Energy Fuels 2010, 24, 1753–1761 Published on Web 02/04/2010
: DOI:10.1021/ef901195w
Method to Determine the Wax Solubility Curve in Crude Oil from Centrifugation and High Temperature Gas Chromatography Measurements Shanpeng Han,† Zhenyu Huang,‡ Michael Senra,‡ Rainer Hoffmann,§ and H. Scott Fogler*,‡ †
Beijing Key Laboratory for Urban Oil and Gas Distribution Technology, China University of Petroleum, Beijing, 102249, China, ‡ Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, and §Herøya Research Centre, Statoil ASA, N-3908 Porsgrunn, Norway Received October 20, 2009. Revised Manuscript Received January 19, 2010
Wax precipitation and deposition are major flow assurance problem in crude oil production and transportation. Knowledge of the amount of wax that precipitates from the crude oil at different temperatures, delineated by the solubility curve, is necessary for accurate predictions of wax deposition in subsea pipelines. The solubility curve is obtained from the wax precipitation curve, which is determined using centrifugation and high temperature gas chromatography (HTGC). However, previous studies have overestimated the amount of precipitated wax by assuming that all heavy alkanes or heavy n-alkanes exist solely in the solid phase. This work addresses this issue by conducting mass balances on the noncrystallized carbon numbers in the centrifuged cake and in the crude oil. A new equation was developed to obtain the solid fraction of the centrifuged cake and crude oil. The wax precipitation curve developed by this new method was compared with the curves determined using the previous methods and differential scanning calorimetry (DSC). The curve determined by this new method was consistent with the results obtained by DSC, while previous methods overpredicted the amount of precipitated wax.
temperature, heavy molecular weight alkane molecules precipitate out of the crude oil.1-19 The resulting wax deposition that occurs poses a significant transportation problem by progressively restricting the flow of crude oil, increasing the pressure drop or even plugging the pipeline.1-10 Proper implementation of mechanical remediation techniques, such as pigging, requires knowledge of both the deposit thickness and the wax fraction as a function of time. Computer simulations developed by our research group for wax deposition have been used to obtain these two quantities.4,5 In general, the major components of wax deposition simulation models are hydrodynamics, heat and mass transfer and the wax deposition mechanism. The temperature and wax concentration profile can be obtained by simultaneously solving the heat and mass transfer equations. The wax concentration profile is then combined with the wax deposition mechanism to obtain the deposit growth rate. Numerous wax deposition mechanisms have been proposed including molecular diffusion, Brownian diffusion, shear removal, shear dispersion, settling, and particle diffusion. Of these mechanisms, radial diffusion of wax molecules has been confirmed to be the major driving force for wax deposition.4-7 The radial diffusion of wax molecules from the centerline to the cold pipeline wall results from a radial wax concentration gradient caused by a radial temperature gradient, which in turn causes a decrease in the wax solubility. This decrease of the wax solubility in crude oil can be determined by measuring the increase in the amount of precipitated wax with temperature decreasing. The amount of wax remaining dissolved in the crude oil at each temperature can be obtained by subtracting the amount of precipitated wax from the total wax content of the original crude. Using this technique, a wax solubility curve can be obtained by plotting the amount of wax remaining dissolved in the crude oil as a function of temperature.
