Wax Deposition in the Presence of Suspended Crystals - Energy

Nov 30, 2015 - The interior part of the tank, where the solution was kept, was ..... are seen to decelerate, stop, and incorporate into the existing d...
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Wax Deposition in the Presence of Suspended Crystals José P. Cabanillas, Andrea T. Leiroz,† and Luis F. A. Azevedo* Department of Mechanical Engineering, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Rio de Janeiro, Rio de Janeiro 22451-900, Brazil S Supporting Information *

ABSTRACT: Wax deposition in pipelines is one of the most relevant flow assurance problems faced by the petroleum industry. Molecular diffusion of dissolved paraffin has been considered the dominant deposition mechanism in simulation models available in the literature. In case the pipeline operational conditions are such that the fluid temperature is below the wax appearance temperature (WAT), wax crystals could be present in the bulk of the flowing solution and particle deposition mechanism may play a relevant role. In the present research, bench-scale, well-controlled deposition experiments were conducted for laminar channel flow of a solution with an inlet temperature below the WAT, so that wax crystals were available for deposition. In the experiments, visualizations of the deposition process were sought for three distinct heat flux conditions at the channel boundary: negative, zero, and positive heat flux. Detailed information on the temporal and spatial distributions of the wax deposited along the channel walls was obtained for three values of the laminar channel Reynolds number. It was verified that a channel wall cooler than the flowing fluid (the negative heat flux condition) is a necessary condition to produce deposition. For all of the experimental conditions tested, no deposition was verified under zero or positive heat flux boundary conditions. In all cases studied, the deposits measured were significantly thicker than those obtained for similar flow conditions and fluid-to-wall temperature differences but for inlet fluid temperatures above the WAT. The visualization experiments revealed that wax crystals and crystal agglomerates presented trajectories nearly parallel to the channel wall. These crystals and agglomerates were seen to be decelerated and stopped, being incorporated on a thin wax deposit formed at the initial cooling stages.

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INTRODUCTION Wax deposition in pipelines has been studied continuously for decades because it is one of the most relevant flow assurance problems faced by the petroleum industry. In subsea petroleum production, the crude oil flows from the reservoir at a relatively high temperature into the production lines. Oil is carried in these pipelines to the platforms and to shore. The temperature of the ocean at large depths can be as low as 5 °C. The solubility of wax in the oil decreases with a decreasing temperature. The oil flowing in the pipelines loses heat to the external ambient water and, if the crude temperature falls below a critical value, wax precipitates from the oil and may deposit on the inner walls of the pipe, causing an increased pressure drop or even the blockage of the pipeline. The ability to predict whether wax deposition will occur in a specific installation is relevant information for pipeline designers and operators. For instance, the indication of a probability of occurrence of deposition will influence the type and amount of thermal insulation to be specified for the pipeline, with direct impact on the cost of the installation. Also, information on the temporal and spatial distributions of the deposit along the line as well as its composition would be useful to guide the strategy of pipeline maintenance, such as selecting pig type and frequency of passage. Wax deposition simulation models are useful tools to aid pipeline design and operation. Because of the complexity of the phenomena controlling wax deposition, the existing simulation models make use of empirical constants and correction factors that tune the model to a particular set of field data. If, on one hand, this approach produces reasonable results that can be used in studies of the particular field from which the data were © 2015 American Chemical Society

obtained, then, on the other hand, it limits the applicability of the model to other fields with different characteristics, because the fundamental physics behind the deposition phenomena is not properly modeled. Deposition models have also been developed on the basis of fundamental principles, taking into consideration several aspects of the phenomena, such as wax precipitation, crystallization kinetics, convective and diffusive heat and mass transport, and wax removal processes. The prediction of wax precipitation is the first building block of a fundamental wax deposition model. It can be incorporated into the model via experimental solubility curves or through elaborated thermodynamic models. Several thermodynamic models with different degrees of complexity have been developed to predict wax precipitation in petroleum mixtures. Examples of such models are the ideal solid solution model1 and the multisolid model.2,3 Wax precipitation in the flowing oil is a necessary but not sufficient condition for deposition. Transport of paraffin in the liquid or solid phases will determine whether the precipitated paraffin will be driven toward the pipe wall and form solids at the pipe wall or solids that are carried along with the flow without contributing to the formation of the deposit. Several mechanisms have been described in the literature as being potentially responsible for the transport of precipitated wax. A definitive understanding of the relative importance of these mechanisms for different pipeline operating conditions has not Received: May 14, 2015 Revised: November 26, 2015 Published: November 30, 2015 1

DOI: 10.1021/acs.energyfuels.5b02344 Energy Fuels 2016, 30, 1−11

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mechanisms could be present. For higher shear rates, the deposit grew rapidly at first, approximating the expected diffusion rate, but then the rate began to decrease. At these flow rates, even in laminar conditions, waxes were sloughed when the wall shear stress exceeded the strength of the wax deposit. Brown et al.10 conducted a deposition study based on the mass-transfer equation proposed by Burger et al.7 to model molecular diffusion and shear dispersion mechanisms. To test the shear dispersion contribution, the flow loop was operated at constant inlet and wall temperatures, for different shear rates. As per the equation by Burger, deposition should linearly increase with the shear rate, which was not verified. Also, experiments were conducted for the same bulk and wall temperatures, presenting no deposition. On the basis of these findings, the authors concluded that shear dispersion of wax crystals was not contributing to the deposit formation. Hamouda and Davidsen11 conducted experiments in a pipe section divided into three sectors. In the first sector, the pipe wall was cooled, while in the second sector, the wall was insulated. In the third sector, the wall was again cooled. They observed deposition in the first sector, almost no deposition along the insulated pipe sector, and deposition again in the cooled third sector. They concluded that deposition mechanisms based on lateral motion of the crystals, such as shear dispersion or Brownian motion, are not relevant. Merino-Garcia et al.12 have analyzed the possible contributions of other transport mechanisms, such as Soret diffusion, thermophoresis, and turbophoresis. The authors present arguments that indicate that the contributions of these three mechanisms are negligible. However, Hoteit et al.13 present results (Figure 13 of their work) where the contribution of Soret diffusion to the deposit thickness is of the same order as that due to molecular diffusion. As seen by this example, the relative importance of wax deposition mechanisms is still an open question in the literature. As the crude oil flows in long subsea pipelines, large portions of the lines may exhibit oil temperatures well below the wax appearance temperature as a result of the continuous heat losses to the cold external environment. Also, gas in a twophase flow may expand as it flows up along in a riser and lead to cold regions in the bulk of the flowing fluid. In these cold regions, it is probable that the necessary degree of subcooling for wax crystal formation is attained and that a large number of wax crystals will be formed in the bulk of the flowing oil. Todi14 developed a numerical model based on wax deposition measurements performed in laminar flow conditions with the oil mixture injection temperature below the WAT, which produced suspended crystals in the solution. Particle image velocimetry and laser scattering techniques were used to obtain information on the flow velocity profiles and crystal distribution profiles, respectively. The experiments revealed that the concentration of wax crystals at the channel crosssection is determined by two competing mechanisms. While shear dispersion tends to concentrate the particles at preferred radial positions, Brownian diffusion works toward dispersing the particles evenly in the cross-section. The author concluded that, because shear dispersion acts to move the particles away from the wall, Brownian diffusion is the only possible mechanism responsible for particle deposition. Contrary to results that will be presented in the present paper, the author verified deposition for all three possible thermal boundary conditions, namely, cooling, heating, and zero heat flux, as long as the wall temperature was below the WAT.

