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SPE/DOE

SPE/DOE Paper No. 17376

The Role of Asphaltene Deposition in EOR Gas Flooding: A Predictive Technique by Seido Kawanaka1, Sang Jin Park2, and G.Ali Mansoori, 3,* U. of Illinois at Chicago

This paper was submitted and appeared as (SPE/DOE 17376), Pages 617-627 inProceedings of SPE/DOE Enhanced Oil Recovery Symposium, held in Tulsa, Oklahoma, April 17-20, 1988.

Abstract It is well recognized that the existence of asphaltene in

crude oil can add significantly to the petroleum field problems. This may result in asphaltene deposition inside the reservoir which is likely to affect the efficiency and cost of petroleum production. In the present paper a molecular model is presented to predict the onset and amount of deposition of asphaltene from petroleum crudes under the influence of a miscible solvent. This model is based on the application of the theory of continuous mixtures and the theory of polymer-monomer solution. The theory of continuous mixtures is employed because of the fact that asphaltene consist of a large number of similar compounds with varying sizes and because of the simplification which it can produce in performing deposition calculations. The optimization parameters in the proposed model are specified using the available experimental titration data. The proposed model allows us to calculate the distributions of asphaltene in the solvent rich liquid phase, in the solid phase, and in the original petroleum crude. Furthermore, the proposed model is used successfully to predict the phase behavior and deposition region of asphaltene in CO

2-crude oil mixtures at different pressures,

temperatures and compositions of the injection fluid.

Introduction Asphaltene is defined as the normal-pentane-insoluble and benzene-soluble fraction whether it is derived from

petrstructure oleumo,f caoal, sphaltenesor oil ashrea lenot1 -

3• known.The On exactheat ing, chemictheyalare not melted, but decompose, forming carbon and

volatile products above 300-400 °c.

References and illustrations at end of paper

They react with sulfuric acid forming sulfonic acids, as might be expected on the basis of the polyaromatic structure of these components. The color of dissolved asphaltenes is deep red at very low concentration in benzene as 0.0003 percent makes the solution distinctly yellowish.

The devastating effect of asphaltene deposition in the economy of petroleum , processing and oil recovery techniques is well recognized. Asphaltene deposition

. during oil production and processing is a very serious problem in many areas throughout the world4-8. Thepresence of asphaltene in heavy petroleum crudes causes a number of severe technological problems. One such problem is the untimely precipitation of asphaltene in the petroleum reservoir, in the wells, tubings, pipelines, and in the refinery components. At the present mechanical and chemical cleaning methods are being improvised to maintain production, transportation, and processing of petroleum at or close to non-economical levels.

According to Long3 asphaltenes contain a broad distribution of polarities and molecular weights. The molecular weight of asphaltenes is very high. Published data for the molecular weight of petroleum asphaltenes range from approximately 500. to 500,000. The extensively wide range of asphaltene size distribution suggest that asphaltene is partly disolved and partly in colloidal state dispersed and stabilized primarily by resin molecules that are adsorbed on asphaltene surface9• The degree of dispersion of asphaltenes in petroleum oils depends upon the chemical composition of the petroleum. In heavy highly aromatic products the asphaltenes are well dispersed; but in the presence of an excess of petroleum ether and similar paraffinic hydrocarbons they are coagulated and then precipitate.

617

*SPE Member, Email addresses: 1. [email protected]; [email protected]; [email protected]

petroleum, coal, or oil shale 1 – 3. The exact chemical structure of asphaltenes are not known. On heating they are not melted, but decompose, forming carbon and

Preprint

The compounds which constitute complex petroleum crudes, coal liquids, and the like are mutually soluble so long as a certain ratio of each kind of molecule is maintained in the mixture. By introduction of a solvent into. the mixture this ratio is altered. Then the heavy and/or polar molecules separate from the mixture either in the form of another liquid phase or to a solid precipitate. Hydrogen bonding and the sulfur (and/or the nitrogen) containing segments of the separated molecules could start to aggregate (or polymerize) and as a result produce the irreversible asphaltene deposits which are insoluble in solvents. Development of predictive techniques of asphaltene deposition, which could describe the behavior of asphaltenes in hydrocarbon mixtures, calls for detailed analyzes of asphaltene containing systems from fundamental standpoints. One major question of interest in the oil industry is "when" and "how much" asphaltene will flocculate out under certain conditions. Since the heavy crude consists generally of a mixture of oil, aromatics, resins, and asphaltenes it has become possible to consider each of the constituents of this system as a continuous or discrete mixture interacting with each other as pseudo-pure-components10

. The theory o1 continuous mixtures, the statistical mechanical theory of monomer/polymer solutions, the concept of Hildebrand's solubility parameter, and the concept of psuedoization are utilized here to analyze and predict the onset and amount of asphaltene precipitation in petroleum crudes.

Since asphaltene particles have a wide range of size, or molecular weight, distribution one may consider asphaltene as a heterogeneous (polydispersed) polymer. Then, in order to predict the behavior of asphaltene one can assume that the properties of asphaltene fractions are dependent on their molecular weights. Such a treatment of asphaltene properties is initially proposed by Mansoori and Jiang 11

• In their proposed formulation, the Scott and Magat theory of polymer mixtures12•13 is employed, which is the statistical thermodynamic model of the mixture of solvents and heterogeneous (polydispersed) polymers.

