Asphaltene Deposition Modeling during Natural Depletion and Developing a New Method for Multiphase Flash Calculation

Transcription

1 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No. 2, pp Asphaltene Deposition Modeling during Natural Depletion and Developing a New Method for Multiphase Flash Calulation Gholamreza Fallahnejad 1 and Riyaz Kharrat 2* 1 M.S. Student, Department of Petroleum Engineering, Petroleum University of Tehnology, Ahwaz, Iran 2 Professor, Department of Petroleum Engineering, Petroleum University of Tehnology, Ahwaz, Iran Reeived: August 17, 2014; revised: January 06, 2015; aepted: January 08, 2015 Abstrat The speifi objetive of this paper is to develop a fully impliit ompositional simulator for modeling asphaltene deposition during natural depletion. In this study, a mathematial model for asphaltene deposition modeling is presented followed by the solution approah using the fully impliit sheme. A thermodynami model for asphaltene preipitation and the numerial methods for performing flash alulation with a solid phase are desribed. The pure solid model is used to model asphaltene preipitation. The transformation of preipitated solid into floulated solid is modeled by using a first order hemial reation. Adsorption, pore throat plugging, and re-entrainment were onsidered in the deposition model. The simulator has the apability of prediting formation damage inluding porosity and permeability redution in eah blok. A new set of independent unknowns in a fully impliit sheme is presented for asphaltene deposition modeling. In order to find the solution of these variables, the same number of equations is also presented. The desription of how to solve the nonlinear system of equations is also desribed. Keywords: Asphaltene Deposition, Composition Simulation, Multiphase Flash, Solid Model, Modeling 1. Introdution Asphaltene preipitation and deposition is a very serious problem that ours during oil prodution and proessing. Although the problem has been usually observed in the wellbore and the prodution system, asphaltene preipitation and deposition may our anywhere in the reservoir-wellbore system inluding near-wellbore region and inside the wellbore (Darabi et al., 2014). Various models have been proposed to desribe the phase behavior of asphaltene preipitation. Aording to the literature, there are four main groups for asphaltene preipitation modeling. The first one is the liquid solubility whih is based on the Flory-Huggins theory (Flory, 1942). The seond models are the solid models whih assume that asphaltene is treated as a single omponent in the solid phase. The third one is the olloidal solution model proposed by Leontaritis and Mansoori (1987) with the onsideration of asphaltene as solid partiles in a olloidal suspension stabilized by adsorbed resins on asphaltene surfae. The fourth one is the thermodynami miellization model presented by * Corresponding Author: kharrat@put.a.ir

2 46 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No. 2 Firoozabadi and Pan (1998). The minimization of the molar Gibbs free energy is the basis of this thermodynami model. Few mathematial models were orrelated to simulate asphaltene deposition. Aording to the literature, there are three ategories for the asphaltene deposition modeling. The first one is the Leontaritis model (1998) whih assumes that asphaltene deposition ours only around the wellbore viinity. The seond model is the model of Nghiem et al. (1998) supposing that only adsorption mehanism ontributes to the asphaltene deposition. The third one is the model of Wang and Civian (2000) whih onsiders primary physial deposition proesses inluding adsorption, pore throat plugging, and re-entrainment to desribe the phenomenon of solid partile deposition. In this study, the pure solid model is used to model asphaltene preipitation. Also, a deposition model inluding adsorption, pore throat plugging, and re-entrainment is used. The redution in the rok porosity and permeability are also inluded in the asphaltene model. A one-dimensional simulation was arried out for investigating the results of asphaltene deposition model. 2. Mathematial model desription The transportation equations, asphaltene preipitation model, asphaltene deposition model, and the porosity and permeability redution are onsidered as the main part of the mathematial model for modeling asphaltene deposition. To develop a simulator for asphaltene deposition, the asphaltene preipitation and deposition models and the porosity and permeability redution are inorporated into a ompositional simulator Asphaltene preipitation model In this study, a pure solid model is used for prediting the amount of preipitation, while a ubi EOS is applied to the modeling of oil and gas phase behavior. The solid partiles are divided into three parts: preipitated, floulated, and deposited solid. Kohse and Nghiem (2004) proposed a model whih assumes that the heaviest omponent of oil an be split into a non-preipitating and a preipitating omponent. The preipitated solid is divided into solid 1 whih is in equilibrium with the heaviest omponent in the oil phase and solid 2 that is reated from solid 1 via a first order hemial reation. The fugaity of asphaltene omponent in the preipitated solid 1 (S 1) is given by: ln f ( Vs( P P )) ( RT ) * s1 ln fs 1 * (1) where, f s1 is the fugaity of solid S1 at reservoir pressure, and * fs1 is the referene solid fugaity at * ; Vs is the solid molar volume and P represents the pressure at whih the asphaltene just starts to preipitate. Under the thermodynami equilibrium onditions between S 1, oil, and gas, the following equations must be applied: ln f ln f, i 1,, n (2) io ig * P ln f ln f (3) n, o s1

