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Separation and Semi-Empiric Modeling of Ethanol—Water Solutions by Pervaporation Using PDMS Membrane

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Separation and Semi-Empiric Modeling of Ethanol—Water Solutions by Pervaporation Using PDMS Membrane Article Separation and Semi-Empiric Modeling of Ethanol—Water Solutions by Pervaporation Using PDMS Membrane John Hervin Bermudez Jaimes * , Mario Eusebio Torres Alvarez, Elenise Bannwart de Moraes, Maria Regina Wolf Maciel and Rubens Maciel Filho School of Chemical Engineering, Separation Process Development Laboratory, State University of Campinas, Albert Einstein 500, Campinas 13083-582, Brazil; [email protected] (M.E.T.A.); [email protected] (E.B.d.M.); [email protected] (M.R.W.M.); [email protected] (R.M.F.) * Correspondence: [email protected]; Tel.: +57-32-2603-5815 Abstract: High energy demand, competitive fuel prices and the need for environmentally friendly processes have led to the constant development of the alcohol industry. Pervaporation is seen as a separation process, with low energy consumption, which has a high potential for application in the fermentation and dehydration of ethanol. This work presents the experimental ethanol recovery by pervaporation and the semi-empirical model of partial fluxes. Total permeate fluxes between 2 1 2 1 15.6–68.6 mol m− h− (289–1565 g m− h− ), separation factor between 3.4–6.4 and ethanol molar fraction between 16–171 mM (4–35 wt%) were obtained using ethanol feed concentrations between 4–37 mM (1–9 wt%), temperature between 34–50 ◦C and commercial polydimethylsiloxane (PDMS) membrane. From the experimental data a semi-empirical model describing the behavior of partial- permeate fluxes was developed considering the effect of both the temperature and the composition of the feed, and the behavior of the apparent activation energy. Therefore, the model obtained shows a modified Arrhenius-type behavior that calculates with high precision the partial-permeate fluxes. Furthermore, the versatility of the model was demonstrated in process such as ethanol recovery and both ethanol and butanol dehydration. Citation: Jaimes, J.H.B.; Alvarez, M.E.T.; Keywords: pervaporation; Arrhenius; simulation; modeling; PDMS membrane; bioethanol de Moraes, E.B.; Maciel, M.R.W.; Filho, R.M. Separation and Semi-Empiric Modeling of Ethanol—Water Solutions byPervaporationUsingPDMSMembrane. 1. Introduction Polymers 2021, 13, 93. https://dx.doi.org/10.3390/ Pervaporation is a membrane separation process used in the separations of mixtures, polym13010093 such as water–organic [1], organic–water [2] or organic–organic [3]. In the pervapora- tion separation, a membrane acts as the separating barrier for the component of minor Received: 21 September 2020 affinity. When both the membrane and feed are in contact, some molecules can be recov- Accepted: 27 November 2020 ered from the feed due to its higher affinity and quicker diffusivity in the membrane [4], Published: 29 December 2020 which can be carried out applying a differential pressure between the membrane walls through a vacuum pump or a carrier gas [5]. The main advantage of pervaporation is Publisher’s Note: MDPI stays neu- the low energy consumption compared with traditional processes such as distillation tral with regard to jurisdictional claims and liquid-liquid extraction [6–8], but also the possibility to work at moderate temper- in published maps and institutional ature can be an advantage for the separation of temperature sensitive products, be an affiliations. environmentally friendly process [9], reduces the cost of production, generates products free from solvent contamination and can be adapted to both continuous and batch pro- cesses [10]. Initially, pervaporation was intended for the selective separation of azeotropic Copyright: © 2020 by the authors. Li- mixtures. Currently, its application extends to various areas of industry, standing out censee MDPI, Basel, Switzerland. This in the extraction of aromas (alcohols, esters, organic compounds) from agro-food sys- article is an open access article distributed tems (wastes, by-products, fruit juices, food processed products), ethanol removal from under the terms and conditions of the alcoholic drinks towards the production of non-alcoholic beverages [11], development Creative Commons Attribution (CC BY) of chemical (water removal: esterification, acetalization, ketalization, etherification) and license (https://creativecommons.org/ bio-chemical reactions (alcohol production) [12–18], dehydration of organics (methanol, licenses/by/4.0/). ethanol, isopropanol, butanol) [19–22] and waste water treatment [23]. Pervaporation can Polymers 2021, 13, 93. https://dx.doi.org/10.3390/polym13010093 https://www.mdpi.com/journal/polymers Polymers 2021, 13, 93 2 of 19 be coupled