Paraffin Wax

Paraffin wax is a white or colorless soft solid derivable that is solid at room temperature. Paraffin wax is in different grades and the main difference between them is the percentage of oil content. Paraffin wax is mostly used for candle, textile, rubber, PVC paper, MDF, sealing, cable jelly, paint, glue, laboratories and many other industrial purposes.







Oil Content



3-5 %wt

5-7 %wt

Melting Point



62-66 °C

62-65 °C

Flash Point



220-240 °C

220-240 °C

Kinematic Viscosity @ 100 °C


6-7.5 CST

6-7.5 CST

6-7.5 CST


Method (2”cell)



Yellowish White

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paraffin wax products

paraffin wax productsMutual effects of paraffin waxes and clathrate hydrates: A multiphase
integrated thermodynamic model and experimental measurements
a b s t r a c t
This paper presents an extensive analysis of complex wax and hydrate forming systems employing an
integrated wax-hydrate thermodynamic model. The developed model uses integration of the UNIQUAC
activity coefficient model, CPA equation of state and van der Waals-Platteeuw model, for the description
of waxes, fluids and hydrates, respectively. Our recently published multiphase “Gibbs energy minimization” flash algorithm [1] is extended here to identify waxy solid phase(s) and is shown to be robust in
characterizing complex systems where several phases, i.e., solid wax, vapour, liquid hydrocarbon, liquid
aqueous, ice and hydrate phases (structure sI and sII) may coexist.
The accuracy of model predictions is first validated by calculating the wax amount and composition in
water-free systems for which experimental data are available. It is then used to explore the mutual effects of hydrates and waxes starting from a simple binary system of methane þ n-heptadecane in the
presence of water. The model is then used to analyze four multicomponent mixtures and a recombined
light oil.
The analysis includes investigations into the impact of hydrate formation on wax phase boundary,
amount and composition and vice versa, as well as a variety of secondary important effects including the
influence of the amount of light end in the feed and impact of the free aqueous phase on the wax amount
and phase boundary.
Formation of hydrates and waxes are well-known flow assurance problems causing considerable operational expenses and hazards mainly through loss of production or pipeline blockage.
Experimental studies have revealed that simultaneous formation ofwaxes and hydrates can synergistically escalate their precipitationand deposition [3]; hence promoting the possibility of pipeline
blockage. Despite the high chances of formation of both hydratesand waxes at the same time (see for example [4,5]), especially involatile oils and gas condensates under operational conditions, thesubject of mutual interactions of hydrates and waxes from a thermodynamic modeling viewpoint has been scarcely (and never insome aspects) addressed in the open literature. In view of thisomission, it is critical to have an in-depth understanding of thephase behavior of systems prone to form both waxes and hydrates, gained by utilizing a robust thermodynamic model.
The only works available in the literature concerning the thermodynamic aspects of mutual interactions of hydrates and waxesare those of Tabatabaei et al. [6,7] and Ji [8]. The fluid phases in bothworks are described with cubic EoSs, though obviously, neglectingquasi-chemical forces due to hydrogen bonding in the presence ofwater would result in the poor accuracy of non-associating EoSs(see for example [9]). Also, in the work of Tabatabaei et al. [6,7], theRegular Solution Theory (RST) has been utilized to describe thewaxy solid phase non-ideality. However, the RST has major drawbacks such as the overestimation of wax melting temperature [10]and inability to identify if more than one waxy solid phase hasprecipitated. More importantly, thorough investigation of thecomplex wax-hydrate systems requires a robust multiphase flashalgorithm. Among the works mentioned only Tabatabaei et al. [6,7]
have presented some flash calculation results. However, they haveused sequential hydrate-free and wax-free flashes to calculate thephase fractions and compositions in the equilibrium state. Inaddition, the hydrate flash calculation algorithms utilised in theworks of Tabatabaei et al. [6,7] are established on only satisfying theisofugacity criteria and are not based on a Gibbs energy minimization approach. There are many problems with these type of flashcalculations in the presence of hydrates [1], as they fail to identify
the presence of more than one structure of hydrate. Seemingly, thistype of flash calculation algorithm has prevented the authors fromanalyzing the mutual effect of hydrates and waxes on their compositions and amounts and only the mutual effects on the phaseboundaries was investigated.
In the current study, the CPA EoS, originally presented by Kontogeorgis et al. [11], is utilized to describe the non-ideality of fluids.
In the case of analysis of the systems containing water, it is vital forthe applied EoS to take into account the associative hydrogen bondscontributions due to water associations in the fluids non-ideality.
Additionally, the well-known and widely used model of van derWaals and Platteeuw (vdWP) [12] has been applied to describe thenon-ideality of hydrate phases of different structures (here sI andsII). The accuracy of the coupled CPA-vdWP model for thedescription of the number and nature of the hydrates formed inequilibrium, in systems under hydrate forming conditions, has beenvalidated in our previous work [1]. Finally, the UNIQUAC activitycoefficient model, initially developed by Abrams and Prausnitz [13],and applied for the first time by Coutinho [14] for calculatingparaffinic solids non-ideality, is exploited here to describe the waxysolid phase(s). The UNIQUAC is proven to be one of the most accurate thermodynamic models, to date, to evaluate Wax Disappearance Temperature (WDTP), Wax Precipitation Curve (WPC) andcomposition of precipitates [15,16]. In the present study, to avoid
confusion between the wax phase boundary data calculated by themodel with the same value measured experimentally, which caneither be Wax Appearance Temperature (WAT) or Wax Disappearance
Temperature (WDT), the term WDTP is referring to model predictions. This is because of several uncertainties while measuringthese variables [17]. Obviously, if WDT is measured properly, it
should correspond to the true wax melting point (thermodynamicliquidus point) [18] mainly due to less chance of superheatingcompared to subcooling [19].
Here, these three accurate thermodynamic models for the corresponding phases are integrated into a single framework: “UNIQUAC-CPA-vdWP” model which is abbreviated as UCV. The
description of the model formulations will be presented in section
In the present work, our recently published multiphase “Gibbsenergy minimization” flash algorithm [1] is extended to identifythe presence of wax phase(s). Such a flash algorithm coupled with a
strong stability analysis scheme has a proven record of robustness[20]. The robustness of the devised algorithm is tested here withseveral examples with up to 8 phases of different natures may
coexist. This robust flash algorithm is an essential requirement forthe analysis of complex hydrate-wax forming systems, in particularfor identifying the mutual effect of waxes and hydrate on their
amount and composition. The steps required to extend the flashalgorithm to take paraffin solid phases into consideration will bepresented in the “Methodology” section.
