Thermodynamic and hydrodynamic study of a gas-liquid flow in a cyclone separator downstream supercritical drying

J. of Supercritical Fluids 118 (2016) 27–38

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Thermodynamic and hydrodynamic study of a gas-liquid flow in a cyclone separator downstream supercritical drying Mouna Lazrag a,b,c , Deisy Lizeth Mejia-Mendez a,b , Cécile Lemaitre a,b , Philippe Hugh Emmanuel Stafford a,b , Rainier Hreiz a,b , Romain Privat a,b , Ahmed Hannachi c , Danielle Barth a,b,∗ a

Laboratoire Réactions et Génie des Procédés, UMR 7274, Université de Lorraine, BP20451-54001 Nancy, France Laboratoire Réactions et Génie des Procédés, UMR 7274, CNRS, BP20451-54001 Nancy, France c Laboratoire de Recherche, Génie des Procédés et Systèmes Industriels (LR11ES54), Ecole Nationale d’Ingénieurs de Gabés, Université de Gabés Avenue Omar Ibn El Khattab, Zrig Eddakhlania, 6072, Tunisie b

a r t i c l e

i n f o

Article history: Received 16 March 2016 Received in revised form 21 July 2016 Accepted 21 July 2016 Available online 22 July 2016 Keywords: Aerogel Supercritical CO2 Organogel Cyclone separator Thermodynamic modeling CFD

a b s t r a c t Aerogels may be synthesized by extracting the liquid solvent from an organogel using supercritical CO2 . The mixture (CO2 -solvent) leaving the autoclave should be separated and all the solvent in the sample should be recovered at the end of the extraction. This paper deals with a pilot-scale unit where CO2 and the solvent, here toluene, are separated using a cascade of cyclone separators. During the separation, the toluene recovery rate during is below 65%. In order to determine the reasons behind this malfunction, a thermodynamic study and a hydrodynamic study (Computational Fluid Dynamics, CFD) of the mixture separation in the cyclones were carried out. According to CFD, cyclones allow an efficient mechanical separation of the liquid solvent and the gaseous CO2 . On the other hand, the thermodynamic model revealed that under the actual operating conditions, a large fraction of the solvent remains in gaseous state and is carried away through the cyclone gas outlet, hence the poor overall separation performance. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Aerogels are ultra-light solid materials derived from gels. They are composed of up to 99.98% volume of air. Thereby, they are almost weightless and are very efficient heat insulators. These unique properties make aerogels attractive for a variety of applications in the chemical, aerospace and car industries. In particular, aerogels could be used as super-insulators in building walls [1]. They can also be integrated into transparent walls, particularly in double glazing [2,3]. Therefore, during the last 30 years, aerogels have been the subject of an increasing number of research works [4]. Different techniques, have been developed to obtain aerogels from gels containing a solvent such as the processes of evaporative drying [5], freeze drying [6,7] and supercritical drying. Supercritical drying of gels has been so far the option with the most satisfying results [4]. This process consists in extracting the solvent from the gel using supercritical CO2 (SC CO2 ). In these

∗ Corresponding author at: Laboratoire Réactions et Génie des Procédés, UMR 7274, Université de Lorraine, BP20451-54001 Nancy, France. E-mail address: [email protected] (D. Barth). http://dx.doi.org/10.1016/j.supflu.2016.07.017 0896-8446/© 2016 Elsevier B.V. All rights reserved.

conditions, the density difference between the two phases disappears, nullifying the surface tension [8]. The resulting aerogel shows good thermo-mechanical properties. The first aerogels produced were silica aerogels in the early 1930s [9]. They were obtained by drying silica gel. The solvent, to be extracted, was generally an alcohol (ethanol [10–14], methanol [15], liquid isopropanol [16], or 1-butanol [17]). Extensive research has been carried out on supercritical drying of silica gel. A drying mechanistic model showed that the drying process was conducted by the dissolution phenomena of CO2 into ethanol, the solvent, rather than convective evaporation. It indicated that the production of crack-free transparent aerogels depends on pressure, temperature, gel thickness, and CO2 velocity [12]. Other studies provided mathematical models and simulations of alumina/silica gels drying [14,17]. It was also shown that the aerogels properties depend on the nature of the gel (organic or inorganic) and the drying process duration [13]. The gel considered in this paper is an organogel, which is a physical gel composed of gelator molecules organized in a three-dimensional supramolecular network able to trap solvent molecules and preventing them from flowing [18]. The organogelation phenomenon involves some low molecular weight molecules

