Thermodynamic analysis of biodiesel production systems at supercritical conditions

Thermodynamic analysis of biodiesel production systems at supercritical conditions

Accepted Manuscript Thermodynamic analysis of biodiesel production systems at supercritical conditions Kallynca Carvalho dos Santos, Fernando A. Peder...

2MB Sizes 0 Downloads 41 Views

Accepted Manuscript Thermodynamic analysis of biodiesel production systems at supercritical conditions Kallynca Carvalho dos Santos, Fernando A. Pedersen Voll, Marcos L. Corazza PII:

S0378-3812(18)30488-6

DOI:

https://doi.org/10.1016/j.fluid.2018.11.029

Reference:

FLUID 12016

To appear in:

Fluid Phase Equilibria

Received Date: 10 May 2018 Revised Date:

20 November 2018

Accepted Date: 23 November 2018

Please cite this article as: K. Carvalho dos Santos, F.A. Pedersen Voll, M.L. Corazza, Thermodynamic analysis of biodiesel production systems at supercritical conditions, Fluid Phase Equilibria (2018), doi: https://doi.org/10.1016/j.fluid.2018.11.029. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT 1

Thermodynamic analysis of biodiesel production systems at supercritical

2

conditions

3 Kallynca Carvalho dos Santos, Fernando A. Pedersen Voll, Marcos L. Corazza*

RI PT

4 5 6

Department of Chemical Engineering, Federal University of Paraná, 81531-980, Curitiba,

7

PR, Brazil.

SC

8

*Corresponding author: Dr. Marcos L. Corazza, Department of Chemical Engineering,

10

Federal University of Paraná, PO Box 19011 Polytechnic Center, Curitiba 81531-980, PR,

11

Brazil. Email: [email protected]; Telephone: + 55-41-33613190.

M AN U

9

12 13 ABSTRACT

15

This work reports thermodynamic analysis of systems involved in the biodiesel production

16

using ethanol at supercritical conditions. PC-SAFT equation of state was used from ASPEN

17

Plus simulator for modeling all investigated systems. Binary and ternary phase equilibrium

18

data at high pressure and temperature were used to assess the PC-SAFT capability of

19

predicting the thermodynamic behavior of the complex mixture of interest in this work. The

20

results showed that the PC-SAFT is a reliable tool to represent the phase behavior of mixtures

21

involving ethanol, vegetable oil, fatty acid, ethyl esters of fatty acid and glycerol. Phase

22

behavior of the reaction system was evaluated under specified experimental conditions and

23

considering different reaction conversions. Pressure-temperature diagrams demonstrated that

24

the two-phase region for the reaction mixture decreases as the extension of reaction is

25

increased. The PC-SAFT equation of state was used to estimate the density of the reactant

AC C

EP

TE D

14

1

ACCEPTED MANUSCRIPT 26

mixture and the effect of this parameter over the residence of the reaction was assessed,

27

where it was clearly demonstrated that the density of the mixture greatly affects the residence

28

time calculation for the reactions of biodiesel production at high pressure conditions.

29 Keywords: Supercritical, phase behavior, PC-SAFT, biodiesel, density.

RI PT

30 31 32

1 Introduction

SC

33

Biodiesel has been considered one of the main substitutes for non-renewable fossil

35

fuels. In addition to environmental benefits such as biodegradability, low sulfur content and

36

reduce harmful emissions and non-toxic properties, another advantage of biodiesel is the

37

similarity of its properties when compared to diesel, so few modifications are necessary in the

38

current engine systems [1].

M AN U

34

Biodiesel is derived from renewable raw materials, such as vegetable oils and animal

40

fats, which are converted to biodiesel via transesterification/esterification of fatty acids. This

41

method is applied industrially, where triacylglycerol reacts with a short chain alcohol, for

42

example methanol or ethanol, in the presence of alkali catalyst (KOH and NaOH), generating

43

fatty acid alkyl esters (biodiesel) and glycerol as by-product. However, alkaline

44

transesterification is only suitable for raw materials with low content of free fatty acids

45

(FFA), less than 1% by mass, such as refined vegetable oils [2]. This specificity of the raw

46

material makes the biodiesel production economically uncompetitive with petroleum-based

47

fuels.

AC C

EP

TE D

39

48

Glisic and Orlović [3] presented a review considering the costs involved in the

49

biodiesel production and for its reduction two factors must be taken into account: raw

50

materials costs reduction and energy consumption. Raw material represents about 60 to 80%

2

ACCEPTED MANUSCRIPT of the total cost of biodiesel production. In order to minimize the costs related to the lipid

52

source, residual raw materials with lower value added (for example, acid oils, waste

53

frying/cooking oils and non-edible vegetable oils) can be used in substitution of refined oils

54

[4,5]. However, the conventional method of producing biodiesel, e.g., alkaline

55

transesterification, it is not suitable for converting these materials into esters [6]. In addition,

56

modifications are required in the production route due to some impurities contained in these

57

alternative lipid sources. And, some techniques that allow the processing of high free acidy

58

raw materials to produce biodiesel are: acid transesterification, esterification followed by

59

transesterification and supercritical technology. This last technique presents positive points

60

such as no need for catalyst, less steps for the purification of the final product and higher

61

reaction rates [7].

M AN U

SC

RI PT

51

Supercritical technology is a non-catalytic biodiesel production route that allows a

63

simple and high yield process at high temperature and pressure (above the critical point of the

64

alcohol). Using such conditions, simultaneous transesterification of triglycerides and

65

esterification of fatty acids efficiently take place at same time. As a result, this technology

66

can be applied to acid oils and waste raw materials in general [7,8].