This work also includes experimental measurement of HydrateDissociation Points (HDP) for three synthetic multicomponentmixtures of diverse phase behaviors as well as a recombined lightoil.
 These data are used to check the accuracy of the model.
The “Analysis and Discussions” section present the interpretations, based on several different types of calculations on themutual interactions of hydrates and waxes, in particular:
 paraffin wax productsEffect of the overall composition distribution (heavy end andlight end impacts) on the phase diagrams of hydrates and waxesInfluence of the hydrates on the wax phase boundaryImpact of the waxes on the hydrate dissociation lineInfluence of the hydrates on the amount and composition of
wax precipitatedImpact of waxes on the amount and compositions of hydrates
formedThe analysis is first performed to understand how the wax phase
boundary is influenced by the formation of sI hydrate (HI) in a binary system of methane þ n-heptadecane in the presence ofdifferent water to hydrocarbon molar ratio in the feed (W/H). The
aspects mentioned above are then evaluated in the three multicomponent synthetic mixtures for which experimental wax phaseboundary data are available [8] as well as SHF4 mixture of Ungerer
et al. [21]. Finally, the analysis of the effect of hydrates on the waxamount and phase boundary for a recombined light oil mixture iscarried out. This is performed to assess the validity of analysis for a
real mixture.
2. Methodology
Accurate determination of the number and nature of phases atequilibrium requires not only precise thermodynamic models,capable of describing corresponding phases but also a robust
multiphase flash calculation algorithm. Accordingly, this section isdevoted first to describe the flash calculation algorithm. Then theformulation of the exploited thermodynamic models will be
2.1. Multiphase flash calculationThe flash calculation used here is an extension of our recently
published multiphase flash calculation in the presence of hydrates[1] to systems where wax phase(s) may be present. The devisedflash algorithm includes a combination of a Gibbs free energy
minimization approach, with the Michelsen [22] multiphase algorithm applied in the inner loop, and the Michelsen [23] tangentplane distance (TPD) stability analysis to perform the initial “NoHydrate Flash” (NHF) step [1]. Similar to the original work [1] thestability analysis here uses the BFGS algorithm [24] to find stationary points of the Michelsen TPD function starting with trialcompositions defined in by Li and Firoozabadi [25]. The NHF stepresults are then employed as a part of the initial guess compositions
for the “Hydrate Flash” (HF) step [1].In the current work, the following changes have been made to
the original algorithm to model the presence of waxes correctly:
1) Initialization of the compositions for the NHF step
2) Initialization of the compositions for the HF step
3) Considerations for components non-precipitating in the wax
phase(s)Details of each of these changes are presented below.
2.1.1. Initialization of the compositions for the “No-Hydrate Flash”
stepFor the initial guess of compositions in the presence of water, itis assumed that for the first flash calculation in the NHF step, atleast 4 phases should be initialized corresponding to vapour (V),
liquid hydrocarbon (L), liquid aqueous (Aq) and a single solid waxphase (S). The first phase for which the initial compositions areevaluated is the liquid hydrocarbon phase by observing mass balance criteria, i.e.:
In Eq. (1), z is the overall composition, qj is the molar phasefraction of phase j and xL i is the mole fraction of component i in theliquid hydrocarbon phase. The method of Ballard and Sloan [26] is
used to evaluate equilibrium constants between liquid and vapourphases, KVL. Aqueous to liquid equilibrium ratios, KAL, is set equal to(KVL/KVA), where KVA is the vapour to aqueous equilibrium ratiocalculated by the method of Ballard and Sloan [26]. The paraffins'solid to liquid equilibrium ratios are estimated by:
The thermophysical properties used in Eq. (2), for each precipitating paraffin, are fusion temperature Tif, order-disorder solidsolid transition temperature, Titr, enthalpy of fusion, DHif, and
enthalpy of order-disorder solid-solid transition DHitr. The methodof calculating these parameters will be presented later on. Havingcalculated xLi , the composition of the remaining phases for the
initial flash calculation are evaluated by:
where xSi and xA i are the mole fractions of component i in the solidwax and liquid aqueous phases, respectively, and yi is the molefractions of component i in the vapour phase. The initial molar
phase fractions can be estimated by:
here, zw is the mole fraction of water in the feed and np is theinitialized number of phases which for the initial flash is set equalto four. When convergence is achieved, the stability analysis isperformed to check whether the solution is corresponding to theGibbs energy surface global minimum. If not, for the next flashcalculation np is increased by one and this new phase is assumed tobe a waxy solid phase with the composition calculated by:
where ih is the heaviest paraffinic component for which the Eq. (5)composition is not created. Therefore, for example, if the flash results where again unstable, for the next flash, ih would be the
penultimate heavy component, and so on. This way the presence ofexcept that in their work the compositions defined by Eq. (5) aretreated as liquid phases. For subsequent flashes, Eq. (4) is again
used for initializing the molar phase fractions.2.1.2. Initialization of the compositions for the “hydrate flash” stepIn the original work [1], when the NHF step solutions are obtained, the fugacities of components at the converged solution areused to calculate the initial guess composition of the hydrate
phase(s). The same approach is applied here with one difference. Aswill be shown later on, there are conditions under which the NHFstep would not result in the presence of wax, while in reality, the
introduction of hydrates leads to the formation of waxes. Thiscondition corresponds to a region near (and inside) the wax phaseboundary. Therefore, here, to avoid removing possible waxy phase,the number of phases at the start of the HF step is increased bythree. These three additional phases are corresponding to sI and sIIhydrates and a single waxy solid phase. The compositions of themore than one waxy solid phase can be safely modelled. This issimilar to the initialization scheme of Phoenix and Heidemann [27],
hydrate phases are initialized as outlined in the original work [1]and the composition of the waxy phase is initialized as detailedin section Considerations for components non-precipitating in the waxphase(s)The flash calculations in the presence of waxes require some
measures for components non-precipitating in wax. These components are divided into: (1) non-paraffins (in this work CO2, N2and water) and (2) paraffins with carbon number smaller than thecarbon number cut-off (CNCO). It is indeed of high importance tointroduce a reasonable CNCO. Partly, if all the paraffinic fractions areallowed to be precipitable, it would result in an overestimation of
the amount of precipitates [28]. Also, as confirmed by experimentalevidence, even for wax precipitation in a mixture with a widecontinuous range of alkanes, e.g. a mixture of n-hexane to n-hexatriacontane in the work of Pauly et al. [29], where partial miscibility exists between all constituents, the components lighter thann-tridecane are not present in wax precipitates even at low temperatures around 250 K. More experimental works confirming theabsence of light components in the waxy solid precipitates can be
