Wax formation in oil pipelines.pdf

International Journal of Multiphase Flow 37 (2011) 671–694

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International Journal of Multiphase Flow

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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 Department of Chemical Engineering, The University of the West Indies, Trinidad and Tobagob 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 2010Received in revised form 9 February 2011Accepted 20 February 2011Available online 27 February 2011

Keywords:Waxy crude oilOil-pipeSolid–solid transitionSolid–liquid equilibriumWax precipitationwax removal

0301-9322/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijmultiphaseflow.2011.02.007

⇑ Corresponding author. Address: Dept. of Chemical868 6624414.

E-mail address: [email protected] (D.P. C

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 pipelinespresent a costly problem in the production and transportation of oil. The timely removal of depositedwax is required to address the reduction in flow rate that it causes, as well as to avoid the eventual lossof a pipeline in the event that it becomes completely clogged. In order to understand this problem andaddress it, significant research has been done on the mechanisms governing wax deposition in pipelinesin order to model the process. Furthermore, methods of inhibiting the formation of wax on pipelinewalls and of removing accumulated wax have been studied to find the most efficient and cost-effectivemeans of maintaining pipelines prone to wax deposition. This paper seeks to review the current state ofresearch into these areas, highlighting what is so far understood about the mechanisms guiding thiswax deposition, and how this knowledge can be applied to modelling and providing solutions to thisproblem.

� 2011 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6722. Detection of deposited wax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672

2.1. Detecting blockages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6722.2. Detecting wax deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672

3. Wax deposition mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673
3.1. Molecular diffusion mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6733.2. Soret diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6733.3. Brownian diffusion mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6733.4. Gravity settling mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6733.5. Shear dispersion mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6733.6. Shear stripping mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6743.7. Nucleation and gelation kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6743.8. Deposition in two-phase flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674
4. Effect of emulsified water on gelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6755. Cloud point, pour point and gel point correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6756. Review of some existing wax deposition models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675

6.1. Thermodynamic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6766.2. Hydrodynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677

7. Wax aging models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679
7.1. Counter diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6797.2. Ostwald ripening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680
8. Correct analogies for correlated heat and mass transfer in turbulent flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6809. Inhibition of wax deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681

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9.1. Chemical inhibitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6819.2. Types of chemical inhibitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682

9.2.1. Ethylene copolymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6829.2.2. Comb polymers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6829.2.3. Wax dispersants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6839.2.4. Polar crude fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6839.2.5. Short-chain alkanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685

9.3. Surfaces that prevent wax deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6869.4. Cold flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686

10. Wax removal methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687
10.1. Pigging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68710.2. Inductive heating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68710.3. Biological treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687
11. Restart of gelled pipelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 688
11.1. Time-dependent gel degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68811.2. Examples of restart models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689
12. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692

1. Introduction

Wax build-up is a complex and very costly problem for thepetroleum industry, widely reported and studied by researchersin decades past (Reistle, 1928, 1932; Bilderback and McDougall,1963; Haq, 1978). For subsea pipelines, in particular, it has becomeespecially important to solve the issue of wax build-up, as large-scale oil production in colder regions will be faced with moresevere wax precipitation (Smith and Ramsden, 1978; Aspergeret al., 1981).

Wax precipitation within pipelines at and below the CloudPoint or Wax Appearance Temperature (WAT) can lead to gellingthat inhibits flow by causing significant non-Newtonian behaviourand increasing effective viscosities as the temperature of a waxycrude oil approaches its Pour Point (Pedersen and Rønningsen,2003). Alternatively, when just the pipeline wall is below theWAT, this promotes the deposition of a layer of paraffin moleculesthat can grow over time, constricting flow. This is especially prob-lematic for pipelines in deep-sea environments, as, even in rela-tively warm climates, the water temperature will be on the orderof 5 �C (Azevedo and Teixeira, 2003).

Some researchers, such as Carmen García et al. (2001) andCarmen García and Urbina (2003), have studied correlations be-tween 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 precipita-tion and the deposition of wax along pipeline walls. However,accurately modelling deposition in pipelines can be a complexand difficult undertaking, because, while precipitation is mainly afunction of thermodynamic variables such as composition,pressure and temperature, deposition is also dependent on flowhydrodynamics, heat and mass transfer, and solid–solid and sur-face–solid interactions (Hammami et al., 2003). Only recently hasa model been developed that incorporates correct analogies forheat and mass transfer.

This paper reviews cases where researchers have studiedways to model wax deposition and the aging of wax depositsin 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. Indoing so, this paper, as one goal, seeks to show how our under-standing of these mechanisms has developed, to highlight areaswhere further understanding of these mechanisms is still needed,and to show how well our current correlations can be applied tothe accurate prediction of wax deposition. Furthermore, this pa-per seeks to highlight the progress that has been made in devel-

oping methods to mitigate and treat the formation of paraffinlayers in pipelines.

2. Detection of deposited wax

2.1. Detecting blockages

In order to experimentally explore wax deposition in the field orto determine the locations of particularly large wax deposits oreven complete plugs, methods are needed for detecting the extentof wax deposition at different points in a pipeline or of detectingthe location of plugs. Pressure echo techniques can be used to findthe location of a blockage by measuring the time for a pressurewave to be reflected back along the pipeline from the point ofblockage (Chen et al., 2007). Alternatively, the pipeline could bepressurized and then a special tool with a calliper and video cam-era on a remotely-operated submersible could be used to measurethe external diameter of the pipeline. Upstream of the blockage,but not downstream of it, an appreciable difference in the diametercan be detected when the pipeline is pressurized (Sarmento et al.,2004).

2.2. Detecting wax deposits

Traditional experimental methods for measuring the extent ofwax deposits include direct methods such as pigging and the‘‘take-out’’ method, in which a section of pipe is removed andthe volume of wax inside measured. Additionally, pressure dropand heat transfer methods can be used to measure wax depositsindirectly without down time (Chen et al., 1997). Zaman et al.(2004) explored alternative methods of measuring wax depositionin pipelines. Firstly, they experimented with measuring lightabsorption through crude oil using a light source and a detectorcircuit mounted within a pipe. They found that, in laboratory tests,this detector circuit proved capable of detecting contaminationeven with a very small percentage present. The use of ultrasoundfor solid detection, also explored by Zaman et al. (2004) provedvery successful in detecting extremely small solid grains. Finally,they were able to use a strain gauge to detect very small changesin pipeline weight associated with wax deposition. However, allof these methods were only tested with small-scale laboratory rep-resentations of actual systems. Practical methods for application ofthese tools to actual subsea pipelines would still need to be de-signed. Zaman et al. (2006) have also experimented with the use

A. Aiyejina et al. / International Journal of Multiphase Flow 37 (2011) 671–694 673

of a laser spectroscope to detect paraffin in paraffin-contaminatedoil samples.

3. Wax deposition mechanisms

The behaviour of waxy crudes is usually approximated by mod-elling them as Bingham-like fluids. Different mathematical modelshave been proposed ranging from a general one-dimensional mod-el of a waxy crude oil to models that describe crude oils depositingwax in closed flow loops. For example, Fusi (2003) and Fasano et al.(2004) delineate many models of differing complexity for the rep-resentation of waxy crude oils. In order to fully model the flow ofthese crude oils, the mechanisms governing the deposition and re-moval of solid wax must be incorporated into the model. Thenmodels can be developed, informed by a theoretical understandingof the mechanisms at play and the properties of the mixtures un-der study. However, the question arises of which mechanismsare actually relevant.

Investigations in this area have been ongoing for decades byresearchers such as Hunt (1962); Burger et al. (1981), and Leirozand Azevedo (2005). Azevedo and Teixeira (2003)did a critical re-view of wax deposition mechanisms, starting with wax depositionby molecular diffusion as described by Burger et al. (1981). In thisreview it is acknowledged that, in most models of wax deposition,molecular diffusion is treated as the dominant mechanism, and it isalso argued that experimental evidence suggests that gravity set-tling and shear dispersion play no significant role in wax deposi-tion. However, Azevedo and Teixeira point out that sheardispersion may play a role in wax deposit removal, which wouldaffect the rate at which wax accumulates. Other authors, such asSolaimany Nazar et al. (2005b) and Correra et al. (2007), haveincorporated wax removal mechanisms involving shear forces(sloughing, ablation) into their wax deposition models. Othermechanisms including thermo phoresis, the Saffman effect andturbophoresis have also been considered in modelling wax deposi-tion (Merino-Garcia et al., 2007).

3.1. Molecular diffusion mechanism

It is assumed that, for the flow of crude oil in the turbulent re-gime, the turbulent diffusivities of momentum, chemical speciesand 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 gradientsprevailing at the laminar sub-layer close to the wall (Azevedo andTeixeira, 2003). In a subsea pipeline in which the walls are cooledbelow the cloud point, there will be a radial temperature gradientand wax crystallization will occur in cooler regions nearest to thewall. Thus, solid wax crystals will exist in equilibrium with the li-quid phase. Since wax solubility decreases with temperature, therewill also be a concentration gradient established by the tempera-ture gradient within the pipeline, with the cooler regions nearthe wall having the lowest concentration of wax in the liquidphase. This is what leads to the molecular diffusion of wax fromthe bulk fluid to the walls of the pipeline.

Azevedo and Teixeira (2003) suggested that the mass flux of thewax be estimated by Fick’s Law as

dmm

dt¼ qdDmA

dCdr

ð1Þ

Here mm is the mass of deposited wax, qd is the density of the solidwax, Dm is the diffusion coefficient of liquid wax in oil, A is the sur-face area over which deposition occurs, C is the concentration ofwax in solution (volume fraction), and r is the radial coordinate.

3.2. Soret diffusion

Soret diffusion or the Soret effect refers to thermal diffusion,which accounts for mass separation caused by the existence of atemperature gradient within the pipeline (Ekweribe et al., 2009).Some researchers, such as Merino-Garcia et al. (2007), have classi-fied its effect in wax deposition as negligible. However, expressingdiffusion in terms of molecular and thermal diffusion allows for awax deposition model to more correctly account for thermal ef-fects in diffusion (Banki et al., 2008). Thus, total mass flux would,ideally, have to be represented as a combination of Fick’s Law, interms of Dm and the concentration gradient, and transport by theSoret effect, in terms of a thermo diffusion coefficient, DT, andthe temperature gradient.

3.3. Brownian diffusion mechanism

This would occur when wax crystals that have precipitated outof the oil solution collide with excited oil molecules. The use of thismechanism in modelling deposition was also explored by Azevedoand Teixeira (2003). This diffusion mechanism can also be repre-sented by Fick’s Law as shown in equation.

dmB

dt¼ qdDBA

dC�

drð2Þ

Here mB is the mass of wax deposited by Brownian motion, DB is theBrownian motion diffusion coefficient of the solid wax crystals andC� is the concentration of solid wax out of solution.

Azevedo and Teixeira (2003) acknowledge that many authorsdismiss Brownian diffusion as a relevant mechanism for wax depo-sition. However, they conclude that there is not enough evidenceto warrant this, citing an argument used by Majeed et al. (1990),which suggests that Brownian diffusion flux will be away fromthe wall, where the solid concentration would be highest. They dis-miss this argument, because if the wax crystals are trapped in theimmobile solid layer at the wall, the concentration of solid crystalsin the liquid at the wall is zero, or nearly zero, allowing for Brown-ian diffusion toward the wall. The review concludes that Browniandiffusion remains a possible contributing mechanism for waxdeposition.

3.4. Gravity settling mechanism

Azevedo and Teixeira (2003) classify gravity settling as insignif-icant in contributing to wax deposition, citing experimental evi-dence from Burger et al. (1981), which showed that the settlingvelocities of wax crystals under typical conditions do not contrib-ute significantly to deposition. This was further supported byexperimental evidence from Burger et al., which demonstrated thatdeposition under horizontal and vertical flow is identical withinthe limits of experimental error.

3.5. Shear dispersion mechanism

Shear dispersion could contribute to wax deposition throughthe lateral motion of particles immersed in a shear flow. Someauthors, such as Fusi (2003), include deposition in terms of a sheardispersion coefficient in the modelling of wax deposition. Also,Fasano et al. (2004) claim that, based on the literature, for temper-atures much lower than the cloud point and for moderate heatfluxes the dominant process is shear dispersion, while for slightlyhigher temperatures the dominant process is molecular diffusion.However, Azevedo and Teixeira (2003) claim that shear dispersiondoes not contribute to deposition, because experimental evidenceshows no deposition of wax under conditions of zero heat flux,when it would only be possible if driven by a flow-induced


mechanism, such as shear dispersion. However, Azevedo andTeixeira concede that shear forces can still contribute to theremoval of wax deposits. Regardless of conflicting theories withregard to the role of shear dispersion in wax deposition, the impor-tance of this mechanism in the overall accumulation and aging ofwax deposits cannot be ignored.

3.6. Shear stripping mechanism

Removal of wax deposits by shear forces becomes especiallyimportant under turbulent conditions when the rate of removalwill be significantly higher compared to laminar flow. Therefore,in order to accurately model wax deposition, especially for turbu-lent flow, it is necessary to incorporate shear stripping effects intothe model. Additionally, modelling wax removal by shear forcescould help in the design of flow improver chemicals, as some ofthese may act by causing the formation of softer gel structures thatare more susceptible to removal by shear forces. Some researchers,such as Matzain (1999), have tried to represent this effect as anempirical correlation for the reduction in rate of deposit formationcaused by shear forces.