TE D

62

Non-catalyzed supercritical method is relatively new for biodiesel production and has

68

received increasing interest [9–12]. Therefore, thermodynamic studies regarding the

69

components involved in the supercritical production of biodiesel have been investigated using

70

different equations of state, such as Peng-Robinson, Redlich-Kwong, Cubic-Plus-Association

71

(CPA), SAFT equation of state and its variants, such as SAFT-VR, soft-SAFT, GC-SAFT

72

and PC-SAFT [13–21]. It is worth mentioning that soft-SAFT in the liquid-vapor equilibrium

73

of methanol/ethanol with methyl myristate/oleate/laurate represented the systems

74

satisfactorily for conditions of high pressures and temperatures up to 523 K [20]. The

75

Perturbed Chain form of the Statistical Associating Fluid Theory (PC-SAFT), proposed by

AC C

EP

67

3

ACCEPTED MANUSCRIPT Gross and Sadowski [22–24], using the association term as proposed by Chapman and co-

77

workers [25,26] has been successfully applied to a wide range of associating and non-

78

associating systems, especially in some engineering applications for which other classical

79

equation of state has failed [23,27,28]. The PC-SAFT comprises terms of hard-chain,

80

dispersion, association and dipolar contributions. The pure compounds parameters involved

81

are the temperature-independent segment diameter (σ), number of segments per chain (m),

82

dispersion energy between segments (ε), association energy (εHB) and effective association

83

volume (κHB) [23,28].

SC

RI PT

76

Thermodynamic model definition is essential for the development of the industrial

85

design of any production plant [14,23,29], where the thermodynamic properties are essential

86

for the process modeling and optimization. For example, studies of phase diagrams following

87

the kinetic modeling of a reaction can indicate the homogeneity of the system and the

88

requirement for considering or not the mass transfer terms in the model [14,30].

M AN U

84

For the design, modeling, and optimization of continuous reactors, the residence time

90

is a key parameter of process and it is calculated as the ratio of the reactor capacity by the

91

volumetric flow rate of the reactants. Considering the continuous reactors used in

92

supercritical biodiesel reaction, the literature mentions different ways of obtaining the

93

volumetric flow: volumetric flow obtained directly from the feed pump or from the ratio

94

between the mass flow and the density of the reactants as pure compounds or the reactant

95

mixtures [7,30–33]. For example, Silva et al. [33] considered the volumetric flow rate of each

96

reactant (in the feed pump), but with a correction factor between the density of each

97

component at ambient and at reaction conditions. In all those studies, it is noted the

98

importance of the density in the reaction time calculation. Thus, considering the calculation

99

of this property correctly, it is necessary to define a reliable thermodynamic model to

100

AC C

EP

TE D

89

consider the non-ideality of reactant system.

4

ACCEPTED MANUSCRIPT The thermodynamic knowledge is fundamental for the process development,

102

especially for multicomponent systems and complex mixtures with highly molecular

103

asymmetry as related in the biodiesel industry. Thus, the availability of phase diagrams and

104

density calculation are fundamental to the reaction and also in order to the process

105

optimization [29]. Thus, the main subject of this work is related to the thermodynamic

106

behavior analysis of reactant systems aiming the alkyl ester (biodiesel) production at high

107

temperature and pressure conditions, and to evaluate the influence of the density calculation

108

on the reaction residence time. The PC-SAFT equation of state was used to take into account

109

the non-idealities of the systems involved in this study.

M AN U

110 111 112

SC

RI PT

101

2 Methodology

Systems of interest in this study are related to the transesterification/esterification of

114

soybean oil with different content of free fatty acid (acid oil) and ethanol. Thus, triolein, oleic

115

acid and ethyl oleate were used as model compounds for the vegetable oil, FFA, and

116

biodiesel (a mixture of fatty acid alkyl esters), respectively. Additionally, ethanol and

117

glycerol compose the entire mixture of reactants/products involved in this set of reactions.

EP

TE D

113

All calculation and analysis were performed using the Aspen Plus simulator (ASPEN

119

Plus® v8.4 software). The procedure used for the simulation was to define the components of

120

the system followed by the choice of the thermodynamic model.

121 122

AC C

118

2.1 VLE calculations of binary and ternary systems

123

Different binary and ternary systems were assessed to check the performance of PC-

124

SAFT equation of state in representing the phase behavior of systems involved in the

125

biodiesel production at high pressure and temperature conditions. For binary mixtures, P-x-y

5

ACCEPTED MANUSCRIPT 126

diagrams were generated and for ternary mixtures a flash calculation was used, where all

127

results were compared to experimental data of vapor-liquid equilibrium of different systems,

128

which were taken from the literature, as presented in Table 1.

130

Table 1

131

RI PT

129

Binary interaction parameters, regarding the dispersion energy (kij), were set to zero

133

and the dipolar contributions term of PC-SAFT was neglected. According to Corazza et al.

134

[28], the polar contribution is indifferent to supercritical methanol systems and PC-SAFT

135

predictions of systems with supercritical ethanol were worse when considering the PC-SAFT

136

dipolar term. PC-SAFT parameters used in this work are presented in Table 2, as they were

137

set in the Aspen Plus simulator.

138

Table 2

TE D

139

M AN U

SC

132

140

For the glycerol, the PC-SAFT parameters used in this work were the same used in a

142

previous work presented by Corazza et al. [27], where different self-association approaches

143

(considering different association site numbers) for the glycerol were tested and the pure

144

parameters were fitted using experimental density and vapor pressure of the pure glycerol

145

[27]. Both two parameter sets that presented better results, previously evaluated [27], were

146

tested in the present work for calculations of systems involving glycerol at high temperatures

147

and high pressures, which were the parameter sets considering 2 and 4 association sites, as

148

presented in Table 2.

AC C

EP

141

149

6

ACCEPTED MANUSCRIPT 150

2.2 Residence time estimation of simultaneous esterification and transesterification

151

reactions Santos et al. [7] carried out simultaneous esterification and transesterification

153

reactions of acid oils at supercritical ethanol conditions in a continuous tubular reactor. The

154

acid oil was composed of soybean oil with 20 wt% of oleic acid. To complete the reaction

155

mixture, ethanol was added in different ethanol to acid oil molar ratios (Et:AO), as calculated

156

by the Equation 1.

