Molecular Thermodynamics in the Design of Substitute Solvents

Molecular Thermodynamics in the Design of Substitute Solvents

Renhong Zhao† and Heriberto Cabezas*

National Risk Management Research Laboratory, Sustainable Technology Division, System Analysis Branch,U.S. Environmental Protection Agency, 26 West Martin Luther King Drive, Cincinnati, Ohio 45268

The use of physical properties and fluid behavior from molecular thermodynamics can lead tobetter decision making in the design of substitute solvents and can greatly reduce the expenseand time required to find substitutes compared to designing substitute solvents by experiment.This paper systematically discusses the equilibrium and dynamic properties and the fluidbehavior which are important for designing substitute solvents. For each property, it discussesthe rationale for using the property, the current level of understanding from molecularthermodynamics, the general methodology for estimating the property for single chemicals, andsuggested methods for liquid mixtures. In addition to bulk physical solvent properties such asviscosity, other solution properties such as activity coefficients are also important for designingsubstitute solvents. The use of limiting or infinite dilution activity coefficients in the context ofsubstitute solvent design is discussed. Lastly, other requirements such as solvent safetyproperties including flash point and solvent phase and chemical stability are fully discussed.

Introduction

Solvents are widely used in industry for absorption,extraction, painting, coating, cleaning, and many otherpurposes. Since the signing of the 1987 MontrealProtocol, legislation and public environmental aware-ness have become the two main driving forces forreducing or eliminating the use of harmful solvents. Twomain approaches have been pursued. One is to findalternative technologies that do not use solvents, andanother is to find alternative solvents. The latter, whichis also called solvent substitution, is preferable to theformer because it can use existing processes with minoror no modifications. But on the other hand, the solventsubstitution approach also presents a significant techni-cal challenge: designing substitute solvents which areas efficient as the current solvents but are different insome other undesirable aspect such as toxicity. Manyresearch workers have studied solvent substitutionusing multiple physical property matches. These effortscan be roughly classified into following three categoriesdetailed below.

The first category is that of screening the availablesolvent databases for single chemical substitutes. Herethe user needs to specify the allowed range or extremevalues for each physical property. After screening, onlythose substitutes which meet the requirements for allspecified physical properties are taken as substitutioncandidates for performance and evaluation testing. Abasic requirement for the work in this category is a morecomplete solvent database. Computer programs can beused to greatly reduce the time required by databasescreening. Some efforts in this category include theSolvent Substitution for Pollution Prevention (Joback,1994), the Solvent Database Software Program (Her-mansen, 1993), and the Tool for Systematic SolventScreening for Batch-Process Development and Revamp-ing (Modi and Stephanopoulos, 1996). Database screen-ing cannot always find substitutes as expected, either

because the information provided by the database islimited or because no existing chemicals can meet thespecified property requirements.

The second category approaches the problem bydesigning new chemicals that meet the specified re-quirements. The principal work in this category is thatof molecular design, and the challenge is to determinethe structures of feasible chemical compounds thatpossess the required properties. Depending on how itis used, this category of approaches can design entirelynew chemicals or identify already existing chemicals.However, it is most useful when no single chemicalreplacements are found or available. Some efforts inthis category include Molecular Design of Solvents forLiquid Extraction based on UNIFAC (Gani andBrignole, 1983), Designing Molecules Possessing De-sired Physical Property Values (Joback and Stephan-opoulos, 1990), Computer-Aided Molecular Design byGroup Contribution (Nielsen et al., 1990), Group Con-tribution Approach to Computer-Aided Molecular De-sign (Gani et al., 1991), Design of Optimal Solvents forLiquid-Liquid Extraction and Gas Absorption Pro-cesses (Macchitto et al., 1990), Computer-Aided Molec-ular Design of Solvents for Separation Processes (Pretelet al., 1994), and Design of Environmentally SafeRefrigerants Using Mathematical Programming (Duve-di and Achenie, 1996).

The third category is that of designing mixturereplacements if no single chemical replacement is foundor available. The key issues in this category are (1) toselect adequate components, (2) to determine the mix-ture composition, and (3) to use the least number ofcomponents. Because of the problem complexity, com-puter programs or software tools are required in thiscategory. If adequate methods can be found and enoughinformation used, the formulations designed by computer-aided methods have a good chance of success in subse-quent testing. Some efforts in this category includeSolvent Selection by Computers (Hansen, 1973), Com-puter Aided Mixture Design with Specified PropertyConstrains (Klein et al., 1992), Computer Program forAssisting the Design and Replacement of Environmen-

* To whom correspondence should be addressed. FAX: 513-569-7111. E-mail: [email protected].

† Research Associate, National Research Council.

3268 Ind. Eng. Chem. Res. 1998, 37, 3268-3280

S0888-5885(97)00861-0 This article not subject to U.S. Copyright. Published 1998 by the American Chemical SocietyPublished on Web 06/24/1998

tally Objectionable Solvents (Zhao et al., 1996), andComputer Aided Solvent Substitution for PollutionPrevention (Cabezas et al., 1996).

In this paper, some concepts and ideas which areimportant for the design of substitute solvents arediscussed, and those physical properties which shouldgenerally be used to design substitute solvents arediscussed one by one, including some suggested predic-tion models or methods for mixtures. Two importantthermodynamic considerations, phase stability andchemical reactivity, are also discussed. An importantarea, which will not be discussed extensively, is theapplication of mathematical optimization and the de-velopment of computer algorithms for the design ofsubstitute solvents. Another important area, which isnot discussed, is environmental properties such astoxicity, ozone depletion potential, etc. The reason isthat these two areas are outside the main theme of thepaper, which is the application of molecular thermo-dynamics to the design of substitute solvents. Envi-ronmental properties in particular are far removed frommolecular thermodynamics.

Substitute Solvent Design

The objective of substitute solvent design is to findsingle chemicals or mixtures to replace currently usedsolvents or solvent mixtures. The following are someimportant concepts or ideas which are required forsuccessful design of substitute solvents.

Procedure for Designing Successful SubstituteSolvents. A complete procedure for designing substi-tute solvents should have three steps: (1) to determinethe substitute candidates or the replacement formula-tions, (2) to do the performance and evaluation test, and(3) to do the full scale operation test.

Step 1 is the most important and most difficult stepof all three steps because it is the decision making stepand no generally accepted rules or procedures exist thatcan be used, although a number of algorithms have beenadvanced under the first and second categories of themethods previously discussed. For most previous effortsin designing substitute solvents, the step 1 decisionmaking has often been completely based on the users’experience. Because of the limitations of both the users’experience and the information available, it is verydifficult to make optimal decisions without doing manytests on step 2 and step 3. To reduce the required timeand expense, making better decisions on step 1 is crucialin all substitute solvent design.

Task-Specific Properties and General Proper-ties. Better decision making on step 1 can be achievedwith better understanding of solvent behavior. Solventbehavior can be represented by general properties andtask-specific properties. Solvent general properties arethose which are more or less relevant to essentially allsolvent applications. Molecular mass, density, boilingor bubble point, vapor pressure, surface tension, viscos-ity, thermal conductivity, diffusivity, and flash point areexamples of general properties. Solvent task-specificproperties are those which are likely to be relevant toonly by very specific applications. For example, gassolubility is used by absorption, selectivity and distribu-tion coefficients are used by extraction, and solventpower and selectivity are important in separationoperations. However, none of these task-specific prop-erties would be important for a solvent being used in asimple application such as a coolant, whereas most of

the general properties would still be relevant. Betweengeneral and task-specific properties, the study of generalproperties is basic and more important. The reason isthat task-specific properties are often derived propertiesthat cannot be studied without knowing the generalproperties first. In addition, similarity between thecurrent solvent and the substitute solvents in terms oftask-specific properties alone may not be enough forachieving a successful design of a substitute solvent. Itis, therefore, important to address the substitute solventdesign problem in terms of general properties first andthen add enough task-specific properties to fully coverthe intended application.

