13 Poly(oxymethylene) dimethyl ethers (OME) are interesting synthetic fuels : they have better 14 combustion properties than fossil diesel fuel and can be obtained from renewable resources. 15 Furthermore, they can be blended with hydrogenated vegetable oils (HVO) to obtain a new class 16 of environment ally benign fuels. However, it has been observed in technical processes that initially 17 homogen eous mixtures of (OME + HVO) split into two liquid phases after some time , which is 18 unacceptable for use as fuel s. It is assumed that this de-mixing is a conseque nce of the uptake of 19 small amounts of water from the air by the mixtures. However, u p to now, only qualitative 20 information on this phenomenon was available. We have, therefore, carried out systematic 21 experimental studies of liquid -liquid equilibria (LLE) a nd liquid -liquid -liquid equilibria (LLLE) 22 in ternary model systems of the type (OME + n -alkane + water) at temperatures between 265 to 23 293 K. The n -alkanes were (n -dodecane, n -hexadecane); two different OME were studied, OME 2 24 HVO Hydrogenated vegetable oils LLE Liquid -liquid equilibria LLLE Liquid -liquid -liquid equilibria NMR Nuclear magnetic resonance OME Poly(oxymethylene) dimethyl ethers PC-SAFT Perturbated chain statistical associating fluid theory UNIFAC Universal quasichemical functional group activity coefficients Tol Toluene W Water 3 and OME 4, respectively. Additi onally, also multicomponent mixtures containing different OME 25 and mixtures containing additionally the aromatic hydrocarbon toluene were studied. The results 26 were modeled using UNIFAC, a group -contribution model of the Gibbs excess energy, and a good 27 corre lation of the observed comple x phase behavior was obtained. The results from the present 28 work confirm that the uptake of small amounts of water is the reason for the phase split observed 29 in technical ( OME + HVO ) mixtures. Measures to circumvent this proble m are discussed. 30 31 1. Introduction 32 33 The use of synthetic fuels produced from renewable resources can make a significant 34 contribution to moving away from fossil fuels and , thus, reducing greenhouse gas emissions. [1– 35 4] Furthermore, s ynthetic fuels can offer also additional advantages such as lower emissions of 36 soot or nitrous oxides. [3,5] Two particularly interesting synthetic fuels are poly(oxymethylen e) 37 dimethyl ether s (OME) and hydrogenated vegetable oil s (HVO). 38 OME are oligomers with the general st ructure CH 3-O-(CH 2O)n-CH 3 with n ≥ 2. We use OME 39 here to designate OME in general and OME n to designate a specific OME. For the use as fuel s 40 OME n with 3 ≤ n ≤ 5 are most interesting . [4,6,7] These oligomers have similar physical 41 properties as fossil diesel but produce much less soot upon combustion bec ause they contain 42 oxygen in their backbone. OME are produced from methanol, which, in turn, is produced from 43 synthesis gas, which can be obtained from biogas as well as from carbon dioxide and hydrogen, 44 i.e. OME can be obtained from renewable resources. [8,9] This enables establishing a closed 45 carbon cycle to minimize greenhouse gas emission s. Efficient production of OME is a major focus 46 of recent research, e.g. [10–19] 47 4 HVO are produced from triglyceride acids obtained from plants such as oilseed rape, and are 48 often designated simply as “oils”. HVO contain mainly n -alkanes, but also some branched alkanes, 49 with C -numbers typically between 15 and 20, but basically no sul fur, nitrogen , or aromatics . [4,20 – 50 23] HVO have similar physical properties as fossil diesel , but higher cetane numbers and lower 51 toxic emission s. [24,25] It can be us ed directly as a diesel substitute without any modification of 52 the engine . Only at low temperatures , the high viscosity can cause problems in some cases. [25] 53 HVO are already produced on a large scale, whereas there are only a few facilities for OME 54 production. T he use of blends of (OME + HVO) is of great interest for a market launch of OME. 55 [4,19,26] 56 One problem wi th the application of blends of (OME + HVO) is the miscibility [3,18,27 –29]. 57 HVO are non-polar , while OME are moderately polar, due to the oxygen in the backbone. This 58 can induce a miscibility gap in mixtures of (OME + HVO), which, however, is typically not large 59 and can be avoided by a suitable c hoice of the composition. This is mandatory for the application 60 as fuel s, where homogen eity of the fluid is required. However, it is known that initially 61 homogen eous mixtures of (OME + HVO) show a liquid -liquid phase split after some time in many 62 technical applications. Typically, not only a small amount of the second phase is formed, but the 63 amounts of both phases can be of the same order of magnitude, with one ph ase being OME -rich 64 and the other HVO -rich. Only qualitative information on this phenomenon is available in the 65 literature [3,18,27 –29] and its reasons are not fully understood. A hypothesis is that the initially 66 homogen eous (OME + HVO) mixture takes up small amounts of water from the air, which in duces 67 the phase split – however not by forming a (small) second water -rich phase, but by leading to a 68 separation of OME and HVO. 69 5 This phenomenon was studied in the present work by phase