International Journal of Multiphase Flow 37 (2011) 671–694 Contents lists available at ScienceDirect International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w Review Wax formation in oil pipelines: A critical review Ararimeh Aiyejina a, Dhurjati Prasad Chakrabarti a,⇑, Angelus Pilgrim a, M.K.S. Sastry b a b Department of Chemical Engineering, The University of the West Indies, Trinidad and Tobago Department of Electrical and Computer Engineering, The University of the West Indies, Trinidad and Tobago a r t i c l e i n f o Article history: Received 23 December 2010 Received in revised form 9 February 2011 Accepted 20 February 2011 Available online 27 February 2011 Keywords: Waxy crude oil Oil-pipe Solid–solid transition Solid–liquid equilibrium Wax precipitation wax removal a b s t r a c t The gelling of waxy crudes and the deposition of wax on the inner walls of subsea crude oil pipelines present a costly problem in the production and transportation of oil. The timely removal of deposited wax is required to address the reduction in flow rate that it causes, as well as to avoid the eventual loss of a pipeline in the event that it becomes completely clogged. In order to understand this problem and address it, significant research has been done on the mechanisms governing wax deposition in pipelines in order to model the process. Furthermore, methods of inhibiting the formation of wax on pipeline walls and of removing accumulated wax have been studied to find the most efficient and cost-effective means of maintaining pipelines prone to wax deposition. This paper seeks to review the current state of research into these areas, highlighting what is so far understood about the mechanisms guiding this wax deposition, and how this knowledge can be applied to modelling and providing solutions to this problem. Ó 2011 Elsevier Ltd. All rights reserved. Contents 1. 2. 3. 4. 5. 6. 7. 8. 9. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detection of deposited wax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Detecting blockages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Detecting wax deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wax deposition mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Molecular diffusion mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Soret diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Brownian diffusion mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Gravity settling mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Shear dispersion mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6. Shear stripping mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7. Nucleation and gelation kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8. Deposition in two-phase flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of emulsified water on gelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cloud point, pour point and gel point correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review of some existing wax deposition models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Thermodynamic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Hydrodynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wax aging models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Counter diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Ostwald ripening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Correct analogies for correlated heat and mass transfer in turbulent flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inhibition of wax deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672 672 672 672 673 673 673 673 673 673 674 674 674 675 675 675 676 677 679 679 680 680 681 ⇑ Corresponding author. Address: Dept. of Chemical Engineering, The University of The West Indies, St. Augustine, Trinidad and Tobago. Tel.: +1 868 6622002x4001; fax: +1 868 6624414. E-mail address: dhurjatiprasad@yahoo.co.in (D.P. Chakrabarti). 0301-9322/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2011.02.007 672 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 9.1. 9.2. Chemical inhibitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Types of chemical inhibitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1. Ethylene copolymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.2. Comb polymers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.3. Wax dispersants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.4. Polar crude fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.5. Short-chain alkanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3. Surfaces that prevent wax deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4. Cold flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. Wax removal methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1. Pigging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2. Inductive heating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3. Biological treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Restart of gelled pipelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1. Time-dependent gel degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2. Examples of restart models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Introduction Wax build-up is a complex and very costly problem for the petroleum industry, widely reported and studied by researchers in decades past (Reistle, 1928, 1932; Bilderback and McDougall, 1963; Haq, 1978). For subsea pipelines, in particular, it has become especially important to solve the issue of wax build-up, as largescale oil production in colder regions will be faced with more severe wax precipitation (Smith and Ramsden, 1978; Asperger et al., 1981). Wax precipitation within pipelines at and below the Cloud Point or Wax Appearance Temperature (WAT) can lead to gelling that inhibits flow by causing significant non-Newtonian behaviour and increasing effective viscosities as the temperature of a waxy crude oil approaches its Pour Point (Pedersen and Rønningsen, 2003). Alternatively, when just the pipeline wall is below the WAT, this promotes the deposition of a layer of paraffin molecules that can grow over time, constricting flow. This is especially problematic for pipelines in deep-sea environments, as, even in relatively warm climates, the water temperature will be on the order of 5 °C (Azevedo and Teixeira, 2003). Some researchers, such as Carmen García et al. (2001) and Carmen García and Urbina (2003), have studied correlations between the properties of crude oils and their flowing properties, including the precipitation and deposition of wax during flow. Models have been developed to predict the onset of wax precipitation and the deposition of wax along pipeline walls. However, accurately modelling deposition in pipelines can be a complex and difficult undertaking, because, while precipitation is mainly a function of thermodynamic variables such as composition, pressure and temperature, deposition is also dependent on flow hydrodynamics, heat and mass transfer, and solid–solid and surface–solid interactions (Hammami et al., 2003). Only recently has a model been developed that incorporates correct analogies for heat and mass transfer. This paper reviews cases where researchers have studied ways to model wax deposition and the aging of wax deposits in pipelines; methods of measuring wax build-up in pipelines; methods of inhibiting this deposition; wax removal methods; and restart procedures for pipelines gelled with waxy crude. In doing so, this paper, as one goal, seeks to show how our understanding of these mechanisms has developed, to highlight areas where further understanding of these mechanisms is still needed, and to show how well our current correlations can be applied to the accurate prediction of wax deposition. Furthermore, this paper seeks to highlight the progress that has been made in devel- 681 682 682 682 683 683 685 686 686 687 687 687 687 688 688 689 692 692 oping methods to mitigate and treat the formation of paraffin layers in pipelines. 2. Detection of deposited wax 2.1. Detecting blockages In order to experimentally explore wax deposition in the field or to determine the locations of particularly large wax deposits or even complete plugs, methods are needed for detecting the extent of wax deposition at different points in a pipeline or of detecting the location of plugs. Pressure echo techniques can be used to find the location of a blockage by measuring the time for a pressure wave to be reflected back along the pipeline from the point of blockage (Chen et al., 2007). Alternatively, the pipeline could be pressurized and then a special tool with a calliper and video camera on a remotely-operated submersible could be used to measure the external diameter of the pipeline. Upstream of the blockage, but not downstream of it, an appreciable difference in the diameter can be detected when the pipeline is pressurized (Sarmento et al., 2004). 2.2. Detecting wax deposits Traditional experimental methods for measuring the extent of wax deposits include direct methods such as pigging and the ‘‘take-out’’ method, in which a section of pipe is removed and the volume of wax inside measured. Additionally, pressure drop and heat transfer methods can be used to measure wax deposits indirectly without down time (Chen et al., 1997). Zaman et al. (2004) explored alternative methods of measuring wax deposition in pipelines. Firstly, they experimented with measuring light absorption through crude oil using a light source and a detector circuit mounted within a pipe. They found that, in laboratory tests, this detector circuit proved capable of detecting contamination even with a very small percentage present. The use of ultrasound for solid detection, also explored by Zaman et al. (2004) proved very successful in detecting extremely small solid grains. Finally, they were able to use a strain gauge to detect very small changes in pipeline weight associated with wax deposition. However, all of these methods were only tested with small-scale laboratory representations of actual systems. Practical methods for application of these tools to actual subsea pipelines would still need to be designed. Zaman et al. (2006) have also experimented with the use A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 of a laser spectroscope to detect paraffin in paraffin-contaminated oil samples. 3. Wax deposition mechanisms The behaviour of waxy crudes is usually approximated by modelling them as Bingham-like fluids. Different mathematical models have been proposed ranging from a general one-dimensional model of a waxy crude oil to models that describe crude oils depositing wax in closed flow loops. For example, Fusi (2003) and Fasano et al. (2004) delineate many models of differing complexity for the representation of waxy crude oils. In order to fully model the flow of these crude oils, the mechanisms governing the deposition and removal of solid wax must be incorporated into the model. Then models can be developed, informed by a theoretical understanding of the mechanisms at play and the properties of the mixtures under study. However, the question arises of which mechanisms are actually relevant. Investigations in this area have been ongoing for decades by researchers such as Hunt (1962); Burger et al. (1981), and Leiroz and Azevedo (2005). Azevedo and Teixeira (2003)did a critical review of wax deposition mechanisms, starting with wax deposition by molecular diffusion as described by Burger et al. (1981). In this review it is acknowledged that, in most models of wax deposition, molecular diffusion is treated as the dominant mechanism, and it is also argued that experimental evidence suggests that gravity settling and shear dispersion play no significant role in wax deposition. However, Azevedo and Teixeira point out that shear dispersion may play a role in wax deposit removal, which would affect the rate at which wax accumulates. Other authors, such as Solaimany Nazar et al. (2005b) and Correra et al. (2007), have incorporated wax removal mechanisms involving shear forces (sloughing, ablation) into their wax deposition models. Other mechanisms including thermo phoresis, the Saffman effect and turbophoresis have also been considered in modelling wax deposition (Merino-Garcia et al., 2007). 