Article Cite This: Energy Fuels XXXX, XXX, XXX-XXX
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Wax Deposit Thermal Conductivity Measurements under Flowing Conditions H. M. B. Veiga,† F. P. Fleming,‡ and L. F. A. Azevedo*,† †
Department of Mechanical Engineering, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Rio de Janeiro 22451-900, Brazil ‡ CENPES, Petrobras Research and Development Center, Rio de Janeiro 21941-915, Brazil ABSTRACT: Thermal conductivities of wax deposits formed on the cooled wall of a channel were measured under flowing conditions, for different values of the Reynolds number (Re) in laminar flow. To this end, a laboratory-scale experiment was especially designed, employing a rectangular channel flow loop. The thermal conductivities were directly measured for steadystate conditions in deposits formed after 7 h of deposition. The cooled wall on which the deposits were formed was equipped with embedded heat flux and thermocouple sensors. A micrometer-driven temperature probe of small dimensions was installed at the opposite channel wall and could be traversed across the channel, yielding the temperature profile of the deposited wax layer, as well as the liquid/deposit interface temperature. Deposit compositions were obtained by high-temperature gas chromatography. Thickness-averaged deposit thermal conductivities were obtained from the deposit thickness, heat flux, and interface-to-wall temperature measurements. The thermal conductivity results obtained for these well consolidate deposits did not display any sensitivity to the Re values tested, although the deposit wax content was seen to increase with Re. This finding was related to the nonhomogeneous character of the thick deposits studied. Temperature profiles within the wax deposit measured with the traversing temperature probe revealed small deviations from the linear profile expected for a one-dimensional, steadystate solution, considering a constant value for the thermal conductivity across an homogeneous deposit. These deviations were attributed to transverse variations of the deposit thermal conductivity. Local values of the thermal conductivity across the deposit were measured, revealing higher values closer to the deposit/liquid interface region, compared to those observed in the near-wall region. This variation was associated with the higher liquid fraction present in the deposit near the cold wall. The sensitive of the deposit thermal conductivity to the deposit liquid fraction was used as the basis for a novel technique developed to estimate the liquid and solid fraction distribution across the deposit. The technique was able to capture the increase in liquid fraction close to the cold wall, compared to the near-interface region, for the experimental conditions tested.
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INTRODUCTION Wax deposition in pipelines is one of the most relevant problems faced by the industry, with regard to the task of ensuring the continuous flow of petroleum. The ability to predict whether wax deposition will occur in a certain pipeline installation is of fundamental importance for designers and operators. Indeed, advanced information on the probability of wax deposition and estimates of wax deposit spatial and temporal distributions can be used as input in the pipeline design phase. The information can aid in the specification of the proper amount of thermal insulation for the line, in the decision on the need of pigging, on the need of injection of chemicals, or even for active heating of the line. Wax deposition models are valuable tools to aid pipeline designers and operators in the design phase. Models have been developed based on fundamental principles, considering several aspects of the phenomena, such as wax precipitation, convective and diffusive heat and mass transport, and wax removal processes.1−12 Heat transfer from the flowing oil to the colder environment seems to be a necessary condition for wax deposition to occur on the internal pipe wall. No matter the level of sophistication of a deposition model, heat transfer across the deposit wax layer plays a significant role in determining the deposit geometric and physical characteristics.6 Simplified numerical calculations © XXXX American Chemical Society
have shown that the thermal resistance of a deposit layer becomes the dominant resistance when the deposit thickness attains only 5% of the pipe diameter, in the case of a typical noninsulated subsea line.10 In order to stress the importance of the knowledge of the deposit thermal conductivity for an accurate wax deposition prediction, a simulation exercise was performed by employing the elaborated compositional deposition model developed by Souza,13 based on the work of Banki et al.11 In this exercise, the simulation model was run for an annular pipe geometry, with laminar flow of a solvent and wax solution. Different values of the deposit thermal conductivity were tested, keeping all other input information constant. The range of variation of the thermal conductivity input to the model reflects the range encountered in the literature for wax deposit thermal conductivities. The results from the simulation exercise for the wax deposit thickness, for a particular annular pipe axial position, are presented in Figure 1. As can be seen in the figure, the variation of the deposit thermal conductivity from 0.1 W/ (m K) to 0.4 W/(m K), produced a variation of ∼50% on the predicted deposit thickness, which confirms that an accurate Received: April 21, 2017 Revised: September 27, 2017 Published: September 29, 2017 A
DOI: 10.1021/acs.energyfuels.7b01131 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
the thermal conductivities of the solid and liquid wax phases.6,9,11,12,29−31 However, the Maxwell model was originally proposed to predict thermal conductivities of solids formed by a continuous matrix of a base material, sparsely populated by a second material, forming a homogeneous composite solid. Wax deposits, especially the thick ones, may significantly deviate from these basic assumptions.9 In the work of Bidmus and Mehrotra,10 the authors proposed a 1-D heat-transfer model to investigate wax deposition. The thermal conductivity of the wax deposit was analyzed in order to determine the best fit, between experiments and the numerical model, for laminar flow. The thermal conductivity that best-fitted the model results was in the range of 0.2−0.3 W/(m K), which is slightly higher than the thermal conductivity of solid paraffin wax. However, the authors stated that convective effects could be taking place within the deposit, causing the thermal resistance of the deposit to drop. In a later work by the same group, the thermal conductivity of deposit formed under turbulent flow was estimated to be on the order of 0.34−0.37 W/(m K)).32 Recently, Singh et al.33 employed the Maxwell correlation to estimate the thermal conductivities of wax deposits formed in a flow loop employing Gulf of Mexico condensate. The thin deposits formed had their thermal conductivities interpolated between 0.25 W/(m K) and 0.14 W/(m K), which are the values for the solid and liquid wax phases, respectively. Different values for the thermal conductivities of solid nalkanes under C20 are reported by Vélez and co-workers27,28 to be on the order of 0.35−0.45 W/(m K). As demonstrated in this brief introduction, despite its relevance for the proper modeling of the wax deposition process, there is still a need for reliable information on the thermal conductivity of the deposit, particularly under flowing conditions. The present work describes experiments designed to yield direct measurements of the thermal conductivities of wax deposits obtained under flowing conditions. As will be shown, the study also proposed a method for measurement of the deposit solid and liquid fractions obtained with the experiments under operation, with no requirement for deposit sampling. The description of the experiments will be presented next.
Figure 1. Variation of the dimensionless wax deposit thickness with the deposit thermal conductivity for an annular pipe geometry. Based on the work by Souza.13
value for the thermal conductivity of the deposit is a relevant input to the deposition models. In the figure, the deposit thickness is plotted in dimensionless form by using the annular gap space dimension. Typically, wax deposits are composed by a porous structure formed by solid wax crystals, saturated by a mixture of liquid wax and solvent. Some authors have suggested that as little as 2% solid wax is sufficient to form an imobile deposit layer.6,14,15 Considering the high content of solvent found in the deposits, the use of the solvent thermal conductivity was proposed for modeling the deposit properties.16−18 However, as deposits age, the solid wax fraction has a tendency to increase and can attain proportions as much as 80% of the total wax content.19 In these cases, the thermal conductivity value would approach the thermal conductivity of the solid. Thermal conductivity experimental data are scarce in the literature, even for the solid and liquid phases of n-alkanes. Most works address n-alkanes with carbon numbers
