paper ADE.pdf

Petroleum Science and Technology, 25:949965, 2007

Copyright Taylor & Francis Group, LLC

ISSN: 1091-6466 print/1532-2459 online

DOI: 10.1080/10916460500526981

Empirical Equations for Estimating ADE

of Crude Oils

M. A. Fahim

Chemical Engineering Department, Kuwait University, Safat, Kuwait

Abstract: There has been an increasing interest in the construction of asphaltene

deposition envelope (ADE) to determine a safe zone of operation during oil pro-

duction. Equations of state are usually used for calculations of ADE; however, the

method requires tuning some experimental Pressure Volume Temperature (PVT) data

of the reservoir fluid. The objective of this study is to develop a simple, accurate,

and reliable empirical equation for estimating the ADE by determining the upper

and lower onset pressures as well as the saturation pressures. Three simple empiri-

cal equations are developed to calculate these onset pressures of several crude oils.

Experimentally measured compositions, saturation, and onset pressures of 33 crude

oil samples, primarily from the Middle East, at different temperatures were used to

develop the equations. Another set of compositions and upper saturation and lower

onset pressures of different crude oil samples from the literature were used to test the

accuracy of the empirical equations. The results were also compared with equations of

state predictions. The results indicate that the method is accurate, valid, reliable, and

eliminates the splitting and characterizing of the heavy fraction, which is necessary

for the equations of state predictions. The method is useful for estimating the ADE

of crude oils where experimental data is not available.

Keywords: asphaltene, deposition, emperical, envelope

INTRODUCTION

The formation of asphaltene is a flow assurance problem experienced by a

large number of operators. It can be caused be thermodynamic considerations

such as pressure and temperature changes. It can also be caused by compo-

sitional changes during production. For example, it can be caused during

CO2 or gas injection operations. Gas breakthrough can cause it as well. The

stability of oils under reservoir conditions can be studied by construction of

Address correspondence to M. A. Fahim, Kuwait University, Department of

Chemical Engineering, P.O. Box 5969, Safat, Kuwait. E-mail: [email protected]

949

950 M. A. Fahim

what is called the asphaltene deposition envelope (ADE). A key evaluation in

asphaltene formation and stabilization in the determination of the pressure/

temperature phase envelope of asphaltene flocculation onset (ADE) will be

studied in this work.

Several previous attempts have been made to model asphaltene deposi-

tion with varying degrees of success. The colloidal method of Leontaritis was

used to calculate asphaltene flocculation conditions for CO2 C oil mixtures

but only at one temperature. Both Hirschberg et al. (1984), Chung (1992),

and Burke et al. (1990) have treated asphaltene as a pure liquid phase in

equilibrium with a solvent using the Flory-Huggins polymer solution the-

ory. The modeling of the temperature and pressure dependence of asphaltene

deposition, using an equation of state for vapor-liquid equilibrium, was rea-

sonably successful. Chung (1992) also used a simple regular solution theory

approach for solid asphaltene liquid equilibrium and was able to fit solubility

data for asphaltene in various solvents at ambient conditions, but this method

seems unlikely in giving good results under typical reservoir conditions. His

regressed asphaltene molar volume is an order of magnitude smaller than

Hirschbergs and seems suspect as the specific gravity of asphaltene is un-

acceptably high. Finally, Kawanaka et al. (1991) used a similar approach

to Hirschberg but with a continuous mixture for the asphaltene phase, and

obtained good agreement with solvent titration experiments and correct qual-

itative behavior at reservoir pressures.

Hirschbergs model appeared to be a good starting point but was not eas-

ily incorporated into multi-flash as it treats asphaltene-liquid equilibrium sep-

arately from vapor-liquid equilibrium, which is physically unrealistic. There-

fore, the approach chosen was to treat asphaltene as a solid phase in equi-

librium with the reservoir fluid, which was used with an equation of state.

Multi-flash can handle either a pure solid phase or a solid mixture. Although

in reality an asphaltene deposit is a complex mixture, given the lack of ex-

perimental data on asphaltene compositions, it was decided to treat it as a

pure solid pseudo component phase in the examples investigated to date.