equilibrium experiments, in which 70 liquid -liquid equilibria (LLE) , as w ell as liquid -liquid -liquid equilibria (LLLE), were measured, 71 and by accompanying modeling and simulation . A challenge in designing a such study is that both 72 HVO and technical OME are mixtures. The composition of HVO depend on the raw material and 73 producti on process, and also the composition of technical OME varies. We have therefore decided 74 to carry out experiments with model components. Two OME were used: OME 4 because it is in the 75 middle of the typical range of OME n components in OME -fuels (OME 3 – OME 5). Additionally, 76 we have also included OME 2 in the study, to get information on the influence of the chain length 77 of the OME n on the results. Longer OME n were not used, as they were not available in sufficient 78 amounts as pure components. As model component fo r HVO, n -hexadecane was used. Also here, 79 the influence of the chain length on the results was investigated by including n -dodecane in the 80 study. Longer n -alkanes were not studied to avoid experimental problems with solid -precipitation 81 at room temperature. Hence, LLE and LLLE in well -defined binary and ternary mixtures of the 82 type (OME n + n-alkane + water) were studied. 83 Additionally, also an OME -mixture, as it is used in fuels, was included in the study. Furthermore , 84 also mixtures containing toluene were in vestigated, to see whether problems with de -mixing could 85 also occur in mixtures of OME with fossil diesel fuel, which contains considerable amounts of 86 aromatic hydrocarbons , in contrast to HVO. 87 There are only a few studies in the literature on LLE in the s ystems that are of interest here , 88 Table 1 gives an overview. 89 90 91 6 Table 1 Overview of experimental studies of LLE in systems that are related to the ones studied 92 in the present work. 93 system source OME n + water Schmitz et al. [30] n-alkanes + water Mokbel et al. [31] n-alkanes + water Sutton et al. [32] OME n + n-hexane + water Zhuang et al. [33] OME 3 + (n-heptane, p -xylene, toluene) + water Shi et al. [34] OME 1 + (cyclohexane, n -heptane) + water Shi et al. [35] OME n + o-xylene + water Li et al. [36] OME n + toluene + water Li et al. [37] 94 In none of these studies , a phase split between OME and hydrocarbons was observed . The 95 present work is the first in which this phenomenon is studied in detail, in particula r regarding the 96 important influence of water. 97 Modeling LLE in mixtures containing small, highly polar components, such as water, and large 98 non-polar or weakly polar components (as the n -alkanes and OME studied here) is challenging. 99 We have tried two options: modeling with molecular equations of state (EOS), namely PC -SAFT 100 [38,39 ], and modeling with UNIFAC [40], a group -contribution model of the Gibbs excess energy. 101 In both cases , the model parameters were fitted to the experimental data. The latter is distinctly 102 simpler and, as preliminary tests with P C-SAFT indicated no advantages, we have decided to 103 continue only with UNIFAC, and report here on the results, which were obtained with this method . 104 The UNIFAC model enables predictions of the complex phase behavior of the studied ternary 105 systems, some of w hich show not only LLE but also liquid -liquid -liquid equilibria (LLLE). 106 There are only two modeling and simulation studies of related systems in the literature, in which, 107 however, other models were used. Recently, Yang et al. [41] carried out a simulation study on the 108 miscibility of OME n with model components of diesel fuel using the COSMO -RS method. [42] 109 7 Yu et al. [43] investigated the miscibility of OME with diesel fuel components using molecular 110 dynamics simulations. These simulation studies focus on similar systems like the already 111 mentioned experimental studies and do not me ntion the phase split between OME and 112 hydrocarbons or they are predictive and show no experimental proofs. 113 114 2. Experimental Apparatus and Procedure 115 116 2.1 Chemicals 117 118 OME 2 and OME 4 were provided by BASF SE with a purity of 0.985 g g-1. The main impurities 119 are minor amounts of shorter OME, which were identified using the NMR method from Breitkreuz 120 et al. [44]. As they are only present in small amounts and chemically similar to the main 121 component, the influence of these impurities on the results is expected to be only minor. The OME - 122 mixture was provided by ASG Anal ytik-Service. The OME -mixture comprised OME 3 (0.58 g g-1), 123 OME 4 (0.27 g g-1), OME 5 (0.11 g g-1), and OME 6 (0.04 g g-1). n-dodecane (C12), purity > 0.99 g g-1, 124 was purchased from ThermoFisher. n-hexadecane ( C16), purity > 0.99 g g-1, and toluene ( Tol), 125 purity > 0.998 g g-1, were purchased from Merck. The purified water (specific resistance > 15 126 MΩ cm-1) was prepared with a Milli -Q system from Merck Millipore . 127 128 2.2 Phase equilibrium measurements 129 130 For the measurement of LLE, feed mixtures of different compositions were prepared from the 131 pure components , except for the feed mixtures with low water fraction , for which not pure water 132 8 but OME was used that was saturated with water at 293 K. Where appropriate, OME was dried 133 with molecular sieve (3A) before use. For the preparation of the feed mixtures, a n analytical 134 balance (AG 204, Mettler Toledo ) was used and the composition was calculated based on the 135 masses of the pure substances. 