The statistical mechanical theory of the mixtures of high polymer solutions was originally introduced by Meyer14

,

15

who employed the hypothetical lattice cells, one of which may be filled with either a segment of a polymer molecule or a solvent molecule, and discussed the theory qualitatively. Later, Flory16, 17 and Huggins18

independently developed the thermodynamic models of the lattice theory for homogeneous polymer solutions; i.e., the solution containing uniform polymer molecules in a solvent in which the partial molar entropies of mixing are obtained by utilizing the lattice theory. Furthermore, Flory applied his lattice theory to homogeneous chain polymer solutions and used the van Laar's rule for calculation of the heat of mixing . Then by combining the entropy and heat of mixing, he derived the expression of the partial molar free energy for the homogeneous polymer solutions. Later, Scott and Magat proposed a statistical mechanical method to drive expressions for partial molar free energies of heterogeneous polymer solutions. Their method is based on Huggins' theory, in which less restrictive assumptions

·are made than those in Flory's theory which makes theirmethod more general fo r hetero geneouspolymer-monomer solutions. For the heat of mixing, Scottand Magat utilized the Scatchard-Hildebrand formula.

In the present paper by using the Scott and Magat theory astatistical thermodynamic model is presented for thepredictions of the onset point and amount of asphaltenedeposited from petroleum crude under the influence ofmiscible solvents. In the proposed model, it is assumedthat asphaltene consists of very many kinds of similarpolymeric molecules so that a continuous distributionfunction for asphaltene can be employed. By using acontinuous gamma distribution function properties ofasphaltene are approximated with respect to themolecular weight. The adjustable parameters in this modelare optimized by employing the experimental titrationdata 19 of asphaltene deposition due to addition of normalparaffin hydrocarbons. In order to demonstrate theapplicability of the proposed model it is used to predict thehigh pressure phase behavior and the pressure versuscomposition region of asphaltene deposition · forCO

2-crude oil mixtures.

A PolydJspersed Polymer Model of Aspha1tene

The original attempt for the application of the polymertheory for the development of a model to predict theasphaltene deposition was made by Hirschberg, et al.19

• Intheir formation of the problem, they assumed asphaltene toconsist of a uniform (homogeneous) component ofpetroleum crude. Mansoori and Jiang 11 applied the Scottand Magat heterogeneous polymer theory in order toformulate a continuous mixture model to predict the onsetpoint and amount of asphaltene deposition from petroleumcrude oil. The basic technique used in the present report isthe continuous mixture model proposed by Mansoori andJiang.

In a heterogeneous polymer mixture, one can specifydifferent fractions of the polymer based on their molecularweights. Assuming that asphaltene behaves as aheterogeneous polymer, the Scott and Magat theory canbe used to calculate the chemical potential, µ

Ai' of the ith

fraction of asphaltene in a mixture of asphaltene and asolvent as

( JJ. A( JJ. Ai •)/RT =Q.n¢ Ai+1- (mp/<m

A>)(1- ¢8)- mAi¢8+ f mAi¢a2 (1)

Subscripts Ai and B refer to the ith fraction of asphalteneand the solvent, respectively, and superscript O stands fora standard state. The volume fraction, ¢, is defined by thevolume, V, of a component divided by the total volume,V mix• of a mixture. Therefore,

S. Kawanaka, S.J. Park, G.A. MansooriThe Role of Asphaltene Deposition in EOR Gas Flooding: A Predictive Technique

Proceed. SPE/DOE EOR Symp. (SPE/DOE 17376), Pages 617-627, 1988

618

The segment number of the ith fraction of asphaltene, mAi• is defined by the ratio of molar volume, v Ai• of the ith fraction of asphaltene over the molar volume, v8, of a solvent,

mAi = V Ai/vB = MA/(p Atassva),

where p Atass is the mass density of the ith fraction. The segment number of the solvent is unity. The mass density of the ith fraction of asphaltene is almost independent of the ith fraction molecular weight, MAi• due to the assumption of the uniformity of segments of asphaltene, and it is equal to the average mass density of asphaltene, <P mass>. As aresult

PAtass = <Pmass> and mAi = MA/(<Pmass> Vs)-

The average segment number, <mA>, of asphaltene may be defined by

<mA> = LXAimAi (2)

where xAi is the mole fraction of the ith fraction of

asphaltene with respect to the total asphaltene; i.e., 2'.xAi=1. Furthermore, the parameter f in Eq. (1) is defined by (see Appendix A) f = 1/r + V9{(6 A-69)2 + 2 KAa6 A6iJ / RT (3)

Where r is the coordination number between two successive segments in asphaltene molecules (r has a value 12 between 3 and 4), KAB _is the interaction parameter between asphaltene and asphaltene-free crude oil, 6 A is

the average solubility parameter of asphaltene, and 68 isthe solubility parameter of asphaltene-free crude. It is

assumed that the molecular interaction parameter, KAB• between asphaltene and asphaltene-free oil is linearlyproportional to the average molecular weight ofasphaltene-free oil, <M8>:

KAs = a+ b <Ms>

where a and b are constant. Solubility parameter 6 is

defined by the square root of the molar internal energychange of vaporization, Liuvap, over the molar volume;

6 = (.L\uvap/v)112 (4)

The reason for formulating Eq.(3) with respect to averagesolubility parameter of asphaltene is to be able to use the available (average) experimental solubility data19 ofasphaltene in the present model.

concentration of asphaltene in a solution. This

corresponds to the concentration of asphaltene in asolution in equilibrium with the asphaltene _content of a precipitated phase.

