Diesel fuel is a specific distillate of petroleum oil. When crude oil is refined, it will be separated into several different kinds of fuels, containing kerosene, gasoline and diesel. Generally, diesel fuel is used in diesel engines which are mostly in cars, trains, boats and farms.
Many new diesel engine technologies like high-pressure and multiple-injection systems are being progressed in order to match the reinforced exhaust emission regulations. For instance, a high-pressure ‘common-rail' fuel injection system is applied in modern diesel engines at extremely high pressure.
Common rail direct fuel injection produces from direct fuel injection system of diesel engines and it traits a high-pressure fuel rail feeding single solenoid valves. It is possible to control electronically over the fuel injection time and quantity via solenoid valves (Frederic, B. & Patrice, S., 2009). Diesel engines have various forms of fuel injection and have two ordinary types: the distributor pump systems and the unit injection system (Su Han Park, Se Hun Kim & Chang Sik Lee, 2009).
In this case, it is important to know the physical properties of liquid fuels such as density, heat capacity, sound speed and viscosity. Only known these physical properties under high pressure, the improvement of performance of diesel in common rail fuel injection begins.
However, it is expensive and time-wasting to measure the physical properties of diesel fuels directly and some models are needed. One model has been developed in IFP (French Institute for Petroleum) and our target of this project is to test the validation of this model.
2 Components and analysis equipments
Diesel fuel is a middle distillate product refined from crude oil and it is a complex mixture of many components, because the chains of carbon atoms have different lengths, sizes and shapes and each chain length or molecular size has own properties . Meanwhile, different sources of crude oils and different methods of refinement lead to different compositions of diesel fuels.
2.1 Components in diesel fuels
Diesel fuel contains large number of hydrocarbon molecules which are more than gasoline and it mainly composes of hydrocarbons. Diesel fuels is made up of about 75% saturated hydrocarbons (paraffins and cycloparaffins) and 25% aromatic hydrocarbons (naphthalenes and alkylbenzenes).
Generally, the main paraffinic components are the long-chain alkanes with carbon numbers between 10 and 20. Long-train paraffins have outstanding cetane numbers and show great combustion performance, but higher-boiling n-alkanes tend to own higher cloud points and don't get good cold-flow properties. Both the nature of the crude oil and the blending stocks determine the content of naphthenic components.
There are many types in the aromatic components in diesel fuels such as alkylates benzenes, naphthalenes, biphenyls, indanes, acenaphthenes, tetralins, chtysenes, phenanthrenes and pyrenes.
2.2 Analysis of the mixture components
Diesel fuels are so complicated that have large numbers of components and the some exact compositions are never known. Therefore, the primary task is to find a proper method to analyze the mixture components.
2.2.1 ASTM method
ASTM which is short for American Society for Testing and Materials is an international organization that publishes and develops consensus technical standards for a wide range of materials, systems, products and services. In the field of fuels, ASTM offers many testing methods which are commonly accepted. For example, D2425 for hydrocarbon types in middle distillates by mass spectrometry; D2887 for boiling range distribution of petroleum fractions by gas chromatography; D86 for distillation of petroleum products at atmospheric pressure; D975 is Standard Specification for Diesel Fuel Oils (table 1) and so on.
Table 1 ASTM D975-Diesel Fuel Specification
In our project, one obvious distinction of different compositions is the boiling point and some ASTM methods can get the boiling point curve.
ASTM D86 is the basic test method to determine the boiling point range of a petroleum product via a simple batch distillation (Marco, A.S. & Harvey, Y., 2009). The results are plotted on a distillation curve which shows the distillation or volatility characteristics of hydrocarbons. These characteristics have a significant effect on the safety and performance and the boiling range gives the information about the compositions, the properties and the behaviour of fuels. Volatility is an important factor in the application because it influences the rate of evaporation (Tareq, A.A, 2006). Consequently, the main limitation of ASTM D86 method is that it can not be used for very light gases or very heavy components that can't be vaporized.
ASTM D2887 is referred to the simulated distribution (SD). An insight into the components of feedstock and products is supplied by the boiling range distribution of petroleum fractions which are tested by gas chromatography (GC).
