Application of the Minka and Myers Theory of Liquid Adsorption to

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Application of the Minka and Myers Theory of Liquid Adsorption to Systems with Two Liquid Phases Christine Wegmann* and Piet J. A. M. Kerkhof Faculty of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands ABSTRACT: Dissolved acrylonitrile can be separated from a water stream by adsorption onto a polymeric sorbent (Dowex Optipore L-493) in a fixed bed and desorbed again by flushing the column with acetone. When the acetone fraction in the ternary mixture acrylonitrile/acetone/water is low and the acrylonitrile fraction is high, a phase separation between a water rich and an acrylonitrile rich phase occurs. In order to find the operating parameters for this separation process, the adsorbed amounts for all possible compositions of the bulk mixture need to be known. By use of a thermodynamic model, the loading in the ternary system was predicted from the three binary isotherms acrylonitrile/water, acrylonitrile/acetone, and acetone/water. These isotherms were determined experimentally. From the binary isotherms, the activity coefficients in the adsorbed phase were estimated. The binary model for the adsorbed phase activity coefficients was then extended to a ternary model. From this ternary activity coefficient model, the composition of the adsorbed phase was calculated as a function of the liquid phase composition. The agreement between the calculated adsorbed phase composition and the experimentally determined adsorbed phase composition is good to fair.

1. INTRODUCTION Acrylonitrile is a monomer which is polymerized for the production of plastics such as polyacrylonitrile or different copolymers. In some of these production processes, wastewater streams are generated containing up to 10 g/L dissolved acrylonitrile. Because of its toxicity as well as its raw material price, the recovery of this dissolved acrylonitrile from the wastewater stream is required. An adsorption based separation process is being developed for this system. In contrast to many adsorption processes where the purification of the water stream is the main goal, in our process the recovery of the acrylonitrile is equally important as the water purification. The acrylonitrile needs to be desorbed in an efficient way from the spent adsorbed material. A desorption by temperature increase cannot be applied as acrylonitrile is prone to polymerization, mainly at temperatures >30 °C.1 Therefore the acrylonitrile will be desorbed from the adsorbent material by a change of the liquid phase composition, whereas acetone was selected as the desorption solvent.2 Dowex Optipore L-493 is used as adsorbent material because of its high adsorption capacity for acrylonitrile, the absence of functional groups on its internal surface (which might catalyze chemical reactions of acrylonitrile), and the fast intraparticle mass transfer.3 The aim of this work is the theoretical description of the adsorption equilibrium in the ternary system acrylonitrile/acetone/water and finally the prediction of the adsorption equilibrium for all possible solution compositions with a theoretical model. In 1931, Markham and Benton4 developed a method to predict multicomponent adsorption equilibria for gas adsorption from pure component adsorption data. The Langmuir parameters for multicomponent adsorption are given as simple functions of the Langmuir parameters of the pure component adsorption. Hill5 and Arnold6 later extended the theory of Markham and Benton to mixtures for which the BET isotherm © 2012 American Chemical Society

applies. The ideal adsorbed solution theory (IAST) has been proposed by Myers and Prausnitz7 in 1965 for multicomponent gas adsorption. This model is based on basic thermodynamic equations. It is assumed that the gas phase obeys the ideal gas law and that in the adsorbed solution all activity coefficients are equal to unity. The multicomponent adsorption isotherms are then predicted by use of only pure-component adsorption isotherms. In 1972, Radke and Prausnitz8 extended this theory to multicomponent adsorption from dilute liquid solutions. They assumed that the activity coefficients in the adsorbed solution as well as in the dilute solution are equal to unity. In 1971, Sircar and Myers9 and Larionov and Myers10 presented the application of the thermodynamic model for nonideal twocomponent liquid systems, using the surface excess instead of the adsorbed amount as an experimental variable. Nonidealities in the bulk phase and in the adsorbed phase are taken into account. This model was extended in 1973 by Minka and Myers11 to an arbitrary number of components. They describe a procedure to predict multicomponent adsorption equilibria from binary data, taking into account nonidealities in the bulk as well as in the adsorbed phase. This real adsorbed solution theory (RAST) is widely applied.12−14 On the basis of the RAST, Berti et al.15 developed the adsorbate−solid solution theory. The adsorbed phase is treated as a mixture of the adsorbate with the adsorbent as additional component. The activity coefficients in the mixture are calculated by use of group contribution methods. This method was successfully applied to liquid adsorption onto zeolites. For the adsorption in macroporous polymers, however, this method is not applicable Received: Revised: Accepted: Published: 7340