3.7. Nucleation and gelation kinetics

The crystallization of waxes is a kinetic process, the onset ofwhich can be described by classical homogeneous nucleation the-ory (Paso, 2005). While much work has been done to approach waxdeposition as a thermodynamic problem, modelling based on thekinetics of deposit formation has not been widely explored(Merino-Garcia et al., 2007). Paso (2005) sought to address theinsufficient understanding of the crystallization and gelation pro-cesses, as well as the assumption that paraffin precipitation kinet-ics does not limit deposition rates; an assumption that could leadto the prediction of wax deposition in cases where a stable gelcannot form. He used model fluids consisting of n-paraffin compo-nents dissolved in petroleum mineral oils, and applied homoge-nous nucleation and crystallization theory, along with differentialscanning calorimetry to measure the onset of crystallization andthe crystallization rate.

Paso (2005) compared experimental and equilibrium crystalli-zation rates to show that there were three regimes in the crystal-lization process at low cooling rates. The first is a nucleation lagperiod starting at high-temperature conditions. The second is asupersaturation growth period, driven by the supersaturationestablished during the nucleation lag period as well as by decreas-ing solubility conditions, and during which the crystallization ratecan spike well above the equilibrium crystallization rate. The third,meanwhile, is an equilibrium growth period, which starts whenthe supersaturation ratio is diminished and the crystallization rateconverges with the equilibrium predictions of the van’t Hoff rela-tion. One thing noted by Paso about these regimes was that thetemperature span of the supersaturation growth regime wasindependent of the model fluid viscosity, providing evidence ofthe absence of transport limitations in the crystallization rate.

Through the application of the van’t Hoff solubility model with-in the framework of classical homogeneous nucleation theory, Paso(2005)demonstrated that nucleation represents the primarykinetic limitation associated with the crystallization of n-alkanesin organic solution at low cooling rate conditions, with crystalliza-tion rate limitations becoming significant at high cooling rates. Healso highlighted that the initial nucleation event is dependent uponthe solubility behaviour of the highest fraction of n-alkane compo-nents in the fluid, and that the introduction of chain-length varia-tions effects a reduction in the critical nucleus surface energy byco-crystallization of dissimilar chain-length paraffins.

Paso (2005) also investigated the mechanical properties of waxymodel fluids at constant cooling rates using controlled-stress rheo-metric measurements, applying an oscillatory upon the fluid sam-ples in order to characterize their mechanical properties duringgelation. The crystal structure in samples was also studied viamicroscopy and, furthermore, Paso applied an extension to anestablished three-dimensional analytical percolation approxima-tion to wax–oil gel systems. This allowed for the prediction of the-oretical gelation via the percolation threshold, the fractionalvolume of the solid crystalline phase at which it forms a continu-ous, domain-spanning path connected by crystal–crystal interac-tions. For this purpose, paraffin crystals were represented byellipsoidal geometries with spherical rotational volume of interac-tion. The primary and secondary ellipsoidal aspect ratios of thecrystals, a1 and a2, were related to the solid phase fraction at thepercolation threshold, ug, by equation.

/g ¼ hp1a1

1a2

ð3Þ

Here hp = 0.295 represents the spherical percolation threshold.While this would give a prediction of the formation of a crystal per-colation network, it was noted that this will lead to gelation only ifthe number density and strength of the crystal–crystal interactionsare sufficient to impart solid-like properties to the fluid (Paso,2005).

Overall, Paso (2005) noted that the gel point of a waxy petro-leum fluid is dependent on the morphologies and surface charac-teristics of the randomly oriented paraffin crystals, and thataspect ratios on the order of 100 allowed mechanical gels to formfrom these oils with paraffin content as low as 0.5%. Also, thatmono disperse crystals exhibited ordered surfaces and sharp edges,providing minimal crystal–crystal contact and weak interactions,while polydisperse n-alkane crystals exhibited nano-scale surfaceroughness, which provides contact points for strong crystal–crystalinteractions, allowing for mechanical gelation at smaller wax con-tents. Additionally, Paso concluded that percolation thresholdmodels provide accurate gel point predictions for physical gelationsystems that exhibit strong crystal–crystal interactions, while un-der-predicting the solid fraction necessary to induce gelation inweakly-interacting particle systems.

Other recent studies that approached the subject of nucleationand gelation kinetics include those by Lopes-da-Silva and Coutinho(2007) and Ekweribe (2008). They analyzed gelation kinetics withthe phenomenological Avrami model and noted an apparentdependence of nucleation and crystal growth mechanisms andrates on the degree of supercooling below the WAT at which crys-tallization is occurring. Lopes-da-Silva and Coutinho (2007) alsonoted an apparent predominance of heterogeneous nucleationand diffusion-controlled growth, especially at higher supercoolingand/or higher oil complexity composition and molecular weight.These results and those of Paso (2005) and further studies shouldprove invaluable in the development of more robust wax deposi-tion models, which take kinetic considerations into account. Theycan also be useful in determining mechanisms by which wax gela-tion can be inhibited or wax deposits weakened by wax crystalmodification.

3.8. Deposition in two-phase flow

Analyzing and modelling liquid–liquid two-phase flow has pre-viously been explored by many researchers as well as presentauthors (Raj et al., 2005; Chakrabarti et al., 2006, 2007). Depositionin two-phase flow shows some characteristics similar to liquid–liquid two-phase flow. Matzain et al. (2002) found that thethickness, hardness and profile of wax deposition in two-phasegas–oil flow show dependence on flow patterns. They used a closed


flow loop and the liquid displacement–level detection (LD–LD)technique, proposed by Chen et al. (1997), to measure wax depos-its under different conditions. For horizontal flow, the thickness ofdeposits varied around the circumference of the pipe depending onflow pattern, as shown in Fig. 1.

Matzain et al. (2002) account for these distributions by describ-ing how, in stratified flow, only the lower part of the wall will be incontact with the oil phase, and the heat transfer rate will be high-est at the bottom of the pipe and will decrease upward, resulting indecreasing deposit thickness in a crescent shape. In the case ofwavy stratified flow, the wavy gas–oil interface is cooled becauseof the waves, increasing heat transfer rate and, thus, deposit thick-ness along the interface. With intermittent flow, the passing of li-quid slugs induces high shear force and stress along the bottom ofthe test pipeline and shearing of wax deposits, resulting in thinnerdeposits at the bottom of the pipe. With annular flow, the waxthickness is uniform around the circumference, as oil is uniformlyin contact with the entire wall surface.

The results of Matzain et al. (2002) also showed changes inhardness of the wax deposits for different flow patterns. Stratifiedflow gave a soft deposit at the bottom of the pipe, with harder andthicker deposits along the edge of the wavy gas–liquid interface.Intermittent flow resulted in a hard deposit, with increasing hard-ness from the top to the bottom of the pipe. Lastly, annular flow re-sulted in a very hard deposit, uniform across the circumference ofthe pipe. Their results for vertical two-phase flow, on the otherhand, showed very uniform thickness distribution in the differentflow regimes, with very hard deposits for annular flow, depositsof medium to high hardness for intermittent flow, and hard depos-its for bubbly flow with high superficial velocity.

4. Effect of emulsified water on gelation

Crude oil emulsions, in particular, can pose significant flowassurance risks and, with the increase in multiphase productionin offshore environments, it has become important to evaluatethe impact of emulsified water on crude oil gelation (Visintinet al., 2008). The presence of water over a threshold value can pro-mote gel formation and viscous wax–oil gel emulsions. Theseemulsions may be stabilized by the presence of polar compoundssuch as asphaltenes and resins, and can have water cuts as highas 70% (de Oliveira et al., 2010). Paso et al. (2009c) attributed thestability of waxy emulsions to the stabilizing effect of asphalteneparticles on oil–water interfaces. They also suggested that, atlow-temperature conditions, molecular asphaltene adsorptiononto precipitated wax crystals may increase the water wettabilityof the crystals, thus promoting adsorption at the oil–waterinterface.

Visintin et al. (2008) hypothesized that the solid paraffin stabi-lizes the emulsion by being strongly adsorbed at the liquid–liquidinterface forming Pickering emulsions. They suggested that, bymeans of the strong interaction between wax crystals and the dropsurface, growth of the gel network involves the droplets them-selves, forming a volume-spanning wax crystal network with

Stratified Smooth

Stratified Wavy

Fig. 1. Approximation of wax thickness distribution for various h

entrapped dispersed water, as shown in Fig. 2. They observed asharp increase in shear viscosity, yield stress and pour point forwaxy crude oil emulsions with above 25–30% volume of dispersedwater, as demonstrated in Fig. 3.

It was similarly noted by de Oliveira et al. (2010) that these vis-cous emulsions can increase gel strength and hinder pipeline re-start by increasing the magnitude of the rheological properties ofthe waxy crude oil gel. They attributed this change to the networkdeveloped by the aggregation of the waxy crystals and water. Pasoet al. (2009c) also noted drastic increases in fluid viscosities andshear thinning rheological behaviour due to the presence of emul-sified water. These observations show the significance of consider-ing the effect of emulsified water on gelation, and Visintin et al.(2008) note the importance of accounting for the impact of emul-sified water during field development studies. Water fraction pro-duced by a well generally increases over its lifetime (Lockhart andCorrera, 2005; Visintin et al., 2008). Thus it would be very useful toaccount for the increasing impact of emulsified water on gelationand gel rheology during continued operation.

5. Cloud point, pour point and gel point correlations

Some authors have focused on developing correlations betweenmeasurable properties of crude oils, such as the pour point, and theconditions under which disruptive wax deposition will occur.Work such as this may help in predicting if and when fatal waxdeposition would occur in pipelines carrying particular crudes. Liet al. (2005) cited the results of Holder and Winkler (1965) as indi-cating that 2 wt.% precipitated wax is sufficient to cause gelling ofvirgin waxy crudes. Li et al. thus started with previously developedcorrelations and tried to develop their own correlation linking thetemperature at which this 2 wt.% precipitation would occur, Tc (2wt%), and the pour point, Tpp, and gel point, Tgp, of various waxycrude oils., represented graphically by Figs. 4 and 5. These resultsand future research could be useful in both determining the ten-dency for different waxy crudes to gel and harden at particulartemperatures, and in devising chemical means of inhibiting thisoccurrence.

6. Review of some existing wax deposition models

Many different authors have proposed models for the flow ofwaxy crude oils and the associated deposition of solid wax withinpipelines, including Farina and Fasano (1997), and Fusi and Farina(2004). Additionally, there are commercial software codesdeveloped to describe these processes, such as those comparedby Bagatin et al. (2008). Fasano et al. (2004) reviewed variousmathematical models for the flow of waxy crude oils in laboratoryexperimental loops, in which the oils are assumed to behave likenon-Newtonian Bingham fluids, a common assumption for model-ling these fluids. Torres and Turner (2005) approached the problemby developing a method of straight lines for solving a Binghamproblem for modelling the flow of waxy crude oils.

AnnularIntermittent

orizontal flow patterns (as described in Matzain et al., 2002).

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 ondroplet 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 entrappedby a wax crystal network (D): the system spans the entire volume and the gelation is complete (Visintin et al., 2008).

Fig. 3. Pour point of waxy crude oil emulsion with increasing water content(Visintin et al., 2008).

Fig. 4. Tc (2 wt%) vs. ASTM pour point (Li et al., 2005).


The earlier models presented here incorporate the wax deposi-tion processes for pipelines containing waxy crude oils, and con-sider cases where either molecular diffusion or shear dispersionis considered the dominant mechanism involved in wax deposi-tion. However, one of the mistakes commonly introduced to waxdeposition models is the assumption that the temperature andconcentration gradients are independent, and that, therefore, wax

concentration can be determined using the chain rule. This is aproblem that has been corrected in more recent deposition modelssuch as the one used in the Michigan Wax Predictor developed byHyun Su Lee.

6.1. Thermodynamic models

Many researchers have studied the thermodynamics of waxdeposition in hopes of creating a model that accurately describesthe process. In one example of earlier work, Lira-Galeana et al.(1996)developed a thermodynamic framework for calculatingwax precipitation in petroleum mixtures as several distinct solidphases. Solaimany Nazar et al. (2005a) later developed a

Fig. 5. Tc (2 wt%) vs. gel point (Li et al., 2005).

Table 2Experimental WAT data and model predictions for crude oils (Wuhua and Zongchang,2006).

Sample Experimentalresults

Leelavanichkulmodel

Deviation Presentmodel

Deviation

CrudeOil A

298.2 K 298.8 K 0.4 K 301.3 K 3.1 K

CrudeOil B

295.2 K 293.4 K �1.8 K 295.4 K 0.2 K

CrudeOil C

294.2 K 296.0 K 1.8 K 297.8 K 3.6 K


multi-solid phase thermodynamic model for predicting wax pre-cipitation in petroleum mixtures, by using the Peng–Robinsonequation of state to evaluate the phase behaviour of both liquidand vapour phases. The model is solved for equilibrium, in whichthe fugacity of each component is equal in every phase, using Eq.(4), proposed by Prausnitz et al. (1986).

f s

f l

� �i

¼ exp�DHf

i

RT1� T

Tfi

!� DHtr

i

RT1� T

Ttri

!"

þ 1RT

Z Tfi

TDCpidT þ 1

R

Z Tfi

T

DCpi

TdT

#ð4Þ

Here f si is the solid phase fugacity, DHr

i is the enthalpy of solid–solid transition between different solid phases, Tf

i is the tempera-ture of fusion, Ttr is the transition temperature, Cp is the heat capac-ity, and R is the ideal gas constant.

