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Letter to the Editor: Regarding the Role of the Critical Particle Size in the Asphaltene Deposition Model Dmitri Eskin, and John Ratulowski Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 02 Nov 2015 Downloaded from http://pubs.acs.org on November 2, 2015
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Letter to the Editor: Regarding the Role of the Critical Particle Size in the Asphaltene Deposition Model Dmitry Eskin* and John Ratulowski Schlumberger DBR Technology Center 9450-17 Avenue, Edmonton, AB, Canada T6N 1M9
It is recognized in a significant number of recent publications [1-4] that asphaltene deposition on the pipe wall in a vertical wellbore flow is governed by the Brownian motion of nano-sized particles. Eskin et al. [1, 2] shared with Hoepfner et al. [3] the common view on the asphaltene deposition mechanism. These authors considered that asphaltene particles of a few nanometers in size precipitate from a fluid due to thermodynamic destabilization, grow agglomerating with each other, and also deposit on the wall. The authors [1, 2, and 5] modeled the particle agglomeration by using the population balance equation. Eskin et al. [1] assumed that the particle agglomeration is driven by both the turbulence and the Brownian motion, and also employed the same mechanisms for deposition modeling. In the paper [2] the authors concluded that the Brownian motion is a dominating mechanism of agglomeration and deposition of asphaltenes. Intensity of the Brownian motion is reduced with an increase in the particle size; therefore, only nano-sized particles significantly contribute into the deposition process. Depletion of a hydrocarbon fluid of small asphaltene particles, able to deposit, is caused by agglomeration and leads to deposition slowing down and termination. Hoepfner et al. [3] expressed a doubt in validity of an introduction of the critical particle size, which limits the maximum size of asphaltene particles that are able to deposit, as the model parameter. They wrote: “Eskin et al. modeled the deposition of asphaltenes induced by pressure ∗ - corresponding author,
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depletion by imposing a critical asphaltene aggregate size, above which no deposition could occur and at a size below previous estimates for shear inhibition. However, a geometric population balance is successful at modeling batch asphaltene aggregation without imposing a critical particle size and maintaining constant collision efficiency [5]. Both aggregation and deposition after an initial layer has formed are due to asphaltene−asphaltene interactions, so there should not be a different mechanism for adhesion/sticking between the two processes. Once an initial asphaltene deposit has formed, additional deposition can be considered to be aggregation between a large and immobile particle and a small and mobile one. Thus, if aggregation can occur in the bulk, deposition should occur at the deposit interface unless shear forces, which are largest at the deposit interface, limit either process”.
Thus, the authors [3] agree that
agglomeration of a particle moving in a fluid with a particle attached to the wall is limited by shear forces. However, they do not recognize the finding of the authors [1, 2], who identified that the maximum size of a particle, able to deposit on the wall, is smaller than that limited by shear forces. We would like to emphasize that in the work [1] the maximum size of a particle that can be maintained attached to the wall by the Van-der-Waals attraction force being under action of a viscous drag force was estimated. A simple force balance for an asphaltene particle located on the wall of a production pipeline showed that for realistic production conditions the critical size normally exceeds 2 micrometers. However, the experiments [1, 2] conducted in a laboratory Taylor-Couette (TC) device under turbulent flow conditions showed the results, which deviated from the expectations. The investigators used the TC device, where the inner cylinder rotates creating a turbulent flow and the mass of a deposit accumulated on the outer immobile wall is measured. Most of experiments were done in a flow-through regime, in which a hydrocarbon fluid was constantly flowed
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through the TC device with low flow rates. The authors [1, 2] identified the model coefficients for different oils at different flow-through rates and at different rotation speeds. It is important to emphasize that the determined particle-wall sticking efficiencies (collision efficiencies for particle aggregation in a flow) were always of the same order of magnitude as those identified for asphaltene particle agglomeration ([1], [2], and [5] cited by Hoepfner et al. [3]). However, it turned out that an accurate matching between the computations and measurements was obtainable only if the maximum size of a particle able sticking to the wall was artificially limited to approximately 100 nm. Thus, an introduction of the critical particle size that is an order of magnitude smaller than that predicted based on the force balance, was driven by necessity to match the experimental data. These results were achieved assuming the same mechanism of deposition and agglomeration, which was employed by the authors [5] for modeling the asphaltene agglomeration process. The only difference of the deposition modeling [1, 2] from the agglomeration modeling [5] was the use of unequal particle collision and particle-wall sticking efficiencies. Understanding that the governing mechanisms of agglomeration and deposition are nearly the same, the authors [1, 2] found out that experimental data can be more accurately matched if the particle-wall sticking efficiency is smaller than the particle collision efficiency whereas both these parameters are of the same order of magnitude. Note, an introduction of this difference in the parameters has no any effect on the critical particle size (~ 100 nm) identified from the experimental data. Thus, the critical particle size, which is significantly lower than that estimated from the force balance, was introduced only with the purpose to fit the experimental data. Actually, this parameter hides the lack of description of a physical phenomenon preventing deposition of particles, sizes of which are larger than the threshold identified. A possible explanation of the
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difference between the critical particle size based on the force balance and that identified from the experiments was suggested in [1]. Large particles attached to the wall represent asperities that can be easily impacted and removed with relatively large agglomerates, moving with a flow and fluctuating, driven by turbulence, near the deposit surface. This bombardment prevents attachment of relatively large asphaltene particles. Because the models of particle agglomeration, used by the Eskin et al. [1, 2] and Maqbool [5] are nearly identical, the objection of Hoepfner et al. [3] regarding the particle critical size can be related to only the experimental data [1, 2]. However, it is worth to emphasize that these data are well verified and no alternative experimental results for a turbulent flow have been ever published. In our opinion, an unexpectedly small critical particle size is an engineering approximation that can be explained only beyond the agglomeration model physics [1].
References [1] Eskin, D.; Ratulowski, J.; Akbarzadeh, K.; Pan, S. Can. J. Chem. Eng. 2011, 89, 421 −441. [2] Eskin, D.; Ratulowski, J.; Akbarzadeh, K.; Andersen, S. AIChE J. 2011, 58, 2936 −2948. [3] Hoepfner, M.P., Limsakoune, V., Chuenmeechao, V., Maqbool, T., Fogler, S. H., Energy and Fuels 2013, 27 (2), 725-735 [4] Kurup, A.S.; Wang, J.; Subramani, H.J.; Buckley, J.S.; Creek, J.L.; Chapman W.G., Energy Fuels 2012, 26, 5702-5710. [5] Maqbool, T.; Raha, S.; Hoepfner, M. P.; Fogler, H. S. Energy Fuels 2011, 25, 1585 −1596
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