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The importance of supersaturation on determining the solid-liquid equilibrium temperature of waxy oils
Fuel 206 (2017) 516–523
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Full Length Article
The importance of supersaturation on determining the solid-liquid equilibrium temperature of waxy oils Diogo E.V. Andrade a,b,c,⇑, Moisés A. Marcelino Neto a,b,d, Cezar O.R. Negrão a,b,c a
Federal University of Technology-Paraná – UTFPR, 81280-340, R. Deputado Heitor Alencar Furtado, 5000 – Bloco N – Ecoville, Curitiba, PR, Brazil Postgraduate Program in Mechanical and Materials Engineering – PPGEM c Research Center for Rheology and Non-Newtonian Fluids – CERNN d Multiphase Flow Center – NUEM b
h i g h l i g h t s A supercooling is required for the onset of wax precipitation in waxy oils. The higher the cooling rate the higher the metastable region width. The cooling experiment is not appropriate to determine the saturation temperature. At a high heating rate, there also exists a superheating during the dissolution. The saturation temperature can be determined at a very low heating rate.
a r t i c l e
i n f o
Article history: Received 10 March 2017 Received in revised form 2 June 2017 Accepted 8 June 2017
Keywords: Crystallization temperature Supercooling Superheating Highest solid-liquid thermodynamic equilibrium temperature Viscometry DSC
a b s t r a c t Crystallization is a process where an ordered solid structure is formed from a disordered phase. This event is divided in two main stages, namely nucleation and crystals growth. As paraffin nucleation is a stochastic process, a supercooling is needed to initiate the process. In other words, the beginning of crystal precipitation does not coincide with the highest thermodynamic solid-liquid equilibrium temperature. Therefore, during the cooling it is required that the fluid reaches a certain temperature below saturation, i.e., a metastable state, to initiate the crystal nucleation process. The difference between the saturation temperature and the crystallization temperature is called degree of supercooling. As this metastable condition may exist during not only the crystallization but also the dissolution of crystals, this work proposes a procedure to determine consistently the highest solid-liquid thermodynamic equilibrium temperature by using the results of rheometer and DSC experiments. It can be anticipated that the proposed protocol states that the highest solid-liquid thermodynamic equilibrium temperature is considered to approach the dissolution temperature when the material is heated at a very low heating rate. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Crude oil is a complex mixture of hydrocarbons, heteroatoms (e.g. N, S, O) and inorganic components as salts, sand and water [1,2]. More than 90% of the oil can be composed of hydrocarbons [3] that are usually divided in four major fractions: saturates – known as paraffin, aromatics, resins and asphaltenes (SARA) [4–6]. At oil reservoir conditions, i.e. high temperatures
⇑ Corresponding author at: Federal University of Technology-Paraná – UTFPR, 81280-340, R. Deputado Heitor Alencar Furtado, 5000 – Bloco N – Ecoville, Curitiba, PR, Brazil. E-mail address: [email protected] (D.E.V. Andrade). http://dx.doi.org/10.1016/j.fuel.2017.06.042 0016-2361/Ó 2017 Elsevier Ltd. All rights reserved.
(70–150 °C) and pressures (50–100 MPa), all the paraffin molecules are dissolved in the oil so that this mixture of hydrocarbons is in liquid phase [7] and behaves as a Newtonian fluid [8]. At low temperatures, the solubility of high molecular weight components in the oil decreases and mainly the n-paraffins tend to precipitate out of the solution as crystal structures. These crystals that render a non-Newtonian behavior to the fluid [9,10], with a variety of characteristics such as pseudo-plasticity, elasticity, timedependency [11,12] and/or deformation dependency [13], may deposit in the inner surface of pipelines [14,15] and are responsible for oil gelation when the flow is interrupted [5,16]. The risk of wax crystal precipitation during offshore production is quite high, as the ocean floor temperature could be as low as 4 °C [17].
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The wax deposition in pipeline inner surfaces increases pump power, decreases flow rate and, consequently, reduces oil production [14,18]. The common methods employed to remediate wax deposition (e.g. the use of chemical inhibitors, pipeline heating and mechanical removal by using pigs) are extremely costly in deep and ultra-deep water production scenarios [17]. In flow interruption for pipeline maintenance, gelation takes place and start-up pressures much larger than the usual operational pressure are required to break down the gel structure [19,20]. If the rheological properties of waxy crude oils at low temperatures are not accurately determined, restart pressures can be overrated leading to overestimation of pipe dimensions, and consequently making pipeline projects unfeasible [21,22]. A key point in crude oil production and transportation is the wax crystallization onset temperature. The accurate determination of this temperature is important to design production and/or transportation pipelines to work above this temperature and to know when the crystallization becomes a real problem in oil production. This temperature, however, may be distinct from the highest temperature in which the solid and liquid phases co-exist in equilibrium at a fixed pressure. The latter is a thermodynamic property and is known as the highest solid-liquid thermodynamic equilibrium temperature, Teq,SL. In petroleum area, this temperature is usually called the Wax Appearance Temperature (WAT) or cloud point [1]. Although there is not a consensus in the open literature, Tiwary and Mehrotra [23] claimed that ‘‘WAT is the true solidliquid phase boundary temperature”. Researchers have made significant effort to model the thermodynamic solid-liquid equilibrium [24–39]. The general solid-liquid equilibrium is reached when the fugacities of each component ‘‘i” in the solution are identical in solid and liquid phases. Many assumptions have been made to determine the solid-liquid equilibrium of waxy oils by means of thermodynamic models. Some authors assume that the difference between the heat capacities of each component is negligible (DC SL p;i ¼ 0) [25,28,31] and the decrease in component volume due to phase transition is disregarded in some cases [27]. The liquid phase is assumed to be an ideal solution (cLi ¼ 1) by some authors [34,40] and some others consider that cSi ¼ 1 [36,40], where ci is the activity coefficient of each component present in the solution. The regular solution is used in many works [25–28,33,40] to take the non-idealities of the liquid and solid phases into account. In addition to these assumptions, the liquid phase activity coefficient was also determined by Flory-Huggins model [36], by Flory free-volume equation added to a UNIFAC residual term [41] and by Flory free-volume model [35]. The solid phase non-ideality was also considered by Wilson equation [40,41] and by UNIQUAC model [32,34,35,37,39,40]. Although some models performed better than others in many comparisons, there is not a capable model to predict the solid-liquid equilibrium temperature of all waxy oils. The differences between experimental and calculated Teq,SL are generally higher than 2 °C for the cases in which Teq,SL is approximately 20 °C and the crystals mass fraction below the equilibrium temperature is not accurately determined but only qualitatively well represented. On the other hand, the experimental methods to find the highest solid-liquid equilibrium temperature of waxy oil are not well consolidated. Several techniques have been used to determine the WAT: Visual Method [23,42,43] as normalized by ASTM [44], Filter Plugging (FP) [45,46], Viscometry [46–51], Densitometry [52], Cross Polar Microscopy (CPM) [23,47,48], Differential Scanning Calorimetry (DSC) [5,12,53–60], cold finger [45], ultrasonic experiments [61], Fourier Transform Infrared (FTIR) energy scattering technique [45] and Near Infrared (NIR) scattering technique [62]. Rønningsen et al. [47] analyzed 17 crude oils by comparing
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the three more usual methods – microscopy, differential scanning calorimetry and viscometry – and concluded that microscopy is the best method to determine the WAT. In contrast, Kok et al. [48] used the same three techniques to investigate 15 different crude oils and claimed that the best method to determine the wax appearance temperature depends on the solution composition. Tiwary and Mehrotra [23] examined different model waxy oils using the same three techniques again and compared with a visual method. The authors concluded that the DSC was the best technique to determine the solid-liquid equilibrium temperature because provided the highest WAT values. Different techniques proposed to determine more accurately the WAT [45,52,62] have been compared with the usual techniques and some interesting conclusions were obtained. Although Marchesini et al. [9] have made a wise discussion saying that the temperature determined by viscometry/rheometry is not the solid-liquid equilibrium temperature because the first crystal that appears in the solution is too small to change the oil viscosity (the same can be concluded from the other techniques [23]), a key point in wax crystallization, i.e., the supercooling has been forgotten or neglected by the majority of the authors. It is worth mentioning that just few authors [17,31,43,63] recognized the existence of this metastable region before the wax crystallization. Crystallization is a process of building up an ordered solid structure from a disordered phase and involves two main stages: nucleation and crystal growth [47,64]. As well known and consolidated in the inorganic chemistry area, nucleation is a stochastic process that requires a supercooling (or supersaturation) to start it up [65–67]. In other words, crystals precipitation begins at a temperature that is below the solid-liquid equilibrium temperature, which is a thermodynamic property [37]. In the current work, the highest solid-liquid equilibrium temperature is represented by Teq,SL and the onset of wax precipitation is defined by the crystallization temperature, Tc, as proposed by Marchesini et al. [9]. To avoid confusion with the solid-liquid equilibrium state, the term WAT (Wax Appearance Temperature) is not used here. The difference between the solid-liquid equilibrium temperature and the crystallization temperature is defined as degree of supercooling, DT sup , [65,66]:
DT sup ¼ T eq;SL T c
ð1Þ
Considering that during heating solid may also exist in a nonequilibrium condition in the solution [60,68] and consequently metastable states may occur in either crystallization or dissolution of crystals, this work presents a discussion about how to evaluate consistently the highest solid-liquid equilibrium temperature of waxy oil. The discussion is based on the results of rheometer and mDSC experiments performed at different rate of change of temperature and calls the attention for metastable regions that exist during the crystallization and dissolution of paraffin. Although not considered in the open literature that deals with waxy oils, these metastable regions may interfere directly in the measurement of the highest solid-liquid equilibrium temperature. 2. Experimental section The experiments presented in the current work were conducted with model waxy oils. The model oils were formulated by adding a paraffin wax with a melting point between 58 and 62 °C (Sigma Aldrich 327212 CAS-No:8002-74-2) to a mineral oil (Sigma Aldrich 330779 – CAS-No: 8042-47-5). The paraffin wax and mineral oil were the same used in Dimitriou’s thesis [69], by others in his group [70] and by IFP Energies nouvelles’s work [71]. The wax is composed of 60 wt% n-paraffins and 40 wt% iso and cycloparaffins [70]. The normal alkane carbon distribution of both
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mineral oil and paraffin wax can be found elsewhere [69]. Three different compositions were used: 5, 10 and 20 wt% of paraffin in oil. Model waxy oil samples were prepared by dissolving the paraffin wax in the mineral oil and heating them up in a roller oven to 80 °C within a closed bottle. The samples were then stirred at this temperature for 30 min. Two techniques used to determine the crystallization and dissolution temperatures are now presented: viscometric and DSC analyses. It is worth noting that the purpose is neither to compare the techniques nor to state which is the more accurate but rather, to use the results to discuss the supercooling during wax crystallization. 2.1. Viscometry tests The viscometry tests were performed by employing a Haake Mars III (Haake Co., Germany) rotational rheometer that can measure a minimum torque of 5.108 Nm. A 35 mm diameter parallelplate geometry with a gap of 0.3 mm and sandblasted surface was used in the rheometer and the temperature was controlled by a Peltier-thermostatic bath system. Before any test, the model waxy oil sample was mixed at 80 °C in a roller oven during 30 min in order to guarantee that the wax was completely dissolved in the oil [72,73]. A small sample was then collected and placed in the rheometer plate at 80 °C by using a syringe. The rotor was lowered to its measuring position and the temperature was kept at 80 °C for another 30 min to assure thermal homogenization. The viscometry tests consisted of shearing the specimen at a constant rate of 5 s1 and while shearing, the material was cooled to a temperature below the crystallization point and then heated again to the initial temperature at a constant rate of change of tem_ Except the T_ that changed from test to test, all other perature, T. test parameters were kept constant. Five different T_ were used: 8.5, 5.0, 1.0, 0.5 and 0.1 K/min. The highest rate of change of temperature of 8.5 K/min was imposed by the limit of the cooling and heating systems. Although not done in the current work, the crystallization and dissolution temperatures can still be determined by performing oscillatory rheometer experiments of small amplitude [63]. 2.2. DSC tests The calorimetric analyses were performed by employing the SETARAM HP mDSC VIIa differential scanning microcalorimeter. The resolution of the equipment is 2.108 W, the cells used are made from Hastelloy C276 and have a volume of 1.0 cm3. In all the experiments, approximately 37 mg of the specimen is loaded in the microcalorimeter cell and maintained at 80 °C for 5 min. The sample is then cooled to 10 °C and heated again to the initial temperature of 80 °C. Two rate of change of temperature were used: 0.8 and 0.1 K/min. 3. Results and discussion The results presented here focus on the evaluation of the influence of the rate of change of temperature (cooling and heating) on the crystallization and dissolution temperature of the model waxy oils. 3.1. Viscometric analysis Fig. 1(a) shows the viscosity as a function of the temperature for the model waxy oil with 20 wt% of paraffin and rate of change of temperature of 1.0 K/min and Fig. 1(b) presents the same set of data as a function of the inverse of the absolute temperature. As