January 31, 2012 April 26, 2012 May 3, 2012 May 3, 2012 dx.doi.org/10.1021/ie300273x | Ind. Eng. Chem. Res. 2012, 51, 7340−7348

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during 12−16 h with a shaking speed of 220 1/min. The same analytical method was used as for the determination of acrylonitrile. The results of the batch experiments with all three componentsacrylonitrile, acetone, and waterwere not used as an input to the model, but only for its validation. The acetone concentration in these experiments was always much higher than the acrylonitrile concentration. Because the affinity of Dowex Optipore is lower for acetone than for acrylonitrile, the relative acetone concentration decrease in the flasks was low and could not be measured accurately. For this reason, the acetone loading in Dowex Optipore at the end of the experiment was calculated from the acetone isotherm. The influence of the acrylonitrile adsorption on the acetone adsorption was as a first approach neglected. From the results of our model it could eventually be seen that this approach is indeed justified for low acrylonitrile liquid phase concentration (Figure 13).

as the sorbates do not form a well-defined, homogeneous mixture with the sorbent. The method of Minka and Myers was selected for the prediction of adsorption equilibria in our ternary system. The method takes into account activity coefficients in the bulk as well as in the adsorbed phase. This is crucial for our implementation, as the system acrylonitrile/acetone/water is highly nonideal. It is shown in this work how the method of Minka and Myers can be applied to systems with phase separation. To our knowledge, this method has not been applied for two-phase liquid systems until now.

2. MATERIALS AND METHODS 2.1. Substances. Demineralized water was used for all experiments. Acrylonitrile (>99%, containing 35−45 mg/L monomethyl ether hydroquinone as inhibitor, Sigma-Aldrich, The Netherlands) and acetone (technical, VWR, Belgium) were used without further treatment. Dowex Optipore L-493 (Sigma-Aldrich, USA) was used in wet condition as received. Dowex Optipore L-493 is a styrenic polymer cross-linked with divinylbenzene. It is commercially available in particles with a diameter of 0.31−0.85 mm. Most particles belong to the fraction with a relatively large diameter (85% have a diameter > 0.5 mm). Dowex Optipore ideally does not contain any functional groups on its internal surface which allows a reversible adsorption (physisorption) of acrylonitrile. 2.2. Batch Experiments. 2.2.1. Determination of Equilibrium Acrylonitrile Loading. Equilibrium experiments were done for the adsorption of acrylonitrile onto Dowex Optipore from pure water, from pure acetone, and from water/ acetone mixtures (20, 30, 40, 50, 60, 70, 80, and 90 vol % acetone; acetone fraction refers to the solution before acrylonitrile was added to it). These equilibrium isotherms were determined by a conventional batch bottle technique using Schott glass flasks. Dowex Optipore was used in wet condition, but all calculations are based on dry mass, since the water content of different sorbent batches can vary. For each experiment the water content of the adsorbent was determined separately (52−65 wt %), and the dry mass was calculated. A total of 0.5−2.0 g of wet Dowex Optipore and 25 mL of solution were used per batch. The initial acrylonitrile concentrations in the solution ranged between 0.1 g/L and 5 g/L. The flasks were shaken in an incubator at 25 °C during 12−16 h with a shaking speed of 220 1/min. It was shown in preliminary experiments that the adsorption equilibrium for the adsorption from water is reached after less than an hour.3 The use of solvents other than water might decrease the diffusion velocity. To make sure that equilibrium was still reached, the flasks were shaken for one night. The equilibrium concentration of acrylonitrile was measured with a gas chromatograph (Varian CP-3800, column: CP-Wax 52CB), using acetonitrile as internal standard. The adsorbed amount was determined by use of a mass balance (eq 1). V qeq = (c0 − ceq) (1) M 2.2.2. Determination of Equilibrium Acetone Loading. The isotherm of acetone from water onto Dowex Optipore was determined in a similar way. A total of 25 mL of a solution containing 5−500 g/L acetone in water were mixed with 1−2 g wet Dowex Optipore. All calculations were done based on dry weight; the water content of Dowex Optipore varied between 59 and 67 wt%. The flasks were shaken in an incubator at 25 °C

