# Optimization of the Production of 1,1-Diethoxybutane by Simulated Moving Bed Reactor

^{*}

## Abstract

**:**

## 1. Introduction

_{2}in the atmosphere. Combustion of fossil fuels accounts for 82% of the increase of CO

_{2}concentration [1]; therefore, a lot of research is focused on finding alternative fuels. The interest is even further increased due to the predicted shortage of fossil fuel reserves.

_{2}and releases less hydrocarbons and non-gaseous emissions [4]. However, biodiesel has some drawbacks, namely high particles and NOx emissions [5]. Additionally, petroleum diesel has better properties regarding oxidization stability, energy content and operability at low temperatures [6]. A promising method to overcome these drawbacks is the blending of biodiesel with other compounds like acetals. The use of 1,1-diethoxyethane has shown promising results, but the flashpoint is below the European regulation limit [7]. Therefore, the use of acetals with higher molecular weights is an interesting option. In this context, 1,1-diethoxybutane (DEB) has been identified as a potential alternative additive.

## 2. Methods

#### 2.1. Mathematical Model

_{0}refers to pure eluent concentration, which means there is only ethanol present. In the equations, u refers to the interstitial velocity, K

_{L}is the global mass transfer coefficient, D

_{ax}is the axial dispersion coefficient, t is the time variable, z is the axial coordinate, v

_{i}is the stoichiometric coefficient, ρ

_{b}is the bulk density and $r\left({\overline{C}}_{p,i}\right)$ is the reaction rate based on the average particle concentration. The reaction rate is shown in Equation (6),

_{i}corresponds to the activity coefficient. These coefficients are based on the average particle concentration and are calculated via the universal quasichemical functional-group activity coefficient (UNIFAC) method. The equilibrium constant K

_{eq}, the water equilibrium constant K

_{S}

_{,D}and the reaction kinetic constant k

_{c}were determined in a previous study [11] and are represented by Equations (7)–(9).

_{i}represents the total molar capacity for each component per volume of adsorbent and K

_{i}represents the equilibrium constant for each component. These values, determined in a previous work [22], are presented in Table 1.

_{mol}is the molar volume of component I, with the following boundary condition:

_{in}and Q

_{out}represents the volumetric flow in and the volumetric flow out, respectively, in l/s.

_{p}, Re

_{p}and Sc are, respectively, the particle Sherwood number, the particle Reynolds number and the Schmidt number, which are determined via Equations (17)–(19).

_{AA}represents the self-diffusion coefficient, K

_{B}represents the Boltzmann constant, ${\tilde{N}}_{A}$ represents the Avogadro number and ${\stackrel{\u02c7}{V}}_{A}$ represents the molar volume. The results are in the same order of magnitude as those reported in other studies [27].

#### 2.2. Performance Parameters

_{x}represents the extract flowrate, Q

_{R}the raffinate flowrate, Q

_{F}the feed flowrate and C

_{B}

_{,F}the butanal concentration in the feed.

_{D,R}represents the DEB concentration in the raffinate stream and V

_{unit}represents the volume of all the columns.

_{D}represents the flowrate of the eluent going into the SMBR and V

_{mol,A}represents the molar volume of ethanol.

#### 2.3. Numerical Solution

## 3. Results and Discussion

#### 3.1. Fixed Bed Adsorptive Reactor Model Validation

#### 3.2. Sensitivity Analysis to the SMBR Operating Parameters

_{1}and γ

_{4}should be a set value, to ensure that at all times the desorbent and solvent are cleaned properly. This is called a sensitivity analysis, because the influence of the switching time on the performance parameters is determined. These values are determined via Equations (36) and (37),

_{1}and γ

_{4}, a value of 1 must be added to Equations (36) and (37). This results in a value of 3.465 and 1.635 for γ

_{1}and γ

_{4}, respectively. When these values are used, Section 1 and Section 4 work properly, and the desorbent and solid are cleaned completely. For the rest of the simulations in this section, these values should be maintained. This means that the recycle flow rate and the eluent flow rate are set for each specific switching time value. The γ

_{2}and γ

_{3}values need to be determined regarding a purity requirement of the extract and the raffinate. The ratios in Section 2 and Section 3 can be changed by altering the feed flowrate and the extract flowrate. From these flowrates, the raffinate flowrate is calculated by closing the mass balance.

_{2}–γ

_{3}plane that satisfies the purity requirement is delimited. This is called the separation region in the case of SMB and reactive-separation region in the case of SMBR. In Figure 8 an idealized situation of the separation region is shown.