3 Error Gh. Fallahnejad and R. Kharrat/ Asphaltene Deposition Modeling during 47 The equality of fugaity of i th omponent in the oil and gas phases is shown in Equation 2. Equation 3 expresses the equality of fugaity of the preipitating omponent in the oil phase and in the preipitated solid S 1. a. Speifiation of solid molar volume for asphaltene model For the modeling purpose, solid molar volume is used as a mathing parameter. The solid molar volume is initially alulated at referene pressure (P * ) by EOS. Then, we plot the error term versus solid molar volume to find an optimum fit between the alulated and experimental data. The solid molar volume whih is used in the plot ontains the values around the alulated solid molar volume at the referene pressure. The error term is defined as follows: n error ( W W ) i1 (i)exp (i)model 2 (4) Figure 1 shows the error term as a funtion of solid molar volume. The estimated molar volume for the asphaltene omponent from EOS is ft 3 / lbmole. As an be seen, the minimum error for the given values of solid molar volume is found at ft 3 / lbmole Figure 1 Error term as a funtion of solid molar volume. b. Stability test analysis In multiphase flash alulation, the number of phases is generally unknown beforehand. We use the phase stability analysis to determine the number of phases in eah gridblok. In this study, stability test analysis is separated into two parts: fluid-fluid and fluid-solid stability test. b.a. Fluid-fluid stability test Solid molar volume (ft 3 /lb mole) The following set of equations (Nghiem and Li, 1984) should be solved to hek the stability of a fluid phase (oil) with omposition x, pressure P, and temperature T.

4 48 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No. 2 g lnk lnφ y, P, T ln φ x, P, T 0 (5) i i i i Yi K i i 1,, n x i (6) where y i Y i n Y j 1 j (7) If Equation 5 is solved for Y i at a given P and T, a solution is found that n Yj 1 (8) j1 The mixture x is unstable at P and T. Equation 5 an be solved with the QNSS method (Nghiem and Li, 1984). With the QNSS, let α be the vetor with elements lnk i, and let α k be the k ih iteration value for the vetor α. The QNSS iteration is given by: 1 k k k α α α k k k α ξ g (9) (10) And ξ is a salar given by: k1 k1 k k 1 Δ α. g ξ ξ k1 k1 Δ α.δg (11) where g = norm g (12) α norm α (13) The proess is initialized with ξ (0) = 1 and α is started with Wilson equation. Figure 2 shows a flow hart for this proedure.

5 Gh. Fallahnejad and R. Kharrat/ Asphaltene Deposition Modeling during 49 Start Input initial guess α k =α (0) Using α (k) to evaluate y (k) and Y (k) Calulation of g k Convergene hek Yes End of QNSS iteration No Calulation of ξ (k) Update α α k+1 = α k ξ (k) g (k) Figure 2 QNSS iteration for fluid-fluid stability test. b. Fluid-solid stability test To test the existene of solid phase, the following riteria should be satisfied. The solid phase exists if: ln f ln f n o s1 (14) This implies that if the fugaity of the asphaltene omponent in the solid phase is less than the fugaity of the n th omponent in the oil phase, more asphaltene preipitation will our until both fugaities beome equal. Figure 3 depits the stability test alulation proedure.