Boiling range distributions obtained by ASTM D2887 method are basically equivalent to those obtained by true boiling point (TBP) distillation (Tarifa, E.E. et al, 2008). This test method is applicable to petroleum products with a final boiling point of 538℃ or lower at atmospheric pressure and is limited to samples with a boiling range bigger than 55.5℃ and with a vapour pressure adequately low.
ASTM D2425 method is used to distinct the hydrocarbon types in middle distillates by mass spectrometry (MS). Each component has a special spectrogram to determine the compositions of the mixture and usually the components are separated in 11 families based on their chemical groups (Glavincevski, B. & Gardner, L., 1985).
2.2.2 Equipments of analysis
There are several devices used to obtain the compositions in diesel fuels.
GC is an ordinary type of chromatography used for separating chemicals in a complex sample and analyzing the compositions which can't be vaporized without decomposition (Petroff, N. Hoscheitt, A. & Durand, J.P., 1987).
The basis of this separation is the different volatility of components. As a small amount of sample is injected into the GC unit, the port of entry of the liquid (injector) is kept at a high temperature so that the liquid vaporizes. The vaporized mixture is pushed through chromatographic column (stationary phase) which is filled with particles in terms of a high purely inert carrier gas (mobile phase). The different compositions of the sample move through the column that is inside of a heated oven at different rates and hence elute at different times. Once a composition elutes, it is sent to a flame ionization detector (FID) which then heats the composition with a hydrogen flame to ionize it. This FID is highly sensitive to all organic compounds. The ions then generate a current that proportionate to the concentration of the composition. The detector transmits information to an integrator which produces a chromatogram and thus it is so critical for the accuracy of the separation (Glavincevski, B. & Gardner, L., 1985). The components and concentration of the sample are determined by the analysis of this chromatogram. A schematic of the gas chromatography unit is described in 1.
Sometimes, one GC can not individually separate all components in samples because some components may have the same volatility and thus lead to the same peak which corresponds to a number of possible components.
The MS is a powerful analytical technique to determine the unknown composition of a sample and to elucidate the structures and chemical properties of molecules. The compounds can be identified at very low concentrations in the complex mixtures due to the detection can be accomplished with very minute quantities (Lucas, J.M. et al, 2009).
A MS does not measure molecule mass directly but measure the mass-to-charge ratio of ions formed. The fundamental unit of charge and the magnitude of the charge on an electron are used because it is inconvenient to measure the charge on a single ion in everyday units of an electron. The charge on an ion is denoted by the integer number z of fundamental units of charge. A schematic of the mass spectrometer unit is described in 2.
A significant improvement to the mass determining capabilities of MS is combined with chromatographic separation techniques. The common combinations are gas chromatography-mass spectrometry (GC-MS) and liquid chromatography-mass spectrometer (LC-MS). Meantime, MS can be combined to capillary electrophoresis and superficial fluid chromatography (Chun, Y. et al, 2009). For these combinations, the data comprises of a series of mass spectra gained sequentially in time.
Gas chromatography-Mass spectrometry
In GC-MS, a gas chromatography is used to separate different components in this technique. The stream of separated compounds is fed into the ion source online and a metallic filament to which voltage is applied. The filament discharges electrons to ionize the compositions. To yield predictable patterns, the ions can further segment. Finally, the intact ions and segments pass into the mass spectrometer's analyzer and are detected (Elghawi, U. et al, 2008).
Liquid chromatography-Mass spectrometer
LC-MS is similar to the GC-MS and it separates components chromatographically before they are fed into the ion source and mass spectrometer (Georg, D. et al, 2004). What is the difference between LC-MS and GC-MS is that the mobile phase is liquid in LC-MS, usually a mixture of water and organic solvents, rather than gas in GC-MS.
Mid Infrared Spectroscopy
Another device for distinction of different components is the mid infrared spectroscopy (IR) which is used to identify compounds or investigate sample composition by the infrared wavelengths they can absorb (Pasadakis, N. Sourligas, S. & Foteinopoulos, C., 2006)
The basis of IR spectroscopy is the selective absorption of certain parts of the infrared spectrum by molecules or certain portion of the molecules which contain functional groups with specific bonds vibrating at a specific frequency. The IR energy is absorbed by the stretching and bending of certain bonds or vibrations of portions of molecules. The vibrations are obvious when they absorb energy and the absorbed energy should accurately match for transitions between discrete vibration energy levels (Robert, E. et al, 2009). Then the instrument scans a range of frequencies. When the instrument's frequency matches the bond vibrating, a peak appears on the IR (Liliana, F.B. et al, 2010). A schematic of the IR spectroscopy is described in 3.