DATA COLLECTION

The input data required to build the method are:

a compositional analysis of the reservoir fluid C7C molecular weight and gravity the amount of asphaltene and resin in the oil reservoir temperature.

A total of 33 samples of different crudes were collected from literature

and used. The following parameters should be available: compositional anal-

yses, C7C density and molecular weight, reservoir temperature, asphaltene,

Empirical Equation for ADE 951

and resin weight percentage. These parameters were used to calculate upper

and lower onset pressure and saturation pressure and constructing ADE. The

compositional data collected and onset experimental pressures and satutation

are shown in Table 1 (Fahim and Andersen, 2005).

EQUATION DEVELOPMENT

The molecular weight and specific gravity of the heptane plus-fraction are

used as an input variable distinguishing the plus-fraction. The density and

molecular weight of the total plus-fraction is important in the proposed

method because it reflects the paraflinic-naphthenic-aromatic (PNA) content

of the plus-fraction. A large density indicates a high content of aromatic com-

pounds and a low density indicates a high content of paraffinic and naphthenic

content. Extending the plus-fraction into C10 might increase the accuracy of

the proposed method. However, it would reduce its simplicity. No distinction

is made between iso-paraffins and normal paraffins for two reasons: first,

concentrations of these hydrocarbons are usually very small when compared

with methane and heptane plus-fraction, and second, the simulation results

have indicated minor change in the estimated pressure when iso and normal

are lumped as a single component. A similar treatment has been used by

Elsharkawy (2003) in predicting the saturation pressure by EOS.

The objective function in this case is:

P D f.H2S;N2;CO2;C1;C2; : : : ;C7C; C7C;MWC7C; aspht%;Resin%;T/

(1)

where P is the calculated pressures (upper, saturation, and lower) of the

crude oil sample. The objective is to minimize the average relative error

(ARE) between measured (P) and estimated pressure for all the experimen-

tally measured samples in this study. The average relative error is defined

as:

ARE D

X

.P Pcalc/=Pcalc

=n (2)

Multiple regression and error minimization resulted in the following em-

pirical equations.

For the upper onset pressure the following equation is obtained:

Ponsu D 4:3243H2SC 2:6047

N2 C 0:6890CO2 C 0:6503

C1

C 0:9273C2 C 0:0086C3 3:981

C4 0:5878C5 C 0:1817

C6

0:0811CC7 0:1305MWCC7 C 210:89

CC7 C 0:908Asph

0:2003Resin 0:8988TC 0:001T2 C 12:4148LN.T/ (3)

with r2 D 0:992.

Table 1. Crudes that were used in generation of ADE methods

Sample

no.

Mole%

H2S

Mole%

N2

Mole%

CO2

Mole%

C1

Mole%

C2

Mole%

C3

Mole%

C4

Mole%

C5

Mole%

C6

Mole%

C7

C7C

MW

C7C

Asph.

Wt%

Resin

Wt%

T,

K

Upper

press.,

MPa

Sat.

press.,

MPa

Lower

press.,

MPa

1 0.000 0.000 0.830 40.690 11.630 7.150 3.540 2.860 2.410 30.870 0.930 217.0 1.240 4.6 386 65.0 27.4 14.0

2 0.000 0.570 2.460 36.370 3.470 4.050 1.930 1.570 1.620 47.960 0.959 329.0 15.800 8.3 373 35.6 20.1 12.0

3 0.000 0.970 0.200 27.550 7.430 9.020 6.140 4.160 3.160 41.390 0.856 217.9 1.200 7.3 365 20.1 12.9 9.7

4 0.050 0.090 1.020 42.410 10.780 6.920 4.460 3.290 2.860 28.110 0.853 209.0 0.550 7.3 322 65.5 17.6 8.2

5 0.370 0.090 1.220 23.990 10.140 8.390 5.330 4.390 4.690 42.190 0.874 245.5 0.900 7.0 386 27.4 12.6 6.9

6 0.000 0.800 0.050 51.020 8.090 6.020 3.970 3.210 2.670 24.170 0.875 368.9 4.600 7.6 361 36.4 29.4 26.4