yet been reached, being the subject of current research (e.g., the work of Aiyejina et al.4). The first systematic study on wax deposition reported in the literature is the work of Jessen and Howell,5 where deposition on different metallic and plastic pipe materials was investigated for laminar and turbulent flow conditions. This pioneer work already mentioned several key issues regarding wax deposition in pipes, such as possible deposition mechanisms, hardening of the deposit with increased shear and cooling rates, shear removal of deposited wax, and affinity of the deposit to the pipe surface material. The study proposed that two competing mechanisms were responsible for wax deposition at the pipe wall. One mechanism was related to the diffusive transport of dissolved wax, while the other was based on the deposition of solid wax crystals in suspension. The authors state that the diffusive mechanism is dominant, arguing that experiments with the waxy mixture inlet temperature above the wax appearance temperature (WAT) yielded much thicker deposits than those with the inlet fluid temperature well below the WAT and, therefore, containing wax crystals in suspension. This argument failed to consider the direction of the heat flux from the working fluid to the outside fluid environment. As will be mentioned in the discussion of the results of the present study, the heating or cooling of the solution flowing in the pipe is crucial to the deposition process. From the description of the experiments conducted by Jessen and Howell,5 it can be inferred that no proper control of the sign of the radial heat flux was maintained and that the experiments displaying suspended crystals were conducted with the working fluid at a lower temperature than the outside environment. Hunt6 conducted adhesion tests of wax deposits to different types of surfaces. In his work, no deposition was verified when the bulk fluid temperature was the same as the wall temperature, which led the author to conclude that molecular diffusion of liquid wax is the controlling deposition mechanism. Burger et al.7 discussed the relative importance of the deposition mechanisms, considering gravity settling of wax crystals, molecular diffusion of liquid wax, Brownian diffusion of wax crystals, and shear dispersion of crystals. In their analysis, the contributions of gravity settling, Brownian diffusion, and shear dispersion were considered negligible in the presence of molecular diffusion. Since then, the vast majority of the models developed and available in the literature incorporate molecular diffusion as the only deposition mechanism. Predictions of molecular-diffusion-based models were adjusted to available laboratory and field data by the tuning of physical properties. Azevedo and Teixeira8 have pointed out that this procedure is probably responsible for the dominance of the molecular diffusion mechanism over other transport mechanisms in the available deposition models. In their work, Azevedo and Teixeira8 argued that, on the basis of the available data at that time, there was no firm basis to rule out the contribution of particle transport mechanisms, such as Brownian diffusion, to the formation of the deposited wax layer. Weingarten and Euchner9 have conducted experiments in a test loop under controlled conditions. The tests measured the total deposition by the pressure differential method and compared it to the expected contribution of molecular diffusion obtained from tests with a cell with stagnant fluid. By this procedure, the authors intended to separate the contributions from molecular diffusion and particle transport. For low shear rates, the deposition rate was greater than that predicted by molecular diffusion only, indicating that other deposition 2

DOI: 10.1021/acs.energyfuels.5b02344 Energy Fuels 2016, 30, 1−11

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Figure 1. (a) Schematic view of the test section for deposition studies. (b) Pictorial view and details of the transparent rectangular channel test section.

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Some attempts have been reported in the literature to take advantage of the transport of suspended wax crystals, avoiding the unwanted deposition on the pipe walls. This technology, called cold flow, was reviewed by Merino-Garcia and Correra.15 A relevant question to be answered is whether these crystals will be carried along by the flow or will contribute to the wax deposits at the wall. Huang et al.16 investigated the effect of bulk precipitation of wax crystals on deposition rates, establishing upper and lower bounds for the phenomena. In their analysis, suspended crystals are not allowed to deposit and are carried by the flow. Recently, Haj-Shafiei et al.17 developed a model based on steady-state heat transfer to predict deposition for conditions where the oil is above and below the WAT, termed the hot and cold flow regimes, respectively. Again, in their model, suspended crystals in the cold flow regime were not allowed to contribute to the deposit. This restriction was based on information gathered from the literature. The issue of wax deposition in the form of crystals has received relatively little attention in the literature when compared to the deposition processes involving the transport of liquid wax in solution. The present paper presents an experimental, laboratory-scale study of wax deposition in a rectangular channel in laminar flow. The experiments were designed to be operated at thermodynamic conditions, in which the working fluid enters the test section at a temperature below the WAT. Under these conditions, suspended wax crystals are present in the flow and available for deposition. The focus of the work is on the visualization of the wax deposition process and the measurement of the spatial and temporal evolution of the wax deposits under the presence of suspended crystals. The tests were conducted in a laboratory-scale test section with simple geometry with well-defined boundary and initial conditions, employing working fluids with known thermophysical properties. Special attention was directed to the effect of the thermal boundary condition at the wall and its effect on crystal deposition. Tests were conducted for cases where the wall was hotter, colder, or at the same temperature as that of the flowing fluid. The experiments and experimental procedures employed in the study will be described in the following section.

