Energy & Fuels 2004, 18, 1005-1013
1005
Bulk Stabilization in Wax Deposition Systems K. G. Paso and H. Scott Fogler* Department of Chemical Engineering, University of Michigan, 2300 Hayward Street, Ann Arbor, Michigan 48109-2136 Received December 19, 2003. Revised Manuscript Received April 8, 2004
Managing paraffin deposition in crude oil transport pipelines comprises a significant operating expense for petroleum producers. Incipient wax-oil gel deposits age with time via a counterdiffusion mechanism where there exists a critical carbon number (CCN); wax molecules with carbon numbers greater than the CCN diffuse from the bulk fluid into the gel, and vice versa. Paraffin deposit samples were obtained from a real crude oil using a coldfinger wax deposition device and were analyzed by gas chromatography. Comparison of bulk oil and deposit compositions demonstrates that crystallization of n-paraffin components occurs at lower carbon numbers than analogous non-n-paraffin hydrocarbon components. A new concept is introduced of using the depletion of paraffin components from the bulk solution to delineate aging and incipient gelation phenomena. Depletion is defined as the normalized decrease in mass fraction of a paraffin component in the bulk fluid during deposition. Deposition performed using model fluids demonstrates that depletion is dependent upon the bulk fluid temperature. When the bulk fluid temperature is maintained lower than the cloud point, the highest molecular weight components form stable crystals in the bulk fluid, effectively sequestering the components from the liquid phase and reducing molecular diffusion into the gel deposit. At sufficiently low bulk fluid temperature conditions, an “upper CCN” value establishes an upper bound to the molecular weight range of paraffin components which contribute to the aging process. An analysis of a field deposit confirms the aging behavior of paraffin deposits observed on the coldfinger, and indicates that CCN values are in the mid 20’s at field conditions.
Introduction Paraffin precipitation and deposition in crude oil transport pipelines is an increasing challenge faced in the development of deepwater sub-sea hydrocarbon reservoirs. When the temperature of a waxy crude oil drops below the wax appearance temperature (WAT), commonly referred to as the cloud point, the heaviest n-paraffin fractions precipitate as crystals. Incipient wax-oil gel deposits form on the interior surface of a cold pipe wall due to the agglomeration of orthorhombic wax crystals.1 A significant fraction of liquid oil is occluded within the volume-spanning crystal matrix structure of a wax deposit, which behaves as a porous medium facilitating diffusion of paraffin molecules between the bulk fluid and the liquid phase of the deposit.2 The existence of radial temperature gradients causes analogous radial n-paraffin solubility gradients, resulting in a flux of heavy n-paraffin molecules from the bulk oil penetrating into the gel deposit. This diffusive behavior, whether by thermal or molecular diffusion, is collectively termed “aging,” and results in a gel deposit which hardens with time. As a result of the hardening, the deposit becomes increasingly difficult to remove by conventional mechanical methods. The * Author to whom correspondence should be addressed. E-mail:
[email protected]. (1) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. AIChE J. 2000, 46, 1059-1074. (2) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. AIChE J. 2001, 47, 6-18.
buildup of paraffin deposits decreases the pipeline radius available for flow, limits operating capacities, and places additional strain on pumping equipment. Uninhibited, wax deposition can cause complete flow blockage and costly production shutdowns. According to the U.S. Minerals Management Service,3 51 severe waxrelated plugs were reported in Gulf of Mexico flow lines between 1992 and 2002. The U.S. DOE4 reports that remediation of plugged pipelines in water depths of 400 m can cost $1 million/mile. Deferred revenue from large deepwater production facilities can readily exceed $3 million/day.4 A plethora of thermal, chemical, and mechanical measures are available to manage paraffin deposition, on either a preventative or a remediative basis.3,4 Decisions are typically made early in a pipeline design process to address paraffin deposition issues and to select feasible management methods. Typical paraffin managements systems include the use of chemical wax inhibitors and the implementation of mechanical pigging operations.3 Prior knowledge of the paraffin stability of a crude oil is necessary for designing appropriate remediation systems. Laboratory scale wax deposition devices such as coldfingers,5 spinning disks,6 and flow (3) Makagon, T. Y.; Johnson, T. L.; Angel, K. F. Proceedings of the 4th International Conference on Petroleum Phase Behavior and Fouling, Trondheim, Norway, 2003. (4) DOE, University of Tulsa embark on wax deposition study. Oil Gas J. 2001, 99, 56. (5) Weispfennig, K. Proceedings of the 2001 SPE International Symposium on Oilfield Chemistry. SPE 64997, 2001.
