A NEW COMPUTER MODEL FOR GAS HYDRATES AND HYDRATEINHIBITION

by

B. Edmonds, R. A. S. Moorwood and R. Szczepanski,Infochem Computer Services Ltd.,

90 London Road,London SE1 6LN.

Background and ObjectivesThe theoretical understanding of gas hydrates stems from the work of van derWaals and Platteeuw (1) who proposed that gas hydrates are ice-like crystallinestructures into which light gas molecules are adsorbed. Van der Waals andPlatteeuw derived the statistical mechanics of gas hydrates modelling theinteraction between the gas molecules and the hydrate lattice using theLennard-Jones potential. Their model was refined by Parrish and Prausnitz (2)who used instead the Kihara potential and devised a computer method forsolving the model to predict the hydrate dissociation point. The Parrish andPrausnitz model predicted the dissociation curves of simple hydrates of singlegases well, but was not reliable for gas mixtures. An empirical modificationwas made to the Parrish and Prausnitz model by Ng and Robinson (3) whichimproved the results for the dissociation points of mixed hydrates. However,Ng and Robinsons modification is thermodynamically incorrect; despite this,it has been used as the basis of the hydrate predictions in some widely usedcommercial simulation programs (4).

Other effects that influence the formation of hydrates, such as the presence ofinhibitors or the effect of gas solubility, are usually handled by addingempirical corrections to the value of the activity of water in thethermodynamic expressions for the properties of the hydrates, i.e. the trueinfluence of these effects on the fluid phases is ignored and a hiddenassumption is made that a liquid water phase is present, which is not alwayscorrect. See (4) again, for example.

The aim of this work, which was carried out in collaboration with ShellResearch, was to produce a practical engineering model for gas hydrates andhydrate inhibitors that is thermodynamically consistent, that accuratelyrepresents all the published phase equilibrium data of relevance to theproblem, and that is capable of solving all phase equilibrium problemsassociated with gas hydrates, not just determining the hydrate dissociationpoints. To achieve this, three complementary facilities had to be developed,namely, the mathematical techniques to solve the phase equilibrium problemsinvolved, the thermodynamic model for the gas hydrates and thethermodynamic model for the fluid phases which include the hydrateinhibitors. These are described below.

Mathematical TechniquesThe basis of all the calculations is a new computer algorithm, Multiflash,developed by the authors for solving multiphase equilibrium problems (5).Multiflash is able to perform all the normal engineering flash calculations,dew and bubble point searches etc. for problems involving any number andcombinations of phases. The phases may have quite different properties

calculated from different thermodynamic models. The software automaticallydetermines which phases will be present under given conditions and returnsthe relative amounts, compositions and properties of the phases. In this study,Multiflash was applied to problems involving up to six different phases: oil,gas, liquid water, ice, hydrate structure I and hydrate structure II, all phasesbeing treated in an equivalent manner. The advantages of this approach are:

The same methods and models can be used whatever combination ofphases is present. For example, formation of hydrates from gases in theabsence of a free water phase or from crude oils in the absence of a gasphase is predicted automatically. Because the thermodynamic models usedare completely consistent, the predictions are as reliable as for the morenormal situation where gas and liquid water are present. For example,Figure 1 illustrates the calculated values of the hypothetical vapourpressure of water over empty structure I hydrate compared with the valuespredicted by Sloan by analysis of experimental data (4). This result indicatesthat the program will reliably calculate the transition from gas to hydrate inthe absence of free water as the underlying thermodynamic properties areaccurately represented.