The IR spectrum results from the complicated overlapping of different compositional structures and thus includes information about the overall molecular composition of the sample.
Two-dimensional gas chromatography
Sometimes, the two-dimensional gas chromatography (2D GC) of multidimensional separation is chosen to analyze the mixture in order to save the time and the cost. A multidimensional separation means the sample dispersed in different time dimensions and applies the concept of peak capacity or the maximum number of compositions in a mixture that a chromatographic system can resolve (Kevin, M.N. Riccardo, L. & Andreas, H., 2003). The schematic of a system which provides total flexibility for GC-GC is shown in 4.
(1= injector for either oven; 2= PTV inlet on instrument 1; 3= PTV inlet on instrument 2 or 3; 4= monitor FID on instrument 1; 5= sulphur chemiluminescent detector; 6= nitrogen chemiluminescent detector; 7= pneumatics unit for column switching device.)
(Kevin, M.N. Riccardo, L. & Andreas, H., 2003)
Comprehensive 2D GC
Furthermore, the comprehensive 2D GC (GC x GC) is a rapidly developing technique for analysis of complex samples because it is both a quantitative and qualitative technique.
The difference between the 2D GC with middle distillation (GC-GC) and comprehensive 2D GC (GC x GC) is well defined. A fraction from the first retention axis is transferred for separation on the second retention axis in the 2D GC method, while in contrast, in the comprehensive method, the whole sample is subjected to the two different separations after a single introduction to the first column (Leonid, B. & Matthew, S.K., 2010). There is a comparison of conventional multidimensional GC and comprehensive 2D GC shown in 5.
After introducing the devices of analysing the components in diesel fuels, the comprehensive 2D GC is a better choice compared with others. The comprehensive 2D GC has some advantages.
– It has considerably higher separation power.
– It offers better sensitivity owning to the narrow peak shapes.
– It is compatible with all types of injection systems and sample handling techniques because the first column is conventional.
– Its separation admits better peak identification as the peak elution is characterized by a couple of retention times.
– It is more suitable for sample screening as it gives considerably more information about the sample in comparable analysis times.
– It reduces the need of complicated sample preparation procedures as the separation power of the technique is so large to eliminate the interferences critical in conventional GC separations.
3 Physical properties of diesel fuels
The partial purpose of our project is to improve the performance of diesel fuels, thus physical properties of diesel fuels must be known as precisely as possible. Diesel fuels have many physical properties, such like density, cetane number and cetane index, heat capacity, cold flow properties, viscosity, flash point, cloud point, sound speed, sulphur and so on. The most important physical properties of diesel fuels in our project are density, heat capacity, sound speed and viscosity.
Density is a measure of a fuel's mass per unit volume and it depends on temperature. It can indicate a fuel's composition and performance-related characteristics. Hence, density is powerfully correlated with other fuel parameters, especially with cetane number, viscosity and the distillation characteristics (Chunsham, S., 2000).
Density plays a meaningful role in diesel engine because fuel is directly injected into the combustion chamber using a volume based metering system. Due to the different mass of fuel injected which is approximately proportionate to the energy content of fuel, variations in density will lead to a change in the energy content of the fuel injected and consequently affect engine output, emission and fuel consumption (Marzena, D. & Piotr, P., 2007). A fuel with higher density will incline to produce more smokes and more power. In contrast, lower density fuel will decrease the production of smoke but also reduce power if the fuel injection system is not set up for such lower density. For a constant maximum power output, the volumetric fuel consumption will increase with lowering density and decrease with increasing density.
3.2 Heat Capacity
Heat capacity is an intensive property to measure the heat energy which is needed to increase the temperature of fluid by a certain temperature interval (Voss, S.F. & Sloan, E.D., 1989).
The mathematical definition of heat capacity is the ratio of a small amount of heat added to the object corresponding to a little increase of temperature:
In most cases, the value of heat capacity for constant volume CV and constant pressure CP are used widely. Their expressions are:
The increment of internal energy is:
Therefore, at constant volume, the heat capacity is:
Then, because the definition of enthalpy is H=U+PV, the increment of enthalpy is:
And thus: .