10.1021/ef034105+ CCC: $27.50 © 2004 American Chemical Society Published on Web 05/11/2004
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loops,2 are commonly used for paraffin stability screening and to test inhibitor effectiveness. For quantitative deposition rate estimates, small-scale flow loop systems may be utilized, where the deposit thickness buildup is accurately gauged as a function of time via calibrated pressure drop measurements.2 Quantifying Aging Phenomena. The two primary mechanisms of paraffin depositionsgelation and agings have been described in the literature by the University of Michigan research group.1,2 Particulate deposition mechanisms such as gravity settling, Brownian diffusion, and shear dispersion have been described by Burger et al.,7 but are generally neglected in pipeline deposition models.8,9 Gelation involves the occlusion of liquid oil in a 3-D paraffin crystal matrix, such that an incipient wax-oil gel deposit formed on a cold surface retains the bulk fluid composition.10 The aging of wax deposits involves a molecular diffusion mechanism10 where there exists a critical carbon number (CCN). Paraffin components having a number of carbon atoms greater than the CCN diffuse from the bulk oil into the liquid phase of the gel deposit, subsequently precipitating and causing an increase in the solid wax content of the deposit. Paraffin components containing a number of carbon atoms less than the CCN diffuse out of the deposit with time. Interfacial wax precipitation by gelation continues as long as the interfacial temperature remains below the fluid WAT and a negative radial temperature gradient exists near the deposition surface. For conditions at which the bulk fluid temperature is higher than the WAT, the interfacial temperature eventually approaches the fluid WAT as a result of thermal insulation by the deposit on the cold surface. Subsequently, interfacial precipitation ceases and the deposit thickness remains static, although interfacial penetration and aging continue. Knowledge of CCN values for waxy crude oils has significant application in managing pipeline operations. The CCN establishes an accurate lower bound to the molecular weight range of hydrocarbon components which contribute to the aging process, and is a useful quantity in estimating from a compositional basis the deposition potential of a waxy crude oil. Consideration of CCN values is vital for the effective selection of chemical wax inhibiting agents. Wax inhibitors are chemical additives which hinder the growth and/or agglomeration of paraffin crystals via co-crystallization and/or surface adsorption, and are highly effective in reducing pour point temperatures11,12 and deposition rates.12 Inhibiting agents are generally tailored to specific wax deposit molecular weight distributions rather than bulk fluid compositions, and should target (6) Wu, C. W.; Wang, K.; Shuler, P. J.; Tang, Y.; Creek, J.; Carlson, R. M.; Cheung, S. AIChE J. 2002, 48, 2107-2110. (7) Burger, E. D.; Perkins, T. K.; Striegler, J. H. J. Pet. Technol. 1981, 33, 1075-1086. (8) Brown, T. S.; Niesen, V. G.; Erickon, D. D. Proceedings of the 68th Annual Conference of the Society of Petroleum Engineers. SPE 26548, 1993. (9) Ribeiro, F. S.; Souza Mendez, P. R.; Braga, S. L. Int. J. Heat Mass Transfer 1997, 40, 4319-4328. (10) Singh, P.; Youyen, A.; Fogler, H. S. AIChE J. 2001, 47, 21112124. (11) Dong, L.; Xie, H.; Zhang, F. Proceedings of the 2001 SPE International Symposium on Oilfield Chemistry, SPE 65380, 2001. (12) Tung, N. P.; Phong, N. T. P.; Long, B. Q. K.; Thuc, P. D.; Son, T. C. Proceedings of the 2001 SPE International Symposium on Oilfield Chemistry, SPE 65380, 2001.