RI PT

152

Et : AO =

mol of ethanol mol of triacylglycerol+ mol of oleic acid

(1)

M AN U

158

SC

157

159

For the biodiesel production (kinetic analysis), the three soybean oil transesterification

161

reactions and the esterification of acid oleic were considered, being all the reactions

162

reversible, elementary and self-catalytic by the free fatty acid present in the reactant mixture

163

[7]. In the molar balance of the reactor, the reaction time was calculated according to

164

Equation 2, as presented by Santos et al. [7].

165

167 168

τ=

VR

υ

where,

υ=

q&

ρ mix , R

(2)

AC C

166

EP

TE D

160

Where VR is the reactor volume (22 cm3), υ is the volumetric flow rate (mL/min) at

169

the reactor inlet conditions, q& is the mass flow (g/min) and ρmix , R is the density (g/cm3) of

170

the reactant mixture obtained at the temperature and pressure reactor inlet conditions (TR and

171

PR), which was estimated using the PC-SAFT equation of state. Further details about the

172

residence time calculations can be obtained from the study presented by Santos et al. [7].

7

ACCEPTED MANUSCRIPT 173

The reaction system previously studied by Santos et al. [7] may be relevant for

174

biorefineries development, since they propose the production of ethyl esters from acid raw

175

materials. In this context, the thermodynamic study of this system is of summit importance

176

for evaluating possible process conditions and optimization. Pressure-temperature diagrams were generated to assess the phase behavior of

178

simultaneous esterification and transesterification supercritical reactions of soybean oil with

179

20 wt% of oleic acid. The Et:AO chosen for the analysis were 4:1 and the highest molar ratio

180

of 20:1, as presented by Santos et al. [7]. The phase diagrams were calculated/generated

181

considering the mixture composition for the initial (reactor inlet) and final reaction time

182

(reactor outlet) of each condition. These data were obtained from the supplementary material

183

presented by Santos et al. [7].

M AN U

SC

RI PT

177

As mentioned before, the density of the reactant mixture (soybean oil, oleic acid and

185

ethanol mixture) under the temperature and pressure conditions of the reactor is needed to

186

calculate the residence time (Equation 2). Thus, a density study was carried out aiming to

187

obtain the most accurate method for the reaction time estimation. Additionally, it was

188

analyzed the influence of density variations (deviations) on the reaction time considering the

189

following reaction condition: soybean oil with 20 wt% oleic acid and Et:AO at 4:1 at 553 K,

190

10 MPa.

192 193

EP

AC C

191

TE D

184

3 Results and Discussion

194 195

3.1 VLE calculations of binary and ternary systems

196

Cross-association parameters in the PC-SAFT equation of state were evaluated for the

197

alcohols + ester systems. As mentioned, esters are non-self-associative molecules, but they

8

ACCEPTED MANUSCRIPT can bond with self-associative molecules like alcohols. Thus, it was considered the possibility

199

that the esters can be induced by alcohols (which are highly associative molecule) forming

200

cross-association between them [28]. In this case, it was considered that the parameters of the

201

associative term result in an association energy equivalent to half of the self-association

202

energy of alcohol and the associating volume equal to the alcohol [28], as presented in

203

equations 3 and 4, respectively. This approach was used for the cross-association between

204

alcohols (including glycerol) and esters and it was allowed for both binary and ternary

205

systems investigated in this study. To verify this hypothesis, P-x-y diagrams for short chain

206

alcohols (methanol and ethanol) + alkyl esters (methyl and ethyl myristate) systems at 493,

207

523 and 543 K were evaluated, and the results are compared to experimental data, as

208

presented in Figure 1.

ε iiHB + ε HB jj

209

ε

210

κ ijHB = κ iiHBκ HB jj

=

2

(3)

(4)

TE D

HB ij

M AN U

SC

RI PT

198

Where, ii and jj states for the self-associating compounds (methanol, ethanol and glycerol),

212

and when a non-self-association compound is present in the mixture (binary or ternary) the

213

HB HB index jj represents the non-self-associating compound (where ε HB jj = 0 , and κ jj = κ ii ) in

214

binary combination with a self-associating compound.

216 217

AC C

215

EP

211

Figure 1

218

From Figure 1, it can be observed that the PC-SAFT results are similarly for both

219

alcohols with or without considering the cross-association interaction between alcohol –

220

ester, where the PC-SAFT equation of state with the association term (allowing the cross-

221

association of ester-alcohol) slightly better predicts the phase behavior of the binary systems.

9

ACCEPTED MANUSCRIPT However, at such high temperature and pressure conditions, the cross-association energy

223

between a short chain alcohol (methanol or ethanol) with long chain esters tested do not

224

affect the phase behavior predictions probably due to the ester chain size, where the chain and

225

dispersion energy terms are the most important interaction for this type of systems. Thus, for

226

an engineering modeling and simulation purpose, the cross-association between short chain

227

alcohol and a long chain alkyl ester could be neglected without a greater loss in the results

228

reliability.

RI PT

222

The glycerol plays an important role in the phase behavior of the system because it is

230

a triol and highly self-associative (a molecule with three hydroxyl groups) and associates to

231

other alcohols, water and to esters molecules. Therefore, it is important to evaluate their

232

interaction in terms to the number of association sites that must be considered to correctly

233

represent the thermodynamic interaction in the PC-SAFT framework. Figure 2 shows the

234

phase diagram for methanol + glycerol and ethanol + glycerol systems at 493, 523, 543 and

235

573 K, where the PC-SAFT calculations were performed considering glycerol with two and

236

four active sites and the results are compared to experimental data.

TE D

M AN U

SC

229

Figure 2 shows that assuming glycerol with four associative sites is the best

238

configuration for the cross-association with both short alcohols (methanol and ethanol). The

239

deviations between experimental and PC-SAFT predictions were lower for the liquid phase

240

and slightly larger for the vapor phase. As the temperature rises the deviations observed for

241

saturated vapor phase increased.