Finally, at constant pressure, the heat capacity can be expressed:
3.3 Sound Speed
The speed of sound is the rate of a sound wave through an elastic medium. The key point of sound speed is to determine the thermodynamic equation of state in form of a relation between density, temperature and pressure. The heat capacity also can be determined from speed of sound because it is a function of temperature as mentioned above. Then, all the thermodynamic properties of a fluid can be calculated from combination of sound speed and other experimental quantities (Trusler, J.P.M., 1991).
The fundamental equation to calculate the speed of sound is:
However, it is difficult to out the density and heat capacity because it is hard to measure the entropy (Mustafa, E.T. & Jonh, V.G., 2003). Thus, another set of differential equations with measurable quantities is required. These equations are:
The solution cannot be obtained analytically but can be expressed roughly by a predictor-corrector algorithm which was illustrated by Trusler and then was tested by Sun.
There is another advantage of the speed of sound measurement. It is probable to obtain other thermodynamic properties of the fluid once the density and the heat capacities are determined (Marzena, D. & Piotr, P., 2007).
Viscosity is generally used to measure a fuel's resistance to flow and it influences on the extent of attractive forces and the performance of diesel pumps and injection systems. The higher the viscosity is, the greater the resistance to flow. Because the viscosity depends on fuel composition, it is reflected in the distillation parameters, density and cold flow properties (Chunsham, S., 2000).
Why is the viscosity so important for fluid? On one hand, high viscosity may reduce the fuel flow rates which lead to insufficient flow and if the viscosity is too high, it even may result in fuel pump distortion. On the other hand, low viscosity can raise leakage from the pumping elements and lead to unsatisfactory fuel delivery and hot starting difficulties.
4 Measurement of properties
Even though we get some basic knowledge of physical properties of diesel fuels, it is necessary to know how to measure them.
4.1 Measurements of Density
There are some direct methods to measure the liquid density, such as Oscillating U-tube and online measurement devices. The oscillating U-tube technique is based on an electronic measurement oscillation frequency, from which the density value is calculated.
Another direct method is to use Archimedes' principle. Any object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. Stephen W Hughes stated an improved measurement using Archimedes' principle. In this technique, a container of the liquid is put under test on an electronic balance and a probe attached to a length of line is suspended under the surface of the liquid. If the volume of the probe is known, the density of the liquid is obtained by the difference between the balance reading before and after immersion of the probe (Stephen, W.H., 2006).
The common method to measure the liquid density in the lab is the pycnometer which is a glass flask including a close-fitting ground glass stopper that has a capillary hole through it. After closing a top-filled pycnometer, the capillary hole releases an extra liquid and allows for receiving a given volume of measured liquid with a high accuracy (Anon, Density determination by pycnometer).
The advantages of pycnometer are obvious, such as the easy operation, simple materials and high accuracy and the primary disadvantage is about the limited range of pressure.
4.2 Measurements of Heat Capacity
The most ordinary method of measuring the heat capacity is to use calorimeter. A calorimeter is an experimental device used for calorimetry of a chemical reaction or physical process. According to the analysis in Chapter 3, it is possible to get the heat capacity at constant pressure CP, because most calorimeter operates at constant pressure and temperature. There are many common types of calorimeters, like differential scanning calorimeters, isothermal microcalorimeters, titration calorimeters and accelerated rate calorimeters.
One case is the isothermal flow calorimeter. The principle of isothermal flow calorimeter is the compensation of the heat effects and the measurement of the required power. Two calibrated flow pumps (ISCO) allow for altering the mixture composition and a back pressure regulator supplies the possibility to measure at higher pressure and to prevent evaporation (Heintz, A. & Lichtenthaler, R.N., 1979) schematic of the isothermal flow calorimeter unit is described in 6.
4.3 Measurement of sound speed
For any sound-speed measurement apparatus, an independent procedure is required to evaluate some geometric features of the system which is related to the physical path length travelled by the sound wave directly or indirectly (Higuti, R.T. & Adamowski, J.C., 2002). There are two main types of techniques used to measure the speed of sound, i.e. steady state techniques and transient state techniques. The steady state techniques rely on the standing waves which are formed inside an acoustic cavity. The transient state techniques have two kinds. One is pulse methods, in which the sound speed is measured with high precision, basically from a pulse propagation time over a known distance in fluid. The other is reverberation techniques in which the logarithmic decrement is measured by a freely oscillating ordinary mode of a resonator (Trusler, J.P.M., 1991). However, in our project, only the pulse methods are relevant.