3.1. Molecular diffusion mechanism It is assumed that, for the flow of crude oil in the turbulent regime, the turbulent diffusivities of momentum, chemical species and temperature will lead to a uniform distribution of velocity, temperature and concentration profiles in a pipe cross-section. Therefore, the transport of wax will be controlled by the gradients prevailing at the laminar sub-layer close to the wall (Azevedo and Teixeira, 2003). In a subsea pipeline in which the walls are cooled below the cloud point, there will be a radial temperature gradient and wax crystallization will occur in cooler regions nearest to the wall. Thus, solid wax crystals will exist in equilibrium with the liquid phase. Since wax solubility decreases with temperature, there will also be a concentration gradient established by the temperature gradient within the pipeline, with the cooler regions near the wall having the lowest concentration of wax in the liquid phase. This is what leads to the molecular diffusion of wax from the bulk fluid to the walls of the pipeline. Azevedo and Teixeira (2003) suggested that the mass flux of the wax be estimated by Fick’s Law as dmm dC ¼ qd Dm A dt dr ð1Þ Here mm is the mass of deposited wax, qd is the density of the solid wax, Dm is the diffusion coefficient of liquid wax in oil, A is the surface area over which deposition occurs, C is the concentration of wax in solution (volume fraction), and r is the radial coordinate. 673 3.2. Soret diffusion Soret diffusion or the Soret effect refers to thermal diffusion, which accounts for mass separation caused by the existence of a temperature gradient within the pipeline (Ekweribe et al., 2009). Some researchers, such as Merino-Garcia et al. (2007), have classified its effect in wax deposition as negligible. However, expressing diffusion in terms of molecular and thermal diffusion allows for a wax deposition model to more correctly account for thermal effects in diffusion (Banki et al., 2008). Thus, total mass flux would, ideally, have to be represented as a combination of Fick’s Law, in terms of Dm and the concentration gradient, and transport by the Soret effect, in terms of a thermo diffusion coefficient, DT, and the temperature gradient. 3.3. Brownian diffusion mechanism This would occur when wax crystals that have precipitated out of the oil solution collide with excited oil molecules. The use of this mechanism in modelling deposition was also explored by Azevedo and Teixeira (2003). This diffusion mechanism can also be represented by Fick’s Law as shown in equation.  dmB dC ¼ qd DB A dt dr ð2Þ Here mB is the mass of wax deposited by Brownian motion, DB is the Brownian motion diffusion coefficient of the solid wax crystals and C is the concentration of solid wax out of solution. Azevedo and Teixeira (2003) acknowledge that many authors dismiss Brownian diffusion as a relevant mechanism for wax deposition. However, they conclude that there is not enough evidence to warrant this, citing an argument used by Majeed et al. (1990), which suggests that Brownian diffusion flux will be away from the wall, where the solid concentration would be highest. They dismiss this argument, because if the wax crystals are trapped in the immobile solid layer at the wall, the concentration of solid crystals in the liquid at the wall is zero, or nearly zero, allowing for Brownian diffusion toward the wall. The review concludes that Brownian diffusion remains a possible contributing mechanism for wax deposition. 3.4. Gravity settling mechanism Azevedo and Teixeira (2003) classify gravity settling as insignificant in contributing to wax deposition, citing experimental evidence from Burger et al. (1981), which showed that the settling velocities of wax crystals under typical conditions do not contribute significantly to deposition. This was further supported by experimental evidence from Burger et al., which demonstrated that deposition under horizontal and vertical flow is identical within the limits of experimental error. 3.5. Shear dispersion mechanism Shear dispersion could contribute to wax deposition through the lateral motion of particles immersed in a shear flow. Some authors, such as Fusi (2003), include deposition in terms of a shear dispersion coefficient in the modelling of wax deposition. Also, Fasano et al. (2004) claim that, based on the literature, for temperatures much lower than the cloud point and for moderate heat fluxes the dominant process is shear dispersion, while for slightly higher temperatures the dominant process is molecular diffusion. However, Azevedo and Teixeira (2003) claim that shear dispersion does not contribute to deposition, because experimental evidence shows no deposition of wax under conditions of zero heat flux, when it would only be possible if driven by a flow-induced 674 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 mechanism, such as shear dispersion. However, Azevedo and Teixeira concede that shear forces can still contribute to the removal of wax deposits. Regardless of conflicting theories with regard to the role of shear dispersion in wax deposition, the importance of this mechanism in the overall accumulation and aging of wax deposits cannot be ignored. 3.6. Shear stripping mechanism Removal of wax deposits by shear forces becomes especially important under turbulent conditions when the rate of removal will be significantly higher compared to laminar flow. Therefore, in order to accurately model wax deposition, especially for turbulent flow, it is necessary to incorporate shear stripping effects into the model. Additionally, modelling wax removal by shear forces could help in the design of flow improver chemicals, as some of these may act by causing the formation of softer gel structures that are more susceptible to removal by shear forces. Some researchers, such as Matzain (1999), have tried to represent this effect as an empirical correlation for the reduction in rate of deposit formation caused by shear forces. 3.7. Nucleation and gelation kinetics The crystallization of waxes is a kinetic process, the onset of which can be described by classical homogeneous nucleation theory (Paso, 2005). While much work has been done to approach wax deposition as a thermodynamic problem, modelling based on the kinetics of deposit formation has not been widely explored (Merino-Garcia et al., 2007). Paso (2005) sought to address the insufficient understanding of the crystallization and gelation processes, as well as the assumption that paraffin precipitation kinetics does not limit deposition rates; an assumption that could lead to the prediction of wax deposition in cases where a stable gel cannot form. He used model fluids consisting of n-paraffin components dissolved in petroleum mineral oils, and applied homogenous nucleation and crystallization theory, along with differential scanning calorimetry to measure the onset of crystallization and the crystallization rate. Paso (2005) compared experimental and equilibrium crystallization rates to show that there were three regimes in the crystallization process at low cooling rates. The first is a nucleation lag period starting at high-temperature conditions. The second is a supersaturation growth period, driven by the supersaturation established during the nucleation lag period as well as by decreasing solubility conditions, and during which the crystallization rate can spike well above the equilibrium crystallization rate. The third, meanwhile, is an equilibrium growth period, which starts when the supersaturation ratio is diminished and the crystallization rate converges with the equilibrium predictions of the van’t Hoff relation. One thing noted by Paso about these regimes was that the temperature span of the supersaturation growth regime was independent of the model fluid viscosity, providing evidence of the absence of transport limitations in the crystallization rate. Through the application of the van’t Hoff solubility model within the framework of classical homogeneous nucleation theory, Paso (2005)demonstrated that nucleation represents the primary kinetic limitation associated with the crystallization of n-alkanes in organic solution at low cooling rate conditions, with crystallization rate limitations becoming significant at high cooling rates. He also highlighted that the initial nucleation event is dependent upon the solubility behaviour of the highest fraction of n-alkane components in the fluid, and that the introduction of chain-length variations effects a reduction in the critical nucleus surface energy by co-crystallization of dissimilar chain-length paraffins. Paso (2005) also investigated the mechanical properties of waxy model fluids at constant cooling rates using controlled-stress rheometric measurements, applying an oscillatory upon the fluid samples in order to characterize their mechanical properties during gelation. The crystal structure in samples was also studied via microscopy and, furthermore, Paso applied an extension to an established three-dimensional analytical percolation approximation to wax–oil gel systems. This allowed for the prediction of theoretical gelation via the percolation threshold, the fractional volume of the solid crystalline phase at which it forms a continuous, domain-spanning path connected by crystal–crystal interactions. For this purpose, paraffin crystals were represented by ellipsoidal geometries with spherical rotational volume of interaction. The primary and secondary ellipsoidal aspect ratios of the crystals, a1 and a2, were related to the solid phase fraction at the percolation threshold, ug, by equation. /g ¼ hp 1 1 a1 a2 ð3Þ Here hp = 0.295 represents the spherical percolation threshold. While this would give a prediction of the formation of a crystal percolation network, it was noted that this will lead to gelation only if the number density and strength of the crystal–crystal interactions are sufficient to impart solid-like properties to the fluid (Paso, 2005). Overall, Paso (2005) noted that the gel point of a waxy petroleum fluid is dependent on the morphologies and surface characteristics of the randomly oriented paraffin crystals, and that aspect ratios on the order of 100 allowed mechanical gels to form from these oils with paraffin content as low as 0.5%. Also, that mono disperse crystals exhibited ordered surfaces and sharp edges, providing minimal crystal–crystal contact and weak interactions, while polydisperse n-alkane crystals exhibited nano-scale surface roughness, which provides contact points for strong crystal–crystal interactions, allowing for mechanical gelation at smaller wax contents. Additionally, Paso concluded that percolation threshold models provide accurate gel point predictions for physical gelation systems that exhibit strong crystal–crystal interactions, while under-predicting the solid fraction necessary to induce gelation in weakly-interacting particle systems. Other recent studies that approached the subject of nucleation and gelation kinetics include those by Lopes-da-Silva and Coutinho (2007) and Ekweribe (2008). They analyzed gelation kinetics with the phenomenological Avrami model and noted an apparent dependence of nucleation and crystal growth mechanisms and rates on the degree of supercooling below the WAT at which crystallization is occurring. Lopes-da-Silva and Coutinho (2007) also noted an apparent predominance of heterogeneous nucleation and diffusion-controlled growth, especially at higher supercooling and/or higher oil complexity composition and molecular weight. These results and those of Paso (2005) and further studies should prove invaluable in the development of more robust wax deposition models, which take kinetic considerations into account. They can also be useful in determining mechanisms by which wax gelation can be inhibited or wax deposits weakened by wax crystal modification. 