_{1}and γ

_{4}are set, the recycle and eluent flow are also set. The simulations are run until the cyclic steady state is reached, and then the raffinate and extract purities are known. At the beginning of the simulation, the extract and feed flowrates are set, and the raffinate flowrate is calculated, in order to close the mass balance. At the first simulation, a low value should be set to the feed flow and extract flow. This way, both γ

_{2}and γ

_{3}values are high, and should be outside the reactive-separation region. The next simulation should have a higher extract flowrate with the same feed flowrate. This way, the point on the graph moves parallel to the diagonal. At a certain extract flowrate, the point gets inside of the separation region, and at some point, with an even higher extract flow rate, the point gets outside the region. At this moment, the boundaries of the reactive-separation region are known, with a certain feed flowrate. The next point is with the same extract flowrate that is just outside the region, but with a higher feed flowrate. Increasing the feed flowrate moves the point perpendicular to the diagonal. Because it is known that at best, the reactive-separation region is a triangle, as presented in Figure 8, this point should still be outside of the region. Now the extract flowrate is decreased, and will move inside the region, and eventually get outside of the region again. From that point, the feed flowrate is increased, and after that, the extract flowrate will be increased again. This goes on until a certain point where the purity requirements will not be met anymore by changing the extract flowrate. From that moment, the maximum feed flowrate is reached, corresponding to the vertex of the region. At this moment, the separation region can be drawn (with several discrete points corresponding to simulations with different γ and switching time values combinations that ran until the cyclic steady state was reached), and the performance parameters of the vertex will be compared with other vertexes, obtained using different switching times, in a first approach. It has to be noted that conversion is an important factor, but since the conversion is computed regarding butanal (the limiting reactant), and the desorbent is ethanol, the conversion will almost go to completion in all the cases.

_{2}and γ

_{3}values, but the shape will be similar. The main thing that will change is its area, because a more appropriate switching time will result in a larger separation region. The conditions used for the simulation are presented in Table 4. For the further simulations that are done in this work, these conditions were maintained.

#### 3.3. Optimization of DEB Synthesis by SMBR: Separation Volumes

_{1}and γ

_{4}were kept constant, considering a 20% safety factor relatively to the values provided by the Equilibrium Theory (Equations (34) and (35)). The optimization procedure that will be implemented in this section will allow the maximization of the productivity and the minimization of the desorbent consumption through the optimization of γ

_{2}and γ

_{3}values as a function of γ

_{1}and γ

_{4}, defining a minimum purity requirement of 97%.

_{1}, γ

_{4}and switching time values), coupled with a sensitivity analysis to the flow rate ratios in Section 1 and Section 4. The limit values for the latter variables can be determined through the Equilibrium Theory, as explained earlier, which defines the maximum eluent recycling flow rate in Section 4 and the minimum desorbent flow rate in Section 1, which allow the regeneration of the liquid and solid phases, respectively. Therefore, in the Reactive Separation Volumes methodology, several reactive-separation regions are determined for different combinations of γ

_{1}and γ

_{4}values, sequentially approaching the limit values imposed by the Equilibrium Theory to these variables. The procedure to determine each of these reactive-separation regions is described in detail in the previous section and basically consists of determining the (γ

_{2}, γ

_{3}) sets that meet the target species purity specifications for each (γ

_{1}, γ

_{4}) set. Repeating the process for different (γ

_{1}, γ

_{4}) combinations, as detailed before, will allow the determination of the reactive separation volumes.

_{3}–γ

_{2}), since this corresponds to the highest feed flow rate that the unit can treat; and the second is the optimization of the desorbent consumption, which corresponds to the minimum (γ

_{1}–γ

_{4}), since the desorbent flow rate will decrease as this difference decreases. At the end of this procedure, the optimum flow rates are known for the predetermined optimum switching time (which is 2.4 min, according to the results reported in the previous section).

_{1}and γ

_{4}.

_{1}value of 4.24 and a γ

_{4}of 1.35. From the plot with the desorbent consumption it can be seen that this point is not the optimum point, but the optimum point regarding the desorbent consumption corresponds to a significantly lower productivity. Since ethanol is used as a desorbent and this is a widely available bulk chemical, the optimum point is chosen regarding the highest productivity. At this point a productivity of 19.8 kg DEB per liter of adsorbent per day, a desorbent consumption of 6.1 L of ethanol per kg of DEB is reached.