4.3.1 Single-pulse methods
In the basic method, two plane parallel transducers which are placed between a known distances consist of a delay line in the fluid and single pulses are utilised to one transducer and detected by the other.
Pulse-echo ultrasound estimation
This method directly estimates the longitudinal speed of sound in a medium. By analysing the pulse-echo data received through a single transducer array following a single transmission, the estimator obtains the speed of sound (Martin, E.A. & Gregg, E.T., 1998).
The pulse-echo technique is widely applied in the available automated ultrasonic test systems for defect detection (Benedetto, G. et al, 2005). A schematic of the pulse-echo technique is described in 7.
4.3.2 Double-pulse methods
The basis of principle of this method is the phase cancellation. There are two transducers, one for the pulses generation and the other for the pulses detection. A first pulse is emitted and travels inside by being reflected on the mirrors several times and then a second pulse is produced after a time interval by the same transducer. Since the time interval is adjusted, two pulses arrive at the receiving transducer at the same time. Then, the adjustability of the phase aims to get destructive interference with the first pulse and the adjustability of the amplitude is to accurately wipe out the first pulse.
4.3.3 Multiple-pulse methods
All echoes of the original pulse are allowed to die off before a new method is begun. Pulse superposition measurements can be applied to pulses produced in a continuous order at a variable repeating. One case is that the pulse repeating rate is adjusted manually when echoes of different order add in phase at the detector. The other case is that two transducers are utilized and each pulse arriving at the receiver is used to start a new pulse from the transmitter (Trusler, J.P.M., 1991).
4.4 Measurement of viscosity
The most common instrument used to measure the viscosity of a fluid is the viscometer. There are many kinds of viscometers but they can be divided into 4 types: capillary, falling body, oscillating body and vibrating viscometers. The first two types of viscometer are considered as ‘absolute' viscometers which rely on rigorous working equations. However, these viscometers still need calibration with a fluid of known viscosity at a specified temperature and pressure to acquire correction factors in the equations. By contrast, the last two types of viscometers do not require correction factors because the working equations are complete under specific conditions (Mohamed, K., 2005).
4.4.1 Capillary viscometer
Usually, it has two types of capillary instruments: one for concentrated solutions or polymer melts and the other for measuring dilute solution viscosities. The most widely used one is the glass capillary tube of second type. The time used for a known volume of solution flow through the tube under the force of gravity is compared with the time taken for the same volume of liquid of measured viscosity through the same capillary of a known diameter of a certain factor. Then the viscosity is obtained by multiplying the time taken by the factor of the viscometer.
4.4.2 Falling body viscometer
Although nearly all viscometer configurations have been pressurized, the falling body type is preferred for simplicity and accuracy in measuring low-shear viscosity. This equipment uses a sphere falls through a mass of the test fluid inside a cylindrical tube and the time for the sphere to fall a certain distance is measured and correlated with viscosity.
This viscometer is a cylindrical sinker with lugs offered by cross arrangement at each end. The sinker falls within a cylindrical tube with minimal pressure difference across its thickness (Scott, B., 2004). The position of the sinker is monitored continuously by a linear variable differential transformer (LVDT) which constructs the sinker from magnetic material ( 8). The cylindrical bore end fitted with a volume compensation piston at the other end.
4.4.3 Oscillating body viscometer
This viscometer is sometimes referred as electromagnetic viscometer which was first invented at Cambridge Viscosity in 1986. The electromagnetic viscometer (EMV) is a precision instrument which is designed to accurately measure the viscosity of fluids under high pressures.
The accurate temperature control is maintained by the recirculation bath, the clamshell design and the stainless-steel insulating jacket. The precise pressure and temperature are measured by the onboard electronic transducer and a resistance temperature detector (RTD). The menu-driven EMV electrometer provides viscosity and temperature-compensated-viscosity data of extraordinary accuracy and auto-output in real time. This instrument shows a valuable component for petroleum fluid by performing viscosity measurement over the range of 0.1 to 10,000 cp on very small volumes (Anon, 2003).