136 For the measurements at 293 K, 20 g of the fee d mixture was filled into a glas s vial which 137 contained a magnetic stir bar , and was closed with a septum cap. The closed vial was stored in a n 138 air-thermostatted cabinet on a magnetic stir plate. The mixture was stirred for at least 24 hours. 139 Then , the stir rer was turned off and the phases were allowed to settle for at least 48 hours. These 140 values were chosen based on preliminary experiments, which showed that a further prolongation 141 did not yield significantly different results. Subsequently, samples of the different phases were 142 taken with syringes through the septum. Before use, the syringes were dried in an exsiccator that 143 was filled with dried molecular sieve for at least 48 hours. The temperature was measured in the 144 cabinet with a calibrated platinum resistance thermometer. In preliminary experiments, in which 145 the temperature was also measured in a vial, the maximal temperature difference between the air 146 and the vial was measured. The overall uncertainty of the reported temp erature in the vial is 147 estimated to be 0.1 K. 148 For the measurement s at 278 and 265 K , 40 g of the feed mixture was filled into a glas s vial with 149 a cooling jacket , which, in turn, was isolated from the surroundings by a vacuum jacket . The vial 150 was equipped w ith a magnetic stir bar . The cooling medium was a mixture of water and 151 monoethylene glycol and was thermostatted with a cryostat. The temperature inside the vial was 152 measured with a platinum resistance thermometer (uncertainty of 0.1 K) . The times for mixi ng and 153 settling were the same as in the measurements at 293 K. After the settling period samples from the 154 9 different phases were taken through septa which are located at different heights of the vial. For the 155 sampling dried syringes were used. 156 All experimen ts were carried out at ambient pressure (1 bar ± 0,05 bar ); as only equilibria with 157 liquid phases were studied variations of the pressure have no significant influence on the results. 158 This could, however, be different for the pressures used in injection s ystems in diesel engines, 159 which can be more than 1000 bar. No replica measurements were done, as the number of 160 experiments for each studied system was large enough to check the quality of the data by 161 considering their continuity. 162 163 2.3 Chemical Analysis 164 165 Only the samples from the coexisting phases were analyzed. The composition of the feed was 166 known from the gravimetric preparation. The uncertainty of the feed composition is better than 167 0.001 g g-1. 168 All samples were first analyzed with quantitative 1H-nuclear magnetic resonance (NMR) 169 spectroscopy to determine the concentrations of OME, water, and the hydrocarbons . The 170 equipment was the same as described by Breitkreuz et al. [44] The acquisition parameters were 171 the following: flip angle : 90°, acquisition time : 4 s, repetition time : 20 s, 8 scans, and 65 k data 172 points. The peak assignment was done in preliminary studies based on experiments with pure 173 components and mixtures . For the evaluation of the spectra , the software MestReNova 14.2 was 174 used and it was assumed that the proportionality constant relating the peak area to the amount of 175 substance is the same for all peaks. Sample spectra and the peak assignment are reported in the 176 Supporting Information. Results from test measurements with samples that were prepared 177 10 gravimetrically showed that the uncertain ty for the results for the concentrations of the different 178 components do es not exceed 0.01 mol mol-1. For the measurements with the OME -mixture, 179 additionally 13C NMR spectroscopy was used to avoid problems with peak overlaps. The procedure 180 was adopted from Breitkreuz et al. [44] For samples with water -content s below 0.1 g g-1, 181 additionally , Karl-Fischer titration was used to determine the water concentration ( for mass 182 fractions in the range of 0.1 to 0.005 g g-1 volumetric Karl -Fischer titration and below 0.005 g g-1 183 coulometric Karl -Fischer titration) . Each t itration was carried out at least three times and the mean 184 value was used as the result . The uncertainty of the Karl-Fischer titration results for the water 185 concentration is estimated to be 80 ppm for the coulometric titration and 0.001 g g-1 for volumetri c 186 titration , based on experiments with gravimetrically prepared samples. Further information on the 187 Karl-Fischer titration is given in the Supporting Information. When Karl -Fischer titration results 188 were available, they were used and the NMR results were neglected . 189 190 3. Modeling 191 192 The phase equilibria were calculated using the isoactivity criterion in Equation 1 which is given 193 here for LLLE. 194 𝑥𝑖′∙𝛾𝑖′=𝑥𝑖′′∙𝛾𝑖′′=𝑥𝑖′′′∙𝛾𝑖′′′, i = 1…N (1) Therein is xi the mole fraction of component i and γi the corresponding activity coefficient ; N is 195 the number of components in the mixture and the primes refer to the phases. The activity 196 coefficient was calculated with the group contribution model UNIFAC with parameters from 197 Schmitz et al. [45], or, where this was not possible, from the original UNIFAC model [46]. 