Summary of species properties and molecular weight (MW) .
The modeling and simulation of transesterification require an understanding of the chemical reactions that take place inside the reactor. The development of reaction mechanism of the multiple step triglyceride, triglycerides and mono-glycerides and their reversal reaction is beyond the interest of chemical or mechanical engineers, whose main interests are to assess the conversion overall and to establish performance process metrics. This chapter undertakes the transesterification conversion by firstly establishing and formulating the overall process kinetics as far as the rate constant and activation energy. Secondly, use the obtained kinetic values to carry out high fidelity reactive flow of the multiple species which are co-present inside the reactor and otherwise complex to capture experimentally. Following these two steps, this work provides qualitative and quantitative information on the concentration of the reactants, intermediates and the overall yield. This two-step-approach can also be utilized as reactor design tool and gaining in-depth insight on reaction progress and species distribution. Experimental results, high-fidelity numerical results, and parametric sensitivity studies will be introduced and discussed.
- chemical kinetic
- crude glycerol
Stoichiometrically and theoretically speaking, transesterification consumes 1 mole of triglyceride and 3 moles of alcohol to produce 3 moles of fatty acid methyl esters (FAME) and 1 mole of crude glycerol. Practically, unconverted triglyceride (TG) and intermediates (i.e. diglyceride (DG) and monoglyceride (MG)) co-present in the yield which signifies the incompletion of the reaction . As these reactions are mildly influenced by temperature and pressure because of their nearly equal heat of formation and liquid phase, the increase in the molarity of the alcohol promotes the desired forward reaction . Contrary to well-known hydrocarbon fuels that are characterized by fixed thermodynamic and physical properties, the TG, DG, MG have no fixed chemical formula and neither their thermodynamic properties, such as standard enthalpy or specific heats, nor physical ones like density or viscosity, are consistent throughout the literature [3, 4]. Therefore, material characterization is an essential step in the modeling of the transesterification process. The extent of these properties depends on the complexity and comprehensiveness of the simulation, from a simple incompressible flow that requires only viscosity and density, to a complex non-isothermal flow that requires heat of formation, specific heat, thermal conductivity and their associated diffusions. However, as these properties can be derived following the American Society for Testing and Materials (ASTM) standards, their reactions are more complex. Table 1 summarizes some of the utilized properties for the waste oil, TG, DG, and MG used in the work of Noureddine and Zhu who were amongst the pioneers of quantifying transesterification reaction kinetics .
|Species||Chemical formula||Molecular weight (g/mol)||Viscosity (kg/m.s)||Cp (J/kg.°C)||Density (kg/m3)|
|Waste oil or Triglyceride||C54H105O6||848||1.61E-2||2.2E3||883.3|
Setting up a reaction mechanism of numerous species or elements and hundreds of reactions, while accounting for reaction radicals, is rather impractical for engineers. The overall reaction can be captured through well controlled conditions and yield assessment procedures that can save the pain of the development or use these reaction mechanisms. This chapter undertakes the conventional transesterification at different process temperatures, highlighting their influence on the yield and their distribution inside the reactor.
2. Biodiesel feedstock and the reactor device
While corn, sunflower, and palm oil are readily available in the market, their utilization may raise a strong debate on land for food vs. land for energy. To rule out this debate, waste cooking oil (WCO) is used instead, because it is abundantly available feedstock, inexpensive and most of the time its disposal into sewerage systems is associated with environmental concerns. The supply chain of collecting this abundant source is beyond the scope of this chapter. However, it is important to state that residential communities are in general in favor of trapping this problematic sewerage source that is responsible for clogging the plumbing systems. Collection also can be facilitated by using drum type or smaller plastic containers provided to the local restaurant, school/university canteens, residential communities as a privately owned small business, or through municipality.