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paraffin components with carbon numbers above the CCN. A CCN value can be determined by comparing the composition of an aged gel deposit and its corresponding bulk fluid, using a laboratory scale wax deposition device such as a coldfinger or a spinning disk. Paraffin components with carbon numbers greater than the CCN increase in weight fraction within the gel deposit, and vice versa. From a thermodynamic perspective, the CCN is measure of the carbon number of the heaviest paraffin component soluble in the liquid phase of the incipient deposit. Singh et al. demonstrated using model fluids that CCN values increase nearly linearly with deposit temperature.10 Accurate theoretical CCN predictions were obtained by application of an excess Gibbs free energy model to predict solid-phase compositions. CCN values also vary with n-paraffin composition; a higher fraction of low carbon number hydrocarbon components increases n-paraffin solubilities, as well as CCN values, and vice versa.13 This article presents an investigation of the diffusive aging process of wax deposits in terms of composition analysis. Wax deposits were obtained from both a crude oil and a model fluid using a finite-volume coldfinger deposition apparatus. The counter-diffusive aging process induces depletion of paraffin components heavier than the CCN from the bulk fluid. The concept of quantified component bulk depletion values is presented as a means of investigating crystallization in the bulk fluid. The bulk crystallization of high molecular weight paraffin components occurs at conditions where the bulk fluid temperature remains below the fluid WAT. The stabilization of paraffin components by crystallization in the bulk fluid is responsible for the decrease in wax deposition rates observed at large distances from the wellhead in sub-sea pipelines where the bulk fluid temperature approaches the pipe wall temperature. In addition, crystallization in the bulk fluid results in a changing wax deposit composition along a pipeline length, influencing the mechanical properties of a gel deposit. Quantification of bulk stabilization on a component basis is important for the accurate prediction of location, amounts, and mechanical characteristics of wax deposits. Deposition Experiments Crude Oil Deposition. A single crude oil, known to precipitate paraffin solids, was obtained from an industrial source and used without fractionation. The pour point of the crude oil was known to be 15.6 °C. The wax appearance temperature (WAT) of the crude was measured to be 26.7 °C using a cross-polarized microscopy technique where a sample of the crude is cooled to and maintained at a specified temperature for 30 min in order to minimize sub-cooling effects. Similarly, the wax dissolution temperature (WDT) of the crude was determined to be 31.7 °C by cross-polarized observation while heating at 0.5 °C/min. The density of the oil was measured to be 0.77 g/mL, and the results of gas chromatography-FID analysis of the C5+ hydrocarbon composition is shown in Figure 1. Component weight fractions, quantitatively distinguished between n-paraffin and non-nparaffin hydrocarbon components, are plotted versus carbon number. Retention times of non-n-paraffin hydrocarbon components are assumed to be analogous to n-paraffin retention times, based on the column elution sequence. (13) Paso, K. G.; Fogler, H. S. AIChE J. 2003, 49, 3241-3252.
Bulk Stabilization in Wax Deposition Systems
Figure 1. Crude oil n-paraffin and non-n-paraffin composition, analyzed by gas chromatography.
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Figure 3. Coldfinger gel deposit compositions obtained from the crude oil at a deposition time of 24 h at wall temperatures of 2 °C and 10 °C. absence of branched, cyclic, and other functionalized hydrocarbon components in the model fluid allows for more precise GC composition analyses due to improved peak segregation. The model oil was formulated by mixing various commercial paraffin waxes with single component n-alkanes to provide an approximate exponential decaying n-paraffin distribution from n-C12 to n-C48. This exponential decay in n-paraffin composition is typical of real crude oils.14 The WAT of the model oil solution was measured to be 27.8 °C by a visual turbidity observation procedure, where the sample is first heated to a temperature of at least 10 °C above the WAT to remove any thermal history, and is subsequently cooled to a specified temperature and maintained isothermally for at least 2 h, to minimize subcooling effects. Procedural repetition yields precise and accurate WAT values. Five coldfinger deposition experiments were performed using the model fluid, with the bulk fluid temperature maintained at 29.8 °C, 25.8 °C, 21.8 °C, 17.8 °C, and 13.8 °C. The coldfinger surface temperature was maintained at 10.0 °C during all model oil deposition experiments, and wax deposits were recovered at 24 h and subsequently weighed and analyzed.