EXPERIMENTAL SECTION

The test section used in the wax deposition experiments in laminar channel flow will now be described. The test section was designed with the objective of providing visual access to the interior of the channel, yielding instantaneous and spatial information on the transient wax deposition process. Also, the design aimed at providing well-defined boundary and initial conditions to facilitate future comparisons to simulations. Other flow loop wax deposition experiments are reported in the literature, providing valuable global information on the deposited wax obtained via weighing the integrated wax deposit over a certain test period.18 Pressure drop measurements were also employed to yield transient information on wax deposition over a specified pipe length.19 It is believed that the test section employed in the present studies provides original, visual, and quantitative temporal and spatial distributions of wax deposition that can contribute to the information available from the loop experiments described in the literature. Panels a and b of Figure 1 show schematic views of the test section constructed. The oil and wax solution employed in the experiments was kept in an 8-liter stainless steel tank equipped with an agitator and connected to a temperature-controlling bath. The interior part of the tank, where the solution was kept, was cylindrical to allow for the motion of the agitator impeller blade. The blade was made of polypropylene and was designed in a rectangular shape with a height that matched the level of the operating solution and width slightly larger than the tank internal diameter. With this custom design, the blade gently scraped the internal surface of the cylinder, removing possible wax deposits formed during tests conducted at temperatures below the wax formation point. The internal cylindrical tank just described was housed in a larger rectangular tank. The space between the cylindrical and rectangular tanks was filled with circulating water from the temperaturecontrolling bath. With this storage system, the solution could be maintained at temperatures below the WAT. It should be noted that the literature reports that a better estimate for the solid−liquid equilibrium temperature is obtained by the wax disappearance temperature (WDT) rather than the WAT.20 This is attributed to the fact that the degree of subcooling necessary to produce the first wax crystal under cooling is larger than the degree of superheating necessary to eliminate the last wax crystal under heating. In the present work, however, the WAT was employed to characterize the crystal formation temperature. As will be seen, the levels of temperature employed in the experiments were well below both the WAT and the WDT, which made either parameter suitable to characterize the experimental phenomena observed. Both the WAT and the WDT are reported in the work for completeness. The solution was pumped through the test section and back to the tank, employing a progressive cavity pump that was precalibrated to yield the volume flow rate as a function of the pump motor revolutions set at a frequency controller. The frequency controller was capable of 3

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Figure 2. (a) Schematic view of the jet heating system employed. (b) Detail of the jet heating system. controlling the motor frequency to within ±0.1 Hz, which translated through the volume flow rate calibration procedure into an uncertainty level of ±0.5% in the solution volume flow rate. The average velocity of the solution in the channel was obtained by dividing the volumetric flow rate by the cross-sectional area of the channel. The 20 mm diameter rubber hoses that ducted the solution from the tank to the test section and back to the tank were thermally insulated. The total length of these hoses was 2.5 m to minimize heat transfer with the ambient. Besides, heat tracer tapes where wrapped around the hoses and connected to voltage regulators. With this system, the temperature of the hoses was maintained slightly above the flowing solution temperature, a condition expected to avoid wax deposition. In fact, the study of wax deposition under these heat flux conditions was one of the main focuses of the research, and at the time of the construction of the test section, we had no certainty that deposition would not occur under these heating conditions. In view of that, the pumping and return lines received pieces of transparent pipes that allowed for the verification of possible wax deposition in the inner surfaces of the lines. These transparent pipe pieces were 20 mm long and were kept under the thermal insulation layer that was temporarily removed to allow for the visual inspection. No wax deposition was verified in these visualization pipe pieces during the experiments conducted. The progressive cavity pump body was also thermally insulated and equipped with heat tracer tapes. The main part of the test section was a rectangular channel with internal dimensions of 3 × 10 × 300 mm (width × height × length). Visual access to the interior of the channel was provided by the vertical walls of the channel, made of 3 mm thick glass plates. The upper and lower walls were made of copper and were part of T-shaped hollow copper blocks to control the temperature boundary conditions. Water from two temperature controlling baths was pumped through each of the copper blocks. A total of 10, precalibrated Chromel−Constantan thermocouples, made from 0.125 mm diamter wires, were installed in each of the copper walls to monitor their temperature. After the calibration procedure, the estimated uncertainty level on the temperature measurements was ±0.2 °C. Plexiglas channels with the same internal dimensions as the copper test section were mounted upand downstream of the test section. Care was taken during the machining and assembling of these pieces to ensure that no steps were present in the transition from the Plexiglas to the copper walls, which would, otherwise, produce flow disturbances that could influence the wax deposition process on the test section copper walls. The upstream piece was 100 mm long, which provided an adiabatic entry length of approximately 20 channel hydraulic diameters. The downstream Plexiglas piece was 50 mm long. These transparent inlet and exit Plexiglas pieces also allowed for the visual observation of the solution with suspended wax crystals entering and leaving the copper test section. To facilitate the viewing of the channel interior part, Figure 1b only shows the upstream Plexiglas piece, with the downstream piece removed. The temperature of the solution entering and leaving the test section was monitored by two additional thermocouples installed

through the brass pieces that connected the rubber hoses to the test section body. These thermocouples were mounted inside stainlesssteel needle tubes having one end closed. The needles with the thermocouple junctions were positioned radially at the centerline of the entrance and exit sections. Because the experiments were to be conducted at relatively low temperature levels, deposition of wax was expected to happen at the inner surface of the glass lateral walls, thereby obstructing the visual access to the channel. To avoid this effect, a set of six air jet nozzles with controlled temperature and flow rate was positioned at each side of the glass walls, producing a controlled heating of the glass surface and avoiding the deposition. Ambient air was driven by a blower through a box containing electrical resistances and then through a manifold connected to 12 jet exits. Each lateral glass wall received the flow from six, 6 mm diameter jets spaced of 50 mm from each other and positioned at a distance of 50 mm from the glass surface. The flow rate to the manifold and electrical power to the heaters could be adjusted to control the heating of the glass surfaces. A total of 15 finegauge thermocouples were installed on the external surface of one of the glass walls, with the surface exposed to the air jets. These thermocouples were used to monitor the temperature variation of the glass surface. Figure 2 shows schematic views of the air jet setup. All thermocouple readings were performed by an Agilent 34970A data acquisition unit. The process of wax deposition on the channel walls was registered by employing a 640 × 480 pixel digital camera operating at a frame rate of 30 Hz. Lenses with magnifications of 6×, 11×, and 45× were employed to image the wax deposits. The camera was mounted orthogonally to the channel glass wall and could be moved along the length of the channel. To allow for this axial motion, the camera was mounted on a x−y coordinate table, having its main axis aligned with the channel axis. A precision screw connected to the transverse axis of the coordinate table allowed for the motion of the camera in the crossstream direction of the channel with a resolution of 1/100 mm. This fine motion was necessary to adjust the image focus. Back illumination through the opposite glass wall of the channel was employed. The main objective of the present study was to investigate the wax deposition process for a condition where the inlet solution temperature was below the WAT. This condition required a careful preparation procedure, as will be outlined. A data run was initiated by circulating the oil−wax solution to be tested through the channel and back to the tank in a closed loop at a temperature level above 36.6 °C, the WAT measured for the solution. Additional characteristics of the solution employed are given below. The mass flow rate desired for the particular experiment was set in the pump controller. The copper walls of the test section were also maintained at that same temperature above the WAT by circulating warm water from the circulating units though the copper blocks connected to the copper walls. Once a steady condition was achieved at this elevated temperature level, the cooling of the solution to a desired level below the WAT was initiated. To this end, cooling of the solution in the tank started at a slow rate with the agitator on. The temperature of the copper walls of the test 4