3. EQUILIBRIUM MODEL 3.1. Introduction. The method of Minka and Myers11 and Larionov and Myers10 is based on the use of activity coefficients in both phases, bulk and adsorbed. Activity coefficients are macroscopic quantities and can be used only for components which are present in a homogeneous phase with dimensions that are much larger than the molecular dimensions of the component itself. Kalies et al.16 developed a method for calculating excess adsorption quantities which is based on the activity coefficients in the bulk phase only and not on the activity coefficients in the adsorbed phase. This method can be applied even for microscopic sorbents. As Kalies et al. states, the construction of separation diagrams is not possible only on the basis of adsorption excess quantities. When, as in our case, the estimation of separation efficiencies is the aim of the calculations, the method cannot be applied without making further assumptions. Kalies et al. describe the adsorption of benzene, cyclohexane, and ethyl acetate on a molecular sieve of which the most frequent pore size is 0.53 nm. The molecular diameter of the adsorbed components is in the same dimension as the pore size of the sorbent. In our system, the molecular diameter of all components is less than 1 nm. The pore size distribution of Dowex Optipore is given in Figure 1. An active porosity of 0.86 mL/g (based on dry adsorbent) was found

Figure 1. Pore size distribution as determined by mercury intrusion porosimetry. Pores with a diameter ≥ 6.6 nm were determined. The total pore volume and the total surface area are given from the supplier. 7341

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experimentally (Section 5.1.1). The supplier gives a total particle porosity of 1.16 mL/g. The active porosity excludes the largest pores of the sorbent as in those pores no specific adsorption occurs; the composition of the pore fluid is the same as the composition of the bulk liquid. In our system, the largest part of the active porosity is formed by the pores with a pore size of 10−100 nm. This is much more than the diameter of the sorbates, and the method of Minka and Myers can therefore be applied. This method assumes that the volume change is zero when the components of the solution are mixed in the pores of the adsorbent. It is further assumed that the pore volume is constant (no swelling) and that the pores are always filled with liquid completely. 3.2. Theory. 3.2.1. Determination of Activity Coefficients in Adsorbed Phase for Binary Mixtures. The method of Minka and Myers, which was described for systems with one liquid phase, was in this work extended to systems with two liquid phases. Acetone is completely miscible with water as well as with acrylonitrile. For water−acetone mixtures, however, two phases are formed for acrylonitrile mass fractions between 0.074 and 0.966 at 25 °C.17 From the Gibbs adsorption isotherm (eq 2) Larionov and Myers derived eq 3, based on the prerequisite that in equilibrium the fugacity for each component is the same in the liquid phase as in the adsorbed phase. The free energy of immersion (eq 4) is used as defined by Minka and Myers instead of the spreading pressure, since it is not possible to define an active surface area per unit mass of adsorbent for a macroporous polymeric sorbent. A dπ = −nia dμia

(2)

⎛ Φ − Φ0 ⎞ i ⎟ γi bxib = γiaxia exp⎜ − ⎝ miRT ⎠

(3)

dΦ = −

RTn1E x1bx 2bγ1b

Φ − Φ10 = −RT = −RT

x1b

= −RT

⎡

⎛ ∂ ln γ b ⎞⎤ 1 ⎟⎥ ⎟⎥ d ξ ∂ ξ ⎝ ⎠⎦

b 1

⎣

(10)

(11)

x1b = 0

∫x =1 b 1

⎡ ⎛ ∂ ln γ b ⎞⎤ n1E(ξ) ⎢ 1 ⎟⎥ 1 + ξ⎜⎜ ⎟ dξ ξ(1 − ξ) ⎢⎣ ⎝ ∂ξ ⎠⎥⎦

(12)

The activity coefficients of species 1 and 2 in the adsorbed phase can now be described with an appropriate activity coefficient model, as, for example, NRTL or Margules. 3.2.2. Prediction of the Adsorption Equilibrium for Ternary Systems. Minka and Myers described a procedure for the prediction of the adsorption equilibrium for ternary systems which we extended to systems with two liquid phases. On the basis of eqs 3, 8, and 13, Minka and Myers derived eqs 14 and 15. Equation 13 is based on the assumption that the volume change of the liquid is zero when the solution is formed in the pores from the pure liquids. Equation 16 is derived by summation of both sides of eq 8 over all the components. 1 = na

x1a =

K12 =

∑

xia mi

(13)

x1b x1b + x 2bK12 + x3bK13 ⎛ Φ − Φ0 Φ − Φ10 ⎞ 2 ⎟ ⎜ exp − m1RT ⎠ γ1bγ2a ⎝ m2RT

(14)

