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RESEARCH PAPER

Prediction of asphaltene precipitation during CO2 injection Huang Lei1,*, Shen Pingping1, Jia Ying2, Ye Jigen1, Li Shi1, Bie Aifang1 1. PetroChina Research Institute of Petroleum Exploration & Development, Beijing 100083, China; 2. Sinopec Exploration & Production Research Institute, Beijing 100083, China

Abstract: Aimed at the possible phenomenon of asphaltene precipitation during CO2 injection, the equation of state established by Anderko was introduced to describe the phase behavior of precipitated asphaltene because of its strong polarity. The fugacity of the precipitated asphaltene component was derived and a calculation model of gas-liquid-asphaltene equilibrium was constructed. After matching of PVT experimental data from a reservoir, the model was used to calculate the volume of precipitated asphaltene during CO2 injection. The precipitation model suggests that for a constant injection pressure, the asphaltene precipitation first increases and then decreases as CO2 increases with the asphaltene precipitation reaching a maximum when the gas phase occurs in the system. When the CO2 mole percentage of the CO2-oil system is constant, the precipitated asphaltene reaches a maximum at the saturation pressure. Key words: CO2 flooding; asphaltene precipitation; fugacity calculation; phase behavior simulation; phase equilibrium calculation

Introduction Carbon dioxide flooding is regarded as one of the most efficient oil development methods because carbon dioxide can enhance oil recovery significantly by swelling oil, decreasing viscosity of crude oil, and reducing interfacial tension between the displacing phase and displaced phase. Thus, research on the theories and methods of utilizing carbon dioxide injection has been developing rapidly in China and abroad recently. However, carbon dioxide injection for enhancing oil recovery may trigger asphaltene precipitation because of the interaction between injected gas and heavy components in oil. Oil production indicates that asphaltene deposits caused by gas injection may heavily damage the reservoir and negatively influence production, which has been observed in many domestic and oversea oilfields[1–4]. Thus, construction of a phase prediction model that can accurately predict asphaltene precipitation has its practical value for carbon dioxide flooding plan design, to avoid or reduce the adverse effects of precipitated asphaltene on oil production. In this paper, the method proposed by Nghiem L X, et al.[5] is used to represent the asphaltene components in oil. The compression factor of compounds put forward by Anderko[6] is introduced to describe the non-ideal behavior of precipitated asphaltene based on its strong polarity. Also considered are the self-associated characteristics of precipitated asphal-

tene inter-molecule behavior and the fugacity of precipitated asphaltene derived from thermodynamics. The equation of state (AEOS), is used to construct a gas-liquid-asphaltene phase equilibrium calculation model during gas injection. Furthermore, numeric solving methods for the model mentioned above are discussed in detail. Finally, asphaltene precipitation change during carbon dioxide injection is predicted using the model and the results are shown to be in agreement with experimental observations.

1 Determination of thermodynamic parameters for precipitated asphaltene during carbon dioxide injection When a mixed system reaches thermodynamic equilibrium at given pressure and temperature, the chemical potential of each component throughout all the co-existing phases is equal. However, it is difficult to calculate the chemical potential of each component directly, so the chemical potential is usually related to some measurable physical quantity, which can be realized by introducing an auxiliary thermodynamic function of fugacity to express the chemical potential. The requirement of equal chemical potential of each component is then transformed into equal fugacity for each component as phase equilibrium is achieved for a given mixture system. The fugacity can be calculated through the equation of state, whose pre-requisite is to determine thermodynamic parameters of each component.

Received date: 28 Feb. 2008; Revised date: 18 Mar. 2010. * Corresponding author. E-mail: [email protected] Foundation item: Supported by National Science and Technology Major Project, China (2008ZX05016) and National “973” Project, China (2006CB705800). Copyright © 2010, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.