Single Property Match or Multiple PropertyMatch. There are no two species or mixtures that arealike in every way. Some differences in propertiesalways exist between any two substances or mixtures.So, in the design of substitute solvents, the substitutescan only have values of specified properties close tothose of the current solvents or formulations. The term“match” is then used to represent the property closenessrequired for the successful design of substitute solvents.For any solvent, a single physical property reflects onlyone aspect of its behavior, but, in many practical solventapplications, it is the solvent behavior as a whole ratherthan any one aspect that is important. Therefore, itshould be the match of multiple physical propertiesrather than the match of one single physical propertythat needs to be used to design substitute solvents. Twopossible exceptions are substitutions for very specificapplications such as some paint formulations or withina closely related family of solvents. In these cases onemay be able to use a single property such as thesolubility parameter to find reasonably successful sub-stitutes. However, the substitute solvent found withonly one property matched will very likely not performwell outside a limited range of conditions and cannotbe considered a true substitute. One last point to noteis that, in general, mixture properties always need tobe considered in the design of substitute solvents. Evenwhen a single solvent is to be replaced with anothersingle solvent, the most important behavior is oftenrelated to the interaction of the solvent with solutes,and this interaction is a mixture property. This inter-action gives rise to mixture nonidealities on which allseparation processes depend, it determines the diffu-sivity of solutes, it changes the rate of chemical reac-tions, etc., and it cannot be neglected.

Equilibrium and Dynamic Behavior and Per-formance Requirement. The effectiveness of a sol-vent is dependent on its comprehensive behavior. Thereare no general rules about what and how the propertiesshould be matched in the design of substitute solvents.Usually, better results can be expected if more proper-ties are matched and less differences, i.e., lower toler-ances, can be allowed between the properties of theoriginal and the substitute solvent. But in any substi-tute solvent design for any application, it is impossibleand unnecessary to match all properties and to use tooa small property difference. To find the “necessary”physical properties for the specific application, therelationship between solvent behavior and solventphysical properties should be analyzed carefully.

In the design of substitute solvents, the solventbehavior that needs to be matched includes the equi-librium and the dynamic behavior and the performancerequirements. Solvent equilibrium behavior is its be-

Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3269

havior in the equilibrium state and can be representedby solvent equilibrium properties. Solvent dynamicbehavior is its behavior in nonequilibrium states andcan be represented by nonequilibrium or transportproperties. Many of the solvent equilibrium propertiesare directly measurable, such as the vapor pressure andthe boiling point. Some of the solvent equilibriumproperties such as heat capacity and solubility param-eters are derived from expressions by using othermeasurable quantities. Solvent transport properties aresolvent nonequilibrium properties that represent thedeparture from equilibrium. Solvent transport proper-ties are not directly measured but are derived frommeasurable flux and gradient quantities.

In addition to equilibrium and dynamic behavior,solvent performance is also a major concern in thedesign of substitute solvents. The properties represent-ing the performance requirement are usually directlymeasurable but may not always be physical properties,such as the flash point and flammability limits. Thesemeasures of safety performance requirements shouldalways be considered for any substitute solvent designand any application.

Generic Equations for All Solvents. If is veryoften that property data for specified solvents, especiallyfor solvent mixtures, are not available. For equilibriumproperties, thermodynamics is a useful tool which doesnot depend on individual species but can relate un-known property data to other known property data. Fortransport properties, transport equations are a usefultool which do not depend on the individual species butcan reduce the experimental or theoretical efforts byassuming simple proportional relationships between thefluxes and their driving forces. The method used bytransport equations is the phenomenological approach,which is based on experimental observation rather thanany underlying assumptions about the molecular inter-actions in the system.

The viscosity µ, the thermal conductivity k, and thediffusion coefficient DAB are defined as measurableproperties which are just the proportionality factors inthe following three transport equations which representthe three known modes of transport in their simplestform.

These equations are Newton’s law for momentumtransport, Fourier’s law for energy transport, and Fick’slaw for mass transport, respectively. Starting withthese simple expressions plus momentum, energy, andmass balances, one can derive general transport equa-tions that can in principle represent all possible usesor applications of solvents. The difference between oneapplication and another depends on the initial andboundary conditions and other assumptions, such asisothermal conditions that are imposed on the equa-tions. There is elaborate literature (Bird et al., 1960)in this area. What is important here is that, in thesethree simple equations as well as in the more general

transport expressions, the fluxes and driving forces donot depend on individual components present; i.e., theform of these equations is independent of the particularchemical components present. The only place where theidentity of the components present appears in the threesimple expressions above is in the proportionality fac-tors µ, k, and DAB. For the more general expressions,other properties such as density, which are also char-acteristic properties of the individual components ad-ditionally, appear. Therefore, the most general way ofmatching the transport behavior of a currently usedsolvent to that of a proposed substitute solvent is tomatch the solvent properties µ, k, DAB, density, etc.Matching solvents at this level is general and indepen-dent of the applications where the solvents might beused. This is equivalent to mapping the behavior of onesolvent to that of another in a space where the coordi-nates are the solvent properties. As will be illustratedbelow, this type of reasoning is also applicable toequilibrium and other solvent properties and require-ments.

In addition to all properties mentioned above, proper-ties representing the condition for phase equilibriumshould also be considered in the design of substitutesolvents because all practical uses of solvents mustinvolve phase-contacting operations. In thermodynamicanalysis, the condition for phase equilibrium is that, forany species i, the chemical potentials must be the samein all phases.

The phase equilibrium condition of eq 4 can be alsowritten as fugacity equivalent expressions that are ofteneasier to use.

Because solvents are normally used in the liquidstate, the fugacity-composition relationship for liquidshas special significance for substitute solvent design.The fugacity of a component i in a liquid solution is mostconveniently related to the mole fraction xi by thefollowing expression, whose form again does not dependon the individual species.

In eq 6, the activity coefficient γi is a measure ofdeviation from ideality in the liquid phase. Activitycoefficients are solution properties that are dependenton both the components and the compositions. The mostreliable way to obtain the activity coefficients is throughphase equilibrium measurements. But since there aretens of thousands chemicals, even for a specified systemwith the limited number of components, the possiblecompositions are nearly infinite. When trying to designsubstitute solvents, mixtures formed by different com-ponents with different compositions need to be com-pared in order to design potential substitutes, and inmost cases experimental component activity coefficientsare not available. Different excess Gibbs free energymodels are available to correlate known activity coef-ficient data and to predict activity coefficients at otherconditions. Molecular thermodynamics can help us toget a better understanding of the diversity of liquid-state properties by studying the shapes of molecules and

τyx ) -µdvx

dy(1)

qy ) -λ dTdy

(2)

JAy ) -DAB

dCA

dy(3)

µi(1) ) µi

(2) ) ... ) µi(k) i ) 1, 2, ..., n (4)

fi(1) ) fi

(2) ) ... ) fi(k) i ) 1, 2, ..., n (5)

fi(l) ) xiγifi° i ) 1, 2, ..., n (6)

3270 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998

the forces that act between them. One proposed methodis to use the structural group contribution approach thatassumes that each physical property is contributed bya group of atoms within the molecules. This approachis especially useful for designing substitute solventsbecause no other methods can provide enough data forso many formulations to be compared and studied. TheUNIFAC method (Fredenslund et al., 1975) and theASOG model (Wilson and Deal, 1962; Derr and Deal,1969) are two significant development works in thisfield. With the appearance of more advanced comput-ers, activity coefficient prediction by using the structuregroup contribution approach has found wider use.

Physical Properties

On the basis of the above analysis, the essential workof substitute solvent design is that of studying andmatching solvent behavior. Physical properties describesolvent behavior, and, therefore, the design of substitutesolvents has to be based on physical properties amongother considerations. Physical properties used in sol-vent substitution include equilibrium properties, dy-namic properties, performance properties, and otherproperties. Each of these properties plays its own rolein the design of substitute solvents.

Equilibrium Properties

Density. Density is a quantity widely employed toidentify substances. Many relations depicting the be-havior of matter require a density value. From amolecular point of view, density is due to the cohesiveforces that hold the molecules of a liquid together andthe volume occupied by the molecules. The grammolecular weight of a liquid is characteristic of eachsubstance and depends on the volumes of the constitu-ent atoms. So a liquid under a given set of conditionsof temperature and pressure, but otherwise free fromexternal forces, has a certain characteristic density.

The data on liquid density for single chemicals canbe found either from solvent data banks or from estima-tion methods. The liquid density of a substance can bederived from its molecular mass and liquid molarvolume. For most liquids, the space allotted to an atomin a molecule is essentially constant regardless of thecompound of which it is a part. The sum of the atomicvolumes yields a molar volume value which agreesreasonably well with that obtained from the measure-ments. The rule is especially applicable to organiccompounds. So if the atomic volume values are known,the molar volume of a liquid can be approximated bythe sum of atomic volumes, and the liquid density canbe estimated by calculating the ratio of molecular weightand molar volume.