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(<2000 g mol−1 ), like n-alkanes (hexatriacontane [19]), crown ether [20], calixarene [21] and retains the interest of some scientists. These small molecules generally lead to thermoreversible gels, very attractive for numerous industrial applications [22–32]. Organogels are generally dried by an extraction process with supercritical CO2 to obtain aerogels [33]. These aerogels, besides the properties given above have another interesting characteristics: their hydrophobicity. In particular in the field of thermal insulation, hydrophobicity is a major advantage in the choice of material [34]. The Laboratory of Macromolecular Physical Chemistry (LCPM, Nancy, France) showed that it was possible to obtain gels from amino acid derivatives and appropriate organic solvents yielding the organogels employed in this study [35,36]. Once the solvent is extracted from the gel, the CO2 -solvent mixture needs to be separated. Several techniques may be used for gas-liquid separation, among which active centrifuges (i.e. rotational devices) and passive inertial equipment, e.g. cyclonic separation devices [37,38]. Cyclones are mechanical separators used to separate liquidliquid, solid-liquid, gas-solid or gas-liquid mixtures. They consist of a vertical pipe fed with the mixture through a tangential inlet, and of two outlets, one at the bottom and one at the top of the device. The tangential feed provides swirl motion to the incoming mixture which enhances the separation efficiency compared to gravity separators. Indeed, denser components undergo higher centrifugal forces and tend to accumulate near the wall and to fall down, being discharged from the bottom outlet, while lighter components exit from the top outlet. Cyclones do not require much maintenance (no moving parts) and their operating costs are low since they do not need much energy to operate [39,40]. A study of the CO2 /solvent separation is required after the supercritical extraction. For some processes, this separation was carried out by simple cooling of the mixture, a very economical technique [10,14,15]. Meanwhile, depressurization technique was also adopted by using cyclone separators [41,42]. The coupling of extraction/separation led some authors to study and model the two steps together [43]. However, few researchers have used or modeled cyclones to separate CO2 gas from a liquid, regardless of the extraction step as it is used in this work [44,45]. In this study, drying of organogels made of amino acids and toluene solvent are studied. Drying experiments are presented in Section 2. In these experiments, SC CO2 is blown around the organogel in order to extract the toluene. The CO2 -toluene mixture is then separated using cyclones. But poor separation efficiency is achieved: a large amount of solvent is not recovered in the liquid outlets. In order to determine the reasons behind this malfunction, a thermodynamic study and a hydrodynamic (Computational Fluid Dynamics, CFD) study of the cyclones are performed. CFD simulations were carried out, using the commercial code ANSYS Fluent, Section 3. They aimed at determining the efficiency of the mechanical separation in the cyclone. In Section 4, thermodynamic modeling is performed using PRO/II software, with the purpose of calculating the composition and state of the mixture at the cyclone outlet.

2. Experimental study 2.1. Products First, an amino acid organogelator is synthesized (see [35] for details). The obtained organogelator is then dissolved into the toluene solvent (C7 H8 ) under heating in a flask fitted with a reflux condenser. After cooling, the mix is poured into a cylindrical mold (30 mm diameter and 15 mm height) and stored at 4 ◦ C.

Fig. 1. Simplified scheme of supercritical drying.

2.2. Experimental set-up As it is shown schematically in Fig. 1, a cylindrical organogel of 30 mm of diameter and a thickness varying between 5 and 15 mm is initially submerged in toluene, in an extractor (autoclave) of 210 mL. It is then dried by pumping supercritical CO2 through the extractor at a flow rate ranging from 300 to 750 g/h. Temperature and pressure of supercritical drying are set to 45 ◦ C and 90 bar respectively, so that the toluene-CO2 mixture is supercritical [46]. The experiment duration varied from 90 min to 250 min depending on the run. Downstream of the drying unit, the mixture of SC CO2 and solvent (toluene) is depressurized in order to liquefy the toluene. The mixture is then transferred to a cascade of three cyclone separators, so as to mechanically separate the liquid toluene and the CO2 gas phases: hence, the solvent is recovered and CO2 is discharged outside of the unit. The drying process is composed of three main systems detailed in Fig. 2. In the feed line A, gaseous CO2 is initially fed from the cylinder at a pressure of 50–60 bar using valve 1. The gas is then cooled in the cold exchanger (I) down to a temperature of 4 ◦ C to be liquefied and flows through the LEWA pump (EK1). Next, the CO2 enters the damper (III), which reduces pressure fluctuations so as to provide steady operating conditions for drying. The CO2 flow then goes through a pressure regulator (IV) and a heat exchanger (V) so that it reaches the operating conditions of 90 bar and a temperature of 15 ◦ C (during step 1, Fig. 3) or 45 ◦ C (during step 2, Fig. 3). The second stream returns upstream the pump through the CO2 tank (II). At the outlet of the heat exchanger, the supercritical CO2 leaves the feed zone at 15 ◦ C or 45 ◦ C (Fig. 3) and 90 bar. A Coriolis mass flowmeter Micromotion (VI) measures the cumulative mass of CO2 (±1g.) and the instantaneous CO2 flow rate. In the autoclave B, the organogel is dried using SC-CO2 . Firstly, the organogel sample is introduced into the autoclave (VII), at an initial temperature of 15 ◦ C. In order to prevent premature evaporation of the solvent contained in the gel at the process starting up, it is submerged with a pure solvent volume (quantity of solvent added = 3.5 g). Valve 4 is opened while valve 5 is kept closed in order to fill the autoclave with liquid CO2 (15 ◦ C, 90 bar), which comes into contact with the organogel and the free solvent. A Bourdon manometer (P3, Fig. 2) provides a reading of the pressure in the autoclave. The system remains in these conditions for 35 min (Fig. 3: step 1 and 2). The temperature is increased in less than 10 min up to 45 ◦ C (Fig. 3, step 3). These conditions are maintained