3.8. Deposition in two-phase flow Analyzing and modelling liquid–liquid two-phase flow has previously been explored by many researchers as well as present authors (Raj et al., 2005; Chakrabarti et al., 2006, 2007). Deposition in two-phase flow shows some characteristics similar to liquid– liquid two-phase flow. Matzain et al. (2002) found that the thickness, hardness and profile of wax deposition in two-phase gas–oil flow show dependence on flow patterns. They used a closed 675 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 flow loop and the liquid displacement–level detection (LD–LD) technique, proposed by Chen et al. (1997), to measure wax deposits under different conditions. For horizontal flow, the thickness of deposits varied around the circumference of the pipe depending on flow pattern, as shown in Fig. 1. Matzain et al. (2002) account for these distributions by describing how, in stratified flow, only the lower part of the wall will be in contact with the oil phase, and the heat transfer rate will be highest at the bottom of the pipe and will decrease upward, resulting in decreasing deposit thickness in a crescent shape. In the case of wavy stratified flow, the wavy gas–oil interface is cooled because of the waves, increasing heat transfer rate and, thus, deposit thickness along the interface. With intermittent flow, the passing of liquid slugs induces high shear force and stress along the bottom of the test pipeline and shearing of wax deposits, resulting in thinner deposits at the bottom of the pipe. With annular flow, the wax thickness is uniform around the circumference, as oil is uniformly in contact with the entire wall surface. The results of Matzain et al. (2002) also showed changes in hardness of the wax deposits for different flow patterns. Stratified flow gave a soft deposit at the bottom of the pipe, with harder and thicker deposits along the edge of the wavy gas–liquid interface. Intermittent flow resulted in a hard deposit, with increasing hardness from the top to the bottom of the pipe. Lastly, annular flow resulted in a very hard deposit, uniform across the circumference of the pipe. Their results for vertical two-phase flow, on the other hand, showed very uniform thickness distribution in the different flow regimes, with very hard deposits for annular flow, deposits of medium to high hardness for intermittent flow, and hard deposits for bubbly flow with high superficial velocity. 4. Effect of emulsified water on gelation Crude oil emulsions, in particular, can pose significant flow assurance risks and, with the increase in multiphase production in offshore environments, it has become important to evaluate the impact of emulsified water on crude oil gelation (Visintin et al., 2008). The presence of water over a threshold value can promote gel formation and viscous wax–oil gel emulsions. These emulsions may be stabilized by the presence of polar compounds such as asphaltenes and resins, and can have water cuts as high as 70% (de Oliveira et al., 2010). Paso et al. (2009c) attributed the stability of waxy emulsions to the stabilizing effect of asphaltene particles on oil–water interfaces. They also suggested that, at low-temperature conditions, molecular asphaltene adsorption onto precipitated wax crystals may increase the water wettability of the crystals, thus promoting adsorption at the oil–water interface. Visintin et al. (2008) hypothesized that the solid paraffin stabilizes the emulsion by being strongly adsorbed at the liquid–liquid interface forming Pickering emulsions. They suggested that, by means of the strong interaction between wax crystals and the drop surface, growth of the gel network involves the droplets themselves, forming a volume-spanning wax crystal network with Stratified Smooth Stratified Wavy entrapped dispersed water, as shown in Fig. 2. They observed a sharp increase in shear viscosity, yield stress and pour point for waxy crude oil emulsions with above 25–30% volume of dispersed water, as demonstrated in Fig. 3. It was similarly noted by de Oliveira et al. (2010) that these viscous emulsions can increase gel strength and hinder pipeline restart by increasing the magnitude of the rheological properties of the waxy crude oil gel. They attributed this change to the network developed by the aggregation of the waxy crystals and water. Paso et al. (2009c) also noted drastic increases in fluid viscosities and shear thinning rheological behaviour due to the presence of emulsified water. These observations show the significance of considering the effect of emulsified water on gelation, and Visintin et al. (2008) note the importance of accounting for the impact of emulsified water during field development studies. Water fraction produced by a well generally increases over its lifetime (Lockhart and Correra, 2005; Visintin et al., 2008). Thus it would be very useful to account for the increasing impact of emulsified water on gelation and gel rheology during continued operation. 5. Cloud point, pour point and gel point correlations Some authors have focused on developing correlations between measurable properties of crude oils, such as the pour point, and the conditions under which disruptive wax deposition will occur. Work such as this may help in predicting if and when fatal wax deposition would occur in pipelines carrying particular crudes. Li et al. (2005) cited the results of Holder and Winkler (1965) as indicating that 2 wt.% precipitated wax is sufficient to cause gelling of virgin waxy crudes. Li et al. thus started with previously developed correlations and tried to develop their own correlation linking the temperature at which this 2 wt.% precipitation would occur, Tc (2 wt%), and the pour point, Tpp, and gel point, Tgp, of various waxy crude oils., represented graphically by Figs. 4 and 5. These results and future research could be useful in both determining the tendency for different waxy crudes to gel and harden at particular temperatures, and in devising chemical means of inhibiting this occurrence. 6. Review of some existing wax deposition models Many different authors have proposed models for the flow of waxy crude oils and the associated deposition of solid wax within pipelines, including Farina and Fasano (1997), and Fusi and Farina (2004). Additionally, there are commercial software codes developed to describe these processes, such as those compared by Bagatin et al. (2008). Fasano et al. (2004) reviewed various mathematical models for the flow of waxy crude oils in laboratory experimental loops, in which the oils are assumed to behave like non-Newtonian Bingham fluids, a common assumption for modelling these fluids. Torres and Turner (2005) approached the problem by developing a method of straight lines for solving a Bingham problem for modelling the flow of waxy crude oils. Intermittent Annular Fig. 1. Approximation of wax thickness distribution for various horizontal flow patterns (as described in Matzain et al., 2002). 676 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 Fig. 2. Schematic representation of the gelation of waxy crude oil emulsions. Paraffin crystals that precipitate after a decrease of temperature below the WAT can adsorb on droplet surface (A) or cover it (B), and stabilize the emulsion. Flocs of solid paraffin continuously grow on drops of water or between them (C). Dispersed water is entrapped by a wax crystal network (D): the system spans the entire volume and the gelation is complete (Visintin et al., 2008). Fig. 4. Tc (2 wt%) vs. ASTM pour point (Li et al., 2005). Fig. 3. Pour point of waxy crude oil emulsion with increasing water content (Visintin et al., 2008). concentration can be determined using the chain rule. This is a problem that has been corrected in more recent deposition models such as the one used in the Michigan Wax Predictor developed by Hyun Su Lee. 6.1. Thermodynamic models The earlier models presented here incorporate the wax deposition processes for pipelines containing waxy crude oils, and consider cases where either molecular diffusion or shear dispersion is considered the dominant mechanism involved in wax deposition. However, one of the mistakes commonly introduced to wax deposition models is the assumption that the temperature and concentration gradients are independent, and that, therefore, wax Many researchers have studied the thermodynamics of wax deposition in hopes of creating a model that accurately describes the process. In one example of earlier work, Lira-Galeana et al. (1996)developed a thermodynamic framework for calculating wax precipitation in petroleum mixtures as several distinct solid phases. Solaimany Nazar et al. (2005a) later developed a 677 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 Fig. 5. Tc (2 wt%) vs. gel point (Li et al., 2005). multi-solid phase thermodynamic model for predicting wax precipitation in petroleum mixtures, by using the Peng–Robinson equation of state to evaluate the phase behaviour of both liquid and vapour phases. The model is solved for equilibrium, in which the fugacity of each component is equal in every phase, using Eq. (4), proposed by Prausnitz et al. (1986). " ! !  s DHfi f T DHtri T 1  1   ¼ exp fl i RT RT T tri T fi # Z Tf Z f i 1 1 T i DC pi þ dT DC pi dT þ RT T R T T ð4Þ Here fis is the solid phase fugacity, DHri is the enthalpy of solid– solid transition between different solid phases, T fi is the temperature of fusion, Ttr is the transition temperature, Cp is the heat capacity, and R is the ideal gas constant. Table 1 shows a comparison of experimentally determined WATs for five synthetic paraffin systems and those predicted by the model of Solaimany Nazar et al. (2005a) and a UNIQUAC model developed by Coutinho (1998). The synthetic systems were each composed of decane and a bimodal paraffin distribution. It should be noted that with this and other models which use experimentally determined cloud points to validate the model, there is a limit to how accurately cloud points can be measured which is highly dependent on the particular oil mixture, as discussed by Coutinho and Daridon (2005) and Hammami et al. (2003). Therefore, agreement with experimental data may not prove definitively the accuracy of a model, especially as far as its applicability to a wide range of wax–oil mixtures. Wuhua and Zongchang (2006) also developed a more recent thermodynaamic model, based on the equality of fugacities at equilibrium, which estimates solid precipitation as a function of temperature and composition. For this study, Eq. (5) was used for the condition of equal fugacities in the solid and liquid phases. xSi cL f L ¼ iS iS exp L xi ci fi Z 0 P V Li  V Si dP RT ! and liquid phase respectively. For their model, there was an added level of specificity for modelling particular n-alkane species. Different correlations were used for the fusion enthalpies of n-alkanes and for their enthalpies of solid–solid transition based on both carbon number and whether that number is odd or even. Similarly, transition enthalpies were calculated for different components based on chain lengths. Table 2 shows a comparison of experimentally determined WATs for three crude oils and those predicted by the model of Wuhua and Zongchang (2006) and a similar model developed by Leelavanichkul et al. (2004) and Fig. 6 compares the predictions of the two models to experimental data for wax precipitation as a function of temperature. The data indicates that refinement of thermodynamic correlations, as performed by Wuhua and Zongchang, can increase model accuracy in predicting precipitation as a function of temperature. Further studies, for example, by Edmonds et al. (2008), have also explored ways of representing the wax phase in order to more accurately model wax deposition. Edmonds et al. modelled the wax phase as a continuous distribution of n-alkane components, showing how this eliminated physically unrealistic artefacts found in the predictions of models that lumped n-alkanes into pseudo components. Edmonds et al. carried out simulations with numbers of components approaching 100 and, in order to increase the computational speed, converted phase equilibrium and physical property data into empirical expressions, fitted to the rigorous model. They also noted the importance of considering the deposit limiting mechanism of wax shearing in order for both their model and others from the literature to more accurately agree with the limited field data available from actual pipelines. 6.2. Hydrodynamic model Ramírez-Jaramillo et al. (2001) also developed a multi-solid phase thermodynamic model for predicting wax deposition. In addition, Ramírez-Jaramillo et al. (2004) developed a multicomponent liquid-wax hydrodynamic model for simulating wax deposition in pipelines, which treated molecular diffusion as the dominant mechanism. Fig. 7a shows the computational domain Table 2 Experimental WAT data and model predictions for crude oils (Wuhua and Zongchang, 2006). Sample Experimental results Leelavanichkul model Crude Oil A Crude Oil B Crude Oil C 298.2 K 298.8 K 295.2 K 294.2 K Deviation Present model Deviation 0.4 K 301.3 K 3.1 K 293.4 K 1.8 K 295.4 K 0.2 K 296.0 K 1.8 K 297.8 K 3.6 K ð5Þ Here x is the mole fraction, c is the activity coefficient, V is volume, P is pressure and the S and L superscripts indicate the solid Table 1 Comparison of the WAT between experimental data, UNIQUAC model and Solaimany Nazar et al. model (Solaimany Nazar et al., 2005a). WAT (K) UNIQUAC This model Bim 0 Bim 3 Bim 5 Bim 9 Bim 13 308.75 307.05 308.45 309.65 307.55 309.05 310.37 308.47 309.55 311.33 309.63 310.7 312.81 311.41 312.75 Fig. 6. Wax precipitation as a function of temperature for crude oil A (Wuhua and Zongchang, 2006). 