Results and Discussion
Figure 2. Coldfinger apparatus. The laboratory coldfinger apparatus is a method of emulating a cold pipeline wall in contact with warm oil. The apparatus consists of a temperature-controlled steel cylinder immersed in a jacketed vessel containing the crude oil. A photo of a coldfinger apparatus is shown in Figure 2. The cylinder area in contact with the oil is 12.6 cm2, and the volume of crude used in the deposition experiments is 204 ( 1 mL. During a depositional run, the bulk oil was maintained at a temperature of 28.8 °C, and a stir bar was placed in the bottom of the jacketed vessel to induce bulk mixing. Deposition experiments were performed while maintaining the coldfinger wall temperature at 2 °C and at 10 °C. After a deposition time of 24 h, the coldfinger was carefully removed from the jacketed vessel, and the deposit weighed and analyzed by GC. Deposit samples were obtained at deposition times of 1, 3, 9, and 24 h at the coldfinger wall temperature condition of 10 °C. Model Oil Deposition. Coldfinger deposition experiments were performed at varying bulk fluid temperatures using a model fluid consisting of only n-paraffin components. The
Crude Oil Deposition. Figure 3 provides GC analysis carbon number distributions for coldfinger wax deposits obtained at wall temperatures of 2 °C and 10 °C, yielding deposit masses of 2.59 and 1.76 g, respectively, at 24 h. Figure 4 shows the 24-hour deposit n-paraffin composition alongside the incipient gel nparaffin composition, obtained at a wall temperature of 2 °C. The composition of the incipient gel is assumed to be identical to that of the initial bulk fluid. From this figure, the n-paraffin CCN is 22, indicating that nparaffin components containing a number of carbon atoms greater than 22 contribute to the aging process. An identical n-paraffin CCN value of 22 was obtained for the 10 °C deposit. Figure 5 shows aged and incipient compositions of non-n-paraffin hydrocarbon components. At coldfinger wall temperatures of 2 °C and 10 °C, the numerical non-n-paraffin CCN values are 27 and 24, respectively, with error margins of (3 carbon numbers due to inaccuracies associated with FID signal peak (14) Kaminsky, R. D., Proceedings of the AIChE Spring National Meeting, New Orleans, LA, 2002.
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Figure 6. Buildup and aging profile of crude oil wax deposit on coldfinger. Coldfinger wall temperature ) 10 °C. Bulk fluid temperature ) 28.8 °C.
Figure 4. Experimental n-paraffin carbon number distributions of incipient and aged gel deposits derived from crude oil. Coldfinger wall temperature ) 2 °C.
A buildup and aging profile is calculated for the 10 °C deposition condition by summing the n-C20+ wax fraction of the deposits obtained at 1, 3, 9, and 24 h. The density of the n-C20+ fraction at the deposit temperature condition is assumed to be 0.9 g/mL, based on literature values of petroleum wax densities.15 The calculated deposit density increases from 0.77 g/mL to 0.79 g/mL as a result of aging behavior. Deposit thicknesses were calculated from deposit masses and analyzed compositions, and were not independently measured. The n-C20+ fraction and deposit thickness profile are plotted in Figure 6. Bulk Depletion Analysis. To delineate aging behavior from gelation, bulk depletion is calculated for n-paraffin and non-n-paraffin components heavier than the CCN. Gelation, a liquid occlusion phenomenon, causes no depletion of components from the bulk fluid. The component bulk depletion, Di, accounts for only molecular diffusion of components across the fluiddeposit interface after incipient gelation, and is defined as
Di ) 1 -
Yi,f Yi,0
where Yi,0 and Yi,f represent the mass fraction of component i in the bulk fluid at the beginning and end of a deposition run, respectively. Statistical errors are minimized by computing bulk depletion via deposit mass balance computations, expressed as
Di ) Figure 5. Experimental non-n-paraffin carbon number distributions of incipient and aged gel deposits derived from crude oil. Coldfinger wall temperature ) 2 °C.
overlap. Non-n-paraffin CCN values cannot be interpreted in terms of single species solid-liquid equilibrium, but account for summed solubility behavior of a large number of hydrocarbon isomers grouped by boiling point range. Observed non-n-paraffin CCN values are 2-5 carbon numbers higher than n-paraffin CCN values, affirming that straight chain paraffin components are favored to crystallize over analogous non-nparaffin components, owing to geometric symmetry.