Table 1 shows a comparison of experimentally determinedWATs for five synthetic paraffin systems and those predicted bythe model of Solaimany Nazar et al. (2005a) and a UNIQUAC modeldeveloped by Coutinho (1998). The synthetic systems were eachcomposed of decane and a bimodal paraffin distribution. It shouldbe noted that with this and other models which use experimentallydetermined cloud points to validate the model, there is a limit tohow accurately cloud points can be measured which is highlydependent on the particular oil mixture, as discussed by Coutinhoand Daridon (2005) and Hammami et al. (2003). Therefore, agree-ment with experimental data may not prove definitively the accu-racy of a model, especially as far as its applicability to a wide rangeof wax–oil mixtures.

Wuhua and Zongchang (2006) also developed a more recentthermodynaamic model, based on the equality of fugacities atequilibrium, which estimates solid precipitation as a function oftemperature and composition. For this study, Eq. (5) was used forthe condition of equal fugacities in the solid and liquid phases.

xSi

xLi

¼ cLi

cSi

f Li

f Si

expZ P

0

VLi � VS

i

RTdP

!ð5Þ

Here x is the mole fraction, c is the activity coefficient, V is vol-ume, P is pressure and the S and L superscripts indicate the solid

Table 1Comparison of the WAT between experimental data, UNIQUAC model and SolaimanyNazar et al. model (Solaimany Nazar et al., 2005a).

Bim 0 Bim 3 Bim 5 Bim 9 Bim 13

WAT (K) 308.75 309.65 310.37 311.33 312.81UNIQUAC 307.05 307.55 308.47 309.63 311.41This model 308.45 309.05 309.55 310.7 312.75

and liquid phase respectively. For their model, there was an addedlevel of specificity for modelling particular n-alkane species. Differ-ent correlations were used for the fusion enthalpies of n-alkanesand for their enthalpies of solid–solid transition based on both car-bon number and whether that number is odd or even. Similarly,transition enthalpies were calculated for different componentsbased on chain lengths.

Table 2 shows a comparison of experimentally determinedWATs for three crude oils and those predicted by the model ofWuhua and Zongchang (2006) and a similar model developed byLeelavanichkul et al. (2004) and Fig. 6 compares the predictionsof the two models to experimental data for wax precipitation asa function of temperature. The data indicates that refinement ofthermodynamic correlations, as performed by Wuhua andZongchang, can increase model accuracy in predicting precipita-tion as a function of temperature.

Further studies, for example, by Edmonds et al. (2008), havealso explored ways of representing the wax phase in order to moreaccurately model wax deposition. Edmonds et al. modelled thewax phase as a continuous distribution of n-alkane components,showing how this eliminated physically unrealistic artefacts foundin the predictions of models that lumped n-alkanes into pseudocomponents. Edmonds et al. carried out simulations with numbersof components approaching 100 and, in order to increase the com-putational speed, converted phase equilibrium and physical prop-erty data into empirical expressions, fitted to the rigorous model.They also noted the importance of considering the deposit limitingmechanism of wax shearing in order for both their model and oth-ers from the literature to more accurately agree with the limitedfield data available from actual pipelines.

6.2. Hydrodynamic model

Ramírez-Jaramillo et al. (2001) also developed a multi-solidphase thermodynamic model for predicting wax deposition. Inaddition, Ramírez-Jaramillo et al. (2004) developed a multi-component liquid-wax hydrodynamic model for simulating waxdeposition in pipelines, which treated molecular diffusion as thedominant mechanism. Fig. 7a shows the computational domain

Fig. 6. Wax precipitation as a function of temperature for crude oil A (Wuhua andZongchang, 2006).

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 pipeof length, L, and radius, r, along which a mixture of hydrocarbonsflows. The pipe was divided to form a computational mesh, withboundary conditions applied at the ends and along the exteriorsurface of the pipe, and finite differences were used in the solutionof differential equations.

Ramírez-Jaramillo et al. (2004) modelled the fluid as consistingof n hydrocarbon components in thermodynamic equilibrium, withmole fractions, in both the liquid and solid phases, that are func-tions of pressure and temperature. They considered the wax depo-sition rate to depend on oil composition, oil temperature, externaltemperature around the pipe, flow conditions, pipeline size andpressure. The model assumed wax deposition by molecular diffu-sion and removal by shear forces, which would be especially signif-icant at high Reynolds numbers [( quDh /l), where q = density,u = velocity, l = dynamic viscosity, Dh = hydraulic diameter]. Inaddition, the model included aging by the diffusion of wax intoand within the gel-like deposit, which is discussed later in thispaper. The mass flux was calculated for all components in thesystem and summed to give the total flux.

Ramírez-Jaramillo et al. (2004) used mass, momentum andenergy balances, shown in Eqs. (6)–(8) and assumed mixtureincompressibility and quasi-steady state for all rate processesconcerning mass, momentum and energy.

@qm

@tþr � qmm ¼ 0 ð6Þ

qm@m@tþ m � rm

� �¼ �rP þr � sþ qmg ð7Þ

qmCv@T@tþ m � rT

� �¼ kr2T ð8Þ

Here P, s and g are the pressure, stress tensor and gravitationalconstant; Cm and k are the heat capacity and thermal conductivity(which is assumed constant), respectively; and m is the averagemacroscopic velocity of the mixture. They expressed the totalamount of deposited wax, M(t,z), in terms of the deposited mass


of each component due to molecular diffusion, MMDi(t,L), the massremoved by shear forces, MSR(t,L), and the mass of wax moleculesdiffusing into the gel deposit, MGD(t,L), as shown in equation.

Mðt; zÞ ¼Xn

i¼1

MMDiðt; LÞ �MSRðt; LÞ �MGDðt; LÞ ð9Þ

Ramírez-Jaramillo et al. (2004) solved for the total depositionrate, @M/@t. The output of their model included solid fractions, den-sity, viscosity, radial mass flux and deposited mass calculations.The model showed reasonable agreement with previously devel-oped models and experimental data for a binary mixture reportedby Cordoba and Schall (2001), as shown in Fig. 8 Ramírez-Jaramilloet al. found that the Peclet number and Reynolds number parame-ters 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 crystalsand wax deposits formed from crude oils. Nautiyal et al. (2008)studied the crystal structure of n-alkane paraffins crystallized fromcrude oil. Other studies have specifically looked at the way waxdeposits change after the initial formation. This is important be-cause, in addition to understanding the mechanisms involved inthe deposition of wax in pipelines, in order to fully model the flowof crude oil and accumulation of wax, it is vital to understand themechanisms that govern the aging of wax deposits. These depositsare not simply static and unchanging. Rather, after a layer of waxhas formed along a pipeline wall, its composition graduallychanges. The crystalline wax deposit actually behaves like a porousmedium with oil trapped within its three-dimensional network(Singh et al., 2000, 2001a). The wax content of this deposited gelcan therefore increase with time by diffusion. As this happens,hardness, melting point and heat of fusion of the deposit canchange, which could affect decisions about the appropriate methodof wax removal to employ in a pipeline.

Singh et al. (2000) studied this phenomenon by use of foodgrade wax dissolved in a mineral oil–kerosene mixture, whichwas pumped through a closed flow loop setup. Their experimentalprocedure involved heating a wax–oil mixture to 30–35 �C in astirred tank and maintaining the temperature of this vessel above

Fig. 8. Dimensionless wax thickness distribution vs. time. Comparison of modelpredictions with experimental data for the 30:70 (cyclo C6C19:C8) ratio (Ramírez-Jaramillo et al., 2004).

the cloud point, while pumping the wax–oil mixture through theflow loop. The flow loop consisted of a 5/8 in. OD steel tubing testsection, which was cooled by a heat exchange jacket, and an iden-tical but non-cooled reference section. Pressure taps connected topressure transducers were used to measure the increase in differ-ential pressure during operation in order to determine the thick-ness of the deposit within the test section. The bulk fluid inlettemperature, tb, and wall temperature, ta, were also monitored.

Singh et al. (2000) determined that a counter diffusion phenom-enon, in which wax molecules diffuse into the gel deposit and oilmolecules diffuse out of the deposit, is responsible for the agingof the deposit. They furthermore determined that the rate of agingis dependent on oil flow rate as well as the pipeline wall tempera-ture. In their experimental setup with oil in a closed flow loop withcooled walls, there was a rapid decrease in internal radius mea-sured over the first day followed, which then plateaued. Similarly,the increase in the measured weight fraction of wax slowed after arapid change in the first day. The wax content (determined usinghigh-temperature gas chromatography, HTGC) of the gel depositalso changes over time, with the proportion of lighter componentsdecreasing after the first day, while the proportion of heavier com-ponents increases. The data recorded by Singh et al., showed thatthe wax content of the deposit continued to increase even afterthe thickness stabilized, and that waxes of chain length higher than29 diffused into the deposit while the ones with lengths less than29 diffused out. 29 is the critical carbon number, CCN, for the givenoperation conditions; a value that could be useful in determiningwhat inhibitors to use in a particular well or pipeline, based onwhether or not they can inhibit crystallization of waxes abovethe CCN (Paso and Fogler, 2003).

Singh et al. (2000) were able to develop a mathematical modelto describe the wax deposition process in a laboratory flow loop bysolving numerically a coupled system of differential and algebraicequations of heat and mass transfer inside and outside the gel de-posit. Eq. (10) shows the mass balance they used to relate the rateof change of wax in the gel deposit to the radial convective flux ofwax molecules from the bulk of the fluid–gel interface.

ddt½pðR2 � r2

i ÞFwðtÞLqgel� ¼ 2priLk1½Cwb � CwsðTiÞ� ð10Þ

Here R is the original internal radius of the pipe, ri is the internalradius during deposition (average radius available for flow of oil),Fw is the weight fraction of solid wax in the oil, L is the length ofpipe, qgel is the density of the gel deposit (considered constant),k1 is the mass transfer coefficient, Cwb is the bulk concentrationof wax, Cws is the solubility of the wax in the oil solvent derivedin terms of Ti, and Ti is the interfacial temperature, which was ob-tained from the energy balance shown in equation,

2prihiðTb � TiÞ ¼2pkeðTi � TaÞ

lnðR=riÞ� 2prik1½Cwb � CwsðTiÞ�DHf ð11Þ

where hi is the interface heat transfer coefficient, ke is the effectivethermal conductivity of the gel, and DHf is the heat of solidificationof the wax. The heat and mass transfer coefficients were obtainedusing Hausen, Seider and Tate correlations.

Eq. (12) shows the deposit growth equation derived by Singh etal. (2000), by relating the rate of addition of wax to the gel depositin the flow loop to the radial convective flux of wax molecules fromthe bulk to the fluid–gel interface and the diffusive flux into the gelat the gel interface.

2priFwðtÞqgeldri

dt¼ 2prik1½Cwb � CwsðTiÞ� � 2pri �De

dCw

dr

��i

� �ð12Þ

Here De is the effective diffusivity of wax inside the gel deposit.Coupled differential equations from Eqs. (10) and (12) were solvedby Singh et al. throughout the length of the pipe at each time

Fig. 9. Kinetic growth of crystals for oil sample from X-ray diffraction analysis at10 �C (Coutinho et al., 2003).


instant using Runge–Kutta algorithms, along with equations fordTi/dr. This system of equations was used to obtain the trajectoriesof thickness and wax content at each location in the pipe. Thismodel showed excellent agreement with experimental data. How-ever, Lee (2008) has shown that the mass-heat transfer correla-tions used by Singh et al. incorrectly assume independent heatand mass transfer, and were successfully applied only because ofa high degree of supersaturation in the laminar boundary layer.

Other researchers, such as Hernandez et al. (2004), modellingwax deposition in pipelines has begun incorporating wax aginginto their models. Additionally, Singh et al. (2001b) were able todevelop a thermodynamic model to predict both cloud point tem-peratures and CCNs of wax–oil mixtures, where CCN is a functionof the mixture composition as well as the wall temperature. Thismodel also showed good agreement with experimental data, pre-dicting the cloud points and the CCNs of model oils with goodaccuracy.

7.2. Ostwald ripening

It must be noted that the diffusion mechanism used by Singhet al. (2000, 2001a,b) is not the only possible mechanism forexplaining the aging process. In fact Continuo et al. (2003) foundthat aging of wax deposits takes place even for samples kept underisothermal conditions. The diffusion mechanism for aging cannotaccount for this as it is driven by temperature-composition gradi-ents. Coutinho et al. reported broadening of peaks on X-ray diffrac-tion and Cross Polar Microscopy (CPM) images showing an increasein the crystallite’s size. Fig. 9 shows an example of their resultsfrom X-ray diffraction analysis, for which the crystallite size, r, isrelated to a shape factor K, and the measured peak position, h,and breadth, b, by equation.

Fig. 10. Thermogram for oil C (thick line). The isothermal region above 5000 s shows tha2003).

r ¼ Kkb cos h

ð13Þ

Coutinho et al. (2003) noted an increase in crystal size observedby 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 thefraction of a CPM image occupied by crystals. Furthermore, theyobtained Differential Scanning Calorimetry (DSC) thermogramsunder the same conditions, which did not show detectable heateffects associated to this change in the crystal size, as seen inFig. 10. They noted that this can only occur when the heat of crys-tallization released is used by the melting of an equivalent mass ofcrystals. This indicates that wax deposits in crudes suffer recrystal-lization. Coutinho et al., thus, conclude that Ostwald Ripening isalso a mechanism responsible for the aging of wax deposits.