γ1aγ2b

∑ niE = 0

(15) (16)

Using the Gibbs−Duhem equation and eqs 13−16, Minka and Myers found an equation for the free energy of immersion for a fixed ratio r = xb3/xb2 (eq 17). xb2 and xb3 are here expressed as functions of the mole fraction of component 1, which is ξ, and the ratio of mole fractions of the components 2 and 3, r, as given in eqs 18 and 19. Equation 17 has to be used for one component only. The free energy of immersion for the other two components can be found by use of eq 11.

nE

da1b

n E (ξ )

Φ02(x1b = 0) − Φ10(x1b = 1)

b 1

∫

x1b

∫x =1 ξ(11 − ξ) ⎢⎢1 + ξ⎜⎜

Φ − Φ02 = Φ − Φ10 − (Φ02 − Φ10)

(6)

1 2 1 n1E b b a1b(x1b = 1) x 2 a1

(9)

If the activity coefficient of species 1 in the liquid solution is known and the isotherm (from which the surface excess can be calculated) has been determined, the adsorbed phase activity coefficient of species 1 can be calculated from eq 3. For species 2, following Price and Danner,18 we use eqs 11 and 12 and calculate the activity coefficient again from eq 3.

∫x =1 x bx1bγ b d(γ1bx1b) a1b(x1b)

d(γ1bx1b) = γ1b·dx1b + x1b·dγ1b

= −RT

(5)

d(γ1bx1b)

(8)

Φ(x1b) − Φ10(x1b = 1)

(4) Φ = σA For eq 3, the difference in the free energy of immersion between the mixture and the pure liquid needs to be known. On the basis of the Gibbs−Duhem relationship for the bulk liquid (eq 5), Sircar and Myers9 derived eq 6 in order to determine this difference in free energy of immersion. They integrated eq 6 from a pure species xb1 =1 to a given mole fraction xb1 in a mixture according to eq 7 at constant temperature and pressure. nEi is the surface excess as defined by eq 8. By use of eq 9 and by defining ξ as the integration variable for the mole fraction, the more consistent eq 10 was found.

x1b dμ1 + x 2b dμ2 = 0

niE = na(xia − xi b)

(7)

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Φ(x1b)

−

Φ10(x1b RT

= 1)

=

∫

Article

⎛ ⎜

ξ m1

x1b = 1

x2 =

x3 =

1−ξ r+1

+1

−

1 ⎞ ⎟ 1−ξ⎠

+ K12

(

+

( 1r +− 1ξ )

1−ξ 1/r+1

+ K13

m2

(

)(1 − K

13)

1−ξ 1/r+1

)

⎛ d ln γ3b − ⎝ dξ

⎜

1 ⎞ ⎟ 1−ξ⎠

dξ

m3

(17)

calculated from the surface excess and the activity coefficients in the liquid phase by use of eq 10. The activity coefficients in the liquid phase were calculated using UNIFAC. The activity coefficients in the adsorbed phase were finally calculated by use of eq 3 and are given as functions of the adsorbed phase mole fractions. This method had to be adapted for the two-phase system acrylonitrile/water. For acrylonitrile mass fractions > 0.966 (which corresponds to mole fractions > 0.906), the integral in eq 10 is evaluated conventionally. For mass fractions < 0.074 (which corresponds to mole fractions < 0.026), however, the nonexisting mole fractions between 0.026 and 0.906 had to be left out which means that the integral was split into two parts as shown in eq 20. In the two-phase region the activity does not change. From eq 7 it can be seen that one therefore does not have to integrate in this region. In this manner, the activity of both components could again be given as a function of the adsorbed phase mole fractions.

