Wax Formation from Synthetic Oil Systems and Reservoir Fluids

based on the previously proposed wax model (Zuo, J. Y.; Zhang, D.; Ng, H.-J. An improved thermodynamic model for wax precipitation from petroleum flui...
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Energy & Fuels 2008, 22, 2390–2395

Wax Formation from Synthetic Oil Systems and Reservoir Fluids Julian Y. Zuo* and Dan Zhang DBR Technology Center, Schlumberger, 9450-17 AVenue, Edmonton, Alberta T6N 1M9, Canada ReceiVed January 24, 2008. ReVised Manuscript ReceiVed March 17, 2008

In this work, an effort has been made to further improve the predictions of the wax formation conditions based on the previously proposed wax model (Zuo, J. Y.; Zhang, D.; Ng, H.-J. An improved thermodynamic model for wax precipitation from petroleum fluids. Chem. Eng. Sci. 2001, 56 (24), 6941-6947). The model framework consists of the three-parameter Peng-Robinson equation of state for describing the nonideality of the vapor and liquid phases and the predictive universal quasi-chemical (UNIQUAC) model proposed by Coutinho for the solid (wax) phase. The characterization procedure for plus fractions proposed by Zuo and Zhang (Zuo, J. Y.; Zhang, D. Plus fraction characterization and PVT data regression for reservoir fluids near critical conditions. SPE 64520, 2000.) has been modified and extended to reservoir fluids using high-temperature gas chromatography (HTGC) data. The wax model developed in this study has been applied to predict wax appearance temperature (WAT) and wax cut curves for a number of defined component systems, diesel fuels, and reservoir fluids. The average deviation of the predicted WAT is within 1.5 K at low and high pressures for defined component systems. For reservoir fluids, the predicted thermodynamic WAT locus tends to be much higher than the measured WAT. It is observed that a very small amount of wax precipitated in the fluids could shift the WAT to the measured WAT. The prediction of wax compositions in the solid phase is in good agreement with the experimental data. The results indicate that the proposed wax model is a useful tool to the flow assurance industry.

Introduction Wax formation is a serious problem in the gas and oil industry because it can block oil production facilities and transportation pipelines. It is, therefore, of great importance to have a reliable tool to predict wax formation under various operational conditions. A number of thermodynamic models have been proposed to model wax precipitation from reservoir fluid systems, for instance, the models proposed by Pedersen,3 Lira-Galeana et al.,4 Pan et al.,5 Zuo et al.,1 and Ji et al.6 However, all of these models fail to predict the phase behavior of waxy crude oils and gas condensates precisely. The challenges are generally associated with proper characterization of heavy wax molecules and determination of their physical properties. A model tuning process is usually involved to obtain more accurate calculation results. Wax appearance temperature (WAT) is generally used to tune wax thermodynamic models. The accuracy of WAT mainly depends upon experimental techniques, sample quality, proper sample handling, and cooling rate. Up to now, all of the * To whom corresponding should be addressed. E-mail: [email protected]. (1) Zuo, J. Y.; Zhang, D.; Ng, H.-J. An improved thermodynamic model for wax precipitation from petroleum fluids. Chem. Eng. Sci. 2001, 56 (24), 6941–6947. (2) Zuo, J. Y.; Zhang, D. Plus fraction characterization and PVT data regression for reservoir fluids near critical conditions. SPE 64520, 2000. (3) Pedersen, K. S. Prediction of cloud point temperatures and amount of wax precipitation. SPE 27629, 1995. (4) Lira-Galeana, C.; Firoozabadi, A.; Prausnitz, J. M. Thermodynamics of wax precipitation in petroleum mixtures. AIChE J. 1996, 42 (1), 239– 248. (5) Pan, H.; Firoozabadi, A.; Fotland, P. Pressure and composition effect on wax precipitation: Experimental data and model results. SPE Prod. Facil. 1997, 12 (4), 250–258. (6) Ji, H.-Y.; Tohidi, B.; Danesh, A.; Todd, A. C. Wax phase equilibria: Developing a thermodynamic model using a systematic approach. Fluid Phase Equilib. 2004, 216 (2), 201–217.