1. Introduction Crude oil cools as it flows through subsea pipelines on the ocean floor from offshore platforms to shore. When the temperature of waxy crude oil drops below the cloud point *To whom correspondence should be addressed. Telephone: (734) 763-1361. Fax: (734) 763-0459. E-mail:
[email protected]. (1) Roehner, R. M.; Fletcher, J. V.; Hanson, F. V. Energy Fuels 2002, 16, 211–217. (2) Ronningsen, H. P.; Bjorndal, B.; Hansen, A. B.; Pedersen, W. B. Energy Fuels 1991, 5, 895–908. (3) Senra, M.; Panacharoensawad, E.; Kraiwattanawong, K.; Singh, P.; Fogler, H. S. Energy Fuels 2008, 22, 545–555. (4) Singh, P.; Venkatesan, R.; Fogler, H. S. AIChE J. 2000, 46 (5), 1059–74. (5) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. AIChE J. 2001, 47 (1), 6–18. (6) Weispfennig, K. Advancements in Paraffin Testing Methodology; SPE 64997; Society of Petroleum Engineers: Richardson, TX, 2001; pp 1-6. (7) Venkatesan, R.; Nagarajan, N. R.; Paso, K.; Yi, Y.-B.; Sastry, A. M.; Fogler, H. S. Chem. Eng. Sci. 2005, 60, 3587–98. (8) Coto, B.; Martos, C.; Pena, J. L.; Espada, J. J.; Robustillo, M. D. Fuel 2008, 87, 2090–2094. (9) Martos, C.; Coto, B.; Espada, J. J.; Robustillo, M. D.; Gomez, S.; Pena, J. L. Energy Fuels 2008, 22, 708–714. (10) The University of Tulsa Paraffin Deposition Prediction in Multiphase Flowlines and Wellbores Joint Industry Project.: “Fluid Characterization and Property Evaluation Final Report” (February 1999) (11) Chen, J.; Zhang, J.; Li, H. Thermochim. Acta 2004, 410, 23–26. (12) Kok, M; Letoffe, J.; Claudy, P.; Martin, D.; Garcin, M.; Volle, J. Fuel 1996, 75 (7), 787–790. (13) Elsharkawy, A. M.; As-Sahhaf, T. A.; Fahim, M. A. Fuel 2000, 79, 1047–55. (14) Coutinho, J. A. P. Ind. Eng. Chem. Res. 1998, 37, 4870–4875. (15) Hansen, A. B.; Larsen, E.; Pedersen, W. B.; Nielsen, A. B.; Ronnigsen, H. P. Energy Fuels 1991, 5, 914–923. (16) Pedersen, K. S.; Skovborg, P. Energy Fuels 1991, 5, 924–932. (17) Roehner, R. M.; Hanson, F. V. Energy Fuels 2001, 15, 756–763. (18) Hansen, A; Pedersen, W; Larsen, E.; Nielsen, A.; Ronningsen, H. Energy Fuels 1991, 5 (6), 908–913. (19) Dauphin, C.; Daridon, J. L.; J. Coutinho, J. A. P.; Baylere, P.; Potin-Gautier, M. Fluid Phase Equilib. 1999, 161, 135–151. r 2010 American Chemical Society
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Energy Fuels 2010, 24, 1753–1761
: DOI:10.1021/ef901195w
Han et al.
The importance of the wax solubility curve on wax deposition modeling can be seen in the model developed by Singh, Venkatesan and Fogler to predict the deposit thickness, δ, as a function of time, t.4 On the basis of the diffusion of heavy components from the bulk fluid to the deposit surface and the light components from the deposit to the bulk, the growth rate of the deposit dδ/dt is determined by the difference between the convective mass flux, kl[Cwb - Cws(Ti)], and the diffusive mass flux, -De(dCws/dr)|i, as shown in eq 1.4 0 1 dδ dCws A ðF w ðtÞFgel RÞ 3 ¼ kl ½Cwb - Cws ðTi Þ - @-De dt dr term 1
Fourier transform infrared spectroscopy (FTIR) is another method used to determine the wax precipitation curve by measuring the increase in the infrared absorbance of the crude oil sample caused by wax precipitation.17 The increase in the integrated absorbance from 735 to 715 cm-1, which corresponds to the CH2 rocking band of n-alkanes, is assumed to be linearly related to the increase of weight percent of precipitated solid wax. However, for different n-alkanes, the same amount of increased absorbance in this band will not correspond to the same amount of n-alkane precipitated because the alkane CH2 content varies, meaning that the linear relationship is not completely accurate. Filtration and centrifugation provide direct methods to measure the amount of precipitated wax by separating the precipitated wax from the cooled crude oil.1,8,10 However, a significant amount of liquid crude oil can be entrapped in the filtered and centrifuged cakes, requiring the use of techniques, such as 1H NMR or HTGC, is also needed to evaluate the solid wax content. The 1H NMR technique provides the amount of aromatics in crude oil by measuring the amount of hydrogen atoms in the aromatic rings (Har) and also the amount of hydrogen atoms next to functional groups (HR), methylene hydrogen atoms (Hβ), and methyl hydrogen atoms (Hγ).9,18 Because aromatics are highly soluble in crude oil, they are assumed to exist solely in the liquid phase.9 Using the amount of Har in crude oil (HarC) and filtered cake (HarM), Martos et al. proposed an equation to calculate the percent of entrapped oil in the cake. HarM 100% ð3Þ entrapped oil ðwt %Þ ¼ HarC
i
term 2
