Linear Function Of Pressure Research Articles

Simple correction for variable post column split ratios using pure carbon dioxide in packed column supercritical fluid chromatography with independent pressure and flow control

Packed column supercritical fluid chromatographs (SFC) with independent control of pressure and flow produce constant efficiency but suffer from variable response factors when using a post column split into a mass sensitive detector. Most of the flow passes through a backpressure regulator, but a small fraction of the flow passes through a fixed restrictor in the base of a detector like the FID. Since the flow through a fixed restrictor increases with pressure, a changing split ratio into the detector and non-linear response results. For samples requiring a pressure program to elute both light and heavy components, distorted mass distribution measurements result. A simple correction for this variable response is presented. Restrictor flow is a linear function of pressure. Division of the FID detector signal by the current pressure corrects for variations in post column split ratios. The correction only works for constant mass flow pumps and does not work for mixed fluids, syringe pumps or reciprocating pumps with inadequate compressibility compensation.

Modeling of a deep-seated geothermal system near Tianjin, China.

A geothermal field is located in deep-seated basement aquifers in the northeastern part of the North China Plain near Tianjin, China. Carbonate rocks of Ordovician and Middle and Upper Proterozoic age on the Cangxian Uplift are capable of yielding 960 to 4200 m3/d of 57 degrees C to 96 degrees C water to wells from a depth of more than 1000 m. A three-dimensional nonisothermal numerical model was used to simulate and predict the spatial and temporal evolution of pressure and temperature in the geothermal system. The density of the geothermal water, which appears in the governing equations, can be expressed as a linear function of pressure, temperature, and total dissolved solids. A term describing the exchange of heat between water and rock is incorporated in the governing heat transport equation. Conductive heat flow from surrounding formations can be considered among the boundary conditions. Recent data of geothermal water production from the system were used for a first calibration of the numerical model. The calibrated model was used to predict the future changes in pressure and temperature of the geothermal water caused by two pumping schemes. The modeling results indicate that both pressure and temperature have a tendency to decrease with time and pumping. The current withdrawal rates and a pumping period of five months followed by a shut-off period of seven months are helpful in minimizing the degradation of the geothermal resource potential in the area.

Structural evolution of rutile-type and CaCl 2 -type germanium dioxide at high pressure

Germanium dioxide was found to undergo a transition from the tetragonal rutile-type to the orthorhombic CaCl2-type phase above 25 GPa. The detailed structural evolution of both phases at high pressure in a diamond anvil cell has been investigated by Rietveld refinement using angle-dispersive, X-ray powder-diffraction data. The square of the spontaneous strain (a−b)/(a+b) in the orthorhombic phase was found to be a linear function of pressure and no discontinuities in the cell constants and volume were observed, indicating that the transition is second-order and proper ferroelastic. Compression of the GeO6 octahedra was found to be anisotropic, with the apical Ge-O distances decreasing to a greater extent than the equatorial distances and becoming shorter than the latter above 7 GPa. Above this pressure, the GeO6 octahedron exhibits the common type of tetragonal distortion predicted by a simple ionic model and observed for most rutile-type structures such as those of the heavier group-14 dioxides and the metal difluorides. Above the phase transition, the columns of edge-sharing octahedra tilt about their two fold axes parallel to c and the rotation angle reaches 10.2(5)° by 36(1) GPa so as to yield a hexagonal close-packed oxygen sublattice. The compressibility increases at the phase change as is expected for a second-order transition at which an additional compression mechanism becomes available.

