Diesel fuel in general is liquid fuel used in the Diesel engines. The most common is a specific fractional distillation of crude oil fuel oil but now nowadays options that are non derived from crude oil such as biodiesel, biomass to liquid ( BTL ) or gas to liquid ( GTL ) Diesel are increasing being developed. To separate these types, petroleum-derived Diesel is progressively called gasoline Diesel. Ultra-low sulfur Diesel ( ULSD ) is a criterion for specifying Diesel fuel with contain lowered sulfur content ( Gerhard et al, 2006 ) .

Petrol Diesel fuel besides called fossil Diesel is produced from the fractional distillment of rough oil between 200 EsC and 350 EsC at atmospheric force per unit area, ensuing in a mixture of C ironss that typically contain between 8 and 21 C atoms per molecule. The chief step of the Diesel fuel quality is its cetane figure. A higher cetane figure indicates the fuel ignites more readily when sprayed into hot compressed air ( Chris, 2007 ) .

High degrees of S in Diesel are harmful for the environment because they prevent the usage of the catalytic Diesel particulate filter to command diesel particulate emanations such as nitrogen oxide adsorbers to cut down emanations. In add-on, S in the fuel is oxidized during burning that can bring forth sulfur dioxide and S trioxide, which in presence of H2O quickly convert to sulphuric acid, one of the chemical processes that consequence in acid rain ( Gerhard et al, 2006 ) .

## 2.2 Vapor-Liquid Equilibrium

The binary mixture vapor-liquid equilibrium informations at atmospheric force per unit area, demoing mole fraction vapour and liquid concentration when boiling at assorted temperatures can be shown as planar graph called boiling point diagram show at Figure 2.1. The mole fraction of constituent 1 in the mixture can be represented by the symbol and the mole fraction of constituent 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 )

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

In add-on, for each constituent in binary mixture could do a vapor-liquid equilibrium diagram show at Figure 2.2. In the vapor-liquid equilibrium diagram, liquid mole fractions for constituent 1 and component 2 can be represented as and severally, and vapor mole fractions of the corresponding constituents are normally represented as and. Similarly for the binary mixtures in this vapor-liquid equilibrium diagram ( Smith et Al, 2001 ) .

( 2.2 )

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

On the other manus, the concentration of the vapour in contact with it liquid is term of vapor force per unit area, which can be a partial force per unit area. The vapor force per unit area of liquid is depending on the temperature. At vapor-liquid equilibrium, a liquid with single constituent in certain concentrations will hold an equilibrium vapour in which the concentrations or partial force per unit areas of the vapour constituents will hold certain set values depending on all of the liquid constituent concentrations and the temperature. Vapor-liquid equilibrium informations can be determined with the aid 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 force per unit area at 70 and 100 kPa and 40, 70 and 100 kPa, severally. Vapor-liquid equilibrium informations for hydrocarbon systems are of great importance to the design and operation of separation units and besides to develop mixture theoretical accounts ( Humberto et al, 2002 ) .

Another research worker is Armando et Al. ( 2001 ) reported the vapor-liquid equilibria for the binary systems decane+1,1-dimethylethyl methyl quintessence ( MTBE ) and decane+1,1-dimethylpropyl methyl quintessence ( TAME ) at 308.15, 318.15 and 328.15 K. This widely used as gasolene blending agents and a plan is underway at the research lab to mensurate the vapor-liquid equilibrium informations of mixtures formed by MTBE or TAME and a hydrocarbon or an intoxicant ( Armando et al, 2002 ) .

Jean et Al. ( 2004 ) describe the vapor-liquid equilibrium anticipation with the Peng-Robinson equation of province and temperature dependent Kij calculated through a group part method. A cardinal point in the Peng-Robinson equation is that the Kij between two constituents one and J is a map of temperature ( T ) and of the pure constituents critical temperatures ( TCi and TCj ) , critical force per unit areas ( PCi and PCj ) and acentric factors ( ?i and ?j ) .This means there are no extra belongingss besides those required by the equation of province itself ( TC, Personal computer and ? ) ( Jean and Fabrice, 2004 ) .