7 0.013 0.070 0.910 43.080 10.690 6.860 4.400 3.230 2.810 27.940 0.846 205.2 0.260 7.4 384 42.7 21.8 12.7

8 0.000 0.480 0.920 43.430 11.020 6.550 4.490 3.530 2.700 26.880 0.865 228.1 1.300 7.0 389 42.9 23.1 13.5

9 0.000 0.480 0.920 43.430 11.020 6.550 4.490 3.530 2.700 26.880 0.865 228.1 1.300 7.0 313 52.0 22.2 12.3

10 0.000 0.480 0.920 43.430 11.020 6.550 4.490 3.530 2.700 26.880 0.865 228.1 1.300 7.0 354 44.0 22.6 13.0

11 0.000 0.480 0.920 43.430 11.020 6.550 4.490 3.530 2.700 26.880 0.865 228.1 1.300 7.0 414 42.0 22.7 13.5

12 0.000 0.510 1.420 6.040 7.000 6.860 4.180 4.160 3.160 66.680 0.902 281.0 7.800 7.5 377 20.8

13 3.220 0.490 11.370 27.360 9.410 6.700 3.980 3.200 1.980 32.290 0.877 248.8 1.400 10.4 361 37.2 17.0 10.7

14 3.220 0.490 11.370 27.360 9.410 6.700 3.980 3.200 1.980 32.290 0.877 248.8 1.400 10.4 383 27.9 18.4 18.8

15 3.220 0.490 11.370 27.360 9.410 6.700 3.980 3.200 1.980 32.290 0.877 248.8 1.400 10.4 400 25.2 19.7 16.1

16 3.220 0.490 11.370 27.360 9.410 6.700 3.980 3.200 1.980 32.290 0.877 248.8 1.400 10.4 422 26.2 20.8 20.3

17 0.000 0.480 0.920 43.430 11.020 6.550 3.490 3.530 2.700 26.880 0.865 228.1 1.300 18.8 372 46.6 21.9

18 0.000 0.480 0.920 43.430 11.020 6.550 3.490 3.530 2.700 26.880 0.865 228.1 1.300 18.8 377 44.8 22.3

19 0.000 0.480 0.920 43.430 11.020 6.550 3.490 3.530 2.700 26.880 0.865 228.1 1.300 18.8 383 43.7 22.3

20 0.000 0.480 0.920 43.430 11.020 6.550 3.490 3.530 2.700 26.880 0.865 228.1 1.300 18.8 389 42.2 22.4 13.3

21 0.000 0.800 0.050 51.020 8.090 6.020 3.970 3.210 2.670 24.170 0.875 368.9 4.600 13.5 361 36.1 29.0 26.1

22 0.000 0.210 2.560 25.200 7.080 5.560 6.200 4.920 3.940 43.330 0.832 208.7 0.940 4.6 328 26.2 10.8

23 0.000 0.210 2.560 25.200 7.080 5.560 6.200 4.920 3.940 43.330 0.832 208.7 0.940 4.6 394 8.4

24 0.000 0.310 3.020 44.290 6.360 4.880 4.620 3.710 2.890 29.920 0.833 213.1 0.490 6.4 328 33.0 23.4

25 0.000 0.310 3.020 44.290 6.360 4.880 4.620 3.710 2.890 29.920 0.833 213.1 0.490 6.4 394 20.3

26 1.510 0.690 2.000 29.770 14.400 9.460 5.300 3.950 4.020 29.450 0.860 230.3 1.500 2.1 383 26.2 17.2 13.0

27 0.370 0.090 1.220 23.990 10.140 8.390 5.330 4.390 4.690 41.390 0.874 245.5 3.300 2.3 386 27.2 11.8

28 0.050 0.090 1.020 42.410 10.780 6.920 4.470 3.290 2.860 28.110 0.852 209.5 0.500 11.3 322 59.9 17.6 9.5

39 0.050 0.090 1.020 42.410 10.780 6.920 4.470 3.290 2.860 28.110 0.852 209.5 0.500 11.3 339 53.5 19.7 8.8