678 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 Fig. 7. (a) Computational domain for a model pipe. (b) Sections of a model pipe with concentric layers (Ramírez-Jaramillo et al., 2004). used by Ramírez-Jaramillo et al. (2004), consisting of a model pipe of length, L, and radius, r, along which a mixture of hydrocarbons flows. The pipe was divided to form a computational mesh, with boundary conditions applied at the ends and along the exterior surface of the pipe, and finite differences were used in the solution of differential equations. Ramírez-Jaramillo et al. (2004) modelled the fluid as consisting of n hydrocarbon components in thermodynamic equilibrium, with mole fractions, in both the liquid and solid phases, that are functions of pressure and temperature. They considered the wax deposition rate to depend on oil composition, oil temperature, external temperature around the pipe, flow conditions, pipeline size and pressure. The model assumed wax deposition by molecular diffusion and removal by shear forces, which would be especially significant at high Reynolds numbers [( quDh /l), where q = density, u = velocity, l = dynamic viscosity, Dh = hydraulic diameter]. In addition, the model included aging by the diffusion of wax into and within the gel-like deposit, which is discussed later in this paper. The mass flux was calculated for all components in the system and summed to give the total flux. Ramírez-Jaramillo et al. (2004) used mass, momentum and energy balances, shown in Eqs. (6)–(8) and assumed mixture incompressibility and quasi-steady state for all rate processes concerning mass, momentum and energy. @ qm þ r  qm m ¼ 0 @t qm   @m þ m  rm ¼ rP þ r  s þ qm g @t qm C v   @T þ m  rT ¼ kr2 T @t ð6Þ ð7Þ ð8Þ Here P, s and g are the pressure, stress tensor and gravitational constant; Cm and k are the heat capacity and thermal conductivity (which is assumed constant), respectively; and m is the average macroscopic velocity of the mixture. They expressed the total amount of deposited wax, M(t,z), in terms of the deposited mass A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 of each component due to molecular diffusion, MMDi(t,L), the mass removed by shear forces, MSR(t,L), and the mass of wax molecules diffusing into the gel deposit, MGD(t,L), as shown in equation. Mðt; zÞ ¼ n X M MDi ðt; LÞ  M SR ðt; LÞ  MGD ðt; LÞ ð9Þ i¼1 Ramírez-Jaramillo et al. (2004) solved for the total deposition rate, @M/@t. The output of their model included solid fractions, density, viscosity, radial mass flux and deposited mass calculations. The model showed reasonable agreement with previously developed models and experimental data for a binary mixture reported by Cordoba and Schall (2001), as shown in Fig. 8 Ramírez-Jaramillo et al. found that the Peclet number and Reynolds number parameters had a significant impact on the amount of wax deposited. 7. Wax aging models 7.1. Counter diffusion Researchers have also explored the properties of wax crystals and wax deposits formed from crude oils. Nautiyal et al. (2008) studied the crystal structure of n-alkane paraffins crystallized from crude oil. Other studies have specifically looked at the way wax deposits change after the initial formation. This is important because, in addition to understanding the mechanisms involved in the deposition of wax in pipelines, in order to fully model the flow of crude oil and accumulation of wax, it is vital to understand the mechanisms that govern the aging of wax deposits. These deposits are not simply static and unchanging. Rather, after a layer of wax has formed along a pipeline wall, its composition gradually changes. The crystalline wax deposit actually behaves like a porous medium with oil trapped within its three-dimensional network (Singh et al., 2000, 2001a). The wax content of this deposited gel can therefore increase with time by diffusion. As this happens, hardness, melting point and heat of fusion of the deposit can change, which could affect decisions about the appropriate method of wax removal to employ in a pipeline. Singh et al. (2000) studied this phenomenon by use of food grade wax dissolved in a mineral oil–kerosene mixture, which was pumped through a closed flow loop setup. Their experimental procedure involved heating a wax–oil mixture to 30–35 °C in a stirred tank and maintaining the temperature of this vessel above 679 the cloud point, while pumping the wax–oil mixture through the flow loop. The flow loop consisted of a 5/8 in. OD steel tubing test section, which was cooled by a heat exchange jacket, and an identical but non-cooled reference section. Pressure taps connected to pressure transducers were used to measure the increase in differential pressure during operation in order to determine the thickness of the deposit within the test section. The bulk fluid inlet temperature, tb, and wall temperature, ta, were also monitored. Singh et al. (2000) determined that a counter diffusion phenomenon, in which wax molecules diffuse into the gel deposit and oil molecules diffuse out of the deposit, is responsible for the aging of the deposit. They furthermore determined that the rate of aging is dependent on oil flow rate as well as the pipeline wall temperature. In their experimental setup with oil in a closed flow loop with cooled walls, there was a rapid decrease in internal radius measured over the first day followed, which then plateaued. Similarly, the increase in the measured weight fraction of wax slowed after a rapid change in the first day. The wax content (determined using high-temperature gas chromatography, HTGC) of the gel deposit also changes over time, with the proportion of lighter components decreasing after the first day, while the proportion of heavier components increases. The data recorded by Singh et al., showed that the wax content of the deposit continued to increase even after the thickness stabilized, and that waxes of chain length higher than 29 diffused into the deposit while the ones with lengths less than 29 diffused out. 29 is the critical carbon number, CCN, for the given operation conditions; a value that could be useful in determining what inhibitors to use in a particular well or pipeline, based on whether or not they can inhibit crystallization of waxes above the CCN (Paso and Fogler, 2003). Singh et al. (2000) were able to develop a mathematical model to describe the wax deposition process in a laboratory flow loop by solving numerically a coupled system of differential and algebraic equations of heat and mass transfer inside and outside the gel deposit. Eq. (10) shows the mass balance they used to relate the rate of change of wax in the gel deposit to the radial convective flux of wax molecules from the bulk of the fluid–gel interface. d ½pðR2  r 2i ÞF w ðtÞLqgel  ¼ 2pr i Lk1 ½C wb  C ws ðT i Þ dt ð10Þ Here R is the original internal radius of the pipe, ri is the internal radius during deposition (average radius available for flow of oil), F w is the weight fraction of solid wax in the oil, L is the length of pipe, qgel is the density of the gel deposit (considered constant), k1 is the mass transfer coefficient, Cwb is the bulk concentration of wax, Cws is the solubility of the wax in the oil solvent derived in terms of Ti, and Ti is the interfacial temperature, which was obtained from the energy balance shown in equation, 2pr i hi ðT b  T i Þ ¼ 2pke ðT i  T a Þ  2pri k1 ½C wb  C ws ðT i ÞDHf lnðR=r i Þ ð11Þ where hi is the interface heat transfer coefficient, ke is the effective thermal conductivity of the gel, and DHf is the heat of solidification of the wax. The heat and mass transfer coefficients were obtained using Hausen, Seider and Tate correlations. Eq. (12) shows the deposit growth equation derived by Singh et al. (2000), by relating the rate of addition of wax to the gel deposit in the flow loop to the radial convective flux of wax molecules from the bulk to the fluid–gel interface and the diffusive flux into the gel at the gel interface. 2pr i F w ðtÞqgel Fig. 8. Dimensionless wax thickness distribution vs. time. Comparison of model predictions with experimental data for the 30:70 (cyclo C6C19:C8) ratio (RamírezJaramillo et al., 2004).   dr i dC w ¼ 2pr i k1 ½C wb  C ws ðT i Þ  2pri De dt dr i ð12Þ Here De is the effective diffusivity of wax inside the gel deposit. Coupled differential equations from Eqs. (10) and (12) were solved by Singh et al. throughout the length of the pipe at each time 680 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 r¼ Fig. 9. Kinetic growth of crystals for oil sample from X-ray diffraction analysis at 10 °C (Coutinho et al., 2003). instant using Runge–Kutta algorithms, along with equations for dTi/dr. This system of equations was used to obtain the trajectories of thickness and wax content at each location in the pipe. This model showed excellent agreement with experimental data. However, Lee (2008) has shown that the mass-heat transfer correlations used by Singh et al. incorrectly assume independent heat and mass transfer, and were successfully applied only because of a high degree of supersaturation in the laminar boundary layer. Other researchers, such as Hernandez et al. (2004), modelling wax deposition in pipelines has begun incorporating wax aging into their models. Additionally, Singh et al. (2001b) were able to develop a thermodynamic model to predict both cloud point temperatures and CCNs of wax–oil mixtures, where CCN is a function of the mixture composition as well as the wall temperature. This model also showed good agreement with experimental data, predicting the cloud points and the CCNs of model oils with good accuracy. 7.2. Ostwald ripening It must be noted that the diffusion mechanism used by Singh et al. (2000, 2001a,b) is not the only possible mechanism for explaining the aging process. In fact Continuo et al. (2003) found that aging of wax deposits takes place even for samples kept under isothermal conditions. The diffusion mechanism for aging cannot account for this as it is driven by temperature-composition gradients. Coutinho et al. reported broadening of peaks on X-ray diffraction and Cross Polar Microscopy (CPM) images showing an increase in the crystallite’s size. Fig. 9 shows an example of their results from X-ray diffraction analysis, for which the crystallite size, r, is related to a shape factor K, and the measured peak position, h, and breadth, b, by equation. Kk b cos h ð13Þ Coutinho et al. (2003) noted an increase in crystal size observed by CPM at a temperature in the neighbourhood of the pour point. They reported an increase from 6.4% to 15.3%, over 110 h, for the fraction of a CPM image occupied by crystals. Furthermore, they obtained Differential Scanning Calorimetry (DSC) thermograms under the same conditions, which did not show detectable heat effects associated to this change in the crystal size, as seen in Fig. 10. They noted that this can only occur when the heat of crystallization released is used by the melting of an equivalent mass of crystals. This indicates that wax deposits in crudes suffer recrystallization. Coutinho et al., thus, conclude that Ostwald Ripening is also a mechanism responsible for the aging of wax deposits. 