Phase Egujljbrium Calculation

To perform phase equilibrium calculation one needs to equate chemical potentials of every asphaltene fraction in the liquid phase, µ L Ai• and the solid phase, µ 8 Ai;

, ,S L . . 1 2 ""'Ai=J.J. Ai• I= , , ... (5)

Provided Eq.(1) is valid for every fraction of asphaltene inthe liquid and solid phases Eq.(5) will take the followingform; Q.n ¢SAi + 1 - (mSAf<mSA>)(1-¢ss) -mSAi ¢SB

+ fS mS Ai (¢ss)2 = Q.n ¢L

Ai + 1 - (mLAf<mLA>)(1-¢Ls)- ml Ai ¢Ls+ fl mLAi (¢Ls)2 (6)

In Eq.(6) it is assumed that the molar volumes of the ith

fraction of asphaltene in both phases are identical; vs Ai=vLAi=v Ai• Furthermore, since vS

8=v L8=v

8, then

m8Ai=mLAi=mAi· Now if we assume that the solid phase is

free of the solvent, i.e., ¢ss=0, Eq.(6) will take the followingform;

¢LA/ ¢SAi = exp(mAi e)

where

(7)

e = (1/<mLA>-1/<mSA>) + (1-1/<mLA>) ¢Ls - fl (¢Ls)2 (8)

Eq.(7), in conjunction with a continuous distribution function for asphaltene, can be used for calculation of the total volume fraction of asphaltene in a liquid mixture in equilibrium with an solid phase.

Continuous Model of Asphaltene

To calculate the total volume fraction of asphaltene in a liquid mixture in equilibrium with an solid phase we needto assume a molecular weight distribution function for thecontinuous asphaltene components. The molecularweight distribution function of asphaltene can be definedas follows

F(MAi) = (1/NA) (dnAi /dMAi)

where 00

J F(MAi) dMAi = 1 0

(9)

MAi is the molecular weight of the ith fraction of asphaltene, By using the above equations and the principle of _phase I dnAi is the differential of the number of moles of the ith

equilibria, one can derive an expression for calculating the

619



fraction of asphaltene whose molecular weight is in the range of MAI to MAi+dMAi• and NA

is the total number of moles of asphaltene.

The expression for the average segment numbers of asphaltene in a given phase, Eq.(2), can be defined by using the continuous distribution function of asphaltene as

the following. 00

<mA> = f mAi F(MA1) dMAi (1 O) 0

Upon partial deposition of asphaltene from a petroleum crude due to the introduction of a miscible solvent there will be two phases (one liquid and one solid) formed. As a result of the mass balance for the ith fraction of asphaltene between the original crude oil (C), solid phase (S), and solvent-rich liquid phase (L) one can write

dnc Ai= dns

Ai + dnL Ai

fC(MAi)NCA = fS(MAi)NS

A + fL(MAi)NLA

where

(11)

(12)

dncA,= vcd¢c

A/vAi• dns

Ai. vsd¢sA/v

Ai• dnLA1= VLd¢L

A/vAi•

ye = vs + yL; ye A= w

A, -rl <Pmass>

vc, vs and vL are the total volumes of the crude oil, solid phase, and the liquid phase, respectively, w

A,T is the total weight of asphaltene in the crude oil, and <P mass> is the mass average density of asphaltene.

Eq.(7), which is valid for a given fraction of asphaltene, can be written in the following differential form when considering a differential fraction of asphaltene in the context of its continuous model

d¢L Ai /d¢s

Ai= exp(mAie) (13)

By joining Eqs.(9), (11 ), (12), and (13) the following expressions can be derived;

fL(MA1) = [VLt{VL + vs exp(- mAie)}] (NCA-'NLA) fC(MAi) (14)

and

fS{MA1) = [VS/{VL exp{m

Aie) + vs}] {Nc.A-'NSA) fC{MAi) {15)

00 00

Since J fL(MAi) dMAi = 1 and J fS(MAi) dMAi = 1 ,

0 0

then by rearranging Eqs.(14) and (15) one can get

00

NCA/NL

A = 1 / J [VL/{VL+yS exp(-mAie)}] fC(MAi) dMAi (16) 0

and 00

NfA/NS

A = 1 / J [vs1{VL exp(mAie) +VS}] fC(MAi) dMAi (17)

0

Provided the asphaltene distribution functions are available Eqs.{16) and {17) can be used for calculation of total numbers of moles of asphaltene in the separated solid, Ns

A • and liquid, NLA, phases. Also by substituting

Eqs.(14) or {15) into Eq.(10), the expression of the average segment numbers, <mL

A> or <ms A>, in a phase can be

obtained.