30 0.050 0.090 1.020 42.410 10.780 6.920 4.470 3.290 2.860 28.110 0.852 209.5 0.500 11.3 355 49.6 20.4 9.5

31 0.050 0.090 1.020 42.410 10.780 6.920 4.470 3.290 2.860 28.110 0.852 209.5 0.500 11.3 372 46.8 21.3 10.6

32 0.050 0.090 1.020 42.410 10.780 6.920 4.470 3.290 2.860 28.110 0.852 209.5 0.500 11.3 389 49.1 22.4 10.5

33 0.050 0.090 1.020 42.410 10.780 6.920 4.470 3.290 2.860 28.110 0.852 209.5 0.500 11.3 425 40.5 23.4 11.9

Experimental values not available.

952


For the saturation pressure the following equation is obtained:

Psat D 1:1107H2SC 1:5585N2 C 0:5764

CO2 C 0:469C1 C 0:0751

C2

C 0:7932C3 0:314C4 0:303

C5 C 0:763C6 0:0217

CC7

0:0284MWCC7 20:41CC7 C 0:011

Asph

0:025ResinC 0:0296T (4)

with r2 D 0:996:

For the lower onset pressure the following equation is obtained:

PonsL D 7:115H2S 17:603

N2 6:706CO2 4:842

C1 C 8:098C2

11:931C3 0:600C4 2:477

C5 37:166C6 C 0:201

CC7

C 0:569MWCC7 571:4:3CC7 2:422

Asph 0:052Resin

0:333TC 139:32LN.T/ (5)

with r2 D 0:992:

In all equations, P is the pressure in MPa, T is the reservoir temperature

in K, composition analysis of (N2;CO2;H2S;C1, :C6;CC

7 ) is in the mole

percent, MWC7C is the molecular weight of the heptane plus, andCC7 is

the specific gravity of the heptane plus fraction and Asph% and Resin% is the

weight percent of asphaltene and resin in the crude. It is important that the

summation of mole percentages of all components forming the hydrocarbon

must be equal to 100%. The degree of fitness of these equations are shown

in Figure 1. The range of variables used to develop Eqs. (3)(5) are given in

Table 2.

Estimation of Resin Content

Resin is a very important factor in asphaltene precipitation since it precipitates

simultaneously with asphaltene and its quantity should be known, but in

many cases resin content is not available for crude oil. A correlation has

been developed to estimate resin content of any crude by knowing asphaltene

Table 2. Summary of error analysis for the proposed empirical method

Upper pressure Saturation pressure Lower pressure

ARE 0.20 0.20 0.98

AAE 3.3 2.94 5.83

R2 0.992 0.996 0.991

954 M. A. Fahim

Figure 1. Comparison of experimental pressure and calculated pressure from empir-

ical equations: (a) upper pressure, (b) saturation pressure, (c) lower pressure.

content, sulphure content, and American Petroleum Institute (API) gravity of

crude oil. A total of 37 different crudes (with known resin contents) were

used (Speight, 1993) to generate the proposed correlation. The objective is

to minimize the ARE between measured resin wt% and estimated resin wt%

for all the experimentally measured samples in this study. Multiple regression

and error minimization resulted in the following empirical equations:

Resin wt% D 0:326375asph wt% 0:12388Oil wt%

C 6:089721S wt%C 0:493571API (6)

with r2 D 0:92:

It can be observed that properties used in this equation are measured at

ambient conditions, and we first assume that the resin and asphaltene % in

Eq. (6) will have the same values at high pressures. Resin and asphaltene that

precipitated on depressurizing redissolve at pressures lower than the saturation

pressures and that assumption might be justified.


COMPARISON WITH EQUATION OF STATE MODEL

The proposed model is compared with an equation of state model (EOS) and

with experimental data to show the accuracy of the proposed model.

The Soave-Redlich Kwong equation of state (SRK-EOS) is under consid-

eration in this work because it is commonly used by the petroleum industry

for predicting phase behavior and volumetric properties of hydrocarbon reser-

voir fluid mixtures. The equation is given by:

P DRT

V b

a

V.V C b/(7)

where P is the pressure, V is the molar volume, T is the absolute temperature,

and R is the universal gas constant.