198 Furthermore, group interaction parameters representing interactions between groups in OME and 199 11 in hydrocarbons were fitted to experimental results from the present work. Details on the 200 paramet erization are reported in the Supporting Information . The s plit of the considered 201 components into UNIFAC groups is reported in Table 2, the group parameters , and the interaction 202 parameters in Table 3. Tables 2 and 3 also contain detailed information on the source of all 203 parameters. As the activity coefficients cal culated with UNIFAC depend only on a temperature 204 and composition, the model does not account for the pressure. 205 206 Table 2 Group assignment and size and surface parameters of the groups for the UNIFAC -based 207 activity coefficient model. 208 Comp. i group count Ri Qi Ref. OME n MAL FA OME 1 (n-1) 2.9644 0.9183 2.7160 0.7800 [45] [45] C12 CH 3 CH 2,alk 2 10 0.9011 0.6744 0.8480 0.5400 [47] [45] C16 CH 3 CH 2,alk 2 14 Tol ACH ACCH 3 5 1 0.5313 1.2663 0.4000 0.9680 [47] [47] W H2O 1 0.9200 1.400 0 [45] 209 Table 3 Group interaction parameters for the UNIFAC activity coefficient model. 210 group j → group i ↓ MAL FA OME CH 3 / CH 2 ACH ACCH 3 H2O MAL - 26.0a -45.522 c -103.618 c -45.522c 1031.0 -1.749 · T/K a FA OME 141.5 a - 265.483 c 52.13 b 265.48c 670.7 a CH 3 / CH 2 51.251 c 148.309 c - 61.13 b 76.5 b 1318 b ACH 6400.299 c 32.14 b -11.12 b - 167.0 b 903.8 b ACCH 3 51.251 c 148.309 c -69.7 b -146.8 b - 5695.0 b H2O -225.5+0.7205 ·T/K a 168.9 -0.8776 ·T/K a 300 b 362.3 b 377.6 b - aSchmitz et al. [45] bGmehling et at. [47] cthis work 211 212 12 Isothermal flash calculations were used to determine the two -phase and the three -phase 213 equilibria studied in the present work. The feed composition for the flash -calculation was 214 calculated from the experimental phase compositions assuming an equimolar phase split and the 215 initial guess for the algorithm was calculated with the method of Ohanamah and Thompson [48]. 216 The flash model was implemented in the software Matlab. Details on the calculation can be found 217 in the Supporting Information. 218 219 4. Results and discussion 220 221 4.1 Overview 222 223 Before the experimental and model results are presented, we discuss the topologies of t he 224 corresponding phase diagrams. Both the experimental results and the model show that there are 225 three types of phase diagrams in the systems studied here (in the temperature range that was 226 investigated). The three topologies, labeled here as type A , B, and C, respectively, are depicted in 227 Figure 1. 228 229 13 OME n-alkaneW LLE LLType A 230 OME n-alkaneW L LLE LLLE LLE LType B 231 OME n-alkaneW L LLE LLLE LLE L LType C 232 14 Figure 1: Schematic representation of the three topolog ies of the phase b ehavior of the systems 233 studied in this work. The straight lines represent LLE conodes. The point mark in the type B 234 diagram is a critical point. 235 Type A was observed in all experiments with OME 2: OME 2 and the n -alkanes are completely 236 miscible, while there are miscibility gaps in the bina ry systems with (OME 2 + water) and (n -alkane 237 + water). A ternary LLE region connects these two binary LLE. 238 In the type C phase diagram, there is also a miscibility gap in the binary system (OME + 239 n-alkane). This is the case for (OME 4 + C16) for all tempera tures and (OME 2 + C16) for the two 240 lower studied temperatures (278 and 265 K). In the ternary system, there are three (two -phase) 241 LLE regions that stretch out from the binary sides of the phase diagram and meet in a (three -phase) 242 LLLE in the center of the diagram 243 Type B phase diagram has features from the other two types, which are, however, combined 244 differently. As in the type C phase diagram, there is a (three -phase) LLLE. On the three sides of 245 this LLLE -region, there are two phase LLE regions. However, o nly two of them are connected to 246 binary sides of the phase diagram, whereas the third one, that on the side with low water 247 concentrations, ends in a critical point, as there is no miscibility gap on the (OME + n -alkane) side 248 of the phase diagram. This phas e behavior was observed in the system (OME 4 + C12) at the highes t 249 studied temperature 293 K. 250 For some of the studied systems and temperatures, it is not possible to decide whether the phase 251 behavior is of type B or C. An overview of the assignments of syst ems and temperatures to the 252 phase behavior is given in Table 4. 253 The phenomenon of the unexpected phase split in technical mixtures of OME and HVO is very 254 likely related to the occurrence of phase behavior of type B, cf. Figure 1. In the absence of water, 255 15 OME and HVO are completely miscible. However, upon taking up water, the closed LLE region 256 is reached and the mixture splits up in to a OME -rich phase and a HVO -rich phase. If larger 257 amounts of water are added (more than is usually taken up from the air), the three -phase region is 258 reached and an additional third, water -rich phase forms. 259 260 Table 4 Overview of the systems studied in this work. The third or fourth component was always 261 water. 