8. Correct analogies for correlated heat and mass transfer inturbulent flow

Many existing wax deposition models assume that heat andmass transfer can be related by the chain rule, which assumes thatthe system is at thermodynamic equilibrium (which may not betrue), or use mass-heat transfer analogies, such as the Chilton–Colburn analogy, which are valid only when the temperature andconcentration fields are independent. Venkatesan and Fogler(2004) noted that such heat-mass transfer analogies are not appli-cable for predicting the mass transfer rates in turbulent flows,where the concentration field is correlated to the temperature fieldand the concentration boundary layer and temperature boundarylayer thicknesses are not independent. They showed that use ofthe Colburn analogy in this case would result in a significantover-prediction of wax deposition. They also proposed a methodfor estimating the convective mass transfer rate using the Nusseltnumber and the experimentally obtained solubility curve. How-ever, this method would only be valid for thermodynamic equilib-rium in the mass transfer boundary layer, when precipitationkinetics are not limiting.

For the development of more rigorous and accurate models, ithas been necessary for researchers to explore the correct relation-ship between heat and mass transfer. Lee (2008) investigated thecombined heat and mass transfer phenomenon under laminarand turbulent flow conditions using the finite difference method.He developed a model based on that of Singh et al. (2000), whichcould be applied for any precipitation kinetics. For turbulent flow,Lee showed that the solubility method proposed by Venkatesan

t there are no detectable heat effects related to the aging of the wax (Coutinho et al.,


and Fogler (2004) under-predicts deposition by assuming that theconcentration profile in the mass transfer boundary layer followsthe thermodynamic equilibrium limit between temperature andconcentration at every point. This was contrasted with the over-prediction of the Chilton–Colburn analogy, which gave maximumsupersaturation. The comparison showed that these two ap-proaches constitute the limiting cases for deposition, and thatthe actual concentration profile, which is dependent on the precip-itation kinetics, falls between those calculated by the two methods.

Instead of using those two limiting cases, Lee (2008) employeda computational approach for calculating the Nusselt numbers[(hL/kf), where L = characteristic length, kf = thermal conductivityof the fluid, h = convective heat transfer coefficient] and Sherwoodnumbers [(KL/D) where L is a characteristic length, D is mass diffu-sivity, K is the mass transfer coefficient] according to followingequations.

Nu ¼ð�2riÞ@T

@r

��r�ri

Tb � Ti¼ ð2riÞhi

kð14Þ

Sh ¼ð�2riÞ@C

@r

��r�ri

Cb � Ci¼ ð2riÞkM

Dw0ð15Þ

The temperature and concentration gradients at the fluid-de-posit interface, needed for these calculations, were obtained bysolving mass and energy balance equations, as shown in followingequations.

mz@C@z¼ 1

r@

@rrDwo

@C@r

� �� krðC � CwsÞ ð16Þ

mz@T@z¼ 1

r@

@rraT

@T@r

� �� bðC � CwsÞ ð17Þ

Here vz is the axial velocity, Dwo is the molecular diffusivity ofwax in oil, kr is the thermal conductivity, aT is the thermal diffusiv-ity, and the precipitation term b(C–Cws) is considered negligible.Lee first did this for laminar flow. Using a discretized form of themass-heat transfer equation along with their appropriate bound-ary conditions, Lee wrote the governing equations in matrix form.Then by inverting these matrices to give the radial temperatureand concentration profiles, and numerically marching from the in-let of the tube to the exit he could obtain the complete set of tem-perature and concentration profiles with respect to the radial andaxial position.

From this, Lee (2008) showed how the Sherwood numberprofile as a function of axial distance would change for differentprecipitation rate constants. This showed that if there was no pre-cipitation in the boundary layer, the heat and mass transfer ratesbecome independent of each other, resulting in a supersaturationcurve. However, as the precipitation rate constant increases theSherwood number is decreased, because wax molecules wouldnot reach the oil–deposit interface, and would instead flow downto exit as solid particles.

To obtain the Sherwood and Nusselt numbers under turbulentconditions, Lee (2008) used the same procedure with governingequations modified for turbulent flow to include the turbulentaxial velocity profile and the thermal and mass transfer eddy diffu-sivities. The wax concentration profiles in the turbulent boundarylayer obtained this way showed that heat and mass transferbecome independent as the precipitation rate constant approacheszero, resulting in the Chilton–Colburn analogy-derived concentra-tion profile. Conversely, as the precipitation rate constantincreases, precipitation in the boundary layer increases, with con-centration approaching the solubility limit for thermodynamicequilibrium.

In his model, after calculating the Sherwood and Nusselt num-bers, Lee (2008)could then solve the growth and aging governingequations from Singh et al. (2000)’s model to solve for depositthickness and wax fraction at each time step in his computationalprocedure. Lee (2008)showed that there was excellent agreementbetween the results of his model and lab-scale laminar flow loopexperimental data. There was also good agreement with turbulentlab-scale results, though there was significant discrepancy for earlytimes at higher volumetric flow rates, possibly due to sloughing.The results of the computational model also closely matchedlarge-scale flow loop data. The results obtained by Lee (2008) showthat this model is applicable for varying precipitation kinetics, andprovides a robust and rigorous way of predicting wax depositionunder a range of turbulent conditions.

9. Inhibition of wax deposition

The most effective way of dealing with the problem of waxdeposition in crude oil pipelines would be to prevent it from occur-ring in the first place. Thus, researchers have investigated differentmethods of inhibiting the deposition process. These include theheat insulation of subsea pipelines to actually inhibit precipitationby keeping pipeline temperatures as high as possible (Quenelle andGunaltun, 1987), the internal coating of pipelines with plastics(Patton, 1970; Bummer, 1971), and also methods of preventingwax deposition on pipeline walls, such as the use of chemicalinhibitors, which will be discussed in more detail in this paper.

9.1. Chemical inhibitors

Many researchers have studied the efficacy of different inhibi-tors of wax deposition and the mechanisms by which they inhibitthis 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 commerciallyavailable inhibitors tends to be limited, and has to be evaluatedon a case-by-case basis. Wang et al. (2003), for instance, found,when testing some wax inhibitors, that the inhibitors they hadstudied reduced the total amount of deposition, but had only lim-ited success in suppressing the deposition of the high molecularweight paraffin components (C35 and above). This resulted in hard-er wax deposits than in the absence of an inhibitor. They also foundthat inhibitors most able to depress the WAT were more likely tobe superior products for decreasing total wax deposition, and thatthe addition of the corrosion inhibitor, oleic imidazaline (OI), sig-nificantly increased the efficacy of deposition inhibition. Fig. 11shows some of their results, where PIE is the paraffin inhibitionefficiency, 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 waxinhibitors, particularly on Nigerian crude oils. They found thatthe use of a trichloroethylene–xylene, TEX, binary system as anadditive was actually more effective and economically feasiblethan the use of commercial inhibitors. Other researchers havenoted the need to tailor inhibitor treatments to particular crudesin order to maximize efficacy. Manka and Ziegler (2001), for in-stance, found that additives work best when matched to the paraf-fin distribution in the crude oil being treated. Similarly, CarmenGarcía (2001) noted a strong relationship between a specific paraf-fin inhibitor’s efficiency and the crude oil composition, whichwould require case-by-case consideration for selecting inhibitorsfor use in the field.

Additionally, there is the consideration of the environmentalconditions under which a wax inhibitor is to be used, since, for

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 formula-tion must be winterized to allow effective delivery under thoseconditions (Manka et al., 1999; Jennings and Breitigam, 2009).Also, while work continues towards developing new, more effec-tive wax inhibitors, it remains the case that inhibitors typicallydo not provide 100% inhibition, and so are used in conjunction withremediation methods such as pigging (Jennings and Breitigam,2009; Kelland, 2009).

9.2. Types of chemical inhibitors

There are different mechanisms by which chemical inhibitorscan prevent wax deposition or gelling in pipelines. They can lowerthe WAT or pour point or can modify the wax crystals so as to pre-vent their agglomeration and deposition (Kelland, 2009). Thechemicals that modify the WAT are usually referred to as waxinhibitors or wax crystal modifiers, while those that affect the pourpoint are known as pour point depressants (PPDs) or flow improv-ers; although there is a great deal of overlap in terms of the chem-istry and mechanisms of these two classes (Kelland, 2009). Somedetergents or dispersants that act as wax inhibitors, such as poly-esters and amine ethoxylates, may act partly by modifying the sur-face of the pipe wall, rather than just the wax crystals, to preventadhesion (Pedersen and Rønningsen, 2003), and many effectivewax inhibitors create weaker deposits that are more easily re-moved by shear forces (Manka et al., 1999; Kelland, 2009). Themain types of wax inhibitors and PPDs include ethylene polymersand copolymers, comb polymers and assorted other branched

Fig. 12. Ethylene/vinyl acetate (left) and ethylene/a

polymers with long alkyl groups, such as alkyl phenol–formalde-hyde, which are not as effective as comb polymers when actingon their own as flow improvers (Kelland, 2009).

9.2.1. Ethylene copolymersThis group includes ethylene/small alkene copolymers, ethyl-

ene/vinyl acetate (EVA) copolymers, and ethylene/acrylonitrilecopolymers (Kelland, 2009). More specifically, examples of thesepolymers used in wax inhibition studies include poly (ethylene-b-propylene) and poly(ethylene butene) polymers (Tinsley et al.,2007; Kelland, 2009). Random, low molecular weight EVA copoly-mers, illustrated in Fig. 12, are widely used and investigated as waxinhibitors (Kelland, 2009). The effectiveness of the EVA copolymeras an inhibitor is influenced greatly by the percentage of vinyl ace-tate in the copolymer. The, more polar, vinyl acetate content aidssolubility and lowers crystallinity and so is necessary for thedepression of the WAT, whereas the polyethylene content is neces-sary to allow for co-crystallization with structurally similar wax,but, on its own, has little effect on crystallization (Kelland, 2009).

9.2.2. Comb polymersComb-shaped polymers, illustrated in Fig. 13, have been studied

extensively as wax inhibitors by researchers such as Duffy andRodger (2002), Duffy et al. (2004), Jang et al. (2007), and Soni etal. (2008). They are usually made from (meth)acrylic acid or maleicanhydride monomers, or both, and generally provide improvedwax inhibition compared to the ethylene copolymers (Kelland,2009). One proposed mechanism for their action as PPDs is that

crylonitrile copolymers (right) (Kelland, 2009).

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 agglomerateinto a gel structure by introducing defects or repulsive forces (Janget al., 2007; Soni et al., 2008; Kelland, 2009). As illustrated by Figs.14 and 15, they can accomplish this by providing nucleating sitesfor wax crystals on their paraffin-like pendant chains while a polarbackbone impedes the formation of an interlocking wax network(Soni et al., 2008).

In selecting the most effective comb polymers for use with aparticular crude oil, researchers have found that the length of theside chains plays an important role. For example, Manka andZiegler (2001) found that matching the average pendant chainlength of comb polymer PPDs with the paraffin distribution of acrude oil provided the greatest pour point depression. Also, Janget al. (2007) obtained results which suggested that using combstructures with side arms of such length as to interact favourablywith the fraction of oil most likely to crystallize into the hardwax phase provided the best wax inhibition. This creates a prob-lem for especially long-chained waxes, for which it would be diffi-cult to introduce a comb polymer (or ethylene copolymer) ofsufficient length to provide efficient inhibition, and also makes itimportant to have a range of comb polymers available for treat-ment of different crudes (Kelland, 2009).

9.2.3. Wax dispersantsThese are surfactants that adsorb onto pipe surfaces and reduce

the adhesion of waxes to those surfaces, possibly by changing thewettability of the pipe surface to water-wet, or by creating a weak

Fig. 14. Characteristic structure of a com

layer from which wax crystals are easily sheared off, or by adsorb-ing onto the wax crystals and reducing their tendency to sticktogether (Kelland, 2009). Some researchers have worked on devel-oping their own dispersant formulations. Groffe et al. (2001), forinstance, developed their own inhibitor that shows wax dispersantbehaviour and anti-sticking properties. They suggest that thischemical, referred to as P5, interferes with the wax crystal growthmechanism by preventing the formation of a three-dimensionalnetwork, and thus reduces the pour point and improves the flowcharacteristics of crude oils. Fig. 16 shows the effectiveness of P5in preventing the adherence of wax from crude oils to a steelsurface.

Typical, low-cost wax dispersants include alkyl sulfonates, alkylaryl sulfonates, fatty amine ethoxylates and other alkoxylatedproducts, but these dispersants have shown limited effectivenessin the field when not blended with polymeric wax inhibitors (Kel-land, 2009). Dispersants, however, have been used successfully tosupport the functions of polymeric flow improvers because of theirability to hinder wax settling and deposition (Al-Sabagh et al.,2007).

9.2.4. Polar crude fractionsIt has been found that polar extracts from crude and distillate

oils, which can be extracted using super critical gases such as car-bon dioxide or ethylene, and which contain asphaltenes, resins andaromatics, can be a potential source of low-cost flow improvers(Kelland, 2009). Venkatesan et al. (2003) studied the effects of

b polymer PPD (Soni et al., 2008).

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 theco-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. Theyfound that the addition of asphaltenes depressed the gelation tem-perature of model wax–oil mixtures, as summarized in Figs. 17 and18; 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 asphalteneson wax crystallization in crude oils. They found that this effect

Fig. 17. Gelation temperature depression (cooling rate of 1 �C min�1) for a food-grade paraffin wax (Wax 1) and a laboratory-grade paraffin wax (Wax 2) byaddition of asphaltene (Venkatesan et al., 2003).

