A.M.Sous,H.A.Mtos,L.Guerreiro

a CERENA,Department of Chemical Engineering,Instituto Superior Técnico,Universidade de Lisboa,Av.Rovisco Pais 1,Lisboa,Portugal

b Partex Oil and Gas,Rua.Ivone Silva 6,Lisboa,Portugal

ABSTRACT Wax deposition inside the tubing walls endures being a critical operational challenge faced by the petroleum industry.The build-up of wax deposits may lead to the increase of pumping power,as well as the decrease of flow rate or,even,to the total blockage,with production losses and high operational costs.

Keywords:Wax deposition mechanism Molecular diffusion Brownian diffusion Shear dispersion Shear removal Thermal diffusion Emulsions Carbon dioxide

1.Introduction

Under certain environmental conditions,producing paraffinic crude oil includes dealing with wax deposition phenomena.As the temperature inside the well decreases below the cloud point (such point is the temperature below which wax forms with a cloudy appearance)or wax appearance temperature (WAT),wax precipitation will occur.This phenomenon constraints the flow,inducing non-Newtonian behaviour and increasing effective viscosities,as the temperature of a waxy crude oil reaches the Pour Point (the temperature below which liquid becomes semi-solid and loses its flowing characteristics).Thus,a heterogeneous layer of sticky freshly precipitated paraffin waxes develops near the tubing wall or the well borders.Over time,the crystallized wax particles aggregate to one another and form a paraffin deposit that can continue growing,leading to the reduction of the flow available section.

Numerous studies on wax deposition were performed during the past decades.Most of them dealt with the problem in pipelines,whose sectional homogeneity and improved traceability for experimental purposes allowed endeavouring very important results.Nevertheless,the wax deposition problem is extremely significant in wells [1].

Considering the previous,this document was prepared with the purpose of critically reviewing the current knowledge on wax deposition mechanisms,from the classical to the most recent,applied to the case of vertical waxy crude oil wells.

Furthermore,it is also expected to highlight the issues that need further understanding and to present the progress that has been made.

2.Wax deposition mechanisms and its validity for vertical wells

Numerous mathematical models have been deduced to describe the wax deposition behaviour [2].With the purpose of fully model the flow of waxy crude oils,it is necessary to understand the mechanisms at play and the fluid properties.The mechanisms governing the deposition and removal of solid wax must be incorporated into global simulation models.The main question is: what are the relevant wax deposition mechanisms? Investigations have been ongoing for decades.In fact,this question was intensively studied since 1955.Since then,several studies were developed to better understand the phenomenon.The following topics will describe and explain the main wax deposition mechanisms encountered.

2.1.Molecular diffusion

During the oil production,the crude oil will lose heat to the surrounding areas.Once the temperature decreases below the wax appearance temperature,the dissolved wax precipitate out of the crude oil.It is expected that the inner wall is colder than the bulk fluid,resulting in a higher wax precipitation at the wall,rather than in the bulk.Consequently,it results in a greater concentration of dissolved wax in the bulk,than on the pipe wall,which creates a radial concentration gradient of the waxes between the bulk and the wall (Fig.1).

For turbulent flow regime,the distribution of velocity,temperature and concentration profiles in the cross-section does not show as significant differences in value as the ones observed in laminar flow.Thus,wax transport will be governed by the dominant gradients at the laminar sub-layer,close to the tubing wall or well outer frontier [3].

Molecular diffusion occurs due to the concentration gradient and it is responsible for the wax migration from the bulk (which has a higher concentration of the dissolved waxes)toward the wall (which has a lower concentration).

The precipitation of waxes on the wall surface contributes to the formation of the wax deposit.As soon as the emerging deposit layer is formed,the flow boundary becomes the surface of the wax deposit.

The precipitation of the dissolved waxes on the deposit surface leads to the development of the deposit.

As the waxy crude continues to flow through the tubing,the molecular diffusion toward the deposit continues to occur,resulting in the accumulation of the wax deposit.However,not all of these waxy molecules form a new deposit layer.Some of them continue to diffuse into the wax deposit,which results in the increase of wax fraction in the wax deposit,leading to a phenomenon known as deposit aging [4].

Fig.2 shows a schematic representation of molecular diffusion of waxy components in a well since the initial stage of deposition,until the aging of the wax deposit [4].