8. Correct analogies for correlated heat and mass transfer in turbulent flow Many existing wax deposition models assume that heat and mass transfer can be related by the chain rule, which assumes that the system is at thermodynamic equilibrium (which may not be true), or use mass-heat transfer analogies, such as the Chilton– Colburn analogy, which are valid only when the temperature and concentration fields are independent. Venkatesan and Fogler (2004) noted that such heat-mass transfer analogies are not applicable for predicting the mass transfer rates in turbulent flows, where the concentration field is correlated to the temperature field and the concentration boundary layer and temperature boundary layer thicknesses are not independent. They showed that use of the Colburn analogy in this case would result in a significant over-prediction of wax deposition. They also proposed a method for estimating the convective mass transfer rate using the Nusselt number and the experimentally obtained solubility curve. However, this method would only be valid for thermodynamic equilibrium in the mass transfer boundary layer, when precipitation kinetics are not limiting. For the development of more rigorous and accurate models, it has been necessary for researchers to explore the correct relationship between heat and mass transfer. Lee (2008) investigated the combined heat and mass transfer phenomenon under laminar and turbulent flow conditions using the finite difference method. He developed a model based on that of Singh et al. (2000), which could be applied for any precipitation kinetics. For turbulent flow, Lee showed that the solubility method proposed by Venkatesan Fig. 10. Thermogram for oil C (thick line). The isothermal region above 5000 s shows that there are no detectable heat effects related to the aging of the wax (Coutinho et al., 2003). A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 and Fogler (2004) under-predicts deposition by assuming that the concentration profile in the mass transfer boundary layer follows the thermodynamic equilibrium limit between temperature and concentration at every point. This was contrasted with the overprediction of the Chilton–Colburn analogy, which gave maximum supersaturation. The comparison showed that these two approaches constitute the limiting cases for deposition, and that the actual concentration profile, which is dependent on the precipitation kinetics, falls between those calculated by the two methods. Instead of using those two limiting cases, Lee (2008) employed a computational approach for calculating the Nusselt numbers [(hL/kf), where L = characteristic length, kf = thermal conductivity of the fluid, h = convective heat transfer coefficient] and Sherwood numbers [(KL/D) where L is a characteristic length, D is mass diffusivity, K is the mass transfer coefficient] according to following equations. Nu ¼ Sh ¼ ð2ri Þ@T @r rr i Tb  Ti ð2r i Þ@C @r rri Cb  Ci ¼ ð2r i Þhi k ð14Þ ¼ ð2r i ÞkM Dw0 ð15Þ The temperature and concentration gradients at the fluid-deposit interface, needed for these calculations, were obtained by solving mass and energy balance equations, as shown in following equations. mz   @C 1 @ @C  kr ðC  C ws Þ ¼ rDwo @z r @r @r ð16Þ mz   @T 1 @ @T  bðC  C ws Þ ¼ r aT @z r @r @r ð17Þ Here vz is the axial velocity, Dwo is the molecular diffusivity of wax in oil, kr is the thermal conductivity, aT is the thermal diffusivity, and the precipitation term b(C–Cws) is considered negligible. Lee first did this for laminar flow. Using a discretized form of the mass-heat transfer equation along with their appropriate boundary conditions, Lee wrote the governing equations in matrix form. Then by inverting these matrices to give the radial temperature and concentration profiles, and numerically marching from the inlet of the tube to the exit he could obtain the complete set of temperature and concentration profiles with respect to the radial and axial position. From this, Lee (2008) showed how the Sherwood number profile as a function of axial distance would change for different precipitation rate constants. This showed that if there was no precipitation in the boundary layer, the heat and mass transfer rates become independent of each other, resulting in a supersaturation curve. However, as the precipitation rate constant increases the Sherwood number is decreased, because wax molecules would not reach the oil–deposit interface, and would instead flow down to exit as solid particles. To obtain the Sherwood and Nusselt numbers under turbulent conditions, Lee (2008) used the same procedure with governing equations modified for turbulent flow to include the turbulent axial velocity profile and the thermal and mass transfer eddy diffusivities. The wax concentration profiles in the turbulent boundary layer obtained this way showed that heat and mass transfer become independent as the precipitation rate constant approaches zero, resulting in the Chilton–Colburn analogy-derived concentration profile. Conversely, as the precipitation rate constant increases, precipitation in the boundary layer increases, with concentration approaching the solubility limit for thermodynamic equilibrium. 681 In his model, after calculating the Sherwood and Nusselt numbers, Lee (2008)could then solve the growth and aging governing equations from Singh et al. (2000)’s model to solve for deposit thickness and wax fraction at each time step in his computational procedure. Lee (2008)showed that there was excellent agreement between the results of his model and lab-scale laminar flow loop experimental data. There was also good agreement with turbulent lab-scale results, though there was significant discrepancy for early times at higher volumetric flow rates, possibly due to sloughing. The results of the computational model also closely matched large-scale flow loop data. The results obtained by Lee (2008) show that this model is applicable for varying precipitation kinetics, and provides a robust and rigorous way of predicting wax deposition under a range of turbulent conditions. 9. Inhibition of wax deposition The most effective way of dealing with the problem of wax deposition in crude oil pipelines would be to prevent it from occurring in the first place. Thus, researchers have investigated different methods of inhibiting the deposition process. These include the heat insulation of subsea pipelines to actually inhibit precipitation by keeping pipeline temperatures as high as possible (Quenelle and Gunaltun, 1987), the internal coating of pipelines with plastics (Patton, 1970; Bummer, 1971), and also methods of preventing wax deposition on pipeline walls, such as the use of chemical inhibitors, which will be discussed in more detail in this paper. 9.1. Chemical inhibitors Many researchers have studied the efficacy of different inhibitors of wax deposition and the mechanisms by which they inhibit this deposition, including Jorda (1966), Mendell and Jessen (1970), Fulford (1975), Addison (1984), Newberry and Barker (1985), Fielder and Johnson (1986), Singhal et al. (1991), Jang et al. (2007), and Tinsley et al. (2007). The efficacy of commercially available inhibitors tends to be limited, and has to be evaluated on a case-by-case basis. Wang et al. (2003), for instance, found, when testing some wax inhibitors, that the inhibitors they had studied reduced the total amount of deposition, but had only limited success in suppressing the deposition of the high molecular weight paraffin components (C35 and above). This resulted in harder wax deposits than in the absence of an inhibitor. They also found that inhibitors most able to depress the WAT were more likely to be superior products for decreasing total wax deposition, and that the addition of the corrosion inhibitor, oleic imidazaline (OI), significantly increased the efficacy of deposition inhibition. Fig. 11 shows some of their results, where PIE is the paraffin inhibition efficiency, the amount of wax deposited with inhibitor as a wt.% of amount deposited without it. Bello et al. (2006) also studied the efficacy of commercial wax inhibitors, particularly on Nigerian crude oils. They found that the use of a trichloroethylene–xylene, TEX, binary system as an additive was actually more effective and economically feasible than the use of commercial inhibitors. Other researchers have noted the need to tailor inhibitor treatments to particular crudes in order to maximize efficacy. Manka and Ziegler (2001), for instance, found that additives work best when matched to the paraffin distribution in the crude oil being treated. Similarly, Carmen García (2001) noted a strong relationship between a specific paraffin inhibitor’s efficiency and the crude oil composition, which would require case-by-case consideration for selecting inhibitors for use in the field. Additionally, there is the consideration of the environmental conditions under which a wax inhibitor is to be used, since, for 682 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 Fig. 11. Effect of wax inhibitors (100 ppm) and oleic imidazoline, OI, (200 ppm) on paraffin deposition from a mixture of paraffin wax in C10 solution (Wang et al., 2003). operations at particularly low temperatures, the inhibitor formulation must be winterized to allow effective delivery under those conditions (Manka et al., 1999; Jennings and Breitigam, 2009). Also, while work continues towards developing new, more effective wax inhibitors, it remains the case that inhibitors typically do not provide 100% inhibition, and so are used in conjunction with remediation methods such as pigging (Jennings and Breitigam, 2009; Kelland, 2009). 9.2. Types of chemical inhibitors There are different mechanisms by which chemical inhibitors can prevent wax deposition or gelling in pipelines. They can lower the WAT or pour point or can modify the wax crystals so as to prevent their agglomeration and deposition (Kelland, 2009). The chemicals that modify the WAT are usually referred to as wax inhibitors or wax crystal modifiers, while those that affect the pour point are known as pour point depressants (PPDs) or flow improvers; although there is a great deal of overlap in terms of the chemistry and mechanisms of these two classes (Kelland, 2009). Some detergents or dispersants that act as wax inhibitors, such as polyesters and amine ethoxylates, may act partly by modifying the surface of the pipe wall, rather than just the wax crystals, to prevent adhesion (Pedersen and Rønningsen, 2003), and many effective wax inhibitors create weaker deposits that are more easily removed by shear forces (Manka et al., 1999; Kelland, 2009). The main types of wax inhibitors and PPDs include ethylene polymers and copolymers, comb polymers and assorted other branched polymers with long alkyl groups, such as alkyl phenol–formaldehyde, which are not as effective as comb polymers when acting on their own as flow improvers (Kelland, 2009). 9.2.1. Ethylene copolymers This group includes ethylene/small alkene copolymers, ethylene/vinyl acetate (EVA) copolymers, and ethylene/acrylonitrile copolymers (Kelland, 2009). More specifically, examples of these polymers used in wax inhibition studies include poly (ethyleneb-propylene) and poly(ethylene butene) polymers (Tinsley et al., 2007; Kelland, 2009). Random, low molecular weight EVA copolymers, illustrated in Fig. 12, are widely used and investigated as wax inhibitors (Kelland, 2009). The effectiveness of the EVA copolymer as an inhibitor is influenced greatly by the percentage of vinyl acetate in the copolymer. The, more polar, vinyl acetate content aids solubility and lowers crystallinity and so is necessary for the depression of the WAT, whereas the polyethylene content is necessary to allow for co-crystallization with structurally similar wax, but, on its own, has little effect on crystallization (Kelland, 2009). 9.2.2. Comb polymers Comb-shaped polymers, illustrated in Fig. 13, have been studied extensively as wax inhibitors by researchers such as Duffy and Rodger (2002), Duffy et al. (2004), Jang et al. (2007), and Soni et al. (2008). They are usually made from (meth)acrylic acid or maleic anhydride monomers, or both, and generally provide improved wax inhibition compared to the ethylene copolymers (Kelland, 2009). One proposed mechanism for their action as PPDs is that Fig. 12. Ethylene/vinyl acetate (left) and ethylene/acrylonitrile copolymers (right) (Kelland, 2009). A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 683 Fig. 13. Traditionally depicted structure of a comb polymer (left). X is a spacer group. The structure looking down the helical backbone (right) (Kelland, 2009). comb polymers reduce the ability of wax crystals to agglomerate into a gel structure by introducing defects or repulsive forces (Jang et al., 2007; Soni et al., 2008; Kelland, 2009). As illustrated by Figs. 14 and 15, they can accomplish this by providing nucleating sites for wax crystals on their paraffin-like pendant chains while a polar backbone impedes the formation of an interlocking wax network (Soni et al., 2008). In selecting the most effective comb polymers for use with a particular crude oil, researchers have found that the length of the side chains plays an important role. For example, Manka and Ziegler (2001) found that matching the average pendant chain length of comb polymer PPDs with the paraffin distribution of a crude oil provided the greatest pour point depression. Also, Jang et al. (2007) obtained results which suggested that using comb structures with side arms of such length as to interact favourably with the fraction of oil most likely to crystallize into the hard wax phase provided the best wax inhibition. This creates a problem for especially long-chained waxes, for which it would be difficult to introduce a comb polymer (or ethylene copolymer) of sufficient length to provide efficient inhibition, and also makes it important to have a range of comb polymers available for treatment of different crudes (Kelland, 2009). 