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Figure 3. (a) Carbon number distribution of spindle oil and wax. (b) Viscosity of the 10% solution of spindle oil and wax. section was also slowly lowered by controlling the cooling rate of the water-circulating unit. Cooling of the copper walls was performed in such a way that the temperature of the walls was always above the temperature of the flowing solution, thereby avoiding wax deposition on the walls prior to the initiation of a data run. The heating tracer tapes installed around the hoses conducting the solution and around the pump were activated to maintain the wall temperatures above the flowing solution. Preliminary data runs were performed to determine the required power input for the heating tracer tapes. This cooling procedure was monitored until the steady-state temperature of the solution and copper wall desired for a particular data run was achieved. During the cooling process, visual inspection of the interior of the tank and of the transparent pipe sections installed in the hoses was performed to spot any possible wax deposition. In all tests conducted, no deposition was verified. After attainment of the steady state, the temperature of the circulating water in the copper blocks was set to the desired value to initiate the deposition experiment. With the new temperature conditions at the cooper walls, it was possible to create the different heat flux boundary conditions needed for the experiments, as will be described shortly. Any wax deposition along the copper walls could be registered by the digital camera. The temporal evolution of the wax deposit thickness could be measured by analyzing the recorded images obtained with the camera fixed at a particular channel axial position. However, the limited field of view of approximately 15 × 15 mm2 was not sufficient to image the whole 300 mm of channel length, although it was sufficient to observe the whole 10 mm of channel height. A special experimental procedure was employed to allow for the measurement of the time evolution of the deposited wax along the complete channel length, employing this limited field of view. The procedure was initiated by positioning the camera at the channel entrance, imaging the first 15 mm of its length. The time evolution of the wax deposit was registered by the camera up to the attainment of a steady-state condition for the wax deposit thickness, for the particular mass flow rate being studied. After the steady state was obtained, the temperature of the copper walls was raised to a value above the WAT, by pumping hot water through the copper walls. By this way, all of the deposited wax was removed. The camera was then moved to a new position adjacent to the previous position, by moving the coordinate table. After attainment of the steady state, the temperature of the copper walls was lowered and set to the same value used in the experiments for the previous position of the camera. The time evolution of the wax deposit was again registered by the camera up to the attainment of the steady-state condition for the deposit thickness. This procedure of forming, registering, removing the deposit, and moving the camera was repeated until the whole length of the channel was visited. The accuracy associated with the procedure just described was estimated by preliminary experiments conducted prior to the data runs. In these experiments, the camera was kept at a fixed axial position

and registered the time evolution of the wax deposit. After steady state, the deposit was removed by increasing the wall temperature. The experiment was then repeated without, however, moving the camera. The results for the time evolution of the wax deposit thickness from several replications were compared. In all cases, the maximum deviations among different replications were within ±5%, a value considered satisfactory. Measurement of the transient deposit thickness in the captured images was performed by a manual operation. First, the captured images were processed to enhance contrast using a histogram equalization procedure.21 The images for a particular axial position and at pre-selected time intervals were visualized in the computer screen using the software Axiovision 4.4 by Zeiss. The position of the interface was manually identified using the measuring feature offered by the program. Image calibration was obtained by measuring the known distance between the copper walls of the channel prior to the initiation of the deposition process. Typically, in each image frame corresponding to a field of view of 15 mm, five measurements of the interface position were performed at equally spaced axial positions. Because images of the deposit were measured at 20 axial stations, the deposit shape at any particular time was formed by approximately 100 measured points. Test Solution. The solution employed in the tests was a 10% in weight mixture of commercial paraffin and spindle oil. The paraffin was obtained from VETEC (Rio de Janeiro, Brazil) and displayed a melting point in the range of 56−58 °C. The molecular weight distribution of n-paraffin is presented in Figure 3a. The spindle oil, furnished by Petrobras (Brazil), was non-volatile in the temperature range of the experiments. The n-paraffin distribution of the spindle oil is also presented in Figure 3a, as the distribution to the left. The composition of the solvent and wax was analyzed using the hightemperature gas chromatography (HTGC) method in a Agilent 7890A gas chromatographer. The density of the 10% solution employed varied linearly from 856.6 to 837.0 kg/m3 for the temperature range of 10−50 °C. A 25 mL pycnometer was employed in the density measurements. The temperature variation of the solution viscosity is presented in Figure 3b. The measurements were performed with a UDS 200 Paar Physica rheometer. The amount of precipitated wax as a function of the temperature was measured using differential scanning calorimetry, with a microDSC model VII by Setaram. Figure 4 presents the mass percentage of dissolved wax in solution for the temperature range of the experiments. The WDT was measured to be 2 °C above the WAT, using microscopy. The cooling and heating rates employed in the WAT and WDT measurements were 0.8 °C/min.