Density is also an important property to be matchedin designing substitute solvents. The reason is thatmatching density is necessary to avoid changes incapacity and/or transport power in the process that usesthe current solvents; e.g., the power required to pumpa liquid depends on its density. Also when solvents areused for an extraction operation, a density differenceof saturated liquid phases is necessary for both thestagewise and the continuous-contact equipment opera-tions. Very often in estimating the densities of organicsolvent mixtures, neglecting the liquid volume changesof mixing will not bring significant errors. So thedensity of a mixture can be calculated from its compo-

nent densities as

where mi /∑mj is the weight fraction of component i.Vapor Pressure. The vapor pressure of a liquid is

the pressure exerted by its vapor at equilibrium. Thevapor pressure of a liquid is dependent on intermolecu-lar forces. The ease or difficulty with which a moleculecan leave the liquid phase is dependent on the strengthof attraction to other molecules. When intermolecularforces are strong, we can expect the vapor pressure tobe low. As the temperature increases, the kineticenergy of molecular motion becomes greater, and thevapor pressure increases.

For a single-component liquid, the vapor pressure isa function only of the temperature. There are a numberof relations (Reid et al., 1987) for vapor pressure suchas the Antoine equation below which has been widelyused to correlate the vapor pressure and temperaturefor liquid pure substance.

For a liquid consisting of more than one component,the vapor pressure is a function of composition as wellas temperature. For most solvent applications, we canassume the vapor phases to be ideal gases withoutincurring significant errors, and the mixture vaporpressure can be calculated from

Vapor pressure is a very important property thatshould be considered in designing substitute solvents.One reason is that the solvents with higher vaporpressure evaporate more easily, and, in some applica-tions, a higher vapor pressure is desired. For example,a higher vapor pressure will reduce the drying time inprinting or cleaning processes. In some other applica-tions a lower vapor pressure may be required. Forexample, health and environmental regulations maymandate the reduction of emissions from volatile organiccompounds. Lastly, when solvents are used for gasabsorption, the lower pressure will result in less loss ofsolvents saturated with the absorbed gas.

Vapor pressure is a kind of measurement for theescaping tendency for both pure substances and mix-tures. For mixtures, the component relative escapingtendency also needs to be considered in designingsubstitute solvents. For example, the relative volatilityis an important quantity used in distillation to representthe degree of difficulty in separating two substances.When ideal gas is assumed for the vapor phase of puresubstances, the relative volatility of a component 1 anda component 2 is defined by

where P1s/P2

s is the ratio of the vapor pressure ratio of

dmix )

∑i

mi

∑i

mi/di

)1

∑i

(mi/di∑j

mj)(7)

ln P ) A + BT + C

(8)

Pmix ) ∑i

xiγi(x,T) Pisat.(T) (9)

R12 )y1/x1

y2/x2)

γ1P1s

γ2P2s

(10)


component 1 to component 2 in the mixture. R12 canbe regarded as the component vapor pressure ratiocorrected by the activity coefficient ratio γ1/γ2 fornonideal behavior in the mixture. So in addition tomatching the total vapor pressure, the corrected vaporpressure ratio may also be considered in designingsubstitute solvents when relative volatility is important.

Boiling Temperature. The vapor pressure of a pureliquid substance is dependent on temperature. Theboiling point of a substance is that temperature at whichits vapor pressure is equal to the external pressure. Theboiling point of a substance represents the uppertemperature for most experimental investigations of theliquid state. At the boiling temperature, the thermalenergy of the molecules is great enough to overcome thecohesive forces that hold them in the liquid, and theliquid-phase molecules continuously escape into thevapor phase until the vapor pressure is equal to theexternal pressure. For pure substances, there are anumber of available methods for estimating the normalboiling temperature, that is, the boiling point when theexternal pressure is 1 atm. Generally, the boiling pointincreases with increasing molecular mass owing to theincreased London dispersion forces. For organic com-pounds, a branch-chain isomer usually has a lowerboiling point than a straight-chain isomer owing to thereduced molecular surface area and the weaker inter-molecular forces.

For a pure liquid substance under a given externalpressure, there is usually only one temperature at whichits vapor pressure is equal to the external pressure. Soa pure substance is boiled at a point in temperature.For solutions, except for azeotropic mixtures, the vapor-phase concentration and the liquid-phase concentrationare different and continuously change in the boilingprocess. A nonazeotropic solution can achieve equalityof vapor pressure and external pressure over a temper-ature range rather than only at one temperature. Theboiling process of a nonazeotropic solution begins at itsbubble point and ends at its dew point. In a puresubstance, its boiling point is both its bubble point andits dew point. In the design of substitute solvents, thesolution bubble point should be treated like the puresubstance boiling point because of two reasons. Onereason is that the bubble point is the beginning boilingtemperature and having gas bubbles inside a liquidsolvent is generally undesirable. Another reason is thatabove the bubble point the liquid-phase concentrationand the solvent properties are different from that beforeboiling. In substitute solvent design and in manyapplications, the “bubble point” temperature Tb can becalculated through

Except for a small number of applications such asvapor degreasing, most solvents are used well below theboiling point of pure substances or the bubble point ofmixtures. A match on the boiling point or bubble pointenables the substitutes to work in the same conditionsas current solvents without boiling; i.e., it ensures thatthe substitute solvents will remain liquid under theoperating conditions for the particular application. Forsolvents used for vapor degreasing, it is the solution dewpoint rather than the bubble point that should bematched for selecting substitutes.

Surface Tension. Many solvent applications involveliquid- and gas-phase contacting. The boundary layerbetween a liquid phase and a gas phase may beconsidered a third phase with properties different fromthose of the liquid and gas. The surface tension, whichis defined as the energy required to increase the surfacearea of a liquid by a unit amount, is the most commonway to represent the tension on the surface layer.Intermolecular forces of attraction are responsible forthe surface tension of liquids. A molecule at the surfaceof a liquid has a net attraction by other moleculestoward the interior of the liquid. So the surfacemolecules experience more attraction from the bulkliquid than from the bulk gas. As a result, there is atendency for the surface area of a liquid to be reducedas much as possible. The surface tension of liquidsdecreases as the temperature is increased. For a pureliquid, the surface tension becomes zero at the criticalpoint because vapor and liquid phases become indistin-guishable.

For pure liquid, unknown surface tension values areusually estimated by using one of two kinds of methods.One is the well-known MacLeod-Sugden (MacLeod,1923) correlation, and another uses different corre-sponding state correlations. In the MacLeod-Sugdencorrelation, a proportional relation is assumed betweenthe one-fourth power of the surface tension and thedensity difference of the liquid and gas.

In this expression, the parachor [P] is the tempera-ture-independent factor of eq 12. One advantage ofusing the MacLeod-Sugden correlation is that for apure liquid the parachor value can be estimated frommolecular structure information when experimentalvalues are not available. The MacLeod-Sugden cor-relation can also be extended as follows to estimatesurface tension of nonaqueous mixtures.

Neglecting the vapor density and composition termin eq 13, the following equation can be used to estimatesurface tension of nonaqueous mixtures at low pressure.

In Eqs 13 and 14, the parachor is a dimensionalquantity, and its value is dependent on not only thevalues but also the units of surface tension and density.The parachor data available from the literature (Reid,et al., 1987) or the structure or group contribution data(Reid, et al., 1987) used for calculating the parachorshould be used carefully considering units consistence.

In substitute solvent design, the reasons for matchingof the surface tension are many. For example, incleaning operations it is used to ensure that thesubstitute solvent will have penetration ability on aporous surface that is similar to that of the solvent thatis being replaced. In solvent extraction, the surfacetension affects settling time and power consumption.The movement of a liquid through a porous medium isalso affected by surface tension; i.e., the higher thesurface tension the more pressure that is required topush a liquid through a porous medium.