9.2.3. Wax dispersants These are surfactants that adsorb onto pipe surfaces and reduce the adhesion of waxes to those surfaces, possibly by changing the wettability of the pipe surface to water-wet, or by creating a weak layer from which wax crystals are easily sheared off, or by adsorbing onto the wax crystals and reducing their tendency to stick together (Kelland, 2009). Some researchers have worked on developing their own dispersant formulations. Groffe et al. (2001), for instance, developed their own inhibitor that shows wax dispersant behaviour and anti-sticking properties. They suggest that this chemical, referred to as P5, interferes with the wax crystal growth mechanism by preventing the formation of a three-dimensional network, and thus reduces the pour point and improves the flow characteristics of crude oils. Fig. 16 shows the effectiveness of P5 in preventing the adherence of wax from crude oils to a steel surface. Typical, low-cost wax dispersants include alkyl sulfonates, alkyl aryl sulfonates, fatty amine ethoxylates and other alkoxylated products, but these dispersants have shown limited effectiveness in the field when not blended with polymeric wax inhibitors (Kelland, 2009). Dispersants, however, have been used successfully to support the functions of polymeric flow improvers because of their ability to hinder wax settling and deposition (Al-Sabagh et al., 2007). 9.2.4. Polar crude fractions It has been found that polar extracts from crude and distillate oils, which can be extracted using super critical gases such as carbon dioxide or ethylene, and which contain asphaltenes, resins and aromatics, can be a potential source of low-cost flow improvers (Kelland, 2009). Venkatesan et al. (2003) studied the effects of Fig. 14. Characteristic structure of a comb polymer PPD (Soni et al., 2008). 684 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 Fig. 15. Prevention of interlocking of wax crystals by polymer additives by (a) providing nucleating sites to asphaltene as well as wax molecules; (b) polar parts hinder the co-crystallization of both wax as well as asphaltenes (Soni et al., 2008). Fig. 16. Effect of 500 ppm of P5 on wax adherence to a steel surface exposed to three different crude oils (Groffe et al., 2001). asphaltenes on the formation of paraffin gels in crude oil. They found that the addition of asphaltenes depressed the gelation temperature of model wax–oil mixtures, as summarized in Figs. 17 and 18; although they found that beyond certain thresholds, further addition resulted in macroscopic phase separation of the mixture, attributable to gravity settling. Kriz and Andersen (2005) also studied the effect of asphaltenes on wax crystallization in crude oils. They found that this effect A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 685 certain degree. These are all properties associated with PPDs and proposed mechanisms for their action, which include co-precipitating with waxes and hindering crystal network growth or coating wax crystals to prevent agglomeration. Thus, as also suggested by the observations of Kriz and Andersen (2005), it stands to reason that asphaltenes affect wax precipitation by the same mechanisms as other flow improvers such as comb polymers. Fig. 17. Gelation temperature depression (cooling rate of 1 °C min1) for a foodgrade paraffin wax (Wax 1) and a laboratory-grade paraffin wax (Wax 2) by addition of asphaltene (Venkatesan et al., 2003). Fig. 18. Depression in yield stress of Wax 1 system (at temperature, Tys, below the gelation temperature) upon asphaltene addition (Venkatesan et al., 2003). depends strongly on the degree of asphaltene dispersion or flocculation more than on the asphaltene type or origin. They reasoned that the asphaltenes, when well dispersed at very low concentrations, are easily accessible for any kind of interaction with the paraffins and can be fully incorporated into the wax structure. They noted a delay in crystallization, which indicated that building the asphaltene molecules into this structure would require a higher driving force because of asphaltene–paraffin spatial interference. This would suggest that the asphaltenes are acting by some of the same mechanisms proposed for inhibition by polymeric inhibitors. In agreement with the results of Venkatesan et al. (2003), Kriz and Andersen (2005) also saw a depression in yield stress and WAT, which they accounted for by suggesting that asphaltene molecules flocculate together when over a critical concentration, with possible co-precipitation with waxes, resulting in an unorganized asphaltene–paraffin composite rather than a proper wax network. They note, though, the need for further understanding of the way asphaltenes and waxes interact during wax crystallization, and another study by Yang and Kilpatrick (2005) indicated that asphaltenes and waxes do not co-precipitate in solid organic deposits. In accounting for the observed flow improver properties of asphaltenes, Venkatesan et al. (2003) noted that asphaltenes have polar groups as well as alkane chains and are soluble in oil up to a 9.2.5. Short-chain alkanes Senra et al. (2008) analysed how n-alkanes impact the crystallization of one another, and Senra et al. (2009) studied the gelation characteristics of long-chained n-alkanes in a short-chained n-alkane solvent, looking at the inhibition of gel formation caused by the addition of other crystallizable n-alkanes to long-chained n-alkanes, which are the primary component of wax deposits. As is the case with polymeric inhibitors, the results obtained by Senra et al. (2009) indicate that the ability of a particular short-chained n-alkane to inhibit gel formation by a longer-chained one depends on the particular pairing. The trend of this inhibition was found to depend on the extent of differences in size and solubility characteristics between the long-chained n-alkane and the added shorter-chained one as demonstrated by the results in Figs. 19 and 20. Senra et al. (2009) found that, for a given wax percent of a longchained n-alkane, polydispersity and co-crystallization weaken the gel formed in spite of the fact that more crystallizable wax is present in solution. In cases where co-crystallization was possible, such as in a C36/C32 system, they witnessed a noticeable decrease in pour point and gelation temperature with the addition of small amounts of the shorter n-alkane. This, they accounted for by the defects in the crystal structure that would be required to accommodate the C32 crystals that co-crystallize with the C36. This would make the formation of large crystals and a volume-spanning network gel more difficult, in the same way that the inclusion of polymeric flow improvers into wax crystal structures inhibits aggregation and gel formation. The addition of increasing concentrations of the shorter-chained co-crystallizing n-alkane, however, resulted in a minimum pour and gel point followed by an increase. This was accounted for by a limit to how much the addition of the shorter-chained n-alkane can decrease crystal size, beyond which further addition only adds more material to form wax crystals. On the other hand, with n-alkanes of similar size which did not co-crystallize, such as in a C36/C28 system, Senra et al. (2009) saw a very different trend. In this case, low concentrations of the shorterchained n-alkane had no effect on the pour and gel points, until a Fig. 19. Effect of varying the wax percent of C28 and C32 on the pour points and gel points of 4% C36 solutions in dodecane (Senra et al., 2009). 686 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 C32/C24 system, where co-crystallization does not occur, the C24 was seemingly too small to influence the crystal structure and impact C36 gelation, and so simply acted like a solvent. These results show that an understanding of how oil composition affects wax–oil gel formation can help significantly in implementing inhibition measures. 9.3. Surfaces that prevent wax deposition Fig. 20. Effect of varying the wax percent of C28 and C30 on the pour points and gel points of 4% C32solutions in dodecane (Senra et al., 2009). concentration at which a sharp decrease was witnessed in both followed by a gradual increase. This was accounted for by the fact that, at low concentrations, the more soluble shorter-chained nalkane will not crystallize out and will not be present in high enough concentration to disrupt the crystallization of the longerchained n-alkane, so will have no effect. Then, at a high enough concentration, the association of the shorter-chained n-alkane molecules with the longer-chained n-alkane crystals would disrupt gel formation. Then gelation will occur as the more soluble shorterchained alkane is added in high enough concentration to crystallize sufficiently to form a gel. Senra et al. supported this analysis with the results of cross-polarized microscopy experiments. Furthermore, for a C32/C30 system, Senra et al. (2009) noted that, due to the very similar chain length and solubility characteristics, there was only a slight initial decrease in pour point due to the formation of co-crystals, which would have relatively few vulnerable points since the two n-alkanes are so similar. Beyond that, the C32/ C30 system behaved much like a monodisperse system. Also, for a There is an obvious appeal to developing wax-repellent surfaces for use in oil pipelines as this would limit or eliminate the need for wax inhibition and removal measures to maintain normal operation. With a proper understanding of the mechanisms by which waxes adhere to oil pipeline walls it would be possible to create pipelines in which the nature of the walls makes adhesion unfavourable. Paso et al. (2009a) performed a comprehensive review of the use of non-stick and anti-adhesive coatings for inhibiting solid–liquid deposition phenomena, including the use of metal surface treatments and synthesized polymers. The classes of materials that they found promising included fluoro-siloxanes, fluoro-urethanes, oxazolane-based polymers and hybrid diamondlike carbon and polymer coatings. Fig. 21 shows some of the reported surface free energies of surfaces for paraffin control investigated by Paso et al. (2009a), which gives an indication of the ability for waxes to interact with those surfaces, and thus the potential of these surfaces for preventing wax deposition. Further study of the mechanisms involved in wax adhesion, hopefully, will result in even more effective surface treatments in the future. 9.4. Cold flow Heating or insulation of subsea pipelines can be used to try to prevent cooling of the pipeline wall below the WAT. However, a Fig. 21. Surface energy reduction possible with novel surface technologies (Paso et al., 2009a). A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 very different method of inhibiting wax deposition on pipeline walls, discussed by Merino-Garcia and Correra (2008), is the use of Cold Flow technology. This approach suggests that it might be possible to prevent deposition on pipeline walls by reducing the bulk temperature within the pipeline to be equal to the temperature of the sea water around it, thus eliminating the temperature gradient. This would allow for the waxes to be transported as a solid dispersion within the bulk fluid. While wax deposition may, in fact, become negligible in the case of zero heat flux, even below the WAT, much work would still be required to develop the technology required for effectively cooling the bulk fluid to this condition and for transporting the resulting cold slurry over long distances. Ilahi (2005) also discussed SINTEF and NTNU Cold Flow technology. Additionally Haghighi et al. (2007) and Azarinezhad et al. (2010) proposed a wet cold flow-based concept, termed HYDRAFLOW, for preventing gas hydrate agglomeration, with the potential benefit of wax inhibition. Gas hydrates are the solid solutions of gas components and water. Hammerschmidt (1934) discovered the formation of hydrates in natural gas systems. Hydrates like waxes have concerned deep-water production at seafloor depths of 1–3 km and temperatures between 2 and 4 °C (Gudmundsson, 2002), conditions which encourage hydrate plug formation. Several studies have been done on kinetics of hydrate formation. Those previous studies can be categorized into two main subjects: nucleation and growth. In contrast to previous studies, gas pipelines hydrate agglomeration plays an important role. After the break-up of the hydrate film along the interface, hydrate particles agglomerate to form a hydrate plug (Lingelem et al., 1993) like wax. Herri et al., 1999 analyzed the particle size distribution of hydrate particles with the particle balance equations and a mass transfer model. However it is difficult to describe agglomeration from experimental observation. The particles start to agglomerate just after the nucleation process (Mersmann, 2002). The observed particle size distribution is a result of kinetic contributions such as nucleation, growth, agglomeration, breakage, and attrition. Viscosity is also a contributory factor to particle agglomeration (Mersmann, 2002). 