The wax transport rate is given by Eq (1),the Fick diffusion equation [5]:

where,Wmis the wax deposition rate(kg.s1),wis thewax density(kg.m3),Ais the surface area available for deposition(m2),Dmis the diffusion coefficient or diffusivity of wax in oil(m2.s1),is the variation of dissolved wax concentration with the temperature(°C1)andis the radial temperature gradient(°C.m1).

Base don experimentaldata,Wilkeand Chang[6]proposed Eq.(2)to estimate the molecular diffusion coefficient,Dm(cm2.s1),using 155 experimental points,with 123 different solute-solvent systems:

where,Tis the absolute temperature (K),MWsolventis the molecular weight of solvent (g.mol1),xis the Wilke and Chang association parameter (x=1 for non-associated solvents,andx=2.6 for water),μsolutionisthe solution dynamic viscosity (cP),andVsoluteis the molar volu me ofsolute atnormal boilingpoint (cm3.mol1).

The diffusion coefficient of the waxy components in the oil typically 109m2.s1[6,7].

2.2.Brownian diffusion

It is suggested that wax deposition can occur due to the Brownian motion of wax crystals,but not many existing deposition models take it into account.

Brownian diffusion in the mechanism by which wax solid crystals,in suspension within the crude oil,collide with thermally agitated oil molecules [5].From those collisions,random Brownian movements of the wax suspended particles are generated [8].Considering the wax concentration gradient,it is possible that the net effect of Brownian motions results in the transportation of wax crystals towards the concentration decreasing.

For spherical,noninteracting particles,the Brownian diffusion coefficient (m2s1)isgiven by Eq (3)[9]:

whereRis the gas constant(8.314JK1mol1),Tis the temperature (K),risthe radiusofthemolecule(m),μsolventis thesolvent dynamicviscosity(Pas1)andNis theAvogadro'snumber (6.022×1023mol1).

The Brownian diffusion mechanism is not likely to be relevant for wax deposition since at wall the temperature is lower than in the bulk.This results in a higher amount of precipitated wax components at the wall than in the bulk.It is expected that Brownian movements will transport these solid waxes from the wall toward the bulk oil,instead of moving them toward the wall and deposit.

Therefore,many authors have dismissed Brownian diffusion significance for wax deposition mechanisms.Nevertheless,it has not been ruled out as a possible contributing factor [10,11].

2.3.Shear dispersion

Burger et al.[5]described the lateral movement of particles from a region of higher velocity towards a region of lower velocity,due to the shear effect near to a pipe wall.Shear dispersion could contribute to wax deposition through this lateral motion of particles immersed in the flow.

The shear dispersion coefficientDs(cm2s1)was experimentally determined by Eckstein et al.[12],as a linear relation betweenDs/r2,whereris the particle radius (cm)and is the mean shear rate of s uspending fluid(s1),andthevolumetricconcentration of waxsuspendedparticles,(m3/m3)for0＜ ＜0.20:

Fig.1.Temperature profile and wax concentration gradient.

Fig.2.Schematic of molecular diffusion and deposit axing.

Furthermore,diffusion coefficient proportionality towas highlighted by Leighton and Acrivos [13].

Some researchers,such as,Hsu et al.[14]and Fusi [15]claimed that shear dispersion mechanism is important to model the wax deposition.Another perspective,presented by Fasano et al.[16]claimed that for temperatures much lower than the cloud point and for moderate heat fluxes the governing process is shear dispersion,while for slightly higher temperatures the dominant process is molecular diffusion.

However,opposite results were achieved by previews studies,developed by Bern et al.[17].It was found that the wax deposition rate did not rise with the increase of shear rate,casting the doubt on the shear dispersion mechanism.Actually,some discoveries about particle fluid dynamics mechanisms give the idea that the wax components in the fluid flow are not to be dispersed toward the wall.Saffman found that particles located in the viscous layer,near the wall,tend to be re-integrated into the bulk flow due to the lifting force produced by the turbulent flow [18].These results suggested that the shear dispersion mechanism is not significant or even likely.

Azevedo and Teixeira claimed that shear dispersion shall not contribute to deposition since experimental evidence shows no deposition of wax under conditions of absent heat flux [11].In those conditions,deposition would only be possible if driven by a flow-induced mechanism,such as shear dispersion.