in Newtonian fluids (see Fig. 1(b)), the increase of the viscosity is well represented by the Arrhenius fit (log m 1/T) from the beginning of the test, at T = 80 °C, to approximately 40 °C [74]:
DH R
l ¼ lref e
1 1 T T ref
ð2Þ
where lref is the fluid viscosity at temperature Tref and DH is the activation energy for flow. During the cooling, crystals precipitate out of the solution at some point and start to affect the measured viscosity of the model oil. From this point forward, the Arrhenius fit cannot represent the viscosity behavior anymore, and the temperature at which the curve slope changes is defined as the crystallization temperature, Tc. For this particular case, Tc = 39 °C. Because of the wax crystallization, the apparent viscosity of the solution increases from 0.01 to 2.0 Pa.s when the temperature is reduced from 40 to 35 °C. Similar behaviors of the viscosity have already been reported for crude oils [9,10,47,75]. At the end of the cooling at 35 °C, the specimen is heated again at the same rate of change of temperature to the initial temperature of 80 °C. As the temperature increases, the wax solubility increases and the crystals dissolve in the solution decreasing the apparent viscosity of the model oil. When all the paraffin is dissolved in the solution, the material starts to behave again as a Newtonian fluid. In the current work, the first point where the Arrhenius fit was able to predict the viscosity behavior during the heating is called dissolution temperature, Td. For this specific case, Td = 46 °C. It is worth noting that some authors [37,40,76] named this temperature as WDT (Wax Disappearance Temperature). 3.2. DSC analysis The DSC curves of the waxy oil with 20 wt% of paraffin wax are presented in Fig. 2. Fig. 2(a) shows the heat flux as a function of the temperature during the cooling. While the cooling rate was kept constant at 0.8 K/min, the heat flux to maintain this cooling rate was measured during the DSC test. As noted, the heat flux needed to reduce the oil sample temperature from 80 °C to approximately 40 °C is constant and then increases significantly. This significant heat flux release characterizes the appearance of the first crystals in the solution and the temperature at which this event takes place is called crystallization temperature, Tc. The crystallization temperature is indicated by a green arrow in Fig. 2(a) (Tc = 40.5 °C). This behavior was also observed by Paso et al. (2005) [63] that performed DSC experiments with model oils and stated that the supersaturation crystal growth regime can also be determined by using this raw data. Fig. 2(b) presents the DSC curve for the heating process. As shown, the energy needed to dissolve the paraffin increases as the oil sample is heated. At 43.9 °C, the energy required reduces significantly characterizing the end of the dissolution process and consequently, defining the dissolution temperature, Td. Despite the cooling and heating rates being the same, the dissolution temperature is 3.4 °C higher than the crystallization temperature. 3.3. Discussion The literature has reported [40,45,52,54,77] that the cooling rate affects the onset temperature for wax crystallization in the waxy oils. As discussed by [35,62,78,79], the lower the cooling rate the higher the crystallization temperature and also that this dependency is linear. The reason for the influence of the cooling rate on the crystallization temperature resides on the supersaturation. Supersaturation is a metastable condition in which liquid is
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Fig. 1. Viscosity of the model waxy oil with 20 wt% of paraffin wax for T_ = 1.0 K/min as a function of (a) Temperature and (b) as a function of 1000/Temperature. For the Arrhenius fit, lref (80 °C) = 5.8 mPa.s; DH=R = 2700 K.
0 exo.
10 9
-2
8 7 6
cooling
5 4 3
Heat Flux [10 mW/mg]
-2
Heat Flux [10 mW/mg]
11
(a)
Tc 0
10
20
30
40
50
60
70
Temperature [ºC]
endo.
-1 -2 -3
heating
-4 -5 -6 -7 -8
(b)
Td 0
10
20
30
40
50
60
70
Temperature [ºC]
Fig. 2. Heat flux in DSC tests of the model waxy oil with 20 wt% of paraffin wax for T_ = 0.8 K/min as a function of temperature for (a) the cooling and (b) the heating process.
supercooled below the equilibrium saturation temperature or solid is superheated above it [68,80]. In other words, liquid or solid exists in a non-equilibrium condition. Fig. 3 shows a diagram at constant pressure, as proposed by Mullin [65], that helps the understanding. A hypothetic solution with a solute concentration represented by the horizontal dash-dotted line is cooled from the temperature A to C. At high temperatures in the stable region (condition A), all the solution in the liquid state is in equilibrium. The point B represents the highest thermodynamic solid-liquid equilibrium temperature or the saturation temperature for this specific solute concentration and for this pressure. As shown experimentally in the literature [65,66], the first solid does not precipitate out in the solution exactly at the saturation temperature and a supercooling or supersaturation is necessary for the onset of
Fig. 3. The saturation - supersaturation diagram as proposed by Mullin [65].
precipitation. The point C, in Fig. 3, represents the condition in which the first solid precipitates out in the solution. The conditions between the saturation (point B) and the precipitation temperature (point C) are commonly named metastable region. Although the saturation temperature is a thermodynamic property that does not depend on the cooling condition, the precipitation temperature and consequently, the metastable region width, DT sup , are affected by many factors, such as: impurities, solution concentration, mechanical stirring and cooling rate [65,66]. For instance, the higher the cooling rate the larger is the metastable region width when all the other parameters are kept constant. The main reason for the required supercooling resides on the entropy of the system. From the thermodynamics viewpoint, a closed system of fixed energy and mass achieves a state of maximum entropy at the equilibrium. Sloan and Koh [81] claim that entropy favors disorder over order so that the paraffin in liquid phase, that is disordered in a molecular level, requires a supersaturation to be rearranged into the molecularly ordered crystals in the solid phase. The solution must then reach the metastable region to compensate for lowering the system entropy. Few works in the petroleum area [17,23,31,37,43,60,63,82–84] recognized the need of supersaturation for the first crystal to precipitate in the solution. Keeping in mind that for the same rate of change of temperature, the supercooling is higher than the superheating for the same material [43,52,60,76,85], some authors [31,37,43,60,85,86] have suggested that the saturation temperature is closer to the dissolution temperature than it is to the crystallization temperature, as usually established in the area of hydrates [81]. An interesting discussion was proposed by Taggart et al. [82] for a pure alkane (C18H38), which determined the solidification and
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melt temperatures for different rate of change of temperature. They showed that these temperatures are different even for very slow rates. Motivated by the Taggart’s et al. [82] discussion, a similar analysis is now conducted for the model waxy oils. Fig. 4(a) shows the cooling (or heating) rate versus the crystallization (or dissolution) temperature for the model oil composed of 20 wt% of paraffin wax obtained from the viscometric test results. The dots are average values of Tc and Td computed from three measurements and the error bars represent the standard deviation of each test condition. As already reported in prior works [62,78], the crystallization temperature is inversely proportional to the cooling rate; the lower the T_ the higher the Tc. The minimum crystallization temperature can then be estimated by extrapolating the cooling rate to zero from _ the linear blue line shown in Fig. 4(a), i.e., Tc,min (at T=0 K/min) = 41.3 °C. It is noteworthy that the correlation coefficient for the blue straight line was found to be greater than 0.99. As shown, not only the crystallization temperature but also the dissolution temperature is linear dependent on the rate of change of temperature; the lower the T_ the lower the Td. Similar conclusions can be taken from DSC results presented elsewhere [35]. As the dissolution temperature is heating rate dependent, this variable should not be used to estimate the solid-liquid equilibrium temperature, which is a thermodynamic property that does not dependent on any experimental condition. The literature [82], however, has _ suggested that the dissolution temperature at T=0 K/min is the best approximation for the thermodynamic solid-liquid equilibrium temperature once the superheating reduces with the heating rate. The accuracy of Teq,SL will depend on the equipment used to determine the dissolution temperatures along with the whole range of heating rate employed. From the red trend line depicted in Fig. 4 _ (a), Teq,SL (Td at T=0 K/min) is estimated to be 42.9 °C for this model waxy oil using the viscometry technique. The assumption that the dissolution temperature tends to the saturation temperature as the heating rate approaches zero is again based on the thermodynamic condition of maximum entropy at the equilibrium. During the dissolution of crystals, the material goes from the solid state that is ordered and has a lower entropy to the liquid state that is molecularly disordered and has a higher entropy [81] so that the supersaturation is not required for the system to reach the equilibrium. However, the superheating still exists if the dissolution is performed too fast and the material does not have time to reach the equilibrium condition. As the heating rate is reduced to zero, the superheating tends to disappear and the dissolution temperature approaches the equilibrium solidliquid temperature. _ In order to better visualize Tc and Td close to T=0 K/min, the
Heating or cooling rate [K/min]
results of Fig. 4(a) are shown in Fig. 4(b) for the rate of change of temperature ranging from 0.1 to 1.0 K/min. As noted, not even
10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
Dissolution Temperature
Crystallization Temperature
Teq,SL
(a) 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Temperature [ºC]
for the lowest rate of change of temperature of 0.1 K/min, the crystallization temperature equals the dissolution temperature. The minimum metastable region width is thus assumed to take place at zero rate of change of temperature, i.e., DT sup;min = 42.9 – 41.3 = 1.6 °C. The same experiments were performed to the other two model waxy oils. The effect of the rate of change of temperature on Tc and Td for the model waxy oils with 10 and 5 wt% of paraffin wax are presented, respectively, in Fig. 5(a) and (b). The blue and red straight lines were used again to define the dependency of the crystallization and dissolution temperatures on the rate of change of temperature, respectively. The correlation coefficients for Fig. 5 (a) and Fig. 5(b) were greater than 0.99 and 0.95, respectively. _ While Tc (at T=0 K/min) was estimated as 34.3 °C, Teq,SL (Td at
_ T=0 K/min) as 36.0 °C and the minimum degree of supercooling as 1.8 °C for the oil with 10 wt% of paraffin wax, these values were, respectively, 26.7 °C, 32.0 °C and 5.3 °C for the oil formulated with 5 wt% of paraffin wax. It is worth noting that not only the crystallization and dissolution temperatures reduce but also the metastable region width increases with the wax concentration reduction. In other words, the reduction of the solute concentration diminishes the saturation temperature and consequently, requires a higher supercooling for the precipitation of the first crystal in solution [65,66]. For the sake of comparison, the same analysis was performed with the model oil composed of 20 wt% of paraffin wax using the DSC technique with rate of change of temperature of 0.8 and 0.1 K/min. The crystallization and dissolution temperatures for these experiments are presented in Fig. 6(a). The dots shown are the average values of Tc and Td obtained from the DSC test results that were repeated twice and the error bars are the standard deviation. As depicted, the same tendency of viscometric tests is observed in the DSC measurements, i.e., the higher the rate of change of temperature the lower the Tc and the higher the Td. From the green and _ orange trend lines shown in Fig. 6(a), Tc (at T=0 K/min) was esti_ mated as 40.8 °C, Teq,SL (Td at T=0 K/min) as 42.6 °C and DT sup;min as 1.8 °C for this model waxy oil using the DSC technique. Fig. 6(b) compares the viscometry and the DSC measurements within the range of 0.1 to 1.0 K/min, showing that the results are _ 0.1 K/min for this specific waxy oil. Except for very similar at T=
the crystallization temperature at 0.5 K/min in which the viscometric result is well represented by the dashed trend line of the DSC experiment, the DSC and viscometric results diverge from each other at higher rate of change of temperature. Nevertheless, the Teq, SL determined by both technique was very similar. While the solidliquid equilibrium temperature estimated from the viscometric experiment was 42.9 °C, this same temperature obtained from the DSC measurements was 42.6 °C.
