# The Petrol Diesel Fuel Biology Essay

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Diesel fuel in general is liquid fuel used in the diesel engines. The most common is a specific fractional distillate of petroleum fuel oil but now nowadays alternatives that are not derived from petroleum such as biodiesel, biomass to liquid (BTL) or gas to liquid (GTL) diesel are increasing being developed. To distinguish these types, petroleum-derived diesel is increasingly called petrol diesel. Ultra-low sulfur diesel (ULSD) is a standard for defining diesel fuel with contain lowered sulfur content (Gerhard et al, 2006).

Petrol diesel fuel also called fossil diesel is produced from the fractional distillation of crude oil between 200 ËšC and 350 ËšC at atmospheric pressure, resulting in a mixture of carbon chains that typically contain between 8 and 21 carbon atoms per molecule. The principal measure of the diesel fuel quality is its cetane number. A higher cetane number indicates the fuel ignites more readily when sprayed into hot compressed air (Chris, 2007).

High levels of sulfur in diesel are harmful for the environment because they prevent the use of the catalytic diesel particulate filter to control diesel particulate emissions such as nitrogen oxide adsorbers to reduce emissions. In addition, sulfur in the fuel is oxidized during combustion that can produce sulfur dioxide and sulfur trioxide, which in presence of water rapidly convert to sulfuric acid, one of the chemical processes that result in acid rain (Gerhard et al, 2006).

## 2.2 Vapor-Liquid Equilibrium

The binary mixture vapor-liquid equilibrium data at atmospheric pressure, showing mole fraction vapor and liquid concentration when boiling at various temperatures can be shown as two-dimensional graph called boiling point diagram show at Figure 2.1. The mole fraction of component 1 in the mixture can be represented by the symbol and the mole fraction of component 2 in the mixture can be represented by the symbol and is related to in a binary mixture as follows (Smith et al, 2001):

(2.1)

http://upload.wikimedia.org/wikipedia/commons/thumb/6/60/Binary_Boiling_Point_Diagram_new.svg/391px-Binary_Boiling_Point_Diagram_new.svg.png

Figure2.1: Boiling point diagram (Smith et al, 2001)

In addition, for each component in binary mixture could make a vapor-liquid equilibrium diagram show at Figure 2.2. In the vapor-liquid equilibrium diagram, liquid mole fractions for component 1 and component 2 can be represented as and respectively, and vapor mole fractions of the corresponding components are commonly represented as and. Similarly for the binary mixtures in this vapor-liquid equilibrium diagram (Smith et al, 2001).

(2.2)

http://upload.wikimedia.org/wikipedia/commons/4/4c/Vapor-Liquid_Equilibrium_Diagram.PNG

Figure 2.2: Vapor-liquid equilibrium diagram (Smith et al, 2001)

On the other hand, the concentration of the vapor in contact with it liquid is term of vapor pressure, which can be a partial pressure. The vapor pressure of liquid is depending on the temperature. At vapor-liquid equilibrium, a liquid with individual component in certain concentrations will have an equilibrium vapor in which the concentrations or partial pressures of the vapor components will have certain set values depending on all of the liquid component concentrations and the temperature. Vapor-liquid equilibrium data can be determined with the help of certain theories such as Raoult's Law and Dalton's Law (Smith et al, 2001).

In the current research, Humberto et al. (2002) reported the vapor-liquid equilibria for pentane+dodecane and heptane+dodecane at low pressure at 70 and 100 kPa and 40, 70 and 100 kPa, respectively. Vapor-liquid equilibrium data for hydrocarbon systems are of great importance to the design and operation of separation units and also to develop mixture models (Humberto et al, 2002).

Another researcher is Armando et al. (2001) reported the vapor-liquid equilibria for the binary systems decane+1,1-dimethylethyl methyl ether (MTBE) and decane+1,1-dimethylpropyl methyl ether (TAME) at 308.15, 318.15 and 328.15 K. This widely used as gasoline blending agents and a program is underway at the laboratory to measure the vapor-liquid equilibrium data of mixtures formed by MTBE or TAME and a hydrocarbon or an alcohol (Armando et al, 2002).