Pmix ) ∑i

xiγi(x,Tb) Pisat.(Tb) (11)

σ1/4 ) [P](Fl - Fv) (12)

σmix1/4 ) ∑

i

[Pi](Flmixxi - Fvmixyi) (13)

σmix1/4 ) ∑

i

[Pi]Flmixxi (14)


Limiting Activity Coefficients. Matching the physi-cal properties above may not always get substitutes thatperform as we expected. For example, if one wants tofind substitutes for benzene at 25 °C and matchesmolecular mass, molar volume, boiling temperature,vapor pressure, surface tension, viscosity, thermalconductivity, and flash point to screen candidate sub-stitute solvents, on the basis of the data in Table 1 itwould seem that cyclohexene is better than toluene asa substitute for benzene. The reason is that theproperty values of cyclohexene are closer to the propertyvalues of benzene than those of toluene. But actually,both benzene and toluene are aromatic compounds whilecyclohexene is an alicyclic hydrocarbon compound. Thereason this is important is that, in many solventapplications, solvents act through direct contact withsolutes that are dissolved in the solvents.

Thus, in addition to the physical properties of thesolvents in Table 1, those properties that can representinteractions between molecules of solvents and mol-ecules of the solutes should be also considered indesigning successful substitute solvents.

In many solvent applications, the concentrations ofthe solutes are small, not known, or varying. A practicalway to study the interaction between solvent moleculesand the solute molecules is to use the infinite dilutionactivity coefficients of solutes in the solvents. These canbe estimated for most chemicals using any number ofcorrelations (Reid, et al., 1987) including group contri-bution methods such as UNIFAC (Fredenslund et al.,1975). The infinite dilution activity coefficients, whichare also called limiting activity coefficients, are definedby

The infinite dilution activity coefficients can be usedto characterize the interactions between a single mol-ecule of solute and the molecules of solvents withoutthe interference of interactions among the molecules ofsolute. Most of the available group information usedfor calculating the solution activity coefficients areregressed from vapor-liquid equilibrium data at finiteconcentration rather than at the infinite dilution, andthis leads to some inaccuracy when infinite dilutionactivity coefficients are calculated by extrapolation fromfinite concentrations. But in designing substitute sol-vents, it is the difference of property values estimatedthrough the same method rather than the accuracy ofproperty values themselves that is used for selecting thesubstitutes. Additionally, it should be noted that anymethod for designing substitute solvents is really ascreening and preliminary design method that requiressome validation before the results are put into practice.This kind of application reduces the requirement foraccuracy of property estimation. If the natures of the

solutes are known, the infinite dilution activity coef-ficients of these substances should certainly be used.But it is very often that the solutes are not exactlyknown. For example, in some cleaning processes thesubstances cleaned by the solvents may not be allknown.

The easiest way to incorporate infinite dilution activ-ity coefficients in the substitute solvent design process,not knowing what kinds of solutes would eventually beused with the solvent, is to consider the infinite dilutionactivity coefficient of representative solutes from dif-ferent chemical families. One can then compare theinfinite dilution activity coefficients for the originalsolvent to the proposed substitute. If these match, onecan then generally assert that the molecular interac-tions between the representative solutes and the twosolvents are generally similar. This means that pro-posed substitute solvent will likely dissolve and havesimilar effects on solutes as the original solvent did. Asa first step, six representative solutes were chosensethanol, diethyl ether, acetone, water, octane, andbenzenesto represent six chemical familiessalcohols,ethers, ketones, water, normal hydrocarbons, and aro-matics. The infinite dilution activity coefficients forthese six representative solutes in benzene, cyclohexene,and toluene are shown in Table 2. However, there isno dogma to be associated with this particular choiceof chemicals, and anyone could choose any other set ofchemicals that are deemed appropriate.

The infinite dilution activity coefficients were calcu-lated using the UNIFAC group contribution method(Fredenslund et al., 1975) with a recent UNIFACLibrary (Magnussen and Pretel, 1997). It should alsobe pointed out that there is nothing prescriptive aboutthe use of a UNIFAC method in estimating the infinitedilution activity coefficients. Rather, the method waschosen for its wide applicability. When the infinitedilution activity coefficients in Table 2 are examined,even if one were to assume a large uncertainty of say20% in the calculation, a picture which is ratherdifferent from that inferred by looking at the physicalproperties starts to emerge. Even when large uncer-tainties are present in the estimation of the infinitedilution activity coefficients, it should be noted thatthese are only one of the criteria considered in thedesign of a substitute solvent, and it is, therefore,unlikely that one bad estimate for the activity coef-ficients or even a few bad estimates would completelyskew the substitute solvent design process. On theother hand, the case has been made here that com-pletely neglecting the infinite dilution activity coef-ficients can, in fact, lead to poor solvent design. Pleasenote that while the physical properties of benzene werea bit closer to those of cyclohexene than those of toluene,it is clear that the infinite dilution activity coefficientsand, therefore, the solute-solvent molecular interac-tions of benzene are much closer to those of toluene that

Table 1. Physical Properties of Benzene, Cyclohexene,and Toluene

benzene cyclohexene toluene

molecular mass (kg/kmol) 78.114 82.145 92.141molar vol (m3/kmol) 0.0895 0.1019 0.1066boiling temp (K) 353.24 356.12 383.78vapor pressure (kPa) 12.659 11.823 3.793surface tension (N/m) 0.0282 0.0261 0.0279viscosity ×104 ((N‚s)/m2) 6.009 6.180 5.548thermal conductivity (W/(m‚K)) 0.138 0.130 0.133flash point (K) 262.04 266.48 277.59

γi∞ ) lim

xif0γi (15)

Table 2. Infinite Dilution Activity Coefficients ofRepresentative Solutes in Benzene, Cyclohexene, andToluene

benzene cyclohexene toluene

ethanol 10.2 26.6 11.3diethyl ether 0.97 1.2 1.1acetone 1.5 4.7 1.9water 1770 369 2700octane 2.2 0.95 2.5benzene N/A 1.3 1.0


those of cyclohexene. Thus, as one might reasonablyexpect, toluene or, perhaps, a mixture of toluene andcyclohexene may be a far better substitute for benzenethan cyclohexene alone. The activity coefficient ofbenzene in benzene is, of course, meaningless in thissituation.

Dynamic Properties

Many solvent applications involve irreversible ortransport processes. The solvent behavior in irrevers-ible processes can be described by the dynamic proper-ties of solvents along with the corresponding transportequations. Because most engineering work using fluidsconcerns macroscopic or bulk behavior rather thanmicroscopic or molecular behavior, the transport equa-tions are macroscopic expressions of conservation lawsrelating the pressure tensor, heat flow, and diffusionto the transport of momentum, energy, and mass.Dynamic properties are nonequilibrium properties ona macroscopic scale. Both the equilibrium and thenonequilibrium properties of solvents reflect the effectof solvent molecular motion and interaction. Nonequi-librium properties, like equilibrium properties, arefunctions of state and may be used to define the stateof substances. For gases, the transport property valuesmay be calculated on a molecular basis from kinetictheory. The key parameter is the average distancetraveled by molecules between collisions, i.e., the meanfree path. But the concept of distinct binary collisionsused by the kinetic theory of gases is inappropriate toliquids because the molecules in liquids are very closeto each other, resulting in frequent many body collisions.

Viscosity. Viscosity is a particularly importantconsideration in the design of substitute solvents. Forexample, in many solvent applications low viscosity ispreferred for ease in handling; i.e., the lower theviscosity the lower the power required to pump liquids,the faster the settling time, the faster the diffusivetransport, etc. In absorption, low viscosity is preferredfor rapid absorption rate, improved flooding character-istics in absorption towers, low-pressure drops onpumping, and good heat-transfer characteristics. How-ever, in some applications such as adhesives, a highviscosity may be preferable.

Viscosity is the physical property that characterizesthe flow resistance of fluids. Viscosity forces appearonly when adjacent parts of a fluid move with differentvelocities, and viscosity is a measure of the internalfriction of the fluid. If the friction between layers of afluid is small, an applied shearing force will result in alarge velocity gradient. As the viscosity increases, eachfluid layer exerts a larger frictional drag on adjacentlayers and the velocity gradient decreases. The viscosityof a medium is defined as the shear stress per unit areadivided by the velocity gradient at the same point inthe medium. The viscosity of a liquid can be consideredto be due to the restraint caused by intermolecularforces. As a liquid heats, the molecules become moremobile; this results in less restraint from intermolecularforces, so the viscosity decreases.

Because the molecular theory of liquids for viscosityis much less advanced, the major source of knowledgeconcerning liquid viscosities is experiment, and liquidviscosities cannot generally be estimated from otherphysical properties. As concluded by Reid, Prausnitz,and Poling (Reid et al., 1987), at high reduced temper-atures, pure liquid viscosities are usually correlated

with some variation of the law of corresponding states,while, at lower temperatures, most methods are empiri-cal and involve a group contribution approach. On thebasis of observations, the viscosity of most pure liquidsdecreases exponentially with temperature increases inlow-temperature ranges. The viscosity of liquids in-creases with pressure, but the effect is generally insig-nificant at pressures below 40 atm.