Fig. 18. Depression in yield stress of Wax 1 system (at temperature, Tys, below thegelation temperature) upon asphaltene addition (Venkatesan et al., 2003).

Fig. 19. Effect of varying the wax percent of C28 and C32 on the pour points and gelpoints of 4% C36 solutions in dodecane (Senra et al., 2009).


depends strongly on the degree of asphaltene dispersion or floccu-lation more than on the asphaltene type or origin. They reasonedthat the asphaltenes, when well dispersed at very low concentra-tions, are easily accessible for any kind of interaction with the par-affins and can be fully incorporated into the wax structure. Theynoted a delay in crystallization, which indicated that building theasphaltene molecules into this structure would require a higherdriving force because of asphaltene–paraffin spatial interference.This would suggest that the asphaltenes are acting by some ofthe same mechanisms proposed for inhibition by polymericinhibitors.

In agreement with the results of Venkatesan et al. (2003), Krizand Andersen (2005) also saw a depression in yield stress andWAT, which they accounted for by suggesting that asphaltene mol-ecules flocculate together when over a critical concentration, withpossible co-precipitation with waxes, resulting in an unorganizedasphaltene–paraffin composite rather than a proper wax network.They note, though, the need for further understanding of the wayasphaltenes and waxes interact during wax crystallization, and an-other study by Yang and Kilpatrick (2005) indicated that asphalt-enes and waxes do not co-precipitate in solid organic deposits.

In accounting for the observed flow improver properties ofasphaltenes, Venkatesan et al. (2003) noted that asphaltenes havepolar groups as well as alkane chains and are soluble in oil up to a

certain degree. These are all properties associated with PPDs andproposed mechanisms for their action, which include co-precipi-tating with waxes and hindering crystal network growth or coatingwax crystals to prevent agglomeration. Thus, as also suggested bythe observations of Kriz and Andersen (2005), it stands to reasonthat asphaltenes affect wax precipitation by the same mechanismsas other flow improvers such as comb polymers.

9.2.5. Short-chain alkanesSenra et al. (2008) analysed how n-alkanes impact the crystalli-

zation of one another, and Senra et al. (2009) studied the gelationcharacteristics of long-chained n-alkanes in a short-chainedn-alkane solvent, looking at the inhibition of gel formation causedby the addition of other crystallizable n-alkanes to long-chainedn-alkanes, which are the primary component of wax deposits. Asis the case with polymeric inhibitors, the results obtained by Senraet al. (2009) indicate that the ability of a particular short-chainedn-alkane to inhibit gel formation by a longer-chained one dependson the particular pairing. The trend of this inhibition was foundto depend on the extent of differences in size and solubility char-acteristics between the long-chained n-alkane and the addedshorter-chained one as demonstrated by the results in Figs. 19and 20.

Senra et al. (2009) found that, for a given wax percent of a long-chained n-alkane, polydispersity and co-crystallization weaken thegel formed in spite of the fact that more crystallizable wax is pres-ent in solution. In cases where co-crystallization was possible, suchas in a C36/C32 system, they witnessed a noticeable decrease inpour point and gelation temperature with the addition of smallamounts of the shorter n-alkane. This, they accounted for by thedefects in the crystal structure that would be required to accom-modate the C32 crystals that co-crystallize with the C36. This wouldmake the formation of large crystals and a volume-spanningnetwork gel more difficult, in the same way that the inclusion ofpolymeric flow improvers into wax crystal structures inhibitsaggregation and gel formation. The addition of increasing concen-trations 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 theshorter-chained n-alkane can decrease crystal size, beyond whichfurther addition only adds more material to form wax crystals.

On the other hand, with n-alkanes of similar size which did notco-crystallize, such as in a C36/C28 system, Senra et al. (2009) saw avery different trend. In this case, low concentrations of the shorter-chained n-alkane had no effect on the pour and gel points, until a

Fig. 20. Effect of varying the wax percent of C28 and C30 on the pour points and gelpoints of 4% C32solutions in dodecane (Senra et al., 2009).


concentration at which a sharp decrease was witnessed in bothfollowed by a gradual increase. This was accounted for by the factthat, at low concentrations, the more soluble shorter-chained n-alkane will not crystallize out and will not be present in highenough concentration to disrupt the crystallization of the longer-chained n-alkane, so will have no effect. Then, at a high enoughconcentration, the association of the shorter-chained n-alkanemolecules with the longer-chained n-alkane crystals would disruptgel formation. Then gelation will occur as the more soluble shorter-chained alkane is added in high enough concentration to crystallizesufficiently to form a gel. Senra et al. supported this analysis withthe 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 for-mation of co-crystals, which would have relatively few vulnerablepoints since the two n-alkanes are so similar. Beyond that, the C32/C30 system behaved much like a monodisperse system. Also, for a

Fig. 21. Surface energy reduction possible with n

C32/C24 system, where co-crystallization does not occur, the C24

was seemingly too small to influence the crystal structure andimpact C36 gelation, and so simply acted like a solvent. Theseresults show that an understanding of how oil composition affectswax–oil gel formation can help significantly in implementinginhibition measures.

9.3. Surfaces that prevent wax deposition

There is an obvious appeal to developing wax-repellent surfacesfor use in oil pipelines as this would limit or eliminate the need forwax inhibition and removal measures to maintain normal opera-tion. With a proper understanding of the mechanisms by whichwaxes adhere to oil pipeline walls it would be possible to createpipelines in which the nature of the walls makes adhesion unfa-vourable. Paso et al. (2009a) performed a comprehensive reviewof the use of non-stick and anti-adhesive coatings for inhibiting so-lid–liquid deposition phenomena, including the use of metal sur-face treatments and synthesized polymers. The classes ofmaterials that they found promising included fluoro-siloxanes, flu-oro-urethanes, oxazolane-based polymers and hybrid diamond-like carbon and polymer coatings.

Fig. 21 shows some of the reported surface free energies of sur-faces for paraffin control investigated by Paso et al. (2009a), whichgives an indication of the ability for waxes to interact with thosesurfaces, and thus the potential of these surfaces for preventingwax deposition. Further study of the mechanisms involved inwax adhesion, hopefully, will result in even more effective surfacetreatments in the future.

9.4. Cold flow

Heating or insulation of subsea pipelines can be used to try toprevent cooling of the pipeline wall below the WAT. However, a

ovel surface technologies (Paso et al., 2009a).


very different method of inhibiting wax deposition on pipelinewalls, discussed by Merino-Garcia and Correra (2008), is the useof Cold Flow technology. This approach suggests that it might bepossible to prevent deposition on pipeline walls by reducing thebulk temperature within the pipeline to be equal to the tempera-ture of the sea water around it, thus eliminating the temperaturegradient. This would allow for the waxes to be transported as a so-lid dispersion within the bulk fluid. While wax deposition may, infact, become negligible in the case of zero heat flux, even below theWAT, much work would still be required to develop the technologyrequired for effectively cooling the bulk fluid to this condition andfor 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 potentialbenefit of wax inhibition. Gas hydrates are the solid solutions ofgas components and water. Hammerschmidt (1934) discoveredthe formation of hydrates in natural gas systems. Hydrates likewaxes have concerned deep-water production at seafloor depthsof 1–3 km and temperatures between �2 and 4 �C (Gudmundsson,2002), conditions which encourage hydrate plug formation. Severalstudies have been done on kinetics of hydrate formation. Thoseprevious studies can be categorized into two main subjects:nucleation and growth. In contrast to previous studies, gas pipe-lines hydrate agglomeration plays an important role. After thebreak-up of the hydrate film along the interface, hydrate particlesagglomerate to form a hydrate plug (Lingelem et al., 1993) likewax. Herri et al., 1999 analyzed the particle size distribution ofhydrate particles with the particle balance equations and a masstransfer model. However it is difficult to describe agglomerationfrom experimental observation. The particles start to agglomeratejust after the nucleation process (Mersmann, 2002). The observedparticle size distribution is a result of kinetic contributions suchas 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 toregularly remove accumulated wax from the inside of pipelinewalls in order to prevent the total blockage of the line. Severalmethods have thus been developed for the removal of wax depos-its, including complete blockages of pipelines. Traditional methodsof wax removal in the petroleum industry have always had prob-lems and limitations, and they include mechanical removal, theuse of bottom hole heaters, the use of exothermic reactions suchas that between magnesium bars and hydrochloric acid, and theuse of paraffin solvents (Woo et al., 1984). Research continues tobe done to find the most efficient, cost-effective and safe methodsof removing wax deposits and blockages. Furthermore, someresearchers have worked on modelling the operating conditionsnecessary for the successful and safe restart of gelled pipelines,in which gelled waxy crude needs to be displaced using appliedpressure.

10.1. Pigging

The practice of pigging is a way in which wax removal is com-monly accomplished in the field. With this method, deposited waxis mechanically removed by launching a pipeline pig along the lineto scrape wax from the walls as it is forced along by the oil pres-sure. This, however, poses the risk of forming a wax plug down-stream from the pig as the scraped wax accumulates and is

compressed ahead of the pig. In such an event the pipeline couldbe lost. The use of bypass pigs tries to address this problem. Whenthe differential pressure across such a pig becomes too high, be-cause of the accumulation of solid wax and debris ahead of it,the bypass pig allows liquid to flow through it and disperse theaccumulated solid ahead. However, there is always the danger thatif pigging has to be temporarily suspended due to mechanical fail-ure, or that if the pigging frequency for a pipeline is not correctlyoptimized, that the result will be a stuck pig and sizable productionlosses (Fung et al., 2006).

Wang et al. (2008) studied the use of regular and bypass pigs inthe removal of wax from pipelines in a laboratory system. The testfacility used consisted of a 20 ft test section of carbon steel pipe, amineral oil tank, a pump to push the pig with liquid as in real pig-ging operations, and a receiving tank to observe the structure ofthe pigged materials. Four pressure transducers were installed tomonitor pressure change along the test section during piggingoperation. Candle wax with different oil contents was cast as a filmor plug for measuring wax breaking force or plug transportationforce, respectively. After casting, the waxy spool pieces weremounted on the test section and the pig was pushed through thepipe by oil from the pump, removing the wax film or plug whilethe pressures at four locations along the test section wererecorded.

They concluded that the wax breaking force increases with thedecrease 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 tolubrication effects; and bypass pigs exhibit a very similar breakingforce behaviour when compared with regular pigs. Other studieshave focused on determining the optimal frequency of pigging tomaintain a pipeline and avoid plug formation.

10.2. Inductive heating

Another possible wax removal process, studied by Sarmento etal. (2004), is the use of inductive heating of a plugged section ofpipe. They proposed this as an alternative to the use of chemicalsthat react exothermically at the wax blockage to melt it, for caseswhen the pipeline is completely blocked in a horizontal section sothat it is impossible to flow chemicals to the blockage. They testedthis method using the experimental setup shown in Fig. 22. Theyfound that the steel layers which compose commercial flexiblelines can be heated by induction and the heat transferred to a solidwax plug in the interior of the line. They also found that theirmathematical model, which agreed well with available experimen-tal results, suggested that the power levels required for large-scaleinductive heating might be feasible for removing wax blockage infield applications with undersea pipelines.

10.3. Biological treatment

Biological wax removal methods have also been studied in re-cent years by researchers such as Rana et al. (2010), who developedsystems of paraffin-degrading bacterial consortiums with nutrientsupplements and growth enhancers for controlling paraffin deposi-tion 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 periodof several months. These methods are especially important be-cause, if successfully implemented, they have the benefit of provid-ing continuous control of wax deposition in pipelines throughconstant biodegradation, rather than just providing a very tempo-rary fix.

Etoumi et al. (2008) studied the use of Pseudomonas bacteria forthe reduction of wax precipitation in waxy crude oils. Their results

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 immisciblehydrocarbons such as kerosene, toluene, xylene and crude oil, aneffect also studied by others, such as Sifour et al. (2007). The ob-served overall effect of Pseudomonas treatment on crude oilshowed a reduction in the concentration of long-chain hydrocar-bons (C22+). Etoumi et al. concluded that Pseudomonas speciesmay be an efficient species for reducing paraffin deposition, andthat the speed of the biochemical action on crude oil is faster with-in the first 7 days. They also concluded that an observed reductionin viscosity and WAT is indicative of the conversion of long-chainalkenes to short ones.

Additionally, He et al. (2003) determined through field tests,that two Bacillus species and a Pseudomonas species showed goodparaffin removal properties in test wells, increasing oil productionand eliminating the need for more expensive wax removal pro-cesses. Thus, biological wax removal methods may prove to bequite effective and economically beneficial and warrant furtherstudy. If a biological system can be successfully and cheaply ap-plied under the conditions in subsea pipelines then it will providean extremely effective method of controlling wax deposition.

11. Restart of gelled pipelines

In subsea pipelines carrying waxy crude oils that have to beshut down temporarily for operational or emergency reasons, theoil will eventually cool below its gel and pour points resulting inthe formation of a gel throughout the pipeline consisting of precip-itated wax in a viscous matrix (Chang et al., 1999). This occurrencecomplicates the restart procedure, as the gelled oil would need tobe displaced in order to resume normal operations. Numerousresearchers have addressed this problem, including Smith andRamsden (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 applica-tion of higher than normal operating pressures. In this start-upscenario, oil is pumped into the gelled line at high enough sus-tained pressure to overcome the static yield stress of the gel, thusbreaking up the blockage and clearing the line.