ð1Þ The convective mass flux, term 1, accounts for wax molecules transferring from the centerline to the deposit-fluid interface and governed by the mass transfer coefficient kl and the difference between the wax concentration in the bulk and at the deposit-fluid interface, [Cwb - Cws(Ti)]. The diffusive mass flux, term 2, refers to wax diffusing from the gel-oil interface into the deposit where the entrapped liquid crude oil serves as a medium. The flux is governed by the effective diffusion coefficient De and the radial wax concentration gradient, dCws/dr. The wax concentration gradient in the deposit layer can also be described using the changes in wax solubility with temperature and the temperature gradient, as shown in eq 2. dCws dCws dT ¼ dr dT 3 dr
ð2Þ
Unfortunately, the low ratio of signal-to-noise of 1H NMR gives a significant relative error.9,18 The carbon number distribution obtained by high temperature chromatography (HTGC) provides another means to determine the solid fraction in the filtered and centrifuged cakes. For the filtered cakes, Martos et al. chose a starting carbon number of 15, meaning that components with carbon numbers less than 15 will remain in the liquid phase and components with carbon numbers greater than fifteen will solidify.9 However, Roehner et al. developed a different method to determine the starting carbon number of precipitated wax as a function of temperature.1 Assuming that the non n-alkane components are present entirely in the liquid, Roehner et al.’s starting carbon number is the carbon number where the ratio of weight percent of n-alkane to non n-alkane in the cake is higher than that in the crude oil.1 The major limitation in these previous studies using HTGC comes from their methods to calculate the solid fraction from the experimental results. Using the n-alkanes distribution provided by Nenniger Engineering Company, the Marathon Oil Company accounted for all of the heavy n-alkanes (C22þ) as solid wax (referred to as Marathon-Nenniger method in this work).10 Roehner et al. and Martos et al. account for all the heavy components including both n-alkane and nonn-alkanes as precipitated wax.1,9 However, research has shown that those heavy components in the crude oil exist both the solid and liquid phases at a particular temperature because of solid-liquid equilibrium.14,19-21 If there are significant
Because both the convective and diffusive mass fluxes require solubility data as a function of temperature, an accurate solubility curve is crucial for wax deposition modeling. A number of techniques have been developed to determine the amount of precipitated wax in crude oil at different temperatures, including DSC, FTIR, NMR, HTGC, filtration and centrifugation, which can be categorized as direct methods and indirect methods.1,8-14,16,17 Direct methods, such filtration and centrifugation, obtain the amount of precipitated wax by separating solid wax from the cooled crude oil. Indirect methods rely on measuring the change of another property that occurs because of wax precipitation. A widely used indirect method to determine the wax precipitation curve is differential scanning calorimetry (DSC), which measures the heat released from wax precipitation.8,11-15 By assuming a constant enthalpy of crystallization, the heat released by the crude during cooling is proportional to the amount of precipitated wax. The amount of precipitated wax at different temperatures can be determined by dividing the accumulated heat released by the enthalpy of crystallization. DSC is widely used because of its simplicity and fast response. However, because the composition of precipitated wax changes as a function of temperature, the enthalpy of crystallization is temperature dependent.15 In addition, the enthalpy of crystallization of the wax can vary widely depending on the composition of the crude oil. Hansen and Rønningsen showed that the enthalpies of crystallization for fourteen different crude oils from the North Sea ranged from 100 J/g to 297 J/g.15 Although DSC provides a range for both the wax content and the wax precipitation curve; it cannot give an exact wax precipitation curve without knowing the enthalpy of crystallization.
(20) Zuo, J. Y.; Zhang, D. Energy Fuels 2008, 22, 2390–2395. (21) Pauly, J.; Dauphin, C.; Daridon, J. L. Fluid Phase Equilib. 1998, 149, 191–207.
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: DOI:10.1021/ef901195w
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amounts of heavy components dissolved in the liquid phase, the amount of precipitated wax will be drastically overestimated. Our work overcomes this problem by utilizing a mass balance on the centrifugation process and by using HTGC to appropriately address how each carbon number distributes in the liquid and solid phases. The wax solubility curve of a crude oil was developed using this method and compared with the solubility curves determined by DSC, Marathon-Nenniger method, and Roehner et al.’s method.
Figure 1. Sketch of the experimental procedure for determining the weight percent of precipitated wax in crude oil using centrifugation and HTGC.