CHARACTERISATION OF CAKE COMPRESSIBILITY IN DEAD-END MICROFILTRATION OF MICROBIAL SUSPENSIONS

Culture broths of Saccharomyces cerevisiae and Kluyveromyces marxianus var marxianus NRRLy2415, suspensions of rehydrated active dry bakers yeast and suspensions or calcium carbonate were filtered in dead-end mode at pressures below 200 kPa. In the case of all the microbial suspensions, the specific cake resistance was found to be a linear function of pressure. Cake compression was found to be reversible or weakly irreversible with respect to changes in pressure, i.e., the specific resistance measured at a given pressure was only weakly dependent on whether the filter cake had previously been exposed to higher pressures. The greatest irreversibility effects were obtained with unwashed active dry yeast suspensions, consistent with the breakdown of cell aggregates in these suspensions. The specific cake resistance of calcium carbonate suspensions was found to be a non-linear function of pressure. The compression of calcium carbonate cakes was irreversible, consistent with the breakdown of the large number of particle aggregates in these suspensions.

Measurements of the Thermal Conductivity of Aqueous CoCl2 Solutions at Pressures up to 100 MPa by the Parallel-Plate Apparatus.

The thermal conductivity of H2O + CoCl2 solutions was measured over the temperature range 293 to 473 K using a parallel-plate apparatus. Data cover the pressure range from 0.1 to 100 MPa. Measurements were made on ten isotherms, namely: 293, 313, 333, 353, 373, 393, 413, 433, and 473 K. The concentrations studied were 2.5, 5, 10, 15, 20, and 25 wt % CoCl2. The uncertainty of thermal conductivity measurements was estimated to be ±1.6%. The pressure effect on thermal conductivity behavior was similar for H2O and H2O + CoCl2. In the temperature range of our experiments, isotherms of thermal conductivity were almost linear function of pressure at all temperatures for each concentrations. Along each isobar a given concentration the thermal-conductivity of H2O + CoCl2 solutions exhibits a maximum at temperatures between 405 and 419 K. The measured values of thermal conductivity are compared with the experimental and correlation results of other investigators. A new correlation which yields the correct temperature, pressure, and concentration behavior of thermal conductivity is proposed. This maximum is displaced to higher temperature when the pressure is increased at each compositions. For fixed pressure the maximum is displaced to lower temperature when the composition is increased.

Pressure and temperature electron paramagnetic resonance studies of crystal

The effect of temperature and hydrostatic pressure on the spin-Hamiltonian parameter for in elpasolite is studied up to a pressure of 700 MPa over the temperature range 180 - 360 K. It is found that 56% of the temperature change in is caused by the spin - phonon interaction, and the remaining 44% is related to the thermal expansion of the crystal. The temperature at which the phase transition from the cubic to the tetragonal phase occurs is a linear function of pressure, with the pressure coefficient . The dependence of on the lattice constant and hydrostatic pressure is interpreted within the rigid-sphere model. No precursive behaviour above is observed.

Ultrasonic measurement of relaxation behavior in polystyrene

We report measurements of the temperature and pressure dependence of ultrasonic modulus and specific volume in polystyrene between 50 and 280°C and applied pressures up to 775 bar. The volumetric glass transition temperature is found to vary linearly with pressure. Furthermore, it coincides with the temperature at which the velocity of sound and the attenuation in the material show pronounced change from solid-like to liquid-like behavior. The storage and loss moduli are analyzed within the Havriliak-Negami model and very good agreement is found over the entire temperature and pressure ranges. Using the Vogel-Tammann-Fulcher equation for the relaxation time, the Kauzmann temperature Tk and the fragility parameter D of polystyrene were determined from fits to the data. Tk is also a linear function of pressure, but D is constant over the whole pressure range. The value of D allows us to classify polystyrene among the fragile-glass formers. © 1996 John Wiley & Sons, Inc.

Ultrasonic measurement of relaxation behavior in polystyrene

We report measurements of the temperature and pressure dependence of ultrasonic modulus and specific volume in polystyrene between 50 and 280°C and applied pressures up to 775 bar. The volumetric glass transition temperature is found to vary linearly with pressure. Furthermore, it coincides with the temperature at which the velocity of sound and the attenuation in the material show pronounced change from solid-like to liquid-like behavior. The storage and loss moduli are analyzed within the Havriliak-Negami model and very good agreement is found over the entire temperature and pressure ranges. Using the Vogel-Tammann-Fulcher equation for the relaxation time, the Kauzmann temperature Tk and the fragility parameter D of polystyrene were determined from fits to the data. Tk is also a linear function of pressure, but D is constant over the whole pressure range. The value of D allows us to classify polystyrene among the fragile-glass formers. © 1996 John Wiley & Sons, Inc.