(Xi - Yi,0) (Mb - Md) Yi,0 Md
where Xi represents the mass fraction of component i in the aged gel deposit; Mb and Md represent the total mass of the initial bulk fluid and the aged deposit, respectively. The depletion of individual carbon numbers at 24 h are plotted in Figure 7 for n-paraffin components and in Figure 8 for non-n-paraffin components. The depletion of paraffin components is greater at a coldfinger temperature of 2 °C than at 10 °C, due to increased aging rates at the lower temperature. (15) Srivastava, S. P.; Handoo, J.; Agrawal, K. M.; Joshi, G. C. J. Phys. Chem. Solids 1993, 54, 639-670.
Bulk Stabilization in Wax Deposition Systems
Figure 7. Bulk n-paraffin depletion values for crude oil deposition at 24 h at indicated coldfinger wall temperature. Bulk fluid temperature ) 28.8 °C.
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Figure 9. Bulk n-paraffin and non-n-paraffin depletion values for crude oil deposition at 24 h. Coldfinger wall temperature ) 10 °C. Bulk fluid temperature ) 28.8 °C.
Figure 8. Bulk non-n-paraffin depletion values for crude oil deposition at 24 h at indicated coldfinger wall temperature. Bulk fluid temperature ) 28.8 °C.
The depletion of n-paraffin components from the bulk fluid increases with carbon number up n-C39 due to decreasing component solubility in the occluded liquid. Above n-C39, the depletion of n-paraffins decreases due to crystallization of these paraffins in the bulk fluid. The paraffin crystals form in the fluid regions adjacent to the deposit interface, where the temperature is below the fluid WAT. Fluid flow patterns return the paraffin crystals to the bulk fluid, where the crystals do not dissolve because the bulk fluid temperature is below the fluid wax dissolution temperature. The formation of paraffin crystals reduces the molecular concentration of the paraffin components in the bulk fluid, resulting in reduced molecular diffusion into the deposit. Solid paraffin crystals in the bulk fluid do not deposit at the interface due to the agitation induced by the stir bar; hence, the paraffin crystals are stable in the bulk fluid. The depletion of non-n-paraffin components does not go through a maximum with respect to carbon number, although the analysis is limited to components up to C46. From a thermodynamic perspective, it is possible that non-n-paraffin components with carbon numbers above C46 may also crystallize in the bulk fluid. Hence, the non-n-paraffin depletion curve may show a maximum beyond C46 which is beyond the limit of detection.
Figure 10. n-Paraffin/non-n-paraffin ratios of bulk crude oil and crude oil wax deposits at 24 h at specified coldfinger wall temperature. Bulk fluid temperature ) 28.8 °C.
The depletion of n-paraffin and non-n-paraffin components is compared in Figure 9. The abundant single carbon number components in the 20’s and mid 30’s exhibit depletion which is an order of magnitude higher for n-paraffins than for non-n-paraffins, confirming that straight chain hydrocarbons are primarily responsible for aging. Figure 10 provides n-paraffin/non-n-paraffin component ratios in the initial crude oil and aged wax deposits. Low carbon number components exhibit nearly identical n-paraffin/non-n-paraffin ratios in the crude oil and deposits. Above the n-paraffin CCN, the n-paraffin/nonn-paraffin ratio in the deposit increases drastically above the n-paraffin/non-n-paraffin ratio in the crude oil due to the influx of n-paraffin components. Roehner et al.16 exploited the divergent carbon number on an n-paraffin/non-n-paraffin ratio plot to distinguish between components in the solid phase and in the occluded liquid. Establishing the single carbon number at which the deposit n-paraffin/non-n-paraffin ratio diverges from (16) Roehner, R. M.; Fletcher, J. V.; Hanson, F. V. Energy Fuels 2002, 16, 211-217.