to fermentation creating a hybrid pervaporation-fermentation process, which is used to recovery the bioproduct, such as acetone-butanol-ethanol (ABE) [24], butanol [25], and ethanol [26], in order to eliminate inhibition products, further improvement on product productivity and enhancement of the substrate conversion rate [27]. In the alcohol industry, pervaporation is gaining space in hybrid systems, such as distillation–pervaporation and fermentation–pervaporation, in which the pervaporation membrane can be located inside the main unit or in an external pervaporation module [28–31]. Therefore, the development of pervaporation models are essentials in the study of these systems. Mass transfer for the separation of binary solutions in pervaporation can be described using semi-empirical models. The main models are developed from the mathematical description of two independent variables, measured experimentally, such as total permeate flux and separation factor [32], permeability of permeants [33] or permeate fluxes [34] and the model parameters are mainly calculated by objective functions [35,36]. Most of the reported models are based on the solution–diffusion model [37]. However, it is common to use the Arrhenius model to describe the dependence of permeate fluxes on temperature [38]. In general, pervaporation can be described using the solution–diffusion model [39] and the Arrhenius equation or a combination of them, which are used to describe the permeate flux mainly. However, the solution–diffusion model is the most accepted to describe the transport of mass across the membrane [40]. The solution–diffusion model involves a more complex mathematical development than that required by the Arrhenius model. In this sense, the latter ones have gained space, being used in the modeling of processes for industrial application [41]. Table1 shows some permeate flux models reported in the literature. Commonly, pervaporation models are based on the mathematical modeling of per- meate flux (J) and the separation factor (bij). However, to compare the performance of the membranes it is necessary to present the results based on driving force normalized properties such as permeability (∏i), permeance (∏i /`) or membrane selectivity (aij) as proposed by [42]. The aim of this work was to develop a semi-empirical model from the analysis of the effects of temperature and feed concentration on the partial-permeate flux (ethanol and water), using a commercial polydimethylsiloxane (PDMS) membrane. The relative mathematical simplicity of this semi-empirical model, its high adjusted R-squared and low mean square error promote its application in the study of industrial processes such as fermentation–pervaporation or distillation–pervaporation. Table 1. Permeate flux models. Model Ref. 1 D exp(B x 1) J = i · i i 1+D exp(B x )/(Q P g ) gi i · i1 0· i0· i · · Pi1 P13 P− [36] h i0 i Ei 1 1 Di = D∗ exp ; gi = pgi1gi3; i R T∗ − T n J J 2 i,mesured− i,modeled OF = ∑ J 1 i,mesured J = ax2 + bx + c i i i [43] a, b, c: parameters = Dij f p Ji L Coni Coni E − 0 p T+273.15 p P [44] D = D e ; Con = p ij 0 i y RTp 1+ B i ( Vm ) Polymers 2021, 13, 93 3 of 19 Table 1. Cont. Model Ref. J = h i i Ei 1 1 sat wi exp(#ixi) exp xigiP yiPp [45] R Tre f − T i − wi, #i, Ei: parameters J = L (T, x ) P0(T )x g P y i i i i F F,i F,i − p p,i L (T, x ) = ih i i EAct,i(xi) 1 1 L0,i(T0, xi) exp [46] − R T0 − Tf = Li T, xH2O h 1 1 i ai exp bi + cixH O T0 − Tf 2 (hydrophilic membrane) Li(T, xBuOH) = h 1 1 i (ai ln(xBuOH) + bi) exp ci T0 − Tf (hydrophobic membrane) D0 c2 J = i i + b c (1 c ) i L 2 ij i − i [47] 0 Di , bij: parameters K J = PF gF xF PP K exp 2 W Wsat W W − W · 1 T [48] JP = K h K i PF gF xF PP exp K + 4 1 + J exp K + 6 Psat P P − P 3 T W 5 T K1 6: parameters − Ji = [49] DCm P2x2,i vi(Pv,i Pl ) m gl,ixl,i exp − lg i − Pv,i RT E − p J = A0 exp T 0.5 y = 440.9 112700 x 2 + 98.3 2 − [50] − T − A0 = 2995 exp(2.8441x); E = 330.04 + 839.58x; a = 440.9 112700 p − T ¯ w1D2,m+D12 Dw1 J1 = D¯ 1,m rm + D12+w1D¯ 2,m+w2D¯ 1,m d ¯ w1D2,m Dw2 D¯ 1,m rm D12+w1D¯ 2,m+w2D¯ 1,m d J2 = ¯ ¯ w2D1,m + D12 Dw2 w2D1,m Dw1 D¯ 2,m rm + D¯ 2,m rm D12 + w2D¯ 1,m + w1D¯ 2,m d D12 + w2D¯ 1,m + w1D¯ 2,m [51] d D¯ 1,m = D [exp(# w¯ + # w ) exp(# w¯ + # w )] 10 11 1 12 2,F − 11 1 12 2,P # (w w ) 12 2,F − 2,P D¯ 2,m = D [exp(# w¯ + # w ) exp(# w¯ + # w )] 20 21 1 22 2,F − 21 1 22 2,P # (w w ) 22 2,F − 2,P 2. Materials and Methods 2.1. Reagent Absolute ethanol from JT Baker. 2.2. Ethanol Quantification Ethanol permeate was determined by high-performance liquid chromatography (HPLC), employing a chromatograph (Agilent 1260, Campinas, SP, Brazil) equipped with Polymers 2021, 13, 93 4 of 19 a refractive index detector and a Bio-Rad Aminex HPX-87H column (300 7.8 mm) op- × erated at 30 °C and sample injection volume of 20 µL.
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