The viscosity of methane at 273 K up to 1 GPa

Abstract Absolute measurements of the viscosity coefficient of methane were performed at a temperature of 273 K and at pressures from 1 to 953 MPa, the latter pressure being very near to the melting point at this temperature. The apparatus employed was a vibrating wire viscometer, using the free damped oscillation method. The accuracy of the measurements is estimated to be 1 %. The results show a qualitative resemblance to those obtained at 298 K. A close analysis shows that, for pressures above 58 MPa, the viscosity can be described with three slightly different linear functions of pressure. Again, in the Batschinski-Hildebrand representation of the fluidity, three corresponding linear functions of the molar volume can be distinguished. The occurrence of the third linear relation between the fluidity and the molar volume, in the range adjacent to the melting density, is attributed to hindered rotation of the molecules. This type of behaviour can also be seen by comparison of the results with molecular dynamic computations for hard spheres.

Three-dimensional convection of an infinite-Prandtl-number compressible fluid in a basally heated spherical shell

A numerical investigation is made of the effects of compressibility on threedimensional thermal convection in a basally heated, highly viscous fluid spherical shell with an inner to outer radius ratio of approximately 0.55, characteristic of the Earth’s whole mantle. Compressibility is implemented with the anelastic approximation and a hydrostatic adiabatic reference state whose bulk modulus is a linear function of pressure. The compressibilities studied range from Boussinesq cases to compressibilities typical of the Earth’s whole mantle. Compressibility has little effect on the spatial structure of steady convection when the superadiabatic temperature drop across the shell AT,, is comparable to a characteristic adiabatic temperature. When AT,& is approximately an order of magnitude smaller than the adiabatic temperature, compressibility is significant. For all the non-Boussinesq cases, the regular polyhedral convective patterns that exist at large AZ, break down at small AT, into highly irregular patterns ; as AZ, decreases convection becomes penetrative in the upper portion of the shell and is strongly time dependent at Rayleigh numbers only ten times the critical Rayleigh number, (Ra),,. Viscous heating in the compressible solutions is concentrated around the upwelling plumes and is greatest near the top and bottom of the shell. Solutions with regular patterns (and large AEJ remain steady up to fairly high Rayleigh numbers (100(Ra),,), while solutions with irregular convective patterns are time dependent at similar Rayleigh numbers. Compressibility affects the pattern evolution of the irregular solutions, producing fewer upwelling plumes with increasing compressibility.

Inflow Performance Relationships for Solution-Gas-Drive Reservoirs

In this theoretical study, a numerical model was used to examine the influence of pressure level and skin factor on the inflow performance relationships (IPR's) of wells producing under solution-gas-drive systems. Examination of the synthetic deliverability curves suggests that the exponent of the deliverability curve is a function of time and that the exponent is usually greater than unity. The implication of this observation to field data is discussed. The accuracy of procedures given in the literature to predict oilwell deliverabilities is also examined. It is shown that these methods can be used to predict future performance provided that the exponent of the deliverability curve is known and that extrapolations over large time ranges are avoided. If single-point tests are used to predict future performance (such tests assume that the exponent of the deliverability curve is constant), then errors in predictions will be minimized. Although relative permeability and fluid property data are required, the Muskat material-balance equation and the assumption that GOR is independent of distance can be used to predict future production rates. This method avoids problems associated with other methods in the literature and always yields reliable results. New methods to modify the IPR curve to incorporate changesmore » in skin factor are presented. A new flow-efficiency definition based on the structure of the deliverability equations for solution-gas-drive reservoirs is proposed. This definition avoids problems that result when the currently available methods are applied to heavily stimulated wells.« less

ChemInform Abstract: Reactivity and Intersystem Crossing of Singlet Methylene in Solution.