By utilizing Eqs.(9), (11 ), (12), and (13) the total volume fraction of asphaltene in the liquid phase, ¢ L

A • in equilibrium with the solid phase can be derived in the following form:

¢LA= I d¢L

Ai =

00

J [{MAfM-A) yF

A/{VL + ys exp(-mAie)}] F{MA1) dMAi (18) 0

All the terms in the above equation are already defined except for ye

A which is the total volume of asphaltene in the crude oil {Vc

A=Vc-¢L6vL). Using Eq.(18), the onset of asphaltene deposition from a petroleum crude and the amount of asphaltene in a liquid mixture in equilibrium with a solid phase can be calculated. Appendix B describes the special case19 when the asphaltene is considered to consist of a homogeneous compound.

ca1cu1at100 and P1scuss100

Knowing the total volume fraction of asphaltene in the liquid phase, ¢ L

A• as given by Eq.(18) the amount of asphaltene in the liquid phase in equilibrium with the solid phase will be equal to p

A¢LA vL. Therefore, the amount of asphaltene d�posited will be given by

wA,o=WA,T - P

A¢LA yL (19)

where w A,T is the total amount of asphaltene in the crude

oil. Since the amount of asphaltene precipitated at the onset of deposition is zero then the total amount of asphaltene, w

A T• can be calculated by knowing the . '

asphaltene composition of the liquid phase at the onset,

WA,T= Pi¢LAVL)onset_

620



To proceed with the calculation the continuous molecular weight distribution function of asphaltene is represented by the gamma distribution function:

F(MAi) = [(MAi-MAo)°'-1/ r(0<) f3°'] exp[- (MArMAo> /f3] (20)

where

0< = (<MA> - MAo)2tn., f3 = n/(<MA>-MAo), and00

r(0<) = J t°'-1exp(-t)dt

and MAo• <MA>, and n. are the initial value, mean value,

and the variance of gamma distribution function, respectively. The choice of gamma function is rather arbitrary and other equally versatile distribution functions can also be used.

In order to illustrate the application of the proposed model for the asphaltene deposition predictions the data of a tank oil (oil no.1 sample 1 of Ref. 19) is used. The data related to this tank oil is shown in Table 1. In the present calculation it is assumed that hexanes and heptane-plus, both, are pseudocomponents. Their properties are calculated based on their average molecular weights20

-

22

and they are reported in Table 2. The Benedict-Webb-Rubin (BWR) equation of state, along with the Lee-Kesler correlation24, is used for calculation of molar volumes and solubility parameters of asphaltene free oils.

There are four adjustable parameters (a, b, wA,T and n.) in

the proposed model which are to be determined at this stage. These parameters are calculated by minimizing the differences between the experimental titration data of n-pentane and n-decane 19 and the present predictivemodel. Results of the calculations for these parametersare reported in Table 3. The experimental titration data forn-heptane was not used in this calculation· since it seemsnot to conform with the other titration data as it was alsodemonstrated in an earlier publication9•

Using the calculated adjustable parameters in the model, the onsets and the amounts of asphaltene depositions are predicted and they are compared with the experimental data in Table 4. According to this table all the onsets and amounts of deposition data (except for n-heptane case) are in good agreement with the experimental data. Figure 1 consists of the predictions of onsets and amounts of asphaltene deposition versus volumes of different n-paraffin solvents added to the tank oil. According to thisfigure the trend of the deposition predictions for differentn-paraffins are consistent with their molecular weights.This indicates that the amount of asphaltene deposited forthe same volume of n-paraffin solvent added to the tank oildecreases as the n-paraffin molecule gets bigger. Thisobservation is reported in Figure 2 along with the availableexperimental data.

In Figure 3 and 4, the predicted distribution functions of asphaltenes in the original petroleum crude oil (tank oil no. 1) , solid phase, and the liquid phase, are plotted withrespect to the molecular weight in which 5 cc and 20 cc,respectively, of n-heptane added to the tank oil. The molardistribution of asphaltene in the original petroleum crude is·expressed by gamma distribution function [Eq.(20)]. The molar 'distribution of asphaltene in the liquid phase or in the solid phase are defined by NL

AFL(MAi) or NS AF5(MAj),

respectively. According to Figure 3 and 4 the fractions of asphaltene with higher molecular weights tend to deposite sooner than the lower molecular weight fractions. In Figures 5 and 6 the molar distributions of precipitated asphaitenes and remaining asphaltenes in the solvent rich liquid phase of different n-paraffins as miscible solvents are reported along with the distribution of asphaltene in the original petroleum crude (tank oil no.1 ). According to Figures 3 and 4 the distribution of the precipitated asphaltene tends towards the original crude oil distribution as the amount of the added miscible solvent increases. According to Figures 5 the distribution of the precipitated asphaltene tends towards the original crude oil distribution as the molecular weight of the added miscible solvent decreases. The trend of the distributions of the remaining asphaltene in the liquid phase as reported in Figure 6 are opposite to that of the solid phase. Based on these figures the proposed continuous model suggest that the nature of asphaltenes in the solvent rich liquid phase and in the precipitated solid phase due to different solvents are not all the same. This prediction is consistent with the experimental observation of different investigators as to the variations in the nature of asphaltenes which are precipitated due to the introduction of different miscible solvents in a crude oil3,7,29•

In order to demonstrate the applicability of the proposed model for prediction of the pressure/composition region of asphaltene deposition at high pressures under the influence of a miscible gas (carbon dioxide in the present example) the phase behavior (vapor-liquid-solid equilibria) of tank oil no. 1 in contact with carbon dioxide at different