experimental methods available in laboratories need to have a certain small amount of wax precipitated in the tested fluids before it can be detected. This limitation implies that the experimental methods cannot detect the formation of the first wax crystal at least in reservoir fluid systems, which corresponds to thermodynamic WAT. High-temperature gas chromatography (HTGC) results show that a reservoir fluid usually has a long tail in the plot of weight percentage versus carbon numbers of n-paraffins (up to n-C90). Therefore, the measured WAT may be significantly lower than thermodynamic WAT.7 To model wax precipitation from reservoir fluids, it is also essential to understand the phase behavior of wax components in the reservoir fluids. A reservoir fluid is a mixture consisting of thousands of different compounds, including wax and saturates, aromatics, resins, and asphaltenes (SARA) compounds. As a result, it is difficult to calculate phase behavior for such a complex system accurately. To have a “predictive” model, the common approach is to tune the model to some representative experimental data. Obviously, the accuracy of the tuned model relies on that of the experimental data. Thermodynamic models tuned to match the measured WAT may have the intrinsic defect because the measured WAT, to a certain extent, involves the kinetic or crystallization process and does not necessarily represent the true thermodynamic behavior of the system. Alternatively, the experimental wax cut data can be used to tune thermodynamic models. In the present study, a wax precipitation model proposed by Zuo et al.1 has been improved in particular by (1) using the predictive UNIQUAC model proposed by Coutinho8–10 for describing the nonideality of the solid (wax) phase, (2) modify(7) Hammami, A.; Ratulowski, J.; Coutinho, J. A. P. Cloud points: Can we measure or model them. Pet. Sci. Technol. 2003, 21 (3), 345–358. (8) Coutinho, J. A. P.; Edmonds, B.; Moorwood, T.; Zhang, X. Reliable wax predictions for flow assurance. SPE 78324, 2002.

10.1021/ef800056d CCC: $40.75  2008 American Chemical Society Published on Web 05/24/2008

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ing the characterization procedure for plus fractions proposed by Zuo and Zhang2 using HTGC data, (3) assuming potential wax formers are only n-alkanes (n-paraffins). The proposed model has first been tested for synthetic oil systems, where all of the components are well-defined without involving plus fraction characterization. Then, an attempt has been made to compare the amount and composition of the precipitated wax measured in the laboratory and predicted by the wax thermodynamic model for diesel fuel, crude oil, and gas condensate systems with HTGC data. Good results have been obtained for all of the systems. Thermodynamic Wax Precipitation Model To improve the wax thermodynamic model proposed by Zuo et al.,1 the following assumptions have been made: (1) For simplicity, only normal paraffins are considered to be potential wax formers, although branch paraffins are also present in the wax phase. Wax consists predominantly of the C17+ n-paraffins that can be determined by HTGC experimentally or a distribution function. (2) Normal paraffins follow an exponential decay with molecular weights/carbon numbers in naturally existing fluids but different from other components if HTGC data are not available. (3) The solid phase is a nonideal solid solution or multisolid solutions, depending upon the model used for the solid phase, and the number of solid phases is automatically determined by minimizing the Gibbs free energy of the system in question. (4) The nonideality of the solid phase is described by the UNIQUAC or Wilson activity coefficient model proposed by Coutinho et al.8–10 The UNIQUAC model can determine coexisting multisolid phases, while the Wilson model cannot. (5) The three-parameter Peng-Robinson equation of state (EOS) is used for both vapor and liquid phases. According to thermodynamics, the criterion of vapor-liquid-solid equilibria is that the fugacities of component i in the vapor, liquid, and solid phases are identical, that is, fi ) fi ) fi V