Evidence is reported which demonstrates that singlet methylene, produced from the photolysis of diazomethane or diazirine, undergoes intersystem crossing to form triplet methylene in perfluorohexane solvent. The results of triplet sensitized photolysis and of direct photolysis experiments with dilute concentrations of substrate (cis- and trans-2-pentene and chloroform) appear to be essentially identical. Stern-Volmer analyses of the competition kinetics between acetonitrile and 2-pentenes or chloroform for singlet methylene are consistent with the near diffusion controlled reactivity of singlet methylene. With the assumption of diffusion-controlled reactions for singlet methylene, plots of the quantum yield for singlet vs. triplet reaction for methylene allow the first estimate (58 X lo8 s-l) of the rate of intersystem crossing of singlet methylene in the condensed phase. This value is considerably smaller than the value that is extrapolated to the solution phase from results in the gas phase. The possible reasons for this difference are discussed. Methylene (CH,), the parent of the carbene family, has at- tracted the attention of organic chemists,' theorists,, spectro- scopist~,~ and chemical physicist^..^ Almost all of the quantitative information concerning this species is derived from gas-phase investigations,6 from which it has been concluded that CH2 is a ground state triplet (3CH2) and that a low-lying singlet state ('CH,) exists at about 9 kcal/mo17 above the ground state (Figure 1). Methylene possesses one carbon atom, two hydrogen atoms, and two nonbonding electrons. The two nonbonding electrons occupy the u and T orbitals with their spins parallel for the more linear VH, (6 = 136O), while they occupy the u orbital paired spins for the lowest energy singlet methylene (0 = 102O) (Figure 1). Both states have been observed spectroscopically in the gas phase,3 and from kinetic investigation^^.^ it has been concluded that 'CH2 is quenched by all additives, even inert gases, with high efficiency. Indeed, extrapolation of the gas-phase quenching data to the solution phase leads to the expectation that the lifetime of ICH2 will be of the order of picoseconds in the condensed phase. For example, 'CH, is quenched by He in the gas phase4 with a rate constant of ca. 4 X cm3 molecule-' s-', which translates into a bimolecular rate constant of ca. 2 X lo9 M-l s-I. For an organic solvent concentration of 5 M, the rate of quenching for a completely inert solvent (such as helium!) would be 1 X 1O'O s-I, implying a lifetime of the order of 50 ps or less for 'CH2 in solution. This expectation is based on the assumption that the rate of the 'CH2 deactivation is a linear function of pressure even at high pressure (or in the solution phase). Since quenching must involve either reaction or intersystem crossing to 3CH2, one is led

Reactivity and intersystem crossing of singlet methylene in solution

Evidence is reported which demonstrates that singlet methylene, produced from the photolysis of diazomethane or diazirine, undergoes intersystem crossing to form triplet methylene in perfluorohexane solvent. The results of triplet sensitized photolysis and of direct photolysis experiments with dilute concentrations of substrate (cis- and trans-2-pentene and chloroform) appear to be essentially identical. Stern-Volmer analyses of the competition kinetics between acetonitrile and 2-pentenes or chloroform for singlet methylene are consistent with the near diffusion controlled reactivity of singlet methylene. With the assumption of diffusion-controlled reactions for singlet methylene, plots of the quantum yield for singlet vs. triplet reaction for methylene allow the first estimate (58 X lo8 s-l) of the rate of intersystem crossing of singlet methylene in the condensed phase. This value is considerably smaller than the value that is extrapolated to the solution phase from results in the gas phase. The possible reasons for this difference are discussed. Methylene (CH,), the parent of the carbene family, has at- tracted the attention of organic chemists,' theorists,, spectro- scopist~,~ and chemical physicist^..^ Almost all of the quantitative information concerning this species is derived from gas-phase investigations,6 from which it has been concluded that CH2 is a ground state triplet (3CH2) and that a low-lying singlet state ('CH,) exists at about 9 kcal/mo17 above the ground state (Figure 1). Methylene possesses one carbon atom, two hydrogen atoms, and two nonbonding electrons. The two nonbonding electrons occupy the u and T orbitals with their spins parallel for the more linear VH, (6 = 136O), while they occupy the u orbital paired spins for the lowest energy singlet methylene (0 = 102O) (Figure 1). Both states have been observed spectroscopically in the gas phase,3 and from kinetic investigation^^.^ it has been concluded that 'CH2 is quenched by all additives, even inert gases, with high efficiency. Indeed, extrapolation of the gas-phase quenching data to the solution phase leads to the expectation that the lifetime of ICH2 will be of the order of picoseconds in the condensed phase. For example, 'CH, is quenched by He in the gas phase4 with a rate constant of ca. 4 X cm3 molecule-' s-', which translates into a bimolecular rate constant of ca. 2 X lo9 M-l s-I. For an organic solvent concentration of 5 M, the rate of quenching for a completely inert solvent (such as helium!) would be 1 X 1O'O s-I, implying a lifetime of the order of 50 ps or less for 'CH2 in solution. This expectation is based on the assumption that the rate of the 'CH2 deactivation is a linear function of pressure even at high pressure (or in the solution phase). Since quenching must involve either reaction or intersystem crossing to 3CH2, one is led