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Figure 11. Experimental carbon number distributions of incipient and aged gel deposits formed from model oil. Coldfinger wall temperature ) 10 °C. Bulk fluid temperature ) 29.8 °C. Model fluid cloud point ) 27.8 °C.
Figure 13. Expanded carbon number distributions of incipient and aged gel deposits shown in Figure 12. Y-error bars represent 2 standard deviations (obtained from 3 analysis repetitions), in both the positive and negative directions.
Figure 12. Experimental carbon number distributions of incipient and aged gel deposits formed from model oil. Coldfinger wall temperature ) 10 °C. Bulk fluid temperature ) 13.8 °C. Model fluid cloud point ) 27.8 °C.
Figure 14. Deposit masses obtained from coldfinger deposition at 24 h using the model fluid containing only n-paraffin components. In each case the coldfinger temperature was maintained at 10.0 °C.
the crude oil ratio provides an alternate criterion for determining n-paraffin CCN values in crude oil deposition systems. Model Fluid Deposition. The crystallization and resultant stabilization of paraffin components in the bulk fluid of a wax deposition system is highly temperature-dependent. Increasing fractions of heavy paraffin components form stable crystals in the bulk fluid when the bulk fluid temperature decreases below the WAT, thereby reducing molecular diffusion of heavy n-paraffin components to the gel deposit. Deposition experiments performed with model fluids establish depletion dependencies upon the bulk fluid temperature condition. Figure 11 shows the aged deposit composition alongside the incipient gel composition for the bulk temperature condition of 29.8 °C. The incipient gel is assumed to retain the composition of the initial bulk fluid. A CCN value of 22 is evident from the compositional data. Figure 12 provides aged and incipient compositions of the deposition performed at a bulk temperature of 13.8 °C. The incipient and aged compositions intersect twice, exhibiting a lower (i.e., primary) CCN value of 21 and an upper (i.e., secondary) CCN value of 37, which establish the lower and upper bounds of the fractional range of paraffin components which contribute to the aging process, respectively. To establish that the observed “upper CCN” value was not an experimental
artifact, statistical analysis was performed to establish the maximum error in the upper CCN value. Figure 13 shows an enlarged plot of the incipient and aged gel compositions near the second intersection point with statistical error bars, and indicates a maximum error in the upper CCN value of (1. “Lower CCN” values of 21 or 22 were obtained at all bulk fluid temperature conditions. Figure 14 provides the deposit mass recovered from the coldfinger at each bulk temperature condition. The greatest deposit mass occurred at a temperature of 17.8 °C, significantly below the fluid cloud point. Calculated component depletion values for deposition performed at bulk temperature conditions below and above the fluid WAT are shown in Figures 15 and 16, respectively. The depletion of n-paraffin components from the bulk solution increases with carbon number when the bulk fluid temperature is maintained higher than the model fluid WAT during deposition. This increase in the depletion is due to the decreasing solubility of higher molecular weight paraffin components in the occluded liquid. No crystallization occurs in the fluid regions near the deposit when the bulk fluid temperature is above the WAT, due to the absence of natural nucleating agents such as asphaltenes.17 How(17) Garcia, M. C. Energy Fuels 2000, 14, 1043-1048.
Bulk Stabilization in Wax Deposition Systems
Figure 15. Bulk n-paraffin depletion values for model oil coldfinger deposition at 24 h at indicated bulk fluid temperature conditions. Model oil cloud point ) 27.8 °C. Coldfinger wall temperature ) 10 °C.