Liquid mixture viscosities, as with other fluid proper-ties, also depend on temperature, composition, andpressure. Current correlations for liquid mixture vis-cosities are essentially mixing rules relating purecomponent viscosities to composition and require thevalue of interaction parameters specific for each binarypair in the mixture. Currently available data formixtures are generally inadequate for the needs ofdesigning substitute solvents. To achieve better predic-tion of liquid mixture viscosities, the only practical anduseful method is the UNIFAC method. The modeldeveloped by Cao, Knudsen, Fredenslund, and Rasmus-sen (Cao et al., 1993) for predicting liquid mixtureviscosities can directly use the available UNIFAC-VLEparameters. They reported that the average deviationbetween predicted values and experimental results for386 liquid mixtures is within 5%.

Thermal Conductivity. Thermal conductivity is aproperty that arises in energy transfer problems due toheat conduction. It is also very important for the designof substitute solvents. For example, a high thermalconductivity is desirable in applications where rapidheat transfer through the solvent is important such asheat exchangers. On the other hand, if the solvent ispart of an insulator, then a low thermal conductivity isdesirable. A high thermal conductivity is one of theconsiderations in the heating or cooling of a fluid underpoor mixing conditions such a high viscosities or qui-escent conditions.

The thermal conductivity is proportionally related tothe rate at which heat is transported from a region ofhigher temperature to a region of lower temperature.The importance of thermal conductivity in energytransport parallels that of viscosity in momentumtransport. Like viscosity, thermal conductivity is aproperty of the conducting medium. Even though thetransport equations using viscosity and the transportequations using thermal conductivity are in the sameform of phenomenological equations, because energy isa scalar while momentum is a vector, momentumtransport and energy transport are not mathematicallyanalogous except in certain geometrically simple situ-ations.

The mechanism for the conduction of heat is due tomolecular interactions. In a liquid, cohesive forcesprevent molecules from traveling quickly and freelyfrom one position to another. Thus, the extra energyfrom a warmer region is transported by potential energyinterchanges from one molecule to close neighbor mol-ecules, thus transferring thermal energy to the coolerregion. The energy is transferred rapidly through themolecules themselves since the molecules are very closetogether in the liquid state.

The thermal conductivity of liquids varies slightlywith temperature but is relatively independent of pres-sure. The experimental measurement of liquid thermalconductivity requires that the liquid be free of convec-tion. Since the molecular behavior of the liquid phaseis not very clearly understood, only approximate tech-


niques rather than universally accepted mathematicalmodels are available for estimating liquid thermalconductivities.

The thermal conductivities of most mixtures of or-ganic liquids are usually less than those predicted byeither a mole (or weight) fraction average, although thedeviations are often small. There are correlations forcalculating the thermal conductivities of liquid mix-tures. For most of these correlations, either they areonly valid for binary mixtures or the characteristicinteraction parameters used by the correlations needto be experimentally determined. For substitute solventdesign and for many applications, the interpolationmethod of Li (Li, 1976) has been used by the authors.This method gives the thermal conductivity of a mixtureaccording to

where

and where the interaction parameter λij is calculatedby interpolation using eq 20 below and λi and λj, whichare the thermal conductivities of pure components i andj.

Diffusivity. Molecular diffusion is the directionalmovement of molecules of an individual componentthrough a mixture under the influence of gradient inthe chemical potential of the diffusing species. Exceptin highly nonideal solutions, a gradient in the chemicalpotential often correlates with a gradient in the con-centration of the diffusing species. Molecular diffusionis due to the movement of individual molecules througha substance by virtue of their thermal energy, and itmay take place even though there is no bulk flow.Under the influence of a concentration gradient for agiven substance in solution, the molecules of thatsubstance will move continuously from its high-concen-tration region to its low-concentration region, causinga mass flux in that substance. The phenomenon ofmolecular diffusion ultimately leads to a completelyuniform concentration of substances throughout a solu-tion that may initially have been nonuniform.

The diffusivity, or diffusion coefficient, of a substanceis a measure of its mobility in solution under theinfluence of a concentration gradient. Mathematically,the diffusivity of a substance in a solution is defined asthe ratio of its flux and its concentration gradient insolution. Diffusivity is different from momentum andenergy transfer properties because the diffusivity of asubstance in solution is a characteristic of this substanceand the other substances in the solution rather thanthe substance alone. Thus, the diffusivity is a systemproperty rather than a substance property. In mul-tiphase systems, we customarily deal with diffusionprocesses in each phase separately, and the diffusivitiesare usually derived within each phase.

The diffusivity is important in nearly all operationscommonly used in the chemical industry, and it is,

therefore, important in the design of substitute solvents.This reflects the fact that the objective of most opera-tions in the chemical industry is that of separating,concentrating, purifying, or transforming chemical com-ponents, and the diffusivity is important to all of theseoperations. For example, the diffusivity is one of theproperties that sets the required residence time inliquid-liquid extraction. In chemical reactions, thediffusivity determines how fast reactants can cometogether and how fast products can move away fromeach other. In diffusion-limited reactions this deter-mines the reaction rate. In crystallization, the diffu-sivity can in many cases determine the rate of crystalformation.

The diffusion of different components in a given phaseusually differs from each other under conditions wheremolecular diffusion prevails. Diffusion in liquids occursby random motion of the molecules, but the averagedistance traveled between collisions is less than themolecular diameter. Liquid diffusivities also depend oncomposition due to the changes in viscosity with com-position and changes in the degree of ideality of thesolution. Neither is the theory of diffusion in liquidsas advanced nor are the experimental data very plenti-ful, particularly for mixtures.

Some empirical correlations for estimating the binaryliquid diffusivity in dilute solutions of nonelectrolyteshave been proposed. Generally, if the infinite dilutionbinary diffusivities of a substance into each componentof a solution is known, these values can then be used toestimate the dilute diffusion of this substance throughthat solution. One widely used correlation is that ofWike-Chang (Wilke and Chang, 1955) given by

Unlike viscosity and thermal conductivity, diffusivityis difficult to use in the design of substitute solvents.The reason is that most available liquid diffusivityestimation methods are only for binary solutions at verydilute concentration or infinite dilution. But in manysolvent applications such as extraction, the solutions ineach liquid phase have many components, and theinfinite dilution diffusion occurs only at the beginningof the diffusion process.

Performance Requirements

In addition to physical properties, there are othersolvent characteristics that are important in the designof substitute solvents. Perhaps, the most relevant ofthese are related flash and flammability. Many sol-vents, especially most organic solvents, are flammableor combustible which is an important safety consider-ation. Flash point and flammability limits are, there-fore, important for the safe storage, handling, and useof solvents.

Flash Point. The flash point of a liquid is the lowestpoint at which the vapor pressure of a liquid willproduce a flammable mixture. If a source of ignition isbrought into this mixture, the liquid will continuouslyproduce vapors to give a flammable or even explosiveatmosphere. The flash point is one of the most impor-tant fire safety characteristics of substances. It is anindicator of the degree of safety of a material. It is alsoused to classify flammable liquids and combustible

λmix ) ∑i∑

j

φiφjλij (16)

φi )xiVi

∑j

xjVj

(17)

λij ) 2(λi-1 + λj

-1)-1 (18)

DAB )AWC(φBMB)1/2T

µVA0.6

(19)


liquids. This property is, therefore, a very importantconsideration in the design of substitute solvents. Forinstance, it would seem prudent that the flash point ofthe substitutes should be no less than that of the currentsolvents.

The flash point of a flammable or combustible liquidis usually experimentally determined and depends onthe type of method used in its determination. Fourcommonly used methods are the Tagliabue (Tag) ClosedCup Tester, the Pensky-Martens Closed Tester, theTagliabue (Tag) Open Cup Tester, and the ClevelandOpen Cup Tester. Open cup flash points representconditions with the liquid in the open air and aregenerally higher than closed cup flash points for thesame liquids. However, closed cup flash point figuresare generally higher than the actual lower temperaturelimit of flammability as tested in a vertical tub utilizingthe principle of upward flame propagation. The flashpoint also varies with pressure and the oxygen contentof the atmosphere.