262 OME Hydrocarbon Temperature / K Number of feed mixtures Topology type OME 2 C12 293 6 A 278 4 A C16 293 6 A OME 4 C12 293 5 B 278 5 C 265 4 C C16 293 5 C C16 + Tol 3 B or Ca OME mix C12 293 1 B or Ca C16 1 B or Ca a not clarified 263 264 4.2 Experiments in the system (OME + n -alkane + water) 265 266 First, the experimental results for the model systems are presented , in which the chain length of 267 the alkanes and OMEs and the temperature were systematically varied. Then, t he fit of the model 268 to these results is t hen discussed. The numerical results are presented in Tables 5 to 8. The data for 269 each system are grouped in isothermal subsets. In some of these sets, the temperature was only 270 16 constant to about 1 K, which was due to problems with the setting of the temperature. The 271 uncertainty of the reported individual values is as specified above. 272 Table 5 Experimental LLE data for the system (OME 2 + C12 + water ). The composition of the 273 feed is reported in the Supporting Information . Standard uncertainties u are u(T)=0.1 K, 274 u(𝑥̃OME2 )=0.01 mol mol-1, u(𝑥̃C12)=0.01 mol mol-1, u(𝑥̃W)=0.0 1 mol mol-1 (for 0.005 g g-1 < 𝑥̃W(𝑚)< 275 0.1 g g-1: 𝑢(𝑥̃W(𝑚))=0.001 g g-1 and for 𝑥̃W(𝑚)<0.005 g g-1: 𝑢(𝑥̃W(𝑚))=0.00008 g g-1) 276 277 T / K water -rich phase organic phase 𝑥W(m) g g-1 𝑥OME2(m) g g-1 𝑥W(m) g g-1 𝑥OME2(m) g g-1 264.37 solida 0.0008 0.3290 278.28 0.812 3 0.1870 0.0002 0.132 3 278.50 0.7219 0.2781 0.002 4 0.4496 278.71 0.7082 0.291 8 0.0058 0.642 1 293.15 0.7054 0.294 6 0.015 3 0.802 9 0.712 2 0.2878 0.0113 0.734 9 0.754 2 0.2458 0.0018 0.3648 0.7970 0.2030 0.001 2 0.220 9 0.731 3 0.2687 0.0046 0.5420 0.8354 0.164 6 0.0003 0.1231 anot analyzed 278 279 280 281 282 283 17 Table 6 Experimental LLE data for the system (OME 2 + C16 + water). The composition of the 284 feed is reported in the Supporting Information . Standard uncertainties u are u(T)=0.1 K, 285 u(𝑥̃OME2 )=0.01 mol mol-1, u(𝑥̃C16)=0.01 mol mol-1, u(𝑥̃W)=0.01 mol mol-1 (for 0.005 g g-1 < 𝑥̃W(𝑚)< 286 0.1 g g-1: 𝑢(𝑥̃W(𝑚))=0.001 g g-1 and for 𝑥̃W(𝑚)<0.005 g g-1: 𝑢(𝑥̃W(𝑚))=0.00008 g g-1) 287 T / K water -rich phase organic phase 𝑥W(m) / g g-1 𝑥OME2(m) / g g-1 𝑥W(m) / g g-1 𝑥OME2(m) / g g-1 293.15 0.713 2 0.2868 0.0105 0.6971 0.702 3 0.297 8 0.011 6 0.715 2 0.702 1 0.2979 0.0067 0.5991 0.722 9 0.2771 0.003 2 0.438 9 0.7577 0.2423 0.0010 0.256 8 0.848 3 0.1517 0.0003 0.1145 288 Table 7 Experimental LLE and LLLE data for the system (OME 4 + C12 + water). The composition 289 of the feed is reported in the Supporting Information . Standard uncertainties u are u(T)=0.1 K, 290 u(𝑥̃OME4 )=0.01 mol mol-1, u(𝑥̃C12)=0.01 mol mol-1, u(𝑥̃W)=0.01 mol mol-1 (for 0.005 g g-1 < 𝑥̃W(𝑚)< 291 0.1 g g-1: 𝑢(𝑥̃W(𝑚))=0.001 g g-1 and for 𝑥̃W(𝑚)<0.005 g g-1: 𝑢(𝑥̃W(𝑚))=0.00008 g g-1) 292 T / K water -rich phase alkane -rich phase OME -rich phase 𝑥W(m) g g-1 𝑥OME4(m) g g-1 𝑥W(m) g g-1 𝑥OME4(m) g g-1 𝑥W(m) g g-1 𝑥OME4(m) g g-1 264.27 solida 0.0001 0.1418 0.0131 0.9372 265.63 0.0001 0.153 7 0.009 4 0.9339 266.71 0.0001 0.164 3 0.0040 0.925 4 266.78 0.000 8 0.171 6 0.002 1 0.9220 267.19 0.000 2 0.159 2 0.007 6 0.928 2 278.63 0.7542 0.2457 0.0004 0.1953 0.0178 0.9166 278.41 0.000 4 0.221 7 0.009 2 0.904 2 278.43 0.0003 0.2413 0.005 4 0.8922 278.84 0.0004 0.205 7 0.014 4 0.9133 18 Table 7 continued 278.86 0.0002 0.259 9 0.002 7 0.8783 293.15 0.7691 0.230 9 0.001 1 0.2753 0.021 4 0.891 8 293.15 0.001 1 0.3950 0.005 1 0.809 7 293.15 0.0011 0.334 6 0.0087 0.8510 293.15 0.001 1 0.279 6 0.0122 0.872 1 a not analyzed 293 Table 8 Experimental LLE and LLLE data for the system (OME 4 + C16 + water). The composition 294 of the feed is reported in the Supporting Information . Standard uncertainties u are u(T)=0.1 K, 295 u(𝑥̃OME4 )=0.01 mol mol-1, u(𝑥̃C16)=0.01 mol mol-1, u(𝑥̃W)=0.01 mol mol-1 (for 0.005 g g-1 < 𝑥̃W(𝑚)< 296 0.1 g g-1: 𝑢(𝑥̃W(𝑚))=0.001 g g-1 and for 𝑥̃W(𝑚)<0.005 g g-1: 𝑢(𝑥̃W(𝑚))=0.00008 g g-1) 297 T / K water -rich phase alkane -rich phase OME -rich phase 𝑥W(m) / g g-1 𝑥OME4(m) / g g-1 𝑥W(m) / g g-1 𝑥OME4(m) / g g-1 𝑥W(m) / g g-1 𝑥OME4(m) / g g-1 293.15 0.74974 0.25026 0.000 5 0.166 6 0.0279 0.937 8 0.000 5 0.1815 0.0182 0.955 3 0.0004 0.1975 0.0110 0.9419 0.0002 0.2235 0.0035 0.9180 0.000 2 0.235 2 0.0004 0.8770 In Figure 2, the LLE in the systems (OME 2 + C12 + water) and (OME 2 + C16 + water) are shown. 298 The different temperatures are indicated by different colors and the symbol type indicates the 299 n-alkane that was used. The feed compositions for the different tie lines are shown as crosses. 300 19 0.00 0.25 0.50 0.75 1.000.000.250.500.751.000.00 0.25 0.50 0.75 1.00x(m)W / g g -1 x(m)OME2 / g g-1 x(m) alkane / g g-1 OME2 n-alkaneW 301 Figure 2: Experimental results for the LLE in the system (OME 2 + C12 + water, circles) and the 302 system (OME 2 + C16 + water, squares). The color indicates the temperature: ( blue) 293 K, (red) 303 278 K, (orange ) 265 K. Stars indicate data from Schmitz et al. [30] for the binary system (OME 2 + 304 water). Crosses represent the feed compositions. Lines are tie lines. For the measurement at 278 305 K, only one liquid phase could be measured due to ice formation. 