Molecular dynamics, grand canonical Monte Carlo and expert simulations and modeling of water–acetic acid pervaporation using polyvinyl alcohol/tetraethyl orthosilicates membrane
Graphical abstract
Introduction
Membrane processes are one of the most important processes in separation science [[1], [2], [3], [4], [5]]. Pervaporation (PV) separation is particularly applied in organic compounds dehydration or separation of azeotropic mixtures or mixtures with a close-boiling point [6,7]. Thus, many experimental researches have been done to develop more selective membranes. However, they must be combined with scale-up and engineering attempts to obtain a real application in industry [8]. For designing integrated PV processes, developing a model that can explain the mass transfer and can be used in prediction of separation performance is essential [[9], [10], [11], [12], [13], [14], [15], [16]]. Mathematical models cannot commonly explain dynamic process behaviors and they are appropriate for certain feeds within particular conditions [[17], [18], [19]]. Conventional PV models characterize the mass transfer inside the membranes selective layer. Because of the intrinsic nonlinearity and complexity of the PV system, PV modeling by mathematical models is conditioned to the employment of many assumptions [20]. Due to the complexity of mass transfer models and lack of enough accuracy of the models in many PV systems, artificial intelligence can be utilized to model the PV system with high accuracy.
Recently, molecular simulation [21,22] has progressed to such a level that it can predict transport and structural properties of membranes [[23], [24], [25], [26], [27], [28]]. However, few works have been done on property–structure relationships of PVA membranes with molecular simulation. Wei et al. [29] explored effects of different ratios of the blend PVA/poly (acrylic acid) membrane on its properties using MD study. There are other studies on TEOS in polymeric membranes by MD [30,31]. But there are no MD simulation studies on pervaporation separation available for PVA/TEOS membranes. Fuzzy systems have particular benefits over conventional methods, especially when obscure data or related knowledge is involved in a process [[32], [33], [34], [35], [36], [37]]. Throughout the last years, fuzzy systems have recognized their popularity as alternative methods to data processing. These methods can minimize the matter of fuzzy modeling by learning the ability of ANN and have been reported since the beginning of 1990s [38,39]. Because the behavior and structure of ANFIS are extremely applicable [40], it has been considered as a fundamental element for interpretation researches [41]. The training procedure of parameters of ANFIS is the crucial issue. Many of them are on the basis of gradient and gradient determination in many steps is not simple. The chain rule that should be employed might trap in local minima. Hence, this study is attempted to develop an approach that can update the primary variables rapidly and conveniently compared to the gradient approach. In the gradient approach, variables convergence is not so fast and relies on primary variables value and consequently, discovering the optimum learning rate is extremely complicated [42]. In this study, different optimization algorithms namely DE, ACOR and GA were used to find the optimum algorithm in ANFIS training stage.
Sargolzaei et al. [43] applied ANFIS, back propagation artificial neural network (ANN) and radial basis function to predict starch removal efficiency from starchy wastewater by a hydrophilic Poly(ether sulfones) membrane in a plate and frame membrane module. Their study investigated the performance of membrane by estimation of optimum input parameters which have an impact on removal percentage of chemical oxygen demand and the permeate flux. Four inputs were considered, including pH, flow, temperature of feed and concentration of permeate. The results displayed a satisfying agreement but the ANFIS prediction was more accurate than two other simulation methods. Many researchers have used black box models including GP [43] for separation processes modeling in order to derive a mathematical function for a system. Shokrkar et al. [44] utilized a GP to obtain a mathematical model for the flux prediction of mullite ceramic MF membrane in the treatment of wastewaters containing oil. The model employed input variables for operating conditions (filtration time and flux) and feed quality (temperature, cross-flow velocity, pressure, and oil content). The results acquired from the GP model show good accuracy having an average error of <5%.
In this study, the grand canonical Monte Carlo (GCMC) and MD simulation approaches was used to examine effects of different TEOS loading content on transport properties of PVA membranes with Materials Studio simulator program. To avoid the influence of other factors such as pressure, all other effective factors are kept fixed. The water and acetic acid transport properties such as diffusivity, solubility, PSI, and permselectivity have been investigated. Also, X-ray diffraction, glass transition temperatures and fractional free volume (FFV) of these simulated membranes have been calculated and discussed. Also, this simulation study delivers a guideline for tailoring TEOS-filled PVA membrane to gain the best water/acetic acid separation properties, including diffusivity, solubility, PSI and permselectivity. Also, the results will be compared with the results of the ANN simulation of this study and also the results of the experimental works. Besides, for the first time, the main purpose of this study is to model PV process with novel modeling methods under various operating conditions. These models can be utilized to analyze the permeation performance through the membrane at various operating conditions. The complex and nonlinear performance of PSI versus concentration of water, temperature of feed and TEOS mass ratio with respect to PVA were modeled. In this study, ANFIS is optimized with ACOR, DE and GA to modify the ANFIS parameters and generates a balance between generalization ability and complexity of models. Therefore, the principal purpose of this study is to propose ACOR-ANFIS, DE-ANFIS, GA-ANFIS and GP models to investigate the PV process.
Section snippets
Data attainment
The feed water content was changed in a range of 10 up to 90 wt% and the experimental temperature was changed from 30 to 50 °C. The TEOS/PVA mass ratio was changed as 0.5 (namely M-1), 1.0 (namely M-2), 1.5 (namely M-3) and 2 (namely M-4). The prepared membranes were equilibrated in the feed container at the predetermined experimental temperature around 2 h prior to executing the PV with a certain amount of water-acetic acid mixture. Following a steady state was achieved, the permeate was
MS theory
Permeation of target molecules through polymeric (or nanomaterial/polymeric) membranes is typically described by solution–diffusion theory. This theory considers three steps: I: on the membrane surface and the high-pressure side, the molecules are adsorbed. II: the molecules penetrate (diffuse) through the polymeric (or nanomaterial/polymeric) membranes, and III, they desorb at the low-pressure side of the surface of the membrane [46,47]. Permeability can be calculated as follow:where PI
Density
Density of different PVA membranes are indicated in Fig. 5. The density of membranes becomes constant during and at the end of 5000 ps-NPT MD simulation equilibration run. As seen and as mentioned earlier, densities of membranes are between 1.25 and 1.3 g/cm3 and the densities of these membranes become equilibrated after a certain time. In Table 1, the average density of all membranes with different loading content of TEOS has been tabulated. As it reveals, the density of membranes increases
Conclusion
MC, and MD simulation and ACOR-ANFIS, DE-ANFIS, GA-ANFIS and GP models with experimental inputs were compared to predict PSI in water–acetic acid mixtures PV separation. The novelty of GP and usage of optimization methods in ANFIS training stage in obtaining accurate models for water–acetic acid mixtures PV separation were demonstrated. The density of simulated membranes with MS approach increases with the content of the TEOS nanomaterials which is an obvious and desired result. Also, it can be
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