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RESULTS AND DISCUSSION The results obtained in the present study will be presented now. The experimental methodology used allowed for the 5

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The choice of temperatures mentioned above for our experiments guaranteed that, at least, the negative heat flux boundary condition was never imposed. The external temperatures of the channel glass walls were measured by 15 thermocouples distributed along the channel. This temperature was directly influenced by the air jet warming system with a temperature set at Tj = 35 ± 0.5 °C, controlled at the exit of each jet. This higher temperature uncertainty (±0.5 °C) was caused by the laboratory air temperature fluctuations during the day. The experiments under zero heat flux boundary condition conducted with the parameters mentioned above were repeated 3 times. After 4 h of test duration, no deposition was observed on the copper channel walls. An additional experiment for the zero heat flux boundary condition was performed. This time, we aimed at increasing the concentration of wax crystals flowing in suspension. To this end, the oil mixture injection temperature was set at Tinj = 32.0 ± 0.2 °C (2 °C below the injection temperature of the previous experiment). To approximate the zero heat flux condition, the copper walls temperatures were set at Tw = 32.2 ± 0.2 °C, with an air jet temperature of Tj = 33 ± 0.5 °C. The reduction of the oil mixture injection temperature from Tinj = 34 to 32 °C caused a 42% increment in the oil mixture viscosity, as verified in Figure 3b. Because the mixture density only changed 0.1% and the volumetric flow rate from the positive displacement pump employed was kept constant, the Reynolds number based on the hydraulic diameter of the test section dropped from 151 to 106. Despite the more favorable deposition conditions as a result of the higher concentration of suspended crystals, no deposition was observed at the end of the test. A new set of experiments was conducted for a higher value of the Reynolds number, namely, 249. The temperature settings for the fluid and walls were the same as those described in the previous paragraph. At higher Reynolds numbers, higher levels of the shear rate are imposed on the fluid. The presence of deposition would be an indication that shear-induced mechanisms could be relevant for deposition. After 4 h of tests, no deposition was observed. Experiments were also conducted for the positive heat flux boundary condition, a configuration where molecular diffusion does not contribute to wax deposition. The literature on paraffin deposition shows a small number of experimental works investigating this condition. For example, Hsu et al.23 affirm that zero and positive heat fluxes could generate wax deposition as long as the wall and fluid injection temperatures were below the WAT. Another experiment conducted by Todi14 for the positive heat flux condition resulted in an irregular thin layer of wax deposited at the end of the third day of tests. Hence, on the basis of these results, a set of experiments was conducted to investigate the positive heat flux boundary condition. The test sequence was initiated by reducing the fluid injection temperature to the desired value. Then, the channel walls temperatures were set. One more time, the lowest Reynolds number was chosen for the tests, which offered the most favorable conditions for deposition. The positive heat flux condition was obtained by setting the oil injection temperature at Tinj = 32 ± 0.2 °C, the copper walls temperatures at Tw = 35 ± 0.2 °C, and the air jet temperature at Tj = 35 ± 0.5 °C. Contrary to the results obtained by Todi14 after 4 h, there was no deposited wax visualized for this heat flux condition.

Figure 4. Mass concentration of dissolved wax in solution.

determination of the temporal and spatial evolution of the wax deposits and the visualization of the deposition process under conditions of a high concentration of suspended crystals. The experiments explored the effects of three heat flux boundary conditions on the deposition rates as well as the effects of the flow rate and inlet fluid temperature. Deposition Experiments. Positive and Zero Heat Flux Boundary Conditions. As already commented, the literature review revealed that there is some controversy on the interpretation of the results for conditions of zero and positive heat flux. A positive heat flux is defined as the configuration where the channel wall is warmer than the fluid. The zero heat flux boundary condition is obtained when the wall is perfectly insulated or when there is equality between the wall and the fluid temperatures. Hunt,6 Brown et al.,10 Hamouda et al.,11 and Creek et al.22 conducted experiments for the zero heat flux condition, reporting that wax deposition was not present. However, Burger et al.7 and Todi14 conducted experiments for the same heat flux condition observing the formation of a very thin deposit layer after a few hours of the test. These contradictions motivated the development of experiments to reproduce the zero heat flux conditions. The first experiment under zero heat flux boundary condition was performed with the lowest Reynolds number allowed by the test section, Re = 151, which produces the lowest shear rate. The zero heat flux condition between the oil mixture and the copper walls was obtained with an oil mixture injection temperature of Tinj = 34.0 ± 0.2 °C and walls temperatures of Tw = 34.4 ± 0.2 °C. It should be noted that the oil mixture injection temperature was below 36.6 °C, the measured WAT for the fluid; therefore, suspended crystals were present in the flow. The choice of an average temperature of the wall slightly higher than the bulk fluid temperature was an imposition of the uncertainty of the temperature measurements that could, otherwise, allow for moments where negative heat fluxes existed and that could lead to misleading deposition measurements. This uncertainty on the wall and bulk fluid temperatures is an important issue. Although the experiments were seeking for the zero heat flux boundary condition, in reality, there could be an alternation among zero, positive, and negative heat flux boundary conditions as the temperature of the wall fluctuated around the mean value. Indeed, caution should be taken when interpreting the experiments of Todi,14 where wax deposition was reported for the zero heat flux condition. In those experiments, the uncertainty on the wall temperature was reported to be of the order of ±1 °C, which could, conceivably, have led to moments when negative heat fluxes were prevailing. 6

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Figure 5. Measured spatial and temporal evolution of the deposited wax thickness for laminar channel flow for ΔT = 15 °C: (a) Re = 151 and (b) Re = 354.

Figure 6. Measured spatial and temporal evolution of the deposited wax thickness for laminar channel flow for ΔT = 25 °C: (a) Re = 151 and (b) Re = 354.

Negative Heat Flux Boundary Condition. In the case of the channel walls being at a lower temperature than the flowing solution, the negative heat flux boundary condition, larger amounts of wax deposits were expected. To avoid the possibility of plugging the channel cross-section, the experiments were conducted with only one wall being cooled. The other wall was maintained at a temperature approximately equal to the inlet temperature of the solution. The experiments were conducted for three different values of the Reynolds number, namely, 151, 213, and 354. In all of the experiments, the fluid inlet temperature was kept at Tinj = 34 °C, while the top copper wall was kept at Ttw = 35 °C. For each flow rate, three different bottom copper wall temperatures were studied: Tbw = 29, 19, and 9 °C. Again, it should be noted that all of these temperatures are below the WAT for the working solution, 36.6 °C. Figure 5 presents results for the temporal and spatial evolution of the wax deposit thickness for the case where the copper wall was maintained at 19 °C, producing a temperature difference of 15 °C with respect to the fluid inlet temperature. In the figure, the deposit thickness, given in millimeters, is presented as a function of the channel dimensionless axial