For pure organic solvents, most practical methods forestimating the flash point are correlations based onavailable boiling point and the number of differentatoms in the molecule (Horvath, 1992). For solventmixtures, the flash point cannot be determined byadding the component fraction weighted average of theflash points of the individual components. There is nocompletely satisfactory method for predicting the flashpoints of mixtures. A computer based method has beenproposed (Walsham, 1973) for estimating the Tag OpenCup flash points of mixtures for oxygenated and hydro-carbon solvents. Similar work has been done forpredicting Seta Flash Closed Tester flash points ofsolvent mixtures (Wu and Finkelman, 1977). In theWalsham method for Tag Open Cup flash points, thepure solvent flash point indexes are defined as aninverse function of the component’s heat of combustionand vapor pressure at its flash point.

Mixture flash points are then computed by trial anderror or some other search method as the temperatureat which the sum of weighted component indexes equals1.0 as shown in the following.

Flammability Limits. The flammability limits arethe extreme concentration limits of a combustible mate-rial in an oxidant through which a flame, once initiated,will continue to propagate at a specified temperatureand pressure over a range of different vapor-air com-positions. The lower flammable limit is the lowestconcentration at which a combustible vapor forms aflammable vapor-air mixture, and the upper flammablelimit is the highest concentration at which a flammablemixture is formed. Below the lower limit, the concen-tration of solvent vapor is too low to form a flammablemixture, and above the upper limit, there is too littlecombustible oxygen to sustain a flame. The flammabil-ity limits are also very important safety considerationsin the design of substitute solvents.

Some methods are available for estimating the flam-mability limits of flammable or combustible pure liquids(Horvath, 1992), but there are no available methods for

mixtures. For practical solvent applications, it is thelower flammability limit rather than the upper flam-mability limit that is the main concern. The reason isthat it is usually better and safer to work in a conditionbelow the lower flammability limit rather than in acondition above the upper flammability limit. In asolvent mixture, each component has its own puresubstance lower flammability limit. A more conserva-tive and practical way is to use the smallest value ofthese lower flammability limits as a criterion in sub-stitute solvent design. This means that in the proposedsubstitute formulations, no component should have itslower flammability limit value below that of the com-ponent which has the smallest lower flammability limitof all components in the current formulation.

Molecular Mass

Some properties such as molecular mass are notdirectly related to solvent behavior, but it is known thata variety of properties and behavior can be correlatedwith molecular mass. They are, therefore, useful fordesigning substitute solvents. The molecular mass ofa compound is the sum of the weight of all atoms in itsmolecule. In the design of substitute solvents, molec-ular mass is used to try to capture any properties orbehavior that are not explicitly represented, i.e., toensure that properties which are not directly consideredby the program are matched between the currently usedsolvent formulation and the proposed substitute solvent.

Thermodynamic Calculations

Phase Stability. When a substitute is designed fora single-phase solvent, it is critical that the substituteconsists of only one liquid phase in the neighborhood ofthe expected operating temperature, pressure, andcomposition for the particular application. There aretwo different ways by which more than one phase canform in this situation: (1) a mixture proposed as asubstitute solvent can exist as two or more liquid or solidphases, and (2) a proposed substitute solvent whethera single component or a mixture can form more thanone liquid or solid phase when mixed with solutes.However, the formation of multiple phases with solutesis more properly in the area of process design ratherthan solvent design. The reason is that one needs toknow the details of the process such as exactly whatsolute, what solvent, what conditions, and whether thephenomena is or is not desirable. For example, pre-cipitate formation is desirable in crystallization but notin extraction. This will, therefore, be discussed belowbut not extensively.

For one component substitute solvents that are notmixed with solutes, it is sufficient that the operatingconditions are below the boiling point and above thefreezing point of the solvent to ensure that it does existas one liquid phase. For one component solvents thatare mixed with solutes, one must treat the system as amixture and consider whether it forms more than oneliquid or solid phase at the typical compositions foundwhen the solvent is mixed with the solutes. For asubstitute solvent that contains two or more componentswith or without solutes, one must treat the entiresystem (solvents and solutes) as a mixture and considerwhether more than one liquid or solid phase can form.

Ii ) 1(PFi)Mi

1.25(20)

∑i

IixiPiγiMv1.25 ) 1.0 (21)


The most general way of addressing these problems isto investigate the phase stability of the mixture, i.e.,the conditions of temperature, pressure, and composi-tion under which the system can exist as a one phaseliquid. In all of the three cases except the first, the mostimportant consideration is the phase stability of theproposed substitute solvent with respect to temperatureand composition since liquids are not very sensitive topressure. This problem is amenable to treatment withseveral methods that will be discussed here in order ofincreasing sophistication. It should be noted that allof these methods could be used to examine phasestability when a solvent is mixed with a solute asalready mentioned.

Solubility Parameter Method. This method aimsto predict the miscibility of a system using only theparameters of its pure components. For moleculeswhose forces of attraction are due primarily to disper-sion, the solubility parameter was defined (Hildebrandand Scott, 1962) as

Hansen and Skaarup (1967) expanded this conceptwith a three-component expression that extends thesolubility parameters of Hildebrand and Scott to polarand hydrogen bonding systems. The expression ofHansen and Skaarup is given by eq 23. The three termsδd, δp, and δh respectively, represent dispersive, polar,and hydrogen bonding forces.

The hypothesis of this method is that a substancewith a high δ value requires more energy for dispersalinto another substance than is gained by mixing it witha substance of low δ so that immiscibility results. Onthe other hand, two substances with similar δ valuesgain sufficient energy on mutual dispersion to permitmixing. On the basis of this analysis, two pure liquidswith similar solubility parameters should be soluble,and two pure liquids with dissimilar solubility param-eters should not be soluble.

For substitute solvent design, there are two difficul-ties in using the solubility parameter method to analyzefor phase stability. The first difficulty is that it is notcertain how close the solubility parameters need to beto achieve miscibility. The second difficulty is that thesolubility parameter method does not use compositionor any other solution information, so it cannot be usedto analyze for phase stability for a given composition ofpartially miscible liquids. The second limitation, un-fortunately, excludes a commonly encountered problemof partial miscibility, although it should be noted thatthe method is simple to use and does cover a number ofother problems.

Stability Function Method. A method that is morerigorous and more complicated than the solubilityparameter approach is the stability function (Bernardet al., 1967). It gives the necessary and sufficientconditions Ψ > 0 for multicomponent phase stabilitywith composition.

The derivation of the stability function is based onthe minimization of the Gibbs free energy which is therigorous criterion for phase equilibrium at a giventemperature and pressure. The stability function iswritten in terms of activity coefficients and mole frac-tions rather than in terms of the more customary secondderivatives of the Gibbs free energy. Thus, any meth-ods, which are used, for calculating activity coefficientscan be used directly and easily for calculating thestability function. There are two difficulties in usingthe stability function method in the design of substitutesolvents. First, because of model or data errors, thevalue of the stability function cannot be very accuratelydetermined so the criterion of Ψ > 0 is not verypractical. Instead, one uses Ψ > ε where ε is a smallpositive number. This also helps to conservativelyensure that stability has been attained. But there areno general methods of determining values of ε fordifferent specific applications and for different modelsfor calculating the activity coefficients. The seconddifficulty in using the stability function method forsubstitute solvent design is that it cannot distinguishbetween stability and metastability, while practicalsolvent applications require solvents in the stable ratherthan the metastable state.

Gibbs’ Tangent Plane Method. Like the stabilityfunction, the derivation of Gibbs’ tangent method alsoinvolves minimizing the Gibbs free energy at the giventemperature and pressure. The basic principle used inthe Gibbs’ tangent plane method is that stabilityrequires that the hyperplane tangent to each point onthe Gibbs free energy hypersurface should at no pointlie above the hypersurface. The Gibbs’ tangent planemethod can find the miscible composition region ratherthan just the phase stable and metastable region for asystem at given conditions of temperature, pressure,and composition. Work using the Gibbs’ tangent planemethod for liquid mixture stability analysis has beenreported (Baker et al., 1982; Michelson et al., 1982). Forsubstitute solvent design, the difficulty in using theGibbs’ tangent method is that, for mixtures with threeor more components, there are no effective ways oflocating trial compositions to test for instability.