Huang Lei et al. / Petroleum Exploration and Development, 2010, 37(3): 349–353

During gas injection, precipitated asphaltene is composed of strongly polar and strong non-ideal molecules, which results in a liquid-like solid precipitation with strong viscosity under reservoir conditions. Thus, the compression factor of the association compounds established by Anderko[6] is introduced to describe the non-ideal nature of precipitated asphaltene, based on which the fugacity of precipitated asphaltene component in precipitation phase is derived. 1.1 Definition of the compression factor for precipitated asphaltene The thermodynamic properties of the association compounds are the result of equilibrium between association and inter-molecular forces according to the AEOS model. The association compound is treated as an approximate molecular aggregation with an association reaction. Based on the compression factor formula of the association compound constructed by Anderko[6], the compression factor of precipitated asphaltene association reaction is: ZS=ZA+ZF–1 (1) The contribution of intermolecular forces to the compression factor, ZF, can be calculated with a normal equation of state directly. In this paper, it is calculated through a three-parameter Peng-Robinson EOS[7, 8]. The mechanism for the contribution of association to the compression factor of the entire compound is still not clear. In this paper, based on a dimer association mode, the association rule of dimers is extended to the precipitated asphaltene. The self-association only happens between asphaltene components while other components do not contribute to the compression factor affected by the association, ZA. The contribution of the association to the compression factor can be obtained through a thermodynamic derivation: 2 ZA (2) 1 1 4 RTK aa / V

Where, Kaa is a tunable parameter. 1.2

Fugacity determination of precipitated asphaltene

Many experimental studies indicate that 90% of precipitated asphaltene in stock oil is composed of C30—C60, so the heaviest component, C30+, in oil analysis data is used to represent the asphaltene component. The heaviest component, C30+, is split into a non-precipitation component (C30B+) and a precipitation component (C30P+). We assume that the precipitated asphaltene component is composed only of precipitation component (C30P+). According to the expression for fugacity of pure components, the fugacity of the precipitated component in asphaltene is derived from equation (1) as: f ln p

ln I

ln

V ZA V 4 RTK aa V

Z 2

A

1 ªV V 2 4 RTK V º aa » ¼ 2 RTK aa ¬«

B

ZF 1 2 B A 2 ZF ln 2 2 B Z F 1 2 B 1 1 4 RTK aa / V

§ · 2 ln ¨ Z F 1¸ ln 4 1 ¨ 1 1 4 RTK / V ¸ aa © ¹ Where

A

ap

RT

2

B

(3)

bp RT 2

ª § T ·0.5 º ½° R 2Tc2 ° RTc 0.457 235 ®1 m «1 ¨ ¸ » ¾ b 0.077 796 pc pc ° « © Tc ¹ » ° ¬ ¼¿ ¯

a

°m 0.374 64 1.542 26Z 0.269 92Z 2 Z İ 0.49 ® 2 3 °¯ m 0.379 6 1.485Z 0.164 4Z 0.016 67Z Z ! 0.49

2 Gas-liquid-asphaltene equilibrium calculation model 2.1

Gas-liquid-asphaltene equilibrium calculation model

Suppose that a mixture system comprises N components. The non-precipitation component (C30B+) is the N1st component and the precipitation component (C30P+) is the Nth component. Let one mole of mixture be flashed into nG moles of gas, nL moles of liquid and nS moles of solid at a given pressure and temperature. The total material balance for the mixture system is: nG+nL+nS=1 (4) Suppose that the mole fraction of the ith component is zi (i=1,2,…,N) in the mixture system, yi (i=1,2,…,N) in the gas phase and xi (i=1,2,…,N) in the liquid phase. According to the assumptions mentioned above, the solid phase is only composed of the precipitation component, i.e. C30P+ (the Nth component), so the mole fraction of the Nth component in the solid phase is 1 while that of other components is 0. With the material balance for each component calculated, the following equations can be achieved: zi=yinG+xinL (i=1, 2,…, N1) (5) zN=yNnG+xNnL+nS (6) The mole fraction of each component in the gas and liquid phase also should satisfy the following restraint: N

N

i 1

i 1

¦ xi ¦ yi

1

(7)

Equation (7) can be transformed to the following formula: N

¦ yi xi

0

(8)

i 1

From the thermodynamic equilibrium conditions ( f G i f LN

f Li ,

fSN ) and the relationship between fugacity and the

fugacity coefficient, the following equations can be obtained: yi xi

IL i

(i=1, 2,…, N)

IGi 1 xN

IL N IS N

(9)

(10)

Introducing the equilibrium constant of gas to liquid

Huang Lei et al. / Petroleum Exploration and Development, 2010, 37(3): 349–353

onset point of asphaltene precipitation.