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paraffin components which are depleted from the bulk fluid. On a depletion plot, the upper CCN value is defined as the carbon number previous to the second intersection of the depletion curve and the abscissa axis. The upper CCN accounts for crystallization in the bulk fluid on a compositional basis, such that the value of the upper CCN increases with bulk fluid temperature. As the temperature of the bulk fluid is decreased and converges toward the deposition surface temperature, the “upper CCN” value decreases and converges toward the “lower CCN” value. At conditions of identical bulk and surface temperatures, no solubility difference exists between the coldfinger surface and the bulk fluid, such that no deposition is observed. Thermodynamic Modeling. In a multicomponent system, solid-liquid thermodynamic equilibrium is established when component fugacity values in the solid and liquid phase are equal. At equilibrium, solid- and liquid-phase component activities can be related to n-paraffin thermo-physical properties via the relation of Coutinho et al.18
ln
siγsi xi γ
)
L i
(
)
(
)
∆hm,i Tm,i ∆htr,i Ttr,i -1 + -1 RTm,i T RTtr,i T
(
Tm,i ∆Cpm,i Tm,i - ln -1 R T T
)
Coutinho used this relation to develop a robust thermodynamic solid-liquid-phase equilibrium model for n-paraffin solutions, which can be applied to predict CCN values. Liquid-phase component activity coefficients are computed based on the Flory free volume model accounting for entropic effects of size and free volume differences18 Figure 16. Bulk n-paraffin depletion values for model oil coldfinger deposition at 24 h. Coldfinger wall temperature ) 10 °C. Model oil cloud point ) 27.8 °C.
ever, the depletion of n-paraffin components from the bulk solution increases with carbon number only up to a maximum when the bulk fluid temperature is maintained below the fluid WAT during deposition. Beyond the maximum, the depletion of n-paraffin components from the bulk solution decreases as a result of crystallization in the bulk fluid. The carbon number at which the maximum depletion value occurs decreases as the bulk fluid temperature decreases. Paraffin deposits increase in thickness due to gelation of the bulk liquid phase in contact with the deposit interface. Paraffin components stabilized by crystallization in the bulk fluid do not contribute to deposit growth via gelation. Hence, n-paraffin components existing primarily in the bulk crystal phase are excluded from the growing deposit, and become enriched in the bulk fluid. The enrichment is quantified as a negative depletion value, and is evident for n-paraffin components with carbon numbers higher than the upper CCN value. An upper CCN can occur only when the temperature of the bulk fluid is significantly lower than the fluid WAT, such that the highest molecular weight components in the bulk solution exist primarily in the crystal phase, and are entrained in the bulk fluid. The upper CCN establishes an upper bound to the fractional range of
ln γicomb-fv ) ln
φi φi +1xi xi
Solid-phase component activity coefficients are derived from an “a priori” excess Gibbs free energy correlation accounting for the pair interaction energies of n-paraffin molecules in the solid phase, based on the UNIQUAC convention.
gE RT
n
)
si ln ∑ i)1
() Φi si
+
Z
θi
n
∑qisi lnΦ 2 i)1 n
-
[
i
n
(
siqi ln ∑θj exp ∑ i)1 j)1
)]
λji - λii qiRT
The thermodynamic model computes equilibrium solidand liquid-phase compositions of an n-paraffin mixture at a specified temperature condition. Figure 17 illustrates computed solid- and liquid-phase compositions of an n-paraffin mixture corresponding to the analyzed n-paraffin carbon number distribution of the crude oil sample. The lower critical carbon number (CCN) can be predicted from computed equilibrium-phase compositions by comparing the compositions of the bulk fluid and the incipient deposit liquid phases. Components with carbon numbers greater than the CCN exhibit a higher mass fraction in the bulk fluid than in the (18) Coutinho, J. A. P. Fluid Phase Equil. 1999, 159, 447-457.
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Figure 17. Theoretical solid and liquid-phase compositions of an n-paraffin mixture emulating the crude oil composition. The computed solid-phase fraction is 9.9%.
Paso and Fogler
percentage basis. A hydrocarbon CCN value of 26 is evident from the composition analyses, although nparaffin and non-n-paraffin components are not distinguished. The large compositional change in the field deposit during aging provides for less uncertainty in the CCN value. The relatively high observed CCN value demonstrates that paraffin components with carbon numbers in the low 20’s have not actively contributed to the aging process of the pipeline field deposit. Qualitative comparison of Figures 4 and 18 suggests that the evolution of molecular weight distribution in wax deposits is similar in lab-scale deposition and field-scale deposition systems, although the crude oils in Figures 4 and 18 are not identical. Quantitative comparison of aged deposit compositions in lab-scale and field-scale wax deposition systems is difficult because bulk depletion effects are over an order of magnitude higher in the lab-scale systems than in field pipeline systems, affecting differences in deposit buildup and aging rates. Comprehensive pipeline deposition models generally assume local equilibrium within paraffin deposits,19 and relate buildup and aging rates to external and internal heat flux, respectively, based on the model of Singh and Fogler.20 Conclusions
Figure 18. Hydrocarbon carbon number distribution of a pipeline crude oil and corresponding wax deposit. n-Paraffin and non-n-paraffin components are not distinguished.
