirical correlation for estimating Rs. The

correlation was obtained by regression analysis using 5,008 measured gas solubility data

points. Based on oil gravity, the measured data were divided into two groups. This division

was made at a value of oil gravity of 30°API.

Rs = C1 * 𝛾𝑔 * PC2 * exp ( 𝐶3∗𝐴𝑃𝐼

𝑇)

Ranges:

Physical Property, Unit Lower Limit Upper Limit

Pb , Psia 50 5250 Temp , F 70 295

Rsb , SCF/STB 20 2070 API 16 58

γg ( air = 1.0 ) .56 1.18

Constant API ≤ 30 API > 30

C1 .0362 .0178 C2 1.0937 1.187 C3 25.724 23.931

28

References:

1) Some websites to determine the importance of DAK Model.

2) SPE Papers, their numbers are mentioned either on the

footnotes or within the text.

3) Gas Reservoir Engineering, John Lee, Robert and

A. Wattenbarger, SPE TextBook Series, VOL 5.

4) Petroleum Reservoir Rock and Fluid Properties, Abhijit Y.

Dandekar.

5) B. C. Craft and M. F. Hawkins, Louisiana State University, “

Applied Petroleum Reservoir Engineering”, 2nd edition.

6) Petroleum Engineering Handbook, Howard B. Bradley.

7) Ahmed, Tarek. “Hydrocarbon Phase Behavior”, Gulf Publishing

Co., 1989.

8) Donald L. Katz and Robert L. Lee, “ Natural Gas Enginnering ,

Production and Storage”, McGraw-Hill Chemical Engineering

Series, Page 127