4.4.4 Vibrating wire viscometer
The first person used the vibrating wire to measure the viscosity of fluid are Tough et al. in early 1960. From then on, the vibrating wire viscometers were substantially developed with different wire materials, diameters, lengths and clamping devices (Mohamed, K., 2005).
The vibrating wire technique can be applied to measure both viscosity and density. The device may measure these properties simultaneously when tensioned by a suspended mass or sinker (Fausto, C. & J.P. Martin Trusler, 2009).
The vibrating wire viscosity is sometimes designed to be used at high pressure. The wire plays a key role in the design because its features which are shown in the working equations have a direct influence on the performance of the equipment. It indicates that thinner wire provides better results at low viscosity while thicker wire at high viscosity which means that to know the viscosity of a fluid is necessary before to choose the radius of the wire.
5 Modelling and comparison
As mentioned above, the diesel fuels are consists of many compositions which lead to the difficult prediction of the fluid's behaviour because of the large number of variables. Therefore, some methods which are used to reduce the number of variables and simplify the complex components are needed. The most widely used method is the component lumping. Leibovici (1993) indicates a lumping approach in order to minimise the loss of information because of component lumping. The method is consistent with the equation of state used to express the thermodynamic behaviour of the lumped system. Briesen and Marquardt (2004) report an adaptive multigrid method on the basis of wavelet-Galerkin discretization, which makes a model to be defined at various levels of detail.
5.1 Pseudo-component lumping method
A traditional method is pseudo-component lumping even though there is no clear optimum definition of the pseudo-component lumps. In pseudo-component lumping, the chromatogram is divided into some sections and all of the material in each section is lumped into a single component class which is called a pseudo-component (Patrick, K.M. & Rayford, G.A., 1989).
5.1.1 Definition of pseudo-component
Usually, there are two steps to set a system of pseudo-components. The first one is to obtain the standard characterisation curve. In the review, we use the true boiling points (TBP) curve which can be done with some methods in the previous chapter. The TBP curve shows the dependence of temperature which is measured in the laboratory batch column on mass or volume fraction distilled. The second step is to cut the range of boiling points of the TBP curve in order to get non-overlapping temperature intervals (Ti, Ti+1) with in the whole temperature range ( 9). Each pseudo-component is corresponded to each temperature intervals.
Therefore, the reason why there is no universal definition of pseudo-components is the different choices of temperature intervals which lead to the corresponding number of pseudo-components. The way to choose number and size of the intervals should be considered on experience because it may effect directly on the performance of the model (Heiko, B. & Wilfergang, M., 2003). Once the intervals are determined, a normal boiling point is decided to each pseudo-component by calculating the mean temperature over the corresponding interval (Egon, E. & Tomas, V., 2005).
5.1.2 Estimation of pseudo-component properties
After the pseudo-components obtained, we have to estimate the physical properties of each pseudo-component in order to simulate the behaviour of the fluid.
One method inclines to minimise the loss of information by component lumping when completely consistent with the equation of state (EOS) is used to describe the behaviour of the lumped system.
The simplest way is to assume that any property can be described as a linear combination of properties using Kay's rule. More complex methods estimate the physical properties of the groups using the EOS itself and the mixing rules formulation are applied for parameter identification.
The proposed method here is on the basis of a strict identification of the EOS parameters which are obtained at different temperatures for the mixture and the lumped system. Finally, more traditional properties can be generated from the lumped EOS parameters when this parameter identification has been carried out (Leibivici, C.F. Govel, P.L. & Tomas, P., 1993).
5.1.3 Advantages and disadvantages
The primary advantage and main presumption of pseudo-components is that the pseudo-components should be treated as real components in the simulation programs when a set of estimated physical pseudo properties are defined and equipped. Another advantage is that the characterisation procedure is not iterative and it is also convenient and widely accepted.
This method has been developed for a long time, however, since more accuracy results are needed, some problems of pseudo-components arise. First of all, the chemical character cannot be defined for pseudo-components. Secondly, the main definition of a pseudo-component relies on its pseudo boiling point and some other parameters such as specific gravity, molecular weight and viscosity. All of other physical properties must be determined. Thirdly, for pseudo-components, the group contribution methods which need information about the molecular structure of components to calculate some parameters cannot be used. Finally, in the original mixture, the arbitrary combination of pseudo-components is not supported in commercial simulation programs (Egon, E. & Tomas, V., 2005). That means it is impossible to locate a real component into the middle of the temperature range which definite the pseudo-components without knowing its content.