2. Analysis of the Centrifugation-HTGC Method To determine the fraction of precipitated wax in crude oil using centrifugation and HTGC, four major steps are required as shown in Figure 1: (1) cooling a known mass (mcrude) of a crude oil sample to a specific temperature, (2) centrifuging the crude oil at the specified temperature and separating the cake from the supernatant and measuring the mass of the cake (mcake), (3) performing a HTGC analysis on the cake to obtain the fraction of solid wax (FS,cake) in the cake, and (4) Calculating the fraction of precipitated wax in crude oil (FS,crude) using eq 4. FS, crude ¼
mcake 3 FS, cake mcrude
Figure 2. System analysis on the centrifugation process.
supernatant, and the liquid in the precentrifuged crude oil all have the same composition denoted as wL,i.
ð4Þ
mL, cake 3 wL, i þ mS, cake 3 wS, i mcake
ð10Þ
mL, cake 3 wL, i mcake
Wi jcakeði < N C Þ mcake mL, cake ¼ mL, crude Wi jcrudeði < N C Þ 3 mcrude
ð12Þ
ð13Þ
As can be observed from eq 13, for all of the components with a carbon number less than NC, the ratio between its weight percent in the cake and that in the crude oil is a constant, defined as a. Wi jcakeði < N C Þ ð14Þ a ¼ Wi jcrudeði < N C Þ
ð5Þ
ð6Þ
We also define the ratio of the mass of the cake to the mass of the crude oil sample as b. mcake ð15Þ b ¼ mcrude By solving eqs 5-7 and 13 simultaneously, the solid fraction in the cake, FS,cake, and in the crude oil, FS,crude, can be determined. mS, cake 1-a ð16Þ ¼ FS, cake ¼ 1 - ab mcake
ð7Þ
Thus, mcrude 3 FS, crude ¼ mcake 3 FS, cake
Wi jcake ¼
Combining eqs 11 and 12 yields eq 13
(3) Because the centrifugation is performed isothermally, it is assumed that no further wax precipitation occurs. The solid in the crude oil sample will be entirely in the cake after centrifugation. mS, crude ¼ mS, cake
ð9Þ
Wi jcakeði < N C Þ ¼
(2) The mass of the centrifuged cake is the sum of the liquid and solid in the cake. mcake ¼ mL, cake þ mS, cake
mL, crude 3 wL, i þ mS, crude 3 wS, i mcrude
The lowest carbon number present in the precipitated wax is defined as NC. For all the components with carbon numbers less than NC, eqs 9 and 10 can be reduced to eqs 11 and 12 because wS,i = 0. mL, crude 3 wL, i Wi jcrudeði < N C Þ ¼ ð11Þ mcrude
As discussed earlier, the liquid oil entrapped in the centrifuged cakes creates a problem in determining the solid fraction in the centrifuged cake using HTGC. In this work, an equation was derived from a mass balance on the centrifugation process. As shown in Figure 2, the centrifugation consists of one feed stream and two output streams with four unknown variables: the mass of solid wax particles in the cooled crude (mS,crude) and in the cake (mS,cake), the mass of liquid oil in the crude, (mL,crude) and in the cake (mL,cake). Solving for these four unknown variables requires four equations that relate the variables to one another. The mass balance before and after centrifugation yields three equations: (1) The mass of the crude oil sample is the sum of the liquid and solid in the cooled crude oil. mcrude ¼ mL, crude þ mS, crude
Wi jcrude ¼
ð8Þ
In this work, the components, including both n-alkane and non-n-alkane with same carbon number, are regarded as one group. Taking the weight fraction of all the components with carbon number i in the liquid phase as wL,i and the weight fraction in the precipitated solid as wS,i, the weight fraction of all the components with carbon number i in the crude oil sample(Wi|crude) and in the cake (Wi|cake) are given in eqs 9 and 10. The entrapped oil (L) in the cake, the corresponding
FS, crude ¼
mS, cake b - ab ¼ 1 - ab mcrude
ð17Þ
3. Experimental Section 3.1. Crude Oil. The crude oil used for this research is a condensate from the North Sea provided by Statoil. 3.2. Centrifugation. A Beckman Instruments centrifuge (model L8-70) with a temperature-controlled chamber was used 1755
Energy Fuels 2010, 24, 1753–1761
: DOI:10.1021/ef901195w
Han et al.