AC C

242

EP

237

The main raw materials used in the transesterification reaction are vegetable oils that

243

are composed essentially by triacylglycerols, which were represented in this work by the

244

triolein molecule. In order to assess the PC-SAFT capability of predicting the phase

245

equilibrium of alcohol - oil system (here represented by the methanol + triolein system),

10

ACCEPTED MANUSCRIPT 246

results calculated throughout the PC-SAFT equation of state were compared with the

247

experimental data, as presented in Figure 3. Figure 3 shows that as the temperature increases the results obtained from PC-SAFT

249

deviate from the experimental data, mainly considering the saturated-liquid phase. From

250

Figure 3, it can be seen that the model overestimated the phase envelop of the system, for the

251

saturated liquid phase mainly. However, it is worth mentioning that at more severe conditions

252

of temperature and pressure the transesterification reaction is favored, and it takes place in a

253

short period of time, making difficult the reliability of experimental data. Thus, more studies

254

and accurate phase equilibrium measurements must be performed for the systems involving

255

short chain alcohol and triacylglycerol making sure the real equilibrium conditions.

M AN U

SC

RI PT

248

256

Figure 2

257 258

Figure 3

260

TE D

259

As a last analysis to verify the prediction capability of the PC-SAFT state equation,

262

different flash calculations for different ternary systems were considered involving methanol,

263

glycerol and different methyl esters (system I: methyl laurate, system II: methyl myristate and

264

system III: methyl palmitate). The feed stream composition (composition of each

265

component), temperature and pressure were considered the same values as presented by

266

Shang et al. [16]. The dispersion energy (kij) between esters – alcohols and methanol –

267

glycerol was set to zero for the system (methanol + glycerol + ester).

AC C

EP

261

268

Table 3 presents the root mean square deviation (RMSD) calculated for each

269

component in the vapor and liquid phases and the overall RMSD of system considering both

270

phases. The RMSD is represented by Equation 5, where NOBS is the experimental total

11

ACCEPTED MANUSCRIPT 271

number, X iexp and X icalc are the respective experimental and calculated composition, and the ,j ,j

272

subscript represents component (i) and phase (j).

273

RMSD(%) = 100

exp i, j

− X icalc ,j )

2

(5)

NOBS

RI PT

274

∑( X

275

From the results presented in Table 3, it is possible to observe that increasing the ester

277

chain, deviations (RMSD) tend to decrease and its maximum value was up to 2%. This is an

278

indication that the PC-SAFT equation of state is an effective thermodynamic model to

279

represent the phase behavior of such systems, even setting the kij = 0 for this ternary system.

M AN U

SC

276

With the binary and ternary data, it was possible to verify that the PC-SAFT state

281

equation provided good predictions for the phase equilibrium behavior of some systems

282

involved in the biodiesel production at high temperature and pressure.

284 285 286

Table 3

3.2 Phase behavior analysis for the reaction system

EP

283

TE D

280

It is known that for transesterification and esterification reaction kinetics to be

288

favored, it is important that the reaction takes places at homogeneous phase condition, in

289

which mass transfer limitations are diminished. Thus, a pressure-temperature diagram was

290

simulated considering simultaneous esterification and transesterification reaction mixtures of

291

soybean oil with 20 wt% of oleic acid and ethanol to acid oil molar ratios (Et:AO) of 4:1 and

292

20:1, at four different temperatures conditions and its equilibrium conversions presented by

293

Santos et al. [7]. For this analysis were considered only the compositions at the initial

294

condition of the reaction (0% conversion) and at the reactor outlet (maximum conversion

AC C

287

12

ACCEPTED MANUSCRIPT presented by Santos et al. [7]). Figure 4 depicts the four experimental conditions used in the

296

previous study (10 MPa and 493, 523, 553 and 573 K) considering two reaction compositions

297

[7]. Following the PC-SAFT predictions, for the ethanol to acid oil molar ratio of Et:AO =

298

4:1, the reactant mixture was located at a single-phase condition along the reaction course.

299

For reaction system considering an ethanol to acid oil molar ratio of Et:AO = 20:1, for both

300

two lower temperatures the reaction was located into a homogeneous region, however,

301

considering both two higher temperatures evaluated the reaction possibly enters in the

302

heterogeneous (two-phase) region, mainly for the reaction at 553 K.

SC

RI PT

295

In general, it can be observed that with the advance of the reaction the biphasic region

304

decreases (lower saturation pressures at same temperature), as it can be observed comparing

305

the grey line to black, in both Figures 4(A) and 4(B). In addition, the increase in the molar

306

ratio of ethanol moved the phase envelop to the left, getting closer to the pure ethanol line.

307

This observation was also made by Osmieri et al. [14], for the system triolein + methanol.

M AN U

303

In the previous study, Santos et al. [30] carried out the esterification reaction of oleic

309

acid in supercritical ethanol, at 10 MPa, 553 K and an ethanol to fatty acid molar ratio of 6:1.

310

When comparing their diagrams with presented in Figure 4, it is observed that with the acid

311

oil the two-phase region is larger, what means that depending on the ethanol concentration in

312

the reactant mixture higher pressures are need to reach the homogeneous region, when

313

compared to pure oleic acid system.

315

EP

AC C

314

TE D

308

Figure 4

316 317 318

3.3 Density mixture estimation and its effect on the residence time

13

ACCEPTED MANUSCRIPT In order to verify the PC-SAFT reliability in estimating the density of short chain

320

alcohols + vegetable oils (modeled as triolein in the PC-SAFT framework) + fatty acids,

321

density measurements were conducted (using an Anton Paar DMA 5000 M density meter)

322

considering different compositions of the mixtures (data and further information are

323

presented in the Supplementary Material). It is possible to conclude that PC-SAFT equation

324

of state can represent the mixtures involved in the biodiesel production at mild conditions.