found elsewhere [30]. Furthermore, an unreasonable CNCO mayresult in incorrect interpretations of the changes in molecularweight (MW) of the waxy part in mixtures prone to simultaneous
formation of waxes and hydrates as will be discussed in the“Analysis and Discussions” section. Accordingly, in order to matchexperimental evidence, in the current work, a CNCO of 6 is
considered for all the calculations performed, i.e. paraffinic components lighter than n-heptane are not allowed to precipitate in thesolid waxy phase. This choice is based on the fact that the lightest
component in the heavy end of the synthetic multicomponentmixtures investigated here is n-heptane.
To avoid the non-precipitating components to be present in thewaxy solid phases, like what was done in the original work toprevent non-hydrate-formers being present in the hydrate phases,
the fugacity coefficients of non-precipitating components in thewax phase were set to a large value, i.e.,10100 [1]. The capability ofthe multiphase flash calculation algorithm devised in the presence
of waxes and hydrates for one of the multi-phase forming multicomponent systems (with a specific water content) studied here isprovided in Supplementary Materials document.
2.2. Thermodynamic models
2.2.1. Vapour, liquid and aqueous phases non-ideality
As the conventional cubic EoSs do not take the chemical/quasichemical associative hydrogen bonds contribution into consideration, their performance is poor in the presence of water (orgenerally speaking, an associative compound). To overcome thisissue, originally, Kontogeorgis et al. [31], introduced the Cubic PlusAssociation (CPA) equation of state. It is, therefore, essential toexploit CPA, as an associative EoS, in the present study as in thehydrate forming systems under investigations, the systems' thermodynamic properties dependency on water associations isconsiderable. CPA EoS, in essence, combines cubic (due to physicalvan der Waals forces, here calculated by SRK EoS [32]) and associative (due to chemical/quasi-chemical forces) terms, to describefluid phases, as follows:
Complete parameterization of Eq. (6) and the required calculations of CPA EoS can be found elsewhere [33]. In this work, thecritical and physical properties of pure components are taken fromthe DIPPR [34]. Also, Twu [35] correlation for critical properties andMagoulas and Tassios [36] correlation for the acentric factor areused for characterizing the components absent in the DIPPR (in thiswork only n-tetracontane). The binary interaction parameters ofthe cubic part of CPA are here evaluated by the group contributionmethod of Jaubert and Mutelet [37], the complete formulation andparameterization of which is provided in the SupplementaryMaterials document.2.2.2. Hydrate phase non-idealityThe fugacity of water in the hydrate phases are calculated by thevan der Waals and Platteeuw [12] (vdWP) model modified byParrish and Prausnitz [38], through [39]:
here, fwH is the water fugacity in the hydrate lattice filled with guestcomponents and fwb is the fugacity of water in the hypotheticalempty hydrate lattice. The chemical potential difference, Dmb wH , is
calculated by Ref. [12]:
Complete details of the formulation of vdWP model includingcalculation of Langmuir constants ClikðSTÞ and the required parameters can be found elsewhere [1,40,41]. The fugacities of guest
components required in Eq. (8) are calculated by the methoddevised in our previous work [1].
2.2.3. Paraffinic solid phase non-idealityIn the current work, the UNIQUAC activity coefficient model,
originally developed by Abrams and Prausnitz [13] was exploited todescribe non-idealities of the waxy phases. The UNIQUAC modeloffers two major advantages over other activity coefficient models.
First, it is capable of representing the possible formation of morethan one paraffinic solid phases as confirmed experimentally by Xray diffraction and spectroscopy (see for example [42e45]) for
mixtures of continuous exponential decay molar distribution ofnormal alkanes as well as mixtures where a sufficient gap in thechain length of alkanes is observed between the constituents.Spontaneous demixing of binary alkanes' solid solution wasextensively studied in the spectroscopic measurements of Snyder
and co-workers (see for example [46]). Lira-Galeana et al. [28] havebeen the first group to model the multi-solid precipitation ofwaxes. They considered waxes to form several pure solid phases.
Later, Coutinho [14] proposed the predictive UNIQUAC activity coefficient model for describing non-idealities of paraffinic solid solutions. UNIQUAC can grasp the multi-solid phase precipitation
behavior of waxy mixtures which is more emphasized in systemswith multimodal component distribution and a comparable difference in the chain length of the alkanes present. It is also
observed that by using predictive UNIQUAC, better predictions ofsolid-liquid equilibria (SLE) of binary eutectic systems can be obtained [14]. Therefore, the UNIQUAC activity model (in its original
form) is applied here for modeling non-ideality of the waxy solidphases. The UNIQUAC model takes into account the combinatorialand residual contributions on excess Gibbs free energy which are
representative of entropic and enthalpic deviations from ideality,respectively. UNIQUAC calculates the combinatorial, gC i , and residual, gR i , parts of the activity coefficient by:
Combining these two equations, the UNIQUAC activity coefficient is calculated by:
Complete parametrization of Eq. (9) and Eq. (10) and detailedformulation of original UNIQUAC used in this work can be foundelsewhere [15]. Having calculated activity coefficients by UNIQUAC,
the fugacity of components in the waxy solid phase is [47]:
In the current work, the value of thermophysical propertiesrequired, i.e. Tif, Titr, DHif and DHitr are calculated by the proposedcorrelations of Coutinho and Daridon [48] at reference pressures. To
account for the high pressure effect, the modification of the methodof Ji et al. [10] is used where fusion and solid-solid transitiontemperature of alkanes are corrected as a function of pressure.
2.2.4. Ice phase non-ideality
There are few occasions in this study where ice is present. Byapplying the Poynting correction term, one can calculate thefugacity of ice, fwI , through modifying pure water fugacity at the
same temperature [47]:
where PsatI and fsat w are the ice vapour pressure and the fugacitycoefficient of water at the ice vapour pressure, respectively. Also,the molar volume of ice in (m3/mol), vl, is calculated by the correlation of Tohidi [49] and PIsat is calculated by Wagner et al. [50]correlation.
3. Experimental measurements
3.1. Materials
In this work, hydrate dissociation points are measured for threemulticomponent mixtures M1, M2, M3 and a recombined light oil.The suppliers and purity of pure gases and liquid hydrocarbons
used to prepare these mixtures are listed in Table 1. All of thesemixtures were prepared by combining a high-pressure gas gravimetrically with a multicomponent liquid hydrocarbon mixture.
These liquid mixtures were initially prepared gravimetrically usinga Mettler Toledo balance (model PB3002) with a resolution of0.001 g and hence, the relative uncertainty in the concentration of
each compound can be taken equal to the purity of the compound.Once combined the mixtures were kept well above their bubblepoint in variable volume cylinders. The recombined fluids wereprepared by weighting 10e15 g of gas to 200e300 g of liquidhydrocarbons.The composition of the natural gases used to prepare mixturesM1, M3 and the recombined light oil are listed in Table 2.
 Thesegases with certified composition were purchased from BOC. Thelight end of M2 was directly combined by gravimetric means withpure gases, the composition of the light end is also given in Table 2.