2.4.Shear removal,shear stripping or shear sloughing

Shear stripping is the mechanism of wax removal,from the tubing walls,due to shear stress induced by flowing stream on the wax layer.The inflow can slough pieces of wax from the deposit,acting as a wax removal mechanism.

Modelling wax stripping effect by shear forces could help in the design of flowing chemical improvers,as some of them may act by softening gel structures that are more prone to be removed by the shear forces.

Some researchers,such as Sarica and Volk [19],have tried to incorporate this stripping effect in simulation models,in order to reduce the deposit formation rate,while targeting a greater level of fidelity to the actual physical behaviour.

Edmonds et al.[20]express the wax shearing rate,J,as:

where,cis the shear constant (-),is the wax layer thickness (m)is the mass fraction of wax in gel layer (-),is the shear stress (N/m2)and it is as obtained by:

Being,fthe Fanning friction factor (-),the density of the flowing oi l (kg/m3)anduothe oil velocity (m/s).

2.5.Gravity settling

The settling velocity,Vg,can be computed as the balance of the buoyancy and the viscous forces [21],as presented in the Eq.(7):

here,Vgisthesettlingvelocity(m/s),distheparticlediameter(m),is the particledensity(kg/m3),isthefluid density(kg/m3),andμisthe fluid viscosity (Pa.s).

Azevedo and Teixeira [11]classify gravitational settling as insignificant in typically active oil and gas systems,following experimental evidence from Burger et al.[5].Such results showed that the settling velocities of wax crystals under typical conditions do not significantly contribute to deposition.Furthermore,Burger et al.demonstrated that deposition under horizontal and vertical flow is identical within the limits of experimental error.

Generally,it was consensual that gravity settling is irrelevant for wax deposition,as there has not been a report claiming that wax deposits are thicker at the bottom,rather than at the top of the pipe wall.

2.6.Thermal diffusion

Beyond molecular diffusion,shear dispersion,Brownian motion,and gravity settling,which have been considered with different degrees of importance in the classical formulae,there are some other mechanisms worth to consider.Ekweribe et al.[22]argue that thermophoresis[23](also named thermal diffusion,Soret effect (for gaseous or liquid mixtures)or thermomigration)and turbophoresis may play a key role,notwithstanding the fact that further research is clearly in need.

Thermal diffusion is named after the temperature gradient as the driving force for the wax deposition [22].Wax particles can diffuse under the effect of a temperature gradient,and the thermophoretic velocity (m/s)is given by Ref.[21]:

The negative sign means that the particles move from the hotter zone to the colder one,Where the proportionality factorcan be determined by the Eq.(9)[24],which is function of the thermal conductivity of the fluid,k(W/(m.K)),and the thermal conductivity of wax particles,kp(W/(m.K)):

Some researchers,such as Bird et al.[25]and Merino-Garcia et al.[26],have classified the effect of thermal Diffusion on wax deposition as negligible.However,other researchers,like Banki et al.[27]argue that taking thermal diffusion into account,for wax deposition models,is needed to correctly assess the physical phenomenon.

2.7.General considerations and critical review

As presented before,several mathematical models have been developed to describe the wax deposition behaviour.Investigations have been performed to better understand this phenomenon,looking for the cause and the conditions where the wax deposition would consistently occur.It is consensual that wax deposition happens in a flow which is subject to external cooling.

Researchers intended to identify which mechanism plays the primary role on wax deposition.Table 1 summarizes the wax deposition mechanisms adopted by each researcher.

Fig.3 shows the chronology of paper publications on wax deposition mechanisms,considering the aforementioned researchers.

Considering the review above and bearing in mind the extensive experimental observations on wax deposition developed over the past decades,it is now commonly accepted that the molecular diffusion is the key mechanism for wax deposition.However,there are evidences that modelling the molecular diffusion alone does not allow to predict the wax deposition behaviour [78].

From the extensive research on experimental results here presented,it is possible to conclude that no specific flow circumstances are due to influence the preponderance of each of the above-mentioned mechanisms for wax deposition.A sole exception can be regarded for shear dispersion mechanism [5].Indeed,if the heat fluxes are moderate and the temperatures significantly lower than cloud point,shear dispersion shall be taken into consideration,along with molecular diffusion,to model wax deposition [5].Nevertheless,this recommendation is not widely supported by all the available research.

