Abstract
Knowledge on phase equilibrium behavior plays a central role in the prediction of the solubility of the components found in biodiesel. This aids in the separation process of the individual components. These components are normally referred to as volatile organic compounds. It is crucial to use models in the determination of these equilibriums since actual measurements are costly and lingering.
There are several types of biodiesels: methyl oleate, ethyl stearate, and methyl linolenate. UNIFAV procedure can be used in the determination of of an estimate of the infinite dilution activity of several volatile organic compounds in biodiesels. A mole fraction of 9.123*10-8 is used for the VOCs in the calculations done. It is usually expected that different biodiesels have different phase equilibriums. A comparison of the theoretical and experimental results that yields some consistency would prove a successful experimental analysis. Thermodynamic models come in handy in the calculation of phase equilibrium data.
Introduction
An adept knowledge on phase equilibrium of elements and their respective compounds, the effect of pressure and the temperature is crucial for the prediction of the effect of the chemical in the environment and possible applications. Operations carried out on biodiesel such as distillation require profound knowledge on phase equilibrium. Such knowledge plays an equally important role in absorption processes. This helps in removal of volatile organic compounds from contaminated atmospheres. Multiphase reactors and distillation processes also rely on such engineering principles (Ramaswamy, 2013). New legislation on environmental conservation has forced industries to monitor closely any effluence emitted to the environment.
Actual measurements of the levels of pollution of such effluence may be time consuming and costly. This is where thermodynamic models come in to help in simulate actual situations. This involves calculation of the behavior of phase equilibrium from limited experimental data. Where it is difficult to determine accurately exact properties of mixtures with several components, predictive methods are used to estimate possible characteristics. These predictive methods have their drawbacks. They may not be as exact as actual experiments due to variance in environmental conditions. However, data obtained from such experiments will aid in the design and development of the process simulation. Commonly used methods help in the calculation of activity coefficients such as UNIFAC.
Composition of Biodiesel
Biodiesel is a mixture of low volatility, low toxicity, high boiling point, high solubility power compounds. Therefore, biodiesel is technically referred to as fatty acid methyl esthers (FAME). Due to these characteristics, biodiesel is used as a universally accepted solvent when it comes to removal and recovery of volatile organic compounds from waste gas in industrial setups (Speight, 2011). For efficient use of biodiesel as an absorbent in separation processes, a good understanding of the vapor liquid equilibrium is critical. Similarly, the activity coefficient at infinite dilution of the VOCs in biodiesel should be determined.
Theoretical Consideration
Scrubbing is one of the processes through which cleaning of the waste gas and recovery of the VOC is possible by using this knowledge on phase equilibrium behavior. The process is also reversible. The reverse process of absorption is called desorption. The theory of absorption and its reverse process is based on Raoult’s law (Pi=Yi*Xi*Pio ). Pi is the equilibrium vapor pressure of component i at a set pressure, Yi is the activity coefficient of the component in the absorbent, Xi is the mole fraction of the component in the liquid, is the vapor pressure of the pure component at the set temperature. Any contact between the absorbent liquid and the gas stream, then the VOCs will be flowing from the gas to the absorbent, provided the partial pressure is kept below the equilibrium level. If this partial pressure falls below the equilibrium level, desorption occurs. Water may be used as an absorbent despite its drawbacks such as quick saturation.
Group Contribution Methods (UNIFAC Model Peng-Robinson Method)
This is a concept that is used to correlate the limited experimental data with activity coefficients of mixtures with no experimental data. The sum of functional groups constituting a molecule is used in the consideration of a molecule. Correlation of functional groups comprising the mixture is then done based on thermodynamic properties. Activity coefficients are calculated using UNIFAC (Universal quasi chemical functional group activity coefficient model). This is a prediction model is mostly used on non-electrolyte activity estimation and on- ideal mixtures. Activity coefficients are calculated based on the functional groups present in the molecules comprising the mixture.
Methodology and Procedure
Computations were done using Microsoft Excel that provided credible simulation values. The procedure was as below:
- Combinations:
- v, Qi and Ri for each functional group were first obtained
- Calculations of Ri were done based on the formula:
- qi was then calculated as :
- li was calculate using the formula:
- was calculated using the formula:
- was calculated using the formula :
- was computed using the formula:
Residuals:
- values were then computed and obtained.