De-ionized water was used in all hydrate tests.
3.2. Experimental equipment
Dissociation point measurements were conducted using a reliable isochoric step-heating method. Fig. 1 shows the apparatusused to determine the phase equilibrium conditions. The equilibrium setup consisted of a piston-type variable volume (maximumvolume of 300 ml), titanium cylindrical pressure vessel with mixingball, mounted on a horizontal pivot (Fig. 1).
Rocking of the cell through 180 at a constant rate and thesubsequent movement of the mixing ball within it, ensuredadequate mixing of the cell fluids. Cell volume, hence pressure,
can be adjusted by injecting/withdrawal of hydraulic fluid behindthe moving piston. The rig has a working temperature range of203.15e453.15 K, with a maximum operating pressure of 70 MPa.
System temperature is controlled by circulating coolant from acryostat (Julabo F50) within a jacket surrounding the cell. Theequilibrium cell and pipework were thoroughly insulated to
ensure a constant temperature. The temperature is monitoredusing a Platinum Resistance Thermometers located within thecooling jacket (u(T) ¼ 0.1 K). A quartz pressure sensor(u(P) ¼ 0.04 MPa) is used to monitor pressure. The weight of thefluids (i.e., water and hydrocarbon fluid) injected are recorded
before any measurements, and the overall feed composition canthus be calculated. Procedures to determine hydrate dissociationcan be found elsewhere [41,51].
4. Analysis and discussions
4.1. Model validation for wax-free and hydrate-free systemsPrior to applying the integrated UCV model using the devisedmultiphase flash algorithm, it is important to verify the validity of
the model for both wax-free and hydrate-free systems. The CPAvdWP model for wax-free systems has been tested in our previous work [1]. The capability of the UNIQUAC model coupled withcubic EoSs has also been the subject of many papers and tested forseveral systems in the presence of wax in the literature [15,52e55].For the sake of brevity, the accuracy of the applied UNIQUAC modelto quantify the non-ideality of the paraffinic solid phases, wasverified by testing three mixtures BIM3, BIM5 and BIM9 for whichamount and composition of the precipitated solid waxes areavailable [56]. These systems have been selected as their heavycomponents' bimodal distributions have significant n-alkane gaps,which as discussed earlier, results in the possibility of forming twoseparate paraffinic solid solutions at sufficiently low temperatures.
Fig. 2 represent the application of the model to evaluate the WPCfor these systems compared to experimental data [56].As seen in Fig. 2 the model predictions are in good agreementwith experimental data and the UNIQUAC model is capable ofshowing the singularity in the WPC attributed to the appearance ofthe second lighter wax solid phase. Furthermore, examples of thecalculated weight percent of components in the overall waxy solidpart (including all paraffinic solid phases identified) for two
different temperatures in BIM 5 are shown in Fig. 3. The chosentemperatures cover conditions where both single (298.15 K) andtwo (273.45 K) paraffinic solid phases form. Again a very goodagreement between experimental and modeling results isobserved which demonstrates the applicability of UNIQUAC tocharacterize the non-ideality of the paraffinic solid phase in UCV
4.2. Integrated wax-hydrate modeling
The aim here is to perform investigations into the behavior ofsystems prone to form both hydrates and waxes including the
mutual effects of waxes and hydrates (of different structures) ontheir phase boundaries, amount and compositions, as outlinedearlier. Several other aspects including (i) the wax phase behaviour
affected by changing the amount of water in the feed and thecomposition of the heavy end, (ii) the impact of the presence ofaqueous phase on the wax phase boundary and the amount of wax
precipitated in low to high water content conditions (iii) theinfluence of waxes and hydrates on the bubble point pressure (Pb)and dew point pressure (Pd) of the systems under investigation,
especially inside the hydrate phase boundary, will also be covered.
4.2.1. Binary methane þ n-heptadecane mixture in presence ofwaterDue to the lack of experimental data on wax-hydrate systemsin the literature, a “simple” system consisting of 60.14 mol%methane and 39.86 mol% n-heptadecane is presented first as theeffects are easier to comprehend in such systems. For this system,experimental paraffinic solid-fluid equilibrium (SFE) data inwater free conditions for pressures up to 90 MPa were measuredby Pauly et al. [57]. Fig. 4 shows the n-heptadecane solidboundary in the presence of hydrate. As shown in this figure, thepredictions made using the UCV model agree well with theexperimental data for both Pb and SFE phase boundary in waterfree conditions. In this figure the regions of higher importanceare colorized. The phases shown within the parenthesis in someregions are those which their existence is dependent on theamount of water as well as the amount of hydrate formed. Themost noticeable observation is that when water is introduced inthis system in sufficient quantities to form hydrates in thepressure range of investigation, the formation of sI hydratewould result in reducing the methane content in the hydrocarbon rich liquid phase above bubble point. This in turn enhances
stability of n-heptadecane wax. Therefore, one would expect anincrease in paraffin solid phase crystallization temperature at aspecified pressure. Obviously, the greater W/H is, the higher is
the paraffin solid phase crystallization temperature, as represented for W/Hs of 0.5, 1.0 and in the presence of excess water. Itshould be pointed out that throughout the paper, the term
“Excess Water” refers to the lowest fraction of water in the system which guarantees the presence of an aqueous/ice phase atthe investigated pressure and temperature range and corresponds to moderate to high W/Hs ranging in the order of about2e5. This is important because extremely large W/Hs (say more
than 95 mol% water corresponding to W/Hs of more than 20)may result in significant changes on the wax phase boundaries. Asystem composed of such a high water content is of low practically. However, the investigation of the effect of this high amountof water on wax phase boundary is presented for one case(section
According to Fig. 4 the extent to which the presence of hydrates can influence the solid paraffin boundary, depending on
the W/H, can be as high as 5 K. This can be easily observed in“(S)-HI-L-(Aq)” and “(S)-HI-L-(V)-(Aq)” regions. Furthermore, theformation of hydrate (i.e. the consumption of the light components) will result in a decrease of the bubble point pressure,hence a decrease in the singular point of the paraffin solid
appearance boundary. For the water-free condition the singularpoint corresponds to the triple point of the mixture (point A),while for hydrate forming systems the singular point is at least aquadruple system representing “S-HI-L-V” equilibria and aquintuple point when excess water is available (point B) which is
clearly the lowest pressure of singular point for this system atdifferent W/Hs (except for cases where W/Hs are unrealisticallyhigh).The dP/dT slope of the SFE phase boundary at high pressures is
almost a constant value for paraffinic systems [58]. When excesswater is not available in the mixture, as for W/Hs of 0.5 and 1.0, anincrease in dP/dT slope is observed in SLE at higher pressures which