The viscoplastic nature of waxy crude oils and their time-dependent behaviour complicate modelling. In order to describethe breakdown of the gel structure along with a decrease in viscos-ity, Chang et al. (1999) defined the static yield stress of the gel, ss,

as the critical shear stress value for determining whether the startof a flow from a rest state will occur. Furthermore, they defined thedynamic yield stress, sd, as the parameter for describing the rela-tionship between shear stress and shear rate in a flow state afteryielding. However, the description of this yielding behaviour hasseen many variations and disagreements among different authors.

Many studies have been published regarding the rheology ofwaxy crudes and their gels, the dependence of gel properties onshear and thermal histories, and how they yield (Wardhaughet 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 atwhich the gelled oil ceases to behave as a Hookean solid,’’ and re-ferred to bulk yielding phenomena, when gross yielding behaviouris observed, as the yielding stress or yielding point. Houwink(1958) described a transition from elastic behaviour to plasticbehaviour and then to viscous flow, distinguished by a lower anda higher yield stress. Meanwhile some researchers, such as Barnes(1999), who noted the high degree of variation in the definition ofyield stress, maintained that no real yield stress exists, even forvery non-Newtonian liquids. They argue this because these liquidscontinue to flow or creep even below an apparent yield stress.Barnes notes, however, that the concept of a yield stress is usefulfor describing behaviour over a limited range.

11.1. Time-dependent gel degradation

Time-dependent gel-degradation is one of the important com-plications in modelling the restart of gelled pipelines. Ongoing ef-forts to model the time-dependent rheology of gels, in order to beable to model gel breakdown under stress, draw on research suchas that of Cheng and Evans (1965), Petrellis and Flumerfelt (1973),and Rao et al. (1985). Recent studies of the time-dependent rheo-logical behaviour and breakdown of wax–oil gels include that doneby Paso et al. (2009b), in which the mechanical behaviour of amodel wax–oil gel was examined under various shear rates. Pasoet al. observed a convergence of shear stress values for differentshear rates at absolute strain magnitudes greater than 0.1, asshown in Fig. 23. This was indicative of gel strength following apath-independent function of the absolute strain imposed on thegel, and further indicated that the gel structure is a point functionof the absolute strain. Based on this they concluded that, in

Fig. 23. Measured shear stress during breakage of a wax–oil gel at shear ratesranging from 10�5 s�1 to 1 s�1 (Paso et al., 2009b).


modelling the breakdown of a wax gel at low shear rates, the entireshear history could be represented by a single dimensionless vari-able in the form of the absolute strain.

Paso et al. (2009b), furthermore, determined that the maximumshear stress did not provide a useful parameter to characterize thegel structure. Thus, in order to define a structural parameter, k, rep-resenting the fraction of unbroken crystal–crystal linkages remain-ing in the gel structure at a given shear stress, they did so in termsof the experimental stress near the convergence point. They thenused this structural parameter in an nth order degradation modelto describe the gel breakage model, as shown in followingequation.

11� n

ðk� keÞ1�n � 11� n

ðk0 � keÞ1�n ¼ �a _cbt ð18Þ

Here k0 and ke are the initial and equilibrium structural parametervalues, and the degradation rate parameters, n and a _cb, were deter-mined by fitting experimental values of k to equation (18) via a leastsquares minimization procedure, with ke assumed to be 2 � 10�3.

Paso et al. (2009b) were able to obtain good model fits to exper-imental values, as shown in Fig. 24. Their fitted degradation orderfor different shear rates ranged from 2.7 to 3.33, indicating that athird order degradation mechanism controls the breakdown of

Fig. 24. Comparison of experimental and fitted k values at a shear rate of 10�3 s�1.The optimized reaction rate order is 3.07, with a rate constant of 0.131 s�1 (Pasoet al., 2009b).

their model wax–oil gel at constant shear rate conditions. Theyconcluded that a well-defined mechanism controls the rupture ofwax crystal–crystal network linkages, and that the rheologicalmodelling framework based on the structural parameter, k,provides an appropriate physical representation of the breakageprocess, even for crude oils in the field with a variety of hydrocar-bon and additive components that may cause a deviation fromthird order degradation kinetics. They also proposed a model fordescribing shear stress responses associated with changing shearrates during gel degradation by applying a time-dependentBingham constitutive equation to experimental stress–strain dataobtained while increasing the shear rate.

11.2. Examples of restart models

Chang et al. (1999) went onto use a three yield stress modelproposed by Kraynik (1990), which added a dynamic yield stressfor describing behaviour after yielding to the model put forwardby Houwink (1958). The three yield stress model utilized an elas-tic-limit yield stress, se, described as denoting the materials limitof reversibility; a static yield stress, ss, described as the minimumshear stress required to cause the deformation of a material thatmay be described as yielding; and a dynamic yield stress, sd, de-scribed as the shear stress at zero shear rate, extrapolated fromthe flow curve. Chang et al. used this model to describe the threepossible outcomes of applying constant pressure to a gelled pipe-line 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 withthree different regions, as shown in Fig. 25, where R is the totalradius of the pipeline and rf and rc denote the boundaries of theregions:– Flow area – The outermost region (R > r > rf), consisting of a

sheared annulus. Local stress is higher than the static yieldstress (s(r) > ss). The gel structure in this region is immedi-ately broken down and the oil becomes liquid-like, display-ing a dynamic yield stress.

– Creep area – Middle region (rf > r > rc). Local stress is lowerthan static yield stress, but higher than elastic-limit yieldstress (ss > s > se). Gel structure in this region begins todegrade with a viscoelastic deformation.

– Elastic deformation area – Innermost region (r < rc). Localstress is lower than elastic-limit yield stress (s < se). Solid-like core where oil only undergoes elastic deformation. Willinitially move with creep region as an unsheared plug ofradius, r�, until the gel in the creep region degrades fromthe outside in, leaving only the core as the plug.

� Start-up with delay (ss > sw > se) – Flow begins after a delaytime, tdelay. Exterior creep region and interior elastic deforma-tion area exist and, initially, no flow occurs. Flow only beginsonce gel in the creep region has sufficiently degraded, startingat the wall, allowing for movement of an unsheared plug withuniform velocity through the pipe. The size of the plug (r�) willdecrease 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 unaf-fected by shear.

Chang et al. (1999) noted that for a successful start-up, thegelled oil in a cross-section of pipe will become heterogeneous be-cause of differences in the rate of structural breakdown caused bydifferences in local shear stress. Therefore, their model takes intoaccount the time-dependent rheology of the waxy crude oils. Atime-dependent Bingham-style equation, shown in Eqs. (19a)-(19c) was used for an approximation of the time-dependent,

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 con-trolled stress conditions.

s ¼ syðtÞ þ gðtÞ _c; s > syðtÞ ð19aÞ

syðtÞ ¼syð0Þ � syð1Þ

1þ ktþ syð1Þ ð19bÞ

gðtÞ ¼ constant ð19cÞ

Here g is the plastic viscosity, _c is the shear rate, sy is the appar-ent yield stress governing the behaviour of the oil, and k is a rateconstant. sy(0) and sy(1) are the apparent yield stress at timest = 0 and t =1, respectively. sy(0) would be equivalent to ss(0),with an initial wall stress above this value resulting in an instanta-neous finite flow rate, and sy(1) coincides with se(0), with wallstresses below this value resulting in reversible deformation andno possible flow.

The basic physical model used by Chang et al. (1999) to describethe start-up process was the pumping of an incoming fluid (ICF)into a pipe of length, L, and inside diameter, D, to displace the out-going fluid (OGF), as shown in Fig. 26. Here Z(t) is the length of thepipe occupied by the ICF, r�I ðtÞ and r�oðtÞ are the unsheared plug ra-dii of the ICF and OGF respectively at time, t, P1 is the inlet pres-sure, P2 is the exit pressure, and Pz is the interface pressure. Theradius of the unsheared plug in the flow was given by equation,

r�ðtÞ ¼ RsyðtÞswoðtÞ

ð20Þ

where swo(t) is the wall shear stress in the OGF at time t.

Fig. 26. Schematic diagram of two-fluid displacement model. (a)

For the case of start-up without delay (or start-up with delay attime, t > tdelay), Chang et al. (1999) define the initial wall shearstress in terms of the pressure drop. To model the time- and posi-tion-dependent changes in the flow properties of the OGF, Changet al. (1999) used a finite differences method. M time intervalswere used to divide the duration of the flow from start-up(Dt = ti–ti�1), and the flow was treated as approximately steadyin each time interval for sufficiently small Dt. The sheared annulus(r� < r R) was divided, for each instant, ti, into N radial elements ofthickness, Dr, and distance, rj, from the centre of the pipe(rj = rj�1 + Dr = r� + jDr). The volumetric flow rate, Qi, at time ti

was thus given by following equation,

Qi ¼XN

j¼1

Qj þ Q plug ð21Þ

where Qplug is the flow rate of the unsheared plug and Qj is thevolumetric flow rate of the jth annular element. In a later work,However, Davidson et al. (2004) maintained that the finite differ-ences method was unnecessary, because of the quasi-steady stateassumption for the OGF, which was represented as a Bingham fluidthat would have apparent yield stress and plastic viscosity inde-pendent of the shear rate and thus the radial position.

Using their model, Chang et al. (1999) could calculate the plug ra-dius, r�, for each time interval using equations (19b) and (20) with aknown wall stress. The flow rate could then be computed from j = Nat the pipe wall inward to the unsheared plug at j = 0. The onset ofturbulence was predicted by calculation of a critical Reynolds num-ber, with the appropriate adjustment to the friction factor used inthe model. For these calculations the pipe dimensions (L and R),

True interface; (b) simplified interface (Chang et al., 1999).


pump pressure (DPc), properties of the OGF (sy(0), sy(1), g(t), k andqo), and properties of the ICF (sB, gB andqI) need to be known. HereqI

and qo are the fluid densities of the ICF and OGF; sB is the Binghamyield stress; and gB is the Bingham plastic viscosity. Therefore, theaccuracy of this model in predicting the time-dependent flow prop-erties during start-up and the time needed to clear a blockage de-pended greatly on comprehensive knowledge of the system,requiring accurate experimental measurements.

Davidson et al. (2004) developed another model for the restart ofgelled pipelines. This model extended the one developed by Changet al. (1999) to account for the compressibility and inhomogeneityof the gelled oil and displacing fluid. In this model, when the inletpressure creating a wall stress in excess of the static yield stress isapplied to the gelled oil, initially only a narrow region of length Lf de-forms and breaks down under stress. This yielded region is com-pressed by the entering ICF, which is also compressed. Eventually,at time t = t0 the entire gelled oil plug will yield and move togetherwith 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 pre-vious time step). Then the frictional factor, fk, is calculated by iter-ation for each longitudinal ICF and OGF segment at current timestep using the Buckingham–Reiner equation for pipe flow of atime-independent Bingham fluid, and empirical relationshipsdeveloped by other authors for calculating the frictional factor inlaminar and turbulent flow. Equations (22) and (23) are used toevaluate the mean velocity and shearing time, tsk,

q�kQ �k ¼ G� ð22Þ

tskðtÞ ¼ t � k� 1M � 1

t0 ð23Þ

Fig. 27. Schematic of compression

where k is the current subdivision out of M initial subdivisions ofthe gelled oil used in the calculations; and q�k is the dimensionlessdensity and Q �k the dimensionless volumetric flow rate of the cur-rent subdivision. The pressure drop over each segment was calcu-lated using following equation.

s�wk ¼P�k

4DL�k¼ fkq�kt2

k

2ð24Þ

In the calculation procedure used by Davidson et al. (2004), thelength and density of each segment of oil is then updated toaccount for the displacement of the OGF from the length of pipeand the increase in the length of the ICF within the pipe. The ICFrheology is assumed to be time-independent and it is thereforeseparated into segments of equal length in each time step, withthe number of segments increasing by one with each time step.The length of an ICF segment, DLICF, in time interval, i, at timet � t0 is given by following equation.

DLICF ¼ LICF

K þ i¼ DL�

Pmk¼1 LOGF

k

K þ ið25Þ

Here K is the number of ICF segments chosen at time t = t0, m isthe 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 timet � t0. Davidson et al. (2004) also calculated DLOGF

k and the averagedensity for the k th segment in dimensionless form. Next in theircalculation procedure, the location of each segment and the ICF–OGF interface is determined relative to the downstream end ofthe OGF plug. Then the pressure drop over each ICF and OGFsegment is summed to give the overall pressure drop, and thedifference between this value and the applied pressure drop

flow (Davidson et al., 2004).


calculated and mass flow rate adjusted accordingly. This overallprocess is iterated until the difference is negligible. G� iterates tozero in the case that the applied pressure is not high enough tostart flow at a given time, and the calculated pressure drop be-comes the minimum required for start-up. The results of this mod-el were significantly different from those of the earlier modeldeveloped by Chang et al. (1999), indicating the importance of fullyunderstanding the mechanism by which the gelled oil yields and isdisplaced, and of determining the most realistic assumptions thatcan be made during modelling.

Other researchers have also tackled understanding, modellingand optimizing the restart of gelled lines. Borghi et al. (2003)developed a model focusing on solid-like fracture propagation, vis-cous dissipation and compression of the broken gelled oil. Ekwer-ibe et al. (2009), for instance, studied the effect of system pressureon the restart of gelled subsea pipelines. They determined thathigher system pressures in subsea pipelines could lead to the for-mation of a weaker gel with lower yield strength, which wouldmean that the necessary applied pressure for displacing it wouldbe more easily and cheaply achieved than might be predicted.