## 4. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Glossary

List of symbols | |

a | Activity |

A | Cross-sectional area (dm^{2}) |

C | Concentration (mol L^{−1}) |

CO_{2} | Carbon dioxide |

CFDM | Centered finite difference method |

D_{i,m} | Diffusion coefficient of compound i in a mixture |

D_{ax} | Axial dispersion coefficient |

DC | Desorbent consumption (L_{des.} Kg^{−1}_{DEB}) |

DEB | 1,1-diethoxybutane |

k_{B} | Boltzmann constant (1.38064852 × 10^{−23} m^{2} kg s^{−2} K^{−1}) |

K | Adsorption equilibrium constant (L mol^{−1}) |

k_{C} | Reaction kinetic constant (mol g^{−1}s^{−1}) |

K_{E} | External mass transfer (dm s^{−1}) |

K_{eq} | Equilibrium constant |

K_{i} | Internal mass transfer (dm s^{−1}) |

K_{L} | Overall mass transfer coefficient (dm s^{−1}) |

K_{S,D} | Water adsorption constant |

L | Length of the column (dm) |

NO_{x} | Nitrogen oxides |

PR | Productivity (Kg_{DEB} L_{ads.}^{−1} day^{−1}) |

PUR | Raffinate purity (%) |

PUX | Extract purity (%) |

Q | Flow rate (L s^{−1}) |

q | Particle solid concentration (mol L^{−1}) |

Q_{i} | Molar Adsorption capacity of compound i (mol L^{−1}) |

r | Reaction rate (mol g^{−1} s^{−1}) |

Re | Reynolds number |

Sc | Schmidt number |

Sh | Sherwood number |

SMBR | Simulated moving bed reactor |

T | Temperature (K) |

t | Time (s) |

TMBR | True moving bed reactor |

u | Interstitial Velocity (dm s^{−1}) |

V_{mol} | Molar volume (dm^{3} mol^{−1}) |

X | Conversion (%) |

x | Molar fraction |

z | Dimensionless axial coordinate (dm s^{−1}) |

Greek letters | |

β | Safety factor |

γ | Ratio between liquid and solid interstitial velocities |

ε | Porosity (volume void volume bed^{−1}) |

η | Viscosity (cP) |

ρ | Density (g L^{−1}) |

τ | Tortuosity |

Subscripts | |

B | Butanal |

D | Desorbent |

EtOH | Ethanol |

F | Feed |

i | Component i |

m | Mixture |

p | Particle |

R | Raffinate |

Rec | Recycle |

W | Water |

X | Extract |

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**Figure 9.**Separation region using a switching time of 4.5 min and a 20% safety factor for γ

_{1}and γ

_{4}.

**Figure 10.**Sensitivity analysis regarding the influence of switching time on the productivity and the desorbent consumption, by setting a 20% safety factor for γ

_{1}and γ

_{4}.

**Figure 12.**Desorbent consumption performance against γ

_{1}and γ

_{4}at the optimum γ

_{2}and γ

_{3}.

**Table 1.**Multicomponent Langmuir isotherm parameters for the species involved in the synthesis of 1,1-diethoxybutane (DEB) at 303 K [22].

Component | Q (mol L_{Solid}^{−1}) | K (L mol^{−1}) |
---|---|---|

Ethanol | 10.58 | 7.24 |

Butanal | 3.08 | 0.12 |

Water | 34.47 | 8.18 |

DEB | 3.59 | 0.06 |

Experiment | 1 | 2 | 3 |

Bed length (cm) | 10.95 | 11.18 | 11.1 |

Column diameter (cm) | 2.6 | 2.6 | 2.6 |

Temperature (K) | 303 | 303 | 303 |

Bed porosity | 0.42 | 0.42 | 0.42 |

Particle porosity | 0.5 | 0.5 | 0.5 |

Péclet number | 64.4 | 64.4 | 64.4 |

Flowrate (mL min^{−1}) | 5.1 | 7.59 | 7 |

C_{0,ethanol} (mol/L) | 0.579 | 0 | 16.958 |

C_{0,water} (mol/L) | 0 | 55.26 | 0 |

C_{0,DEB} (mol/L) | 5.535 | 0 | 0 |

C_{F,ethanol} (mol/L) | 16.958 | 16.897 | 11.4 |

C_{F,water} (mol/L) | 0 | 0.212 | 3.61 |

C_{F,DEB} (mol/L) | 0.001 | 0 | 0 |

**Table 3.**Correlation factors attained for the breakthrough curves used for the fixed bed reactor model validation.

This Work | Previous Work [22] | |
---|---|---|

Ethanol and Water | 0.991 | 0.989 |

Ethanol and Deb | 0.998 | 0.999 |

Reaction | 0.954 | 0.949 |

Parameter | Value |
---|---|

Temperature (K) | 303 |

Configuration | 3-3-3-3 |

Column Length (cm) | 23.0 |

Column diameter (cm) | 2.6 |

Bed porosity | 0.42 |

Particle porosity | 0.5 |

Péclet number | 64.4 |

Ethanol feed concentration (mol/L) | 12.266 |

Butanal feed concentration (mol/L) | 3.064 |

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**MDPI and ACS Style**

Spitters, J.; Gonçalves, J.C.; Faria, R.P.V.; Rodrigues, A.E.
Optimization of the Production of 1,1-Diethoxybutane by Simulated Moving Bed Reactor. *Processes* **2021**, *9*, 189.
https://doi.org/10.3390/pr9020189

**AMA Style**

Spitters J, Gonçalves JC, Faria RPV, Rodrigues AE.
Optimization of the Production of 1,1-Diethoxybutane by Simulated Moving Bed Reactor. *Processes*. 2021; 9(2):189.
https://doi.org/10.3390/pr9020189

**Chicago/Turabian Style**

Spitters, Jasper, Jonathan C. Gonçalves, Rui P. V. Faria, and Alírio E. Rodrigues.
2021. "Optimization of the Production of 1,1-Diethoxybutane by Simulated Moving Bed Reactor" *Processes* 9, no. 2: 189.
https://doi.org/10.3390/pr9020189