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Fig. 2. Detailed presentation of the drying unit.

for 10 min during which the phenomenon of diffusion of the solvent in the CO2 begins (Fig. 3, step 3). Valve 5 is then opened and the dynamic regime of drying begins with SC CO2 flowing though the autoclave. The circulation is maintained for about 2 h. The different operating steps in the autoclave are explained in Fig. 3. The discharge line C is composed of three cyclonic separators (VIII, IX and X) of volumes 65.4 mL, 95 mL and 95 mL respectively used for CO2 -solvent separation. The cyclones (VIII and IX) are surrounded by a jacket through which water flows keeping the

temperature constant: the temperature is regulated at 20 ◦ C. Valve 5 at the autoclave outlet and valves 6 and 7 at the two first cyclones outlets are adjusted so that the desired flow rate is ensured and that the pressure in the first and second separators is maintained 50 and 30 bar respectively. Two Bourdon manometers (P4 and P5, Fig. 2) provide a reading of the pressure in the two cyclonic separators. Temperature measurements were performed inside the first cyclone (VIII) during a drying experiment and showed that the fluids temperature equals 20 ± 1 ◦ C.

Fig. 3. Temperature and pressure evolution in the autoclave during the different phases 1. Filling 2. Pressurization 3. Heating 4. Supercritical extraction 5. Depressurization 6. Cooling.

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Table 1 Toluene recovery for all conducted experiments. Run no.

Mean CO2 flow rate (g/h)

Drying time (min)

Mean toluene flow rate (g/h)

Initial molar fraction of toluene (%)

Experimental toluene recovery (%)

1 2 3 4 5 6 7

680 608 594 561 368 342 340

130 130 130 90 210 210 210

4.14 4.14 4.14 5.97 4.24 4.26 4.67

0.29 0.32 0.33 0.51 0.55 0.59 0.65

25.20 47.47 39.85 50.55 59.33 62.50 63.58

Experiments were conducted as follows: (i) every 15 min, the liquid phase at the bottom of the separators is collected, weighed (±0.1 mg) and the values of the flow rate and the pressure in the two first separators are noted. (ii) At the end of the drying process, the cumulative quantity of toluene recovered, and the mean values of CO2 flow rate and pressure in the first separator are calculated. (iii) The toluene recovery, ratio of the toluene cumulative quantity recovered at the end of drying over the initial total quantity of toluene in the autoclave, is determined. 2.3. Experimental results The results of seven runs are presented here. They were conducted according to the protocol described in Section 2.2. Only the CO2 flow rate and the initial quantity of toluene in the autoclave varied from an experiment to another. Most of the liquid was collected from the 1st separator and only a very small amount in the two others. In Table 1, the values of mean CO2 and toluene flow rates, mean molar fraction of toluene at the autoclave exit, and toluene recovery are reported for each experiment. The mean CO2 flow rate is the average value of the flows rates measured throughout the experiment; the mean toluene flow rate is the initial total quantity of toluene in the autoclave divided by the drying time; and the mean molar fraction of toluene is the ratio between the toluene and the total flow rate.

Fig. 4. Simulated geometry and main dimensions of the first cyclone separator in mm.

These experimental results show that the separation efficiency of CO2 -toluene mixture is not satisfactory. Indeed, the toluene recovery value does not reach over 64% for an experimental mean molar fraction of toluene varying between 0.2% and 0.7%. It also appears that higher recovery values are obtained at a higher toluene molar fraction. In the following sections, CFD (Section 3) and thermodynamic (Section 4) studies are carried out in order to determine the reasons behind this poor solvent recovery.

3. CFD modeling Gas-solid and liquid-solid cyclones, which have a cylinder-oncone body, are the most widespread in the industry. Accordingly, the swirl flow hydrodynamics in such devices has been widely addressed in the literature. On the other hand, relatively few studies have focused on the flow characteristics in gas-liquid cylindrical cyclones (such as those investigated in this paper) which are generally cylindrical. The flow field in cylindrical cyclones fed with a single-phase was investigated through CFD simulations in [47,48] Motta et al. [49] simulated the gas-liquid hydrodynamics in a cylindrical cyclone using a multi-fluid approach. Hreiz et al. [50] showed that the Realizable k-␧ turbulence model provides an accurate prediction of the hydrodynamics in cylindrical cyclones with a unique inlet. On the other hand, the Large Eddy Simulation (LES) approach is much more efficient for simulating the flow in cyclones with two inlets. Efficient gas-liquid separation in cyclones is limited by two phenomena: (1) Liquid carry-over (LCO) which corresponds to the flow rates beyond which part of the liquid is dragged with the gas through the cyclone’s top outlet. (2) Gas carry-under (GCU) which correspond to gas bubbles being carried by the liquid flow

Fig. 5. Schematic representation of the annular flow regime in a horizontal pipe.