(18)

1−ξ 1 r

b 2

( 1r +− 1ξ )(1 − K12)⎝ d lndξγ

(19)

4. PRACTICAL APPROACH 4.1. Isotherms for Binary Mixtures with and without Phase Separation. Binary isotherms were experimentally determined for the adsorption of acrylonitrile from water and from acetone as well as for the adsorption of acetone from water. We assume that the same pore volume is accessible for all three components. For the description of the isotherms, we take into account only the micro- and nanopores and exclude the macropores. In macropores no specific adsorption occurs; the composition of the pore fluid is the same as the composition of the bulk liquid. The supplier of Dowex Optipore (Sigma-Aldrich) gives a total particle porosity of 1.16 mL/g (based on dry particles). We found the volume of the micro- and nanopores from the isotherm of acrylonitrile from water. This active pore volume was then used to find the isotherms for the two remaining isotherms. The Langmuir isotherm model is thermodynamically consistent as it reduces to Henry’s law at low concentrations. This model was therefore used for the description of all three isotherms. Since acrylonitrile and water form a two-phase system for acrylonitrile mass fractions between 0.074 and 0.966 at 25 °C, the Langmuir model had to be applied for a twophase system. This was done as follows: The concentration of acrylonitrile in the water phase at its maximum solubility is the same as in the water-rich phase when phase separation occurs. The acrylonitrile loading in Dowex Optipore for the two-phase region is therefore the same as the loading at the maximum solubility of acrylonitrile. When the acrylonitrile mass fraction is increased to >0.966, the loading will increase further until it reaches its maximum at a concentration of 800.7 g/L (pure acrylonitrile19). This maximum adsorbed amount, which was found by fitting the experimental data, gives the active porosity (micro- and nanopores). The Langmuir parameters for the isotherms describing the adsorption of acrylonitrile from acetone and acetone from water were found by fixing the maximum adsorbed amount which is the product of the active porosity and the density of the adsorbed liquidand fitting the Langmuir equation to the experimental data. 4.2. Determination of Activity Coefficients in the Adsorbed Phase for Binary Mixtures with and without Phase Separation in the Liquid Phase. For the systems acrylonitrile/acetone and acetone/water, the method which is described in Section 3.2.1 could directly be applied: From the Langmuir isotherms the surface excess was found from eq 8, and the difference in the free energy of immersion was

Φ(x1b) − Φ10(x1b = 1) ⎛ x b= 0.906 ⎡ ⎛ ∂ ln γ b ⎞⎤ 1 n1E(ξ) ⎢ 1 ⎟⎥ ⎜ 1 + ξ⎜⎜ = −RT ⎟⎥ d ξ ⎜ x1b= 1 ⎢⎣ (1 ) ξ ξ ξ − ∂ ⎝ ⎠⎦ ⎝

∫

+

x1b

∫x =0.026 b 1

⎡ ⎛ ∂ ln γ b ⎞⎤ ⎞ n1E(ξ) ⎢ 1 ⎟⎥ ⎟ 1 + ξ⎜⎜ ⎟ dξ ⎟ ξ(1 − ξ) ⎢⎣ ⎝ ∂ξ ⎠⎥⎦ ⎠

(20)

As a next step, different thermodynamic models were tested for the description of the adsorbed phase activity coefficients as functions of the mole fractions. The Redlich−Kister equation, the Nonrandom Two-Liquid equation (NRTL), the Wilson equation, and the four suffix Margules equation were tested. The four suffix Margules equation was most suitable to describe the three binary systems. The Margules equation was used as given by Larson and Tassios20 (eq 21). log γ1 = x 2 2(A12 + 2(A 21 − A12 − D12)x1 + 3D12x12) (21)

By rotating the subscripts in A, the expression for γ2 is obtained. D12 remains the same. The binary constants for all three systems were determined. 4.3. Prediction of the Adsorption Equilibrium for Ternary Systems with Phase Separation. With the binary adsorption isotherms and the binary constants for the four suffix Margules equation, we have all the information we need to calculate the adsorbed amounts for a ternary system. This is done as described in Section 3.2.2 in a stepwise fashion. The activity coefficients in the ternary mixture were calculated from the binary data with eq 22 as given by Larson and Tassios. The activity coefficients for components 2 and 3 are obtained by rotating the subscripts (1 → 2, 2 → 3, 3 → 1). The addition of the ternary constant C* was suggested by Wohl.21 C* was set to 0 in our system. 7343



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log γ1 = x 2 2(A12 + 2(A 21 − A12 − D12)x1 + 3D12x12) + x32(A13 + 2(A31 − A13 − D13)x1 + 3D13x12) + x 2x3((A 21 + A12 + A31 + A13 − A 23 − A32 )/2 + x1(A 21 − A12 + A31 − A13) + (x 2 − x3) (A 23 − A32) + 3x 2x3D23 − (1 − 2x1)C*)

(22)

For a two-phase system, the crucial point is the correct choice of x1, x2 and x3. The integration of eq 17 is carried out along lines with a constant ratio r = xb3/xb2. The two-phase region as shown in Figure 2 (calculated with AspenPlus using Figure 3. Experimentally determined adsorption isotherms of acrylonitrile on Dowex Optipore L-493 for varying acetone volume fractions in the liquid phase.