· pressures and at 24° C is predicted and it is reported byFigures 7 and 8. Figure 8 consists of an expanded scale ofthe region of Figure 7 where the asphaltene precipitationoccurs. In this calculation it is assumed that there is noasphaltene in the gas phase, and that there is no effect byasphaltene content of the liquid phase on the vapor-liquidequilibrium of CO

2-oil system. A flash calculation28 for CO

2

- asphaltene free oil was performed in order to compute thecomposition of the liquid phase leaving the flash tank.Then the present model is applied to the mixture ofasphaltene and the liquid phase leaving the flash tank. InFigure 8, the dashed area is the predicted region ofasphaltene deposition from tank oil no.1. According to thisfigure the asphaltene deposition starts to occur in a regionwhere mole fraction of CO

2 entering the flash tank is about

0.984. In these calculations every gram of tank oil wasassumed to be prediluted with 0.98 cm3 of n-decane beforeinjecting CO2 to the system. For less than 0.98 cm3

n-decane predilutions the model did not predict any

621



precipitation consistent wi th the experimental observations19

. In Figure 9, the pressure dependence of asphaltene precipitation in a mixture of CO2 a n d

Subscripts

A asphaltene asphaltene free oil are reported. According to this Figure, I Ai the amount of asphaltene deposited decreases as pressure increases. The trend of asphaltene depositions I AO at different pressures is consistent with experimental observation 19

. B The proposed model is applicable, in general, for I Cpredicting organic deposition (asphaltene, resin, and wax) from petroleum crude oils under the influence of a miscible solvent at various temperatures, pressures, and compositions. In general it may be necessary to use a multi-parameter concentration distribution funct_ion to account for various families of precipitating heavy organic compounds in the crude.

the ith fraction of asphaltene with respect to molecular weight initial value of the continuous distribution function of asphaltene mixture of asphaltene free crude oil and solvent critical property

Nomenclature

f parameter defined in Eq.(3) F distribution function of asphaltene with respect to

the molecular weight K interaction parameter M molecular weight m

N R r

T ..1.uvap

V

V

segment number total mole number gas constant the coordination number between two successive segmentsin asphaltene molecules temperature molar internal energy change of vaporization total volume molar volume

Notation

<> Average property over the continuous distribution function of asphaltene

Acknowledgements

This research is supported by the National Science Foundation Grant CBT-8706655. The authors would like to thank Dr. L. N. J. de Jong and Dr. A. R. D. van Bergen of Koninklijke/Shell Exploratie en Produktie Laboratorium for helpful experimental data and information.

References

1.

2.

Boduszynski, M. M.: Asphalteoes io Petroleum

Asphalts in The Advances in Chemistry Series, 195, (1981)119.

Speight, J. G., Moschopedis, S. C.: "On the molecular Nature of Petroleum Asphaltene," in Chemistry of Asphaltene, Bunger, J. W. and Li, N. C. (Editors), American Chemical Society, Wash. D. C., (1981)1.

WA,T total weight of asphaltene in the petroleum crude 1 3_oil

Long, R. B.: The Concept of Asphaltene in The Advances in Chemistry Series, No. 195, (1981 )17.

WA,D weight amount of asphaltene deposited from petroleum crude oil

Greek Letters

O<

J3

6

n.

p

¢

(A)

parameter in gamma distribution function parameter in gamma distribution function solubility parameter

variance of the gamma distribution function density volume fraction

acentric factor

Superscripts

L solvent rich liquid phase S solid phase C original petroleum crude oil 0 a standard state

4. Lichaa, P. M. and Herrera, L.: "Electrical and OtherEffects Related to the Formation and Prevention ofAsphaltenes Deposition," Society of petroleumEngineers Journal, paper# 5304 (1975).

5. Katz, D. L. and Beu, K. E.: "Nature of AsphalticSubstances," l&EC 37, (1945)195.

6. Preckshot, G. W., Dehisle, N. G., Cottrell, C. E. andKatz, D. L.: "Asphaltic Substances in Crude Oils,"Transactions, American Institute of Mining,Metallurgical, and Petroleum Engineers 151,(1943)188.

7. David, A.: "Asphaltenes Flocculation During SolventSimulation of Heavy Oils," American Institute ofChemical Engineers, Symposium Series 69, no. 127,(1973) 56.

8. Leontaritis, K. J., Mansoori, G. A. and Jiang, T. S.:"Asphaltene Deposition in Oil Recovery: A Survey ofField Experiences and Research Approaches,"CAPAMA 86 Proceedings (1986 International

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Conference on Advanced Technology), Northern I 22. Edmister, W. C.: Pet. Refiner, 37(4), (1958) 173 .Illinois University, De Kalb, IL, (April, 1986).

9. Leontaritis, K. J. and Mansoori, G. A.: "Asphaltenefloccuiation During Oil Recovery and Processing: AThermodynamic-Colloidal Model," SPE Paper#16258,Proceedings of the 1987 SPE Symposium onOil Field Chemistry, Society of Petroleum Engineers,Richardson, TX (1987).

10. Du, P. C. and Mansoori, G. A.: "Phase EquilibriumComputational Algorithms of Continuous Mixtures,"Fluid Phase Equilibria, 30, p.57 (1986); ibid, SPEPapers #15082 and 15953, Society of PetroleumEngineers, Richardson, TX (1986).