coordinate. The channel length was used to non-dimensionalize the axial coordinate. The spatial distribution of the deposit thickness is presented for four time instants, measured after the initiation of the cooling of the wall, namely, 1, 3, 5, and 10 min. The spatial distribution for 150 min is also presented in the figure and represents the steady-state condition obtained for the wax deposit thickness. The results of panels a and b of Figures 5 were obtained for Reynolds numbers of 151 and 354, respectively. Figure 6 presents similar information as Figure 5 but for the case where the copper wall was cooled to 9 °C, producing a temperature difference of 25 °C with respect to the fluid inlet temperature. The experimental data presented in Figures 5 and 6 are, seemingly, the first published results that display the spatial and temporal variation of the wax-deposited layer under flowing conditions with crystals in suspensions. An observation of Figures 5 and 6 shows the fast growth rate of the deposit layer. Indeed, the first 10 min of deposit accumulation is responsible for nearly 50% of the final thickness attained only after 2 h and 30 min. A comparison of the results from Figures 5 and 6 for the two values of the laminar Reynolds numbers tested shows that the deposited layer is comparatively thinner for the higher flow rates represented by the higher value 7

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Figure 7. Measured temporal evolution of the deposited wax layer at mid-channel length, for three values of the Reynolds number: (a) ΔT = 15 °C and (b) ΔT = 25 °C.

of the Reynolds number. For the conditions tested here, the flow rate increase was associated with a reduction of the deposit thickness. If deposition mechanisms based on shear dispersion were relevant, it would be expected that the experiments with higher values of the Reynolds number and, therefore, presenting higher shear rates should display higher deposit thicknesses because, for this mechanism, the deposition is modeled as being proportional to the shear rate.7 This was not the case in the results observed, indicating that the shear dispersion does not seem to be a relevant factor in the deposition of suspended crystals. It must be said, however, that the shear dispersion mechanism can be responsible for the formation of crystal concentration gradients in regions next to the wall, a necessary requirement for the activation of the Brownian diffusion deposition mechanism.8 Figure 7 presents the temporal growth of the wax deposit thickness for an axial position at the channel mid-length, for the initial stages of the deposition process. Panels a and b of Figure 7 are associated with the inlet fluid-to-wall temperature differences of 15 and 25 °C, respectively. In each panel, three curves are plotted for the three values of the Reynolds number tested. The results conveyed in this figure confirm the observations of the previous figures regarding the rapid growth of the deposit at the early stages of the process and the decrease in the deposit thickness with an increasing Reynolds number. A observation of the results of Figures 5−7, indicates that the spatial and temporal evolution of the measured wax deposit thickness presents the same trends and behavior as that of the deposition process where the fluid enters the channel with the temperature above the WAT and suspended crystals are not present. Several examples of such behavior can be found in the literature (e.g., the work of Azevedo and Teixeira8). However, a direct comparison of the wax deposition thickness for situations where suspended wax crystals are present in a high concentration in the bulk of the fluid and where suspended crystals are not present reveals significant quantitative differences. Such a comparison is presented in Figure 8. In this figure, the wax deposit distribution along the channel length measured in the present work for the condition defined by Re = 341, fluid inlet temperature of 34 °C, and cooling wall temperature of 9 °C is compared to the wax deposit

Figure 8. Measured spatial variation of the wax deposit thickness for 10 min after the initiation of the wall cooling. Comparison for the same inlet fluid-to-wall temperature difference of 25 °C and different fluid inlet temperature levels, above and below the WAT. Data for experiments above the WAT are taken from Leiroz.24

distribution measured by Leiroz,24 employing the same test section used in the present work and the same Reynolds number. In that work, the fluid entered the channel with a temperature of 40 °C, while the cold wall was maintained at 15 °C. This temperature difference of 25 °C is the same imposed in the tests, which results were presented in Figure 6b. The WAT was the same for both tests, 36.6 °C. In both cases, the spatial wax thickness distribution is plotted for 10 min after the initiation of the cooling of the copper wall. The results of Figure 8 show that the deposition thickness for the case where the fluid enters the channel with the temperature below the WAT and suspended crystals are present in the bulk are approximately 2 times thicker than those observed in the experiments conducted by Leiroz,24 where the inlet fluid temperature was above the WAT and suspended crystals were not present, even though the same fluid-to-wall temperature and Reynolds number were employed. This comparison is an indication of the importance of crystal deposition mechanisms when they are present and flowing suspended in the bulk, and the channel wall is cooler than the bulk. At the channel 8

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while a very thin wax deposited layer was growing slowly, in conditions similar to those in the first position. Crystals and crystal agglomerates flowing next to the cold wall adhered to the existent thin wax deposited layer, promoting a rapid increase in its thickness. With the progressive thickness increment of the wax deposit, the high crystal concentration region was less evident as a result of a reduction of the crystal concentration that might, probably, have been caused by the thermal insulation effect of the deposited wax. Figure 10 shows

entrance, however, the wall-normal temperature gradients are expected to be strong and to induce a strong wall-normal diffusive flux of liquid wax, contributing to a higher deposition rate by the diffusive mechanism. This seems to be a plausible argument, even though calculations demonstrate that the solubility function (dC/dT) for the test of Leiroz24 at the wall temperature of 15 °C is larger than that calculated at 9 °C, for the present case. The visualization results to be presented shortly suggest that, at the channel entrance, crystal deposition does not seem to dominate over the diffusive mechanism, indicating that the strong temperature gradients prevailing at the channel entrance compensate for the lower value of dC/dT. For other positions downstream into the channel, the wallnormal temperature gradients decrease and crystal deposition seems to dominate, as indicated by the visualization experiments. Visualization Experiments of Wax Crystal Transport. During the negative heat flux experiments performed in the presence of suspended crystals, a region of high concentration of wax crystals flowing adjacent to the cold wall was observed. Additional experiments with higher magnification lenses (45×) were performed with the objective of trying to identify crystal transport mechanisms in the wall region. Two regions were selected for observation of the motion of the crystals: at the entrance and at the exit section of the channel. A schematic view of the deposition process observed is presented in Figure 9. The figure shows the copper cold wall, the motionless wax

Figure 10. Visualization of wax deposit formation. The dot marks the immobile deposit interface. Flowing suspended crystals are seen as the light gray region above the deposit. Viewing area: 1.2 × 2.5 mm2. A video presenting the deposition process can be viewed in the Supporting Information.