Figure 2. Ternary diagram for the system acrylonitrile/acetone/water with two-phase region, including tie lines. Three integration paths with constant r = xb3/xb2 are given. Component 1 = acetone, component 2 = acrylonitrile, and component 3 = water.

Figure 4. Acrylonitrile isotherm for the adsorption from water at acrylonitrile concentrations lower than the maximum solubility. Experimental data points and Langmuir fit.

UNIQUAC) cannot be crossed during the integration. For this reason the ratio acrylonitrile/water needs to be kept constant during one integration, and acetone is x1. Acrylonitrile is x2, and water is x3. The integration is stopped at the boundary of the two-phase region. By performing the integration many times with different acrylonitrile/acetone ratios, the whole one-phase region is covered. Three integration paths are shown in Figure 2.

5. RESULTS AND DISCUSSION 5.1. Experimentally Determined Binary and Ternary Adsorption Isotherms. The acrylonitrile isotherms as determined by use of batch experiments for different solvent compositions are given in Figure 3. The acetone concentration is given as the fraction in the solvent before acrylonitrile was added to it. The isotherms for 0 vol % and 100 vol % acetone were used for the determination of the model parameters, and the remaining isotherms (20, 30, 40, 50, 60, 70, 80, and 90 vol %) were used for the validation of the model. For the sake of clarity, the isotherms for 30, 50, 70, and 90 vol % acetone are not shown in Figure 3. The acrylonitrile adsorption equilibrium is a strong function of the acetone concentration in the solvent. By increasing the acetone concentration in the solvent, acrylonitrile can be desorbed from Dowex Optipore. 5.1.1. Fitting the Binary Isotherms. The experimentally determined adsorption isotherms for the three binary systems are given in Figures 4−7. The data points for the acetone adsorption at high concentrations are scattered (Figure 7). This is because the relative concentration change during the

Figure 5. Acrylonitrile isotherm for the adsorption from water for the whole range of acrylonitrile concentrations. Experimental data points and Langmuir fit.

experiments was small, which led to relatively large experimental errors. The acrylonitrile isotherm was fitted first, and the active porosity was calculated from the loading at a concentration of 800.7 g/L (pure acrylonitrile). An active porosity of 0.38 mL/ mL, which corresponds to 0.86 mL/g (based on dry adsorbent), was found. The Langmuir parameters of the isotherms are qs = 0.830 kg/kg and kL = 4.98 × 10−2 m3/kg (acrylonitrile from water), qs = 1.47 kg/kg and kL = 1.10 × 10−3 m3/kg (acrylonitrile from acetone), and qs = 0.821 kg/kg and 7344



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Figure 6. Acrylonitrile isotherm for the adsorption from acetone. Experimental data points and Langmuir fit.

Figure 8. Adsorbed phase activity coefficients in the acrylonitrile/ water system, experimental (from isotherms) and fitted with the four suffix Margules equation.

Figure 7. Acetone isotherm for the adsorption from water. Experimental data points and Langmuir fit.

Figure 9. Adsorbed phase activity coefficients in the acrylonitrile/ acetone system, experimental (from isotherms) and fitted with the four suffix Margules equation.

kL = 6.00 × 10−3 m3/kg (acetone from water). These Langmuir isotherms are used in the next step for the determination of the activity coefficients in the adsorbed phase. 5.2. Activity Coefficients in the Adsorbed Phase for Binary Mixtures with and without Phase Separation in the Liquid Phase. The activity coefficients in binary mixtures in the adsorbed phase were calculated from the binary isotherms as described in Section 4.2. The four suffix Margules equation was applied for the description of the adsorbed phase activity coefficients. The calculated activity coefficients and the fit with the four suffix Margules equation are shown in Figures 8−10. The Margules equation can describe the activity coefficients very well. The Margules parameters for all three systems are given in Table 1. 5.3. Adsorption Equilibrium for Ternary Systems with Phase Separation. The adsorbed phase mole fraction of acrylonitrile, as calculated with our model, is given in Figure 11 as a function of the liquid phase composition. It can be seen that especially at low liquid phase acrylonitrile mole fractions the acrylonitrile loading is a strong function of the acetone mole fraction in the liquid phase, whereas at higher acrylonitrile mole fractions this effect is less pronounced. The area of liquid phase acrylonitrile mole fractions < 0.05 is of particular interest for us, as we focus on the separation of acrylonitrile from industrial wastewater streams. The acrylonitrile concentration in such waste streams is typically around 10 g/L, which corresponds to a mole fraction of 0.003. Batch experiments where done for acrylonitrile mole fractions up to 0.05. This area

Figure 10. Adsorbed phase activity coefficients in the acetone/water system, experimental (from isotherms) and fitted with the four suffix Margules equation.