The program can reveal the full complexity of the phase behaviour

especially when soluble gases and inhibitors are present. Figures 2 and 3,for example, show the phase behaviour of a wet gas stream with methanoladded. This example was studied as part of an investigation of a realprocess. Figure 2 shows the phase behaviour of the mixture when only thefluid phases are considered. Figure 3 in contrast also includes the hydrateand ice phases. Figure 3 shows a number of complex effects that arecounter-intuitive and can only be calculated using a program that canhandle the full phase behaviour of the system. The hydrate dissociationcurve shows sharp discontinuities where it crosses the water dew-point lineand the hydrocarbon phase envelope. This behaviour is reminiscent of thediscontinuities that are known to occur at the hydrocarbon phase envelopefor cases when large amounts of carbon dioxide are present (4). Anothersurprising feature is the conversion of hydrate back to liquid water as thetemperature decreases. At low temperatures, the liquid water phasecontains large amounts of methanol which forms because of the decreasingmutual solubility of methanol and hydrocarbons with decreasingtemperature. Also notable is the prediction of a small ice region at lowpressures.

Finally but most importantly, a data regression program has been

developed based on Multiflash that is able to fit model parameterssimultaneously to many different sets of phase equilibrium data. Each dataset may contain data for different combinations of components and phases.This regression program was essential for developing the newhydrate/hydrate inhibition model as it made possible the comparison ofdifferent types of data for consistency. It also ensured that the hydratemodel represented the properties of structure I and structure II hydratesequally accurately.

Hydrate ModelThe Parrish and Prausnitz model was investigated initially as, with themodification of Ng and Robinson, it has been widely used in oil and gasprocessing. Calculations showed that the values of the thermodynamicproperties of the empty hydrate lattices proposed by Parrish and Prausnitz arenot correct. Using this model, it is possible to obtain good predictions forsimple hydrates but not for mixed hydrates. Figure 4, for example, shows thebest fit that could be obtained for the methane hydrate dissociation curvewhen fitting to data for both hydrate structures I and II using the Parrish andPrausnitz empty lattice parameters. In contrast, Figure 5 shows the resultwhen regressing the same data with revised values for the empty latticeparameters. Considering that the data ranges from 1 bar to 4000 bar over atemperature range of 125K the agreement in Figure 5 is very satisfactory.Some deviations are observed for pressures above 2000 bar which is due tothe inability of cubic equations of state to model accurately the properties ofthe gas phase at such high pressures.

From analysing nearly all the published data for simple and mixed hydrates, itwas concluded that it is possible to set parameters in the van der Waals-Platteeuw model to reproduce most of the measurements within 1K. The onlyexception to this is the data for n-butane rich hydrates at low temperatures.However, it is known that due to their size, n-butane molecules cause latticestrain of the hydrate, an effect that is neglected in the van der Waals-Platteeuwmodel.

Bases in this analysis, there seems to be no need to introduce any empiricalmodifications to the van der Waals-Platteeuw model. The modification of Ngand Robinson appears only to be necessary to compensate for inaccurateparameter values in the Parrish and Prausnitz version of the model. Theadvantage of using a thermodynamically rigorous approach is that allproperties of the hydrates can be calculated because they are consistent, andused in calculating the phase equilibria and associated physical properties ofthe system.

Figures 6, 7 and 8 show a selection of typical results for the new model toillustrate the agreement with experiment.

Because the Multiflash algorithm uses rigorous methods to calculate phaseequilibria, it is always possible to check for given conditions whether astructure I or structure II hydrate will form. In the course of the work it wasfound that some of the published hydrate models erroneously predictstructure changes. For example, the Parrish and Prausnitz model predicts thatpure methane hydrate will change from structure I to structure II as thetemperature falls. Computer calculations reveal a change to structure II on thewater-hydrate-vapour line at 263.6K under a pressure of 10 bar. Independentalgebraic analysis of the model confirmed this result. Experimentally, it isknown that methane hydrate is structure I at all temperatures (4). Similarproblems were encountered with other published models. For example, themodel of Munck et al. (6) which uses the Parrish and Prausnitz values for theempty hydrate lattice parameters, erroneously predicts that pure methanehydrate changes to structure II at 252.2K under a pressure of 10 bar. Themodel developed in this work predicts the correct structure of methanehydrate.