10. Wax removal methods If wax deposition cannot be prevented, then it is imperative to regularly remove accumulated wax from the inside of pipeline walls in order to prevent the total blockage of the line. Several methods have thus been developed for the removal of wax deposits, including complete blockages of pipelines. Traditional methods of wax removal in the petroleum industry have always had problems and limitations, and they include mechanical removal, the use of bottom hole heaters, the use of exothermic reactions such as that between magnesium bars and hydrochloric acid, and the use of paraffin solvents (Woo et al., 1984). Research continues to be done to find the most efficient, cost-effective and safe methods of removing wax deposits and blockages. Furthermore, some researchers have worked on modelling the operating conditions necessary for the successful and safe restart of gelled pipelines, in which gelled waxy crude needs to be displaced using applied pressure. 10.1. Pigging The practice of pigging is a way in which wax removal is commonly accomplished in the field. With this method, deposited wax is mechanically removed by launching a pipeline pig along the line to scrape wax from the walls as it is forced along by the oil pressure. This, however, poses the risk of forming a wax plug downstream from the pig as the scraped wax accumulates and is 687 compressed ahead of the pig. In such an event the pipeline could be lost. The use of bypass pigs tries to address this problem. When the differential pressure across such a pig becomes too high, because of the accumulation of solid wax and debris ahead of it, the bypass pig allows liquid to flow through it and disperse the accumulated solid ahead. However, there is always the danger that if pigging has to be temporarily suspended due to mechanical failure, or that if the pigging frequency for a pipeline is not correctly optimized, that the result will be a stuck pig and sizable production losses (Fung et al., 2006). Wang et al. (2008) studied the use of regular and bypass pigs in the removal of wax from pipelines in a laboratory system. The test facility used consisted of a 20 ft test section of carbon steel pipe, a mineral oil tank, a pump to push the pig with liquid as in real pigging operations, and a receiving tank to observe the structure of the pigged materials. Four pressure transducers were installed to monitor pressure change along the test section during pigging operation. Candle wax with different oil contents was cast as a film or plug for measuring wax breaking force or plug transportation force, respectively. After casting, the waxy spool pieces were mounted on the test section and the pig was pushed through the pipe by oil from the pump, removing the wax film or plug while the pressures at four locations along the test section were recorded. They concluded that the wax breaking force increases with the decrease in oil content and the increase in wax layer thickness; transportation force per unit plug length is affected by oil content; transportation force decreases with the presence of oil due to lubrication effects; and bypass pigs exhibit a very similar breaking force behaviour when compared with regular pigs. Other studies have focused on determining the optimal frequency of pigging to maintain a pipeline and avoid plug formation. 10.2. Inductive heating Another possible wax removal process, studied by Sarmento et al. (2004), is the use of inductive heating of a plugged section of pipe. They proposed this as an alternative to the use of chemicals that react exothermically at the wax blockage to melt it, for cases when the pipeline is completely blocked in a horizontal section so that it is impossible to flow chemicals to the blockage. They tested this method using the experimental setup shown in Fig. 22. They found that the steel layers which compose commercial flexible lines can be heated by induction and the heat transferred to a solid wax plug in the interior of the line. They also found that their mathematical model, which agreed well with available experimental results, suggested that the power levels required for large-scale inductive heating might be feasible for removing wax blockage in field applications with undersea pipelines. 10.3. Biological treatment Biological wax removal methods have also been studied in recent years by researchers such as Rana et al. (2010), who developed systems of paraffin-degrading bacterial consortiums with nutrient supplements and growth enhancers for controlling paraffin deposition in the tubular and well bore region and in surface flow lines. Their results showed that their systems were highly effective, eliminating the need for repeated scrapings of wax over a period of several months. These methods are especially important because, if successfully implemented, they have the benefit of providing continuous control of wax deposition in pipelines through constant biodegradation, rather than just providing a very temporary fix. Etoumi et al. (2008) studied the use of Pseudomonas bacteria for the reduction of wax precipitation in waxy crude oils. Their results 688 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 Fig. 22. Schematic view of experimental test section for wax removal by inductive heating (Sarmento et al., 2004). showed the ability of Pseudomonas species to emulsify immiscible hydrocarbons such as kerosene, toluene, xylene and crude oil, an effect also studied by others, such as Sifour et al. (2007). The observed overall effect of Pseudomonas treatment on crude oil showed a reduction in the concentration of long-chain hydrocarbons (C22+). Etoumi et al. concluded that Pseudomonas species may be an efficient species for reducing paraffin deposition, and that the speed of the biochemical action on crude oil is faster within the first 7 days. They also concluded that an observed reduction in viscosity and WAT is indicative of the conversion of long-chain alkenes to short ones. Additionally, He et al. (2003) determined through field tests, that two Bacillus species and a Pseudomonas species showed good paraffin removal properties in test wells, increasing oil production and eliminating the need for more expensive wax removal processes. Thus, biological wax removal methods may prove to be quite effective and economically beneficial and warrant further study. If a biological system can be successfully and cheaply applied under the conditions in subsea pipelines then it will provide an extremely effective method of controlling wax deposition. 11. Restart of gelled pipelines In subsea pipelines carrying waxy crude oils that have to be shut down temporarily for operational or emergency reasons, the oil will eventually cool below its gel and pour points resulting in the formation of a gel throughout the pipeline consisting of precipitated wax in a viscous matrix (Chang et al., 1999). This occurrence complicates the restart procedure, as the gelled oil would need to be displaced in order to resume normal operations. Numerous researchers have addressed this problem, including Smith and Ramsden (1978), Chang et al. (1999), Davidson et al. (2004), Frigaard et al. (2007), and Vinay et al. (2007). Chang et al. (1999) modelled the isothermal restart of gelled pipelines by the application of higher than normal operating pressures. In this start-up scenario, oil is pumped into the gelled line at high enough sustained pressure to overcome the static yield stress of the gel, thus breaking up the blockage and clearing the line. The viscoplastic nature of waxy crude oils and their timedependent behaviour complicate modelling. In order to describe the breakdown of the gel structure along with a decrease in viscosity, Chang et al. (1999) defined the static yield stress of the gel, ss, as the critical shear stress value for determining whether the start of a flow from a rest state will occur. Furthermore, they defined the dynamic yield stress, sd, as the parameter for describing the relationship between shear stress and shear rate in a flow state after yielding. However, the description of this yielding behaviour has seen many variations and disagreements among different authors. Many studies have been published regarding the rheology of waxy crudes and their gels, the dependence of gel properties on shear and thermal histories, and how they yield (Wardhaugh et al., 1988; Chang et al., 1998, 2000; Lopes-da-Silva and Coutinho, 2007; Lee et al., 2008; Oh et al., 2009). Wardhaugh and Boger (1991), for instance, defined yield stress as ‘‘the shear stress at which the gelled oil ceases to behave as a Hookean solid,’’ and referred to bulk yielding phenomena, when gross yielding behaviour is observed, as the yielding stress or yielding point. Houwink (1958) described a transition from elastic behaviour to plastic behaviour and then to viscous flow, distinguished by a lower and a higher yield stress. Meanwhile some researchers, such as Barnes (1999), who noted the high degree of variation in the definition of yield stress, maintained that no real yield stress exists, even for very non-Newtonian liquids. They argue this because these liquids continue to flow or creep even below an apparent yield stress. Barnes notes, however, that the concept of a yield stress is useful for describing behaviour over a limited range. 11.1. Time-dependent gel degradation Time-dependent gel-degradation is one of the important complications in modelling the restart of gelled pipelines. Ongoing efforts to model the time-dependent rheology of gels, in order to be able to model gel breakdown under stress, draw on research such as that of Cheng and Evans (1965), Petrellis and Flumerfelt (1973), and Rao et al. (1985). Recent studies of the time-dependent rheological behaviour and breakdown of wax–oil gels include that done by Paso et al. (2009b), in which the mechanical behaviour of a model wax–oil gel was examined under various shear rates. Paso et al. observed a convergence of shear stress values for different shear rates at absolute strain magnitudes greater than 0.1, as shown in Fig. 23. This was indicative of gel strength following a path-independent function of the absolute strain imposed on the gel, and further indicated that the gel structure is a point function of the absolute strain. Based on this they concluded that, in A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 689 their model wax–oil gel at constant shear rate conditions. They concluded that a well-defined mechanism controls the rupture of wax crystal–crystal network linkages, and that the rheological modelling framework based on the structural parameter, k, provides an appropriate physical representation of the breakage process, even for crude oils in the field with a variety of hydrocarbon and additive components that may cause a deviation from third order degradation kinetics. They also proposed a model for describing shear stress responses associated with changing shear rates during gel degradation by applying a time-dependent Bingham constitutive equation to experimental stress–strain data obtained while increasing the shear rate. 11.2. Examples of restart models Fig. 23. Measured shear stress during breakage of a wax–oil gel at shear rates ranging from 105 s1 to 1 s1 (Paso et al., 2009b). modelling the breakdown of a wax gel at low shear rates, the entire shear history could be represented by a single dimensionless variable in the form of the absolute strain. Paso et al. (2009b), furthermore, determined that the maximum shear stress did not provide a useful parameter to characterize the gel structure. Thus, in order to define a structural parameter, k, representing the fraction of unbroken crystal–crystal linkages remaining in the gel structure at a given shear stress, they did so in terms of the experimental stress near the convergence point. They then used this structural parameter in an nth order degradation model to describe the gel breakage model, as shown in following equation. 