Table 1. Margules Parameters As Found from Binary Adsorption Data Fittinga A12 = −0.0511 A13 = 0.8660 A23 = 0.7023

A21 = −0.0802 A31 = 1.2182 A32 = 0.9690

D12 = 0.0291 D13 = 0.7792 D23 = 0.3048

a

Component 1 = acetone, component 2 = acrylonitrile, and component 3 = water.

of small acrylonitrile fractions is given again in Figure 12. From this figure it can be seen that acrylonitrile can be desorbed efficiently from Dowex Optipore L-493 by use of acetone. 7345



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the acrylonitrile adsorption on the acetone adsorption can be neglectedwhich was made in Section 2.2.2. The thermodynamic model is validated by comparing the calculations with the experimental data points in Figure 14. The

Figure 11. Calculated equilibrium adsorbed phase mole fractions of acrylonitrile as a function of the liquid phase composition.

Figure 14. Calculated and experimentally determined loading of acrylonitrile on Dowex Optipore L-493 for varying acetone mole fractions in the solvent.

model is able to predict the acrylonitrile loading with good accuracy; however, it tends to overestimate the acrylonitrile loading slightly. This overestimation can be due to the imperfect description of the binary isotherms with the Langmuir equation. Furthermore, the assumptions in the method of Minka and Myersthe volume change is zero when the components of the solution are mixed in the pores of the adsorbent, and the pore volume is constantare simplifications of the reality. We observed a swelling of Dowex Optipore L-493 of around 7% in pure acetone compared to pure water. 5.4. Phase Separation in the Bulk Liquid and in the Adsorbed Phase. A mixture splits into two separate liquid phases, if by doing so it can lower its Gibbs energy. If a plot of the Gibbs energy of mixing against one mole fraction is, in part, concave downward, a second liquid phase is formed in the liquid, whereas the phase separation will happen between the two local minima of the curve.22This is what is happening in acrylonitrile/water mixtures for acrylonitrile mole fractions between 0.026 and 0.906. In order to gain insight into the behavior of the acrylonitrile/water liquid mixture in the pores of Dowex Optipore, the isothermal Gibbs free energy of mixing per mole gm was calculated for acrylonitrile/water mixtures in the liquid phase as well as in the adsorbed phase by eq 23.22

Figure 12. Calculated equilibrium adsorbed phase mole fraction of acrylonitrile as a function of the equilibrium liquid phase composition for low acrylonitrile mole fractions in the liquid phase.

Figure 13 shows the adsorbed phase mole fraction of acetone as a function of the liquid phase composition. It can be seen

g m = RT (x1 ln(a1) + x 2 ln(a 2))

(23)

The activity coefficients of acrylonitrile and water in bulk phase acrylonitrile/water mixtures were calculated by use of UNIFAC. The Gibbs energy of mixing could then be calculated for mixtures of these two components. This was first done for the liquid phase; the plot is given in Figure 15. The two minima are located at acrylonitrile mole fractions of 0.031 and 0.923, which corresponds well with the data from literature (0.026 and 0.906). This serves as a validation of the UNIFAC model. The activity coefficients in acrylonitrile/water mixtures in the adsorbed phase are known from our thermodynamic model. A plot of the Gibbs energy of mixing is given in Figure 16. No part of the curve is concave downward. This is a strong indication that no phase separation is happening in the adsorbed phase. The thermodynamic properties of the mixture

Figure 13. Calculated equilibrium adsorbed phase mole fraction of acetone as a function of the equilibrium liquid phase composition for low acrylonitrile mole fractions in the liquid phase.

that, at low liquid phase acrylonitrile mole fractions, for which our experiments were done, the adsorbed phase acetone mole fraction is not very sensitive to the liquid phase acrylonitrile mole fraction. This justifies the assumptionthe influence of 7346



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A a c f gm M m na nE q R T V x

Figure 15. Gibbs energy of mixing for acrylonitrile and water in the liquid phase.