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Fig. 6. Contour plots of the tangential (a) and axial (b) velocity fields at the central section vertical to the cyclone.

through the cyclone’s bottom outlet. These limiting phenomena were investigated in several studies, e.g. [51–53]. From the above-cited studies, it was suspected that the poor CO2 -toluene separation is due to LCO, i.e. liquid toluene carried over through the upper CO2 gas outlet. This may happen if the gas flow rate exceeds a certain threshold permissible by the system. In particular, this could happen if the liquid droplets generated by centrifugal forces were too small to be settled down by gravity. In order to verify this hypothesis, a CFD numerical study is accomplished in this section. This section focuses on the separation efficiency in the first cyclone only, since experimental data (Section 2) have shown that there is no significant recovery of liquid solvent (toluene) in the two remaining separators. The simulated geometry and dimensions are shown in Fig. 4. The CO2 flow rate adopted in this section is the maximum rate found in the experiments, 713 g/h, since the higher the flow rate, the more likely is the LCO. Temperature and pressure were set to their experimental values, 20 ◦ C and 50 bar respectively. 3.1. Simulation method 3.1.1. Turbulence modeling The density and the dynamic viscosity of CO2 under the cyclone operating conditions are 98 kg m−3 [54], and 3.15 × 10−5 Pa s [55] respectively. Hence, the Reynolds number of the CO2 flow in the cyclone inlet equals 4 900 which means that the flow is turbulent in this section. Accordingly, the Reynolds Averaged Navier–Stokes

equations were chosen to model the flow behavior. The Reynolds number calculated in the cyclone (using the cyclone diameter as characteristic length scale) equals 357, which corresponds to a laminar flow. Therefore, the k-kl -␻ model [56] was selected for modeling turbulence effects in the cyclone. Indeed, contrary to most turbulence models, k-kl -␻ is able to address flow conditions where both laminar and turbulent regimes exist within the device. It is supposed to predict a zero turbulent viscosity in laminar flow zones.

3.1.2. Flow pattern at the cyclone inlet The knowledge of the two-phase flow pattern in the cyclone inlet (i.e. the phases’ spatial distribution) is required in order to determine the suitable multiphase modeling approach and to set the inlet boundary conditions for the CFD model. At the cyclone inlet, the superficial velocity (volume flow rate divided by the pipe section) of CO2 gas equals to 1 m s−1 , and that of toluene (density of 866 kg m−3 and viscosity of 5.9 × 10−4 Pa s) under current operating conditions [57] is about 6.6 × 10−4 m s−1 . The surface tension of toluene in CO2 calculated by PRO/II under these operating conditions is equal to 4.7 × 10−3 N m−1 . Under these flow rate conditions, the model of Petalas and Aziz [58] predicts an annular flow pattern (Fig. 5) at the inlet pipe. This flow regime consists of a liquid film flowing on the pipe wall, with liquid droplets entrained in the core of the flow. According to the model of Petalas and Aziz [58], the thickness of the

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parietal liquid film is about 41 × 10−6 m only and the fraction of liquid entrained in the droplets equals 66.55%. 3.1.3. Multiphase flow modeling strategy It is very hard to simulate the hydrodynamics of annular flows since they include a continuous interface, i.e. the annular film, as well as dispersed liquid droplets in the core of the flow. Indeed, multiphase flow models commonly used nowadays are suitable for simulating segregated flows (e.g. the Volume of Fluid, VOF [59], approach) or dispersed flows (e.g. the Euler–Euler or the Euler–Lagrange approaches) [60]. This study aims at determining whether or not liquid entrainment occurs at the top cyclone outlet, rather than predicting the detailed features of the flow at the separator inlet. Accordingly, the following simulation procedure has been adopted: (1) A preliminary single-phase flow simulation was conducted, assuming that CO2 gas only is present in the cyclone because the mole fraction of toluene is very low. Calculations are performed using a steady solver. The goal of this simulation is to provide a realistic initial flow field for the two-phase flow simulations (which require a large computation time). (2) From the flow field obtained previously, two-phase flow simulations are conducted using the VOF approach. VOF is an interface tracking technique: it allows reconstructing the position of the interface between the fluids of interest. The conducted VOF simulation aims at determining whether or not the liquid solvent contained in the annular film reaches and exits from the cyclone top outlet. No consideration is given here to the solvent droplets (since VOF is not suitable for simulating dispersed flows), whose behavior is addressed in the next simulation step. (3) The Euler–Lagrange approach, named DPM (for Discrete Phase Model) [60], is used to simulate the droplets trajectory and to predict whether or not they are carried over to the top cyclone outlet. DPM treats droplets as mass points, and their trajectories are tracked individually using Newton’s second law. According to [61,62], the size of nuclei, arising from homogeneous condensation is in the range of 0.1–50 ␮m. Therefore, DPM simulations were run using different droplets size, between 0.1 to 50 ␮m. Only drag and buoyancy were accounted for in the force balance, since the influence of other forces is expected to be less meaningful. The drag coefficient was calculated using the well-known Morsi and Alexander’s correlation. It is noteworthy that in all simulations, the flow was considered isothermal, and the fluids were treated as incompressible (since pressure is relatively uniform within the cyclone) and immiscible. 3.1.4. Numerical schemes The flow equations are solved using the ANSYS Fluent code. The convective terms are discretized using the QUICK scheme, and the diffusion terms are central-differenced. In multiphasic VOF simulations, advancement in time is achieved through a second-order implicit scheme, and the interface is tracked via the implicit compressive scheme. As noted previously, the objective is to estimate the transport of the liquid film rather than predicting accurately the likely wavy shape of the free interface. In DPM simulations, a 5th order Runge-Kutta scheme is used to compute the trajectories of the liquid droplets. 3.1.5. Computational mesh The computational domain and the mesh were created using the Gambit software. The computational mesh consisted mainly of hexahedral non-uniform elements. The grid was refined near the