325

However, one of the most effective methods to produce biodiesel from high free acid content

326

raw materials is using supercritical technology, as already mentioned in this paper, where the

327

reactions take place at conditions so far from the mild conditions where the densities were

328

measured and compared to the PC-SAFT. Thus, in addition we performed a theoretical

329

analysis of the density behavior as a function of the reaction mixture with 20% acidity and

330

ethanol to acid oil molar ratios ranging from 2:1 to 20:1, and temperature range of 298 to 673

331

K (Figure 5) and fixed pressure of 10 MPa. In Figure 5, two approaches of mixture density

332

calculations are presented: i) considering ideal solutions (black dashed lines), in which

333

densities of the pure components were calculated by the PC-SAFT, and therefore the density

334

of the mixture calculated as an ideal solution (dashed lines in Figure 5(A)); ii) density values

335

were directly calculated using the PC-SAFT equation of state (applied for mixture) (dashed

336

lines in Figure 5(B)). The density values calculated for pure compounds (soybean oil, oleic

337

acid and ethanol) using the PC-SAFT are also presented in Figure 5.

SC

M AN U

TE D

EP

AC C

338

RI PT

319

Figure 5 depicts that the density of both pure components (soybean oil and oleic acid)

339

linearly decrease with the temperature increase. For both high molecular compounds, the

340

density slightly varies with the temperature increase. On the other hand, the density of

341

ethanol sharply varies with the increase of temperature nearly the critical region. Figure 5

342

shows that for temperatures around the critical temperature of ethanol (Tc = 513.6 K, Pc =

343

6.148 MPa and ρc = 0.2742 g/cm3), the density of the mixture is strongly influenced by the

14

ACCEPTED MANUSCRIPT calculation method used, which can be noticed by the different behavior between the two

345

approaches evaluated in this work, as presented by black dashed lines in Figures 5(A) and

346

(B). The mixture with a molar ratio of 2:1 showed the largest difference between the two

347

calculations approaches. For the reaction mixture of 20:1, up to 470 K both calculations

348

approaches presented similar results, except close to the critical point of ethanol. This proves

349

the sensitivity of the density of the mixture close to the critical point of ethanol. However, as

350

well notice in the literature, the standard form of PC-SAFT equation of state poorly

351

represents the volumetric properties near the critical point, especially for self-associating

352

compounds, as the ethanol, which is the key compound in esterification and

353

transesterification in ethanol supercritical conditions. Thus, the alcohol deserves a special

354

attention and further analysis, since it is an excess component in the reactions and that most

355

influences the calculation of the density of the mixture.

M AN U

SC

RI PT

344

The literature [34] presents experimental data of density near the supercritical region

357

of ethanol, these data were compared with different equations: PC-SAFT with the parameters

358

used by Gross and Sadowski [23], PC-SAFT with the parameters readjusted by Corazza et al.

359

[28] and the analytical equation of Dillon and Penoncello [35]. Figure 6 presents the

360

comparison of the equations with the experimental data. It can be observed that the three

361

models exhibit similar behavior up to 6 MPa for the three temperatures. However, increasing

362

the pressure the deviations between experimental density and the values calculated using both

363

set of parameters for the PC-SAFT increased. As expected, the equation proposed by Dillon

364

and Penoncello [35] more accurately predicts the experimental data of ethanol density under

365

higher temperature and pressure conditions. Therefore, as a results of this analysis it is

366

possible that the best way to predict the density of initial reactant mixture at high temperature

367

and high pressure conditions involving ethanol, vegetable oils, fatty acids is using applying

368

the equation proposed by Dillon and Penoncello to predict the density of pure ethanol and the

AC C

EP

TE D

356

15

ACCEPTED MANUSCRIPT PC-SAFT equation to predict the vegetable oil density (using triolein as model component)

370

and fatty acid, and after that the mixture density could be estimated using the ideal solution

371

approach with pure density values previously calculated using the specific approach for each

372

pure compound, as used and presented by Santos et al. [7].

373

Figure 5

374 375

Figure 6

SC

376

RI PT

369

377

As the last evaluation performed in this work, sensitivity analysis aiming to assess

379

how the residence time of the reaction is affected by deviations in the density of the mixture

380

was performed. The best condition obtaiend by Santos et al. [7] was used to perform this

381

evaluation considering simultaneous esterification and transesterification reaction of acid

382

soybean oil with supercritical ethanol (initial condition of the reaction with 20 wt% of oleic

383

acid in soybean oil, 10 MPa, 553 K and Et:AO of 4:1). According to Santos et al. [7] under

384

these conditions the density of the initial mixture is 0.5407 g/cm3. As mentioned, this value

385

was calculated considering the reactant mixture at the reactor inlet as an ideal solution, where

386

the pure density values of soybean oil (as triolein) and oleic acid were estimated using the

387

PC-SAFT equation, and the Dillon and Penoncello [35] equation for ethanol. Thus, for the

388

−1 sensitivity analysis in the residence time of the reaction (at a fixed mass flow ( q& g ⋅ min  )

389

set in the reactor feed pump) deviations of 10% and 40% were considered for the mixture (

390

ρmix ,R = 0.5407 g/cm3 ), where the density values with the respective variations are showed in

391

Table 4. Deviations caused by uncertunties in the mixture density estimation are presented in

392

Figure 7, in a fatty acid ethyl ester yield as a function of the residence time.

AC C

EP

TE D

M AN U

378

393

16

ACCEPTED MANUSCRIPT Table 4

394 395

Figure 7 indicates that the density values greatly affect the calculation of the residence

397

time and it impacts on the kinetic behavior estimated. Variations in the residence time caused

398

by the uncertainties in the density of the mixture is higher for long periods of reaction,

399

reaching values up to ~13 min and ~50 min for deviations of 10% and 40% in the density,

400

respectively. In the work presented by Velez et al. [36], they also showed the importance of

401

the method for calculating the density of the mixture on the reaction time (residence time),

402

which can overestimate or underestimate the reaction time depending on the considerations

403

used in the calculations. The residence time is essential for the reactor design and industrial

404

processes optimization. Thus, the density of the mixture must be carefully estimated mainly

405

for complex mixture at high pressure and temperature conditions and nearly at critical

406

conditions.