L

S

(1)

m Tm i and ∆H i stand for the melting point temperature and the enthalpy of fusion of component i, respectively. T tri and ∆H tri denote the solid-solid transition temperature and the enthalpy of component i, respectively. ∆Cp is the heat capacity difference between 0L the liquid and solid phases. It should be noticed that f pure,i is the fugacity of pure component i in the liquid phase at the reference state (melting point pressure, P0), which is expressed as

(∫

0L 0L (P0) ) fpure,i (P)exp fpure,i

P0

P

)

where fugacity coefficient φΠ i is computed by the three-parameter PR EOS in the vapor and liquid phases. xΠ i and P denote the mole fraction of component i in the phase Π and the pressure, respectively. The fugacity of component i in the solid phase is given by

(∫

)

S P Vi dP P0 RT

0S fi S ) γSi xSi fpure,i (P0)exp

(3)

where x Si denotes the solid mole fraction of component i. γ Si is the activity coefficient of component i in the solid phase (for an ideal solid solution γ Si ) 1), which is used to represent the nonideality 0S of the solid phase. f pure,i represents the fugacity of pure solid 0S 0L component i at the reference state. Thus, f pure,i is related to f pure,i by the following expression:

[ ( ) ( ) ( ( ) )]

∆Hitr ∆Him T T 0S 0L fpure,i 1- m 1 - tr (P0) ) fpure,i (P0)exp RT RT T T i

∆Cpi R

Tim T -1 + T Tim

)

∆Him ∆Hitr T T 1- m 1 - tr RT RT T T i

∆Cpi R

ln

T Tim

i

L S P Vi - Vi dP P0 RT

Tim - 1 exp + T

(6)

where V iL and V iS denote the liquid and solid molar volumes of component i, respectively. The last term on the right-hand side of eq 6 is the Poynting correction. Coutinho’s correlations8–10 are used to estimate physical properties of wax components, which are functions of carbon numbers of n-paraffins. The nonideality of the solid phase is calculated by use of the predictive well-known local composition models: the UNIQUAC model that allows for the equilibrium calculation of multisolid phases or the Wilson model. The UNIQUAC model proposed by Coutinho is given by

( )

( )

N N Φi gE θ Z ) xi ln + q x ln RT i)1 xi 2 i)1 i i Φi

∑

∑

N

[

(

N

∑ q x ln ∑ θ exp i i

j

j)1

λij - λii qi RT

)]

(7)

with Φi )

xi ri N

∑x r

j j

i)1

and

θi )

xi qi N

∑x q

(8)

j j

i)1

and the structural parameters ri and qi are used to take into account the specificity of the interactions in the solid phase. The interaction energy parameters, λi, are estimated from the heat of sublimation of a pure orthorhombic crystal 2 λii ) - (∆Hisub - RT) Z

(9)

with Z being the coordination number () 6). The interaction energy parameter between nonidentical molecules is given by λij ) λji ) λjj(1 + ξ)

(10)

where j is the n-alkane with the shorter chain of the pair ij and ζ is the adjustable parameter (default ζ ) 0).

i

ln

P

VLi dP RT (5)

[ ( ) ( ) ( ( ) ) ] [ ( ∫ )]

0L (P)γSi exp φSi ) φpure,i

i)1

(2)

P0

where φ0L pure,i(P) is the liquid fugacity coefficient of pure component i, which is computed by the three-parameter PR EOS, at the system temperature (T) and pressure (P). The exponential term in eq 5 is used to convert the fugacity from P to P0. Substituting eqs 4 and 5 into eq 3 and rewriting f Si in the form of eq 2, the fugacity coefficient of component i in the solid phase is given by

where the fugacity f Π i of component i in phase Π (Π ) V, L, and S) is calculated by Π fi Π ) φΠ i xi P

(∫

VLi 0L dP ) φpure,i (P)P exp RT

(4)

(9) Coutinho, J. A. P.; Daridon, J. L. The limitations of the cloud point measurement techniques and the influence of the oil composition on its detection. Pet. Sci. Technol. 2005, 23 (9 and 10), 1113–1128. (10) Coutinho, J. A. P.; Pauly, J.; Daridon, J. L. A thermodynamic model to predict wax formation in petroleum fluids. Braz. J. Chem. Eng. 2001, 18 (4), 411–422.