is presented by empty circles in Fig. 4. These points correspond topressure and temperature conditions above which some freeaqueous phase still remains. This is due to the obvious fact that,above the Pb, if a free aqueous phase is present, the overall methanecontent in the liquid hydrocarbon phase is higher than if all thewater is converted into hydrates as much more methane is trappedinto hydrates than dissolved in water.This particular composition is a good example as hydrate andsolid paraffin phase boundaries cross at low and high temperatures.After wax phase boundary crosses the hydrate dissociation line at
high pressures and temperatures (T~305 K and P~110 MPa), whenno hydrate is formed, as shown in the upper right corner of Fig. 4,the presence of water would result in dissolution of considerable
amount of light component in the aqueous phase which makes theliquid hydrocarbon phase heavier and again stabilizing the n-heptadecane wax, hence a marginal increase in SFE phase boundarytemperature (with similar dP/dT slope) is noticed compared to thewater-free condition.
4.2.2. Multicomponent systems
In this section, an in-depth analysis of mutual interactions ofhydrates and waxes are performed using three synthetic multicomponent systems (M1, M2 and M3), for which HDP data aremeasured here, as well as a synthetic condensate (the SHF4 mixtureof Ungerer et al. [21]). The compositions of the mixtures M1, M2and M3, are listed in Table 3. The heavy end compositions of thesemixtures are provided in Supplementary Materials document. Themixtures were chosen as they have different characteristics andexhibit different behaviours. First, the mixtures cover the wholerange of important influences and effects mentioned in the introduction. Here, with a general insight to systems forming both
waxes and hydrates, these compositions are categorised into (i)Mixtures for which hydrates are formed at higher temperaturesthan waxes over most of the pressure ranges. This is typical of
volatile crudes and gas condensates, as tested for several systemse.g. Ref. [59]. M1 and M2 mixtures are of this type and differsignificantly in the fraction of the light end. (ii) Mixtures for which
the wax phase(s) are formed at higher temperatures than the HDPtemperatures (heavier systems). Therefore, hydrate formation doesnot change their wax phase boundary. M3 belongs to this group.
Second, as mentioned, the mixtures differ significantly in theamount of light end (i.e. hydrate forming components). This in turngreatly impacts the hydrate formation and will be discussed later
on. Third, mixtures M1, M2 and M3 show multimodal distributionsof components in the heavy end with comparable paraffin gaps (asshown in Fig. 5 (a)), which will make them good candidates to formmore than one insoluble wax phase. Finally, the chosen mixturesare rich in hydrate formers (some of them capable of forming bothsI and sII under certain conditions [60] i.e. methane, ethane, carbon
dioxide, nitrogen) which would further increase their complexity.The experimental wax phase boundary data for M1, M2 and M3,are reported in the literature [8] and are listed in Table 4. For M2
and M3, the reported data are WDTs, which are better representatives of the true melting points of the mixtures [8,18,19]. However, to be consistent, for M1 the data provided are WAT as for this
mixture WDT were not reported for the heavy end in the work of Ji[8]. In this case, the difference of WAT and WDT data for the livemixture are within the experimental uncertainty. Using the
experimental procedure discussed earlier, the HDPs for M1, M2 andM3 were measured and are reported in Table 5. As shown later, theintegrated UCV model is in good agreement with wax phase
boundary and hydrate dissociation experimental data. Effect of the heavy end n-alkane distribution on wax andhydrate phase diagrams. The phase diagrams of mixtures M1 to M3
calculated by the integrated UCV model are provided in Figs. 6e8.As shown in these figures, the UCV model predictions are in goodagreement with the experimental data. As mentioned earlier, due
to the presence of heavier paraffins (as presented in Fig. 5 (a)) theWDTP s are higher in the case of M3 at constant pressure (Fig. 8)
compared to those of mixtures M1 and M2 (Figs. 6 and 7, respectively). Clearly, as M1 has the “lightest” heavy end of the mixturesM1 to M3 (see Fig. 5 (a)), it has the lowest WDTP range as observed
by comparing Figs. 6e8. The hydrate dissociation line passesthrough the same range of temperatures and pressures for all themixtures M1 to M3. This is because the dissociation pressures and
temperatures are a strong function of the light end compositiondistribution which is very similar (mostly composed of methane)for these mixtures as shown in Fig. 5 (b). Effect of hydrates on the wax phase boundary. The phase
boundary of M1 with a W/H of 2.0 is shown in Fig. 9. This systemcontains sI and sII hydrate formers, and there are regions whereboth structures can form. The wax phase boundary temperature
indicated by a thick line in Fig. 9 will increase (compared to that of water free system) due to consumption of light components andreduction of hydrocarbon fluid phases' solubility of the heavy alkanes inside hydrate boundary. This is a general observation and isalso shown in Fig. 6 for this mixture with different W/Hs in the feed.As shown in this figure, similar to the binary system investigated,increasing the W/H in the feed will increase the hydrate formation,hence increase the WDTP until the free aqueous phase forms.As shown in Fig. 9, due to entrapment of a major part of gaseouscomponents into hydrate cavities, a significant decrease of about8e9 MPa in Pb is observed inside the hydrate phase boundary. As an
example, the pressure of the “intersection point” (where wax phaseboundary and bubble lines cross each other) of the water-freesystem is about 22 MPa (Fig. 6) while the pressure of the intersection point in the system with W/H of 2.0 is about 14 MPa (Fig. 9).Wax formation strips some of the heavy hydrocarbons from theliquid hydrocarbon phase, making it lighter, and hence increasingthe bubble point Pb of the system (not graphically observable Fig. 9).Clearly, this change is emphasized depending on the amount oflight end and waxy part as well as the n-alkanes gaps in the feed for
which examples are presented elsewhere [61].At pressures lower than about 2 MPa a change in the wax phase
boundary shape is observed (around 275 K at Fig. 9). The changehappens when all the water is converted to hydrates and noaqueous phase is present at higher pressures. As also observed inthe binary methane þ n-heptadecane, this phenomenon occursbecause in the presence of an aqueous phase the hydrate forming
components (i.e. light hydrocarbons) content in the vapour/liquidhydrocarbon phases is higher than if all the water is converted intohydrates.
When all the vapour phase is consumed to form hydrates, theremaining aqueous phase will not change the WDTP, though,infinitesimally (see the “Excess Water” wax phase boundaries in
Figs. 6 and 7). This condition is also corresponding to the lowestpossible Pb at the wax phase boundary which coincides with thehydrate dissociation curve (intersection point). At pressures above
this Pb, all the gaseous part is dissolved in the hydrate/liquid hydrocarbon phase (see for example the full triangle point in Fig. 7). Impact of the amount of light end in the feed on wax phase
boundary. As mentioned earlier, mixtures M1 and M2 which bothbelong to the same category (see section 4.2.2) have a significantdifference in the amount of hydrate forming light end components.
Therefore, one can easily conclude that in the presence of sufficientwater more hydrate would form in M1 with 69 mol% light endcompared to that of M2 with 36.25 mol% light end. In such conditions, clearly, the increase in WDTP due to the formation of hydrates is more pronounced in M1 as seen by comparing Figs. 6 and 7. Inother words, in M2, the difference made in WDTP due to hydrate