Fig. 7. Mean velocity profiles at 34, 84,124 and 154 mm below the inlet level (a) Mean tangential velocity, (b) Mean axial velocity.

walls to allow the y+ values (the nondimensional thickness of the mesh cells located at the wall) to be in the correct range, less than 1, as required by the k-kl-␻ turbulence model [56]. In order to perform a grid-dependency test, the preliminary single-phase flow simulations were carried out on two meshes consisting of 450,000 and 700,000 cells respectively. Similar results were obtained using both grids, indicating that these meshes are sufficiently refined to achieve a mesh-independent solution. Accordingly, only the 450,000 cells mesh was used in the multiphase flow simulations in order to reduce the computational efforts. 3.1.6. Boundary conditions An imposed flow rate condition is set at the pipe entrance. In VOF simulations, following the results of Section 3.2, the inlet section has been divided into two parts: a 41 × 10−6 m thick annulus space and a core section from where the liquid and the CO2 gas respectively enter the computational domain. Given that the cyclone is operated in batch mode, its bottom outlet was assumed closed, and was hence treated as a wall. No-slip conditions were imposed at the walls. In the DPM model, droplets reaching the walls of the cyclone were assumed to merge into a parietal liquid film (i.e. separated from the main flow), and hence, they were removed from the calculations.

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3.2. Results of the single-phase flow simulations The numerical results revealed that the flow field is fairly axisymmetric (Figs. 6 and 7) despite the use of a single inlet: vortex warping was not much significant since no nozzle was used to accelerate the flow [52]. Fig. 7(a) shows that the tangential velocity follows the typical mean tangential velocity profile in swirl flows, among others [63]. It corresponds to a forced vortex (i.e. solid body motion flow) near the center of the cylinder, and a free vortex (i.e. irrotational flow) near the wall. The free vortex region becomes larger when moving down from the cyclone inlet (x = 124 mm and x = 154 mm). In the immediate vicinity of the wall, a boundary layer region exists where the tangential velocity decreases with a steep gradient to reach zero at the wall. The axial velocity profile shown in Fig. 7(b) includes a flow reversal near the pipe center, which is typically encountered in cyclone separators. Given the swirl motion, velocities were large in the near-wall region, while low velocities were encountered in the vortex central zone. Velocity magnitudes were found to decrease rapidly in the downward direction because of viscous dissipation. Concerning the pressure field, CFD results have revealed that the difference between the minimum and the maximum pressures occurring in the cyclone is about 35 Pa only. This outcome validates the uniform pressure assumption employed in the thermodynamic model (Section 4). 3.3. Results of VOF simulations VOF simulations were conducted using an unsteady solver, with an adaptive time step in the range of 10−4 to 5 × 10−2 s. As noted before, these simulations aim at estimating the flow path of the annular liquid film rather than predicting accurately the shape of the interface. As shown in Fig. 8, the liquid flows around the walls, and comes down to the underside of the cyclone. The toluene film does not reach the cyclone top outlet: hence, no liquid carry-over occurs under the investigated operating conditions. 3.4. Results of DPM simulations DPM simulations were carried out using different droplet sizes: 0.1, 1, 10 and 50 ␮m. It is noteworthy that, for simplification purposes, only one-way momentum coupling have been considered, i.e. it was assumed that the droplets motion do not influence the CO2 velocity field. For all investigated droplets diameters, DPM predicted 100% liquid separation efficiency, which means that all droplets were ‘trapped’ on the separator walls and none could reach the cyclone top outlet. Although DPM may overestimate the separation efficiency of very small droplets (as the Brownian motion effects are not taken into account), however, VOF and DPM models indicate clearly that the liquid toluene and gaseous CO2 are efficiently separated in the cyclone. Therefore, the poor separation efficiencies observed experimentally are likely to be related to thermodynamic equilibrium issues. This hypothesis is investigated in the next section. 4. Thermodynamic modeling As was shown in Section 3, the low separation efficiency is not caused by problems inherent to the mechanical behavior of the cyclone. It is now investigated whether the poor separation is due to thermodynamic reasons. An equilibrium stage model is used to simulate the behavior of the separator and a thermodynamic model

Fig. 8. Distribution of toluene volume fraction at the central section vertical to the cyclone.

is thus required to generate binary phase diagrams. The effect on the recovery of different parameters such as pressure and inlet composition is investigated. 4.1. Simulated separation process flowsheet The accuracy of the equilibrium stage model for the cyclone strongly depends on the choice of an appropriate thermodynamic model to describe the mixture behavior at the operating conditions (pressure ranging from 40 to 60 bar and temperature fixed at 20 ◦ C). To validate or estimate model parameters, experimental vapor-liquid equilibrium data points related to the CO2 -toluene system and close to the operating conditions of the cyclone are available in the open literature (see Table 2). Different approaches were considered to model the experimental data.