Heating or cooling rate [K/min]
520
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Crystallization Temperature
Dissolution Temperature Teq,SL
(b) 38 39 40 41 42 43 44 45 46 47 Temperature [ºC]
Fig. 4. (a) Influence of the rate of change of temperature on the crystallization and dissolution temperatures measured by using rheometric tests with the model oil composed of 20 wt% of paraffin wax. (b) The same results of (a) within the scale of 0.0 and 1.0 K/min.
521
10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
Crystallization Temperature Dissolution Temperature
Teq,SL
(a) 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Temperature [ºC]
Heating or cooling rate [K/min]
Heating or cooling rate [K/min]
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10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
Dissolution Temperature Crystallization Temperature
Teq,SL
(b) 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Temperature [ºC]
Fig. 5. Influence of the rate of change of temperature on the crystallization and dissolution temperatures measured in the rheometric tests with the model oils composed of (a) 10 wt% and (b) 5 wt% of paraffin wax.
Fig. 6. Influence of the rate of change of temperature on the crystallization and dissolution temperatures of the model oil composed with 20 wt% of paraffin wax measured in the (a) DSC tests and (b) DSC and rheometer experiments.
It is worth mentioning that the same tendency observed for a pure alkane by Taggart et al. [82] was also noted for waxy oils in the current work. One can then conclude that the most coherent way to determine the highest thermodynamic solid-liquid equilibrium temperature is by heating the material rather than cooling it, since the dissolution temperature is the best approximation for the saturation temperature when the heating rate is significantly low. As pointed out by some authors, viscometry is not the most adequate technique to determine accurately either the onset of the crystallization [9,47] or the dissolution temperature [9]. However, the main goal of the current discussion is to call attention for the existence of not only a supercooling on the crystallization of waxy oils but also of a superheating on the dissolution of crystals at high heating rates. It has to be pointed out that a supersaturation is always needed during the precipitation process and consequently, the temperature at which the first crystal precipitates out in the solution – the crystallization temperature – is not the highest thermodynamic solid-liquid equilibrium temperature.
4. Concluding remarks Wax precipitation is a huge problem in production and transportation of crude oils. Many efforts have been made to determine the highest solid-liquid thermodynamic equilibrium temperature – the saturation temperature – for the waxy crude oils. Keeping in mind the existence of a supersaturation, an adequate way to determine the saturation temperature for model waxy crude oils is proposed by using the results of rheometer and mDSC experiments. The main conclusions of the work can be summarized as:
i. The temperature at which the first wax crystal precipitates out in solution is called crystallization temperature, Tc, and because of the necessary supercooling, this temperature never coincides with the highest thermodynamic solidliquid equilibrium temperature; ii. Not only the solute concentration but also the cooling rate affects the metastable region width, in other words, the magnitude of the supercooling. The lower the solute concentration and the higher the cooling rate, the higher is the degree of supercooling; iii. Although the degree of supercooling reduces with the cooling rate, it does not vanish as the cooling rate tends to zero. On the other hand, the superheating during the dissolution of the wax crystals is assumed to disappear as the heating rate becomes zero; iv. The highest solid-liquid thermodynamic equilibrium temperature is considered to approach the dissolution temperature (temperature at which the last crystal disappears from the solution) when the material is heated at a very low heating rate. In other words, the dissolution temperature equals the saturation temperature when the heating rate tends to zero.
Acknowledgements The authors acknowledge the financial support of PETROBRAS S/A (TC 0050.0070318.11.9), CNPq – Brazil (Process: 487091/2013-2), CAPES – Brazil, FINEP, PRH-ANP/MCT (PRHANP/MCTI no. 10-C) and PFRH/PETROBRAS (6000.0067933.11.4
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and 6000.0082166.13.4). We also thank Talita Janaina Heller, an undergraduate student at the Federal University of TechnologyParaná, for her valuable support with the rheometric tests, and Lenise Couto Vieira from Petrobras that kindly performed the mDSC experiments. References [1] Venkatesan R, Östlund JA, Chawla H, Wattana P, Nydén M, Fogler HS. The effect of asphaltenes on the gelation of waxy oils. Energy Fuels 2003;17:1630–40. http://dx.doi.org/10.1021/ef034013k. [2] Sadeghazad A, Christiansen RL, Sobhi GA, Edalat M. The prediction of cloud point temperature: in wax deposition. SPE J 2000. http://dx.doi.org/10.2118/ 64519-MS. [3] Zílio EL, Pinto UB. Identification and distribution of the main groups of components present in brazilian crude oils. Bol Técnico Petrobras 2002;45:21–5. [4] Maqbool T, Srikiratiwong P, Fogler HS. Effect of temperature on the precipitation kinetics of asphaltenes. Energy Fuels 2011;25:694–700. http:// dx.doi.org/10.1021/ef101112r. [5] Oliveira MCK, Teixeira A, Vieira LC, Carvalho RM, Carvalho ABM, Couto BC. Flow assurance study for waxy crude oils. Energy Fuels 2012;26:2688–95. http://dx.doi.org/10.1021/ef201407j. [6] Ilyin S, Arinina M, Polyakova M, Bondarenko G, Konstantinov I, Kulichikhin V, et al. Asphaltenes in heavy crude oil: designation, precipitation, solutions, and effects on viscosity. J Pet Sci Eng 2016;147:211–7. http://dx.doi.org/10.1016/j. petrol.2016.06.020. [7] Venkatesan R, Nagarajan NR, Paso K, Yi YB, Sastry AM, Fogler HS. The strength of paraffin gels formed under static and flow conditions. Chem Eng Sci 2005;60:3587–98. http://dx.doi.org/10.1016/j.ces.2005.02.045. [8] Pedersen KS, Rønningsen HP. Effect of precipitated wax on viscosity – a model for predicting non-Newtonian viscosity of crude oils. Energy Fuels 2000;14:43–51. http://dx.doi.org/10.1021/ef9901185. [9] Marchesini FH, Alicke AA, de Souza Mendes PR, Ziglio CM. Rheological characterization of waxy crude oils: sample preparation. Energy Fuels 2012;26:2566–77. http://dx.doi.org/10.1021/ef201335c. [10] Andrade DEV, Cruz ACB, Franco AT, Negrão COR. Influence of the initial cooling temperature on the gelation and yield stress of waxy crude oils. Rheol Acta 2015;54:149–57. http://dx.doi.org/10.1007/s00397-014-0812-0. [11] Ding J, Zhang J, Li H, Zhang F, Yang X. Flow behavior of Daqing waxy crude oil under simulated pipelining conditions. Energy Fuels 2006;20:2531–6. http:// dx.doi.org/10.1021/ef060153t. [12] Tarcha BA, Forte BPP, Soares EJ, Thompson RL. Critical quantities on the yielding process of waxy crude oils. Rheol Acta 2015;54:479–99. http://dx.doi. org/10.1007/s00397-015-0835-1. [13] Paso K, Kompalla T, Oschmann HJ, Sjöblom J. Rheological degradation of model wax-oil gels. J Dispers Sci Technol 2009;30:472–80. http://dx.doi.org/10.1080/ 01932690802548924. [14] Guozhong Z, Gang L. Study on the wax deposition of waxy crude in pipelines and its application. J Pet Sci Eng 2010;70:1–9. http://dx.doi.org/10.1016/j. petrol.2008.11.003. [15] Aiyejina A, Chakrabarti DP, Pilgrim A, Sastry MKS. Wax formation in oil pipelines: a critical review. Int J Multiph Flow 2011;37:671–94. http://dx.doi. org/10.1016/j.ijmultiphaseflow.2011.02.007. [16] Wardhaugh LT, Boger DV. Measurement of the unique flow properties of waxy crude oils. Chem Eng Res Des 1987;65:74–83. [17] Azevedo LFA, Teixeira AM. A critical review of the modeling of wax deposition mechanisms. Pet Sci Technol 2003;21:393–408. http://dx.doi.org/10.1081/ LFT-120018528. [18] Ribeiro FS, Souza Mendes PR, Braga SL. Obstruction of pipelines due to paraffin deposition during the flow of crude oils. Int J Heat Mass Transf 1997;40:4319–28. http://dx.doi.org/10.1016/S0017-9310(97)00082-3. [19] Jemmett MR, Magda JJ, Deo MD. Heterogeneous organic gels: rheology and restart. Energy Fuels 2013;27:1762–71. http://dx.doi.org/10.1021/ef3014629. [20] Mortazavi-Manesh S, Shaw JM. Thixotropic rheological behavior of maya crude oil. Energy Fuels 2014;28:972–9. http://dx.doi.org/10.1021/ef4022637. [21] Oliveira GM, Negrão COR. The effect of compressibility on flow start-up of waxy crude oils. J Nonnewton Fluid Mech 2015;220:137–47. http://dx.doi.org/ 10.1016/j.jnnfm.2014.12.010. [22] Frigaard IA, Paso KG, de Souza Mendes PR. Bingham’s model in the oil and gas industry. Rheol Acta 2017:259–82. http://dx.doi.org/10.1007/s00397-0170999-y. [23] Tiwary D, Mehrotra AK. Phase transformation and rheological behaviour of highly paraffinic ‘‘ waxy ” mixtures. Can J Chem Eng 2004;82:162–74. http:// dx.doi.org/10.1002/cjce.5450820121. [24] Pedersen KS, Thomassen P, Fredenslund A. Thermodynamics of petroleum mixtures containing heavy hydrocarbons. 1. Phase envelope calculations by use of the Soave-Redlich-Kwong equation of state. Ind Eng Chem Process 1984;23:163–70. http://dx.doi.org/10.1021/i200024a027. [25] Won KW. Thermodynamics for solid solution-liquid-vapor equilibria: wax phase formation. Fluid Phase Equilib 1986;30:265–79. [26] Won KW. Thermodynamic calculation of cloud point temperatures and wax phase compositions of refined hydrocarbon mixtures. Fluid Phase Equilib 1989;53:377–96.