The collected WCO generally requires pretreatment that can be facilitated at a moderate temperature to maintain its liquid and less viscous form. One can use the heat of the summer (45–50°C) at which unsaturated and saturated steric fatty acid stays in liquid form, and 10–20 μm filtration can be used to eliminate any suspended oil solid residuals. Dehydrating of the WCO is also required, during which any water content brought by the processed food into the waste cooking oil is liberated through evaporation. At the laboratory scale, stirring and heating pad at near 110°C for several hours can perfect this task. Process methanol and catalyst NaOH or KOH can also be substituted with commercially available grade instead of high purity pharmaceutical grade/Sigma-Aldrich that can also leverage process economically. Once pretreatment of the feedstock is done, the NaOH solid catalyst in the form of small ballets is dissolved into methanol at the stipulated ratio, i.e. 0.5–1% by mass of WCO. This process can be facilitated under moderate heating and a temperature below 60°C and stirring forming the meth oxide reactant solution. In the lab, multiple transesterification reaction experiments can be conducted simultaneously under the same temperature and stirring rate to reduce experimental sequence and human error. This can be carried out using a multiple dissolution apparatus such as those provided by
The continuous reactor consists of a tubular reactor of two or more upright concentric cylinders. Each is equipped with inflow at the bottom and outflow at the top port, connected by 5-mm ϕ chemically resistive hoses. The inflow and outflow are configured circumferentially in each cylinder, rendering the flow more residence time due to their helical trajectory. The details of the reactor’s dimensions and geometry can be found in the work of Janajreh et al. . A peristaltic or a diaphragm pump type is used to inject the two reactants, i.e. pretreated oil and methoxide into the reactor at the stipulated molar ratio. The mass flow rate is typically being set beyond laminar limits for turbulence mixing that help the transesterification reaction. The mixture from the batch dissolution is periodically recovered in 10 mm vials, and is refrigerated to halt their progressive reactions for downstream species analysis. The analysis of the compositions of TG, DG, MG, FAME, glycerol (GL) and alcohol (AL) is carried out using a standard Gas Chromatography Mass Spectrometry (GC/MS) equipment as those provided by
In the GC/MS analytical equipment, the FAME column is initially calibrated using standard biodiesel and glycerol samples to ensure precise qualitative and quantitative analysis. The collected and refrigerated vials are obtained at numerous and progressive reaction intervals of 15-time steps over 2 hr of reaction time . The breakdown of sample species composition is acquired using methods similar to those carried out by Noureddini and Zhu  and Janajreh et al. . Transesterification is performed at 6:1 alcohol to oil molar ratio and 0.5% NaOH by mass of WCO, and both at different temperatures of 50 and 60°C.
3. Transesterification method
In these equations,
where (s−1) is the pre-exponential constant,
4. Transesterification kinetics evaluation
Transesterification is a slowly reversible reaction, where only the forward reactions are desired for the production of biodiesel. It is easy to say that lower activation energies are favored for forward reactions (
As can be shown in Figure 4 of the GC/MS results obtained at the two temperatures,
|Designated K or E||Rate constant at T = 50°C||Rate constant at T = 60°C||Activation energy (J/mol)||Pre-constant (sec−1)|
|TG + AL—E + DG||0.1213||0.1157||4103||77,983,755.8|
|E + DG—TG + AL||0.1167||0.3276||90,540||449,020.085|
|DG + AL—E + MG||0.8177||0.8947||7896||1.0976 E12|
|E + MG—DG + AL||3.5379||3.1354||10,597||4570,1701.3|
|MG + AL—E + GL||1.5943||1.7922||10,267||767.86|
|GL + E—MG + AL||0.1661||0.1322||19,980||32,870.58|
|TG + 3AL—3E + GL||0.001||0.001||3089||77,983,755.8|
|GL + 3E—TG + 3A||0.8149||0.7568||6490||449,020.085|
The evaluated kinetics will be utilized in the development of a high fidelity reaction model. The model will be based on reactive flow of the six species, TG, AL, DG, MG, E and GL and their eight reactions. These are types of volume homogenous reactions. The considered reactor will be a tube type subjected to appropriate conditions and enabling the assessment of the yield and species distribution.
In summary, the required kinetics that governs the reactions and change of species has been evaluated. Results are intuitively correct, as a higher temperature results in higher rate constants. These data will be used in the high fidelity reactive flow analysis that will be detailed next. It is important to emphasize that importance of these simulations in capturing the overall species and their distribution in the reaction device. This is becoming the tool for the development of the new and innovative reactors. The observations procured from performing the chemical kinetic study enables the shift in conventional transesterification towards a modified sonication kinetic data for further reactive flow analysis. Comparison between regular mixing and ultra- sound assisted procedures proves the supremacy of the latter in terms of fastening the forward reactions by increasing reaction rates and decreasing activation energies of forward reactions. Note that the comparative study is performed to obtain an idea of the trend of sonication and not to get exact chemical kinetics.