formation (DT in Fig. 10) is not as significant as that of M1 even inthe presence of excess water. This is clearly due to lower amount oflight end hydrate formers in M2 compared to M1. Effect of the waxes onhydrate phase boundary. The effect ofthe presence of waxes on the hydrate phase boundary can benoticed, though their effect is limited, for systems where waxes areformed at higher temperatures than hydrates as is the case for M3(see Fig. 8). As mentioned, for these systems the wax phase
boundary is not affected by formation of hydrates. Fig. 11 shows thephase diagram of M3 with a W/H of 2.0. The multimodal composition distribution of this system with considerable n-alkane gapresults in the formation of three distinct paraffinic solid phases inthe investigated temperature range, each of them rich in a particular heavy component. An example of flash calculation results toshow the complexity of this mixture is provided in Table 6 at 279 Kand 5 MPa where the system is capable of forming eight distinct
phases. The flash calculation examples for the rest of the regionsshown in Fig. 11 are provided in the Supplementary Materialsdocument. As can be observed in Fig. 11, for this mixture all threeparaffinic solid phases are formed at temperatures higher than thehydrate dissociation temperatures.
The influence of waxes on the hydrate phase boundary
however, is marginal as seen in Fig.12 for M3. It is observed that at aconstant temperature, the pressure required to form hydrate in thepresence of wax is less than the same parameter in the absence of
wax. When waxes form, the amount of heavy alkanes decreases inthe liquid hydrocarbon phase so it can hold more of the light hydrate forming components, which in turn promotes the formationof hydrate. This is clarified here by performing a multiphase flashcalculation at 289 K and 21 MPa, which corresponds to a point justinside the hydrate phase boundary as presented in Table 7 both in
the presence of waxes and assuming that waxes do not form.Clearly, as the effect of wax precipitation is much less on vapourphase composition (compared to that of liquid hydrocarbon phase),
and the fact that below Pb vapour phase is providing the gaseouspart to form hydrate, the change is not observed in pressures lowerthan Pb.It is important to note that the marginal change is also due to the
low proportions of highly precipitable components in mixtures M1
to M3 (say less than 1 mol% of n-Eicosane and heavier componentsin mixtures M1 and M3 and about 2 mol% in M2). This is alsoobservable by the small molar phase fraction of waxy solids for M3
as presented in Table 7. This impact is more pronounced at highpressures when more wax is precipitated near the hydrateboundary. Such a situation requires significant amounts of heavy
waxy n-alkanes to be present in the feed which contradicts thenormal decay distribution of conventional oil and gas systems inmost of waxy systems. Effect of free aqueous phase on the wax phase boundary andamount. The impact of free water in the system on the wax phaseboundary is limited unless the amount of water is extremely high inwhich case the change in WDTP due to the presence of an aqueousphase would become significant. This effect is shown in Fig. 13 forM3 where the appearance of wax occurs at higher temperaturesthan hydrates. Therefore, the effect of the water content can be
investigated exclusively in this case. Fig.13 shows that even for very high W/Hs of 10 and 20 (corresponding to 91 and 95.2 mol% waterin the feed) the change in the WDTP is less than 0.5 K. Obviously, theincrease in WDTP is due to dissolution of the light components inwater. This change is not observed (is infinitesimal) for pressureslower than the Pb. This is clearly due to the higher solubility of lightcomponents in water compared to the solubility of heavier hydrocarbons hence increasing (infinitesimally) heavy componentscontents in the hydrocarbon phases and stabilizing wax. The
change in WDTP can be significant only when the W/H is extremelyhigh (e.g. 100 and 1000 in Fig. 13) and at pressures higher than Pb. Itis also noteworthy that by assuming that all the light-end part is
dissolved in water (at extremely high water contents say higherthan W/H of 1000) then the Pb will be near water saturation pressure and the wax phase boundary of the live system would become
the same as that of the heavy end part (see Fig. 13).The effect of aqueous phase on the amount of wax is alsoinvestigated in this work. To check different effects on the waxamount, hereafter, the paraffinic solid “wt% wax precipitated”corresponds to the wt% of the alkanes taken into the waxy solid
phase from the overall weight of “perceptible solids” i.e. theparaffinic part of feed with alkane of chain length greater than theCNCO. This way a reasonable comparison of the effect of aqueous/
hydrate on %wt of wax precipitated can be made. To avoid confusion, the wt% wax precipitated which is calculated in the mannerdescribed is abbreviated as WP and WPC correspond to the curve
of change of WP by reducing the temperature.
The effect of water content on the wax amount change bypressure is here shown for the complex SHF4 mixture of Ungereret al. [21]. This mixture presents interesting retrograde wax precipitation behaviour of condensates by increasing pressure at 325 Kas shown in Fig. 14. This behaviour was also observed in the
modelling work of Nichita et al. [62]. For this system, the waxes areformed at much higher temperatures than hydrates due to presentof considerable amount of very heavy component (1.2 mol% n-C36)
in the feed. As also shown in this figure, the high W/H of 5.0 has aninfinitesimal effect on the amount of wax precipitated. A very small decrease in dew point of the system (which is where the liquid
hydrocarbon phase molar fraction becomes zero) is also observablein Fig. 14 when water is present in the mixture. This is obviouslydue to the solubility of some of the light component in the aqueous
phase, therefore, making hydrocarbon phases heavier and reducesthe dew point. This mixture is later used in this work for assessment of the of hydrate formation on both amount of the waxesformed as well as the dew point of the mixture at low temperatureswhere considerable amount of hydrates are formed will be detailed.To conclude, in practical water contents, it is clear that the effect
of hydrate formation is much higher on the WDTP than the impactof the presence of a free aqueous phase. This is due to comparablymuch higher light end content entrapped in hydrate cavities
compared to the gaseous components solubility in water. Effect of hydrates on amount of waxes. In order to observethe effect of hydrate formation on the amount of wax precipitating,
the WPC of M2 is presented. This example covers a range wherehydrates are formed prior to waxes by reducing temperature athigh pressures and the reverse happens at low pressures as shown
Fig. 7. The WPC of this mixture with a W/H of 2.0 at 7 MPa (higherthan Pb and where hydrates are formed at higher temperaturesthan waxes) is shown in Fig.15 (a). The left axis in Fig.15 is showing
the WP and the right axis is showing the percentage increase in theWP (PIWP) due to presence of hydrates compared to that of thewater-free system. The figure clearly shows the importance of hydrate formation on the amount of wax formed. In the temperaturerange shown in Fig. 15 (a) there is as high as ~3 fold increase in WP.However, this high PIWP is of less practical significance down to
