A fluid is composed of atoms and molecules. Depending on the phase of the fluid gas,liquid or supercritical , the distance between the molecules shows orders of magnitude difference, being the largest in the gas phase and shortest in the liquid phase. As the distance between the molecules or the mean free path of the flowing medium approaches to the characteristic size of the flow device, the flow cannot be treated as continuum.
In a solid, molecules form a regular lattice and oscillate around an equilibrium point. At this state, there is a strong attraction between the molecules and kinetic energy of the molecules can not overcome this force in this phase of the matter. When enough energy is given to the molecules, e. The molecules gain kinetic energy as a result of added heat and start to move around in an irregular pattern. However, the density of liquids and solids, in other words the mean molecular distances at these two phases do not differ much from each other.
When the liquid vaporizes and turns into the gas phase, the density drastically drops as the molecules starts to move freely between the intermolecular collisions. A fluid is defined as a substance that continually deforms flows under an applied shear stress regardless of the magnitude of the applied stress. Whereas a solid can resist an applied force by static deformation. Liquids , gases , plasmas and, to some extent, plastic solids are accepted to be fluids. A perfect fluid offers no internal resistance to change in shape and, consequently, they take on the shape of their containers.
Liquids form a free surface that is, a surface not created by their container whereas gases and plasmas do not, but, instead, they expand and occupy the entire volume of the container. The importance of flow phenomena is out of question. Natural phenomena or technological applications are completely or partially involves flow phenomena. It can be met in a diverse range of length of time scales.
Atmospheric flows and blood flows are two examples for this diversity. As a tool making specie, humankind learned also how to utilize flow phenomena. Hence, those, who deal with flowing matter, should be better equipped with theoretical understanding and capability to use experimental and numerical investigation tools.
Fluid mechanics have played an important role in human life. Therefore, it also attracted many curious people. Even in the ancient Greek history, systematic theoretical works have been done. The devlopement of governing equations of fluid flow started already in the 16th century. In the 18th and 19th century, the conservation laws for mass, momentum and energy was already known in its most general form. In the 20th century, developments were in theoretical, experimental and recently numerical.
In the theoretical field, mostly solutions of the governing equations for special cases were provided. Experimental methods have been developed to measure flow velocities and fluid properties. By the developement of computers , the numerical treatment of fluid mechanical problems opened new perspectives in research. It is the common blief that in the 21th century, the activities would be most intensive in the development new experimental and numerical tools and application of those for developing new technologies.
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Although detailed calculation of Joule—Thomson coefficients from such a chart is not recommended. Miller derived the following approximate equation for the Joule—Thomson inversion curve:. This function is plotted in Fig. First, at low temperatures, subcooled liquids, the Joule—Thomson coefficient is positive. In fact, according to the Miller equation, if T R is less than approximately 0. At high temperatures, the Joule—Thomson is also positive. According to the Miller equation, if the T R is greater than approximately 5, then the Joule—Thomson is positive.
Finally, at very high pressures, the Joule—Thomson is also positive. Furthermore, it appears from this figure that, in the limit, as the pressure goes to zero, the ideal gas behavior is not exhibited. That is, at low pressure, the Joule—Thomson coefficient is not zero, which was demonstrated earlier, is the case for ideal gases. However, the Miller equation and the figure derived from it says nothing of the magnitude of the Joule—Thomson coefficient. Low-pressure gases have Joule—Thomson coefficients that are small in magnitude and, thus, for practical purposes, are zero.
For crude oils and other real fluids a detailed composition is generally not available and a fluid characterisation is essential.
The characterization used with this model considers that the fluid consists of two types of compounds: the solute, comprising the n-alkanes that crystallise to form a solid phase, and the solvent, formed by all the non-crystallisable compounds. A different approach is used for the characterization of the two types of compounds. The work developed by our team indicates that an accurate description of n-alkanes Solid-Liquid Equilibrium cannot be achieved unless each n-alkane is considered individually [ 43, 54, 56, 73 ].
The n-alkanes characterization aims at develop a description of the n-alkanes distribution as close as possible to the actual fluid.
This distribution is described by two parameters: the total n-alkane content and their decay. These can be obtained in a number of different ways:. Chromatographic measurements. It can provide both the total n-alkane content and its decay. Solvent precipitation.
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The UOP essay [ 74 ], or any of its variants [ ], are standard procedures that provide a good estimate of the total wax content in a crude oil. In the absence of further analytical information the wax content can be obtained from a correlation involving some known property of the oil. A correlation for paraffinic waxy crudes of the total wax content with the oil average molecular weight, Mw, was proposed by Coutinho and Daridon [ 27 ]. The exponential decay of the n-alkanes in oils is well documented in the literature [ ].
It is defined as the ratio between the mass fractions of two successive n-alkanes. Chromatography: Again GC or HTGC can provide information about the paraffin distribution with even better accuracy than for the wax content.
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All the individual paraffins with concentrations higher than 0. One of the major advantages of the model presented here is that it is independent of the characterisation procedure used for the non-crystallisable compounds. Any solvent characterisation can in principle be used since, as shown by Coutinho and Daridon [ 27 ], the solubility of the n-alkanes is independent of the nature of the solvent.
It is then irrelevant which and how many pseudo-compounds are chosen to describe the solvent as long as the total molar fractions of the n-alkanes and solvent are coherent with the actual oil composition. To fill this requirement the only constraint to the solvent characterization is that the average molecular weight of the oil is conserved through the characterization procedure. For a matter of simplicity it is recommended that for a fluid not containing light gases a single pseudo-compound be used while for the other fluids at least two pseudocomponents, one for the gases and the other for the heavier compounds, be used.
Once the distribution of n-alkanes established and the solvent pseudocomponents defined it is necessary to estimate the thermophysical properties of the n-alkanes used by the model.