306 It can be seen that the feed compositions lie perfectly on the tie lines, indicating a good quality of 307 the experimental results. In all experiments, a split into a water -rich phase and a n organic phase 308 was observed. In the water -rich phase , no n-alkane was found . The concentration is so small that 309 it is below the detection limit of the NMR -measurement. This is consistent with reports from the 310 literature [31,32] for the solubility of C12 and C16 in pure water, which does not exceed 0.1 ppm. 311 The OME fraction in the water -rich phase increases with increasing ratio of OME 2/n-alkane in 312 the feed and approaches the value for the system (OME 2 + water) from Schmitz et al. [30], which 313 is also indicated in Figure 2. There is no data for the composition of the water -rich phase at 265 K, 314 20 for which only the organic liquid phase could be analyzed, due to ice formation. The resolution of 315 the presentation of the data in Figure 2 is too low to dis cern an influence of the temperature or the 316 type of n -alkane. 317 Therefore, t he results for the composition of the organic phase, which is of special interest for fuel 318 applications, are shown separately in Figure 3. Additionally , also the experimental data from 319 Zhuang et al. [33] for the system (OME 2 + n-hexane + water) are shown. 320 0.0 0.2 0.4 0.6 0.8 1.00.0000.0050.0100.0150.0200.0250.030x(m) W / g g-1 x(m) alkane / g g-1 321 Figure 3: Experimental results for the composition of the organic phase in LLE in the system 322 (OME 2 + C12 + water, circles) and the system (OME 2 + C16 + water, squares). The color 323 represents the temperature: ( blue) 293 K, (red) 278 K, (orange ) 265 K. Stars indicate data from 324 Zhuang et al .[33] for the system (OME 2 + n-hexane + water) . 325 As expected, the concentration of water increases with increasing amount of OME 2 (decreasing 326 amount of the n -alkane). The differences between the different data sets from the present work are 327 not l arge (as could be expected from Figure 2) but indicate a tendency for an increasing water 328 21 amount with increasing temperature, which is also not unexpected , due to the weaker influence of 329 H-bonds at higher temperatures . The differences between the results f or C12 and C16 are basically 330 within the scattering of the data. The results of Zhuang et al [33] for the system (OME 2 + n-hexane 331 + water) at 292 K show significantly higher water solubilities in the organic phase than the results 332 from the present work that were , however, obtained with lo nger n -alkanes. 333 The LLLE measured in the systems (OME 4 + C12 + water) and (OME 4 + C16 + water) are shown 334 in Figure 4. For (OME 4 + C12 + water) , results for different temperatures are presented. 335 The variation of the temperature and alkane hardly affects the water -rich phase ( that contains 336 practically no alkane) and has only a moderate influence on the OME 4-rich phase. A stronger 337 influence is observed for the alkane -rich phase. 338 This is discussed in more detail using Figure 5, which shows results for the two o rganic phases of 339 the LLLE together with results for the LLE in the region with low water concentrations (cf. 340 Figure 1). 341 All results shown in Figure 5 belong to the type C phase behavior, except those for the system 342 (OME 4 + C12 + water) at 293 K, which has type B phase behavior. 343 22 0.00 0.25 0.50 0.75 1.000.000.250.500.751.000.00 0.25 0.50 0.75 1.00x(m)W / g g -1 x(m)OME4 / g g-1 x(m) alkane / g g-1 OME4 alkaneW 344 Figure 4: Experimental results for the LLLE in the system (OME 4 + C12 + water , circles ) and the 345 system (OME 4 + C16 + water, squares) . The color represents the temperature: ( blue) 293 K, (red) 346 278 K, (orange ) 265 K. Stars indicate data from Schmitz et al. [30] for the binary system (OME 4 + 347 water). Lines are tie lines. 348 0.0 0.2 0.4 0.6 0.8 1.00.0000.0050.0100.0150.0200.0250.030x(m) W / g g-1 x(m) alkane / g g-1 349 23 Figure 5: Experimental results for the LLE in the system (OME 4 + C12 + water, circles) and the 350 system (OME 4 + C16 + water, squares) at low water fractions. The color represents the 351 temperature: ( blue) 293 K, (red) 278 K, (orange ) 265 K. Crosses represent the feed compositions. 352 Lines are tie lines. The top results for each temperature and alkane represent the phases with low 353 water fractions of the LLLE. 354 Figure 5 shows that decreasing the temperature leads to a widening of the LLE region, i.e. to an 355 increasing mole fraction of OME 4 in the OME 4-rich phase as well as an increasing mole fraction 356 of C12 in the C12-rich phase. The water -content in the alkane -rich phase is always very low; it 357 increases with increasing OME -content of that phase (not discernable in Figure 5). Water from the 358 feed is basically only found in the OME 4-rich phase. Also th e increase in the chain -length of the 359 n-alkane from C12 to C16 increases the width of the miscibi lity gap. Again, the feed concentrations 360 lie on the LLE tie -lines. 361 In the present work , the type A phase behavior was only observed for OME 2. Zhuang et al. [33] 362 mixed OME 4 with the smaller alkane n -hexane and also observed type A phase behavior. Type B 363 phase behavior can be considered as an intermediate between types A and C, the difference is 364 mainly caused by the differences in the solubility of the binary system (OME + n -alkane). 