Characterization of TBP and Plus Fractions To apply the PR EOS to a reservoir fluid, a characterization procedure for the true boiling point (TBP) or single carbon number (SCN) and plus fractions is required.11 The characterization procedure of Zuo and Zhang2 should be significantly modified to (11) Chorn, L. G.; Mansoori, G. A. AdVances in Thermodynamics, C7+ Fraction Characterization; Taylor and Franci: New York, 1989; Vol. 1.

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Zuo and Zhang

satisfy the needs of solid precipitations. For systems without wax and/or asphaltene precipitations, the characterization procedure is reduced to that proposed by Zuo and Zhang,2 which is adopted to estimate the critical temperature, critical pressure, and acentric factor of each TBP or plus fraction. It is also allowed to group the subfractions of C7+ into pseudocomponents by means of a mass average, a molar average, or an arbitrary selection. As mentioned previously, only normal paraffins are assumed to be potential wax formers. Therefore, the distribution of n-paraffins in reservoir fluids must be known/estimated. Each TBP fraction or SCN fraction is split into two parts: the n-paraffin and the residue. The residue is characterized in terms of the method proposed by Zuo and Zhang.2 The following exponential decay expression is used for the residue (Cn-C80): ln zi ) A + Bni

(11)

Mi ) 14ni + η

(12)

where A and B are determined by fitting the residue distribution of C7-C29 and subject to two constraints (measured and predicted mole fraction and the molecular weight of the plus fraction should be identical). η is an adjustable parameter (η ) from -10 to 2, usually fixed ) -4), and zi is the mole fractions of the residue in subfraction i. ni is the carbon number. To obtain n-paraffin distribution in crude oil, two different methods are used for systems with and without experimental HTGC data, respectively. HTGC allows for the direct detection and quantification of n-paraffins up to very high molecular weights (up to n-C90). It can provide both the total n-paraffin content and its decay with carbon numbers/molecular weights. Therefore, the HTGC data are directly used to characterize n-paraffins. For the systems without HTGC data, solvent precipitation, such as the UOP 46-85 assay or any of its variants, is a standard procedure that provides a good estimate of the total wax content of stock tank oil (STO). If no total wax content is available, a correlation must be provided to estimate it. The exponential decay of the n-paraffins in reservoir fluids is well-documented in the literature. It is defined as the ratio between the mass fractions of two successive n-paraffins R)

wCn wCn-1

(13)

We may set R ) 0.88 as a default value. The physical properties of n-paraffins and residue are calculated by different correlations available in the literature.

Results and Discussion Synthetic Oil Systems. The accuracy of the proposed wax thermodynamic model has first been validated for synthetic oil systems without characterization. The adjustable parameter ζ in the UNIQUAC model is set to the default value (ζ ) 0) for all synthetic oil systems. That means that there are no adjustable parameters used for describing the phase behavior of synthetic oil systems, except for default binary interaction parameters kij in the PR EOS taken from PVT Pro. The kij in the PR EOS is usually used to improve the prediction of vapor-liquid equilibria. Daridon et al.12 reported phase boundary (wax formation and bubble point) data for four synthetic oil systems consisting of C1, n-C10, and n-C18-n-C30 at high pressures. The modified wax model is employed to predict the phase diagrams of the four mixtures. The absolute average deviations of the predicted WAT are 1.2, 0.4, 1.1, and 0.7 K for mixtures A, B, C, and D, respectively. It should be noticed that the proposed wax model (12) Daridon, J. L.; Xans, P.; Montel, F. Phase boundary measurement on a methane + decane + multi-paraffins system. Fluid Phase Equilib. 1996, 117 (1 and 2), 241–248.