11. Mansoori, G. A. and Jiang, T. S.: "Asphaltene Deposition and its Role in Enhanced Oil Recovery Miscible Gas Flooding," Proceedings of the the 3rd European Conference on Enhanced Oil Recovery, Rome, Italy, April (1985).

12. Scott, R. L. and Magat, M.: "The Thermodynamics ofHigh-Polymer solutions: I. The Solubility and Fractionof a Polymer of Heterogeneous Distribution", J. Chem.Phys., 13(5), (1945)172.

13. Scott, R. L.: "The Thermodynamics of High-Polymersolutions: II. TheSolubility and Fraction of a Polymer ofHeterogeneous Distribution", J.Chem. Phys., 13(5),(1945)178 .

14. Meyer, K. H.: Zeits. F. Physik. Chemie, B44,(1939)383.

15. Meyer, K. H.: Helv. Chim. Acta, 23, (1940)1063.

16. Flory, P. J.: "Thermodynamics of High PolymerSolutions", J. Chem. Phys., 12, (1942) 51.

17. Flory, P. J.: "Thermodynamics of HeterogeneousPolymers and Their Solutions", J. Chem. Phys.,12(11),(1944)425.

18. Huggins, M.: "Some Properties of Solutions ofLong-Chain Compounds", J. Phys. Chem., 46,(1942)151.

19. Hirschberg, A., de Jong, L. N. J., Schipper, B. A. andMeijer, J. G.: "Influence of Temperature and Pressureon Asphaltene flocculation", Soc. Pet. Eng. J., 24(3),(1984)283 .

20. Katz, D. L. and Firoozabadi, A.: "Predicting PhaseBehavior of Condensate/Crude-Oil Systems UsingMethane Interaction Coefficients", J. Pet. Tech., Nov.,(1978)1649 .

23. van Bergen, A. R .D. and de Jong, L. N. J.: PrivateCommunication, Koninklijke/Shell Exploratie enProduktie Laboratorium, 4/4/1986.

24. Lee, B. I. and Kesler, M. G.: "A GeneralizedThermodynamic Corre l a t ion B a sed onThree-Parameter Corresponding States", AIChE J.,21(3),(1975)510.

26. Kwak, T. Y. and Mansoori, G. A.: "van der WaalsMixing Rules for Cubic Equations of State," Chem.Eng. Sci., 41, (1986)1303.

27. Placker, U., Knapp, H. and Prausnitz, J.: "Calculationof High-Pressure Vapor-Liquid Equilibria from a

Corresponding-State Correlation with Emphasis onAsymmetric Mixtures", Ind. Eng. Chem. Process Des.Dev., 17, (1978)3.

28. Bergman, D. F., Tek, M. R. and Katz, D. L.: "RetrogradeCondensation in Natural Gas Pipelines", MonographSeries, American Gas Association, New York City(1975).

29. Leontaritis, K.J. and Mansoori, G. A.: "Use of HighPerformance Liquid Chromatography and GelPermeation Chromatography for Chracterization ofResins and Asphaltenes", submitted to Energy andFuel Journal, (1987)

Appendix A: Derivation of Eq.(3)

Expression for f, as given by Eq.(3), is more general than the expression originally proposed by Scott and Magat12 , f=1/r+Kv8(6 A-6 8)2/RT. In order to derive Eq.(3) we may start with the van der Waals equation of state for mixtures.

p = RT/(vmix -bmix) - ami/v2mix

�ix = Li Lj xi xi aij

; bmix = Li Lj xi xi bij

(A-1)

The reason for the choice of the van der Waals equation of state is its simplicity and the fact that van der Waals mixing rules for amix and bmix are quite accurate26. Since for thevan der Waals equation of state

(du/av)r= T (dP/dT)v - P = amiJv2

mix

then 00

Auvap = J (amiJv2mix) dv = ami/vmix

V

(A-2)

(A-3)

21. Cavett, R. H.: "P�y�ical �-at� ..

for Distillation I Therefore the solubility parameter is given byCalculations; Vaper-L1qu1d Equ1hbna , Proc. 27th API Meeting, San Francisco, (1962)351.

623



6 = (AuV8Pfv)112 = amix 112/Vmix (A-4)

where Auvap is the internal energy change of vaporization. The combining rule for parameter a11 is

811 = (1- k11> (au8i?12 (A-5)

where a11 is the energy parameter of pure component i. The interaction parameter k11=0 for i=j and and it is nonzerowhen i.cj. By combining Eq's (A-1)-(A-5) and using the volume fraction ¢1=xivi/vmix one can get

62 mix = Li Li xi x1 (1-ki1) (a1a1)

112/v= L14 <1-ki1> ¢1¢16161 (A-6)

It can be also shown that the molar excess internal energy change of mixing is

AumixE = - Aum1/ap + L1 x, Autap = - vmlx Li Li

(1-ki1) ¢1¢16 16 1 + vmix Li ¢16? (A-7)

By assuming that the molar excess volume change of mixing is zero at constant pressure the excess enthalpy change of mixing is given as

AH mil= (L1 n1)(Aumix E - A(Pv)mil) = (L1 n1) Aum1l (A-8)

and the partial molar excess enthalpy change of mixing for component i as

v9, [ L 1 L1 (1-k11) ¢1¢16 161 - 2 L i

(1-k19,) ¢16 ;0 9, + 6 /] (A-9)

For a binary system, the partial molar excess enthalpy change of mixing for component B can be reduced as

Ah·sE = Vs ¢ l [{6A-6B)2 + 2 KAB6A6B] (A-10)

According to the Scott and Magat theory parameter fl consist of two terms: A term (1/r) resulting from entropy of mixing and a term [Ah·8

E/(RT¢ l)l resulting from the heat of mixing

fl = 1/r +Ah·8E / ( RT ¢l ) (A-11)

By substituting Eq.(A-10) into Eq. (A-11 ), the expression of fl, Eq.(3), can be derived.