365 366 4.3 Mod eling of the system (OME + n -alkane + water) 367 368 In the following , modeling results are compared to experimental results in figures that are similar 369 to Figures 2 to 5. However, for the comparison, mole fractions are used, which enables a better 370 resolution of differences than the mass fractions used in Figure s 2 to 5, which were preferred in 371 24 these figures , as they are more convenient for applications. We have refrained from presenting the 372 modeling results already in Figures 2 to 5, to avoid an overloading with information. 373 In Figure 6, the experimental results for the LLE in the studied systems of the type (OME 2 + 374 n-alkane + water) are compared to the results from the model and Figure 7 shows the corresponding 375 results for the LLLE in the system of the type (OME 4 + n-alkane + water) . The modeling results 376 for these two systems in plots that are similar to the ones shown in Figures 4 and 5 are shown in 377 the Supporting Information. 378 0.00 0.25 0.50 0.75 1.000.000.250.500.751.000.00 0.25 0.50 0.75 1.00x W / mol mol -1 xOME2 / mol mol-1 xalkane / mol mol-1 OME2 alkaneW 379 Figure 6: Experimental results (filled symbols and full line) and model results (open symbols and 380 dashed line) for the LLE in the system (OME 2 + C12 + water , circles ) and the system (OME 2 + 381 C16 + water, squares) . The color represents the temperature: ( blue) 293 K, (red) 278 K. Lines are 382 tie lines. 383 384 25 0.00 0.25 0.50 0.75 1.000.000.250.500.751.000.00 0.25 0.50 0.75 1.00x W / mol mol -1 xOME4 / mol mol-1 xalkane / mol mol-1 OME4 alkaneW 385 Figure 7: Experimental results (filled symbols and full line) and model results (open symbols and 386 dashed line) for the LLLE in the system (OME 4 + C12 + water , circles ) and the system (OME 4 + 387 C16 + water, squares) . The color represents the temperature: ( blue) 293 K, (red) 278 K, (orange ) 388 265 K. 389 The model confirms the topologies A to C discussed above. The water -rich phase is described 390 well in all cases. The water mole -fraction in the OME -rich p hase is overestimated and the width 391 of the miscibility gap between the OME -rich and the alkane -rich phase is underestimated, but the 392 trends regarding the influence of the temperature and alkane chain length are described correctly . 393 394 395 396 397 398 26 4.4 Experiments wi th systems with more than three components 399 400 4.4.1 System ( OME 4 + C16 + Tol + water ) 401 402 LLLE in mixtures of ( OME 4 + C16 + Tol + water ) were studied at 293 K. In the experiments, 403 the ratio OME 4/(C16 + Tol)/water was held constant, and only the ratio C16/Tol was varied. The 404 feed composition was chosen so that the resulting mixture split into three phases. The numerical 405 results are presented in Table 9. The results are discussed here using ternary phase diagrams, in 406 which Tol and C16 were lumped into a single c omponent. 407 Figure 8 shows the experimental results together with those for the Tol-free system. Besides the 408 experimental data also the results from the model are depicted. 409 410 Table 9 LLE data of the system (OME 4 + C16 + Tol + water) at 293.15 K. The composition of the 411 feed is reported in the Supporting Information . Standard uncertainties u are u(T)=0.1 K, 412 u(𝑥̃OME 4)=0.01 mol mol-1, u(𝑥̃hydrocarbon )=0.01 mol mol-1, u(𝑥̃W)=0.01 mol mol-1 (for 0.005 g g-1 < 413 𝑥̃W(𝑚)< 0.1 g g-1: 𝑢(𝑥̃W(𝑚))=0.001 g g-1 and for 𝑥̃W(𝑚)<0.005 g g-1: 𝑢(𝑥̃W(𝑚))=0.00008 g g-1) 414 water -rich phase (C16 + Tol)-rich OME -rich phase 𝑥W(m) / g g-1 𝑥OME4(m) / g g-1 𝑥Tol(m) / g g-1 𝑥W(m) / g g-1 𝑥OME4(m) / g g-1 𝑥Tol(m) / g g-1 𝑥W(m) / g g-1 𝑥OME4(m) / g g-1 𝑥Tol(m) / g g-1 0.757 3 0.242 8 0.00000 0.000 5 0.172 2 0.0125 0.026 2 0.928 1 0.009 1 0.7592 0.240 8 0.00000 0.000 6 0.1850 0.0280 0.023 9 0.911 9 0.0218 0.888 6 0.1114 0.00000 0.0016 0.2285 0.3329 0.0140 0.7644 0.1298 415 27 0.00 0.25 0.50 0.75 1.000.000.250.500.751.000.00 0.25 0.50 0.75 1.00x(m)W / g g -1 x(m)OMEmix / g g-1 x(m) alkene + Tol / g g-1 OME4 C16 + TolW 416 Figure 8: Experimental results (filled symbols and straight line) and model results (open symbols 417 and dashed line) for the LLLE in the system (OME 4 + C16 + Tol + water) at 293.15 K . Tol and 418 C16 are lumped in the representation . Results fr om experiments with varying ratios of Tol/C16 419 are shown. The mass fractions of Tol in the (C16 + Tol) feed mixture ( 𝑥Tol,mix(m)) were: (blue 420 squares) 𝑥Tol,mix(m) = 0.0 g g-1, (green circles) 𝑥Tol,mix(m) = 0.02 g g-1, (orange upwards 421 triangle) 𝑥Tol,mix(m) = 0.05 g g-1, (purple downwards triangle) 𝑥Tol,mix(m) = 0.2 g g-1. 422 In the Tol-containing systems, the basic findings regarding the three phases are the same as for 423 the Tol-free system. Upon increasing the amount of Tol, the amount of water in the wate r-rich 424 phase increases and the miscibility gap between the hydrocarbon -rich phase and the OME -rich 425 phase gets smaller, i.e., Tol acts as a solubilizer. This can be attributed to a mediating influence of 426 the pi -electron systems of Tol. The model predicts th ese trends right but underestimates the 427 28 magnitude of the influence of Tol. A detailed analysis of the numerical results presented in Table 9 428 reveals that the ratio of C16/Tol in the different phases is similar, i.e., they do not separate. 