The question arises as to why these incorrect predictions of structure changeshave not been previously reported. It seems likely that many of the computerprograms used to perform hydrate calculations do not use rigorous methodsto determine which hydrate phase actually exists and as a result do not detectwhat their models are actually predicting.

The main features of the new hydrates model are:

It uses thermodynamically consistent models for all phases that may bepresent including the hydrates and the ice phase.

The thermal properties (enthalpies and entropies) of the hydrates and ice

are also returned permitting isenthalpic and isentropic flash calculationsinvolving these phases. This makes it possible, for example, to predict ifhydrates would form in a choke or a turbo-expander by performing theappropriate flash calculation.

Calculations can be made for any possible combination of phases, including

non-free water calculations, and the phases present at equilibrium areautomatically found.

The properties of the hydrates have been fixed by investigating data for

both simple hydrates and mixed hydrates. For simple hydrates, all datafrom the ice-hydrate-vapour lines to the water-hydrate-liquid lines havebeen regressed going through both quadruple points where they exist.Simultaneously the data for mixed hydrates have been regressed to giveaccurate parameters for both structure I and structure II hydrates. Mosthydrate data for both pure gases and mixtures are reproduced typicallywithin 1K.

The properties of the empty hydrate lattices have been investigated, and

earlier values such as those proposed by Parrish and Prausnitz have beenfound not to be compatible with the data.

Proper allowance has been made for the solubilities of gases in water when

developing the model. If this is not done, the model parameters will bedistorted as dissolved gases have an inhibiting effect on hydrate formation.This is particularly important for relatively soluble gases such as carbondioxide and hydrogen sulphide.

Rigorous thermodynamic calculations of the most stable hydrate structure

have been made to ensure that the model agrees with the experimentalevidence. These consistency checks have revealed that some publishedmodels erroneously predict hydrate structure changes and that manycomputer programs used for hydrate calculations are apparently unable todetect this.

Inhibition ModelThe properties of gas hydrates are of interest to engineers as it is necessary toknow when they may form. The properties of hydrate inhibitors are possiblyof even greater interest as the objective with hydrates in gas processing is tosuppress them. The inhibitors studied in this work were methanol,monoethylene glycol (MEG), diethylene glycol (DEG) and triethylene glycol(TEG).

The mechanism of hydrate inhibition is that the inhibitor mainly dissolves inthe free water phase thereby reducing the fugacity of water. As water is theprincipal component of gas hydrates, reducing the fugacity of water alsoreduces the tendency of hydrates to form. It is important to realise thatinhibitors modify the properties of the fluid phases, not the hydrate phase,and as a result they have a number of other effects. The presence of inhibitorsraises the solubility of gases and hydrocarbons in the water phase therebyinhibiting the formation of hydrates still further. The inhibitor also depressesthe ice point. It reduces the vapour pressure of water, i.e. it has a dehydratingeffect on the vapour and hydrocarbon liquid phases. The inhibitor itselfvaporises and also dissolves in the hydrocarbon liquid, i.e. it partitions. Theconventional method of simulating hydrate inhibition is to modify thethermodynamic expressions for the formation of hydrate. This does not modelthe actual mechanism of inhibition and does not therefore give a completepicture of what happens.

In this study, the effect of inhibitors was modelled by adopting new mixingrules for the equation of state. The preferred equation of state is the RKSequation which is known to give better values for the fugacities of thecomponents of natural gases than the Peng-Robinson equation (7). However,the Peng-Robinson equation can be used if required. The mixing rule is relatedto the Huron-Vidal mixing rule (8). It matches the excess Gibbs energy of afluid mixture using an expression derived from the NRTL equation, but itreduces to the conventional van der Waals mixing rule if water or inhibitor isnot present, i.e. for oil and gas mixtures it gives identical results to theconventional equation of state.