[27] Pedersen KS, Skovborg P, Rønningsen HP. Wax precipitation from North Sea Crude Oils. 4. Thermodynamic modeling. Energy Fuels 1991:924–32. http://dx. doi.org/10.1021/ef00030a022. [28] Erickson DD, Niesen VG, Brown TS. Thermodynamic measurement and prediction of paraffin precipitation in crude oil. Proc – SPE Annu Tech Conf Exhib 1993;Pi:933–48. doi:http://dx.doi.org/10.2523/26548-MS. [29] Coutinho JAP, Knudsen K, Andersen SI, Stenby EH. A local composition model for paraffinic solid solutions. Chem Eng Sci 1996;51:3273–82. http://dx.doi. org/10.1016/0009-2509(95)00397-5. [30] Zhou X, Thomas FB, Moore RG. Modelling of solid precipitation from reservoir fluid. J Can Pet Technol 1996;35:35–45. http://dx.doi.org/10.2118/96-10-03. [31] Coutinho JAP, Ruffier-Méray V. Experimental measurements and thermodynamic modeling of paraffinic wax formation in undercooled solutions. IndEngChem Res 1997;36:4977–83. http://dx.doi.org/10.1021/ ie960817u. [32] Coutinho JAP. Predictive UNIQUAC: a new model for the description of multiphase solid-liquid equilibria in complex hydrocarbon mixtures. Ind Eng Chem Res 1998;37:4870–5. http://dx.doi.org/10.1021/ie980340h. [33] Chen W, Zhao Z. Thermodynamic modeling of wax precipitation in crude oils. Chin J Chem Eng 2006;14:685–9. http://dx.doi.org/10.1016/S1004-9541(06) 60135-3. [34] Ghanaei E, Esmaeilzadeh F, Fathikalajahi J. Wax formation from paraffinic mixtures: a simplified thermodynamic model based on sensitivity analysis together with a new modified predictive UNIQUAC. Fuel 2012;99:235–44. http://dx.doi.org/10.1016/j.fuel.2012.03.053. [35] Zhao Y, Paso K, Sjöblom J. Thermal behavior and solid fraction dependent gel strength model of waxy oils. J Therm Anal Calorim 2014;117:403–11. http:// dx.doi.org/10.1007/s10973-014-3660-3. [36] Hansen JH, Fredenslund A, Pedersen KS, Røningsen HP. A thermodynamic model for predicting wax formation in crude oils. AIChE J 1988;34:1937–42. http://dx.doi.org/10.1002/aic.690341202. [37] Ji H-Y, Tohidi B, Danesh A, Todd AC. Wax phase equilibria: developing a thermodynamic model using a systematic approach. Fluid Phase Equilib 2004;216:201–17. http://dx.doi.org/10.1016/j.fluid.2003.05.011. [38] Yang J, Wang W, Huang H, Shi G, Shi B, Cheng B, et al. Prediction of solid-liquid equilibrium in paraffinic systems with new solid solution model. Fluid Phase Equilib 2016;427:504–12. http://dx.doi.org/10.1016/j.fluid.2016.07.030. [39] Bagherinia R, Assareh M, Feyzi F. An improved thermodynamic model for Wax precipitation using a UNIQUAC + PC-SAFT approach. Fluid Phase Equilib 2016;425:21–30. http://dx.doi.org/10.1016/j.fluid.2016.05.008. [40] Aftab S, Javanmardi J, Nasrifar K. Experimental investigation and thermodynamic modeling of wax disappearance temperature for n-undecane +n-hexadecane+n-octadecane and n-tetradecane+n-hexadecane+noctadecane ternary systems. Fluid Phase Equilib 2015;403:70–7. http://dx. doi.org/10.1016/j.fluid.2015.06.004. [41] Coutinho JAP, Stenby EH. Predictive local composition models for solid/liquid equilibrium in n -alkane systems: Wilson equation for multicomponent systems. Ind Eng Chem Res 1996;35:918–25. http://dx.doi.org/10.1021/ ie950447u. [42] Ashbaugh HS, Radulescu A, Prud RK, Schwahn D, Richter D, Fetters LJ. Interaction of paraffin wax gels with random crystalline/amorphous hydrocarbon copolymers. Macromolecules 2002:7044–53. http://dx.doi.org/ 10.1021/ma0204047. [43] Bhat NV, Mehrotra AK. Measurement and prediction of the phase behavior of wax – solvent mixtures: significance of the wax dis appearance temperature. Ind Eng Chem Res 2004;43:3451–61. http://dx.doi.org/10.1021/ie0400144. [44] ASTM. D2500-11 Standard Test Method for Cloud Point of Petroleum Products, American Society for Testing and Materials. 2011. doi:http://dx.doi.org/10. 1520/D2500-11.2. [45] Monger-McClure TG, Tackett JE, Merrill LS. Comparisons of cloud point measurement and Paraffin prediction methods. SPE Prod Facil 1999;14:5–8. http://dx.doi.org/10.2118/54519-PA. [46] Ijeomah CE, Dandekar AY, Chukwu GA, Khataniar S, Patil SL, Baldwin AL. Measurement of wax appearance temperature under simulated pipeline (dynamic) conditions. Energy Fuels 2008;22:2437–42. http://dx.doi.org/ 10.1021/ef7007453. [47] Rønningsen HP, Bjorndal B, Hansen AB, Pedersen WB. Wax precipitation from North Sea crude oils. 1. Crystallization and dissolution temperatures, and Newtonian and non-Newtonian flow properties. Energy Fuels 1991;5:895–908. http://dx.doi.org/10.1021/ef00030a019. [48] Kok MV, Létoffé JM, Claudy P, Martin D, Garcin M, Vollet JL. Comparison of wax appearance temperatures of crude oils by differential scanning calorimetry, thermomicroscopy and viscometry. Fuel 1996;75:787–90. http://dx.doi.org/ 10.1016/0016-2361(96)00046-4. [49] Singh P, Fogler HS, Nagarajan N. Prediction of the wax content of the incipient wax-oil gel in a pipeline: an application of the controlled-stress rheometer. J Rheol 1999;43:1437–59. http://dx.doi.org/10.1122/1.551054. [50] Wardhaugh LT, Boger DV. Flow characteristics of waxy crude oils – application to pipeline design. AIChE J 1991;37:871–85. http://dx.doi.org/10.1002/ aic.690370610. [51] Magda JJ, El-Gendy H, Oh K, Deo MD, Montesi A, Venkatesan R. Timedependent rheology of a model waxy crude oil with relevance to gelled pipeline restart. Energy Fuels 2009;23:1311–5. http://dx.doi.org/10.1021/ ef800628g. [52] Kruka VR, Cadena ER, Long TE. Cloud-point determination for crude oils. J Pet Technol 1995;47:681–7. http://dx.doi.org/10.2118/31032-PA.
D.E.V. Andrade et al. / Fuel 206 (2017) 516–523 [53] Elsharkawy AM, Al-Sahhaf TA, Fahim MA. Wax deposition from Middle East crudes. Fuel 2000;79:1047–55. http://dx.doi.org/10.1016/S0016-2361(99) 00235-5. [54] Jiang Z, Hutchinson JM, Imrie CT. Measurement of the wax appearance temperatures of crude oils by temperature modulated differential scanning calorimetry. Fuel 2001;80:367–71. http://dx.doi.org/10.1016/S0016-2361(00) 00092-2. [55] Claudy P, Létoffé JM, Neff B, Damin B. Diesel fuels: determination of onset crystallization temperature, pour point and filter plugging point by differential scanning calorimetry. Correlation with standard test methods. Fuel 1986;65:861–4. http://dx.doi.org/10.1016/0016-2361(86)90082-7. [56] Hansen AB, Larsen E, Pedersen WB, Nielsen AB, Rønningsen HP. Wax precipitation from North Sea crude oils. 3. Precipitation and dissolution of wax studied by differential scanning calorimetry. Energy Fuels 1991;5:914–23. http://dx.doi.org/10.1021/ef00030a021. [57] He C, Ding Y, Chen J, Wang F, Gao C, Zhang S, et al. Influence of the nano-hybrid pour point depressant on flow properties of waxy crude oil. Fuel 2016;167:40–8. http://dx.doi.org/10.1016/j.fuel.2015.11.031. [58] Yao B, Li C, Yang F, Zhang Y, Xiao Z, Sun G. Structural properties of gelled Changqing waxy crude oil benefitted with nanocomposite pour point depressant. Fuel 2016;184:544–54. http://dx.doi.org/10.1016/ j.fuel.2016.07.056. [59] Mendes R, Vinay G, Ovarlez G, Coussot P. Modeling the rheological behavior of waxy crude oils as a function of flow and temperature history. J Rheol 2015;59:703–32. http://dx.doi.org/10.1122/1.4916531. [60] Gimzewski E, Audley G. Monitoring wax crystallisation in diesel using differential scanning calorimetry (DSC) and microcalorimetry. Thermochim Acta 1993;214:149–55. http://dx.doi.org/10.1016/0040-6031(93)80050-K. [61] Meray VR, Volle J-L, Schranz CJP, Le Marechal P, Behar E. Influence of light ends on the onset crystallization temperature of waxy crudes within the frame of multiphase transport. SPE Annu Tech Conf Exhib 1993:369–78. http://dx.doi. org/10.2118/26549-MS. [62] Paso K, Kallevik H, Sjöblom J. Measurement of wax appearance temperature using near-infrared (NIR) scattering. Energy Fuels 2009;23:4988–94. http://dx. doi.org/10.1021/ef900173b. [63] Paso K, Senra M, Yi Y, Sastry AM, Fogler HS. Paraffin polydispersity facilitates mechanical gelation. Ind Eng Chem Res 2005;44:7242–54. http://dx.doi.org/ 10.1021/ie050325u. [64] Hammami A, Raines MA. Paraffin deposition from crude oils: comparison of laboratory results with field data. SPE J 1999;4:9–18. http://dx.doi.org/ 10.2118/54021-PA. [65] Mullin J. Crystallization. 4th ed. London: Butterworth-Heinemann; 2001. [66] Ny´vlt J, Hostomsky J, Giulietti M. Crystallization (in portuguese). São Carlos – SP/BR: EdUFSCar/IPT; 2001. [67] Stefanescu DM. ASM metals Handbook – Casting. 9th ed, 9th ed., 15. USA: ASM International; 1988. [68] Vehkamäki H. Classical nucleation theory in multicomponent systems. Germany: Springer - Verlag Berlim Heidelberg; 2006. http://dx.doi. org/10.1007/b138396. [69] Dimitriou CJ. The rheological complexity of waxy crude oils: Yielding, thixotropy and shear heterogeneities [Ph.D. thesis]. USA: Massachusetts Institute of Technology; 2013.
523
[70] Dimitriou CJ, McKinley GH, Venkatesan R. Rheo-PIV analysis of the yielding and flow of model waxy crude oils. Energy Fuels 2011;25:3040–52. http://dx. doi.org/10.1021/ef2002348. [71] Mendes R, Vinay G, Ovarlez G, Coussot P. Reversible and irreversible destructuring flow in waxy oils: an MRI study. J Nonnewton Fluid Mech 2015;220:77–86. http://dx.doi.org/10.1016/j.jnnfm.2014.09.011. [72] Geri M, Venkatesan R, Sambath K, McKinley GH. Thermokinematic memory and the thixotropic elasto-viscoplasticity of waxy crude oils. J Rheol (N Y N Y) 2017;61:427–54. http://dx.doi.org/10.1122/1.4978259. [73] Dimitriou CJ, McKinley GH. A comprehensive constitutive law for waxy crude oil: a thixotropic yield stress fluid. Soft Matter 2014;10:6619–44. http://dx. doi.org/10.1039/c4sm00578c. [74] Bird RB, Armstrong RC, Hassager O. Dynamics of polymeric liquids. 6th ed, 6th ed., 1. New York, USA: John Wiley and Sons; 1987. [75] Paso K, Silset A, Soørland G, Gonçalves MD AL, Sjöblom J. Characterization of the formation, flowability, and resolution of brazilian crude oil emulsions. Energy Fuels 2009;23:471–80. http://dx.doi.org/10.1021/ef800585s. [76] Merino-Garcia D, Margarone M, Correra S. Kinetics of waxy gel formation from batch experiments. Energy Fuels 2007;42:1287–95. http://dx.doi.org/10.1021/ ef060385s. [77] Guo X, Pethica BA, Huang JS, Adamson DH, Prud’homme RK. Effect of cooling rate on crystallization of model waxy oils with microcrystalline poly(ethylene butene). Energy Fuels 2006;20:250–6. http://dx.doi.org/10.1021/ef050163e. [78] Hammami A, Mehrotra AK. Thermal behaviour of polymorphic n-alkanes: effect of cooling rate on the major transition temperatures. Fuel 1995;74:96–101. http://dx.doi.org/10.1016/0016-2361(94)P4338-3. [79] Kasumu AS, Arumugam S, Mehrotra AK. Effect of cooling rate on the wax precipitation temperature of ‘‘waxy” mixtures. Fuel 2013;103:1144–7. http:// dx.doi.org/10.1016/j.fuel.2012.09.036. [80] Carey VP. Liquid-vapor phase-change phenomena. 2nd ed. New York, USA: Taylor & Francis Group; 2008. [81] Sloan ED, Koh CA. Clathrate hydrate of natural gases. 3rd ed. FL, USA: Taylor & Francis Group; 2008. [82] Taggart AM, Voogt F, Clydesdale G, Roberts KJ. An Examination of the nucleation kinetics of n-alkanes in the homologous series C13H28 to C32H66, and their relationship to structural type, associated with crystallization from stagnant melts. Langmuir 1996;12:5722–8. http://dx. doi.org/10.1021/la9600816. [83] Bott TR. Aspects of crystallization fouling. Exp Therm Fluid Sci 1997;14:356–60. http://dx.doi.org/10.1016/S0894-1777(96)00137-9. [84] Jones AG. Crystallization process systems. London, UK.: ButterworthHeinemann; 2002. [85] Hammami A, Mehrotra AK. Liquid-solid-solid thermal behaviour of nC44H90 +nC50H102 and nC25H52+nC28H58 paraffinic binary mixtures. Fluid Phase Equilib 1995;111:253–72. http://dx.doi.org/10.1016/0378-3812(95)02777-C. [86] Metivaud V, Rajabalee F, Oonk HAJ, Mondieig D, Haget Y. Complete determination of the solid (RI)-liquid equilibria of four consecutive n-alkane ternary systems in the range C14H30-C21H44 using only binary data. Can J Chem Can Chim 1999;77:332–9. http://dx.doi.org/10.1139/cjc-77-3-332.