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NOMENCLATURE surface area per unit mass of adsorbent [m2/g] activity [−] concentration [kg/m3] fugacity [Pa] Gibbs free energy of mixing [J/mol] mass [kg] capacity of adsorbent [mol/kg] number of moles in adsorbed phase [mol/kg] surface excess [mol/mol] loading [kg/kg] ideal gas constant [J/(mol K)] temperature [K] volume [m3] mole fraction [mol/mol]

Greek symbols

γ μ ξ π σ Φ

activity coefficient [−] chemical potential [J/mol] mole fraction [mol/mol] spreading pressure [J/m2] surface tension of solid−liquid interface [N/m] free energy of immersion of adsorbent in liquid mixture [J/ kg]

Subscripts

AC AN eq WA 0 1,2,3,i

Figure 16. Gibbs energy of mixing for acrylonitrile and water in the adsorbed phase.

to to to to to to

acetone acrylonitrile equilibrium water the initial state components 1, 2, 3, i

Superscripts

a refers to adsorbed phase b refers to bulk phase 0 refers to a pure liquid

are strongly influenced by its interaction with the adsorbent material.

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6. CONCLUSIONS In this work we extended the theory of Minka and Myers to a system with two liquid phases. With our model we are able to predict the acrylonitrile loading on Dowex Optipore L-493 in ternary mixtures (acrylonitrile/acetone/water) from binary data. We found that, whereas phase separation occurs in acrylonitrile/water mixtures, no second phase is formed for acrylonitrile/water mixtures in the adsorbed state. The model as well as the experimental results shows that the adsorption of acrylonitrile is strongly dependent on the acetone concentration in the liquid phase. This is desirable for our separation process as the acrylonitrile can be desorbed from Dowex Optipore by use of acetone in an efficient way.

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refers refers refers refers refers refers

REFERENCES

(1) Seok Lyoo, W.; Do Ghim, H.; Sik Yoon, W.; Lee, J.; Seok Lee, H.; Chul, Ji, B. Solution Polymerization Behavior of Acrylonitrile by Moderate Temperature Azoinitiator. Eur. Polym. J. 1999, 35, 647. (2) Wegmann, C.; Đekić Ž ivković, T.; Kerkhof, P. J. A. M. Solvent Selection for the Desorption of Acrylonitrile from Dowex Optipore L493. Ind. Eng. Chem. Res. 2012, 51, 474. (3) Wegmann, C.; Suárez García, E.; Kerkhof, P. J. A. M. Kinetics of Acrylonitrile Adsorption from an Aqueous Solution Using Dowex Optipore L-493. Sep. Purif. Technol. 2011, 81, 429. (4) Markham, E. C.; Benton, A. F. The Adsorption of Gas Mixtures by Silica. J. Am. Chem. Soc. 1931, 53, 497. (5) Hill, T. L. J. Statistical Mechanics of Multimolecular Adsorption. I. Chem. Phys. 1946, 14, 265. (6) Arnold, J. R. Adsorption of Gas Mixtures. Nitrogen-Oxygen on Anatase. J. Am. Chem. Soc. 1949, 71, 104. (7) Myers, A. L.; Prausnitz, J. M. Thermodynamics of Mixed-Gas Adsorption. AIChE J. 1965, 11, 121. (8) Radke, C. J.; Prausnitz, J. M. Thermodynamics of Multi-Solute Adsorption from Dilute Liquid Solutions. AIChE J. 1972, 18, 761. (9) Sircar, S.; Myers, A. L. A Thermodynamic Consistenct Test for Adsorption from Binary Liquid Mixtures on Solids. AIChE J. 1971, 17, 186. (10) Larionov, O. G.; Myers, A. L. Thermodynamics of Adsorption from Nonideal Solutions of Nonelectrolytes. Chem. Eng. Sci. 1971, 26, 1025. (11) Minka, C.; Myers, A. L. Adsorption from Ternary Liquid Mixtures on Solids. AIChE J. 1973, 19, 453.

AUTHOR INFORMATION

Corresponding Author

*Tel.: 0031402473734. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was carried out within project SC-00-04 of the Institute for Sustainable Process Technology (ISPT), The Netherlands. 7347



Article

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Application of the Minka and Myers Theory of Liquid Adsorption to

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