M AN U

SC

RI PT

396

409

4 Conclusions

EP

Figure 7

408

410

TE D

407

Different binary and ternary systems that represent the reaction components for the

412

biodiesel production from acid oil at ethanol supercritical conditions were investigated and

413

used to validate the prediction capability of the PC-SAFT equation of state, aiming to

414

represents the thermodynamic behavior of such systems. It was observed that the PC-SAFT

415

model can represent with certain reliability the phase behavior of different systems involved

416

in the biodiesel reaction at supercritical conditions. This study showed the importance of

417

cross-association energy between the long chain ethyl ester with self-associating molecules

418

like ethanol and glycerol. Further, the glycerol configuration that presented the best

AC C

411

17

ACCEPTED MANUSCRIPT prediction was one considering four associating sites. From pressure-temperature diagram

420

analysis for the reactant mixture was observed that the biphasic region decreases following

421

the progress of the simultaneous esterification and transesterification reactions. Density of the

422

mixture showed to be a very important property for the residence time calculation, and small

423

variations can generate high deviation in the kinetic profile of the reaction.

RI PT

419

424 425

Supplementary Material

SC

426

Supplementary material presents the density measurements of some pure components

428

involved in the biodiesel production (ethanol, soybean oil and oleic acid and three different

429

mixtures of these components).

430 431

Acknowledgments

TE D

432 433 434

The authors thank the CNPq (grants 406737/2013-4 and 305393/2016-2), CAPES and Fudanção Araucária for financial support and scholarships.

EP

435

AC C

436 437

References

438

[1]

439 440

443

E. Alptekin, M. Canakci, Optimization of transesterification for methyl ester

production from chicken fat, Fuel. 90 (2011) 2630–2638.

[2]

441 442

M AN U

427

H.J. Cho, S.H. Kim, S.W. Hong, Y.-K. Yeo, A single step non-catalytic esterification of palm fatty acid distillate (PFAD) for biodiesel production, Fuel. 93 (2012) 373–380.

[3]

S.B. Glisic, A.M. Orlović, Review of biodiesel synthesis from waste oil under elevated pressure and temperature: Phase equilibrium, reaction kinetics, process design and

18

ACCEPTED MANUSCRIPT 444 445

techno-economic study, Renew. Sustain. Energy Rev. 31 (2014) 708–725. [4]

L.J. Konwar, R. Das, A.J. Thakur, E. Salminen, P. Mäki-Arvela, N. Kumar, J.-P.

446

Mikkola, D. Deka, Biodiesel production from acid oils using sulfonated carbon

447

catalyst derived from oil-cake waste, J. Mol. Catal. A Chem. 388 (2014) 167–176. [5]

S.L. Gonzalez, M.M. Sychoski, H.J. Navarro-Díaz, N. Callejas, M. Saibene, I. Vieitez,

RI PT

448

I. Jachmanián, C. Da Silva, H. Hense, J.V. Oliveira, Continuous catalyst-free

450

production of biodiesel through transesterification of soybean fried oil in supercritical

451

methanol and ethanol, Energy and Fuels. 27 (2013). doi:10.1021/ef400869y.

452

[6]

SC

449

K.T. Tan, K.T. Lee, A.R. Mohamed, Effects of free fatty acids, water content and cosolvent on biodiesel production by supercritical methanol reaction, J. Supercrit. Fluids.

454

53 (2010) 88–91. doi:10.1016/j.supflu.2010.01.012.

455

[7]

M AN U

453

K.C. Santos, F. Hamerski, F.A. Pedersen Voll, M.L. Corazza, Experimental and kinetic modeling of acid oil (trans)esterification in supercritical ethanol, Fuel. 224

457

(2018) 489–498.

458

[8]

TE D

456

P. Patil, S. Deng, J.I. Rhodes, P.J. Lammers, Conversion of waste cooking oil to biodiesel using ferric sulfate and supercritical methanol processes, Fuel. 89 (2010)

460

360–364.

462

[9]

S. Saka, D. Kusdiana, Biodiesel fuel from rapeseed oil as prepared in supercritical

AC C

461

EP

459

methanol, Fuel. 80 (2001) 225–231.

463

[10] Y. Sun, S. Ponnusamy, T. Muppaneni, H.K. Reddy, J. Wang, Z. Zeng, S. Deng,

464

Transesterification of camelina sativa oil with supercritical alcohol mixtures, Energy

465

Convers. Manag. 101 (2015) 402–409.

466

[11] M.M. Gui, K.T. Lee, S. Bhatia, Supercritical ethanol technology for the production of

467

biodiesel: Process optimization studies, J. Supercrit. Fluids. 49 (2009) 286–292.

468

[12] K. Tat Tan, M. Mei Gui, K. Teong Lee, A. Rahman Mohamed, An optimized study of

19

ACCEPTED MANUSCRIPT 469

methanol and ethanol in supercritical alcohol technology for biodiesel production, J.

470

Supercrit. Fluids. 53 (2010) 82–87.

471 472

[13] A. Velez, P. Hegel, G. Mabe, E.A. Brignole, Density and conversion in biodiesel production with supercritical methanol, Ind. Eng. Chem. Res. 49 (2010) 7666–7670. [14] L. Osmieri, R. Alipour Moghadam Esfahani, F. Recasens, Continuous biodiesel

474

production in supercritical two-step process: phase equilibrium and process design, J.

475

Supercrit. Fluids. 124 (2017) 57–71. doi:10.1016/j.supflu.2017.01.010.

477

[15] A. Velez, S. Pereda, E.A. Brignole, Isochoric lines and determination of phase

SC

476

RI PT

473

transitions in supercritical reactors, J. Supercrit. Fluids. 55 (2010) 642–646. [16] Q. Shang, L. Wang, S. Xia, M. Shen, P. Ma, Measurement and correlation of ternary

479

vapor-liquid equilibria for methanol + glycerol + fatty acid methyl ester (methyl

480

laurate, methyl myristate, methyl palmitate) systems at elevated temperatures and

481

pressures, Fluid Phase Equilib. 425 (2016) 15–20.