Figure 1. P-T phase diagram for four synthetic oil systems of Daridon et al.12

Figure 2. Amount of wax precipitated for synthetic oil systems of Dauphin et al.13

has no adjustable parameters, while the previous wax model has one adjustable parameter to match WAT for each mixture. The predicted results are similar by use of the two models. Figure 1 compares the predicted results of phase boundaries with the measured data for the four mixtures. It can seen that the predictions agree well with the experimental data. Dauphin et al.13 measured wax composition as a function of temperatures for several synthetic oil systems made of n-C10 and n-C18-n-C36 at atmospheric pressure (wax cut data). In some systems, intermediate n-paraffins were removed from the series to have various “bimodal” distributions. The wax model is also used to predict the amount of wax precipitated as a function of temperatures and n-paraffins distributions in the solid phase. The typical amount of wax precipitated versus the temperature is shown in Figure 2 for mixtures BIM0, BIM5, BIM9, and BIM13. The predictions are in good agreement with the measured data. It can be observed that the wax model is able to describe the “bimodal” behavior of the synthetic oil systems BIM5, BIM9, and BIM13 well. The predicted and measured percentages of n-paraffins crystallized versus the temperature and carbon number for mixture BIM0 are depicted in Figure 3. Figure 4 compares the measured and predicted n-paraffins distributions in the solid phase for mixture BIM0. The wax model describes heavy n-paraffin distributions in the solid phase well, while the predictions somewhat deviate from the experimental data for light n-paraffins. Pauly et al.14 measured the amount of precipitated wax as a function of temperatures for three synthetic oils composed of n-C10 and n-C18-n-C30 at atmospheric pressure. The predictions of the percentage of crystallization and amount of wax precipitated as a function of the temperature using the wax (13) Dauphin, C.; Daridon, J.L.; Coutinho, J. A. P.; Balyere, P.; PotinGautier, M. Wax content measurements in partially frozen paraffinic systems. Fluid Phase Equilib. 1999, 161 (1), 135–151. (14) Pauly, J.; Dauphin, C.; Daridon, J. L. Liquid-solid equilibria in a decane + multi-paraffins system. Fluid Phase Equilib. 1998, 149 (1 and 2), 191–207.

Wax Formation from Synthetic Oil Systems

Figure 3. Percentage of n-paraffins crystallized versus the temperature and carbon number for synthetic oil mixture BIM0 of Dauphin et al.13

Energy & Fuels, Vol. 22, No. 4, 2008 2393

Figure 6. Amount of wax precipitated versus the temperature for mixtures A, B, and C of Pauly et al.14

Figure 7. Percentage of n-paraffins crystallized versus the temperature for diesel S of Coutinho et al.15 Figure 4. n-Paraffins distributions in the solid phase for synthetic oil mixture BIM0 of Dauphin et al.13

Figure 8. n-Paraffin distributions in the solid phase for diesel NS of Coutinho et al.15 Figure 5. Percentage of n-paraffins crystallized versus the temperature for mixtures A, B, and C of Pauly et al.14

model are compared to the measured values as shown in Figures 5 and 6, respectively. The agreement between the predicted and measured values is good. It can be seen from the tests mentioned above that the proposed wax model is able to describe the phase behavior of synthetic oil systems well without any adjustable parameters. Diesel Fuel Systems. The proposed wax thermodynamic model has been validated for diesel fuel systems as well. Coutinho et al.15 reported the phase behavior of diesels N and NS. They not only measured WAT but also n-paraffin (PNA) distributions using HTGC. In this work, the solvent in diesel fuels is treated as a C10+ fraction and the characterization procedure mentioned above is employed to characterize the C10+ fraction (splitting to five pseudocomponents). Figure 7 compares the predicted weight percentage of wax crystallized versus the temperature with the experimental data for diesel S. The predicted n-paraffin distributions as a function of the carbon (15) Coutinho, J. A. P.; Dauphin, C.; Daridon, J. L. Measurements and modeling of wax formation in diesel fuels. Fuel 2000, 79 (6), 607–616.