This equation can predict the upper, saturation, and lower pressures and

vapor/liquid equilibrium calculations. For saturation pressure, it has reason-

able accuracy if the heptane plus-fraction of the hydrocarbon fluids is properly

characterized (Jhaveri and Youngren, 1988), but it has significant deviation

in predicting the upper and lower pressures.

The ADE is determined by performing flashes at varying pressures for

a number of temperatures. Flash calculations using a small pressure step

are used to locate the precipitation onset pressures. These calculated onset

pressures taken together define the asphaltene precipitation envelope.

TUNING OF EOS

It is important to know that when EOS is used to predict ADE (upper, sat-

uration, and lower pressures), it shows good results for saturation pressure

while the upper and lower pressure have a large deviation from experimental

values (maximum deviation for upper pressure was 165% and for lower pres-

sure 126%, while saturation pressure was 20%). The ranges of variables used

in this work are given in Table 3. To tune EOS, experimental onset pressures

at given temperatures were used. Then the critical properties (mainly critical

temperature and pressure) of the crude oils were changed. This will help in

adjusting the calculated values of upper and lower pressure by EOS. Table 4

and Figures 2 and 3 show the importance of tuning the EOS in the calculation

of upper and lower pressure.

Table 3. Ranges of variables used in the developing proposed empirical method

%,

H2S

%,

N2

%,

CO2

%,

C1

%,

C2

%,

C3

%,

C4

%,

C5

%,

C6

%,

C7

,

C7C

MW,

C7C

W%,

Asph

W%,

resin

Res,

T(K)

Min 0 0 0.05 6.04 3.47 4.05 1.93 1.57 1.62 24.17 0.832 205.2 0.26 2.08 322

Max 3.22 0.97 11.37 51.02 14.4 9.46 6.2 4.92 4.69 73.56 0.959 368.9 15.8 18.8 433

Table 4. Comparison of untuned and tuned EOS in predicting ADE with empirical method versus corresponding experimental values