about 272.1 K. This is because the amounts of WP both in presenceand absence of hydrates are relatively small near the wax crystallization onset. Therefore, even a very small change on this amount
due to the formation of hydrates is translated into high PIWP asshown in the Fig.15 (a). In the single paraffinic solid phase region asthe temperature decreases the PIWP is reduced, as the gap between
WPCs in presence and absence of hydrate is fairly constant, therefore the reduction in PIWP is simply due to precipitation of moreparaffinic solid by reducing temperature. Below 272.1 K and right
after the appearance of the second paraffinic solid phase asignificant difference is observed between WPCs in presence andabsence of hydrate which is translated into a sharp increase in thePIWP curve. The demixing of paraffinic solids is mainly due to theconsiderable gap between the constituents n-alkane chain length.Fig. 16 shows the composition of the wax phases formed at 272 Kand 7 MPa of this mixture in water-free condition. On one hand, asshown in Fig. 16, the second paraffinic solid phase is considerablylighter than the first one and is more dominant in intermediatefractions. On the other hand, the formation of hydrates results inthe consumption of light hydrocarbons and reduces the liquid hydrocarbon phase capability of dissolving heavy solids. Furthermore,the overall feed is rich in the intermediate waxy fractions which arethe major constituents of the second paraffinic solid phase (see
Fig. 16). Therefore, by formation of hydrates, in the two solidparaffinic phase region, from the overall waxy fractions strippedfrom the liquid phase, proportionally more intermediate waxyfractions would precipitate to form and increase the amount of thesecond paraffinic solid phase. That is why a 30 fold increase in themolar phase fraction of the second paraffinic solid phase isobserved when comparing waxy solid precipitation in presenceand assumed absence of hydrates by performing a flash calculation
right after formation of the second waxy solid phase at 272 K and7 MPa (see Table 8). This is while the first paraffinic solid phasemolar fraction only increases marginally. With a further temperature reduction below the temperature of the second paraffinic solidphase appearance the PIWP waxy solid amount decreases. This isagain due to precipitation of more solid wax while the differencebetween the amounts of WP in presence and absence of hydrateremains fairly constant.
As mentioned, at lower pressures for M2, the waxes are formedprior to hydrates. WPC and PIWP curves of this case are shown at1 MPa for a W/H of 0.1 (9.1 mol% water) in Fig. 15 (b). Even for this
low amount of water, the formation of hydrates results inincreasing WP, hence a positive PIWP and an increase of as high asabout 5% in WP is also observed right after the formation of thesecond paraffinic solid phase in presence of hydrates at temperatures around 273 K. The same justifications made for the behaviours observed in Fig. 15(a) are correct in this case (Fig. 15(b)).However, in the case of Fig. 15(b), at temperatures higher than275.5 where hydrates are not yet formed, the presence of an
aqueous phase may decrease the amount of WP, and a negativePIWP value is obtained. Based on our experience, depending on theamount of W/H and the P/T conditions the presence of a free water
phase may result in both negative and positive PIWP values. However, similar to the impact of free aqueous phase on the wax phaseboundary, the effect of free aqueous phase on the amount and
composition of waxes, due to the very low solubility of heavy alkanes in water, is insignificant. Therefore, for the next example, theWPC of M3 with a W/H of 2.0 presented at 12 MPa in Fig. 17, is
exclusively shown below the hydrate dissociation point (287.6 K)where differences become significant. All of the observations madein the case of M1 in Fig. 15((a) and (b)) are also valid in this case.
Additionally, in this figure, it should be noted that the appearanceof sI hydrates at around 285.4 K would again increase the PIWP andfurther enhances wax precipitation. This is because the sI hydrate
consumes relatively higher amount of small molecules to beformed compared to sII hydrates. Adding to this the fact thatmethane is the richest hydrate former in the feed, sI hydrates wouldresult in making the hydrocarbon phases heavier compared to sIIhydrates, and in turn, PIWP increase upon formation of sI hydrates.Second, when all the aqueous phase is consumed to form hydrates(around 275.5 K) a more rapid decrease in the PIWP value isobserved as no more hydrates can form by reducing the
temperature.Finally, in this section, the effect of hydrate formation on the richcondensate SHF4 mixture of Ungerer et al. [21] is investigated bycalculating the WP change by increasing pressure at 275 K, which
corresponds to a condition well inside the hydrate phase boundaryfor the most of the pressure range as shown Fig. 18 for different W/Hs in the feed. As mentioned this system shows interesting retrograde wax formation as it is shown by quality lines in Fig. 18. Forthis systems again the enhancement in the wax precipitation by theformation of hydrates is observed. The enhancement has a rapidly
increasing trend by pressure as long as all the water is consumed toform hydrates (corresponding to empty circles in the Fig. 18.) abovewhich the increase in WP compared to the water-free condition is
still observable. In the presence of excess water (dashed-dotted linein Fig. 18(a)), a significant continuous enhancement in WP isobserved which is due to the formation of more hydrate. This
mixture is, as well, interesting for investigating the effect of hydrateformation on the dew point of the system. In this regard, inFig. 18(b), the change in molar volume of the liquid hydrocarbonphase by pressure is presented. As observed, for low W/Hs in thefeed (W/H 2.0 shown by dotted line), a very small decrease in dewpoint (which are around 31.2 MPa) is observed which is due toconsumption of a part of the light ends in the feed to form hydrates.For higher W/Hs where more hydrates are formed, the remainingfeed excluding hydrates has become much heavier that the saturation point is not a dew point anymore and is now a bubble point.This is clear for W/H of 4.0 and excess water systems. In contrast to
W/H of 2.0 and water-free condition in which a sudden sharpchange is observed in liquid molar volume at dew point of this richcondensate systems, for W/H 0f 4.0 and excess water conditions, anon-zero continuous change in liquid phase molar volume isobserved in saturation (bubble) points. Effect of hydrates on the MW and composition of waxes.The effect of hydrates on the composition of the precipitated waxesis investigated by monitoring the change in WP as well as thechange in the molecular weight of the overall wax phase (allparaffinic solid phases together) for M2 (at one P/T condition below
the Pb) and M3 (at one P/T condition above the Pb) as seen in Fig. 19.As observed in this figure and expected over the full W/H range anincrease in the WP is clear by increasing the W/H due to formation
of more hydrates. Also, the wax phase molecular weight Mw decreases for all the cases. This is because after the formation of hydrates more of the intermediate alkanes are expelled out of theliquid hydrocarbon phases as the feeds are richer in intermediatefractions compared to very heavy alkanes. In fact, the paraffinicsolid phase proportionally has less intermediate fraction prior toformation of hydrates. Therefore, the more hydrates formed, thelower the MW of incipient waxes. When excess water in the form ofa free aqueous phase is present it corresponds to the condition thatno more hydrates can be formed and hence the upper limit ofwaxes to be affected by hydrates is reached.It should be noted here that, in the calculation of MW of waxypart, an unrealistic (too low) value of CNCO may make