429 430 4.4.2 Systems of the type ( OME-mixture + n-alkane + water ) 431 432 Measurements in systems containing a mixture of OME 3, OME 4, OME 5, and OME 6 of a fixed 433 composition (OME mix), water, and either C12 or C16 were carried out at 293.15 K. The feed was 434 again chosen so that it was ins ide the three phase region. The numerical results for the LLLE are 435 reported in Table 10 and are illustrated in Figure 9, which shows a ternary diagram , in which 436 OME 3, OME 4, OME 5, and OME 6 are lumped into one pseudo -component OME mix. Additionally, 437 Figure 1 0 depicts the analytical results for the individual components in the three phases. 438 439 Table 10 Experimental LLLE data of system s of the type (OME mix + alkane + water) at 293.15 K. 440 OME mix is a mixture of OME 3 to OME 6. The composition of the feed is reported in the Supporting 441 Information . Standard uncertainties u are u(T)=0.1 K, u(𝑥̃OMEn )=0.01 mol mol-1, u(𝑥̃alkane )=0.01 442 mol mol-1, u(𝑥̃W)=0.01 mol mol-1 (for 0.005 g g-1 < 𝑥̃W(𝑚)< 0.1 g g-1: 𝑢(𝑥̃W(𝑚))=0.001 g g-1 and for 443 𝑥̃W(𝑚)<0.005 g g-1: 𝑢(𝑥̃W(𝑚))=0.00008 g g-1) 444 alkane phase 𝑥W(m) / g g-1 𝑥alkane(m) / g g-1 𝑥OME3(m) / g g-1 𝑥OME4(m) / g g-1 𝑥OME5(m) / g g-1 𝑥OME6(m) / g g-1 C16 OME -rich 0.0256 0.0923 0.3527 0.287 2 0.1800 0.0622 water -rich 0.7062 0 0.1664 0.1131 0.010 2 0.0041 alkane -rich 0.0004 0.781 3 0.111 2 0.0673 0.0292 0.0106 C12 OME -rich 0.0273 0.092 2 0.352 1 0.2866 0.1796 0.0621 water -rich 0.7170 0 0.1371 0.0841 0.0470 0.0133 alkane -rich 0.001 3 0.717 6 0.1417 0.083 9 0.0434 0.0121 29 0.00 0.25 0.50 0.75 1.000.000.250.500.751.000.00 0.25 0.50 0.75 1.00x(m)W / g g -1 x(m)OMEmix / g g-1 x(m) alkane / g g-1 OMEmix alkaneW 445 Figure 9: Experimental results (filled symbols and straight line) and model results (open symbols 446 and dashed line) for the LLLE in systems of the type (OME mix + alkane + water ) at 293 K. The 447 symbols represent the alkane: (circles) C12, (squares) C16. 448 449 OME3 OME4 OME5 OME6 alkane W0.00.20.40.60.81.0mass fraction water-rich phase alkane-rich phase OME-rich phase ·103} 450 30 Figure 10: Results for LLLE in systems of the type (OME mix + C12 + water) at 293 K. 451 Experimental mass fractions (unhatched bars) are compared to mass fractions from the model 452 (hatched bars) for all three phases . The water fraction in the C12-rich phase was multiplied by 453 1000 for a better visualization. 454 The experimental results are similar to th ose of the measurements with pure OME 4 (cf. Figure 4). 455 The ratios OME 3 / OME 4 / OME 5 / OME 6 do not differ significantly in the different phases and are 456 therefore also basically the same as in the feed mixture. All in all , the model shows a good 457 agreement with the experimental data. The alkane -rich phase is described very well (cf. Figure 10). 458 The distribution of the individual OME is also reproduced well by the model. The water fraction 459 in the water -rich phase is somewhat underestimated. 460 461 5. Conclusion s 462 463 Mixtures of poly(oxymethylene) dimethyl ethers (OME) and hydrogenated vegetable oil (HVO) 464 are interesting synthetic fuels. However, in technical applications of these fuels, a liquid -liquid 465 phase split was observed, which i s unwanted. Up to now , only qualitative information on this 466 phenomenon was available and its causes were unclear. The present work clearly indicates that the 467 hypothesis that the phase separation is a consequence of the uptake of water from the air by the 468 (OME + HVO) mixtures in many technical applications is correct . This leads to a separation into 469 an OME -rich phase, which contains basically all the water, and a HVO -rich phase, which is almost 470 water -free. This can be deduced from the results of the experime ntal studies on liquid -liquid 471 equilibria (LLE) and liquid -liquid -liquid equilibria (LLLE) in model systems of the type (OME + 472 alkane + water) that we have carried out in the present work. 473 31 Depending on the system and temperature, three different topologies of the phase behavior were 474 observed. The unwanted liquid -liquid phase split is induced by a latent incompatibility of the OME 475 with the alkane, which becomes only manifest when water is added. Furthermore, experiments 476 with mixtures that contained not only a lkanes but also toluene were carried out. The presence of 477 the aromatic compound makes the alkane -rich phase more hydrophilic, and, hence, more 478 compatible with OME. This reduces the risk of the phase split. 479 The experimental findings were also confirmed by simulations, in which UNIFAC, a model of 480 the Gibbs excess energy, was used for describing the liquid phases. This comparatively simple 481 modeling approach gave good results. 482 Now that the causes of the phase split are clear, measure s to circumvent it can be found: a 483 straightforward approach is to reduce the humidity in the fuel storage tank, e.g., by common d rying 484 agents, such as molecular sieves. Another approach is to add further fuel components that act as 485 solubilizers. Ranked on a polarity scale, they should lie between OME 4 and the alkanes. The model 486 developed in the present work can be used for a screening of such solubilizers. 487 Acknowledgements 488 The authors gratefully acknowledge funding by the German Federal Ministry of Economic 489 Affairs and Energy within the project “E2Fuels” under Grant 19I18008F . 490