5. High-fidelity transesterification model development
In order to sharpen our understanding of the transesterification reaction progression and species distribution, a high fidelity reactive flow model for transesterification is developed. The basis of the model is computational fluid dynamics (CFD). Several research software have adopted CFD environment to solve multiple physics, whereby some are open sources and others are more commercially tuned. The transesterification model is developed within the finite volume CFD based software of Ansys/Fluent 17.1 .
5.1. Governing equations
We here focus on the modeling of the tubular reactor that depicted earlier in Figure 2 which has numerous advantages over the batch reactor, i.e. continuous, compactness, better yield . Modeling involves the application of flow continuity, momentum, and energy equations. Furthermore, the flow is characterized as a mixture of multiple reacting species, incompressible, viscous, and turbulent. The reaction is assumed to start as soon as the reactant components are met inside the reactor. The flow is governed by the Navier-Stokes equation, which is associated with temporal, advective, viscous, and any source term and is written as:
The left terms govern the advective while the right hand terms govern respectively the generation, the diffusion, and destruction of the turbulent quantities. In these equations, is the eddy viscosity parameter and it overwhelms the laminar viscosity and is written as:
where and are flow dependent constants and C1ε, C2ε,σk and σs are tuning empirical constants. The transport equations that govern the of species
The reaction rate is proportional to the concentration of the reaction species (both reactants and products) to an ordered of specified power coefficients that can be written as:
5.2. CFD setup and mesh sensitivity analysis
|Component||Outer cylinder (glass)||Middle cylinder (metal)||Inner cylinder (metal)|
|Outer diameter (mm)||59.9||42.0||26.2|
|Inner diameter (mm)||51.9||36.7||21.8|
A hybrid mesh of hexagonal and pyramid type is used to maintain the size within the processing capacity of the current laptop for an engineer. The mesh is established in
|Species||Chemical formula||Molecular weight (g/mol)||Viscosity (kg/m.s)||Cp (J/kg.°C)||Density (kg/m3)|
The boundary conditions are assigned as flow, constant velocity at the inlet and isothermal fluid. The boundary at the top outlet was defined as fixed pressure outlet at 0-Pa gauge pressure while the boundary walls are subjected to zero velocity, i.e. no slip and no penetration. The turbulence is accounted for via standard
Results of the unreacted isothermal flow distribution within the reactor, or cold flow as referred to in some literature, is depicted in Figure 7. Velocity vector colored by the residence time is used for the three level meshes. Results of residence time parameter is used as the most pronounced parameter for the intended reactive fluid to assess the mesh accuracy. These results are summarized in Table 5 for the three levels of the mesh for comparison. The baseline residence time is within 2% deviation from the next refined mesh, hence it is used for the rest of the analysis. However, the coarse mesh showed a sustainable deviation of nearly 10% that fails to be qualified as an accurate and representative mesh.
|Mesh type||Coarse||Baseline (Baseline × 1.5)||Fine mesh (Baseline × 1.89)|
|No. of cells||281,382||427,742||534,228|
|Residence time (sec)||1.01 × 103||1.080 × 103||1.100 × 103|
A total resident time of the order of 103 seconds is observed in each of the three meshes. If the flow was injected at relatively high velocity, it would ensure the required homogenize mixing of the reactants that also avoid any of the mass transfer limitation. The circumferential configuration of the entry and exit of the reactor enables it to maintain a long residence time, even at a higher inlet mass flow that forces the flow to move in a swirling trajectory.
5.3. Reactive flow analysis
The reactor tube is setup vertically and is subjected to inlet flow rate at Re = 6000 at the bottom of the tube into the inner reactor chamber. There, the two fluids of TG and methoxide (mixture of the methanol and the catalyst) are injected circumferentially at the stipulated molar/mass ratio and inlet temperature. The outflow is subjected to atmospheric pressure which is admitted at exit boundary condition of the outer tube chamber located at the top. The no-lip no penetration and insulated wall is also applied to all the bounded reactor walls.
To maintain single-phase flow avoiding the complication of other reactivation, the case of reactive flow simulation is carried out below the boiling point of methanol at a temperature of 60°C (333 K). A steady-state solution is sought for the flow. This is achieved by ignoring the temporal term of the governing equation. The flow is introduced to the reactor by means of an external peristaltic or diaphragm pump operating at relatively low head of nearly 2-m to overcome the viscous shear stresses and head losses and the reactor vertical head at an adjustable discharge capacity of up to 5 L/min.