Figure 9. Impact of pressures on WAT for diesel NS of Coutinho et al.15

number of n-paraffins are shown in Figure 8 for diesel NS at 258.15 and 250.15 K. The impact of pressures on WAT of diesel NS is depicted in Figure 9. The predictions are in good concordance with the measured data. To take into account the impact of the number of solvent pseudocomponents, the C10+ fraction was characterized to 5, 7, and 10 pseudocomponents and the WAT of diesel NS were recalculated. The results are

2394 Energy & Fuels, Vol. 22, No. 4, 2008

Figure 10. P-T diagram for live oil fluid WPF1.16

Figure 11. Amount of wax precipitated as a function of the temperature for the dead oil of fluid WPF1.16

compared in Figure 9 as well. It can be seen that the impact of the number of solvent pseudocomponents on WAT is slight. Live Oil Systems. Currently, Alboudwarej et al.16 reported PVT, WAT, and wax cut data for three live oil systems with HTGC data of n-paraffin distributions. The proposed wax thermodynamic model and the modified characterization procedure are used to represent the phase behavior of the systems. For fluid WPF1, the critical properties of pseudocomponents and volume translation parameters are tuned to match the measured bubble point pressure, gas/oil ratio (GOR), and American Petroleum Institute (API) gravity of the fluid. The adjustable parameter ζ in the UNIQUAC model is set to the default value (ζ ) 0). The wax model is then employed to predict thermodynamic WAT locus. The predicted thermodynamic WAT is about 40 K higher than the measured WAT. This is not surprising because the HTGC data show that the fluid (STO) has a long tail in the plot of the weight percentage versus carbon numbers of n-paraffins (up to n-C80). The amount of heavy n-paraffins is very small, and the experimental technique cannot detect the formation of the first wax crystal in the fluid. To observe the sensitivity of WAT to the amount of wax precipitated in the fluid, a series of wax-quality lines at fixed amount of precipitated wax are calculated by the wax model. It is found that the WAT locus can be shifted close to the measured WAT at a small amount of wax precipitated (0.4 wt %) in the fluid, as shown in Figure 10. The small amount of wax precipitated in the fluid approximately corresponds to the weight percentage of n-C48+ (summation from n-C48 to n-C80) in the original STO oil. The wax cut curve is also predicted by use of the wax model, and the results are depicted in Figure 11. The predictions are slightly higher than the measured data. It can be seen that the amount of wax precipitated in the fluid (16) Alboudwarej, H.; Zuo, J. Y.; Mahmoodaghdam, E.; Kharrat, A. M. Presentation at 7th International Conference on Petroleum Phase Behavior and Fouling, Asheville, NC, June 25-29, 2006.

Zuo and Zhang

Figure 12. n-Paraffin distributions in the solid phase for the dead oil of fluid WPF1.16

Figure 13. n-Paraffin distributions in the solid phase for the dead oil of fluid WPF3 at 288.71 K and 1.01 bar.16