All the open literature data for the effect of methanol, MEG, DEG and TEG onhydrate formation have been studied. In order to build up a comprehensivemodel, all relevant types of phase equilibrium data were considered includingfreezing point depression curves, vapour-liquid equilibrium data for water-inhibitor mixtures, vapour-liquid, liquid-liquid and solubility data for lightgases, hydrocarbons and inhibitors. The interaction parameters have all beencorrelated so that they can be automatically generated for any oil or gasmixture with water and inhibitors.

When the dissociation curve of a simple hydrate is reported, the meaning ofthe reported data is clear. The dissociation curve is a three phase equilibriumpoint for a mixture of three components. From the phase rule it follows thatfor a given pressure, there is a unique dissociation temperature and vice versa.A difficulty of assessing published data for hydrate inhibition is the fact thatthe hydrate dissociation point for a gas mixture in the presence of inhibitor isnot a unique point but is dependent on the relative amounts of the phasespresent. Figure 9 illustrates this for a gas mixture where the ratio of waterphase to hydrocarbon phases has been varied. In this example the hydratepoint changes by over 20K. Unfortunately virtually none of the published data

for the effect of inhibitors on hydrate dissociation curves gives the relativeamounts of the phases present so it cannot be properly interpreted. Thepractical consequences of this are:1. The available experimental data only gives an approximate indication of the

effect of inhibitors.2. To calculate the effect of inhibitors in a process accurately, it is necessary to

know the amounts of all phases present and it is necessary to use acomputer model that is able to take these effects into account.

Figures 10, 11 and 12 give a selection of results for the inhibitors studied. Thecalculations reported here were done with the arbitrary assumption ofequimolar mixtures of aqueous phase and hydrocarbon phases.

Inhibitor partitioning is an important factor as it affects the design of recoverysystems. It is difficult to develop a comprehensive model for partitioning asthere are few data available; also, the reliability of some of these data is opento question. Table 1 shows an example of the partitioning of methanolcalculated from the model compared with data reported by Ng and Robinson(9). The calculated methanol mole percent in the vapour at 0.6C shows thelargest deviation, but comparison of the experimental values with the Ng andRobinsons reported feed compositions shows that the methanol compositionsdo not obey mass balance, i.e. the experimental values cannot be accurate. Theresults are also somewhat deviant for carbon dioxide. The chemistry ofaqueous solutions of carbon dioxide is complex and it is very difficult torepresent the solubility of carbon dioxide in water accurately with a simpleengineering model. Apart from this, the model gives good predictions.

In summary, the inhibitor model has the following features:

The model is a thermodynamically consistent model for all fluid phases. Itcan explicitly represent all the effects of inhibitors including hydratesuppression, depression of freezing point, reduction of water vapourpressure and inhibitor partitioning.

The model has been developed using extensive phase equilibrium and

hydrate data for methanol, MEG, DEG and TEG. The model can show the effect of different relative amounts of the phases

present on the hydrate inhibition. The model can be extended to include other hydrate inhibitors as the

methods used are quite general.

Future developmentsThe new model has been developed to the point where it can be used reliablyto calculate hydrate problems both as a stand-alone utility and as a subroutinelibrary that can be called from a larger program.

New developments are being planned to enhance the model. The model for theinhibitors needs to be complemented by a model for the inhibiting effect ofsalinity of the water phase. A practical and consistent method for accountingfor salinity is under development that can be used in conjunction with theexisting model but does not require a full electrochemical treatment ofaqueous electrolyte solutions.

The recent discovery of structure H hydrates is an obvious extension as theMultiflash algorithm can determine which hydrate structure will exist undergiven conditions. All that is required is a new model option to return theproperties of structure H. Structure H hydrates are of importance as they mayexist at higher temperatures than structures I and II under certain conditions(10). Models for other solid depositions such as waxes and asphaltenes areanother obvious extension, again because the numerical methods are in placeto determine when a phase will exist.

AcknowledgementThe authors would like to acknowledge many useful discussions with Dr. EricHendriks of the Royal Dutch Shell Laboratory, Amsterdam, in the course of thework.