K GLi and the equilibrium constant of solid to liquid KSL N : K GLi

yi xi

(i=1, 2,…, N)

(11)

1 xN

KSL N

(12)

yi and xi can be solved by substituting equation (11) into equation (5) and combining equation (4): zi ° xi 1 n K S GLi 1 nG ° (i=1, 2,…, N) (13) ® K GLi zi °y ° i 1 n K 1 n S GLi G ¯ Substituting equation (13) into equation (8) results in:

N

KGL 1 zi S K GL 1 nG

N

¦ yi xi ¦ 1 n i 1

i 1

i

0

(14)

i

Substituting equation (11) and (12) into equation (6) leads to: z N nS 1 (15) 1 nS K GL 1 nG KSL N

N

For known K GLi and KSL N , the value of nG and nS can be determined by combining equations (14) and (15) with a Newton-Raphson iterative method. nG , nL, and nS should satisfy the following restraints: 0 nG 1 ° (16) ®0 nL 1 °0 n 1 S ¯ 2.2

2.3

Three-phase-flash calculation process

The steps of the three-phase-flash calculation are as follows: (1) Initialize K GLi (i=1,2,…,N) and KSL N with the result of phase stability analysis. (2) Solve the equation system composed of equations (14) and (15) with the Newton-Raphson iterative method to determine nG, nS, and nL. (3) Judge whether equation (16) is satisfied. If yes, go to step (4). If no, go out of the program. (4) Use equation (13) to solve xi and yi. (5) Calculate the compression factor for the liquid and gas phases using a three-parameter Peng-Robinson EOS[7,8]. If EOS has a multi-solution, take the minimum value for the gas phase and the maximum value for the liquid phase. (6) Calculate the fugacity of each component in the gas and liquid phases, f Gi , f Li (i=1,2,…,N). (7) Calculate the fugacity of the asphaltene phase in precipitated components using equation (3): fSN pI . (8) Judge whether the convergence condition as follows N

§ fL i

¦ ¨¨ f i 1©

Gi

2

2

· § fL · 1¸ ¨ N 1¸ 1012 is satisfied. If yes, stop to go ¸ ¨ fS ¸ ¹ © N ¹

out of the program. If no, use the following equations to upgrade the equilibrium constants: K GLi and KSL N . K GLi jˇ1 ˙K GLi j

Phase stability analysis of precipitated asphaltene

The first problem encountered during the course of phase equilibrium calculations is that the phase of the mixture is not known at a given pressure, temperature or components, i.e. the number of co-existing phases is not known for the mixed system. In 1982, the literature [9] and [10] proposed a phase stability analysis method based on the requirement of minimum Gibbs energy. The phase equilibrium calculation process after phase stability judgment analysis is as follows: (1) Assume that the mixture system exists in a single phase. (2) Perform phase stability analysis on that mixture system to determine whether the system is split into two phases. (3) If the system can not exist stably in a single phase, a two phase flash calculation should be performed on the mixture system. (4) Perform phase stability analysis on any phase obtained from the two-phase-flash calculation to determine whether the mixture system is split into three phases. (5) Perform threephase-flash calculations if phase stability analysis in the fourth step indicates that the system is more stable in three phases. (6) Perform phase stability analysis on the liquid phase from the results of three-phase-flash calculations until stability of all phases is obtained. According to Nghiem L.X.[5], the judgment condition to determine whether asphaltene precipitation will occur is as follows: If f L N > fSN , asphaltene precipitates. If f L N < fSN , asphaltene does not precipitate. f L N = fSN responds to the

KSL N jˇ1 ˙KSL N j

f Li j fGi j fLN j fS N j

(9) Judge whether the obtained K GLi and KSL N are satisfying the following condition: N

¦ ln KGL ln KSL i 1

2

i

N

2

104 . If yes, the values of

K GLi and KSL N are valid, otherwise not. (10) If the values of K GLi and KSL N are valid, go to step (2).