- Calculation of was done using the formula:
- Calculation of using the formula:
- Calculation ofand using the formula:
- Calculation of using the formula:
- Conclusively,
Peng-Robinson Equations of State(EOS)
In these equations:
P represents the pressure, R represents the ideal gas constant, v is the molar volume, Tc represents critical temperature while T is the temperature, and Pc is the critical pressure. ‘a’ represents the attractive term while b represents the covolume. These two terms are corrective terms.
Mixing Rules of a and b
ZK is representative of the mole fraction component.
Similarly,
- Kij (T) is dependent on temperature and is determined by the equation below:
Fugacity coefficient is calculated using the equation:
Z is the compressibility factor and A and B determined by:
Since R=q24+p3/27
p=3*a1-a223
q=2*a23-9*a2*a1+27*a0
a1=0.03291
a2=-0.9964
a0=-0.0001
p=-0.298
q=-0.0625
Therefore the coefficient m=2*-p/3
=m=2*-(-0.298)/3=0.6304
Discussion of Results
The table depicts the mole fraction based infinite dilution activity coefficients. Values obtained from the tables are substantially below 100. This is contrary to actual industrial water. Such water has great non-ideality with VCOs. Therefore, these biodiesels can be successfully used in the scrubbing of contaminated air effluents.
Solubility of a substance is greatly affected by intermolecular forces (weak van der Waals forces). Van der Waals forces are affected by the polarization of electrons in the atoms concerned. This means the strength with which the electrons are held. This means the larger the atom, the more loosely held the electrons. Conventionally, ‘like dissolves like’ rule is applicable in determining solubility (PSR Centre, 2011).
Alkanes have very long hydrocarbon chains, longer than esters. The biodiesels (methyl oleate and ethyl stearate) also have long carbon chains. This means that alkanes will have higher values of solubility in these solvents than esters. Consequently, it can be concluded that the CCOO group is hydrophilic while the long carbon chain is hydrophobic. Similarly, polar VOC are less soluble than non- polar VOCs. Polar molecules are those with huge dipole moments and large dielectric constants. Polarity variation was found to be the underlying determinant in the difference in solubility of the VCOs (Braunschweig and Joulia, 2008).
Biodiesels are also better solvents than water. They have higher saturation points than water, although water is more readily available. Solubility increases with increase in molecular weight. This can be explained by the fact that molecular surface area increases with the increase in molecular weight. Consequently, there is an increase in the strength o f the van der Waals forces. This would require more energy to separate the molecules hence reduced solubility. Chains that are highly branched, on the other hand, have highly compact molecules, hence reduced surface area, and intermolecular forces. This results in increased solubility. A comparison of cyclohexane and hexane reveals this phenomenon where the former is more soluble. Alkynes and alkenes are more compact than alkanes hence more soluble. Solubility increases with the number of carbon-carbon bonds (World Congress on Engineering, 2012).
Conclusions
The solubility of different compounds in a solvent depends on the structural arrangement of the individual compounds. Similarly, solubility varies from one solvent to another. However, the trends are similar, even in different solvents. The Peng-Robinson thermodynamic model was also found to be very instrumental in the vapor-liquid equilibrium experimental analysis. Solubility also increases with an increase in temperature due to increase in the intermolecular distances in the solvent. Pressure affects solubility. It determines whether the physical reaction will be a desorption or absorption. Biodiesel (methyl oleate) has a low vapor pressure that prevents secondary and unwanted emissions. Predictive methods were also found to be very applicable in feasibility studies, whereby computations based on formulas are used as opposed to actual calculations.
References
Braunschweig, B., & Joulia, X. 2008. 18th European Symposium on Computer Aided Process
Engineering. Oxford: Elsevier.
Ramaswamy, S. 2013. Separation and Purification Technologies in Biorefineries. New York:
Wiley.
Speight, J. G. 2011. The Biofuels Handbook. Cambridge: RSC Pub.
Organics – Biodiesel Systems Phase Equilibrium Computation: Part 1. (2011, December 5).
http://psrcentre.org. Retrieved February 3, 2013, from
psrcentre.org/images/extraimages/1211840.pdf
Influence of Temperature and Molecular Structure on Organics-Biodiesel Interactions using
Group Contribution Methods. (2012, July 4). World Congress on Engineering. Retrieved
February 3, 2012, from www.iaeng.org/publication/WCE2012/WCE2012_pp1411-1416.pdf