Looking to the wide prospect of available research results it is still possible to identify conflicting conclusions.Among those,one can highlight the role of both shear dispersion and thermal diffusion.The remaining mechanisms can be said to show consistent experimental results that endorse the conclusions about Molecular diffusion importance as well as Brownian diffusion,Shear removal and Gravity settling less significance.

Thermal diffusion is presented by some researchers as a subject ofinterest and requiring further research,while others claim its unimportance compared to the remaining mechanisms.However,taking the physical phenomenon into consideration,it is rather straightforward observing that it is,primarily,a molecular diffusion mechanism.

Table 1 Wax deposition models in the literature.

Fig.3.Chronologic paper publications about wax deposition mechanisms.

All the deposition mechanisms reported in the bibliography have their existence,as physical phenomena,proven both in theoretical and experimental grounds.Those phenomena relevance for the wax deposition problem is variable with oil properties and transport conditions,such as temperature,flow rate,flow regime or the solids,gas and water contents.

Reducing complex phenomena to simple mathematical formulae has been a major endeavour,undertaken by distinguished researchers throughout the years.Yet,such task could only be pursued with the aid of experimental data,which is inherently scarce given the time lapse for deposits formation,along which experimental conditions can only be sustained constant under strict and expensive laboratorial conditions.This has led to the development of mathematical independent formulae for each mechanism that have been enhanced throughout the years,when new data is available.Therefore,even if an applicability range for physical phenomena is not possible to define as,per definition,proven phenomena applicability is universal,the current formulae can be relevant in certain ranges of conditions.

To estimate the relative importance of each deposition mechanism,Buongiono's procedure [21]was herein applied for assessing the importance of each transportation mechanism.The time that a waxy crude oil particle takes to diffuse a length equal to its diameter,under the effect of each mechanism,was computed.The mechanism which induces the particle movement,within a lower period of time,will be considered as the predominant mechanism [21].Comparisons are herein established among every two mechanism formulae in order to promote intelligibility and readers' visualisation,given the profuse set of relevant variables.

To estimate the impact of each mechanism on wax deposition,the time that a particle spends to diffuse a length equal to its diameter,by molecular diffusion,is determined by the Eq.(10),which was deduced after rearranging Eq.(2)in SI units:

Here,the following units apply:d2/Dmin (s),μin (Pa.s),Vsolutein(m3/mol),MW in (kg/mol)and T in (K).

Similarly,to estimate the impact of Brownian diffusion on wax deposition mechanism,Eq.(11)was defined.It was deduced after rearranging and converting the Eq.(3)to SI units:

Here,dis the particle diameter (m)andKBis the Boltzmann constant,given by.

To estimate the impact of shear dispersion on wax deposition mechanism,Eq.(12)was deduced after rearranging and converting the Eq.(4)to SI units:

The gravity settling effect on wax deposition mechanism was determined using the Eq.(7)to obtain the Eq.(13):

The effect of thermophoresis diffusion can be assessed considering the Eq.(14),in SI units:

In order to compare the most acknowledged wax deposition mechanisms,Table 2 was built,highlighting input parameters to determine the time that a particle spend to diffuse a length equals to its diameter by diffusion or dispersion:

When analysing molecular diffusion and Brownian diffusion parameters,the time that a particle spends to move by diffusivity is inversely dependent on temperature.On the contrary,it is directly dependent for thermal diffusion.As Arrhenius equation shows (Eq.(15)),higher temperatures result in lower viscosities,which means higher diffusivity coefficient,and consequently lower diffusion time.

whereμis the viscosity (Pa.s),T is temperature (K),μ0is the material coefficient (Pa.s),Eais the activation energy (J/mol),andRis the universal gas constant (J/(mol.K)).

Larger particles will spend more time to diffuse by Thermal,Molecular and Brownian mechanisms,as presented in Table 2.Conversely,gravity settling will trigger the movement more effectively for larger particles.

In order to compare the range where each mechanism is predominant face to another,a one-by-one comparison was performed.Table 3 synthetizes the predominance comparisons that are further developed.