to centrifuge the crude oil samples. The 50-mL centrifuge tubes used to hold the crude oil are equipped with an O-ring and a cap to prevent the loss of light ends during testing. To ensure that no solid wax is present in the sample, the crude oil was heated to 60 °C (30 °C higher than the WAT) and held at that temperature for 2 h before being transferred into the tubes. The filled centrifuge tubes were weighed before being transferred into the rotor head. The tubes and centrifuge chamber were cooled to the specified temperatures (30, 20, 10, and 5 °C). The samples were centrifuged at 25000 rpm for 20 h. After the centrifugation, the liquid phase was drained, and each tube was swabbed to remove any residual liquid. The tubes were reweighed to obtain the mass of the centrifuged cake. 3.3. High-Temperature Gas Chromatography (HTGC). The carbon number distributions of crude oil and centrifuged cake were both measured using gas chromatography. The crude oil is measured using a Hewlett-Packard 6890A GC equipped with capillary column coated with DB-1 (40 m0.100 mm0.20 μm). The oven temperature was initiated at 30 °C and increased to 80 °C at a rate of 2.8 °C/min, then to 170 °C at a rate of 5.7 °C/min. To give a higher resolution on heavy alkanes, the centrifuged cakes were analyzed using a high temperature gas chromatograph (HTGC) Hewlett-Packard 6890A equipped with a CPSimDist Ultimetal column (25 m 0.53 mm 0.09 mm). The oven temperature was initiated at 40 °C and increased to 430 °C at a rate of 10 °C/min. The internal standard method was used for the cake analysis. 3.4. Differential Scanning Calorimeter (DSC). The calorimetric measurements were performed using a TA Q2000 DSC. The crude oil is first heated to 60 °C, held at this temperature for one hour and then cooled from 60 to -50 °C at a rate of 0.5 °C/min.The DSC trials allowed for the determination of the onset of a liquid-solid transition and the amount of heat released in transition from liquid to solid.
Table 1. Starting Carbon Number of Precipitated Wax at Different Temperatures temperature, °C
starting carbon number of precipitated wax, NC
5 10 20 30
21 21 28 34
than 5 °C. The weight percent of those components in the crude oil are shown in Table 2. However, Figure 3 shows that those components have a higher weight fraction in the cake than in the oil. This inconsistency is mainly because of the experimental limitation introduced by the internal standard method used for GC analysis. The internal standard method requires knowledge of the weight percent of internal standard in the sample. The weight percent of component i can then be determined by taking the ratio of peak area of component i to the internal standard. However, because the internal standard can not be properly distributed within the cake samples, the reported weight percent of internal standard in sample will deviate from its true value. As a result of this deviation, it can be seen in Figure 4 that the sum of the components with carbon number larger than 15 do not increase with decreasing temperature as expected. However, because the ratios among the weight percents of the components are unaffected by the internal standard concentration in the sample, a normalization procedure can be used to overcome this issue. The normalization procedure was carried out for the weight percent of components with carbon numbers larger than fifteen. As shown in eq 18, the normalized weight percent of component i, Wi|normalized cake or crude, was obtained by dividing the measured weight percent, Wi|measured cake or crude by the sum of measured C15þ fractions, ΣC15þWi|measured cake or crude
4. Result and Analysis 4.1. Determination of the Starting Carbon Number of Precipitated Wax, NC. The starting carbon number, NC, is the lowest carbon number present in the precipitated wax and thus any components with carbon number below NC will be entirely present in the liquid phase. In this work, the method presented by Roehner et al. was used to determine the starting carbon number of precipitated wax.1 The details of this method are shown in Appendix A. The starting carbon numbers of precipitated wax at 5, 10, 20 and 30 °C were determined and listed in Table 1. It can be seen the starting carbon number of precipitated wax increased as a function of temperature. 4.2. Comparison of Normalized Carbon Number Distribution in the Cakes and in the Crude Oil. To make a proper comparison of the carbon number distribution in the cakes and in the crude oil, the carbon number distribution in the cakes and in the crude oil are optimized using a normalization procedure, discussed in detail as follows: Because the amount of precipitation for a certain component increases with decreasing temperature, if one component does not precipitate at a certain temperature, it does not precipitate at any higher temperatures. Table 1 shows that the lowest starting carbon number was 21 for the cake obtained at 5 °C, indicating that all the components with carbon number less than 21 are solely present in the liquid phase at all temperatures above 5 °C. Additionally, the amount of those components is decreased by discarding the supernatant after centrifugation. Therefore for those components, their weight fractions in the cake are supposed to be lower than their weight fractions in the crude oil, that is, wi,(i