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Full Length Article
The importance of supersaturation on determining the solid-liquid equilibrium temperature of waxy oils Diogo E.V. Andrade a,b,c,⇑, Moisés A. Marcelino Neto a,b,d, Cezar O.R. Negrão a,b,c a
Federal University of Technology-Paraná – UTFPR, 81280-340, R. Deputado Heitor Alencar Furtado, 5000 – Bloco N – Ecoville, Curitiba, PR, Brazil Postgraduate Program in Mechanical and Materials Engineering – PPGEM c Research Center for Rheology and Non-Newtonian Fluids – CERNN d Multiphase Flow Center – NUEM b
h i g h l i g h t s A supercooling is required for the onset of wax precipitation in waxy oils. The higher the cooling rate the higher the metastable region width. The cooling experiment is not appropriate to determine the saturation temperature. At a high heating rate, there also exists a superheating during the dissolution. The saturation temperature can be determined at a very low heating rate.
a r t i c l e
i n f o
Article history: Received 10 March 2017 Received in revised form 2 June 2017 Accepted 8 June 2017
Keywords: Crystallization temperature Supercooling Superheating Highest solid-liquid thermodynamic equilibrium temperature Viscometry DSC
a b s t r a c t Crystallization is a process where an ordered solid structure is formed from a disordered phase. This event is divided in two main stages, namely nucleation and crystals growth. As paraffin nucleation is a stochastic process, a supercooling is needed to initiate the process. In other words, the beginning of crystal precipitation does not coincide with the highest thermodynamic solid-liquid equilibrium temperature. Therefore, during the cooling it is required that the fluid reaches a certain temperature below saturation, i.e., a metastable state, to initiate the crystal nucleation process. The difference between the saturation temperature and the crystallization temperature is called degree of supercooling. As this metastable condition may exist during not only the crystallization but also the dissolution of crystals, this work proposes a procedure to determine consistently the highest solid-liquid thermodynamic equilibrium temperature by using the results of rheometer and DSC experiments. It can be anticipated that the proposed protocol states that the highest solid-liquid thermodynamic equilibrium temperature is considered to approach the dissolution temperature when the material is heated at a very low heating rate. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Crude oil is a complex mixture of hydrocarbons, heteroatoms (e.g. N, S, O) and inorganic components as salts, sand and water [1,2]. More than 90% of the oil can be composed of hydrocarbons [3] that are usually divided in four major fractions: saturates – known as paraffin, aromatics, resins and asphaltenes (SARA) [4–6]. At oil reservoir conditions, i.e. high temperatures
⇑ Corresponding author at: Federal University of Technology-Paraná – UTFPR, 81280-340, R. Deputado Heitor Alencar Furtado, 5000 – Bloco N – Ecoville, Curitiba, PR, Brazil. E-mail address: [email protected] (D.E.V. Andrade). http://dx.doi.org/10.1016/j.fuel.2017.06.042 0016-2361/Ó 2017 Elsevier Ltd. All rights reserved.
(70–150 °C) and pressures (50–100 MPa), all the paraffin molecules are dissolved in the oil so that this mixture of hydrocarbons is in liquid phase [7] and behaves as a Newtonian fluid [8]. At low temperatures, the solubility of high molecular weight components in the oil decreases and mainly the n-paraffins tend to precipitate out of the solution as crystal structures. These crystals that render a non-Newtonian behavior to the fluid [9,10], with a variety of characteristics such as pseudo-plasticity, elasticity, timedependency [11,12] and/or deformation dependency [13], may deposit in the inner surface of pipelines [14,15] and are responsible for oil gelation when the flow is interrupted [5,16]. The risk of wax crystal precipitation during offshore production is quite high, as the ocean floor temperature could be as low as 4 °C [17].
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The wax deposition in pipeline inner surfaces increases pump power, decreases flow rate and, consequently, reduces oil production [14,18]. The common methods employed to remediate wax deposition (e.g. the use of chemical inhibitors, pipeline heating and mechanical removal by using pigs) are extremely costly in deep and ultra-deep water production scenarios [17]. In flow interruption for pipeline maintenance, gelation takes place and start-up pressures much larger than the usual operational pressure are required to break down the gel structure [19,20]. If the rheological properties of waxy crude oils at low temperatures are not accurately determined, restart pressures can be overrated leading to overestimation of pipe dimensions, and consequently making pipeline projects unfeasible [21,22]. A key point in crude oil production and transportation is the wax crystallization onset temperature. The accurate determination of this temperature is important to design production and/or transportation pipelines to work above this temperature and to know when the crystallization becomes a real problem in oil production. This temperature, however, may be distinct from the highest temperature in which the solid and liquid phases co-exist in equilibrium at a fixed pressure. The latter is a thermodynamic property and is known as the highest solid-liquid thermodynamic equilibrium temperature, Teq,SL. In petroleum area, this temperature is usually called the Wax Appearance Temperature (WAT) or cloud point [1]. Although there is not a consensus in the open literature, Tiwary and Mehrotra [23] claimed that ‘‘WAT is the true solidliquid phase boundary temperature”. Researchers have made significant effort to model the thermodynamic solid-liquid equilibrium [24–39]. The general solid-liquid equilibrium is reached when the fugacities of each component ‘‘i” in the solution are identical in solid and liquid phases. Many assumptions have been made to determine the solid-liquid equilibrium of waxy oils by means of thermodynamic models. Some authors assume that the difference between the heat capacities of each component is negligible (DC SL p;i ¼ 0) [25,28,31] and the decrease in component volume due to phase transition is disregarded in some cases [27]. The liquid phase is assumed to be an ideal solution (cLi ¼ 1) by some authors [34,40] and some others consider that cSi ¼ 1 [36,40], where ci is the activity coefficient of each component present in the solution. The regular solution is used in many works [25–28,33,40] to take the non-idealities of the liquid and solid phases into account. In addition to these assumptions, the liquid phase activity coefficient was also determined by Flory-Huggins model [36], by Flory free-volume equation added to a UNIFAC residual term [41] and by Flory free-volume model [35]. The solid phase non-ideality was also considered by Wilson equation [40,41] and by UNIQUAC model [32,34,35,37,39,40]. Although some models performed better than others in many comparisons, there is not a capable model to predict the solid-liquid equilibrium temperature of all waxy oils. The differences between experimental and calculated Teq,SL are generally higher than 2 °C for the cases in which Teq,SL is approximately 20 °C and the crystals mass fraction below the equilibrium temperature is not accurately determined but only qualitatively well represented. On the other hand, the experimental methods to find the highest solid-liquid equilibrium temperature of waxy oil are not well consolidated. Several techniques have been used to determine the WAT: Visual Method [23,42,43] as normalized by ASTM [44], Filter Plugging (FP) [45,46], Viscometry [46–51], Densitometry [52], Cross Polar Microscopy (CPM) [23,47,48], Differential Scanning Calorimetry (DSC) [5,12,53–60], cold finger [45], ultrasonic experiments [61], Fourier Transform Infrared (FTIR) energy scattering technique [45] and Near Infrared (NIR) scattering technique [62]. Rønningsen et al. [47] analyzed 17 crude oils by comparing
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the three more usual methods – microscopy, differential scanning calorimetry and viscometry – and concluded that microscopy is the best method to determine the WAT. In contrast, Kok et al. [48] used the same three techniques to investigate 15 different crude oils and claimed that the best method to determine the wax appearance temperature depends on the solution composition. Tiwary and Mehrotra [23] examined different model waxy oils using the same three techniques again and compared with a visual method. The authors concluded that the DSC was the best technique to determine the solid-liquid equilibrium temperature because provided the highest WAT values. Different techniques proposed to determine more accurately the WAT [45,52,62] have been compared with the usual techniques and some interesting conclusions were obtained. Although Marchesini et al. [9] have made a wise discussion saying that the temperature determined by viscometry/rheometry is not the solid-liquid equilibrium temperature because the first crystal that appears in the solution is too small to change the oil viscosity (the same can be concluded from the other techniques [23]), a key point in wax crystallization, i.e., the supercooling has been forgotten or neglected by the majority of the authors. It is worth mentioning that just few authors [17,31,43,63] recognized the existence of this metastable region before the wax crystallization. Crystallization is a process of building up an ordered solid structure from a disordered phase and involves two main stages: nucleation and crystal growth [47,64]. As well known and consolidated in the inorganic chemistry area, nucleation is a stochastic process that requires a supercooling (or supersaturation) to start it up [65–67]. In other words, crystals precipitation begins at a temperature that is below the solid-liquid equilibrium temperature, which is a thermodynamic property [37]. In the current work, the highest solid-liquid equilibrium temperature is represented by Teq,SL and the onset of wax precipitation is defined by the crystallization temperature, Tc, as proposed by Marchesini et al. [9]. To avoid confusion with the solid-liquid equilibrium state, the term WAT (Wax Appearance Temperature) is not used here. The difference between the solid-liquid equilibrium temperature and the crystallization temperature is defined as degree of supercooling, DT sup , [65,66]:
DT sup ¼ T eq;SL T c
ð1Þ
Considering that during heating solid may also exist in a nonequilibrium condition in the solution [60,68] and consequently metastable states may occur in either crystallization or dissolution of crystals, this work presents a discussion about how to evaluate consistently the highest solid-liquid equilibrium temperature of waxy oil. The discussion is based on the results of rheometer and mDSC experiments performed at different rate of change of temperature and calls the attention for metastable regions that exist during the crystallization and dissolution of paraffin. Although not considered in the open literature that deals with waxy oils, these metastable regions may interfere directly in the measurement of the highest solid-liquid equilibrium temperature. 2. Experimental section The experiments presented in the current work were conducted with model waxy oils. The model oils were formulated by adding a paraffin wax with a melting point between 58 and 62 °C (Sigma Aldrich 327212 CAS-No:8002-74-2) to a mineral oil (Sigma Aldrich 330779 – CAS-No: 8042-47-5). The paraffin wax and mineral oil were the same used in Dimitriou’s thesis [69], by others in his group [70] and by IFP Energies nouvelles’s work [71]. The wax is composed of 60 wt% n-paraffins and 40 wt% iso and cycloparaffins [70]. The normal alkane carbon distribution of both
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mineral oil and paraffin wax can be found elsewhere [69]. Three different compositions were used: 5, 10 and 20 wt% of paraffin in oil. Model waxy oil samples were prepared by dissolving the paraffin wax in the mineral oil and heating them up in a roller oven to 80 °C within a closed bottle. The samples were then stirred at this temperature for 30 min. Two techniques used to determine the crystallization and dissolution temperatures are now presented: viscometric and DSC analyses. It is worth noting that the purpose is neither to compare the techniques nor to state which is the more accurate but rather, to use the results to discuss the supercooling during wax crystallization. 2.1. Viscometry tests The viscometry tests were performed by employing a Haake Mars III (Haake Co., Germany) rotational rheometer that can measure a minimum torque of 5.108 Nm. A 35 mm diameter parallelplate geometry with a gap of 0.3 mm and sandblasted surface was used in the rheometer and the temperature was controlled by a Peltier-thermostatic bath system. Before any test, the model waxy oil sample was mixed at 80 °C in a roller oven during 30 min in order to guarantee that the wax was completely dissolved in the oil [72,73]. A small sample was then collected and placed in the rheometer plate at 80 °C by using a syringe. The rotor was lowered to its measuring position and the temperature was kept at 80 °C for another 30 min to assure thermal homogenization. The viscometry tests consisted of shearing the specimen at a constant rate of 5 s1 and while shearing, the material was cooled to a temperature below the crystallization point and then heated again to the initial temperature at a constant rate of change of tem_ Except the T_ that changed from test to test, all other perature, T. test parameters were kept constant. Five different T_ were used: 8.5, 5.0, 1.0, 0.5 and 0.1 K/min. The highest rate of change of temperature of 8.5 K/min was imposed by the limit of the cooling and heating systems. Although not done in the current work, the crystallization and dissolution temperatures can still be determined by performing oscillatory rheometer experiments of small amplitude [63]. 2.2. DSC tests The calorimetric analyses were performed by employing the SETARAM HP mDSC VIIa differential scanning microcalorimeter. The resolution of the equipment is 2.108 W, the cells used are made from Hastelloy C276 and have a volume of 1.0 cm3. In all the experiments, approximately 37 mg of the specimen is loaded in the microcalorimeter cell and maintained at 80 °C for 5 min. The sample is then cooled to 10 °C and heated again to the initial temperature of 80 °C. Two rate of change of temperature were used: 0.8 and 0.1 K/min. 3. Results and discussion The results presented here focus on the evaluation of the influence of the rate of change of temperature (cooling and heating) on the crystallization and dissolution temperature of the model waxy oils. 3.1. Viscometric analysis Fig. 1(a) shows the viscosity as a function of the temperature for the model waxy oil with 20 wt% of paraffin and rate of change of temperature of 1.0 K/min and Fig. 1(b) presents the same set of data as a function of the inverse of the absolute temperature. As