Azeotropes

The importance of azeotropes in the design of substi-tute solvents generally arises when the solvent is insome way used in a distillation. Solvents are distilledfor two principal reasons: (1) because distillation is anintegral part of the processes where the solvent is usedand (2) because there is a need to recover and purifyused or spent solvent for recycle and reuse. Spentsolvent is normally recycled and reused for cost savingand environmental reasons.

An azeotrope exists when the vapor and liquid com-positions of a mixture at equilibrium are the same. This

δ ) (∆uv

ν )1/2

(22)

δt2 ) δd

2 + δp2 + δh

2 (23)

Ψ )|1 + x2

∂ ln γ2

∂x2x3

∂ ln γ2

∂x3... xm

∂ ln γ2

∂xm

x2

∂ ln γ3

∂x21 + x3

∂ ln γ3

∂x3... xm

∂ ln γ3

∂xm

l l l l

x2

∂ ln γm

∂x2x3

∂ ln γm

∂x3... 1 + xm

∂ ln γm

∂xm

|(24)


can be represented by

where it has been assumed that the gas phase can betreated as an ideal gas and that the liquid phase is notaffected by pressure. The right-hand side of eq 25 canbe used to estimate the composition at which azeotropeswould form in a mixture; i.e., if a composition can befound that satisfies eq 25 at a given pressure andtemperature, then the mixture forms an azeotrope atthat composition.

There are four possible ways to replace one solventwith another solvent: (1) replacing a pure componentwith another pure component, (2) replacing a purecomponent with a mixture, (3) replacing a mixture withanother mixture, and (4) replacing a mixture with apure component. The last possibility is admittedlyunlikely, but it needs to be included for generality. Thedistillation of a solvent consisting of one major compo-nent and very minor amounts of impurities is relativelysimple and will not be further discussed. Therefore, theproblem with azeotropes can arise only with the secondand third cases, i.e., when replacing a pure componentwith a mixture and when replacing a mixture withanother mixture. The problem of azeotropes can alsoarise when the solvent forms an azeotrope with thesolutes present.

In general, one cannot replace a solvent that has noazeotrope with one that does for use in distillationoperations. In addition, one cannot in general replacea solvent that forms no azeotrope with the solutespresent with one that does for use in distillation.However, there are some exceptions and some ways ofdealing with the problem. For example, if an azeotropeexists but the operating composition of the distillationoperation is not near the azeotropic composition, thenthe presence of the azeotrope may not be a problem.Also, it may be possible to break-up the azeotrope byadding certain components such as salts. Nonetheless,if the solvent needs to be purified by distillation forrecycle and reuse, the presence of an azeotrope wouldbe a very serious problem. In this last case, and in allthe others, the problem can be addressed by simplydesigning a substitute solvent that does form azeo-tropes. One could, for example, look for mixtures thatmeet all the necessary criteria and in addition have nocompositions at operation temperatures and pressuresfor which eq 25 is satisfied.

Chemical Reactivity

When different chemicals are mixed or when newchemicals are brought into contact with the materialsin an existing facility, there is reasonable concern thatunexpected chemical reactions may occur. Unfortu-nately, there are no well-established methods for testingfor chemical reactivity apriori. Fortunately, the chemi-cals that are generally used as solvents are usuallychosen because they are relatively inert, and, as a result,one does not find too many solvent mixtures that formviolent or dangerous chemical reactions. Other issuessuch as corrosion are more likely to be the mainproblems. One would, therefore, highly recommend thatany new substitute solvent or solvent mixture be care-fully tested under realistic operating conditions before

it is used. Nonetheless, one can outline at least threerequirements that need to be considered in the designof substitute solvents. These are as follows:

(1) The substitute solvents should be chemicallystable. For example, the substitute solvents should nottake part in exothermic reactions or react on storage togive dangerous reaction products, e.g., peroxides.

(2) The substitute solvents should be chemically inerttoward the other components of the system, includingother solvents, except for those being used as reactants.

(3) The substitute solvents should be inert toward thecommon materials of the contacted parts or construc-tion. For example, the substitutes should not be cor-rosive to the equipment used by current solvents.

Conclusions

There is a growing need to design substitutes forsolvents that are otherwise effective except that theypose serious health or environmental concerns or,perhaps, simply do not meet the requirements of newtechnologies. The goal in both cases is generally thatof designing solvents that perform their technologicalfunction at least as well as the solvents that they arereplacing, but with an improvement in some particularproperty or properties or without some undesirableproperties present.

There are essentially two general approaches fordesigning substitute solvents: (1) experience and ex-perimentation and (2) molecular thermodynamics aidedby a computer. The first approach is limited by thepractitioner’s knowledge and the enormous amounts oftime required to experimentally explore solvent behav-ior. The issue of the practitioner’s knowledge reflectsthe fact that individuals typically focus on a few fluidproperties on the basis of personal experience, e.g.,solubility parameters, which may not be enough infor-mation to avoid choosing a less than optimal substitutesolvent. The question of time can become a very seriousobstacle if mixtures are considered, and if one needs toexperimentally explore their behavior with compositionacross many different fluid properties. The approachof molecular thermodynamics aided by a computer,however, can literally consider many thousands ofpossible chemicals and mixtures of chemicals and asufficiently large set of fluid properties and fluid be-havior very quickly. This paper, therefore, outlines thefluid and physical properties and behavior that mustbe considered in the design of effective substitutesolvents using computer aided molecular thermodynam-ics. These include equilibrium fluid properties (density,boiling point, vapor or solution pressure, surface ten-sion), limiting activity coefficients, dynamic fluid prop-erties (viscosity, thermal conductivity, and diffusivity),performance requirements (flash point and flammabilitylimits), other properties (molecular mass), and fluidbehavior (phase stability, azeotropes, and chemicalreactivity). The paper reviews a number of methodsfrom molecular thermodynamics for estimating theseproperties and the methods from classical thermody-namics that can be used to predict fluid behavior.

For solvents that are used in relatively simple ap-plications such as coolants or hydraulic fluids, thelimiting activity coefficients may well be irrelevant.However, for the typical application in the chemicalindustry the limiting activity coefficients are likely tobe the most important properties. The reason is thatthe limiting activity coefficients determine which solutes

yi

xi) 1 )

γi(x,T) Pisat.(T)

Pi ) 1, 2, ..., n (25)


the solvent will dissolve, what effect it will have onchemical reactions, and what other liquid chemicals itwill mix with. These are, of course, extreme cases, butthey do point out that different properties or behaviorsneed to be emphasized for different applications. Un-fortunately, solvent behavior can be quite subtle, andit is not always clear which properties or fluid behaviorsare most important for a given application; i.e., relyingon intuition does not always yield satisfactory results.It is, thus, important to consider a comprehensive setof properties and solvent behaviors as has been outlinedhere.

Acknowledgment

This work was performed while Renhong Zhao wasin residence at the National Risk Management ResearchLaboratory under a Research Associateship through theNational Research Council. The authors acknowledgehelpful suggestions from Professor J. M. Prausnitz fromthe Department of Chemical Engineering at the Uni-versity of California at Berkeley.

Nomenclature

A ) constant in vapor pressure equation, dimensionlessAWC ) constant in the Wilke-Chang equation, units varyB ) constant in vapor pressure equation, °C or KC ) constant in vapor pressure equation, °C or KCA ) concentration of component A, mol m-3

DAB ) diffusivity of component A in a mixture withcomponent B, m2 s-1

di ) mass density of component i, kg m-3

dmix ) mass density of solvent mixture, kg m-3

fi ° ) fugacity of pure species i in standard state, Pafi

(l) ) fugacity of component i in liquid phase, Pafi

(n) ) fugacity of component i in the nth phase, PaIi ) flashing index, Pa-1 kg-1.25 molJAy ) diffusion flux of component A through the reference

plane y, mol m-2 s-1

MA ) molar mass of solvent A, kg mol-1

mi ) mass of component i, kgMi ) molecular mass of component i, kg mol-1

Mv ) calculated mean vapor molecular mass at the testtemperature, kg mol-1

P ) pressure, Pa[P] ) parachor, (N m-1)1/4 m3 mol-1

Pisat or Pi

s ) vapor pressure of component i, Pa[Pi] ) parachor of component i, (N m-1)1/4 m3 mol-1

Pmix ) vapor pressure of liquid mixture, PaPFi ) vapor pressure of component i at its flash point, Paqy ) thermal flux vector in the y direction, J m-2 s-1

T ) temperature, KTb ) bubble point of mixture, K∆uv) energy of complete vaporization, J mol-1