6 50 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No. 2 Initialize variables Single phase fluid Stability test solid phase? Stable Stability test 2 nd fluid phase? Stable Single phase Unstable Unstable 2-phase fluid-solid Stable Fluid-Solid Flash Fluid-Fluid Flash Stability test 2 nd fluid phase? Stability test solid phase? Stable 2-phase Fluid-Solid Unstable 3-Phase flash fluid-fluid-solid Figure 3 Stability test analysis.. Multiphase flash alulations The set of independent variables involved for the flash alulation are LnKi, Ks, Lg, and Ls, whih gives n +3 unknowns. The following set of equations should be used for solving these variables: ln K ln ln 0 (15) ig ig io ln K ln φ ln φ 0 (16) With n s s n o K ig yig (17) y io

7 Gh. Fallahnejad and R. Kharrat/ Asphaltene Deposition Modeling during 51 fij ij j=o and g yp ij (18) K ns 1 (19) y no f P s s (20) In onjuntion with the above equations, the following material balane equations an be derived: n Kig 1 zi 0 (21) 1 L K 1 L K 1 i1 g ig s is n Kis 1 zi 0 (22) 1 L K 1 L K 1 i1 g ig s is The oil and gas phase omposition an be alulated from the following equations: y y io zi (23) 1 L K 1 L K 1 ig ig io g ig s is K x (24) There are n +3 nonlinear equations and unknowns for multiphase flash alulations. The unknown vetor is onsidered as follows: X Ln( K ), K, L, L (25) i ig s g s To solve the nonlinear system of equations, the Newton method is used, where the residual vetor ( R ) is omputed. The residual vetor onsists of Equations 15, 16, 21, and 22. The detailed multiphase flash alulation proedure is given in Figure 4.

8 52 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No. 2 START Input initial guess X n =X 0 (ln K ig, K s, L g, L s ) Using X n to evaluate dependent variables Calulation of x, y, φ L, φ V Calulation of residual vetor, R(X n ) Convergene hek Yes Next time step No Calulation of Jaobean matrix J X old Solve the system J X old X = R(X old ) Update the independent variables X new = X old + X Figure 4 Flow hart for flash alulations proedure.

9 Gh. Fallahnejad and R. Kharrat/ Asphaltene Deposition Modeling during Asphaltene deposition model In this study, the model of Wang and Civian (2000) is used to simulate the formation damage aused by asphaltene deposition during natural depletion. This model has three terms, inluding adsorption, pore throat plugging, and re-entrainment to desribe asphaltene deposition proess. The deposition equation is presented as follows: E t A C E ( v v ) u C A A L r, L L A (26) 2.3. Porosity and permeability redution model One asphaltene deposition ours, porosity alteration is modeled by the following equation: 0 E A (27) To update the permeability values, a power law relationship is used as given below: R f 3 K0 0 K (28) 2.4. Compositional simulator equations Compositional simulator inludes omponent molar flow equations, phase equilibrium equations, multiphase flash equations, and saturation onstraint equations, whih are solved simultaneously. a. Component molar balane equations The following material balane equation with the onsideration of asphaltene an be written: N o y joo g y jg g q j t N o( yn ) o ys y 1 s 2 o g yn g g qn t where, N i is the moles of omponent i per pore volume (lbmole/ft 3 ); y ik is the mole fration of omponent i in phase k (k = o,g); y sj is the mole fration of suspended solid in oil phase (j = 1, 2); ξ k is the molar density of phase k (k = o,g) (lbmole/ft 3 ); A material balane on solid S 2 ompletes transport equations: j j1,, n 1 (29) n (30) o ys 2 o VbS or qs 2 t N s 2 (31)