Upper ADE Saturation Lower ADE

No. Exp

Empirical

method

EOS

not tuned

EOS

tuned data

EOS

tuned model Exp

Empirical

method

EOS

not tuned

EOS

tuned data

EOS

tuned model Exp

Empirical

method

EOS

not tuned

EOS

tuned data

EOS

tuned model

1 65.0 64.8 * 65.1 64.9 27.4 26.9 27.3 27.1 26.6 4.0 4.0 * 3.7 3.7

2 35.7 35.3 73.9 35.6 35.2 27.3 27.4 24.4 26.1 26.2 23.1 23.2 9.3 21.7 21.8

3 20.1 20.2 * 20.7 20.8 12.9 12.9 12.6 12.3 12.3 9.7 9.7 * 8.9 8.9

4 47.6 45.6 30.0 46.2 44.2 17.6 25.3 24.9 24.5 32.2 8.3 9.8 12.7 11.1 12.6

5 27.4 27.5 30.0 27.5 27.6 12.6 11.4 12.1 12.1 10.9 6.9 6.8 5.3 6.1 6

6 36.4 36.8 43.0 36.6 37 29.4 31.1 32.0 32.6 34.3 26.4 26.3 9.6 30.3 30.2

7 42.7 46.8 24.5 42.8 46.9 21.8 22.8 22.6 21.4 22.4 12.7 11.7 19.5 12.3 11.3

8 42.9 44.3 41.6 43.0 44.4 23.1 22.5 24.2 24.5 23.9 13.5 13.2 16.0 15.8 15.5

9 47.3 46.1 42.5 47.3 46.1 22.2 22.0 23.2 23.5 23.3 12.3 12.8 15.2 13.5 14

10 45.4 45.5 42.2 45.5 45.6 22.6 22.2 23.7 23.9 23.5 13.0 13.0 15.3 14.2 14.2

11 44.3 44.8 42.0 44.6 45.1 22.7 22.3 24.0 24.2 23.8 13.5 13.1 15.7 14.9 14.5

12 20.8 21.3 17.8 21.1 21.6 9.5 9.8 9.7 5.3 8.2 8

13 37.2 32.1 30.3 34.9 29.8 17.0 18.2 17.1 17.1 18.3 10.7 15.8 11.7 10.1 15.2

14 27.9 29.2 30.4 29.5 30.8 18.4 18.9 18.7 18.8 19.3 18.8 16.8 14.3 16.0 14

15 25.2 27.9 30.7 26.9 29.6 19.7 19.4 20.0 19.9 19.6 16.1 16.5 13.2 13.5 13.9

16 26.2 27.0 31.3 24.9 25.7 20.8 20.2 21.1 21.2 20.6 20.3 16.8 15.3 18.8 15.3

17 46.6 45.3 42.3 46.6 45.3 21.9 22.1 23.5 23.6 23.8 12.9 15.8 13.1

18 44.8 44.7 42.0 45.3 45.2 22.3 22.3 23.8 23.9 23.9 13.1 15.9 13.4

19 43.7 44.0 41.6 43.9 44.2 22.3 22.5 24.1 24.2 24.4 13.2 16.1 13.5

20 42.2 43.5 41.7 42.4 43.7 22.4 22.7 24.5 24.5 24.8 13.3 13.4 16.2 15.8 15.9

21 36.1 35.4 95.8 36.2 35.5 29.0 27.2 31.2 32.6 30.8 26.1 26.3 9.7 30.6 30.8

22 26.2 25.1 21.2 26.6 25.5 10.8 10.9 12.1 11.4 11.5 7.7 8.9 8

23 12.3 10.4 12.4 8.4 8.7 8.8 8.7 9 4.1 6.1 4.3

24 35.5 37.2 32.1 35.7 37.4 23.4 22.6 22.0 22.0 21.2 16.2 18.9 16

25 27.2 23.6 27 20.3 20.4 18.4 18.0 18.1 12.5 14.6 12.8

26 26.2 26.2 26.0 26.0 26 17.2 17.1 17.0 17.0 16.9 13.0 13.0 12.2 12.2 12.7

27 27.2 28.8 31.7 31.7 27.7 11.8 12.3 12.0 12.0 12.1 6.8 7.8 6.6

28 59.9 60.6 27.9 58.0 58.8 17.6 19.6 17.5 17.5 19.5 9.5 7.2 6.5 6.9 6.9

39 53.5 54.3 26.2 53.7 53.9 19.7 20.2 18.8 18.8 19.5 8.8 9.1 15.9 8.5 8.9

30 49.6 50.2 26.0 49.7 49.8 20.4 20.7 19.9 20.0 20.4 9.5 10.3 17.2 9.8 11.0

31 46.8 47.5 26.2 46.8 47.2 21.3 21.2 21.2 21.1 21.4 10.6 11.1 18.6 11.0 10.9

32 49.1 45.7 25.1 49.1 46.1 22.4 21.8 22.0 21.9 21.6 10.5 11.5 20.5 10.7 11.1

33 40.5 44.0 27.8 43.5 40.5 23.4 23.0 23.4 23.2 23.5 11.9 11.6 20.3 14.2 11.9

Experimental values not available.No convergence.

956


Figure 2. ADE comparison of proposed method with experimental, tuned, and un-

tuned EOS (Crude 28).

Figure 3. ADE comparison of proposed method with experimental, tuned, and un-

tuned EOS (Crude 9).

958 M. A. Fahim

The heaviest component can be divided into two componentsone is

nonprecipitating and the other is precipitating based on the weight of asphal-

tene in the crude. The mole fraction of asphaltene can be calculated according

to the following:

Zasph D Wt%asph Moil=MWasph: (8)

The asphaltene properties TC and PC are then tuned to satisfy the precipi-

tation condition. Values of P and f a can be found from extrapolation to 0

mole % precipitation.