VA ) molar volume of solute A, m3 mol-1

Vi ) molar volume of species i, m3 mol-1

vx ) x component of velocity vector, m s-1

xi ) mole fraction of component i in liquid phase, (mol of i)mol-1

x ) vector of component mole fractions in liquid phase, molmol-1

y ) spatial coordinate, myi ) mole fraction of component i in vapor phase, (mol of i)

mol-1

Greek Letters

R12 ) relative volatility of component 1 and component 2,dimensionless

γi ) activity coefficient of component i in a mixture,dimensionless

γi∞ ) activity coefficient of component i at infinite dilution,dimensionless

δ ) solubility parameter, (J m-3)1/2

δd ) solubility parameter representing measure of disper-sive forces, (J m-3)1/2

δh ) solubility parameter representing measure of hydro-gen bonding forces, (J m-3)1/2

δp ) solubility parameter representing measure of polarforces, (J m-3)1/2

δ t ) total solubility parameter, (J m-3)1/2

ε ) a small positive number, dimensionlessλ ) thermal conductivity, J K-1 m-1 s-1

λi ) thermal conductivity of species i, J K-1 m-1 s-1

λij ) characteristic parameter for the thermal conductivityexpressing the interactions between component i andcomponent j, J K-1 m-1 s-1

λmix ) thermal conductivity of liquid mixture, J K-1 m-1

s-1

µ ) viscosity, kg m-1 s-1

µi(k) ) chemical potential of component i in the kth phase,J mol-1

ν ) molar volume of the pure liquid, m3 mol-1

Fl ) molar liquid density, mol m-3

Flmix ) liquid mixture molar density, mol m-3

Fv ) vapor molar density, mol m-3

Fvmix ) vapor mixture molar density, mole m-3

σ ) surface tension, N m-1

σmix ) surface tension of mixture, N m-1

φB ) association parameter for solvent B in the Wilke-Chang equation, units vary

φi ) volume fraction of component i, m3 m-3

τxy ) x component of momentum flux in the y direction, Nm-2

Ψ ) phase stability function, dimensionless

Literature Cited

Baker, L.; Pierce, A.; Luks, K. Gibbs Energy Analysis of PhaseEquilibria. Soc. Pet. Eng. J. 1982, 22, 731.

Bernard, G.; Hocine, R.; Lupis, C. H. P. Thermodynamic Condi-tions for Spinodal Decomposition in a Multicomponent System.Trans. Met. Soc. AIME. 1967, 239, 1600.

Bird, R. B.; Steward, W. E.; Lightfoot, E. N. Transport Phenomena;John Wiley & Sons: New York, 1960.

Cabezas, H.; Zhao, R.; Bare, J. C.; Nishtala, S. R. A ComputerProgram for Assisting the Design and Replacement of Envi-ronmentally Objectionable Solvents. AIChE Annual Meeting,Chicago, November 1996; Paper 46h.

Cao, W.; Knudsen, K.; Fredenslund, Aa.; Rasmussen, P. Group-Contribution Viscosity Prediction of Liquid Mixtures UsingUNIFAC-VLE Parameters. Ind. Eng. Chem. Res. 1993, 32,2088.

Derr, E.; Deal, C. Analytical Solution of Groups: Correlation ofActivity Coefficients Through Structural Group Parameters.Institution of Chemical Engineers Symposium Series; Institutionof Chemical Engineers: London, 1969; Vol. 32, Section 3, p 40.

Duvedi, P.; Achenie, K. Designing Environmentally Safe Refriger-ants Using Mathematical Programming. Chem. Eng. Sci. 1996,51, 3727.

Fredenslund, Aa.; Jones, L.; Prausnitz J. M. Group-ContributionEstimation of Activity Coefficients in Nonideal Liquid Mixtures.AIChE J. 1975, 21, 1086.

Gani, R.; Brignole, E. A. Molecular Design of Solvents for LiquidExtraction Based on UNIFAC. Fluid Phase Equilib. 1983, 13,331.

Gani, R.; Nielsen B.; Fredenslund, Aa. A Group ContributionApproach to Computer-Aided Molecular Design. AIChE J. 1991,37, 1318.

Hansen, C. M. Solvent Selection by Computer. In Advances inChemistry Series; Tess, R. W., Ed.; American Chemical Soci-ety: Washington, DC, 1973; Vol. 124, p 48.

Hansen C.; Skaarup, K. The Three-Dimensional Solubility Pa-rameter-Key to Paint Component Affinities. III. Independent


Calculation of the Parameter Components. J. Paint Technol.1967, 39, 511.

Hermansen, R. D. Development of a Solvent Database SoftwareProgram. Pollution Technology Review; U.S. Department ofEnergy, U. S. Air Force; Noyes Data Corp.: Park Ridge, NJ,1993; Vol. 212, p 159.

Hildebrand, H.; Scott R. Regular Solutions; Prentice-Hall: Engle-wood, NJ, 1962.

Horvath, A. Molecular Design; Elsevier Science Publishers: Am-sterdam, 1992.

Joback, K. G. Solvent Substitution For Pollution Prevention. InAIChE Symposium Series; Gaden, E. L., Ed.; American Instituteof Chemical Engineers: New York, 1994; Vol. 90, p 98.

Joback, K.; Stephanopoulos, G. Designing Molecules PossessingDesired Physical Property Values. In Proceedings of the ThirdInternational Conference on Foundations of Computer-AidedProcess Design; Siirola, J. J., Grossmann, I. E., Stephanopoulos,G., Eds.; Elsevier Science Publishers: New York, 1990.

Klein, A.; Wu, T.; Gani, R. Computer Aided Mixture Design WithSpecified Property Constraints. Comput. Chem. Eng. 1992, 16,229.

Li, C. Thermal Conductivity of Liquid Mixtures. AIChE J. 1976,22, 927.

Macchitto, S.; Odele, O.; Omatsone, O. Design of Optimal Solventsfor Liquid-Liquid Extraction and Gas Absorption Processes.Trans. 1nst. Chem. Eng. 1990, 68, 429.

MacLeod, D. On a Relation between Surface Tension and Density.Trans. Faraday Soc. 1923, 19, 38.

Magnussen, T.; Pretel, E. The UNIFAC Library, MAN 8101a;Danish Technical University, IVC-SEP: Lyngby, Denmark,1997.

Michelsen, M. L. The Isothermal Flash Problem, Part I. Stability.Fluid Phase Equilib. 1982, 9, 1.

Modi, A. K.; Stephanopoulos G. SMART: A Tool SystematicSolvents Screening for Batch-Process Development and Re-vamping. AIChE Spring Meeting, New Orleans, February 1996;Paper 90c.

Nielsen, B.; Gani, R.; Fredenslund, Aa. Computer-Aided MolecularDesign by Group Contribution. In Computer Applications inChemical Engineering; Bussemaker, H. Th., Iedema, P. D., Eds.;Elsevier Science Publishers: Amsterdam. 1990.

Pretel, J.; Lopez, A.; Bottini, B.; Brignole, A. Computer-AidedMolecular Design of Solvents for Separation Processes. AIChEJ. 1994, 40, 1349.

Reid, R.; Prausnitz, J. M.; Poling, B. The Properties of Gases &Liquids; McGraw-Hill: New York, 1987.

Walsham, C. Prediction of Flash Points for Solvent Mixtures. InAdvances in Chemistry Series; Tess, R. W., Ed.; AmericanChemical Society: Washington, DC, 1973; Vol. 124, p 56.

Wilke, C.; Chang P. Correlation of Diffusion Coefficients in DiluteSolutions. AIChE J. 1955, 1, 264.

Wilson, M.; Deal H. Activity Coefficients and Molecular Structure.Ind. Eng. Chem. Fundam. 1962, 1, 20.

Wu, T.; Finkleman, R. A Mathematical Model for the Predictionof Closed-Cup Flash Points. 175th ACS National MeetingPreprints, Anaheim, CA; American Chemical Society: Wash-ington, DC, 1977; Vol. 38, p 61.

Zhao, R.; Cabezas, H.; Govind, R.; Fang, Y. Computer AidedSolvent Substitution for Pollution Prevention. AIChE SpringMeeting, New Orleans, February 1996; Paper 40c.

Received for review November 21, 1997Revised manuscript received May 6, 1998

Accepted May 9, 1998

IE970861P


Documents

Molecular Thermodynamics in the Design of Substitute Solvents