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Table 2 Database of binary system CO2 -Toluene. Temperature range (K)

Pressure range (bar)

x1 range (liquid mole fraction)

y1 range (gas mole fraction)

Number of bubble points

Number of dew points

Number of critical points

References

282.9–353.4

2.59–123.50

0.0120–0.9950

0.8560–0.9989

265

142

17

[46,64,70,71]

Tochigi and Hasegawa [46] correlated their data using the Peng Robinson (PR) equation of state (EoS) with one binary interaction parameter and the PRASOG (Peng-Robinson, analytical solutions of groups) group-contribution method; parameters groups relating the pairs CH2 /CO2 and ArCH/CO2 finding a good agreement at pressures below the critical point [46]. Nemati Lay and Taghikhani used the PR EoS as well to correlate the vapor-liquid equilibrium data of the system; an accurate modeling of the data was reached using the PR EoS [64]. The thermodynamic modeling of the CO2 -solvent separation in cyclones downstream of a supercritical drying operation has been the subject of very few studies. The only existing work has been carried out with the simulation software PRO/II, for a CO2 and isopropanol mixture [44,45]. In this study, Camy and Condoret, described in two different ways the separation step; in the first one, the cyclonic separation was regarded as a theoretical stage, in which the vapor outgoing quantity and the liquid hold-up are in equilibrium. In the second approach, the equilibrium is assumed directly after the valve; then, the gas and the liquid phases undergo a perfect segregation in the separator. Many CFD models on cyclone separators of different geometries have shown that the pressure drop is very small for fluid velocities less than 5 m/s [65–67]. The present CFD results, and calculations by empirical and semi-empirical models [68] show that the pressure drop is less than 87 Pa. This value is small and allows to consider the pressure uniform throughout the separator. Therefore, despite the complex nature of the separation process occurring in a cyclone, it was attempted to model the first cyclone as a simple theoretical equilibrium stage, similarly to the approach used by Camy and Condoret [44,45]. The validity of this assumption is discussed at the end of the section. Simulations were carried out using the software PRO/II, a steady state chemical-engineering process simulator, as shown in Fig. 9. The pressure and temperature in stream S1 (upstream of the cyclone separators) are the pressure and temperature of the CO2 toluene mixture leaving the autoclave. They are assumed to be constant and equal to 90 bar and 45 ◦ C, respectively, in accordance with the experiments. The temperature and pressure of the first cyclone were set to 20 ◦ C and 50 bar, respectively. The composition of the inlet stream S1 was calculated using the previous experimental results (Table 1), by taking into account the quantity of toluene initially placed in the autoclave, the carbon dioxide flow rate injected through the system and the time during which the process took place. Based on averaged experimental values, the molar fraction of toluene was assumed to vary between 0.002 and 0.007 (hence a CO2 fraction of 0.998 and 0.993). Note that although the real separation process works in a batch mode, it was decided to assume that the series of cyclones works in a steady state due to the rather long operating times.

Fig. 9. Modelling of the first cyclone as a single flash drum. S1: inlet stream containing a mixture of CO2 -solvent; S2 is the gaseous outlet. S3 is the liquid outlet.

4.2. Presentation of the selected binary mixture thermodynamic model The thermodynamic modelling of a supercritical separation process requires the use of an equation of state (EoS) capable of managing high-pressure fluid-phase behaviour.

Fig. 10. Isothermal phase equilibrium diagrams. Continuous lines: bubble and dew curves. calculated using the Peng–Robinson EoS. (+) experimental bubble point (*) experimental dew point. bold line = tie-line at 293.15 K and 50 bar (operating conditions of the first cyclone). (a) T = 293.15 K, (b) T = 308.15 K.

M. Lazrag et al. / J. of Supercritical Fluids 118 (2016) 27–38

The Peng–Robinson cubic EoS [69] was selected because of both its simplicity and reliability for the class of compounds considered. For pure components, this model writes: P(T, v) =

RT ai (T) − v − bi v(v + bi ) + bi (v − bi )

⎧ R = 8.314472 J · mol−1 · K−1 ⎪ ⎪   ⎪ √ √ ⎪ 3 3 ⎪ −1 + 6 2+8− 6 2−8 ⎪ ⎪ ≈ 0.2531 X= ⎪ ⎪ 3 ⎪ ⎨ bi = b

RTc,i

with : b =

X

Table 3 Deviations resulted from the use of optimized binary interaction parameters (AAD = Average Absolute Deviation; ARD = Average Relative Deviation) of the binary system CO2 -toluene.