Table 3 equations were deduced from Eq.(10)-(14).

If the time spent by a particle to move by molecular diffusion is lower than the time given by Brownian diffusionthen the molecular diffusion will be predominant,and the range is given by Eq.(16):

Table 2 Parameters required to estimate the time that a particle spends to move by diffusivity or dispersion.

Table 3 Comparison between the mechanism's predominance.

If the time spent by a particle to move by molecular diffusion is lower than the time given by shear dispersion,then the molecular diffusion will be predominant,and the range is given by Eq.(17):

If the time spent by a particle to move by molecular diffusion is lower than the time given by gravity settlingthen the molecular diffusion will be predominant,and the range is given by Eq.(18):

If the time spent by a particle to move by molecular diffusion is lower than the time given by thermal diffusionthen the molecular diffusion will be predominant,and the range is given by Eq.(19):

Thermal diffusion and molecular diffusion formulae are much more relevant than any other mechanism formulation and,for some crude oils,thermophoresis can be dominant.

If the time spent by a particle to move by Brownian diffusion is lower than the time given by shear dispersionthen the Brownian diffusion will be predominant,and the range is given by Eq.(20):

If the time spent by a particle to move by Brownian diffusion is lower than the time given by gravity settlingthen the Brownian diffusion will be predominant,and the range is given by Eq.(21):

If the time spent by a particle to move by Brownian diffusion is lower than the time given by thermal diffusionthen the Brownian diffusion will be predominant,and the range is given by Eq.(22):

Brownian diffusion is not expected to act,solely,as the major mechanism involved in wax crystals movement and deposition.However,it may be a significant complementary mechanism for smaller particles and higher temperatures.

If the time spent by a particle to move by shear dispersion is lower than the time given by gravity settlingthen the shear dispersion will be predominant,and the range is given by Eq.(23):

If the time spent by a particle to move by shear dispersion is lower than the time given by thermal diffusionthen the shear dispersion will be predominant,and the range is given by Eq.(24):

If the time spent by a particle to move by gravity settling is lower than the time given by thermal diffusionthen the gravity settling will be predominant,and the range is given by Eq.(25):

Gravity settling is unlike to govern particles movement and deposition,unless very large diameter particles are considered.

For all aforementioned mechanisms,the evolving particle size is a critical parameter to assess solid transport phenomena.Therefore,such parameter was herein used as the comparison factor to assess which is the predominant deposition mechanism,even if a mathematical formula shall take all relevant mechanisms into account.Applying information made available in the Table 3 it is possible to design a flow chart (Fig.4)to assess without ambiguities the predominant mechanism.Nevertheless,to evaluate intermediate scenarios,equations(16)-(25)should be applied.

Fig.4.Flow chart to determine the predominant mechanism.

2.8.Future research directions

Despite the broad consensus about the importance of molecular diffusion as a leading mechanism for wax deposition,there is profuse evidence that many experimental results cannot be fully explained only by it.Furthermore,there are still some mechanisms that are not suffi-ciently studied,as turbophoresis [22]or electrophoresis effects [80].While turbophoresis represents the particles’ tendency to be drifted toward the pipe wall in the direction of lower turbulence [81],electrophoresis characterizes the particles motion due to electrical forces.Simulating diffusion coefficients using molecular dynamics [82]can be a meritorious way to assess which are the best wax deposition mechanisms to explain the phenomena,replacing experimental testing when it is not feasible or for further assessment.Applying stochastic methods,using Monte-Carlo simulations can also be performed to evaluate these phenomena [83].Furthermore,current formulations deemed to describe each of the deposition mechanisms and physical phenomena may be improved.

At last,a global model should be developed with all the mechanisms that play a non-negligible role on wax deposition.For such endeavour special attention should be given to the direction of mass flux,since while some mechanisms contribute to wax deposition (as molecular diffusion and thermal diffusion),others may have a contrary influence(such as shear dispersion or shear removal),and others may even have an ambiguous effect,like Brownian diffusion [26].

Several other aspects that only recently attracted researchers’ attention might provide valuable contributions for attaining more accurate wax deposition predictions.That is the case for the effect of other crude oil components,such as emulsified water [84],inorganics solids[85],naphthenic acids [86],resins,and asphaltenes [87,88],as well as the wax aging mechanisms [10].