## 2.3 Equation of State ( EOS )

An equation of province can be applied to either vapor-liquid or supercritical phenomena without any conceptual troubles. Therefore, in add-on to liquid-liquid and vapor-liquid belongingss, it is besides possible to find passages between these phenomena from the same inputs. In the natural philosophies and thermodynamics, the equation of province is a relation between province variables ( Sadus, 1992a ) .

The equation of province is a thermodynamic equation that depicting the province of affair under a given set of the physical conditions. It is a constituent equation which provides a mathematical relationship of the belongingss temperature, force per unit area, volume, or internal energy. The equations of province are really utile in depicting the belongingss of fluids, mixture of fluids and solids ( Perrot, 1998 ) .

Cubic equations of province are equations, which expanded have volume footings raised to the first, 2nd, and 3rd power. Most normally encountered stage equilibrium computations, such as vapor-liquid equilibrium that involve merely two stages for which a three-dimensional equation is suited ( Martin, 1979 ) .

## 2.3.1 The Equation of Van der Waals of State

The Van der Waals equation of province ( 1873 ) is the simplest three-dimensional equation of province for fluid stage equilibria. It can be regarded as difficult sphere term and attractive term equation of province composed from the part of abhorrent and attractive intermolecular interactions ( Sadus, 1994 ) . The Van der Waals equation was the first equation capable of stand foring vapor-liquid coexistence.

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

( 2.3 )

The force per unit area ( P ) is related to the temperature ( T ) , ideal gas invariable ( R ) and molar volume ( V ) . The Van der Waals equation of province has two pure constituent parametric quantities and. The parametric quantity is a step of the attractive force between the molecules and is related to the size of the molecules.

Normally the values of the parametric quantities at the critical point can be expressed as a map of the critical temperature and critical force per unit area.

( 2.4 )

( 2.5 )

Harmonizing 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 province but seldom sufficient accurate for critical belongingss and stage equilibria computation.

The Van der Waals equation of province can be observed that the equation provide a better representation of the vapour stage than liquid stage. In add-on, the squeezability factor of all fluids that including pure constituent and binary mixture predicted is 0.375 whereas the existent value for different hydrocarbons varies from 0.24 to 0.29. Therefore, the big Numberss of amendments have been proposed to better the quality of the anticipation ( Van Konynenburg and Scott, 1980 ) .

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

Redlich-kwong equation of province was proposed as empirical alteration of the Van der Waals equation of province by modifying the look of force per unit area grinder. In 1949, Redlich and kwong amended by the parametric quantity attractive in which the term is replaced by and depend on the temperature in order to better the computation of vapor force per unit area ( Murdock, 1993 ) .

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

( 2.6 )

The parametric quantities and are normally expressed as:

( 2.7 )

( 2.8 )

Spear et Al. ( 1969 ) showed that the Redlich-kwong equation of province could be used to reliably cipher the vapor-liquid critical belongingss of binary mixture. In add-on, Deiters and Pegg ( 1989 ) used the Redlich-kwong equation of province with the quadratic commixture regulations to cipher the stage diagram for binary fluid mixtures.

Soave ( 1972 ) maintains the function of volume of the Redlich-kwong equation of province and suggested a map dependant on the temperature to modify the parametric quantity attractive. He introduced to replace the term with a more general temperature-dependent term.

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

( 2.9 )

The parametric quantities and are normally expressed as:

( 2.10 )

( 2.11 )

( 2.12 )

Soave ( 1972 ) calculated the vapour force per unit areas of a figure of hydrocarbons and several binary systems with the Soave-Redlich-Kwong equation of province and compared the consequences of the computation with the experimental information. In contrast to the original Redlich-Kwong equation of province, Soave alteration fitted the vapor-liquid curve good and it was able to foretell the stage behaviour of mixture in the critical part.