(1)

where P, T and v denote the pressure, absolute temperature and molar volume of the pure fluid, respectively; ai and bi are the socalled cohesion parameter and covolume given by:

35

AAD ARD(%)

Liq. mole fractions

Gas. mole fractions

Critical mole fractions

Critical pressure (bar)

0.024 9.7

0.005 9.5

0.005 11.8

1.4 1.6

specifically appropriate for the temperature, pressure and composition ranges of interest. For the binary system (CO2 - toluene), the BIPs were expressed as follows:

≈ 0.07780

Pc,i X+3 ⎪ ⎪ ⎪ 2  2 2  ⎪ R T ⎪ 8 (5X + 1) ⎪ ≈ 0.4572 with : a = ⎪ ai (T) = a P c,i 1 + mi 1 − TT ⎪ 49 − 37X c,i c,i ⎪ ⎪ ⎩

(2)

mi = 0.37464 + 1.54226␻i − 0.26992␻2i

Classical one-fluid Van der Waals mixing rules were used to extrapolate the pure-component EoS to mixtures:

kij = Aij +

Bij (T/K)

(WithAij = Aji , Bij = Bji , Aii = 0, Bii = 0)

Constant parameters Aij and Bij were determined in order to minimize deviations between experimental and calculated values of bubble-point compositions, dew-point compositions, critical-point compositions and pressures. The following objective function was considered: Fobj =

Fobj,bubble + Fobj,dew + Fobj,crit. comp + Fobj,crit. pressure nbubble + ndew + 2ncrit

⎧   nbubble ⎪ |x| |x| ⎪ ⎪ Fobj,bubble = 100 0.5 + with |x| = |x1,exp − x1,cal | = |x2,exp − x2,cal | ⎪ ⎪ x1,exp x2,exp ⎪ i ⎪ i=1 ⎪ ⎪  ndew ⎪ ⎪  |y| ⎪ |y| ⎪ ⎪ F = 100 0.5 + with |y| = |y1,exp − y1,cal | = |y2,exp − y2,cal | obj,dew ⎪ ⎨ y1,exp y2,exp i i=1   ncrit ⎪ ⎪ |xc | |xc | ⎪ ⎪ F = 100 0.5 + with |xc | = |xc1,exp − xc1,cal | = |xc2,exp − xc2,cal | obj,crit. comp ⎪ xc1,exp xc2,exp ⎪ ⎪ i ⎪ i=1 ⎪ ⎪  ncrit  ⎪ ⎪ |Pcm,exp − Pcm,cal | ⎪ ⎪ F = 100 ⎪ ⎩ obj,crit.pressure Pcm,exp

⎧ N N 

 ⎪ ⎪ ⎪ a(T, z) = zi zj ai (T) · aj (T) 1 − kij ⎪ ⎨ i=1 j=1

(5)

(6)

i

i=1

N ⎪ ⎪ ⎪ ⎪ zi bi ⎩ b(z) =

(4)

(3)

i=1

where zi represents the mole fraction of component i, ␻i the acentric factor of component i and N is the number of components in the mixture (N = 2 for binary systems). The kij parameter, whose estimation is difficult even for the simplest systems, is the so-called binary interaction parameter (BIP) characterizing the molecular interactions between molecules i and j. The common practice is to fit kij to reproduce the vapour–liquid equilibrium data of the mixture under consideration. 4.3. Estimation of binary interaction parameters (BIPs) Since the separation units work at a unique temperature (20 ◦ C), the BIPs could be considered as constant parameters. However, in order to extend the range of applicability of the Peng–Robinson equation of state (e.g., for determining optimal working temperatures in a future study or to model another separation process involving a temperature gradient), it was decided to consider BIPs as temperature-dependent functions. Note that the PPR78 model could have been used to estimate the BIPs [70]; in the present article, it was however decided to develop a simple correlation for BIPs,

nbubble , ndew and ncrit are the number of bubble points, dew points and mixture critical points respectively; xi and yi are the mole fractions of component i in the liquid and gas phases at given temperature and pressure; xci and Pcm denote the critical mole fraction of component i and the critical pressure at a specified temperature. The references, temperature range, pressure range and composition range of the experimental data (bubble points, dew points and critical points) that were considered to fit parameters of the BIP correlation are reported in Table 2. The quasi-Newton BFGS (Broyden–Fletcher–Goldfarb–Shanno) method was used to perform the regression procedure. The results of the optimization procedure are summarized in Table 3. The values of the fitted parameters for the CO2 -toluene binary system are the following:



A12 = A21 = 0.062255 B12 = B21 = 9.177K

(7)

In order to illustrate the performance of the proposed model, Fig. 10 compares calculated and experimental isothermal phase diagrams. The phase behaviour of the CO2 -toluene system is classically affected by the important size asymmetry between both molecules: the dew curve is indeed almost a vertical line (which means that the gaseous phase only contains nearly-pure CO2 ). The PR EoS shows a good modelling capacity of this binary system. Although, the model tends to slightly underestimate bubble pressures and to overestimate critical pressures, acceptable estimations of solubility in the liquid and gas phases can however be obtained in the pressure domain covered by the separation process.