an image of the deposit formed by crystal agglomeration topped by the flowing suspended crystals. The dotted line on the image marks the interface of the immobile deposit. A video of the deposition process just described is available in the Supporting Information of the present paper. The main information conveyed by the video will be commented next. In the first 10 s of the video, there is no heat flux through the wall, because the wall is maintained at the same temperature as the bulk of the fluid. As observed, there is no deposition during this initial phase, even though a flow of suspended crystals is observed moving in a region adjacent to the wall. This is the light gray area seen in the video above the wall. At the moment that the wall temperature is lowered, producing a negative heat flux, a careful observation of the visualization presented in the video reveals the formation, at a slow rate, of a thin wax layer at the wall. Conceivably, this layer formation could be driven by a molecular diffusion mechanism. Just after the formation of this layer, the growth rate of the deposit increases significantly as a result of the constant incorporation of wax crystals and wax crystal agglomerates to the deposit. The images show no significant lateral motion of the crystals toward the growing deposit interface, but rather, the crystal pathlines are nearly horizontal. The crystals and agglomerates moving close to the interface are seen to decelerate, suddenly stop, and adhere to the deposit. An additional visualization experiment was conducted for Reynolds number equal to 354. Although the general aspects of the visualization were similar to those described previously for the lower value of Re, it was observed that the region of flowing suspended crystals was thinner and presented a lower concentration of crystals. The total deposition thicknesses obtained were smaller than in the previous experiments. Therfore, a higher shear rate led to smaller agglomeration of suspended crystals at the wall. It should be mentioned that, for the low values of Reynolds numbers tested, no deposit removal was observed. The mechanisms mentioned in the literature as possibly responsible for the deposition of wax crystals in suspension do not seem to explain the images presented in the video.

Figure 9. Pictorial view of the region of high concentration of suspended crystals and immobile wax deposit.

deposit, and the region of high concentration of flowing suspended crystals. The locations of the visualization regions are also marked in the figure. The actual dimensions of the visualized regions were 1.2 × 2.5 mm (length × height). A high particle concentration region flowing next to the copper wall appeared immediately after the beginning of the wall cooling. The shape of this region, thin at the entrance and thicker at the exit of the channel, resembled the shape of a thermal boundary layer developed at the cooled wall. The first visualization experiment was performed at the lowest Reynolds number and with the lower wall cooled at the lowest temperature tested (Re = 151 and Tbw = 9 °C) to produce the most favorable deposition conditions allowed by the test section. With the camera positioned at the entrance of the channel (position 1 in Figure 9) and with the wall cooling just initiated, an homogeneous growing of the wax deposit with a thin region with high crystal concentration flowing adjacent to the deposited wax was observed. At this channel position, the wax crystal deposition was not obvious; therefore, it was reasoned that the wax deposit grew mainly as a result of the molecular diffusion mechanism. At the second camera position, a few seconds after the initiation of the wall cooling, a thick region of a high crystal concentration flowing next to the copper wall was observed, 9

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revealed a lack of small-scale fundamental laboratory tests aimed at identifying the relative importance of the deposition mechanisms and revealed some discrepancies in the interpretation of deposition experiments. Therefore, the work was focused on obtaining experimental data that could contribute to the understanding of the deposition phenomena and, in particular, wax particle deposition. The strategy employed in the study was to conduct laboratory experiments in simple geometries under controlled conditions with well-defined boundary and initial conditions, employing fluids with known thermophysical properties. Three distinct thermal boundary conditions were investigated, namely, channel wall at a temperature above the bulk temperature of the fluid entering the channel, wall temperature at the same temperature as the entering fluid, and wall temperature below the entering fluid temperature. These boundary conditions were termed positive, zero, and negative heat flux boundary conditions, respectively. The experiments were conducted for three values of the Reynolds number. The quantitative visualization techniques employed allowed for the determination of the spatial and temporal distribution of the wax deposit along the channel walls. For the positive and zero heat flux boundary conditions, no wax deposition was observed for the three levels of shear rate prevailing, associated with the three values of the Reynolds number tested. This finding indicates that wax deposition mechanisms based solely on hydrodynamic lateral forces are not relevant, an observation that finds support in some previous studies from the literature but contrary to other studies. For the negative heat flux boundary condition, thick wax deposits were measured. The deposits formed under the presence of suspended flowing wax crystals were shown to be approximately twice thicker than the deposits obtained for the same Reynolds number and temperature difference between the inlet fluid and cooling wall but for the case where the inlet fluid temperature was above the WAT. In the latter case, suspended crystals were not present in the flow. This significant difference in deposited thickness is an indication of the importance of crystal deposition in solutions flowing with temperatures below the WAT. Qualitative visualization studies were conducted to help identify the mechanisms that govern wax deposit formation for the case where a high concentration of flowing suspended crystals is present. The images presented show that, after the initiation of the cooling of the channel wall, a thin layer of wax deposit is formed at the wall at a slow growth rate, resembling a diffusion-dominated deposition process. After that initial period, a rapid growth of the deposit is visualized, resulting from the incorporation of crystal and crystal agglomerates to the deposit. Observation of the crystal motion did not reveal significant lateral displacement toward the deposit interface but rather nearly horizontal straight trajectories. Crystals and agglomerates moving closest to the deposit interface are seen to decelerate, stop, and incorporate into the existing deposit. The incorporation process observed seems to be the result of the interaction of the crystals with a gel layer formed at the cold wall. Additional experiments and simulations are needed to validate this hypothesis. The simple experiments conducted indicate that rapid deposit growth rates can be experienced when the wax solution is flowing with temperatures below the WAT with suspended crystals present and the channel wall is being cooled. The cold flow technology proposed in the literature is supposed to avoid