Appendix B: Special Case of a Homogeneous Asphaltene Model

When asphaltene is considered as a single (homogeneous) compound the segment numbers are all identical (<mA>=<mLA>=<m5A>=mA), the molecular weight is equal to the average molecular weight (MA=<MA>), and

the distribution function is F(MA1)=60(MAr<MA>) where 60 is Dirac delta function (60=oo when MA1=<MA> and 60=0 when MA1.c<MA>). Then, Eq.(17), the total volume fraction, of asphaltene in the liquid phase in equilibrium with the solid phase, will reduce to the following expression;

¢LA = exp[(mK1) ¢LB - mA fl (¢Ls>2 1

where

¢LB = 1 - ¢LA

(8-1)

(8-2)

Furthermore, the term 1/r in Eq.(3) disappears for the case of a homogeneous chain polymer of uniform molecular weight in a single uniform solvent. By setting KA8=0 and removing the 1/r term in Eq.(3) and after some manipulations, the total volume fraction of asphaltene in the liquid phase in equilibrium with the solid phase for ahomogeneous model can be obtained as follows 19.

¢LA = exp[ -1 + V p/Vmix - VA (6 A - 6mix)2/RT] (8-3)

where 6mix is defined as the solubility parameter of crude oil mixture 6mix=¢LA 6A+ ¢Ls68•

624



Table1. Data of the tank oil no.1 under study

The compositions of the tank oil19

Compound

Methane Ethane Propane i-butanen-butane 1-pentane n-pentane Hexanes Heptane-plus

mole %

0.10 0.48 2.05 0.88 3.16 1.93 2.58 4.32

84.50

Average molecular weight of tank oi119

Specific gravity of tank 01119

Average mass density of asphaltene23 (g/cm3) Average molecular weight of asphaltene23

Initial molecular weight of asphaltene3

Coordination number <if asphaltene12

221.5 0.873 1.2

4800.0 500.0 (assumed value)

3.5 (assumed value)

The solubility parameter (6A

) of asphaltene19 [MPa0•5] 6A = 20.04 (1 - 1.07 x1 o-a T), T Is in °c

Table 2. Properties of C6 AND c7• pseudocomponents

Critical temperature (°K) Bubble point temperature (°K) Molecular weight

. Critical pressure (aim) Acentric factor Density (glee)

506.6 337.0

84.0 32.3

0.281 0.685

771.2 585.0 249.9 16.7

0.639 0.868

Table 3. Parameters In the model

Interaction parameter KAB = -7.8109 x10·3 +3.8852x10-s <M8> Total amount of asphaltene (wt% of tank oil) wA.T = 4.0234 Variance of the distribution function I'\ = 4.9223 x106

The above parameters are calculated py minimizing the differences between the experimental titration data of n-pentane and n-decane 19 and the present predictive model.

Table 4. The experiment vs. prediction for the onset and amount of asphaltene deposition from the tank oil

Dilution Ratio n-Cs n-C7 n-C10 (cm3 dlluent/g tank oil)

EXP8 CALa EXP CAL EXP CAL

1.35 O.F 1.40 O.F O.F 1.90 N.-r' O.P' 2.22 O.F

5 3.31 1.53 1.52 · 1.34 1.30

10 3.61 3.67 1.82 2.28 1.45 1.53

20 3.79 3.75 1.89 2.43 1.50 1.45

50 3.87 3.73 1.87 2.29 1.13

The experimental titration data (wt% tank oil) are taken from the Ref.19. a; EXP, experimental values; CAL, calculated values . b; N.T denote that Onset of asphaltene deposition Is not determined. c; O.F denote the Onset of Flocculation.

625



bo

�

"' "'

f-< M :a::

DO w ....,.,, (J") Du, (L • w

N

D Wo z ,WN

..... __J �LI? (L -(J") a: L... 0 D..: ..... z :::,u, 0 .:c 0 a:

ci b-.0

/,·· ' ,,, ,::t�···· ,,

f

n-C7

! •••••••••••••••••••••••••• "-

: ;:-·-·-·-· ········)l '1t:-t .. er- - --Il_ -·-·-;:;_-;:;,··=.-:.:::...·::::..:::.·. --�

. o-~..,,,~-

�--....__ n-Cg_.,.,.. --

------

.

: . . . .