12. Conclusions

Contention still remains as to the specific mechanisms that gov-ern wax deposition in pipelines. However, the importance ofmolecular diffusion is generally accepted and shear dispersion isusually not dismissed, at least due to the involvement of shearforces in the removal of wax deposits, the accounting of whichhas been shown by some authors to have a great impact on theaccuracy of wax deposition models. Many models have been devel-oped based on the importance of these mechanisms, for which theapproach to a realistic representation of the solid phase wax com-ponents has a significant impact on accuracy. Recently, a correctheat-mass transfer analogy has been introduced into the modellingof wax deposition, allowing for more accurate prediction across therange of possible precipitation kinetics. In the future even moreaccurate and robust models will be possible by combining thisnew approach with an increased understanding of the mechanismsinvolved in wax deposition and gelation and of the impact of otherspecies present in crude oil, such as asphaltenes and emulsifiedwater.

Understanding wax aging mechanisms is also very important tofully understanding the process of the formation of wax deposits inpipelines. Furthermore, understanding these mechanisms and pre-dicting the CCN of particular crude oils would be helpful in deter-mining what chemical inhibitors would be most effective forpreventing wax build-up in pipelines carrying those oils. Thecontinuing research into methods of inhibiting wax depositionand removing deposits has the potential of making the mainte-nance of crude oil pipelines significantly easier, as it becomes eas-ier to optimize pigging frequency, to determine the minimumpressure required to restart gelled lines, or even to avoid the needfor constant wax removal procedures by finding a way to cost-effectively implement a promising method of control such as theuse of polar crude oil fractions or biological removal measures.

References

Addison, G.E., 1984. Paraffin Control More Cost-Effective. In: SPE Eastern RegionalMeeting. Charleston, 1984. Society of Petroleum Engineers.

Al-Sabagh, A.M., El-Kafrawy, A.F., Khidr, T.T., El-Ghazawy, R.A., Mishrif, M.R., 2007.Synthesis and evaluation of some novel polymeric surfactants based onaromatic amines used as wax dispersant for waxy gas oil. J. Dispersion Sci.Technol. 28, 976–983.

Asperger, R.G., Sattler, R.E., Tolonen, W.J., Pitchford, A.C., 1981. Prediction of WaxBuildup in 24 inch, Cold Deep Sea Oil Loading Line. USMS 10363.

Azarinezhad, R., Chapoy, A., Anderson, R., Tohidi, B., 2010. A wet cold-flowtechnology for tackling offshore flow-assurance. SPE Projects, Facilities andConstruction 5, 58–64.

Azevedo, L.F.A., Teixeira, A.M., 2003. A critical review of the modeling of waxdeposition mechanisms. Petrol. Sci. Technol. 21, 393–408.

Bagatin, R., Busto, C., Correra, S., Margarone, M., Carniani, C., 2008. Wax modelling:there is need for alternatives. In: SPE Russian Oil & Gas Technical Conferenceand Exhibition. Moscow, 2008. Society of Petroleum Engineers.

Banki, R., Hoteit, H., Firoozabadi, A., 2008. Mathematical formulation and numericalmodeling of wax deposition in pipelines from enthalpy–porosity approach andirreversible thermodynamics. Int. J. Heat Mass Transfer 51, 3387–3398.

Barnes, H.A., 1999. The Yield stress—a review or ‘pamsa qei’—everything flows? J.Non-Newtonian Fluid Mech. 81, 133–178.

Bello, O.O., Fasesan, S.O., Teodoriu, C., Reinicke, K.M., 2006. An evaluation of theperformance of selected wax inhibitors on paraffin deposition of Nigerian crudeoils. Pet. Sci. Technol. 24, 195–206.

Bilderback, C.A., McDougall, L.A., 1963. Complete paraffin control in petroleumproduction. SPE J. Petrol. Technol. 21, 1151–1156.

Borghi, G.P., Correra, S., Merlini, M., Carniani, C., 2003. Prediction and scaleup ofwaxy oil restart behavior. In: SPE International Symposium on OilfieldChemistry. Houston, 2003. Society of Petroleum Engineers.

Bummer, B.L., 1971. Improved paraffin prevention techniques reduce operatingcosts, powder river basin, wyoming. In: Rocky Mountain Regional Meeting ofthe Society of Petroleum Engineers of AIME. Billings, 1971. American Instituteof Mining, Metallurgical, and Petroleum Engineers.

Burger, E.D., Perkins, T.K., Striegler, J.H., 1981. Studies of wax deposition in the transalaska pipeline. J. Petrol. Technol. 33, 1075–1086.

Carmen García, M., Urbina, A., 2003. Effect of crude oil composition and blending onflowing properties. Petrol. Sci. Technol. 21, 863–878.

Carmen García, M., 2001. Paraffin deposition in oil production. In: SPE InternationalSymposium on Oilfield Chemistry. Houston, 2001. Society of PetroleumEngineers.

Carmen García, M., Orea, M., Carbognani, L., Urbina, A., 2001. The effect of paraffinicfractions on crude oil wax crystallization. Petrol. Sci. Technol. 19, 189–196.

Chakrabarti, D.P., Das, G., Das, P.K., 2006. The transition from water continuous tooil continuous flow pattern. AIChE J. 52, 3668–3678.

Chakrabarti, D.P., Das, G., Das, P.K., 2007. Identification of stratified liquid–liquidflow through horizontal pipes by a non-intrusive optical probe. Chem. Eng. Sci.62, 1861–1876.

Chang, C., Boger, D.V., Nguyen, Q.D., 1998. The yielding of waxy crude oils. Ind. Eng.Chem. Res. 37, 1551–1559.

Chang, C., Boger, D.V., Nguyen, Q.D., 2000. Influence of thermal history on the waxystructure of statically cooled waxy crude oil. SPE J. 5, 148–157.

Chang, C., Nguyen, Q.D., Rønningsen, H.P., 1999. Isothermal start-up of pipelinetransporting waxy crude oil. J. Non-Newtonian Fluid Mech. 87, 127–154.

Chen, X., Tsang, Y., Zhang, H.Q., Chen, T.X., 2007. Pressure-wave propagationtechnique for blockage detection in subsea flowlines. In: SPE AnnualTechnical Conference and Exhibition. Anaheim, 2007. Society of PetroleumEngineers.

Chen, X.T., Butler, T., Volk, M., Brill, J.P., 1997. Techniques for measuring waxthickness during single and multiphase flow. In: SPE Annual TechnicalConference and Exhibition. San Antonio, 1997. Society of PetroleumEngineers.

Cheng, D.C.H., Evans, F., 1965. Phenomenological characterization of the rheologicalbehavior of inelastic reversible thixotropic and antithixotropic fluids. Brit. J.Appl. Phys. 16, 1599–1617.

Cordoba, A.J., Schall, C.A., 2001. Application of a heat method to determine waxdeposition in a hydrocarbon binary mixture. Fuel 80, 1285–1291.

Correra, S., Fasano, A., Fusi, L., Merino-Garcia, D., 2007. Calculating depositformation in the pipelining of waxy crude oils. Meccanica 42, 149–165.

Coutinho, J.A.P., Daridon, J.L., 2005. The limitations of the cloud point measurementtechniques and the influence of the oil composition on its detection. Pet. Sci.Technol. 23, 1113–1128.

Coutinho, J.A.P., 1998. Predictive UNIQAC: a new model for the description ofmultiphase solid-liquid equilibria in complex hydrocarbon mixtures. Ind. Eng.Chem. Res. 37, 4870.

Coutinho, J.A.P., Lopes-da-Silva, J.A.L., Ferreira, A., Soares, M.S., Daridon, J.L., 2003.Evidence for the aging of wax deposits in crude oils by ostwald ripening. Petrol.Sci. Technol. 21, 381–391.

Davidson, M.R., Nguyen, Q.D., Chang, C., Rønningsen, H.P., 2004. A model for restartof a pipeline with compressible gelled waxy crude oil. J. Non-Newtonian FluidMech. 123, 269–280.

de Oliveira, M.C.K., Carvalho, R.M., Carvalho, A.B., Couto, B.C., Faria, F.R.D., Cardoso,R.L.P., 2010. Waxy crude oil emulsion gel: impact on flow assurance. EnergyFuels 24, 2287–2293.

Duffy, D.M., Rodger, P.M., 2002. Modeling the activity of wax inhibitors: a casestudy of poly(octadecyl acrylate). J. Phys. Chem. B 106, 11210–11217.

Duffy, D.M., Moon, C., Rodger, P.M., 2004. Computer-assisted design of oil additives:hydrate and wax inhibitors. Mol. Phys. 102, 203–210.

Edmonds, B., Moorwood, T., Szczepanski, R., Zhang, X., 2008. Simulating waxdeposition in pipelines for flow assurance. Energy Fuels 22, 729–741.

Ekweribe, C.K., 2008. Quiescent Gelation of Waxy Crudes and Restart of Shut-inSubsea Pipelines (MS Thesis). Norman, Oklahoma: University of Oklahoma.

Ekweribe, C.K., Civan, F., Lee, H.S., Singh, P., 2009. Interim Report on Pressure Effecton Waxy-Crude Pipeline-Restart Conditions Investigated by a Model System.SPE Projects, Facilities & Construction, pp. 61–74.


Etoumi, A., El Musrati, I., El Gammoudi, B., El Behlil, M., 2008. The reduction of waxprecipitation in waxy crude oils by Pseudomonas species. J. Ind. Microbiol.Biotechnol. 35, 1241–1245.

Farina, A., Fasano, A., 1997. Flow characteristics of waxy crude oils in laboratoryexperimental loops. Math. Comput. Model. 25, 75–86.

Fasano, A., Fusi, L., Correra, S., 2004. Mathematical models for waxy crude oils.Meccanica 39, 441–482.

Fielder, M., Johnson, R.W., 1986. The use of pour-point depressant additive in thebeatrice field. In: SPE European Petroleum Conference. London, 1986. Society ofPetroleum Engineers.

Frigaard, I., Vinay, G., Wachs, A., 2007. Compressible displacement of waxycrude oils in long pipeline startup flows. J. Non-Newtonian Fluid Mech.147, 45–64.

Fulford, R.S., 1975. Oilwell paraffin prevention chemicals. In: SPE Regional Meeting.Oklahoma, 1975. American Institute of Mining, Metallurgical, and PetroleumEngineers.

Fung, G., Backhaus, W.P., McDaniel, S., Erdogmus, M., 2006. To pig or not to pig: themarlin experience with stuck pig. In: Offshore Technology Conference. Houston,2006. Offshore Technology Conference.

Fusi, L., Farina, A., 2004. A mathematical model for bingham-like fluids with visco-elastic core. Z. Angew. Math. Phys. 55, 826–847.

Fusi, L., 2003. On the stationary flow of a waxy crude oil with depositionmechanisms. Nonlinear Anal. 53, 507–526.

Groffe, D., Groffe, P., Takhar, S., Andersen, S.I., Stenby, E.H., Lindeloff, N. et al., 2001.A wax inhibition solution to problematic fields: a chemical remediation process.Petrol. Sci. Technol. 19, 205–217.

Gudmundsson, J.S., ‘‘Cold Flow Technology’’. In: Proc. 4th Intnl. Hydrates Conf.,Yokohama (2002), pp. 912–916.

Haghighi, H., Azarinezhad, R., Chapoy, A., Anderson, R., Tohidi, B., 2007. Hydraflow:avoiding gas hydrate problems. In: SPE Europe/EAGE Annual Conference andExhibition. London, 2007. Society of Petroleum Engineers.

Hammami, A., Ratulowski, J., Coutinho, J.A.P., 2003. Cloud points: can we measureor model them? Petrol. Sci. Technol. 21, 345–358.

Hammerschmidt, E.G., 1934. Formation of gas hydrates in natural gastransportation lines. Ind. Eng. Chem. 26, 851–855.

Haq, M.A., 1978. Deposition of Paraffin Wax from its Solution with Hydrocarbons(USMS 10541). Society of Petroleum Engineers.

He, Z., Mei, B., Wang, W., Sheng, J., Zhu, S., Wang, L. et al., 2003. A pilot test usingmicrobial paraffin-removal technology in liaohe oilfield. Petrol. Sci. Technol. 21,201–210.

Hernandez, O.C., Hensley, H., Sarica, C., Brill, J.P., Volk, M., Delle-Case, E., 2004.Improvements in single-phase paraffin deposition modeling. SPE Prod. Oper. 19,237–244.

Herri, J.-M., Pic, J.S., Gruy, F., Cournil, M., 1999. Methane hydrate crystallizationmechanism from in-situ particle size analyzer. AIChE J. 45, 590–602.

Holder, G.A., Winkler, J., 1965. Wax crystallization from distillate fuels. J. Inst. Petrol.51, 228–252.

Houwink, R., 1958. Elasticity, Plasticity and Structure of Matter. CambridgeUniversity Press, New York.

Hunt, E.B.J., 1962. Laboratory study of paraffin deposition. SPE J. Petrol. Technol. 14,1259–1269.

Ilahi, M., 2005. Evaluation of Cold Flow Concepts (MS Thesis). Trondheim, Norway:Norwegian University of Science and Technology.

Jang, Y.H., Blanco, M., Creek, J., Tang, Y., Goddard, W.A., 2007. Wax Inhibitionby comb-like polymers: support of the incorporation-perturbationmechanism from molecular dynamics simulations. J. Phys. Chem. B 111,13173–13179.

Jennings, D.W., Breitigam, J., 2009. Paraffin inhibitor formulations for differentapplication environments: from heated injection in the desert to extreme coldarctic temperatures. Energy Fuels 24, 2337–2349.

Jorda, R.M., 1966. Paraffin deposition and prevention in oil wells. SPE J. Petrol.Technol. 18, 1605–1612.