5.2 Continuous lumping method
The problem of the pseudo-component method leads to the development of continuous lumping method.
5.2.1 Definition of continuous lumping method
The continuous lumping method is based on the continuous thermodynamic theory, in which a hypothetical continuum of components makes the approximation of the distinct mixture using a component distribution function. There are two parts approximation in this method: one is to approximate the exact distinct distribution with a truncated series expansion and the other is to approximate the exact series form of the equilibrium relationship.
A continuous distribution function can be expressed by means of the integral relation to represent the component of a mixture.
Every set of components can be expressed as a continuous distribution function with this equation. The simulation results are also distribution functions and can be converted into a distinct compositional representation using means of molar fractions (Heiko, B. & Wilfergang, M., 2000). The molar fractions are evaluated from the integral equation on the corresponding interval of the characterising variable that can be any property which is characteristic for a component. Continuous representations have been applied as an example for calculations of multi-component mixture (Ronald, L.C. & John, M.P., 1985) or as a basis for development of pseudo-component lumping methods (Miquel & Castells 1993).
5.2.2 Advantages and disadvantages
The continuous lumping method enlarges the application of continuous thermodynamics to mixtures which dissatisfy the continuous-mixture hypothesis. Especially, it is helpful for mixtures described by discontinuous component distributions, such as chromatographic data. Then, the method supplies an effective way to reduce the number of parameters described the mixture. At last, because the method is on the basis of a mathematical approximation rather than the continuous mixture assumption, the errors in the approximation can be estimated by standard mathematical schemes (Patrick, K.M. & Rayford, G.A., 1989).
The disadvantage of this method is the lack of flexibility and the uncontrolled error.
5.3 Real component method
5.3.1 Definition of the real component method
Based on some disadvantages of pseudo-component lumping method, the substitution of real component generates. Certain criteria guide to select the proper real components and derivate the replacing mixture and an appropriate algorithm should be defined. A component is chosen based on its boiling points in the temperature range of the interval. A wider interval is required if there is no boiling point of component in the interval and then the best match is determined. The key element of controlling the accuracy of the method is the quantity of data available in the database (Egon, E. & Tomas, V., 2005). As a result, in the considered temperature range in the database, a significant assumption of the availability and plenty number of real components with normal boiling points is required.
5.3.2 Advantages and disadvantages
There are some advantages of real component method compared with the pseudo-component lumping method. Firstly, the usage of replaced mixtures of real component can be expended from normal calculation of separation processes to chemical reactions processes. In the second place, empirical methods of physical properties are needless in general. Finally, the partial information will influence the selection of components which occur positively in the mixture or the overall character of the mixture (Egon, E. & Tomas, V., 2005). In addition, it is also convenient for this method to implement standard commercial simulation programs and can be improved in the construction of the substitute mixture.
One thing which should be overcome is that the interval defined for each substitute can be overlapping or leave gaps in the temperature range of the TBP curve.
5.4 Other methods
A general automatic lumping method is from direct uses of simulation results required from the elaborate mechanism to generate a lumped scheme effective over user-specified conditions. The method is used to isomer lumping in hydrocarbon oxidation schemes and is independent of equilibrium or quasi-steady state assumptions (P. Pepiot-Desjardins, H. Pitsch, 2008).
Compared some devices used to separate the components in diesel fuels, it is clear that the comprehensive 2D GC (GC x GC) is a better choice, because it can extract the TBP curve of a fluid and provide enough information to trigger the algorithm which can predict the physical properties of diesel fuels and its behaviour in different temperature and pressure. Then, a model may set up based on the algorithm and the components lumping. Though the pseudo-component lumping method has some shortages needed to overcome, it is the most convenient and easy method to lump the components in the lab.
The model cannot be used before testing against the experimental data of different physical properties. Density can be measured by pycnometer due to the simplicity and accuracy. The flow calorimeter is chosen to obtain the heat capacity and the ultrasonic cell can get the sound speed. Finally, vibrating wire viscometer is used to have the viscosity.
The target of our project is to test a model with the measured physical properties data.