10 54 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No. 2 y y s1 s2 ' T N L N N N o s 2 o s (32) (33) r K C K C (34) where, 12 s1, o 21 s2, o C C s1, o s1, o ' T N L S N S o s2 o s (35) (36) b. Phase equilibrium equations The following equations for thermodynami equilibrium between S 1, oil, and gas must be applied: ln f ln f, i 1,, n (37) io ig ln f ln f (38) n, o s1. Phase omposition onstrains The following equations are used to onsider the phase omposition onstrains: n n y io i1 i1 n n y io i1 i1 y y ig is 0 0 (39) (40) d. Volume onstraint equation The volume onstraint equation expresses that the pore volume in eah grid must be oupied by the total fluid volume. This equation an be written as follows: n p j1 S j 10 (41) 3. Solution approah After finite differening, there are (2n + 6)n b nonlinear equations for n b number of gridbloks. Equations 28, 29, 30, 36, 37, 38, 39, 40, and 25 provide a system of nonlinear equations that an be solved for (Ni, Ln(Ki), Ns 2, Ns 3, P, Ks, Lg, Ls) for eah gridblok. A fully impliit tehnique is used

11 Gh. Fallahnejad and R. Kharrat/ Asphaltene Deposition Modeling during 55 to solve the governing equation for these independent variables. The unknown vetor is onsidered as follows: 2 3 X N, Ln Ki, Ns, Ns, P, Ks, Lg, Ls (42) i i A Newton method is used to linearize the governing equations in terms of the independent variables. The solution proedure is desribed as follows: Input initial 1. The solution vetor at the old time step is usually set as the initial guess for the new time step; 2. Using initial guess vetor to ompute dependent variables suh as porosity, molar density, relative permeability, molar omposition, phase visosities, and soure or sink; 3. Calulate the residual vetor and hek for the onvergene. If onvergene is ahieved, the guessed solution vetor is onsidered as the true solution for the new time step. If a tolerane is exeeded, another solution vetor is guessed and the independent variables are updated. The new solution vetor is obtained by solving the system J X old X = R(X old ) where the Jaobian matrix (J) and the residual vetor are omputed using the previous solution vetor. Independent variables are updated as follows: X new = X old + X (43) 4. Results and disussion In this setion, the results of the implemented asphaltene model whih is obtained from a 1D simulation ase are presented. Table 1 shows the omposition of oil used for studying asphaltene preipitation, whih is obtained from the work of Burke et al. (1990). The reservoir properties are given in Table 2. Table 1 Modeled fluid omposition. Component mole % MW CO N C C C i-c n-c i-c n-c FC C 7-C C 16-C C 26-C C31A C31B

12 56 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No. 2 Parameter Table 2 Simulation input data. Value No. of gridbloks 21 Reservoir size ft3 Reservoir Temperature 212 F Initial water saturation 0 Initial reservoir pressure psi Porosity 0.2 Permeability Prodution onstraint Rok ompressibility Ref. P for rok ompressibility 30 md 2.5 bbl./day psi psi The reservoir is one-dimensional homogenous with the size of ft 3 and divided into 21 gridbloks. The porosity and permeability are 0.2 and 30 md respetively. The initial reservoir pressure is psia and reservoir temperature is 212. The well is loated at the enter of the reservoir at the onstant bottomhole reservoir fluid rate (BHF) of 2.5 bbl./day. The input parameters for the preipitation, deposition, and floulation models, whih are taken from Kohse and Nghiem (2004), are shown in Table 3. In this study, it is assumed that the interstitial veloity is less than the ritial interstitial veloity; as a result, the entrainment rate oeffiient β is set to zero. The liquid-gas relative permeability urves and the liquid-gas apillary pressure urve for the simulation ase are shown in Figures 5 and 6. Table 3 Asphaltene preipitation, deposition, and floulation model parameters. Parameter Value P psi lnf n s psi V s lbm/ft 3 k 12 (day -1 ) 0.1 k 21 (day -1 ) 0.08 α (day -1 ) 0.01 β (ft -1 ) 0.0 γ (ft -1 ) 0.05 σ 150

13 Capillary pressure (psi) Relative permeability Gh. Fallahnejad and R. Kharrat/ Asphaltene Deposition Modeling during Krg Krog Gas saturation Figure 5 The liquid-gas relative permeability urves Figure 6 The liquid-gas apillary pressure urve Gas station Figure 7 presents pressure versus time for the gridblok (11,1,1). As an be seen, the initial reservoir pressure, the onset pressure (P * ) of asphaltene, and saturation pressure are , 4550, and 2950 psia respetively. The onset pressure for asphaltene preipitation will be reahed after approximately 13 days of prodution time. The saturation pressure will be reahed after 30 days of prodution time. The pressure depletion ontinues to reah a value of at the end of simulation time.