RESULTS AND DISCUSSION

The accuracy of the empirical method is compared with the experimental

values reported from literature and with EOS (SRK). The statistical results

of various crude oils for the empirical method are shown in Table 2. This

table reports the average relative error (ARE) and the average absolute error

(AAE) for the 33 crude oil samples that were used to derive the equations. The

proposed method has the smallest errors for the measured saturation pressures

of the Middle East crudes that were used to develop the method. The current

method has the advantage of being simple and accurate, eliminating the need

for splitting the heptane plus-fraction.

It is important to know that as the number of points used to tune the

EOS increase, the accuracy of estimating ADE pressure increases. A sample

crude was taken and a different number of tuning points were used and shows

that with three points of tuning it gave ARE D 2.36 and the AAE D 6.52,

while using four points of tuning gave ARE D 2.75 and AAR D 4.69, and

using five points of tuning gave ARE D 0.031 and the AAE D 3.24. The

error analysis for EOS prediction is given in Tables 5 and 6.

A total of five samples of different crudes at different temperatures were

used for testing the proposed empirical equations (Table 7). Also three differ-

ent crude samples were used to test the effect of gas injection and were com-

pared with experimental values as shown in Table 8. The error analysis results

for crudes tested in Table 7 are shown in Table 9. Also an ADE for two differ-

ent crudes was generated by the proposed equations and compared with exper-

imental and tuned and untuned EOS as shown in Figures 2 and 3. As shown

Table 5. Summary of error analysis for ADE pressures calculated by

untuned EOS compared with experimental

Upper pressure

untuned EOS

Saturation pressure

untuned EOS

Lower pressure

untuned EOS

ARE 9.40 1.66 17.44

AAE 30.40 5.00 45.88


Table 6. Summary of error analysis for ADE pressures calculated by

tuned EOS compared with experimental

Upper pressure

tuned EOS

Saturation pressure

tuned EOS

Lower pressure

tuned EOS

ARE 0.60 1.44 0.49

AAE 1.70 4.66 11.90

in the figures, the proposed and tuned EOS are very close to experimental

data while the untuned EOS has a large deviation from experimental points.

Effect of Crude Properties and Composition on ADE

With many parameters such as gas injection, the changing of asphaltene

content has been studied and the effects of each one on ADE have been

studied. The crude oil stability increases as the asphaltene content increases.

Experience has shown that heavy precipitation of asphaltene occurs with

crude of low asphaltene content as in Hasi Masoud wells. The effect of initial

asphaltene content on ADE is predicted and compared with experimental data

as shown in Figure 4.

Figure 4. Effect of asphaltene mole% on ADE (Crude 28).

Table 7. Crudes used for testing the empirical method

No.

%,

H2S

%,

N2

%,

CO2

%,

C1

%,

C2

%,

C3

%,

C4

%,

C5

%,

C6

%,

C7

,

C7C

MW,

C7C

W%,

Asph

W%,

resin

Res,

T(K)

34 1.900 0.090 2.110 29.500 13.710 9.310 5.320 4.030 4.150 29.880 0.832 209.8 0.500 1.050 397.1

35 0.099 0.317 0.830 27.800 9.560 8.000 5.170 4.070 4.410 39.740 0.846 223.2 0.900 1.530 391.6

36 0.014 0.065 0.920 44.221 10.902 7.217 4.427 3.072 2.554 26.608 0.853 215.9 0.500 0.860 390.4

37 0.013 0.173 0.841 40.054 10.346 7.046 4.608 5.237 3.025 30.413 0.846 204.8 0.500 6.000 392.1

38 0.013 0.070 0.914 43.079 10.689 6.861 4.396 3.233 2.814 27.931 0.845 204.1 0.400 7.900 388.8

39 0.050 0.090 1.020 42.410 10.780 6.920 4.470 3.290 2.860 28.110 0.852 209.5 0.500 11.300 432.7

Table 8. Crudes used for testing the empirical method for gas injection

No.