interpretations difficult as shown in Fig. 20 for the cases mentionedin the Fig. 19 but this time with CNCO of 1. Here, no specific trend isobserved for MW. of waxy part by increasing the W/H. The difficultyof interpretations is due to solubility of a small amount of very lighthydrate-forming components in the paraffinic solid phases. Thissignifies the importance of setting a plausible value for CNCO toperform analysis. The same trend is again observed for the WP.The changes in the composition of the wax phase for M2 at282 K and 3 MPa in which it forms single paraffinic solid phase for
different W/Hs of 0.1, 0.25 and 1.0 (corresponding to 9.1, 20 and50 mol% water) and CNCO of 6 are presented in Fig. 21. As the overallcomposition sums to 1.0, the change here is shown by the percentage increase in the ratio of wt% of each component to that ofrichest (heaviest) component in the waxy solid phase (here n-triacontane). The ratio is defined in this way, as obviously the amountof the richest component precipitated in the paraffinic solid phase is the least sensitive one to the hydrate formation effect. As expected, formation of hydrate corresponds to consumption of lightend hydrate formers hence the reduction in the hydrocarbon fluidphase solubility of heavy ends and forcing some of the intermediate
to heavy ends to precipitate in the waxy solid phase. Therefore, thedefined ratio would increase by increasing the hydrate formation asshown in Fig. 21.The same graph, in the same P/T conditions, is provided at W/Hof 0.01 corresponding to 0.99 mol% water (Fig. 22). In contrast tothe previous conditions, the percentage increase in the amount ofthe intermediate components in the wax phase are negative for themost part. This behavior is justified with the “low water content
effect”.To clarify the low water content effect, Fig. 23 for M2 at 3 MPa
and 283 K which corresponds to a condition just outside the hydrate boundary (see Fig. 7) is provided.
As observed, here for W/Hs corresponding to low water contentconditions, a free water phase may not form and all the water would be dissolved in fluid hydrocarbon phases. This in turn increases the hydrocarbon phase solubility of light to intermediate ends, therefore decreasing the tendency of intermediate fractionsto precipitate. This would directly result in increase of MW (incontrast to previous observation in Fig. 19) and decrease of the WPup to an optimum W/H above which a free aqueous phase forms.After formation of the free aqueous phase some of the light endswill be dissolved in it, hence reducing the capability of hydrocarbonfluid phases to solubilize intermediate to heavy hydrocarbons.
Therefore, by further increase of the W/H, the WP would increaseand its MW would decrease. However, this is not strong enough tocompensate the MW increase (and WP decrease) due to complete
solubility of water in hydrocarbon fluid phases in low water contentconditions, unless W/H is high enough or in high pressures or whenenough hydrates are formed. Therefore, in the hydrate forming
regions, if enough hydrates are not yet formed to compensate thelow water content effect, a decrease in the amount of intermediatefractions precipitated can be expected as it is the case for the observations made in Fig. 22 at the specified P/T and W/H conditions.Due to the same reason, it is likely for quite a wide range of W/Hs tohave a negative PIWP value in “no-hydrate” regions as observed in
Fig. 15(b). Effect of waxes and hydrates on the composition and amountof hydrates. The impact of waxes on the hydrate fraction for themulti-structure system M3 with W/H of 1.0 is shown in Fig. 24 bydepicting the molar fraction of hydrate phases in presence andassumed absence of wax phase(s) by increasing pressures at aconstant temperature of 274 K. As observed the change in the molar
phase fraction of hydrate phase (regardless of the hydrate structure) is infinitesimal. This is expected as the constituents of thehydrate phases (water and light end hydrate formers) are notpresent in the waxy part. The result of the multiphase flashcalculation right inside the hydrate phase in presence and assumed
absence of wax, provided in Table 7, as well, shows that almost nochange is observed in the composition of the hydrate formed whichis justified by the same reason.The minor changes, though are not the same for different hydrate structures. In this regard the graph of the change in molarphase fraction of each present phase in the M1 with W/H of 2.0 byincreasing pressure at constant temperature of 273.15 K is presented in Fig. 25. As shown in this figure, by reintroduction of waxphase at high pressure of about 23 MPa a limited increase in sIhydrate fraction and decrease in sII hydrate fraction is observed, as
after formation of paraffin wax, the content of small molecules isincreasing in the liquid hydrocarbon phase it will slightly promotesI hydrate over sII.
4.2.3. Integrated wax-hydrate formation in a real mixture withcontinuous distribution of normal paraffins
Based on the previous results, it is now easier to investigatemixtures of higher complexity. Indeed, checking the validity ofjustifications based on the model results must be carried out for a
real system having a continuous distribution of normal alkanes. Inthis regard, here a light oil recombined mixture is investigated withthe composition provided in Table 9 and HDP data measured by the
experimental procedure outlined in section 3 and listed in Table 10.For this system, from all the effects discussed, just the more significant ones, i.e. the effects of hydrate formation on wax phase
boundary and amount are explored.As shown in Fig. 26, similar observations as that of mixtures M1
and M2 can be made for this light oil system and again a WDTPchange of as high as about 8 K can be observed at high pressureswhen enough water is present in the feed.As with the effects on the amount, PIWP curve is provided inFig. 27 at 5 MPa with W/H of 1.0. Due to continuous distribution on
n-alkanes (as shown in Table 9) and their mutual co-solubility, thePIWP curves have several bumps at very low temperatures wherelighter fractions start to precipitate. Each bump corresponds to a
major wax producing condition in which lighter fractions areprecipitated due to hydrate formation. The aforementioned mutualco-solubility, however, does not allow formation of several
paraffinic solid phases except below 245.75 K where two paraffinsolid phases are present. As before, for the whole temperaturerange shown in Fig. 27, hydrate formation results in having a positive PIWP similar to the observation made for the syntheticmulticomponent mixtures M1 to M3.
5. Conclusions
In this work, an accurate integrated wax-hydrate thermodynamic model, was developed to carry out an in depth analysis ofinteractions between hydrates and waxes, in mixtures where bothphases can form, by devising a robust multiphase flash calculationalgorithm. From the thermodynamic viewpoint, this analysis shows


that hydrates and waxes, can synergistically enhance their precipitation. The formation of hydrates can significantly increase waxmelting temperature, especially at higher pressures and obviously
in the presence of higher proportions of light ends and water in the overall feed. Furthermore, a significant increase in wax precipitation, as well as a considerable change in wax composition, due to
formation of hydrates can be observed. Waxes can also enhance hydrates precipitation though to a limited extent. The effect of waxes on the composition of hydrates is marginal.