5.4. Simulation results
Based on the stoichiometry of transesterification reactive 3 moles of methanol are consumed with 1 mole of triglycerides for the making of 1 mole of biodiesel. Using this ratio(3:1 methanol to WCO molar), which also corresponds to AL/WCO mass fraction of 0.102/0.892, results on the species contour plots depicted in Figure 8 and the outlet fractions are summarized in Table 6.
|Port & ratio/species||C54H104O6 (WCO)||CH4O||C18H36O2 (FAME)||C3H8O3||Conversion|
At this velocity and molar ration, a low conversion of 28% is achieved. The conversion is described by Eq. (16) and is written as:
From Figure 9, the concentration of the TG is reduced as the flow climbs up in the reactor as does the AL due to the production of biodiesel (E) and the two-intermediate species (MG and DG). The figure also clearly shows how DG precedes the formation of the MG and GL observed in the fading blue color contours of the DG concentration near the bottom inlet. The MG and GL show progressive color contours from the nil value represented by dark blue contours and reaching to higher value of 0.07 and 0.02 for each of MG and GL, respectively. Therefore, this allows additional residence time for the reaction in the second reactor tube reduces these intermediates and lead to higher production of the biodiesel and its byproduct glycerol. It must also be noted that these reactions are reversible and hence they can go either way, such that high conversion in the 1st tubular loop may be counter reacted by the second tubular loop and marking lower conversion.
Nevertheless, several sensitivity studies considering AL/WCO ratio, temperature, speed or mass flux of the feedstock etc. can be conducted. Results of the species concentration subjected to higher methanol ratio and larger influx of the feedstock of 600 mL/min (Re = 6000) are listed in Table 7. This result clearly marked a reasonable conversion of 66% which is higher than those obtained at lower influx %. The conversion seems also insensitive for the additional amount of the methanol which sounds counterintuitive initially and defies the experimental observation; this trend may be explained by the used kinetics which are inherited from the experimental work obtained at one ratio. These obtained values failed to capture the influence of the increase of the concentration of specific reactant to steer the reaction forward. Therefore, this may suggest another testing procedure at another molar ratio in parallel, mimicking those obtained and shown in Figure 4. Though, results emphasize the advantage of increasing residence time and efficient mixing of the flow which reduces the additional methanol concentration.
|Port & ratio/Species||C54H106O6 (WCO)||CH4O||C18H36O2 (FAME)||C3H8O3||Conversion|
|3:1 methanol-WCO molar ratio|
|6:1 methanol-WCO molar ratio|
|9:1 methanol-WCO molar ratio|
Transesterification of WCO to biodiesel is presented in this work and experimental and numerical analysis to this green process is presented. Initially, the chemical kinetics for the reaction are evaluated to the multiple reactions of the transesterification and in both the forward and reversal pathways for these reactions. The obtained kinetics presented by the activation energy (E) and the reaction pre-constant are evaluated and used to establish a high fidelity and robust reactive flow model. This model is based on computational fluid dynamics that is governed by the Navies-Stokes equations for isothermal, multiple species reactive flow in turbulent regime. The model is built around the newly patented multiple tube and continuous transesterification reactor. The flow enters the reactor laterally and induces swirling flow. In turn, this results in an order of magnitude residence time higher than the transfer time that is based on the tube length and inlet velocity. Reactive flow at low velocity results in low conversion of the WCO, while actual turbulent flow significantly increases the conversion rate. Excess methanol mass sensitivity was insignificant to the conversion parameter that suggest that modeling can be still limited and suggesting to integrate more kinetics data. This work emphasizes the efficient mixing of the flow, interplaying as a parameter to the additional methanol concentration, thereby avoiding their downstream separation. In closing, numerical simulation of transesterification undoubtedly demonstrates the effectiveness of this tool in analyzing complicated reactive flow as the student faces in transesterification. Still, the process fails to reach completion even at higher reactant concentration and beyond the process stoichiometry. This creates an opportunity in this area to go beyond the conventional methods, such as electrical stimulation or signification and to assess their needed kinetics accordingly. The results demonstrate the feasibility of reactive flow dynamics in capturing and numerically simulating the transesterification process. This work substantiates the practicability of using numerical methods to construct precise and insightful image of the distribution of reaction rates and associated species to design and develop more efficient reactors.
Khalifa University of Science and Technology, Masdar Institute Campus is highly acknowledged for their support.
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