M AN U

478

[17] C. Silva, L. Soh, A. Barberio, J. Zimmerman, W.D. Seider, Phase equilibria of triolein

483

to biodiesel reactor systems, Fluid Phase Equilib. 409 (2016) 171–192.

484

doi:10.1016/j.fluid.2015.09.049.

TE D

482

[18] M.B. Oliveira, V. Ribeiro, A. Onio Jos E Queimada, J. Ao, A.P. Coutinho, Modeling

486

Phase equilibria relevant to biodiesel production: A Comparison of gE Models, Cubic

487

EoS, EoS-gE and Association EoS, Ind. Eng. Chem. Res. 50 (2011) 2348–2358.

AC C

EP

485

488

[19] F.A. Perdomo, B.M. Millán-Malo, G. Mendoza-Díaz, A. Gil-Villegas, A. Galindo, P.J.

489

Whitehead, S. Mills, G. Jackson, A.N. Burgess, Predicting reactive equilibria of

490

biodiesel’s fatty-acid-methyl-esters compounds, J. Mol. Liq. 185 (2013) 8–12.

491

[20] M.B. Oliveira, F. Llovell, M. Cruz, L.F. Vega, J.A.P. Coutinho, Phase equilibria

492

description of biodiesels with water and alcohols for the optimal design of the

493

production and purification process, Fuel. 129 (2014) 116–128.

20

ACCEPTED MANUSCRIPT 494

[21] D. Nguyenhuynh, A. Falaix, J.-P. Passarello, P. Tobaly, J.-C. De Hemptinne,

495

Predicting VLE of heavy esters and their mixtures using GC-SAFT, Fluid Phase

496

Equilib. 264 (2008) 184–200. [22] J. Gross, G. Sadowski, Application of perturbation theory to a hard-chain reference

498

fluid: an equation of state for square-well chains, Fluid Phase Equilib. 168 (2000) 183–

499

199.

502 503 504

perturbation theory for chain molecules, Ind. Eng. Chem. Res. 40 (2001) 1244–1260.

SC

501

[23] J. Gross, G. Sadowski, Perturbed-chain SAFT: An equation of state based on a

[24] J. Gross, G. Sadowski, Application of the perturbed-chain SAFT equation of state to associating systems, Ind. Eng. Chem. Res. 41 (2002) 5510–5515.

M AN U

500

RI PT

497

[25] W.G. Chapman, G. Jackson, K.E. Gubbins, Phase equilibria of associating fluids:

505

chain molecules with multiple bonding sites, Mol. Phys. 65 (1988) 1057–1079.

506

[26] W.G. Chapman, K.E. Gubbins, G. Jackson, M. Radosz, SAFT: Equation-of-state

508

[27] M.L. Corazza, W.A. Fouad, W.G. Chapman, PC-SAFT predictions of VLE and LLE of systems related to biodiesel production, Fluid Phase Equilib. 416 (2016) 130–137. [28] M.L. Corazza, W.A. Fouad, W.G. Chapman, Application of molecular modeling to the

511

vapor–liquid equilibrium of alkyl esters (biodiesel) and alcohols systems, Fuel. 161

512

EP

510

AC C

509

solution model for associating fluids, Fluid Phase Equilib. 52 (1989) 31–38.

TE D

507

(2015) 34–42. doi:10.1016/j.fuel.2015.08.003.

513

[29] J.L.A. Dagostin, M.R. Mafra, L.P. Ramos, M.L. Corazza, Liquid–liquid phase

514

equilibrium measurements and modeling for systems involving {soybean oil + ethyl

515

esters + (ethanol + water)}, Fuel. 141 (2015) 164–172.

516

[30] P.R. Santos, Schizaki, F.A.P. Voll, L.P. Ramos, M.L. Corazza, Esterification of fatty

517

acids with supercritical ethanol in a continuous tubular reactor, J. Supercrit. Fluids.

518

126 (2017) 25–36.

21

ACCEPTED MANUSCRIPT 519

[31] Y.-T. Tsai, H.-M. Lin, M.-J. Lee, Biodiesel production with continuous supercritical

520

process: Non-catalytic transesterification and esterification with or without carbon

521

dioxide, Bioresour. Technol. 145 (2013) 362–369. [32] O. Farobie, Y. Matsumura, Continuous production of biodiesel under supercritical

523

methyl acetate conditions: Experimental investigation and kinetic model, (2017).

524

[33] C. Silva, T.A. Weschenfelder, S. Rovani, F.C. Corazza, M.L. Corazza, C. Dariva, J. V

525

Oliveira, Continuous production of fatty acid ethyl esters from soybean oil in

526

compressed ethanol, Ind. Eng. Chem. Res. 46 (2007) 5304–5309.

SC

RI PT

522

[34] A.R. Bazaev, I.M. Abdulagatov, E.A. Bazaev, A. Abdurashidova, PVT measurements

528

for pure ethanol in the near-critical and supercritical regions, Int. J. Thermophys. 28

529

(2007) 194–219.

533 534

[36] A. Velez, G. Soto, P. Hegel, G. Mabe, S. Pereda, Continuous production of fatty acid

TE D

532

thermodynamic properties of ethanol, Int. J. Thermophys. 25 (2004) 321–335.

ethyl esters from sunflower oil using supercritical ethanol, Fuel. 97 (2012) 703–709.