Jean et al. (2004) report the vapor-liquid equilibrium prediction with the Peng-Robinson equation of state and temperature dependent Kij calculated through a group contribution method. A key point in the Peng-Robinson equation is that the Kij between two components i and j is a function of temperature (T) and of the pure components critical temperatures (TCi and TCj), critical pressures (PCi and PCj) and acentric factors (ωi and ωj).This means there are no additional properties besides those required by the equation of state itself (TC, PC and ω) (Jean and Fabrice, 2004).

## 2.3 Equation of State (EOS)

An equation of state can be applied to either vapor-liquid or supercritical phenomena without any conceptual difficulties. Therefore, in addition to liquid-liquid and vapor-liquid properties, it is also possible to determine transitions between these phenomena from the same inputs. In the physics and thermodynamics, the equation of state is a relation between state variables (Sadus, 1992a).

The equation of state is a thermodynamic equation that describing the state of matter under a given set of the physical conditions. It is a constitutive equation which provides a mathematical relationship of the properties temperature, pressure, volume, or internal energy. The equations of state are very useful in describing the properties of fluids, mixture of fluids and solids (Perrot, 1998).

Cubic equations of state are equations, which expanded have volume terms raised to the first, second, and third power. Most commonly encountered phase equilibrium calculations, such as vapor-liquid equilibrium that involve only two phases for which a cubic equation is suitable (Martin, 1979).

## 2.3.1 The Equation of Van der Waals of State

The Van der Waals equation of state (1873) is the simplest cubic equation of state for fluid phase equilibria. It can be regarded as hard sphere term and attractive term equation of state composed from the contribution of repulsive and attractive intermolecular interactions (Sadus, 1994). The Van der Waals equation was the first equation capable of representing vapor-liquid coexistence.

The Van der Waals equation of state may be written (Smith et al, 2005):

(2.3)

The pressure (P) is related to the temperature (T), ideal gas constant(R) and molar volume (V). The Van der Waals equation of state has two pure component parameters and . The parameter is a measure of the attractive force between the molecules and is related to the size of the molecules.

Usually the values of the parameters at the critical point can be expressed as a function of the critical temperature and critical pressure.

(2.4)

(2.5)

According to Van Konynenburg and Scott (1980), successfully demonstrated the most of the critical equilibria exhibited by binary mixtures could be qualitatively predicted by the Van der Waals equation of state but rarely sufficient accurate for critical properties and phase equilibria calculation.

The Van der Waals equation of state can be observed that the equation provide a better representation of the vapor phase than liquid phase. In addition, the compressibility factor of all fluids that including pure component and binary mixture predicted is 0.375 whereas the real value for different hydrocarbons varies from 0.24 to 0.29. Thus, the large numbers of amendments have been proposed to improve the quality of the prediction (Van Konynenburg and Scott, 1980).

## 2.3.2 Redlich-Kwong (RK) and Soave-Redlich-Kwong (SRK) Equation of State

Redlich-kwong equation of state was proposed as empirical modification of the Van der Waals equation of state by modifying the expression of pressure molar. In 1949, Redlich and kwong amended by the parameter attractive in which the term is replaced by and depend on the temperature in order to improve the calculation of vapor pressure (Murdock, 1993).

The Redlich-kwong equation of state may be written (Redlich and kwong, 1949):

(2.6)

The parameters and are usually expressed as:

(2.7)

(2.8)

Spear et al. (1969) showed that the Redlich-kwong equation of state could be used to reliably calculate the vapor-liquid critical properties of binary mixture. In addition, Deiters and Pegg (1989) used the Redlich-kwong equation of state with the quadratic mixing rules to calculate the phase diagram for binary fluid mixtures.

Soave (1972) maintains the role of volume of the Redlich-kwong equation of state and suggested a function dependent on the temperature to modify the parameter attractive. He introduced to replace the term with a more general temperature-dependent term.