. . . .

n-� --

10,0 20,0 30.0 VOLUME OP SOLVENT ADDED .ICCl

40.0 50,0

Fig, 1-The prediction of the amount of asphaHene deposftion from tank 011 No, 1 vs. the volume of alx different n-paraffln sofvents. The experimental asphahene deposltk>n data (Ref. 19) due to n-pentane, n-heptane, and n-decane oddltlons are shown by A, D, 0. respectively.

bo

� ...... ------------------------------,-o �.: :a::

"' D..; w ..... -0 (fl . Or-> (L w Du, w" z �� -.JN a:, I (L"' (fl . a: -L... oq ..... -z =>.,, D .:c 0 a:

D

II D

D D

• D

ci+----.------,--,---..----..... ----.------,---� 3,0 1,0 5,0 6.0 7.0 8,0

CARBON NUMBER OP SOLVENT ADDED

9.0 10,0

Flg. 2-Ettect of n-,paraffln sotvent chaJn length on the amount of asphaftene deposfflon, The volume of all the n-paralfln solvents added Is 10.0 cc. Experimental data {Ref, 19) are shown by ■ and the predictions are-edby □.

'oo x�.....---------------------� i��------------------------� 'i':si:-.------------

0

�

z 8� I-< N ::,-(I) ;::;::: ..... (fl Do D:'..; a: 5 :,::

0

..

Asphaltene in Solid Phase

ci I t .,,..-:: · - .... ., ::::;:-------.. f 0.0 2,0 4.0 6.0 8.0 10.0 12,0

MOLECULAR WEIGHT OP ASPHALTENE

11.0 �10'

Fig. 3-RelatJons between molar concentration distributions of asphaltene In different phases In equlllbrtum resulting from the addition of a given amount of the mlsclble solvent (S.0 cc n-heptane) to 1 gram of the tank oU,

0

�

z Do � .I-< N :::, -(I] D:'. ..... CJ") D

0

o::.; 5 0 :c

q ..

Asphaltene in Liquid Phase

ci I t <" .... , r :::;:---- I

0.0 2.0 4.0 6.0 8.0 10.0 12.0 MOLECULAR WEIGHT OP ASPHALTENE

11.0 *10

3

Fig. 4-Retatlons between molar concentration distributions of asphahene In dtfferent phases In equlllbrtum resuhing from the addition of a given amount of the mlsclbJe solvent (20,0 cc n-heptane) to 1 gram of the tank oil.

0

�

z 8� I-< N ::, ~ (I) D:'. ..... (/) Do D:'..; a: __J D :c

q ..

Asphaltene in Tank Oil

� 1 / .� .,r- .,,-=;::::::--,-,i

0.0 2.0 4,0 6.0 8.0 10.0 12.0 MOLECULAR WEIGHT OP ASPHALTENE

11.0 *10

3

Fig, 5-Compartson of molar concentration distributions of asphattene In the solid phase for the dtfferent preclpttating solvents. The v�ume of all preclpttaUng solvents added Is 10.0 cc.

626



0

0 w

z Do �N ::,-CD

0:: I-<(f)

oo

0:: .a: a, ...J 0 :,::

0

.... . . . � . ...

Asphaltene·in Tank Oil

o-1--....L. _____ .,..:!.L,-_._..,::::::,.+-::::,..-. ___ ..:;::==-I 0.0 2.0 4.0 6.0 8.0 10,0 12.0

MOLECULAR WEIGHT OF ASPHRLTENE

14,0 �10'

Fig. &-Comparison of motar concentration distributions of asphaltene In the llqukl phase for dtfferent precipitating solvents. The volume of all preclpttatlng solvents added Is 1 o cc,

�-.-----------------------------,

a:

(f)

0 0 0 "'

0 0

�

!'.:; 0

w8 g§� (f) (f) w 0:: CL

�

§

0

§

0 LV LVS

§-1-------"'-..-------,---------,,---------l98.0 ll!M- 98,5 99.0 99.5 100.0

MOLE PERCENT CO2

Fig, 8-Phase diagram for mixtures of oll and carbon dtoxkie, This flgures Is the expanded sea� ve .... on of Fig. 7 In the regions where asphaltene depostUon occurs. Region L Is the homogeneous llquld phase area, LV Is the Hquld-vapor phase equlllbrlum area, LS Is the llqulckoUd (asphattene) phase equlllbrium area, and LVS Is the llqukl-vapor-soUd (asphaHene) phase equlllbrium area, AsphaHene pt'edpHatlon occurs In the LS and LVS areas.

0

0

8-.---------------...-----------. .... Kl

w 0:: :::, (l)O (f) • w8o::o o..~

L

L

LV

0

o..i,,::;__,-----,---,-----,---T"""---r--..----,.--�-'""'

o,o 10.0 20,0 3□,o 10.0 so.□ 6□.o 7□.o 8□.o 9□.o 100.0 MOLE PERCENT CO2

Fig. 7-Phase diagram for mixtures of oll and carbon dioxide. Region L Is the homogeneous liq• uld phase area and LV Is the liquid-vapor phase equlllbrium area. Asphattene preelpltatlon occurs Inside the dashed area.

.. -.--------------------------------,

Onset of Deposition

�+--------,JL::✓:.....-----,-------,--...::>---.-----_; 55,D 60.0 65,0 70,0

PRESSURE !BAR)

75.0 80.0

Fig, 9-Pressure dependence of the amount of asphaltene deposition for a given mixture of oil and carbon dioxide with known composition (Xco2

=0.99).

627



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