%,

H2S

%,

N2

%,

CO2

%,

C1

%,

C2

%,

C3

%,

C4

%,

C5

%,

C6

%,

C7

,

C7C

MW,

C7C

W%,

Asph

Res,

T(K)

16 3.220 0.490 11.370 27.360 9.410 6.700 3.980 3.200 1.980 32.290 0.877 248.8 1.400 400

40 0.01 0.32 2.29 17.6 5.25 6.14 6.63 5.84 5.00 50.92 0.852 210 1.00 389

41 0.00 0.16 0.14 77.44 3.95 2.56 1.78 1.32 0.94 11.71 0.86 233.6 8.3 342

960


Table 9. Error analysis for crude used to test the empirical method

Pupper, Bar Psat, Bar Plower, Bar

No. Exp Calc Exp Calc Exp Calc

34 25.9 26.0 16.2 16.3 10.8 10.8

35 23.1 21.3 13.5 14.2 9.0 9.1

36 55.1 55.1

37 51.7 51.3 20.8 20.9 8.0 8.0

38 52.4 46.8 23.8 22.6 12.2 12.5

39 44.1 44.0 23.6 23.0 12.0 11.5

ARE 3.18 ARE 0.42 ARE 0.43

AAE 3.40 AAE 2.64 AAE 2.43

Table 10. Properties of injected gases

No.

%,

H2S

%,

N2

%,

CO2

%,

C1

%,

C2

%,

C3

%,

iC4

%,

nC4

%,

iC5

%,

nC5

%,

C6

%,

C7 MW

1 0.03 0.59 5.03 65.76 11.32 8.58 2.16 3.62 1.24 1.14 0.51 0.03 25.6

2 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 28.0

3 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 44.0

4 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 44.0

The upper onset pressure equation was used to investigate the effect of

injection of different gases such as scrubber gas (CO2) and H2S;N2;C3, and

natural gas. A list of gases used is given in Table 10. The results of the

injection of nitrogen, gas 1, and C3 on the upper part of ADE and saturation

pressure are shown in Figures 5, 6, and 7. In these figures the prediction by

the corresponding equation and EOS is also shown.

It is important to note that EOS can be tuned using the onset point

generated in this work, and consequently, it can be used to determine the

percentage of asphaltene precipitated. Figure 8 shows the effect of CO2 in-

jection on asphaltene precipitation obtained by EOS tuned by a proposed

model compared to experiential values.

CONCLUSIONS

The empirical methods that have been proposed to estimate upper, saturation,

and lower pressure of ADE for any crude oil have several advantages over the

equation of state. It is simple and gives an approximate estimation for ADE and

eliminates the need for splitting and characterizing the heptane plus-fraction.

962 M. A. Fahim

Figure 5. Effect of N2 injection on upper onset pressure and saturation pressures

calculated from a proposed model versus experimental (Crude 16).

Figure 6. Effect of gas (gas 1) injection on upper onset pressure and saturation

pressures calculated from a proposed model versus experimental (Crude 40).


Figure 7. Effect of C3 injection on saturation pressures calculated from a proposed

model versus experimental.

Figure 8. Effect of CO2 injection on asphaltene precipitation. Comparison of exper-

imental with EOS tuned with model (Crude 2).

964 M. A. Fahim

The proposed methods were tested with different crude oils and were also

tested against EOS and the result was satisfactory. The EOS has a large

deviation compared to the proposed method and experimental values and

tuning of the EOS is very important and will improve it. Injection of different

gasses also showed that the model gave a satisfactory result compared to the

EOS that requires splitting of C7C into different subtractions.

ACKNOWLEDGMENT

M. A. Fahim would like to thank Kuwait University for granting him a sab-

batical year (2002/2003), where he spent a portion of it at Denmark Technical

University.

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NOMENCLATURE

Dimensionless factor

Dimensionless factor

L Fugacity coefficient liquid phase

V Fugacity coefficient in vapor phase

Density

! Acentric factor

a First parameter in EOS

b Second parameter in EOS

f L Fugacity in liquid phase

f V Fugacity in vapor phase

K Equilibrium coefficient

MW Molecular weight

n Number of components

P Pressure

Pc Critical pressure

R Gas constant

r2 Correlation coefficient

T Temperature

Tc Critical temperature

V Molar volume

w Weight fraction

x Mole fraction in liquid phase

y Mole fraction in gas phase

z Mole fraction in feed

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