14 So or Sg Pressure (psi) 58 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No t (Day) Figure 7 Pressure profile at gridblok (11,1,1) after 80 days. Oil and gas saturation are depited in Figure 8. As an be seen, the oil saturation remains onstant until the bubble point pressure is reahed. After 30 days of prodution time the oil saturation gradually dereases and will be reahed the value of 0.9 at the end of simulation time So Sg t (Day) Figure 8 Oil and gas saturation at gridblok (11, 1, 1). Porosity versus time is presented in Figure 9. As this figure shows, the porosity redution shows a sharper trend after saturation pressure is reahed. Both pressure depletion and asphaltene deposition are the auses for porosity alteration.

15 Porosity Gh. Fallahnejad and R. Kharrat/ Asphaltene Deposition Modeling during t (Day) Figure 9 Porosity at gridblok (11, 1, 1). Permeability redution (K/K i) is reported in Figures 10. This parameter has an important role in asphaltene preipitation studies. A uniform deline of permeability an be seen in this plot. Figure 11 shows how the produtivity index varies with time. This parameter also shows the same trend as permeability redution. As an be seen, after 30 days of prodution time, in addition to asphaltene deposition, oil relative permeability redution plays an important role in the produtivity index redution; as a result, this parameter starts dereasing sharply after 30 days K/K i t (Day) Figure 10 Ratio of the damage permeability to the original permeability.

16 Preipitated mole per PV Produtivity index (bbl./day/psi) 60 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No t (Day) Figure 11 Produtivity index versus time at well-blok. Figure 12 illustrates the amount of preipitated asphaltene (mole per pore volume lbmole/ft 3 ) versus time during the simulation time. As an be seen, after 12 days of simulation time, the preipitation is started. The maximum value of preipitation ours around the saturation pressure and dereases as pressure drops further t (Day) Figure 12 Asphaltene preipitated mole per pore volume at gridblok (11,1,1). Figure 13 shows the amount of floulated asphaltene (mole per pore volume lbmole/ft 3 ) versus time during the simulation time. As an be seen, the trend of plot is the same as the plot of asphaltene

17 Deposited Mole per PV Floulated mole per PV Gh. Fallahnejad and R. Kharrat/ Asphaltene Deposition Modeling during 61 preipitation, but there is a time interval between the maximum value of the preipitation and floulation t (Day) Figure 13 Asphaltene floulated mole per pore volume at gridblok (11,1,1). The amount of deposited asphaltene (mole per pore volume lbmole/ ft 3 ) with respet to prodution time is shown in Figure 14. The gradual inrease of deposited asphaltene at gridblok (11,1,1) is shown in this figure t (Day) Figure 14 Asphaltene deposited mole per pore volume at gridblok (11,1,1). Figures 15 and 16 show the omparison of the preipitated and deposited asphaltene profile between Matlab ode and CMG GEM during 80 days of simulation time respetively. As an be seen, beause

18 Deposited mass per BV (lb./ft 3 ) Preipitated mass per BV (lb./ft 3 ) 62 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No. 2 of onsidering new multiphase flash alulation approah, the deposited asphaltene profile gives a better math than the preipitated profile. As a matter of fat, in the deposited profile, in addition to thermodynami equations, material balane equations play a great role, and sine it regards the new approah to multiphase flash alulation, the material balane equations would hange. As a result, a lear differene between Matlab ode and CMG GEM an be seen for the deposited asphaltene profile ompared to the preipitated profile Matlab CMG GEM t (Day) Figure 15 Asphaltene preipitated mass per bulk volume at gridblok (11,1,1) Matlab 0.02 CMG GEM t (Day) Figure 16 Asphaltene deposited mass per bulk volume at gridblok (11,1,1).