in Newtonian fluids (see Fig. 1(b)), the increase of the viscosity is well represented by the Arrhenius fit (log m 1/T) from the beginning of the test, at T = 80 °C, to approximately 40 °C [74]:
DH R
l ¼ lref e
1 1 T T ref
ð2Þ
where lref is the fluid viscosity at temperature Tref and DH is the activation energy for flow. During the cooling, crystals precipitate out of the solution at some point and start to affect the measured viscosity of the model oil. From this point forward, the Arrhenius fit cannot represent the viscosity behavior anymore, and the temperature at which the curve slope changes is defined as the crystallization temperature, Tc. For this particular case, Tc = 39 °C. Because of the wax crystallization, the apparent viscosity of the solution increases from 0.01 to 2.0 Pa.s when the temperature is reduced from 40 to 35 °C. Similar behaviors of the viscosity have already been reported for crude oils [9,10,47,75]. At the end of the cooling at 35 °C, the specimen is heated again at the same rate of change of temperature to the initial temperature of 80 °C. As the temperature increases, the wax solubility increases and the crystals dissolve in the solution decreasing the apparent viscosity of the model oil. When all the paraffin is dissolved in the solution, the material starts to behave again as a Newtonian fluid. In the current work, the first point where the Arrhenius fit was able to predict the viscosity behavior during the heating is called dissolution temperature, Td. For this specific case, Td = 46 °C. It is worth noting that some authors [37,40,76] named this temperature as WDT (Wax Disappearance Temperature). 3.2. DSC analysis The DSC curves of the waxy oil with 20 wt% of paraffin wax are presented in Fig. 2. Fig. 2(a) shows the heat flux as a function of the temperature during the cooling. While the cooling rate was kept constant at 0.8 K/min, the heat flux to maintain this cooling rate was measured during the DSC test. As noted, the heat flux needed to reduce the oil sample temperature from 80 °C to approximately 40 °C is constant and then increases significantly. This significant heat flux release characterizes the appearance of the first crystals in the solution and the temperature at which this event takes place is called crystallization temperature, Tc. The crystallization temperature is indicated by a green arrow in Fig. 2(a) (Tc = 40.5 °C). This behavior was also observed by Paso et al. (2005) [63] that performed DSC experiments with model oils and stated that the supersaturation crystal growth regime can also be determined by using this raw data. Fig. 2(b) presents the DSC curve for the heating process. As shown, the energy needed to dissolve the paraffin increases as the oil sample is heated. At 43.9 °C, the energy required reduces significantly characterizing the end of the dissolution process and consequently, defining the dissolution temperature, Td. Despite the cooling and heating rates being the same, the dissolution temperature is 3.4 °C higher than the crystallization temperature. 3.3. Discussion The literature has reported [40,45,52,54,77] that the cooling rate affects the onset temperature for wax crystallization in the waxy oils. As discussed by [35,62,78,79], the lower the cooling rate the higher the crystallization temperature and also that this dependency is linear. The reason for the influence of the cooling rate on the crystallization temperature resides on the supersaturation. Supersaturation is a metastable condition in which liquid is
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Fig. 1. Viscosity of the model waxy oil with 20 wt% of paraffin wax for T_ = 1.0 K/min as a function of (a) Temperature and (b) as a function of 1000/Temperature. For the Arrhenius fit, lref (80 °C) = 5.8 mPa.s; DH=R = 2700 K.
0 exo.
10 9
-2
8 7 6
cooling
5 4 3
Heat Flux [10 mW/mg]
-2
Heat Flux [10 mW/mg]
11
(a)
Tc 0
10
20
30
40
50
60
70
Temperature [ºC]
endo.
-1 -2 -3
heating
-4 -5 -6 -7 -8
(b)
Td 0
10
20
30
40
50
60
70
Temperature [ºC]
Fig. 2. Heat flux in DSC tests of the model waxy oil with 20 wt% of paraffin wax for T_ = 0.8 K/min as a function of temperature for (a) the cooling and (b) the heating process.
supercooled below the equilibrium saturation temperature or solid is superheated above it [68,80]. In other words, liquid or solid exists in a non-equilibrium condition. Fig. 3 shows a diagram at constant pressure, as proposed by Mullin [65], that helps the understanding. A hypothetic solution with a solute concentration represented by the horizontal dash-dotted line is cooled from the temperature A to C. At high temperatures in the stable region (condition A), all the solution in the liquid state is in equilibrium. The point B represents the highest thermodynamic solid-liquid equilibrium temperature or the saturation temperature for this specific solute concentration and for this pressure. As shown experimentally in the literature [65,66], the first solid does not precipitate out in the solution exactly at the saturation temperature and a supercooling or supersaturation is necessary for the onset of
Fig. 3. The saturation - supersaturation diagram as proposed by Mullin [65].
precipitation. The point C, in Fig. 3, represents the condition in which the first solid precipitates out in the solution. The conditions between the saturation (point B) and the precipitation temperature (point C) are commonly named metastable region. Although the saturation temperature is a thermodynamic property that does not depend on the cooling condition, the precipitation temperature and consequently, the metastable region width, DT sup , are affected by many factors, such as: impurities, solution concentration, mechanical stirring and cooling rate [65,66]. For instance, the higher the cooling rate the larger is the metastable region width when all the other parameters are kept constant. The main reason for the required supercooling resides on the entropy of the system. From the thermodynamics viewpoint, a closed system of fixed energy and mass achieves a state of maximum entropy at the equilibrium. Sloan and Koh [81] claim that entropy favors disorder over order so that the paraffin in liquid phase, that is disordered in a molecular level, requires a supersaturation to be rearranged into the molecularly ordered crystals in the solid phase. The solution must then reach the metastable region to compensate for lowering the system entropy. Few works in the petroleum area [17,23,31,37,43,60,63,82–84] recognized the need of supersaturation for the first crystal to precipitate in the solution. Keeping in mind that for the same rate of change of temperature, the supercooling is higher than the superheating for the same material [43,52,60,76,85], some authors [31,37,43,60,85,86] have suggested that the saturation temperature is closer to the dissolution temperature than it is to the crystallization temperature, as usually established in the area of hydrates [81]. An interesting discussion was proposed by Taggart et al. [82] for a pure alkane (C18H38), which determined the solidification and
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melt temperatures for different rate of change of temperature. They showed that these temperatures are different even for very slow rates. Motivated by the Taggart’s et al. [82] discussion, a similar analysis is now conducted for the model waxy oils. Fig. 4(a) shows the cooling (or heating) rate versus the crystallization (or dissolution) temperature for the model oil composed of 20 wt% of paraffin wax obtained from the viscometric test results. The dots are average values of Tc and Td computed from three measurements and the error bars represent the standard deviation of each test condition. As already reported in prior works [62,78], the crystallization temperature is inversely proportional to the cooling rate; the lower the T_ the higher the Tc. The minimum crystallization temperature can then be estimated by extrapolating the cooling rate to zero from _ the linear blue line shown in Fig. 4(a), i.e., Tc,min (at T=0 K/min) = 41.3 °C. It is noteworthy that the correlation coefficient for the blue straight line was found to be greater than 0.99. As shown, not only the crystallization temperature but also the dissolution temperature is linear dependent on the rate of change of temperature; the lower the T_ the lower the Td. Similar conclusions can be taken from DSC results presented elsewhere [35]. As the dissolution temperature is heating rate dependent, this variable should not be used to estimate the solid-liquid equilibrium temperature, which is a thermodynamic property that does not dependent on any experimental condition. The literature [82], however, has _ suggested that the dissolution temperature at T=0 K/min is the best approximation for the thermodynamic solid-liquid equilibrium temperature once the superheating reduces with the heating rate. The accuracy of Teq,SL will depend on the equipment used to determine the dissolution temperatures along with the whole range of heating rate employed. From the red trend line depicted in Fig. 4 _ (a), Teq,SL (Td at T=0 K/min) is estimated to be 42.9 °C for this model waxy oil using the viscometry technique. The assumption that the dissolution temperature tends to the saturation temperature as the heating rate approaches zero is again based on the thermodynamic condition of maximum entropy at the equilibrium. During the dissolution of crystals, the material goes from the solid state that is ordered and has a lower entropy to the liquid state that is molecularly disordered and has a higher entropy [81] so that the supersaturation is not required for the system to reach the equilibrium. However, the superheating still exists if the dissolution is performed too fast and the material does not have time to reach the equilibrium condition. As the heating rate is reduced to zero, the superheating tends to disappear and the dissolution temperature approaches the equilibrium solidliquid temperature. _ In order to better visualize Tc and Td close to T=0 K/min, the
Heating or cooling rate [K/min]
results of Fig. 4(a) are shown in Fig. 4(b) for the rate of change of temperature ranging from 0.1 to 1.0 K/min. As noted, not even
10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
Dissolution Temperature
Crystallization Temperature
Teq,SL
(a) 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Temperature [ºC]
for the lowest rate of change of temperature of 0.1 K/min, the crystallization temperature equals the dissolution temperature. The minimum metastable region width is thus assumed to take place at zero rate of change of temperature, i.e., DT sup;min = 42.9 – 41.3 = 1.6 °C. The same experiments were performed to the other two model waxy oils. The effect of the rate of change of temperature on Tc and Td for the model waxy oils with 10 and 5 wt% of paraffin wax are presented, respectively, in Fig. 5(a) and (b). The blue and red straight lines were used again to define the dependency of the crystallization and dissolution temperatures on the rate of change of temperature, respectively. The correlation coefficients for Fig. 5 (a) and Fig. 5(b) were greater than 0.99 and 0.95, respectively. _ While Tc (at T=0 K/min) was estimated as 34.3 °C, Teq,SL (Td at
_ T=0 K/min) as 36.0 °C and the minimum degree of supercooling as 1.8 °C for the oil with 10 wt% of paraffin wax, these values were, respectively, 26.7 °C, 32.0 °C and 5.3 °C for the oil formulated with 5 wt% of paraffin wax. It is worth noting that not only the crystallization and dissolution temperatures reduce but also the metastable region width increases with the wax concentration reduction. In other words, the reduction of the solute concentration diminishes the saturation temperature and consequently, requires a higher supercooling for the precipitation of the first crystal in solution [65,66]. For the sake of comparison, the same analysis was performed with the model oil composed of 20 wt% of paraffin wax using the DSC technique with rate of change of temperature of 0.8 and 0.1 K/min. The crystallization and dissolution temperatures for these experiments are presented in Fig. 6(a). The dots shown are the average values of Tc and Td obtained from the DSC test results that were repeated twice and the error bars are the standard deviation. As depicted, the same tendency of viscometric tests is observed in the DSC measurements, i.e., the higher the rate of change of temperature the lower the Tc and the higher the Td. From the green and _ orange trend lines shown in Fig. 6(a), Tc (at T=0 K/min) was esti_ mated as 40.8 °C, Teq,SL (Td at T=0 K/min) as 42.6 °C and DT sup;min as 1.8 °C for this model waxy oil using the DSC technique. Fig. 6(b) compares the viscometry and the DSC measurements within the range of 0.1 to 1.0 K/min, showing that the results are _ 0.1 K/min for this specific waxy oil. Except for very similar at T=
the crystallization temperature at 0.5 K/min in which the viscometric result is well represented by the dashed trend line of the DSC experiment, the DSC and viscometric results diverge from each other at higher rate of change of temperature. Nevertheless, the Teq, SL determined by both technique was very similar. While the solidliquid equilibrium temperature estimated from the viscometric experiment was 42.9 °C, this same temperature obtained from the DSC measurements was 42.6 °C.