3

Case calculation and analysis

The content of asphaltene in oil measured in the laboratory is usually represented by a weight percentage. During the process of precipitated asphaltene measurement, injected gas is mixed with oil at reservoir pressure and temperature. If asphaltene precipitation occurs, the precipitated asphaltene will fall downwards as a sediment and deposit on the bottom of the reaction kettle because of its greater density. If part of the asphaltene precipitates from the oil, then the asphaltene content in the equilibrium oil phase will decrease correspondingly. The quantity of precipitated asphaltene caused by gas injection can be determined by comparing the quantity of asphaltene in liquid phase before and after carbon dioxide injection.

Huang Lei et al. / Petroleum Exploration and Development, 2010, 37(3): 349–353

Table 1 Injection pressure/MPa

Experimental and calculated results of asphaltene precipitated during CO2 injection

CO2 mole fraction when asphaltene precipitation occurs

CO2 mole fraction when gas phase occurs

No injection

Asphaltene content in Precipitated asphaltene/% oil phase/% Experiment Calculation 16.79

0.00

0.00

23.00

0.27

0.60

11.32

5.47

4.99

26.00

0.30

0.64

10.31

6.48

6.40

29.00

0.33

0.68

9.85

6.94

6.98

32.00

0.36

0.71

9.52

7.27

7.32

35.00

0.39

0.73

9.13

7.66

7.56

Taking the actual fluid data from an oilfield in China as an example, based on the matching of experimental results, the precipitated asphaltene quantity during gas injection can be predicted by the model established in this paper (Table 1). From Table 1, the calculation values approach the experimental results; indicating that the prediction model established in this paper for asphaltene precipitation has good accuracy. Based on the calculation of the quanitity of precipitated asphaltene, the asphaltene precipitation rule during CO2 injection is further refined. Fig. 1 shows the pressure-composi- tion phase diagram of a CO2-oil system. From Fig. 1, we can come to the conclusion that the bubble point pressures of the CO2-oil system and pressures on the up and down envelope curves of the precipitated asphaltene increase with the increment of CO2 injected as a mole fraction. Fig. 2 shows the relationship between the precipitated asphaltene quantities with the injected CO2 mole fraction at different injection pressures. From the figure, the precipitated asphaltene quantity rises first and then reduces with the increase in injected CO2 mole fraction at the same injected pressure. In the pressure-composition phase diagram (Fig. 1), the precipitated asphaltene quantity reaches its maximum when the gas phase appears in the CO2-oil system. Furthermore, the maximum precipitated asphaltene quantity increases with increasing injection pressure. Figure 3 shows the relationship of the precipitated asphaltene amount and the mole fraction of gas phase with the change of pressure under different CO2 mole fractions. Under the condition of a fixed CO2 mole fraction in the CO2-oil system, the precipitated asphaltene quantity increases with the pressure drop. The precipitated asphaltene quantity achieves a maximum at the bubble point pressure. With further pressure drops, the precipitated asphaltene quantity shows a decreasing trend. The maximum quantity of precipitated asphaltene increases with the increase in CO2 mole fraction in the CO2-oil system.

4

Fig. 1 Pressure-composition phase diagram of experiment CO2-oil system.

Fig. 2 Relationship between precipitated asphaltene quantity and CO2 mole fraction at different injection pressures.

Conclusions

In this paper, the compression factor formula of association compound established by Anderko is introduced to describe the non-ideal nature of precipitated asphaltene and the fugacity of precipitated asphaltene, derived from the theory of thermodynamics. The equation of state, incorporating association (AEOS), was used to construct a gas-liquid-asphaltene prediction model and the numerical solution of the model is

Fig. 3 Relationship between the precipitated asphaltene quantity and the mole fraction of gas phase with injection pressure at different CO2 mole fractions.