Kelland, M.A., 2009. Production Chemicals for the Oil and Gas Industry. CRCPress.

Kraynik, A.M., 1990. ER fluid standards: comments on er fluid rheology. In: Carlson,J.D., Sprecher, A.F., Conrad, H. (Eds.), Proceedings of the Second InternationalConference on ER Fluids. Raleigh, 1990. Technomic Publishing Company.

Kriz, P., Andersen, S.I., 2005. Effect of asphaltenes on crude oil wax crystallization.Energy Fuels 19, 948–953.

Lee, H.S., 2008. Computational and Rheological Study of Wax Deposition andGelation in Subsea Pipelines (PhD Dissertation). Ann Arbor, Michigan:University of Michigan.

Lee, H.S., Singh, P., Thomason, W.H., Fogler, H.S., 2008. Waxy oil gel breakingmechanisms: adhesive versus cohesive failure. Energy Fuels 22, 480–487.

Leelavanichkul, P., Deo, M.D. Hanson, F.V., 2004. Crude oil characterization andregular solution approach to thermodynamic modeling of solid precipitation atlow pressure. Petrol. Sci. Technol. 22, 973–990.

Leiroz, A.T., Azevedo, L.F.A., 2005. Studies on the mechanisms of wax deposition inpipelines. In: Offshore Technology Conference. Houston, 2005. OffshoreTechnology Conference.

Li, H., Zhang, J., Yan, D., 2005. Correlations between the pour point or gel point andthe amount of precipitated wax for waxy crudes. Pet. Sci. Technol. 23, 1313–1322.

Lingelem, M.N., Majeed A.I., Stange, E. Industrial experience in evaluation of hydrateformation, inhibition, and dissociation in pipeline design and operation. In:Proc. 1st Intnl. Hydrates Conf., New-Paltz, NY (1993).

Lira-Galeana, C., Firoozabadi, A., Prausnitz, J.M., 1996. Thermodynamics of waxprecipitation in petroleum mixtures. AIChE J. 42, 239–248.

Lockhart, T., Correra, S., 2005. Colloid and Surface Science Issues in the PetroleumIndustry. In: Ente Nazionale Idrocarburiz & Istituto della Enciclopedia ItalianaEncyclopaedia of Hydrocarbons. Roma, Italy: Istituto della Enciclopedia Italiana.Ch. 3.2.1. pp. 167–177.

Lopes-da-Silva, J.A., Coutinho, J.A.P., 2007. Analysis of the isothermal structuredevelopment in waxy crude oils under quiescent conditions. Energy Fuels 21,3612–3617.

Majeed, A., Bringedal, B., Overa, S., 1990. Model calculates wax deposition for n. seaoils. Oil Gas J. 88, 63–69.

Manka, J.S., Ziegler, K.L., 2001. Factors affecting the performance of crude oil wax-control additives. In: SPE Production and Operations Symposium. Oklahoma,2001. Society of Petroleum Engineers.

Manka, J.S., Magyar, J.S., Smith, R.P., 1999. A novel method to winterize traditionalpour point depressants. In: SPE Annual Technical Conference and Exhibition.Houston, 1999. Society of Petroleum Engineers.

Matzain, A., 1999. Multiphase Flow Paraffin Deposition Modeling (PhDDissertation). Tulsa, Oklahoma: The University of Tulsa.

Matzain, A., Apte, M.S., Zhang, H., Volk, M., Brill, J.P., Creek, J.L., 2002. Investigationof paraffin deposition during multiphase flow in pipelines and wellbores—part1: experiments. J. Energy Res. Technol. 124, 180–186.

Mendell, J.L., Jessen, F.W., 1970. Mechanism of Inhibition of Paraffin Deposition inCrude Oil Systems. In: Ninth Bienniel Production Techniques Symposium.Wichita Falls, 1970. American Institute of Mining, Metallurgical and PetroleumEngineers.

Merino-Garcia, D., Correra, S., 2008. Cold flow: a review of a technology to avoidwax deposition. Pet. Sci. Technol. 26, 446–459.

Merino-Garcia, D., Margarone, M., Correra, S., 2007. Kinetics of waxy gel formationfrom batch experiments. Energy Fuels 21, 1287–1295.

Mersmann, A. 2002. Crystallization Technology Handbook, second ed. MarcelDekker.

Nautiyal, S.P., Kumar, S., Srivastava, S.P., 2008. Crystal structure of n-paraffinconcentrates of crude oils. Pet. Sci. Technol. 26, 1339–1346.

Newberry, M.E., Barker, K.M., 1985. Formation damage prevention through thecontrol of paraffin and asphaltene deposition. In: SPE Production OperationsSymposium. Oklahoma City, 1985. Society of Petroleum Engineers.

Oh, K., Jemmett, M., Deo, M., 2009. Yield behavior of gelled waxy oil: effect of stressapplication in creep ranges. Ind. Eng. Chem. Res. 48, 8950–8953.

Paso, K.G., Fogler, H.S., 2003. Influence of n-paraffin composition on the aging ofwax-oil gel deposits. AIChE J. 49, 3241–3252.

Paso, K.G., 2005. Paraffin Gelation Kinetics (PhD Dissertation). Ann Arbor, Michigan:University of Michigan.

Paso, K.G., Kompalla, T., Aske, N., Rønningsen, H.P., Øye, G., Sjöblom, J., 2009a. Novelsurfaces with applicability for preventing wax deposition: a review. J.Dispersion Sci. Technol. 30, 757–781.

Paso, K.G., Kompalla, T., Oschmann, H.J., Sjöblom, J., 2009b. Rheological degradationof model wax–oil gels. J. Dispersion Sci. Technol. 30, 472–480.

Paso, K.G., Silset, A., Sørland, G., Gonçalves, M.A.L., Sjöblom, J., 2009c.Characterization of the formation, flow ability, and resolution of Braziliancrude oil emulsions. Energy Fuels 23, 471–480.

Patton, C.C., 1970. paraffin deposition from refined wax-solvent systems. Soc.Petrol. Eng. J., 17–24.

Pedersen, K.S., Rønningsen, H.P., 2003. Influence of wax inhibitors on waxappearance temperature, pour point, and viscosity of waxy crude oils. EnergyFuels 17, 321–328.

Petrellis, N.C., Flumerfelt, R.W., 1973. Rheological behavior of shear degradable oils:kinetic and equilibrium properties. Can. J. Chem. Eng. 51, 291–301.

Prausnitz, J.M., Lichtenthaler, R.N., Azevedo, E.G., 1986. Molecular Thermodynamicsof Fluid-phase Equilibria. Prentice-Hall, Englewood Cliffs, NJ.

Quenelle, A., Gunaltun, M., 1987. Comparison between thermal insulation coatingsfor underwater pipelines. In: Offshore Technology Conference. Houston, 1987.Offshore Technology Conference.

Raj, T.S., Chakrabarti, D.P., Das, G., 2005. Liquid-liquid stratified flow throughhorizontal conduits. Chem. Eng. Technol. 28, 899–907.

Ramírez-Jaramillo, E., Lira-Galeana, C., Manero, O., 2001. Numerical Simulation ofWax Deposition in Oil Pipeline Systems. Petrol. Sci. Technol. 19, 143–156.

Ramírez-Jaramillo, E., Lira-Galeana, C., Manero, O., 2004. Modeling wax depositionin pipelines. Petrol. Sci. Technol. 22, 821–861.

Rana, D.P., Bateja, S., Biswas, S.K., Kumar, A., Misra, T.R., Lal, B., 2010. Novelmicrobial process for mitigating wax deposition in down hole tubular andsurface flow lines. In: SPE Oil and Gas India Conference. Mumbai, 2010. Societyof Petroleum Engineers.

Rao, B.M.A., Mahajan, S.P., Khilar, K.C., 1985. A Model on the breakdown of crude oilgel. Can. J. Chem. Eng. 63, 170–172.

Reistle, C.E.J., 1928. Methods of Dealing with Paraffin Troubles Encountered inProducing Crude Oils. USBM Technical Papers.

Reistle, C.E.J., 1932. Paraffin and Congealing Oil Problems. USBM Bulletins.Sarmento, R.C., Ribbe, G.A.S., Azevedo, L.F.A., 2004. Wax blockage removal by

inductive heating of subsea pipelines. Heat Transfer Eng. 25, 2–12.Senra, M., Panacharoensawad, E., Kraiwattanawong, K., Singh, P., Fogler, H.S., 2008.

Role of n-alkane polydispersity on the crystallization of n-alkanes fromsolution. Energy Fuels 22, 545–555.

Senra, M., Scholand, T., Maxey, C., Fogler, H.S., 2009. Role of polydispersity andcocrystallization on the gelation of long-chained n-alkanes in solution. EnergyFuels 23, 5947–5957.


Sifour, M., Al-Jilawi, M.H., Aziz, G.M., 2007. Emulsification properties ofbiosurfactant produced from Pseudomonas aeruginosa RB 28. Pak. J. Biol. Sci.10, 1331–1335.

Singh, P., Venkatesan, R., Fogler, H.S., 2000. Formation and aging of incipient thinfilm wax–oil gels. AIChE J. 46, 1059–1074.

Singh, P., Venkatesan, R., Fogler, H.S., 2001a. Morphological evolution of thick waxdeposits during aging. AIChE J. 47, 6–18.

Singh, P., Youyen, A., Fogler, H.S., 2001b. Existence of a critical carbon number in theaging of a wax-oil gel. AIChE J. 47, 2111–2124.

Singhal, H.K., Sahai, G.C., Pundeer, G.S., Chandra, K., 1991. Designing and selectingwax crystal modifier for optimum field performance based on crude oilcomposition. In: Annual Technical Conference and Exhibition of the Society ofPetroleum Engineers. Dallas, 1991. Society of Petroleum Engineers.

Smith, P.B., Ramsden, R.M.J., 1978. The prediction of oil gelation in submarinepipelines and the pressure required for restarting flow. In: European OffshorePetroleum Conference and Exhibition. London, 1978. European OffshorePetroleum Conference and Exhibition.

Solaimany Nazar, A.R., Dabir, B., Islam, M.R., 2005a. A multi-solid phasethermodynamic model for predicting wax precipitation in petroleummixtures. Energy Sources 27, 173–184.

Solaimany Nazar, A.R., Dabir, B., Islam, M.R., 2005b. Experimental and mathematicalmodeling of wax deposition and propagation in pipes transporting crude oil.Energy Sources 27, 185–207.

Soni, H.P., Kiranbala, Bharambe, D.P., 2008. Performance-based design of waxcrystal growth inhibitors. Energy Fuels 22, 3930–3938.

Tinsley, J.F., Prud’homme, R.K., Guo, X., Adamson, D.H., Shao, S., Amin, D. et al., 2007.Effects of polymers on the structure and deposition behavior of waxy oils. In:SPE International Symposium on Oilfield Chemistry. Houston, 2007. Society ofPetroleum Engineers.

Torres, G.A., Turner, C., 2005. Method of straight lines for a bingham problem as amodel for the flow of waxy crude oils. Electron. J. Diff. Equat., 1–15.

Venkatesan, R., Fogler, H.S., 2004. Comments on analogies for correlated heat andmass transfer in turbulent flow. AIChE J. 50, 1623–1626.

Venkatesan, R., Östlund, J., Chawla, H., Wattana, P., Nydén, M., Fogler, H.S., 2003. TheEffect of asphaltenes on the gelation of waxy oils. Energy Fuels 17, 1630–1640.

Vinay, G., Wachs, A., Frigaard, I., 2007. Start-up transients and efficient computationof isothermal waxy crude oil flows. J. Non-Newtonian Fluid Mech. 143, 141–156.

Visintin, R.F.G., Lockhart, T.P., Lapasin, R., D’Antona, P., 2008. Structure of waxycrude oil emulsion gels. J. Non-Newtonian Fluid Mech. 149, 34–39.

Wang, K.S., Wu, C.H., Creek, J.L., Shuler, P.J., Tang, Y., 2003. Evaluation of effects ofselected wax inhibitors on paraffin deposition. Petrol. Sci. Technol. 21, 369–379.

Wang, Q., Sarica, C. & Volk, M., 2008. An experimental study on wax removal inpipes with oil flow. J. Energy Resour. Technol., 130.

Wardhaugh, L.T., Boger, D.V., 1991. The measurement and description of theyielding behavior of waxy crude oil. J. Rheol. 35, 1121–1156.

Wardhaugh, L.T., Boger, D.V., Tonner, S.P., 1988. Rheology of waxy crude oils. In: SPEInternational Meeting on Petroleum Engineering. Tianjin, 1988. Society ofPetroleum Engineers.

Woo, G.T., Garbis, S.J. & Gray, T.C., 1984. Long-term control of paraffin deposition.In: Technical Conference and Exhibition. Houston, 1984. Society of PetroleumEngineers.

Wuhua, C., Zongchang, Z., 2006. Thermodynamic modeling of wax precipitation incrude oils. Chin. J. Chem. Eng. 14, 685–689.

Yang, X., Kilpatrick, P., 2005. Asphaltenes and waxes do not interact synergisticallyand coprecipitate in solid organic deposits. Energy Fuels 19, 1360–1375.

Zaman, M., Agha, K.R., Islam, M.R., 2006. Laser based detection of paraffin in crudeoil samples: numerical and experimental study. Pet. Sci. Technol. 24, 7–22.

Zaman, M., Bjorndalen, N., Islam, M.R., 2004. Detection of precipitation in pipelines.Petrol. Sci. Technol. 22, 1119–1141.

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