Heating or cooling rate [K/min]
520
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Crystallization Temperature
Dissolution Temperature Teq,SL
(b) 38 39 40 41 42 43 44 45 46 47 Temperature [ºC]
Fig. 4. (a) Influence of the rate of change of temperature on the crystallization and dissolution temperatures measured by using rheometric tests with the model oil composed of 20 wt% of paraffin wax. (b) The same results of (a) within the scale of 0.0 and 1.0 K/min.
521
10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
Crystallization Temperature Dissolution Temperature
Teq,SL
(a) 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Temperature [ºC]
Heating or cooling rate [K/min]
Heating or cooling rate [K/min]
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10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
Dissolution Temperature Crystallization Temperature
Teq,SL
(b) 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Temperature [ºC]
Fig. 5. Influence of the rate of change of temperature on the crystallization and dissolution temperatures measured in the rheometric tests with the model oils composed of (a) 10 wt% and (b) 5 wt% of paraffin wax.
Fig. 6. Influence of the rate of change of temperature on the crystallization and dissolution temperatures of the model oil composed with 20 wt% of paraffin wax measured in the (a) DSC tests and (b) DSC and rheometer experiments.
It is worth mentioning that the same tendency observed for a pure alkane by Taggart et al. [82] was also noted for waxy oils in the current work. One can then conclude that the most coherent way to determine the highest thermodynamic solid-liquid equilibrium temperature is by heating the material rather than cooling it, since the dissolution temperature is the best approximation for the saturation temperature when the heating rate is significantly low. As pointed out by some authors, viscometry is not the most adequate technique to determine accurately either the onset of the crystallization [9,47] or the dissolution temperature [9]. However, the main goal of the current discussion is to call attention for the existence of not only a supercooling on the crystallization of waxy oils but also of a superheating on the dissolution of crystals at high heating rates. It has to be pointed out that a supersaturation is always needed during the precipitation process and consequently, the temperature at which the first crystal precipitates out in the solution – the crystallization temperature – is not the highest thermodynamic solid-liquid equilibrium temperature.
4. Concluding remarks Wax precipitation is a huge problem in production and transportation of crude oils. Many efforts have been made to determine the highest solid-liquid thermodynamic equilibrium temperature – the saturation temperature – for the waxy crude oils. Keeping in mind the existence of a supersaturation, an adequate way to determine the saturation temperature for model waxy crude oils is proposed by using the results of rheometer and mDSC experiments. The main conclusions of the work can be summarized as:
i. The temperature at which the first wax crystal precipitates out in solution is called crystallization temperature, Tc, and because of the necessary supercooling, this temperature never coincides with the highest thermodynamic solidliquid equilibrium temperature; ii. Not only the solute concentration but also the cooling rate affects the metastable region width, in other words, the magnitude of the supercooling. The lower the solute concentration and the higher the cooling rate, the higher is the degree of supercooling; iii. Although the degree of supercooling reduces with the cooling rate, it does not vanish as the cooling rate tends to zero. On the other hand, the superheating during the dissolution of the wax crystals is assumed to disappear as the heating rate becomes zero; iv. The highest solid-liquid thermodynamic equilibrium temperature is considered to approach the dissolution temperature (temperature at which the last crystal disappears from the solution) when the material is heated at a very low heating rate. In other words, the dissolution temperature equals the saturation temperature when the heating rate tends to zero.
Acknowledgements The authors acknowledge the financial support of PETROBRAS S/A (TC 0050.0070318.11.9), CNPq – Brazil (Process: 487091/2013-2), CAPES – Brazil, FINEP, PRH-ANP/MCT (PRHANP/MCTI no. 10-C) and PFRH/PETROBRAS (6000.0067933.11.4
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and 6000.0082166.13.4). We also thank Talita Janaina Heller, an undergraduate student at the Federal University of TechnologyParaná, for her valuable support with the rheometric tests, and Lenise Couto Vieira from Petrobras that kindly performed the mDSC experiments. References [1] Venkatesan R, Östlund JA, Chawla H, Wattana P, Nydén M, Fogler HS. The effect of asphaltenes on the gelation of waxy oils. Energy Fuels 2003;17:1630–40. http://dx.doi.org/10.1021/ef034013k. [2] Sadeghazad A, Christiansen RL, Sobhi GA, Edalat M. The prediction of cloud point temperature: in wax deposition. SPE J 2000. http://dx.doi.org/10.2118/ 64519-MS. [3] Zílio EL, Pinto UB. Identification and distribution of the main groups of components present in brazilian crude oils. Bol Técnico Petrobras 2002;45:21–5. [4] Maqbool T, Srikiratiwong P, Fogler HS. Effect of temperature on the precipitation kinetics of asphaltenes. Energy Fuels 2011;25:694–700. http:// dx.doi.org/10.1021/ef101112r. [5] Oliveira MCK, Teixeira A, Vieira LC, Carvalho RM, Carvalho ABM, Couto BC. Flow assurance study for waxy crude oils. Energy Fuels 2012;26:2688–95. http://dx.doi.org/10.1021/ef201407j. [6] Ilyin S, Arinina M, Polyakova M, Bondarenko G, Konstantinov I, Kulichikhin V, et al. Asphaltenes in heavy crude oil: designation, precipitation, solutions, and effects on viscosity. J Pet Sci Eng 2016;147:211–7. http://dx.doi.org/10.1016/j. petrol.2016.06.020. [7] Venkatesan R, Nagarajan NR, Paso K, Yi YB, Sastry AM, Fogler HS. The strength of paraffin gels formed under static and flow conditions. Chem Eng Sci 2005;60:3587–98. http://dx.doi.org/10.1016/j.ces.2005.02.045. [8] Pedersen KS, Rønningsen HP. Effect of precipitated wax on viscosity – a model for predicting non-Newtonian viscosity of crude oils. Energy Fuels 2000;14:43–51. http://dx.doi.org/10.1021/ef9901185. [9] Marchesini FH, Alicke AA, de Souza Mendes PR, Ziglio CM. Rheological characterization of waxy crude oils: sample preparation. Energy Fuels 2012;26:2566–77. http://dx.doi.org/10.1021/ef201335c. [10] Andrade DEV, Cruz ACB, Franco AT, Negrão COR. Influence of the initial cooling temperature on the gelation and yield stress of waxy crude oils. Rheol Acta 2015;54:149–57. http://dx.doi.org/10.1007/s00397-014-0812-0. [11] Ding J, Zhang J, Li H, Zhang F, Yang X. Flow behavior of Daqing waxy crude oil under simulated pipelining conditions. Energy Fuels 2006;20:2531–6. http:// dx.doi.org/10.1021/ef060153t. [12] Tarcha BA, Forte BPP, Soares EJ, Thompson RL. Critical quantities on the yielding process of waxy crude oils. Rheol Acta 2015;54:479–99. http://dx.doi. org/10.1007/s00397-015-0835-1. [13] Paso K, Kompalla T, Oschmann HJ, Sjöblom J. Rheological degradation of model wax-oil gels. J Dispers Sci Technol 2009;30:472–80. http://dx.doi.org/10.1080/ 01932690802548924. [14] Guozhong Z, Gang L. Study on the wax deposition of waxy crude in pipelines and its application. J Pet Sci Eng 2010;70:1–9. http://dx.doi.org/10.1016/j. petrol.2008.11.003. [15] Aiyejina A, Chakrabarti DP, Pilgrim A, Sastry MKS. Wax formation in oil pipelines: a critical review. Int J Multiph Flow 2011;37:671–94. http://dx.doi. org/10.1016/j.ijmultiphaseflow.2011.02.007. [16] Wardhaugh LT, Boger DV. Measurement of the unique flow properties of waxy crude oils. Chem Eng Res Des 1987;65:74–83. [17] Azevedo LFA, Teixeira AM. A critical review of the modeling of wax deposition mechanisms. Pet Sci Technol 2003;21:393–408. http://dx.doi.org/10.1081/ LFT-120018528. [18] Ribeiro FS, Souza Mendes PR, Braga SL. Obstruction of pipelines due to paraffin deposition during the flow of crude oils. Int J Heat Mass Transf 1997;40:4319–28. http://dx.doi.org/10.1016/S0017-9310(97)00082-3. [19] Jemmett MR, Magda JJ, Deo MD. Heterogeneous organic gels: rheology and restart. Energy Fuels 2013;27:1762–71. http://dx.doi.org/10.1021/ef3014629. [20] Mortazavi-Manesh S, Shaw JM. Thixotropic rheological behavior of maya crude oil. Energy Fuels 2014;28:972–9. http://dx.doi.org/10.1021/ef4022637. [21] Oliveira GM, Negrão COR. The effect of compressibility on flow start-up of waxy crude oils. J Nonnewton Fluid Mech 2015;220:137–47. http://dx.doi.org/ 10.1016/j.jnnfm.2014.12.010. [22] Frigaard IA, Paso KG, de Souza Mendes PR. Bingham’s model in the oil and gas industry. Rheol Acta 2017:259–82. http://dx.doi.org/10.1007/s00397-0170999-y. [23] Tiwary D, Mehrotra AK. Phase transformation and rheological behaviour of highly paraffinic ‘‘ waxy ” mixtures. Can J Chem Eng 2004;82:162–74. http:// dx.doi.org/10.1002/cjce.5450820121. [24] Pedersen KS, Thomassen P, Fredenslund A. Thermodynamics of petroleum mixtures containing heavy hydrocarbons. 1. Phase envelope calculations by use of the Soave-Redlich-Kwong equation of state. Ind Eng Chem Process 1984;23:163–70. http://dx.doi.org/10.1021/i200024a027. [25] Won KW. Thermodynamics for solid solution-liquid-vapor equilibria: wax phase formation. Fluid Phase Equilib 1986;30:265–79. [26] Won KW. Thermodynamic calculation of cloud point temperatures and wax phase compositions of refined hydrocarbon mixtures. Fluid Phase Equilib 1989;53:377–96.