19 5. Conlusions Gh. Fallahnejad and R. Kharrat/ Asphaltene Deposition Modeling during 63 This paper presents the modeling of the phase behavior and dynami aspets of asphaltene preipitation and deposition for natural depletion. A solid model is used to model asphaltene phase behavior. The thermodynami model for asphaltene preipitation has been suessfully inorporated into a fully impliit ompositional simulator, where the phase equilibrium equations, the saturation onstraint equation, the omponent transport equations, the multiphase flash equations, and the deposition equation are solved simultaneously for eah gridblok. Just a part of the preipitated asphaltene is onsidered to adsorb to the rok and the remaining part is onsidered to stay suspended in the oil phase. A resistane fator model was introdued for the estimation of the effet of asphaltene preipitation on relative permeability. Nomenlature C s1 o : Conentration of suspended solid s 1 in oil phase [lbmole/ft 3 ] C s2 o : Conentration of suspended solid s 2 in oil phase [lbmole/ft 3 ] C s2 f : Volumetri onentration of flowing solid s 2 per volume of oil [-] f ig f io f s1 : Fugaity of omponent i in gas phase [psi] : Fugaity of omponent i in oil phase [psi] : Referene solid fugaity [psi] f s1 n b n : Fugaity of solid s 1 [psi] : Total number of gridells : Number of hydroarbon omponents N i : Moles of omponent i per pore volume [lbmole/ft 3 ] N s1 : Moles of solid s 1 per pore volume [lbmole/ft 3 ] N s2 : Moles of solid s 2 per pore volume [lbmole/ft 3 ] N s3 : Moles of deposited solid per pore volume [lbmole/ft 3 ] N T : Total number of moles per pore volume [lbmole/ft 3 ] N T u o : Total number of moles without floulated and deposited solid per pore volume [lbmole/ft 3 ] : Oil phase Dary veloity [ft/day] V : Gridblok volume [ft 3 ] V r,o : Critial oil phase interstitial veloity [ft./day] V s2 d : Volume of deposited solid s 2 per gridblok volume [-] y ik : Mole fration of omponent i in phase k (k = o,g) [-] y sj : Mole fration of suspended solid in oil phase (j = 1, 2) [-] z i : Global mole fration of omponent i in feed [-]

20 64 Iranian Journal of Oil & Gas Siene and Tehnology, Vol. 5 (2016), No. 2 Greeks α : Surfae deposition rate oeffiient [day -1 ] β : Entrainment rate oeffiient [ft -1 ] γ : Pore throat plugging rate oeffiient [ft -1 ] φ ij : Fugaity oeffiient of omponent i in phase j ξ k : Molar density of phase k (k = o,g) [lbmole/ft 3 ] v o v s Subsripts g : Gas : Oil phase interstitial veloity [ft./day] : Solid molar volume [ft 3 /lbmole] o : Oil Referenes Ali, M. A. and Islam, M. R., The Effet of Asphaltene Preipitation on Carbonate Rok Permeability: an Experimental and Numerial Approah, Paper SPE presented at the SPE Annual Tehnial Conferene and Exhibition, San Antonio, 5 8 Otober, Burke, N. E., Hobbs, R. D., and Kashou, S. F., Measurement and Modeling of Asphaltene Preipitation, JPT, Vol. 42, No. 11, p , Choiri, M., Study of CO 2 Effet on Asphaltene Preipitation and Compositional Simulation of Asphalteni Oil Reservoir, M.S. Thesis, The University of Stavanger, Computer Modeling Group, Win Prop and GEM Manual, Darabi, H., Shirdel, M., Kalaei, M. H., and Sepehrnoori, K., Aspets of Modeling Asphaltene Deposition in a Compositional Coupled Wellbore/ Reservoir Simulator, SPE , Presented at SPE Annual Tehnial Conferene and Exhibition, Tulsa, Oklahoma, USA, April ECLIPSE Tehnial Desription, The Asphaltene Option, p , Fazelipour, W., Development of a Fully Impliit, Parallel, EOS Compositional Simulator to Model Asphaltene Preipitation in Petroleum Reservoirs, M.S. Thesis, The University of Texas at Austin, Fazelipour, W., Pope, G., and Sepehrnoori, K., Development of a Fully Impliit, Parallel, EOS Compositional Simulator to Model Asphaltene Preipitation in Petroleum Reservoirs, SPE , Presented at SPE Annual Tehnial Conferene and Exhibition, Hirshberg, A., Dejong, L. N. J., Shipper, B. A. and Meijer, J. G., Influene of Temperature and Pressure on Asphaltene Floulation, Paper SPE 11202, June, 1984 Kohse B., Nghiem L. X., Modeling Asphaltene Preipitation and Deposition in a Compositional Reservoir Simulator, SPE No , 14 the Symposium Improved Oil Reovery, Tulsa, Oklahoma, April Leontaritis, K. J. and Mansoori, G. A., Asphaltene Floulation during Oil Prodution and Proessing: A Thermodynami-olloidal Model, Paper SPE presented at the SPE International Symposium on Oil Field Chemistry, San Antonio, January1987.