Huang Lei et al. / Petroleum Exploration and Development, 2010, 37(3): 349–353

discussed. After matching of experiment data, the model established in this study can be used to determine the phase envelope curves of precipited asphaltene and precipitation quantity under different thermodynamic conditions precisely. On the basis of the calculation of asphaltene precipitation quantities, the asphaltene precipitation trend during gas injection is predicted. The prediction results show that: given a constant injection pressure, the asphaltene precipitation quantity first increases and then decreases as injected CO2 increases; the asphaltene precipitation quantity reaches a maximum when the gas phase occurs in the CO2-oil system. When the CO2 mole fraction in the CO2-oil system is constant, the precipitated asphaltene quantity reaches a maximum around the bubble point pressure.

dimensionless; ISN —fugacity coefficient of component N (C30P+) in asphaltene phase, dimensionless; K GLi —gas-liquid equilibrium constant for component i, dimensionless; KSL N —solid-liquid equilibrium constant for component N (C30P+), dimensionless; ZG—compress factor of gas phase; ZL—compress factor of liquid phase.

Subscripts G—gas phase; L—liquid phase; S—asphaltene solid phase; i—component i; j—iteration step j.

Nomenclature References ZS—compression factor of precipitated asphaltene considering association;

[1]

Shen Pingping, Liao Xinwei, Liu Qingjie. Methodology for

ZA—compression factor affected by association;

estimation of CO2 storage capacity in reservoirs. Petroleum

ZF—compression factor affected by intermolecular force;

Exploration and Development, 2009, 36(2): 216–220.

R—universal gas constant, 8.314 5 J/(mol·K);

[2]

T—temperature, K;

petroleum asphaltene aggregation. Petroleum Exploration and

Kaa—asphaltene self-association constant, 1/Pa; V—molar volume of ideal mixture, m3/mol;

Lu Guiwu, Li Yingfeng, Song hui, et al. Micromechanism of Development, 2008, 35(1): 67–72.

[3]

Zhang Liang, Wang Shu, Zhang Li, et al. Assessment of CO2

f —fugacity, Pa;

EOR and its geo-storage potential in mature oil reservoirs,

p—pressure, Pa;

Shengli Oilfield, China. Petroleum Exploration and Develop-

ĳ—fugacity coefficient, f; pc—critical pressure, Pa;

ment, 2009, 36(6): 737–742. [4]

Tc—critical temperature, K; Ȧ—eccentric factor, dimensionless;

rich-gas flooding. SPE 18063, 1991. [5]

n—mole, mol; zi—mole fraction of component i in mixture, dimensionless;

[6]

1992, 75: 89–103. [7]

i

Peng D Y, Robinson D. B. A new two-constant equation of state. Ind. and Eng. Chem., 1976, 15(1): 59–64.

[8]

Jhaveri B S, Youngren G K. Three-parameter modification of the Peng-Robinson equation of state to improve volumetric

fSN —fugacity of component N (C30P+) in asphaltene phase, Pa;

IG —fugacity coefficient of component i in gas phase, dimen-

Anderko A. Modeling phase equilibria using an equation of state incorporating association. Fluid Phase Equilibrium,

f Li —fugacity of component i in liquid phase, Pa; f L N —fugacity of component N (C30P+) in liquid phase, Pa;

Nghiem L X, Hassam M S, Nutakki R, et al. Efficient modeling of asphaltene precipitation. SPE 26642, 1993.

xi—mole fraction of component i in liquid phase, dimensionless; yi—mole fraction of component i in gas phase, dimensionless; f Gi —fugacity of component i in gas phase, Pa;

Monger T G, Trujillo D E. Organic deposition during CO2 and

predictions. SPE 13118, 1988.

sionless; ILi —fugacity coefficient of component i in liquid phase, dimen-

[9]

Baker L E, Pierce A C, Luks K D. Gibbs energy analysis of

sionless; IL N —fugacity coefficient of component N (C30P+) in liquid phase,

[10] Michelsen M L. The isotherm flash problem part I: Stability.

phase equilibria. SPE 9806, 1982. Fluid Phase Equilibria, 1982, 9: 1–19.