The Soave-Redlich-kwong equation of state may be written (Soave, 1972):

(2.9)

The parameters and are usually expressed as:

(2.10)

(2.11)

(2.12)

Soave (1972) calculated the vapor pressures of a number of hydrocarbons and several binary systems with the Soave-Redlich-Kwong equation of state and compared the results of the calculation with the experimental data. In contrast to the original Redlich-Kwong equation of state, Soave modification fitted the vapor-liquid curve well and it was able to predict the phase behavior of mixture in the critical region.

Elloitt and Daubert (1987) improved the accuracy of the calculated the critical properties of binary system containing hydrocarbons. Apart from that, Zheng et al. (1999) also used the Soave-Redlich-Kwong (SRK) equation of state to calculate the phase equilibria of system that containing methane, carbon dioxide and nitrogen and compared the result of calculation with experimental data.

However, the compressibility factor critical is lower than the compressibility factor critical Van der Waals equation of state, but it continue to be overestimated. The Soave-Redlich-Kwong equation of state is relatively predictive compound for non-polar.

## 2.3.3 Peng-Robinson Equation of State

The Peng-Robinson Equation of state slightly improves the prediction of the liquid volume and predicts a critical compressibility factor of compare with the critical compressibility factor of the Redlich-Kwong equation of state is 0.333 and that Van der Waals equation of state is 0.375 (Housam, 2008).

The Peng-Robinson equation of state may be written (Peng and Robinson, 1977):

(2.13)

(2.14)

(2.15)

In the current research, Abdulkadirova et al. (2010) reported that an isomorphic Peng-Robinson equation for phase-equilibria properties of hydrocarbon mixtures in the critical region. In addition, Victor and Martin (2008) also reported the thermodynamic modeling of vapor-liquid equilibrium of binary systems ionic liquid + supercritical {CO2 or CHF3} and ionic liquid + hydrocarbons using Peng-Robinson equation of state.

## 2.4 The Activity Coefficient (γ) via UNIFAC Model

The UNIFAC (UNIQUAC Functional-group Activity Coefficient) method used to predict the non-electrolyte activity in non-ideal mixtures. In addition, UNIFAC uses the functional groups present on the molecules that make up the liquid mixture to calculate the activity coefficient. By using the interaction for each of the functional groups that present on the molecules, the activity of each of the solutions can be calculated (Fredenslund et al., 1975).

The UNIFAC model was published in the article by Fredenslund et al. (1975) and UNIFAC model can provide a flexible liquid equilibria model for wider use in the chemistry and the process engineering disciplines. The logarithm of the activity coefficient can be separated into two contributions: combinatorial part, essentially due to the differences in size and shape of the molecules in mixture and residual part, essentially due to energy interactions:

(2.16)

In the combinatorial part, the combinatorial component of the activity can be written (Fredenslund et al., 1975):

(2.17)

Where,

Compound parameter of, and ,

Coordination number of system,

Molar weighted segment,

Area fractional component,

Molecular volume fraction,

Relative molecular volume,

In the residual part, the residual component of the activity can be written (Fredenslund et al., 1975):

(2.18)

Where,

Activity of an isolated group in a solution,

Summation of the area fraction of group ,

Group interaction parameter,

Group mole fraction,

The equation for the group interaction parameter can be simplified,

Gmehling (1986) used the group contribution UNIFAC method for the estimation of the activity coefficient. UNIFAC has become very popular due to the reliability of its result and the wide area of its applicability. Table 2.1 summaries the UNIFAC applications.

Table 2.1: Applications of UNIFAC

Possible application of UNIFAC

Prediction of vapor-liquid equilibrium a) moderate pressure

b) high pressure

Prediction of liquid-liquid equilibrium

Prediction of solid-liquid equilibrium

Prediction of gas solubility

Prediction of excess heat capacity

Selection of solvents for extractive distillation

Representation of petroleum fractions

Source: Gmehling, 1986

Activity coefficient is a factor that used in thermodynamics to explain for the deviations from ideal behavior in a mixture of chemical substances. In an ideal mixture, the enthalpy change of the solution is zero; as a result, properties of the mixtures can be expressed directly in concentration or partial pressure of the substances. The activity coefficient is means to quantify the difference between the ideality and the real mixture (Smith et al., 2005b).