References(1) J. H. van der Waals, J. C. Platteeuw: Adv. Chem. Phys., 2, 1, (1959).(2) W. R. Parrish, J. M. Prausnitz: Ind. Eng. Chem. Proc. Des. Dev., 11, 26,

(1972).(3) H.-J. Ng, D. B. Robinson: Ind. Eng. Chem. Fundam., 15, 293, (1976).(4) E. D. Sloan: Clathrate Hydrates of Natural Gases, Dekker, New York,

(1990).(5) J. F. Counsell, R. A. S. Moorwood, R. Szczepanski: Calculating

Multiphase Equilibria, VLE 90 Conference, Aston University, (1990).(6) J. Munck, S. Skjold-Joergensen, P. Rasmussen: Chem. Eng. Sci., 43,

2661, (1988).(7) L. Lundgaard, J. M. Mollerup: Fluid Phase Equil., 70, 199, (1991).(8) M. J. Huron, J. Vidal: Fluid Phase Equil., 3, 255, (1979).(9) H.-J. Ng, D. B. Robinson: GPA Report RR-66, (1983).

(10) J. A. Ripmeester, C. I. Ratcliffe, G. E. McLaurin: The Role of Heavier Hydrocarbons in Hydrate Formation, Session on Hydrates in the Gas Industry, AIChE Meeting, Houston, (April 1991).

Table 1Temp Mole PercentPressure Phase Componentwt % Methanol Experiment Calculated

Vapour Water 0.045 0.0470.6 C Methanol 0.058 0.0291.48 MPa Nitrogen 6.378 5.92610% Methane 74.640 71.20Methanol Ethane 5.241 4.696

Propane 2.191 1.931n-Butane 0.886 0.780n-Pentane 0.925 0.779CO2 9.636 14.611

Aqueous Water 94.006 93.794liquid Methanol 5.771 5.840

Nitrogen 0.005 0.002Methane 0.059 0.072Ethane 0.005 0.007Propane 0.002 0.004n-Butane - 0.002n-Pentane - 0.003CO2 0.152 0.281

Vapour Water 0.028 0.04415.7 C Methanol 0.077 0.07016.71 MPa Nitrogen 6.219 5.95810% Methane 74.194 71.415Methanol Ethane 5.196 4.726

Propane 2.174 1.947n-Butane 0.872 0.788n-Pentane 0.950 0.788CO2 10.290 14.264

Aqueous Water 93.337 93.704liquid Methanol 5.830 5.749

Nitrogen 0.020 0.016Methane 0.280 0.410Ethane 0.010 0.015Propane 0.002 0.004n-Butane - 0.000n-Pentane - 0.000CO2 0.521 0.731

Vapour Water 0.032 0.023-3.9 C Methanol 0.059 0.0402.11 MPa Nitrogen 6.357 5.99420% Methane 74.828 71.525Methanol Ethane 4.908 4.638

Propane 2.022 1.700n-Butane 0.982 0.760n-Pentane 0.823 0.771CO2 9.989 14.553

Aqueous Water 87.527 86.181liquid Methanol 12.080 13.116

Nitrogen 0.009 0.003Methane 0.107 0.156Ethane 0.010 0.024Propane 0.003 0.002n-Butane - 0.001n-Pentane - 0.002CO2 0.264 0.470

Vapour Water 0.029 0.0319.4 C Methanol 0.115 0.13116.78 MPa Nitrogen 6.242 6.00820% Methane 73.245 71.482Methanol Ethane 5.251 4.662

Propane 2.197 1.844n-Butane 0.804 0.789n-Pentane 0.588 0.795CO2 11.529 14.258

Aqueous Water 86.899 85.76liquid Methanol 11.989 12.644

Nitrogen 0.028 0.018Methane 0.355 0.651Ethane 0.014 0.034Propane 0.002 0.009n-Butane - 0.003n-Pentane - 0.003CO2 0.713 0.878