liquid phase of the incipient deposit, and vice versa. Hence, the carbon number previous to the intersection point can be defined as the lower critical carbon number (CCN). A rigorous definition of the critical carbon number is provided by Singh.10 A theoretical “lower CCN” value of 22 for the n-paraffin components of the crude oil is provided by the thermodynamic computations. The predicted CCN value is in excellent agreement with the experimental n-paraffin CCN value of 22 observed during crude oil deposition. Because solid-phase interaction energies are computed assuming straight chain molecules existing in an orthorhombic crystal lattice configuration, the model of Coutinho cannot be applied to predict the complex phase behavior of isomerized, aromatic, naphthenic, and asphaltenic components. Hence, a theoretical CCN value for the non-n-paraffin crude oil components cannot be computed with the current thermodynamic model. Field Pipeline Deposit Analysis. An analysis of a flow-line paraffin deposit was obtained from ChevronTexaco in order to provide qualitative comparison between the coldfinger deposit compositions and a field deposit composition. Figure 18 provides hydrocarbon carbon number distributions of the pipeline paraffin wax deposit and its parent production crude oil on a mass
Quantification of bulk depletion on a compositional basis provides a systematic methodology for investigating wax deposition in lab-scale devices. At bulk fluid temperature conditions significantly below the fluid WAT, an “upper CCN” value establishes an accurate upper bound to the range of paraffin components which contribute to aging via molecular diffusion. Absent the formation of crystals in the bulk fluid during deposition, component depletion from the bulk fluid increases with carbon number as a result of decreasing component solubility in the liquid phase of the deposit. The first inflection point on a depletion curve after the lower CCN represents the lightest detectable paraffin component which contributes to the formation of crystals in the bulk fluid. Higher carbon number components in the bulk fluid are distributed between the solid and liquid phases. Paraffin components in the bulk fluid with carbon numbers higher than the “upper CCN” value exist primarily in the solid phase. The “upper CCN” value provides a fundamental parameter which describes the composition of the solid phase of the bulk fluid, which is analogous to the compositional description of the deposit solid phase provided by the “lower CCN” value. As such, lower and upper CCN values are determined by solubility conditions in the deposit and in the bulk fluid, respectively. Field conditions in which an “upper CCN” value may exist include cold slurry systems in which a waxy petroleum fluid is pre-cooled in order to decrease wax deposition rates during flow.21 A field pipeline deposit was analyzed and observed to be qualitatively comparable in composition to deposits formed on the coldfinger. Multiple coldfinger deposition (19) Creek, J. Proceedings of the 4th International Conference on Petroleum Phase Behavior and Fouling, Trondheim, Norway, 2003. (20) Perez, O. C. H. M.S. Thesis, Petroleum Engineering, University of Tulsa, OK, 2002. (21) Bufton, S. A. Oil & Gas J. 2003, 101, 66-77.
Bulk Stabilization in Wax Deposition Systems
experiments performed at decreasing bulk fluid temperatures represent varying temporal conditions of a fluid moving through a pipeline system, from which a predicted deposition and aging profile may be constructed. Field pipeline CCN values can be obtained by comparing paraffin distributions of recovered wax deposits and the mother crude oil. Rational analysis of wax deposit molecular weight compositions is paramount in effective wax management.
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Acknowledgment. The authors acknowledge Dr. J. A. P. Coutinho for the use of his thermodynamic solidliquid phase equilibrium model. Financial support was obtained from the following members of the University of Michigan Industrial Affiliates Program: Baker Petrolite, ChevronTexaco, ConocoPhillips, Schlumberger, Shell Oil, and Total. EF034105+