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M. Lazrag et al. / J. of Supercritical Fluids 118 (2016) 27–38

Table 4 Comparison of theoretical and experimental results of recovery at 20 ◦ C and 50 bar. Mean molar fraction of toluene (%)

Experimental recovery (%)

Theoretical recovery (%)

Relative deviation (%)

0.29 0.32 0.33 0.51 0.55 0.59 0.65

25.20 47.47 39.85 50.55 59.33 62.50 63.58

34.1 40.4 42.24 63.1 66.2 68.56 71.57

26.10 17.50 5.66 19.89 10.38 8.84 11.17

4.4. Results and conclusion 4.4.1. Simulation and comparison with experimental results The developed thermodynamic model presented in this section was incorporated into the PRO/II software and the separation of the CO2 -toluene mixture was simulated using a single flash drum. The solvent recovery is defined as: gasphase

solvent recovery = gasphase

n˙ toluene

feed n˙ toluene

=

ytoluene ztoluene − xtoluene · ztoluene ytoluene − xtoluene

(8)

feed

where n˙ toluene and n˙ toluene denote the molar rates of toluene in the gas outlet and in the feed of the cyclone, respectively; ytoluene , xtoluene and ztoluene are the mole fractions of toluene in the outlet gas phase, in the outlet liquid phase and in the feed, respectively. The solvent recovery was evaluated (Table 4) and the results obtained were compared to the average values of experimental recovery (see Table 1) for molar fraction of toluene varying between 0.007 (0.993 of CO2 ) and 0.002 (0.998 of CO2 ). It is thus observed that a single flash drum simulation using the PR EoS with temperature-dependent kij reasonably explains the less satisfactory performances that were observed when toluene is used as a solvent. The deviations observed between theoretical and experimental recoveries can certainly be assigned to the strong assumptions that were previously presented and are now reminded: - The simulation was performed considering a steady state and assuming that the compositions of the inlet stream as well as the inflow rate of CO2 were constant during the process. - Experimentally, a steady state is difficult to reach since the concentration of solvent in the CO2 stream is difficult to control; indeed, it is reminded that carbon dioxide is circulated around a matrix made up of a gel immersed in a fixed quantity of solvent in order to remove the solvent. Consequently, the concentration of solvent in the CO2 stream decreases as time increases. Besides, it is

Fig. 12. Variation of recovery rate as function of pressure for different inlet mole fractions of toluene.

difficult to maintain constant pressure in the separators, thus the pressure in the first separator fluctuated between 45 and 60 bar. - The first cyclone is equivalent to a single flash drum. 4.4.2. Simulation with different input compositions and pressures From the experimental results, it has been observed that a difference of molar fraction of toluene from 0.3 to 0.4% changes considerably the recovery. Therefore, to study the effect of toluene concentration (or equivalently, of CO2 concentration) on the toluene recovery, several simulations were carried out at 50 bar and 20 ◦ C by varying only the inlet fraction of toluene by going up from 0.1% to 2%. The obtained recovery values are shown as a function of concentration of toluene in Fig. 11. For higher inlet toluene concentrations, a good recovery of the solvent is achieved. On the other hand, when concentration is low, especially below 1% molar as in the experimental conditions, separation becomes more difficult. It is also seen that for compositions below 0.25 mol%, the thermodynamic behavior of the mixture allows very little recuperation of toluene in the liquid phase. The effect of pressure was also investigated. The pressure in the cyclone was varied, for 20 ◦ C temperature, in order to obtain the highest possible recovery. This was performed for different inlet compositions. The obtained recoveries are shown in Fig. 12. It seems that the pressure, below 50 bar, does not affect the recovery. Beyond this value, the recovery constantly increases, reaching values up to 95%. Nevertheless, this high performance is due to the fact that, at higher pressure, the mixture is closer to reaching the liquid state; then not only toluene is recovered in the liquid outlet, but also large amounts of liquid CO2 . It is found that at 20 ◦ C, for a molar fraction ranging between 0.2% and 1%, a pressure of 56 bar yields the highest recovery of toluene (98%), thus this value should be chosen for the best operating pressure. 5. Conclusion

Fig. 11. Variation of recovery rates as a function of initial composition of toluene.

Cyclone is a common device adopted for separating a gas-liquid mixture. However, cyclonic separation downstream of the drying process of organogel, studied here is not satisfactory. CFD numerical and thermodynamic studies were carried out in order to determine the reasons behind this malfunction. The CFD numerical study, performed with ANSYS-Fluent, consisted of 3 steps. Firstly, a preliminary single-phase flow simulation was run, assuming that gas CO2 only is present in the cyclone. Calculations were run using a steady solver. Then, from the flow field obtained previously, two-phase flow simulations were conducted

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using the Volume Of Fluid approach. This simulation determined that the liquid toluene film existing at the cyclone walls does not reach the gas outlet. Finally, a Discrete Phase Model simulation, calculated the droplets trajectory and predicted again that they are not carried over to the gas top outlet. The CFD study thus shows that the liquid is not entrained to the exit gas, showing that hydrodynamics favors separation. The thermodynamic modeling was carried out by assuming that the series of cyclones behaves as a simple theoretical equilibrium stage. The Peng-Robinson equation of state combined with classical mixing rules involving a temperature-dependent binary interaction parameter was selected. Several simulations were carried out for varying inlet concentrations and pressures. They predicted a poor recovery rate, in good agreement with the experimental values and indicated that, for a concentration of toluene ranging between 0.2 mol% and 0.7 mol%, pressure should be set to 56 bar in order to recover the maximum quantity of toluene under liquid state.

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