Elloitt and Daubert ( 1987 ) improved the truth of the calculated the critical belongingss of binary system incorporating hydrocarbons. Apart from that, Zheng et Al. ( 1999 ) besides used the Soave-Redlich-Kwong ( SRK ) equation of province to cipher the stage equilibria of system that incorporating methane, C dioxide and N and compared the consequence of computation with experimental informations.

However, the squeezability factor critical is lower than the squeezability factor critical Van der Waals equation of province, but it continue to be overestimated. The Soave-Redlich-Kwong equation of province is comparatively prognostic compound for non-polar.

## 2.3.3 Peng-Robinson Equation of State

The Peng-Robinson Equation of province somewhat improves the anticipation of the liquid volume and predicts a critical squeezability factor of comparison with the critical squeezability factor of the Redlich-Kwong equation of province is 0.333 and that Van der Waals equation of province is 0.375 ( Housam, 2008 ) .

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

( 2.13 )

( 2.14 )

( 2.15 )

In the current research, Abdulkadirova et Al. ( 2010 ) reported that an isomorphous Peng-Robinson equation for phase-equilibria belongingss of hydrocarbon mixtures in the critical part. In add-on, Victor and Martin ( 2008 ) besides reported the thermodynamic mold of vapor-liquid equilibrium of binary systems ionic liquid + supercritical { CO2 or CHF3 } and ionic liquid + hydrocarbons utilizing Peng-Robinson equation of province.

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

The UNIFAC ( UNIQUAC Functional-group Activity Coefficient ) method used to foretell the non-electrolyte activity in non-ideal mixtures. In add-on, UNIFAC uses the functional groups present on the molecules that make up the liquid mixture to cipher the activity coefficient. By utilizing 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 theoretical account was published in the article by Fredenslund et Al. ( 1975 ) and UNIFAC theoretical account can supply a flexible liquid equilibria theoretical account for wider usage in the chemical science and the procedure technology subjects. The logarithm of the activity coefficient can be separated into two parts: combinative portion, basically due to the differences in size and form of the molecules in mixture and residuary portion, basically due to energy interactions:

( 2.16 )

In the combinative portion, the combinative constituent of the activity can be written ( Fredenslund et al. , 1975 ) :

( 2.17 )

Where,

Compound parametric quantity of, and,

Coordination figure of system,

Molar weighted section,

Area fractional constituent,

Molecular volume fraction,

Relative molecular volume,

In the residuary portion, the residuary constituent of the activity can be written ( Fredenslund et al. , 1975 ) :

( 2.18 )

Where,

Activity of an stray group in a solution,

Summation of the country fraction of group,

Group interaction parametric quantity,

Group mole fraction,

The equation for the group interaction parametric quantity can be simplified,

Gmehling ( 1986 ) used the group part UNIFAC method for the appraisal of the activity coefficient. UNIFAC has become really popular due to the dependability of its consequence and the broad country of its pertinence. Table 2.1 summaries the UNIFAC applications.

Table 2.1: Applications of UNIFAC

Possible application of UNIFAC

Prediction of vapor-liquid equilibrium a ) moderate force per unit area

B ) high force per unit area

Prediction of liquid-liquid equilibrium

Prediction of solid-liquid equilibrium

Prediction of gas solubility

Prediction of extra heat capacity

Choice of dissolvers for extractive distillment

Representation of crude oil fractions

Beginning: Gmehling, 1986

Activity coefficient is a factor that used in thermodynamics to explicate for the divergences from ideal behaviour in a mixture of chemical substances. In an ideal mixture, the enthalpy alteration of the solution is zero ; as a consequence, belongingss of the mixtures can be expressed straight in concentration or partial force per unit area of the substances. The activity coefficient is means to quantify the difference between the ideality and the existent mixture ( Smith et al. , 2005b ) .