[27] Pedersen KS, Skovborg P, Rønningsen HP. Wax precipitation from North Sea Crude Oils. 4. Thermodynamic modeling. Energy Fuels 1991:924–32. http://dx. doi.org/10.1021/ef00030a022. [28] Erickson DD, Niesen VG, Brown TS. Thermodynamic measurement and prediction of paraffin precipitation in crude oil. Proc – SPE Annu Tech Conf Exhib 1993;Pi:933–48. doi:http://dx.doi.org/10.2523/26548-MS. [29] Coutinho JAP, Knudsen K, Andersen SI, Stenby EH. A local composition model for paraffinic solid solutions. Chem Eng Sci 1996;51:3273–82. http://dx.doi. org/10.1016/0009-2509(95)00397-5. [30] Zhou X, Thomas FB, Moore RG. Modelling of solid precipitation from reservoir fluid. J Can Pet Technol 1996;35:35–45. http://dx.doi.org/10.2118/96-10-03. [31] Coutinho JAP, Ruffier-Méray V. Experimental measurements and thermodynamic modeling of paraffinic wax formation in undercooled solutions. IndEngChem Res 1997;36:4977–83. http://dx.doi.org/10.1021/ ie960817u. [32] Coutinho JAP. Predictive UNIQUAC: a new model for the description of multiphase solid-liquid equilibria in complex hydrocarbon mixtures. Ind Eng Chem Res 1998;37:4870–5. http://dx.doi.org/10.1021/ie980340h. [33] Chen W, Zhao Z. Thermodynamic modeling of wax precipitation in crude oils. Chin J Chem Eng 2006;14:685–9. http://dx.doi.org/10.1016/S1004-9541(06) 60135-3. [34] Ghanaei E, Esmaeilzadeh F, Fathikalajahi J. Wax formation from paraffinic mixtures: a simplified thermodynamic model based on sensitivity analysis together with a new modified predictive UNIQUAC. Fuel 2012;99:235–44. http://dx.doi.org/10.1016/j.fuel.2012.03.053. [35] Zhao Y, Paso K, Sjöblom J. Thermal behavior and solid fraction dependent gel strength model of waxy oils. J Therm Anal Calorim 2014;117:403–11. http:// dx.doi.org/10.1007/s10973-014-3660-3. [36] Hansen JH, Fredenslund A, Pedersen KS, Røningsen HP. A thermodynamic model for predicting wax formation in crude oils. AIChE J 1988;34:1937–42. http://dx.doi.org/10.1002/aic.690341202. [37] Ji H-Y, Tohidi B, Danesh A, Todd AC. Wax phase equilibria: developing a thermodynamic model using a systematic approach. Fluid Phase Equilib 2004;216:201–17. http://dx.doi.org/10.1016/j.fluid.2003.05.011. [38] Yang J, Wang W, Huang H, Shi G, Shi B, Cheng B, et al. Prediction of solid-liquid equilibrium in paraffinic systems with new solid solution model. Fluid Phase Equilib 2016;427:504–12. http://dx.doi.org/10.1016/j.fluid.2016.07.030. [39] Bagherinia R, Assareh M, Feyzi F. An improved thermodynamic model for Wax precipitation using a UNIQUAC + PC-SAFT approach. Fluid Phase Equilib 2016;425:21–30. http://dx.doi.org/10.1016/j.fluid.2016.05.008. [40] Aftab S, Javanmardi J, Nasrifar K. Experimental investigation and thermodynamic modeling of wax disappearance temperature for n-undecane +n-hexadecane+n-octadecane and n-tetradecane+n-hexadecane+noctadecane ternary systems. Fluid Phase Equilib 2015;403:70–7. http://dx. doi.org/10.1016/j.fluid.2015.06.004. [41] Coutinho JAP, Stenby EH. Predictive local composition models for solid/liquid equilibrium in n -alkane systems: Wilson equation for multicomponent systems. Ind Eng Chem Res 1996;35:918–25. http://dx.doi.org/10.1021/ ie950447u. [42] Ashbaugh HS, Radulescu A, Prud RK, Schwahn D, Richter D, Fetters LJ. Interaction of paraffin wax gels with random crystalline/amorphous hydrocarbon copolymers. Macromolecules 2002:7044–53. http://dx.doi.org/ 10.1021/ma0204047. [43] Bhat NV, Mehrotra AK. Measurement and prediction of the phase behavior of wax – solvent mixtures: significance of the wax dis appearance temperature. Ind Eng Chem Res 2004;43:3451–61. http://dx.doi.org/10.1021/ie0400144. [44] ASTM. D2500-11 Standard Test Method for Cloud Point of Petroleum Products, American Society for Testing and Materials. 2011. doi:http://dx.doi.org/10. 1520/D2500-11.2. [45] Monger-McClure TG, Tackett JE, Merrill LS. Comparisons of cloud point measurement and Paraffin prediction methods. SPE Prod Facil 1999;14:5–8. http://dx.doi.org/10.2118/54519-PA. [46] Ijeomah CE, Dandekar AY, Chukwu GA, Khataniar S, Patil SL, Baldwin AL. Measurement of wax appearance temperature under simulated pipeline (dynamic) conditions. Energy Fuels 2008;22:2437–42. http://dx.doi.org/ 10.1021/ef7007453. [47] Rønningsen HP, Bjorndal B, Hansen AB, Pedersen WB. Wax precipitation from North Sea crude oils. 1. Crystallization and dissolution temperatures, and Newtonian and non-Newtonian flow properties. Energy Fuels 1991;5:895–908. http://dx.doi.org/10.1021/ef00030a019. [48] Kok MV, Létoffé JM, Claudy P, Martin D, Garcin M, Vollet JL. Comparison of wax appearance temperatures of crude oils by differential scanning calorimetry, thermomicroscopy and viscometry. Fuel 1996;75:787–90. http://dx.doi.org/ 10.1016/0016-2361(96)00046-4. [49] Singh P, Fogler HS, Nagarajan N. Prediction of the wax content of the incipient wax-oil gel in a pipeline: an application of the controlled-stress rheometer. J Rheol 1999;43:1437–59. http://dx.doi.org/10.1122/1.551054. [50] Wardhaugh LT, Boger DV. Flow characteristics of waxy crude oils – application to pipeline design. AIChE J 1991;37:871–85. http://dx.doi.org/10.1002/ aic.690370610. [51] Magda JJ, El-Gendy H, Oh K, Deo MD, Montesi A, Venkatesan R. Timedependent rheology of a model waxy crude oil with relevance to gelled pipeline restart. Energy Fuels 2009;23:1311–5. http://dx.doi.org/10.1021/ ef800628g. [52] Kruka VR, Cadena ER, Long TE. Cloud-point determination for crude oils. J Pet Technol 1995;47:681–7. http://dx.doi.org/10.2118/31032-PA.
D.E.V. Andrade et al. / Fuel 206 (2017) 516–523 [53] Elsharkawy AM, Al-Sahhaf TA, Fahim MA. Wax deposition from Middle East crudes. Fuel 2000;79:1047–55. http://dx.doi.org/10.1016/S0016-2361(99) 00235-5. [54] Jiang Z, Hutchinson JM, Imrie CT. Measurement of the wax appearance temperatures of crude oils by temperature modulated differential scanning calorimetry. Fuel 2001;80:367–71. http://dx.doi.org/10.1016/S0016-2361(00) 00092-2. [55] Claudy P, Létoffé JM, Neff B, Damin B. Diesel fuels: determination of onset crystallization temperature, pour point and filter plugging point by differential scanning calorimetry. Correlation with standard test methods. Fuel 1986;65:861–4. http://dx.doi.org/10.1016/0016-2361(86)90082-7. [56] Hansen AB, Larsen E, Pedersen WB, Nielsen AB, Rønningsen HP. Wax precipitation from North Sea crude oils. 3. Precipitation and dissolution of wax studied by differential scanning calorimetry. Energy Fuels 1991;5:914–23. http://dx.doi.org/10.1021/ef00030a021. [57] He C, Ding Y, Chen J, Wang F, Gao C, Zhang S, et al. Influence of the nano-hybrid pour point depressant on flow properties of waxy crude oil. Fuel 2016;167:40–8. http://dx.doi.org/10.1016/j.fuel.2015.11.031. [58] Yao B, Li C, Yang F, Zhang Y, Xiao Z, Sun G. Structural properties of gelled Changqing waxy crude oil benefitted with nanocomposite pour point depressant. Fuel 2016;184:544–54. http://dx.doi.org/10.1016/ j.fuel.2016.07.056. [59] Mendes R, Vinay G, Ovarlez G, Coussot P. Modeling the rheological behavior of waxy crude oils as a function of flow and temperature history. J Rheol 2015;59:703–32. http://dx.doi.org/10.1122/1.4916531. [60] Gimzewski E, Audley G. Monitoring wax crystallisation in diesel using differential scanning calorimetry (DSC) and microcalorimetry. Thermochim Acta 1993;214:149–55. http://dx.doi.org/10.1016/0040-6031(93)80050-K. [61] Meray VR, Volle J-L, Schranz CJP, Le Marechal P, Behar E. Influence of light ends on the onset crystallization temperature of waxy crudes within the frame of multiphase transport. SPE Annu Tech Conf Exhib 1993:369–78. http://dx.doi. org/10.2118/26549-MS. [62] Paso K, Kallevik H, Sjöblom J. Measurement of wax appearance temperature using near-infrared (NIR) scattering. Energy Fuels 2009;23:4988–94. http://dx. doi.org/10.1021/ef900173b. [63] Paso K, Senra M, Yi Y, Sastry AM, Fogler HS. Paraffin polydispersity facilitates mechanical gelation. Ind Eng Chem Res 2005;44:7242–54. http://dx.doi.org/ 10.1021/ie050325u. [64] Hammami A, Raines MA. Paraffin deposition from crude oils: comparison of laboratory results with field data. SPE J 1999;4:9–18. http://dx.doi.org/ 10.2118/54021-PA. [65] Mullin J. Crystallization. 4th ed. London: Butterworth-Heinemann; 2001. [66] Ny´vlt J, Hostomsky J, Giulietti M. Crystallization (in portuguese). São Carlos – SP/BR: EdUFSCar/IPT; 2001. [67] Stefanescu DM. ASM metals Handbook – Casting. 9th ed, 9th ed., 15. USA: ASM International; 1988. [68] Vehkamäki H. Classical nucleation theory in multicomponent systems. Germany: Springer - Verlag Berlim Heidelberg; 2006. http://dx.doi. org/10.1007/b138396. [69] Dimitriou CJ. The rheological complexity of waxy crude oils: Yielding, thixotropy and shear heterogeneities [Ph.D. thesis]. USA: Massachusetts Institute of Technology; 2013.
523
[70] Dimitriou CJ, McKinley GH, Venkatesan R. Rheo-PIV analysis of the yielding and flow of model waxy crude oils. Energy Fuels 2011;25:3040–52. http://dx. doi.org/10.1021/ef2002348. [71] Mendes R, Vinay G, Ovarlez G, Coussot P. Reversible and irreversible destructuring flow in waxy oils: an MRI study. J Nonnewton Fluid Mech 2015;220:77–86. http://dx.doi.org/10.1016/j.jnnfm.2014.09.011. [72] Geri M, Venkatesan R, Sambath K, McKinley GH. Thermokinematic memory and the thixotropic elasto-viscoplasticity of waxy crude oils. J Rheol (N Y N Y) 2017;61:427–54. http://dx.doi.org/10.1122/1.4978259. [73] Dimitriou CJ, McKinley GH. A comprehensive constitutive law for waxy crude oil: a thixotropic yield stress fluid. Soft Matter 2014;10:6619–44. http://dx. doi.org/10.1039/c4sm00578c. [74] Bird RB, Armstrong RC, Hassager O. Dynamics of polymeric liquids. 6th ed, 6th ed., 1. New York, USA: John Wiley and Sons; 1987. [75] Paso K, Silset A, Soørland G, Gonçalves MD AL, Sjöblom J. Characterization of the formation, flowability, and resolution of brazilian crude oil emulsions. Energy Fuels 2009;23:471–80. http://dx.doi.org/10.1021/ef800585s. [76] Merino-Garcia D, Margarone M, Correra S. Kinetics of waxy gel formation from batch experiments. Energy Fuels 2007;42:1287–95. http://dx.doi.org/10.1021/ ef060385s. [77] Guo X, Pethica BA, Huang JS, Adamson DH, Prud’homme RK. Effect of cooling rate on crystallization of model waxy oils with microcrystalline poly(ethylene butene). Energy Fuels 2006;20:250–6. http://dx.doi.org/10.1021/ef050163e. [78] Hammami A, Mehrotra AK. Thermal behaviour of polymorphic n-alkanes: effect of cooling rate on the major transition temperatures. Fuel 1995;74:96–101. http://dx.doi.org/10.1016/0016-2361(94)P4338-3. [79] Kasumu AS, Arumugam S, Mehrotra AK. Effect of cooling rate on the wax precipitation temperature of ‘‘waxy” mixtures. Fuel 2013;103:1144–7. http:// dx.doi.org/10.1016/j.fuel.2012.09.036. [80] Carey VP. Liquid-vapor phase-change phenomena. 2nd ed. New York, USA: Taylor & Francis Group; 2008. [81] Sloan ED, Koh CA. Clathrate hydrate of natural gases. 3rd ed. FL, USA: Taylor & Francis Group; 2008. [82] Taggart AM, Voogt F, Clydesdale G, Roberts KJ. An Examination of the nucleation kinetics of n-alkanes in the homologous series C13H28 to C32H66, and their relationship to structural type, associated with crystallization from stagnant melts. Langmuir 1996;12:5722–8. http://dx. doi.org/10.1021/la9600816. [83] Bott TR. Aspects of crystallization fouling. Exp Therm Fluid Sci 1997;14:356–60. http://dx.doi.org/10.1016/S0894-1777(96)00137-9. [84] Jones AG. Crystallization process systems. London, UK.: ButterworthHeinemann; 2002. [85] Hammami A, Mehrotra AK. Liquid-solid-solid thermal behaviour of nC44H90 +nC50H102 and nC25H52+nC28H58 paraffinic binary mixtures. Fluid Phase Equilib 1995;111:253–72. http://dx.doi.org/10.1016/0378-3812(95)02777-C. [86] Metivaud V, Rajabalee F, Oonk HAJ, Mondieig D, Haget Y. Complete determination of the solid (RI)-liquid equilibria of four consecutive n-alkane ternary systems in the range C14H30-C21H44 using only binary data. Can J Chem Can Chim 1999;77:332–9. http://dx.doi.org/10.1139/cjc-77-3-332.