21 Gh. Fallahnejad and R. Kharrat/ Asphaltene Deposition Modeling during 65 Leontaritis, K. J. and Mansoori, G. A., Asphaltene Deposition: A Survey of Field Experienes and Researh Approahes, Journal of Petroleum Siene and Engineering, Vol. 1, N0. 3, p , Leontaritis, K., Asphaltene Near-wellbore Formation Damage Modeling, SPE 39446, Presented at SPE Formation Damage Control Conferene, Lafayette, Louisiana, February, Leontaritis, K. J. and Mansoori, G. A., Asphaltene Deposition, a Survey of Field Experienes and Researh Approahes, Journal of Petroleum Siene and Engineering, Vol. 1, No. 3, p , Nghiem, L. X., Hassam M. S. and Nutakki R., Effiient Modeling of Asphaltene Preipitation, Presented at the 1993 SPE Annual Tehnial Conferene and Exhibition, Paper SPE 26642, Houston, TX, Ot 3-6, Nghiem L.X., Coombe D.A., Modeling of Asphaltene Preipitation during Primary Depletion, Paper No. SPE 36106, Fourth Latin Amerian and Caribbean Petroleum Engineering Conferene, Port of Spain, Trinidad and Tobago, April Nghiem, L.X., and Dennis, A., Modeling Asphaltene Preipitation during Primary Depletion, Paper SPE Presented at IV Latin Amerian/Caribbean Petroleum Engineering Conferene, Trinidad and Tobago, April, Nghiem, L. X., Phase Behavior Modeling and Compositional Simulation of Asphaltene Deposition in Reservoirs, Ph.D. Thesis, University of Alberta, Department of Civil and Environmental Engineering, Nghiem, L. X., Kohse, B. F., Farouq-Ali, S. M., and Doan, Q., Asphaltene Preipitation: Phase Behavior Modeling and Compositional Simulation, Paper SPE Presented at the SPE Asia Paifi Conferene on Integrated Modeling for Asset Management, Yokohama, April, Pan, H. and Firoozabadi, A., Thermodynami Miellization Model for Asphaltene Aggregation and Preipitation in Petroleum Fluids, SPE Prodution & Failities, Vol. 13, No.2, p , May Shirdel, M., Development of a Coupled Wellbore-reservoir Compositional Simulator for Damage Predition and Remediation, Ph.D. Dissertation, The University of Texas at Austin, Wang, S., Simulation of Asphaltene Deposition in Petroleum Reservoirs During Primary Oil Reovery, Ph.D. Dissertation, The University of Oklahoma, Deember, Wang, S., Civan, F., and Stryker, A. R., Simulation of Paraffin and Asphaltene Deposition in Porous Media SPE Paper No, Presented at the SPE 1999 International Symposium on Oilfield Chemistry, Houston, Texas, February 16-19,1999.