EP

531

[35] H.E. Dillon, S.G. Penoncello, A fundamental equation for calculation of the

AC C

530

M AN U

527

22

ACCEPTED MANUSCRIPT Table 1. References of experimental data for binary and ternary systems at high pressure. System

Glisic et al. [34]

methanol + triolein

Shimoyama et al. [35]

methanol + methyl myristate

Shimoyama et al. [36]

ethanol + ethyl myristate

Shimoyama et al. [37]

methanol + glycerol

Shimoyama et al. [37]

ethanol + glycerol

RI PT

Reference

methanol + glycerol + methyl laurate

Shang et al. [16]

methanol + glycerol + methyl myristate

Shang et al. [16]

methanol + glycerol + methyl palmitate

AC C

EP

TE D

M AN U

SC

Shang et al. [16]

ACCEPTED MANUSCRIPT

Components Parameters

ASPEN Name*

m

Methyl myristate [28]

Methyl palmitate [28]

Ethyl myristate [28]

PCSFTM

6.5942

7.2167

7.7791

7.5140

ε (K)

PCSFTU

249.25

252.17

255.40

σ

PCSFTV

3.7242

3.7782

3.8338

PCSFAU

0

0

0

PCSFAV

0

0

0

ε

(K)

HB

κ

AC C

EP

TE D

* Parameters named in ASPEN Plus data bank. ** Parameters taken from Corazza et al. [27].

Triolein [17]

9.8000

18.3844

8.7192

3.6456

2.7541

251.26

240.79

302.89

254.78

336.48

342.99

3.8093

3.7016

4.3005

3.7118

3.0881

3.4547

0

0

0

810.92

3098.42

2416.37

0

0

0

0.0183

0.0318

0.0271

M AN U

HB

Glycerol Glycerol Oleic acid (2 sites)** (4 sites)** [30]

Ethyl oleate [28]

SC

Methyl laurate [28]

RI PT

Table 2. PC-SAFT parameters of methyl esters, ethyl esters, triolein, oleic acid and glycerol.

ACCEPTED MANUSCRIPT

Table 3. Root mean square deviation for the ternary systems.

II

III

Vapor Phase

Liquid Phase

methanol

0.771

1.731

glycerol

0.701

0.684

methyl laurate

0.247

1.195

methanol

0.435

1.294

glycerol

0.535

0.625

methyl myristate

0.352

0.925

methanol

0.799

0.713

glycerol

0.710

methyl palmitate

0.157

Total RMSD (%)

1.003

RI PT

I

RMSD (%)

Components

0.766

SC

System

0.319

0.595

0.591

M AN U

System I (methanol, glycerol and methyl laurate), system II (methanol, glycerol and methyl myristate) and system III (methanol, glycerol and methyl palmitate) the total data of each system were 156, 72 and 78, respectively. Pressure and temperature ranges from 4 to 8 bar and 493 to 523 K, respectively, according to Shang et al. [16].

Table 4. Negative and positive variation in density in the range of 10 and 40%.

TE D

Density (g/cm3)

AC C

EP

Negative variation Positive variation

10% 0.4866 0.5948

40% 0.3244 0.7570

ACCEPTED MANUSCRIPT

Figure Captions

Figure 1. Pressure-composition diagrams for the system (A) methanol + methyl myristate [35] and (B) ethanol + ethyl myristate [36] at (▲) 493 K, (●) 523 K, (■) 543

RI PT

K. Comparison between experimental data and calculated values using PC-SAFT with (continuous lines) and without (dashed line) cross-association. All interaction parameters (kij) were set to zero.

SC

Figure 2. Pressure-composition diagrams for the systems (A) methanol + glycerol [37] and (B) ethanol + glycerol [37]. Comparison of calculated results from PC-SAFT

M AN U

considering (─) glycerol with 4 active sites and (---) glycerol with 2 active sites and experimental data (▲) 493 K, (●) 523 K, (■) 543 K, (×) 573 K.

Figure 3. Pressure-composition diagram for methanol + triolein [34] system at (▲) 473 K, (●) 483 K, (■) 493 K, (×) 503 K. Comparison between experimental data and calculated values using PC-SAFT: (─) liquid phase, (---) vapor phase, (black line) 473

Figure 4.

TE D

K, (blue line) 483 K, (green line) 493 K, (red) 503 K.

Pressure-temperature diagram for the simultaneous esterification and

transesterification reaction with ethanol to acid oil molar ration (Et:OA) of (A) 4:1 and

EP

(B) 20:1. Typical reaction conditions used: (×) 493 K, (▲) 523 K (●) 553 K, (■) 573 K. Saturation lines (─, liquid phase; ---, vapor phase) were calculated using the PC-SAFT

AC C

for the reactant mixture at the initial condition (0% conversion) (grey line) and assuming complete reaction at the end of reaction (100% conversion) (black line); and pure compounds ethanol (blue line), triolein (red line).

Figure 5.

PC-SAFT density calculations versus temperature at 10 MPa of pure

components (solid lines: ethanol, black line; soybean oil, red line; and oleic acid, blue line) and mixtures with different ethanol to acid oil molar ratio (Et:OA) (black dashed lines: 2:1 to 20:1), (A) considering the mixture as an ideal solution with density of pure components calculated by the PC-SAFT, and (B) density mixture calculated using the PC-SAFT equation of state.

ACCEPTED MANUSCRIPT Figure 6. Comparison of the experimental density (symbols [38]) and calculated values (lines: Dillon e Penoncello [39],──; Gross e Sadowski [23],─ ─ e Corazza et al. [28],−·−·) of ethanol in different temperatures: 523 K (□), 548 K (○) e 623 K (◊).

RI PT

Figure 7. Analysis of the density effects on the residence time estimation. Reaction conditions from Santos et al. [7]: simultaneous esterification and transesterification reaction of soybean oil with 20 wt% of oleic acid and Et:OA of 4:1 at 553 K and 10 MPa. Full symbols represent the experimental data of FAEE yield versus the estimated

SC

residence time using different mass flow, as presented by Santos et al. [7], (continuous line is a smoothed trendline for the symbols). Red bars represent the residence time estimation considering 10% variation in the density of the mixture. And, black dashed

AC C

EP

TE D

M AN U

bars represent the residence time estimated with 40% deviations.

ACCEPTED MANUSCRIPT

AC C

EP

TE D

(B)

M AN U

SC

RI PT

(A)

Figure 1

ACCEPTED MANUSCRIPT

M AN U

SC

RI PT

(A)

AC C

EP

TE D

(B)

Figure 2

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

Figure 3

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Figure 4

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Figure 5

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

Figure 6

Figure 7