Recognizing the specificity of each crude oil,as well as flow conditions,including shear rates [8],will allow organizing the vast knowledge gained with decades of research into better defined validity ranges for the proposed formulations.

On the other hand,experimental investigations are expected to broaden its scope by expanding the research on wax deposition in water-in-oil or oil-in-water emulsions,as well as,in multiphase gas-oil flows,or even when injectingCO2.Very recently,several research work was presented,such as [89-100]is already pursuing such way.In fact,understanding how the water content,the gas,or the carbon dioxide will affect fluids’ rheological behaviour is essential to develop a suitable model to predict wax deposition.Furthermore,additional developments are expected,not only for finding predictive correlations based on mixing rules to characterize the fluid [101],but also simulations to evaluate these binary or ternary mixtures [102]behaviour.

3.Effect of water in waxy crude oil

Presently,most oilfields produce water along with oil,so it is inevitable to deal with,at least,two-phase flows.Water-in-oil emulsions are heterogeneous liquid mixtures,in which water is dispersed as droplets in the oil.Generally,the emulsion viscosity is higher than the oil or water at single-phase [103].The impact of water or brine on waxy crude oil gelation and rheology has been studied for several decades[55,104,105],and [89].

Within the laboratory domain,Couto et al.[55]were able to draw the following conclusion: The presence of salt does not affect the deposition of the conditions tested.In fact,the same deposition tendency was found either with fresh water or brine.Likewise,similar behaviour was experienced for deposits created with different mixing speeds when preparing the emulsion.This means that either emulsions have comparable properties,or their characteristics do not influence the deposition process for the tested range of parameters.

Experimental evidence has been provided,by Visintin et al.[106],showing that the presence of water above a certain threshold can significantly promote gel formation,modifying both the pour point and the yield strength,as shown in Fig.5.

Visintin et al.concluded that the rheological differences among waxy crude oil emulsions and crude oils only become sensible above a certain temperature threshold.Thus,at low temperatures its behaviour is similar.Likewise,it is only when the fraction of water becomes significant (above 25%),that emulsions behave distinctively from the crude oils.In those circumstances,there is a sharp increase in the pour point and yield stress.

Paso et al.[57]and Oliveira et al.[107]also confirmed that the presence of water increases the magnitude of the rheological properties of waxy crude oil gel,denoting a drastic increase in fluid viscosities and shear stress behaviour in the presence of emulsified water.The physical explanation for such behaviour lies,as it was found,on the network developed by the aggregation of the waxy crystals and water.

Fig.5.Pour Point (°C)and Yield Stress (Pa)of the waxy crude oil emulsion,upon the water content [% vol][106].

Concerning the experimental evidence collected on the wax deposition measured thicknesses,Bruno et al.[108]found a decreasing tendency with increasing water cut for different crude oils.Furthermore,the same authors concluded that very high-water cuts (as high as 85%)could lead to the non-formation of wax deposit or the occurrence of a very thin and hard deposit.Considering this,it is legitimate to suggest that the conventional diffusion theory may not be adequate to describe the deposition mechanism under those circumstances,when crude oil is mixed with high water or brine contents.

Later,Zhang et al.[109]were able to confirm that wax deposition rate decreases with the increasing water cut,maintaining the temperature gradient constant.Furthermore,they were also able to conclude that the wax deposition rate decreases,with increasing emulsion temperature,if the temperature difference between the emulsion and the cooler surroundings is kept constant (for the same water cut).On the other hand,the same authors observed that,still maintaining the water cut,wax deposition rate is higher for the higher temperature differences between emulsion and surroundings.Zhang et al.argue that emulsion temperature increase may have contradictory effects [109].On one hand the emulsion will be able to solve mode solid wax but,on the other hand,the molecular diffusion coefficient will increase,increasing the deposition rate.A peculiar phenomenon was found by Zhang et al.as it was noticed that WAT increases with the water cut until a certain threshold,and then decreases for higher water cuts[109].No confirmed explanations were yet offered for this.

Piroozian et al.[110]also studied the effect of water-in-waxy crude oil emulsions on the wax appearance temperatures,using differential scanning calorimetry.They concluded that WAT increases in presence of water.