gradually increases as the temperature decreases at the beginning of the WAT and steeply increases after the temperature is lower than about 308 K. This behavior is similar to the liquid dropout curve as a function of the pressure in a gas condensate system. Figure 12 compares the predicted and measured n-paraffin distributions in the solid phase at 313.48 and 299.82 K for the STO at atmospheric pressure. Although the predictions are deviated from the measured data at some interval (n-C47-nC59), the predictions are quite reasonable. WPF1 is a fluid mixed up from two STO of naturally existing reservoir fluids and recombined with a separator gas. n-Paraffin distributions fluctuate between n-C47 and n-C59 in the commingled STO, and the amount is very small and rounded. The small fluctuation of n-paraffin distributions in the STO causes significant compositional variation in the solid phase when the compositions of n-C47-n-C59 are dominated in the solid phase. Fluid WPF2 has a similar phase behavior to that of fluid WPF1. Therefore, the results of fluid WPF2 are not presented in this paper. For fluid WPF3, the measured bubble point pressure, GOR, and API gravity of the fluid are first matched by tuning the critical properties of pseudocomponents and volume translation parameters. Next, the adjustable parameter ζ (ζ ) -0.08) is adjusted to match the measured n-paraffin distributions in the solid phase at 288.71 K and 1.01 bar (wax cut data). The fitting results are shown in Figure 13. Then, the wax model is used to predict n-paraffin distributions in the solid phase at 288.71 K and 34.47 bar, as shown in Figure 14. The predictions are in good agreement with the experimental data. Figure 15 shows the predicted P-T diagram for fluid WPF3. The thermodynamic WAT is about 50 K higher than the measured WAT. WAT locus can be shifted close to the measured WAT by specifying 0.05 wt % of wax precipitated. This value corresponds to the weight percentage of n-C50+ in the STO.

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measured WAT compared to live oil systems because the tail of heavy waxy n-paraffins, in the plot of weight percent versus carbon numbers of n-paraffins, is a lot shorter in gas condensate systems than in live oil systems. For fluid GC-A, thermodynamic WAT can be shifted close to the measured WAT by specifying 0.28 wt % of wax precipitated. This fixed weight percentage approximately corresponds to the value of n-C30+. While for fluid GC-B, the fixed weight percentage is 0.13 wt %, corresponding to the value of n-C34+. Conclusions

Figure 15. P-T diagram for live fluid WPF3.16

In this work, a wax precipitation model proposed by Zuo et al.1 has been modified by introducing the UNIQUAC model for the solid (wax) phase. The characterization proposed by Zuo and Zhang2 has also extended to crude oil and gas condensate systems. The developed wax thermodynamic model has then been applied to calculate WAT and the amount of precipitated wax for synthetic oil, diesel fuel, dead and live oil, and gas condensate systems. The calculation results are in good concord with the experimental data. Although predicted thermodynamic WAT is usually considerable higher than the experimental data for actual reservoir fluids, WAT locus can be shifted to the measured values by specifying a small amount of wax precipitated in the fluids. To obtain a better representation of the phase behavior for crude oil and gas condensate systems, the proposed wax model provides flexibility to match experimental wax cut data instead of WAT data.

Figure 16. P-T diagram for two gas condensates of Daridon et al.17

Cp ) heat capacity f ) fugacity H ) enthalpy M ) molecular weight n ) carbon number P ) pressure q ) surface parameter in the UNIQUAC model r ) volume parameter in the UNIQUAC model R ) gas constant T ) temperature V ) molar volume w ) weight fraction x and z ) mole fraction Z ) coordination number

Figure 14. n-Paraffin distributions in the solid phase for live fluid WPF3 at 288.71 K and 34.47 bar.16

Nomenclature

Live Gas Condensate Systems. Daridon et al.17 reported the measured vapor-liquid equilibrium (VLE) boundary and WAT data for two gas condensates and HTGC data. The wax model and the modified characterization procedure are employed to calculate a P-T diagram for the two gas condensates (GC-A and GC-B). The saturation points are matched by tuning the properties of heavy pseudocomponents. The predicted thermodynamic cloud points are similar for both fluids, as shown in Figure 16. The predictions of thermodynamic WAT are higher than the measured values similar to live oil systems. However, the predicted thermodynamic WAT is much closer to the (17) Daridon, J. L.; Pauly, J.; Coutinho, J. A. P.; Montel, F. Solidliquid-vapor phase boundary of a North Sea waxy crude: Measurement and modeling. Energy Fuels 2001, 15, 730–735.

Greek Letters ∆ ) variation γ ) activity coefficient in the solid phase φ ) fugacity coefficient Subscripts i ) species i pure ) property of pure component Superscripts f ) state at the melting point L ) liquid S ) solid V ) vapor 0 ) standard state Π ) any phase EF800056D