Study of the Compressions of Several High Molecular Weight Hydrocarbons

Abstract

Isothermal compressions were measured for thirteen high-purity liquid hydrocarbons and two binary mixtures of liquid hydrocarbons. These hydrocarbons have a molecular weight range of 170 to 351 and included normal paraffins, cycloparaffins, aromatics, and fused ring compounds. The pressure range for these measurements was from atmospheric to as high as 10 000 bars, being limited to lower values for some compounds to avoid possible solidification of the liquid. The volume changes due to pressure were measured at six temperatures spaced about equally in the range 37.8°C to 135.0°C. The volume changes and pressures were measured by methods similar to those of P. W. Bridgman. Pressure-volume isotherms can be described adequately by the Tait equation, v0—v=C log(1+P/B), or for pressures above a certain minimum, whose value depends on the compound, by the Hudleston equation log[v2/3P/(v01/3−v1/3)]=A+B(v01/3−v1/3).For the Tait equation the parameter C can be predicted for hydrocarbon liquids from the relation C=0.2058 v0. Compressibility for a given hydrocarbon decreases with increasing pressure at constant temperature and increases with increasing temperature at constant pressure. The compression, and the compressibility, of liquid hydrocarbons are strongly dependent on molecular structure. Cyclization introduces a rigidity of molecular shape which decreases the compressibility markedly. Furthermore, fused ring cyclization as exemplified by naphthyl and decalyl structures has a considerably greater effect in decreasing compressibility than cyclization to nonfused rings such as cyclopentyl, cyclohexyl, or phenyl, even at equivalent carbon atom in ring percentages. Isobars and isochores were drawn and studied over the full range of temperature and pressure. The coefficient of thermal expansion, (1/v0) (δv/δT) P, for a given hydrocarbon, decreases with increasing pressure at constant temperature. (δ2v/δT2) P undergoes a sign change at a certain pressure, whose value depends on the compound; (δv/δT) P increases with increasing temperature below this pressure and decreases with increasing temperature above this pressure. The pressure coefficient, (δP/δT) v, is not a function of volume alone but is also dependent on the temperature and pressure. (δE/δv) T and (δE/δP) T go to zero and then reverse sign for compounds that can be studied to sufficiently high pressures.

Some Remarks on the Navier-Stokes Equations with a Pressure-Dependent Viscosity.

“…In [3], for example, various organic liquids were studied at pressures of up to several thousand atmospheres. It was found that for some of these liquids the viscosity increased by two orders of magnitude compared to its value at atmospheric pressure, while compression was only of the order of 10% [2]. Such data suggest that it is reasonable to consider a pressure dependence of the viscosity, even in fluids that can, to a good approximation, be regarded as incompressible.…”

On Fully Developed Flows of Fluids with a Pressure Dependent Viscosity in a Pipe

“…However, at present we are not aware of any experiments of the laminar flow of fluids in which the pressure varies significantly which we could use to compare with our theoretical predictions. In fact, it would be interesting to carry out an experiment to assess the effect of the pressure dependence of viscosity on pipe flows, as we know from other experiments (see discussion that follows where references [4]- [10] as well as [2] are mentioned) that the viscosity does depend on the pressure. This is an interesting open problem from our perspective.…”

“…There is a considerable body of experimental literature that indicates without a shadow of doubt the dependence of the viscosity on pressure (see Cutler et al [4], Griest et al [5], Johnson and Cameron [6], Johnson and Tevaarwerk [7], Greenwood [8], Bair and Winer [9]). It has been found that the variation of the viscosity with pressure could even be exponential, with the viscosity varying by several orders of magnitude (see also Szeri [10] for a discussion of the variation of viscosity with pressure in elastohydrodynamics).…”

“…Equations of the type (4) do not define a constitutive relation, they define a class of constitutive relations as there could be more than one explicit relationship between T and D that satisfy (1) and (4). A more general implicit constitutive specification that allows for memory effects is…”

Flow of a Fluid Through a Porous Solid Due to High Pressure Gradients

“…Bridgman [6] in his book cites a personal communication from Andrade that provides a relationship of the viscosity to the temperature, density and pressure 1 (see also the discussion in [10]). There has been a great deal of experimental data since Bridgman's book that document the variation of viscosity with pressure (see [11,12,13,14,15,16,17,18,19,20,21,22]). In most liquids, while the variation in the viscosity can be of the order of 10 8 (see Bair and Kottke [21]), the variation of the density due to variation in the pressure is of the order of a few percent (see Dowson and Higginson [23], Rajagopal [24]), and thus it would be reasonable to assume that the liquid is incompressible while the visocity varies with the pressure.…”