4.Effect of CO2 on Wax Appearance Temperature (WAT)

Carbon dioxide flooding is a method for Enhanced Oil Recovery that,despite some practical hindrances [111,112],with its mobility[99,113,114]and modelling complexity [115-119]at the top of the list,has already a history of industrial application [120].However,there are many possible interactions between carbon dioxide and the oil components [113].In fact,carbon dioxide injection is known for triggering asphaltene precipitation [121].Furthermore,practical issues,such as fingering and oil trapping [122]make enhanced oil recovery by carbon dioxide flooding more effective for recovery in non-asphaltenic oil rather than in asphaltenic oil [122].

Therefore,despite the scarcity of studies on the effects of carbon dioxide injection upon wax appearance temperature (WAT),the work of Hosseinipour et al.is noteworthy [123].With it,authors experimentally studied the effect ofCO2injection on the WAT of six crude oil samples (named A to F)using high pressure micro differential scanning calorimetry (HPμDSC)technique.Fig.6 illustrates the effect on WAT due to theCO2injection,for different pressure thresholds.The experimental method included pressurizing the sample by injectingCO2gas,to the selected pressure (16,26,36 and 46 bar)and heating the mixture up to an initial temperature of 70 °C in order to cool it at the rate of 2 °C per minute until 0 °C.

Fig.6.Wax Appearance Temperature (WAT)for six different crude oils,varying the CO2 injection pressure.Adapted from Ref.[123].

For each crude oil,it is possible to observe a decrease on WAT when theCO2injection pressure rises.To quantify the relationship between WAT andCO2pressure,a linear trend line was adjusted from the aforementioned experimental results.The linear slope varies between-8% and -18%.Such result can sustain the possibility ofCO2performing as a flow improver.Thus,it may increase the production rate whilst reducing theCO2release to the atmosphere.

While consideringCO2injection practical applications,such gas solubility in oil must be taken into account.It is a well-known and quantified fact,since Welker and Dunlop [124]and Simon and Graue[125]studies in the 60's,thatCO2gas solubility increases with pressure,and decreases with temperature [126-128].To illustrate this behaviour,Fig.7 was drawn with the experimental data gathered for different crude oil samples [129-131],quoted in Ref.[132].

In fact,recent studies [133],have shown thatCO2gas solubility increases significantly until the bubble point pressure,reducing the growth rate when the pressure is increased beyond such threshold.

5.Conclusions

Currently,molecular diffusion gathers widespread acceptance as the most relevant wax deposition mechanism.Nevertheless,the phenomenon of the removal of wax deposits by shear forces requires recognizing the role of the Shear Dispersion mechanism.

Consequently,these mechanisms have been recently used as the background for many models.Such models’ accuracy is significantly dependent on the approach to a real representation of the solid phase wax components.

Further accuracy in the models’ backed wax deposition predictions has been granted by a more precise heat-mass transfer analogy.

Fig.7.CO2 solubility in crude oil,as function of Pressure.

Improving current models will require conceiving approaches which take into consideration further mechanisms involved in gelation and wax deposition,as well as the effect of other crude oil components,such as emulsified water and asphaltenes.

Formulating and modelling the process of the formation of wax deposits in wells also requires a deep understanding of wax aging mechanisms.The ability to simulate such mechanisms,along with the capacity to predict the characteristics of each crude oil,will be pivotal in assessing what chemical inhibitors can be the most effective for preventing wax formation inside wells.

InjectingCO2in oil reservoirs,which has been done in the context of Enhanced Oil Recovery,can have a beneficial effect towards lowering the WAT and,consequently,mitigating wax deposition severity.Developments and practical applications are expected on this topic in the near future.

Cost-effectiveness in wells maintenance and production flow assurance is the goal of the research on this subject.To such an end,conceiving,modelling and validating better methods of inhibiting wax deposition and removing deposits will enable the optimization,or even dismissal,of wax removal procedures,such as pigging.

Acknowledgments

First author would like to thank to Partex Oil and Gas for the technical and financial support,through the grant UID/ECI/04028/2013 (from September 2017 until March 2018)and Fundação para a Ciência e a Tecnologia,I.P,for the financial support,through the grant SFRH/BD/131005/2017 (from April 2018).