Brownian diffusion associated with shear dispersion should be discarded, because Brownian motion should be negligible for the large size of crystals observed in the images. After observing the trapping process of the crystals and agglomerates shown in the visualization experiments, such as those presented in the video, Minchola et al.25 proposed a deposition model that combined molecular diffusion with a gel formation mechanism. In their model, the flowing solution was modeled as a Bingham-type, non-Newtonian fluid with a temperature-dependent yield stress. At the region close to the wall, the fluid temperature is low and a high yield stress prevails. The fluid shear stress calculated by the solution of the mass, momentum, energy, and species conservation equations is compared to the fluid yield stress at the prevailing temperature, at each point. If the fluid shear stress value was found to be lower than the local yield stress, the particular point was considered as part of the immobile deposit. This mechanism could be a possible explanation for the trapping of crystals observed in the video. By this reasoning, crystal and agglomerates would be trapped by the high yield stress layer formed near the cold wall region. Models that combine the solution of the equations governing the mixture velocity, temperature, and species concentration fields with an appropriate thermodynamic model are capable of predicting the deposition process with acceptable accuracy, for the conditions where the solution enters with temperatures above the WAT.13 In these models, the local temperature and species concentration values are input to the thermodynamic model, yielding the local composition of the wax solid and liquid phases. The deposit is determined by assuming a value for the solid content necessary to form a structured gel, typically 2% of solids. Diffusion within the deposit acts as to change its composition and strength.19 Simplified versions of the model just described were proposed by combining thermodynamic calculations and one-dimensional heat-transfer models.26,27 These simpler models avoid the computational costs of the complete model at a penalty of loss of spatially distributed compositional information. The issue that is still not handled by any model is the possible contribution to the deposit from solids formed in the form of crystals in the bulk, in regions where the solid content is not sufficient to form a structured gel deposit, as seen in the video presented. Conceivably, these crystals can be driven toward the interface and contribute to the already existing deposit or could be driven to regions where the local thermodynamic conditions are such that they will become part of the liquid phase. More research is needed to clarify this issue. The visualization presented in the video also allows one to observe qualitatively the aging process in the deposit. As seen, the deposit becomes darker as time passes, as a consequence of the progressive blocking of the background illumination, resulting from the increase in the deposit solid content.

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CONCLUSION The present paper presented an experimental study of wax deposition in laminar channel flow. The experiments were focused on cases were the fluid entered the test section at a temperature below the WAT, which allowed for the presence of a high concentration of flowing suspended crystals. This situation of practical relevance has received considerable less attention in the literature compared to the situation where the fluid enters the channel with a temperature above the WAT and free of suspended crystals. The literature research conducted 10

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(11) Hamouda, A.; Davidsen, S. An approach for simulation of paraffin deposition in pipelines as a function of flow characteristics with a reference to Teesside oil pipeline. Proceedings of the SPE International Symposium on Oilfield Chemistry; San Antonio, TX, Feb 14−17, 1995; SPE-28966-MS, DOI: 10.2118/28966-MS. (12) Merino-Garcia, D.; Margarone, M.; Correra, S. Kinetics of waxy gel formation from batch experiments. Energy Fuels 2007, 21, 1287− 1295. (13) Hoteit, H.; Banki, R.; Firoozabadi, A. Wax deposition and aging in flowlines from irreversible thermodynamics. Energy Fuels 2008, 22, 2693−2706. (14) Todi, S. Experimental and modeling studies of wax deposition in crude oil carrying pipelines. Ph.D. Thesis, University of Utah, Salt Lake City, UT, 2005. (15) Merino-Garcia, D.; Correra, S. Cold flow: a review of a technology to avoid wax deposition. Pet. Sci. Technol. 2008, 26, 446− 459. (16) Huang, Z.; Lee, H. S.; Senra, M.; Fogler, H. S. A fundamental model of wax deposition in subsea oil pipelines. AIChE J. 2011, 57, 2955−2964. (17) Haj-Shafiei, S.; Serafini, D.; Mehrotra, A. K. A steady-state heattransfer model for solids deposition from waxy mixtures in a pipeline. Fuel 2014, 137, 346−359. (18) Kasumu, A. S.; Mehrotra, A. K. Solids deposition from waxsolvent-water waxy mixtures using a cold finger apparatus. Energy Fuels 2015, 29, 501−511. (19) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. Formation and aging of incipient thin film wax-oil gels. AIChE J. 2000, 46, 1059−1074. (20) Bhat, N. V.; Mehrotra, A. K. Measurement and prediction of the phase behavior of wax-solvent mixtures: significance of the wax disappearance temperature. Ind. Eng. Chem. Res. 2004, 43, 3451−3461. (21) Gonzales, R. C.; Wood, R. E.; Eddins, S. L. Digital Image Processing Using MATLAB, 2nd ed.; Gatesmark Publishing: Knoxville, TN, 2009. (22) Creek, J.; Lund, H.; Brill, J.; Volk, M. Wax deposition in single phase flow. Fluid Phase Equilib. 1999, 158−160, 801−811. (23) Hsu, J.; Santamaria, M.; Brubaker, J. P. Wax deposition of waxy live crudes under turbulent flow conditions. Proceedings of the SPE Annual Technical Conference and Exhibition; New Orleans, LA, Sept 25−28, 1994; SPE-28480-MS, DOI: 10.2118/28480-MS. (24) Leiroz, A. T. Study of wax deposition in petroleum pipelines. Doctoral Thesis, Department of Mechanical Engineering, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Rio de Janeiro, Rio de Janeiro, Brazil, 2004 (in Portuguese). (25) Minchola, L. R.; Azevedo, L. F. A.; Nieckele, A. O. The influence of rheological parameters in wax deposition in channel flow. Proceedings of the 2010 14th International Heat Transfer Conference; Washington, D.C., Aug 8−13, 2010; pp 669−676, DOI: 10.1115/ IHTC14-22952. (26) Bidmus, H. O.; Mehrotra, A. K. Heat-transfer analogy for wax deposition from paraffinic mixtures. Ind. Eng. Chem. Res. 2004, 43, 791−803. (27) Merino-Garcia, D.; Margarone, M.; Correra, S. Kinetics of waxy gel formation from batch experiments. Energy Fuels 2007, 21, 1287− 1295.

deposition by operating at temperatures below the WAT and with zero heat flux at the wall. The results obtained show that large deposition rates may potentially occur if, at some point along a line, cooling of the pipe wall is allowed, which might happen, for instance, in case a subsea line operating in a cold environment presents a region with a faulty thermal insulation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.5b02344. Video of crystal deposition shown in Figure 10 of the text (MPG)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

Andrea T. Leiroz: Mechanical Engineering Program, Alberto Luiz Coimbra Institute of Post-Graduation and Research in Engineering (COPPE)/Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro, Rio de Janeiro 21941-450, Brazil. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the support awarded to this research by the PETROBRAS Research and Development Center and by CNPq, the Brazilian Research Council.

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REFERENCES

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