1 1 ðk  ke Þ1n  ðk0  ke Þ1n ¼ ac_ b t 1n 1n ð18Þ Here k0 and ke are the initial and equilibrium structural parameter values, and the degradation rate parameters, n and ac_ b , were determined by fitting experimental values of k to equation (18) via a least squares minimization procedure, with ke assumed to be 2  103. Paso et al. (2009b) were able to obtain good model fits to experimental values, as shown in Fig. 24. Their fitted degradation order for different shear rates ranged from 2.7 to 3.33, indicating that a third order degradation mechanism controls the breakdown of Fig. 24. Comparison of experimental and fitted k values at a shear rate of 103 s1. The optimized reaction rate order is 3.07, with a rate constant of 0.131 s1 (Paso et al., 2009b). Chang et al. (1999) went onto use a three yield stress model proposed by Kraynik (1990), which added a dynamic yield stress for describing behaviour after yielding to the model put forward by Houwink (1958). The three yield stress model utilized an elastic-limit yield stress, se, described as denoting the materials limit of reversibility; a static yield stress, ss, described as the minimum shear stress required to cause the deformation of a material that may be described as yielding; and a dynamic yield stress, sd, described as the shear stress at zero shear rate, extrapolated from the flow curve. Chang et al. used this model to describe the three possible outcomes of applying constant pressure to a gelled pipeline in terms of the relationship between the wall shear stress, sw, applied to the pipeline and the initial gel strength of the oil:  Start-up without delay (sw > ss) – Flow begins immediately with three different regions, as shown in Fig. 25, where R is the total radius of the pipeline and rf and rc denote the boundaries of the regions: – Flow area – The outermost region (R > r > rf), consisting of a sheared annulus. Local stress is higher than the static yield stress (s(r) > ss). The gel structure in this region is immediately broken down and the oil becomes liquid-like, displaying a dynamic yield stress. – Creep area – Middle region (rf > r > rc). Local stress is lower than static yield stress, but higher than elastic-limit yield stress (ss > s > se). Gel structure in this region begins to degrade with a viscoelastic deformation. – Elastic deformation area – Innermost region (r < rc). Local stress is lower than elastic-limit yield stress (s < se). Solidlike core where oil only undergoes elastic deformation. Will initially move with creep region as an unsheared plug of radius, r, until the gel in the creep region degrades from the outside in, leaving only the core as the plug.  Start-up with delay (ss > sw > se) – Flow begins after a delay time, tdelay. Exterior creep region and interior elastic deformation area exist and, initially, no flow occurs. Flow only begins once gel in the creep region has sufficiently degraded, starting at the wall, allowing for movement of an unsheared plug with uniform velocity through the pipe. The size of the plug (r) will decrease as degradation in the creep region continues.  Unsuccessful start-up (sw < se) – Flow will not start under this condition. Oil only deforms elastically and gel structure is unaffected by shear. Chang et al. (1999) noted that for a successful start-up, the gelled oil in a cross-section of pipe will become heterogeneous because of differences in the rate of structural breakdown caused by differences in local shear stress. Therefore, their model takes into account the time-dependent rheology of the waxy crude oils. A time-dependent Bingham-style equation, shown in Eqs. (19a)(19c) was used for an approximation of the time-dependent, 690 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 Fig. 25. Schematic diagram of start-up without delay (sw>ss when t = 0)(Chang et al., 1999). non-Newtonian behaviour of a gelled waxy crude oil under controlled stress conditions. s ¼ sy ðtÞ þ gðtÞc_ ; s > sy ðtÞ sy ðtÞ ¼ sy ð0Þ  sy ð1Þ 1 þ kt þ sy ð1Þ gðtÞ ¼ constant ð19aÞ ð19bÞ ð19cÞ Here g is the plastic viscosity, c_ is the shear rate, sy is the apparent yield stress governing the behaviour of the oil, and k is a rate constant. sy(0) and sy(1) are the apparent yield stress at times t = 0 and t = 1, respectively. sy(0) would be equivalent to ss(0), with an initial wall stress above this value resulting in an instantaneous finite flow rate, and sy(1) coincides with se(0), with wall stresses below this value resulting in reversible deformation and no possible flow. The basic physical model used by Chang et al. (1999) to describe the start-up process was the pumping of an incoming fluid (ICF) into a pipe of length, L, and inside diameter, D, to displace the outgoing fluid (OGF), as shown in Fig. 26. Here Z(t) is the length of the pipe occupied by the ICF, r I ðtÞ and r o ðtÞ are the unsheared plug radii of the ICF and OGF respectively at time, t, P1 is the inlet pressure, P2 is the exit pressure, and Pz is the interface pressure. The radius of the unsheared plug in the flow was given by equation, r  ðtÞ ¼ R sy ðtÞ swo ðtÞ ð20Þ where swo(t) is the wall shear stress in the OGF at time t. For the case of start-up without delay (or start-up with delay at time, t > tdelay), Chang et al. (1999) define the initial wall shear stress in terms of the pressure drop. To model the time- and position-dependent changes in the flow properties of the OGF, Chang et al. (1999) used a finite differences method. M time intervals were used to divide the duration of the flow from start-up (Dt = ti–ti1), and the flow was treated as approximately steady in each time interval for sufficiently small Dt. The sheared annulus (r < r R) was divided, for each instant, ti, into N radial elements of thickness, Dr, and distance, rj, from the centre of the pipe (rj = rj1 + Dr = r + jDr). The volumetric flow rate, Qi, at time ti was thus given by following equation, Qi ¼ N X Q j þ Q plug ð21Þ j¼1 where Qplug is the flow rate of the unsheared plug and Qj is the volumetric flow rate of the jth annular element. In a later work, However, Davidson et al. (2004) maintained that the finite differences method was unnecessary, because of the quasi-steady state assumption for the OGF, which was represented as a Bingham fluid that would have apparent yield stress and plastic viscosity independent of the shear rate and thus the radial position. Using their model, Chang et al. (1999) could calculate the plug radius, r, for each time interval using equations (19b) and (20) with a known wall stress. The flow rate could then be computed from j = N at the pipe wall inward to the unsheared plug at j = 0. The onset of turbulence was predicted by calculation of a critical Reynolds number, with the appropriate adjustment to the friction factor used in the model. For these calculations the pipe dimensions (L and R), Fig. 26. Schematic diagram of two-fluid displacement model. (a) True interface; (b) simplified interface (Chang et al., 1999). A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 pump pressure (DPc), properties of the OGF (sy(0), sy(1), g(t), k and qo), and properties of the ICF (sB, gB and qI) need to be known. Here qI and qo are the fluid densities of the ICF and OGF; sB is the Bingham yield stress; and gB is the Bingham plastic viscosity. Therefore, the accuracy of this model in predicting the time-dependent flow properties during start-up and the time needed to clear a blockage depended greatly on comprehensive knowledge of the system, requiring accurate experimental measurements. Davidson et al. (2004) developed another model for the restart of gelled pipelines. This model extended the one developed by Chang et al. (1999) to account for the compressibility and inhomogeneity of the gelled oil and displacing fluid. In this model, when the inlet pressure creating a wall stress in excess of the static yield stress is applied to the gelled oil, initially only a narrow region of length Lf deforms and breaks down under stress. This yielded region is compressed by the entering ICF, which is also compressed. Eventually, at time t = t0 the entire gelled oil plug will yield and move together with the ICF at the same mass flow rate, as shown in Fig. 27. For the calculations in this model from Davidson et al. (2004), the bulk mass flow rate, G, is first guessed (can use value from previous time step). Then the frictional factor, fk, is calculated by iteration for each longitudinal ICF and OGF segment at current time step using the Buckingham–Reiner equation for pipe flow of a time-independent Bingham fluid, and empirical relationships developed by other authors for calculating the frictional factor in laminar and turbulent flow. Equations (22) and (23) are used to evaluate the mean velocity and shearing time, tsk, qk Q k ¼ G t sk ðtÞ ¼ t  ð22Þ k1 t0 M1 ð23Þ 691 where k is the current subdivision out of M initial subdivisions of the gelled oil used in the calculations; and qk is the dimensionless density and Q k the dimensionless volumetric flow rate of the current subdivision. The pressure drop over each segment was calculated using following equation. swk ¼ fk qk t2k Pk ¼ 4DLk 2 ð24Þ In the calculation procedure used by Davidson et al. (2004), the length and density of each segment of oil is then updated to account for the displacement of the OGF from the length of pipe and the increase in the length of the ICF within the pipe. The ICF rheology is assumed to be time-independent and it is therefore separated into segments of equal length in each time step, with the number of segments increasing by one with each time step. The length of an ICF segment, DLICF, in time interval, i, at time t  t 0 is given by following equation. DLICF ¼ P OGF LICF DL  m k¼1 Lk ¼ K þi K þi ð25Þ Here K is the number of ICF segments chosen at time t = t0, m is the number of remaining OGF segments within the pipe, and DLOGF k is the length of the k th gelled oil segment in the OGF for time t  t 0 . Davidson et al. (2004) also calculated DLOGF and the average k density for the k th segment in dimensionless form. Next in their calculation procedure, the location of each segment and the ICF– OGF interface is determined relative to the downstream end of the OGF plug. Then the pressure drop over each ICF and OGF segment is summed to give the overall pressure drop, and the difference between this value and the applied pressure drop Fig. 27. Schematic of compression flow (Davidson et al., 2004). 692 A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 calculated and mass flow rate adjusted accordingly. This overall process is iterated until the difference is negligible. G iterates to zero in the case that the applied pressure is not high enough to start flow at a given time, and the calculated pressure drop becomes the minimum required for start-up. The results of this model were significantly different from those of the earlier model developed by Chang et al. (1999), indicating the importance of fully understanding the mechanism by which the gelled oil yields and is displaced, and of determining the most realistic assumptions that can be made during modelling. Other researchers have also tackled understanding, modelling and optimizing the restart of gelled lines. Borghi et al. (2003) developed a model focusing on solid-like fracture propagation, viscous dissipation and compression of the broken gelled oil. Ekweribe et al. (2009), for instance, studied the effect of system pressure on the restart of gelled subsea pipelines. They determined that higher system pressures in subsea pipelines could lead to the formation of a weaker gel with lower yield strength, which would mean that the necessary applied pressure for displacing it would be more easily and cheaply achieved than might be predicted. 12. Conclusions Contention still remains as to the specific mechanisms that govern wax deposition in pipelines. However, the importance of molecular diffusion is generally accepted and shear dispersion is usually not dismissed, at least due to the involvement of shear forces in the removal of wax deposits, the accounting of which has been shown by some authors to have a great impact on the accuracy of wax deposition models. Many models have been developed based on the importance of these mechanisms, for which the approach to a realistic representation of the solid phase wax components has a significant impact on accuracy. Recently, a correct heat-mass transfer analogy has been introduced into the modelling of wax deposition, allowing for more accurate prediction across the range of possible precipitation kinetics. 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