Polarization and pressure dependence of 2p-1s transitions in He-like and Li-like neon recoil ions.

The pressure dependences of 2p-1s transitions in He-like and Li-like neon recoil ions produced in collisions with 1.4-MeV/amu Ar ions were studied for the purpose of assessing effects of polarization and nonstatistical population mechanisms on the relative intensities of prompt and metastable lines. A Johansson-type curved-crystal spectrometer was employed as an x-ray polarimeter by taking spectra with the plane of the focal circle oriented both parallel and perpendicular to the Ar-ion beam. The data indicate that the He-like $^{1}\mathrm{P}$ and $^{3}\mathrm{P}$ lines are only slightly polarized and that the intensity ratio I${(\mathrm{}}^{1}$P)/I${(\mathrm{}}^{3}$P) is not a linear function of pressure. Both of these results appear to be a direct consequence of serious contamination of the spectral region of interest by unresolved spectator-electron transitions.

Hydraulic resistance in bones of the canine shoulder

The hydraulic properties of trabecular bone were explored in both sides of normal canine shoulders by following the hydrostatic pressure response to transchondral injections of saline. In a series of isovolumetric injections at sites 9 mm beneath either joint surface, the pressure consistently rose higher and lasted longer in the humerus than it did in the scapula. Hydraulic resistance, the linear function of pressure per unit flow, averaged 8.8 times higher within the humerus than in the scapula in a second series of experiments. Hydraulic resistance fell by average factors of 9.6 in the humerus and 4.3 in the scapula when the surrounding bone was cut away to leave the injection site centered within a 1 cm ‘cube’ of trabecular bone. Direct determinations of hydraulic resistance provide a useful tool for the study of normal and abnormal physiology in trabecular bone.

Pressure-volume relationships and elastance in the knee joint of the dog.

This study has investigated changes in intra-articular hydrostatic pressure in the knee joints of normal dogs in response to continuous and stepwise infusions of fluids. The relationship between pressure and volume in the joint was examined over the pressure range of -8 to +50 mmHg, and also at much higher pressures often associated with joint disease or injury. The effects of joint angle and dog weight on the pressure-volume relationship and on elastance of the dogs' knees were also examined. With liquid paraffin B.P. the pressure was found to increase more with each unit volume infused at subatmospheric pressures than at pressures around atmospheric, and increased more again at higher pressures. The pressure-volume curve with saline infusions was affected by egress of fluid from the joint at supra-atmospheric pressure. Above +5 mmHg the rise in pressure per unit volume infused was less than that for paraffin at the same volume. Elastance and compliance of the normal joint capsule were calculated from the pressure-volume data. Elastance was high at subatmospheric pressures, decreased rapidly as atmospheric pressure was approached and rose as a linear function of pressure above 12 mmHg. The biphasic shape of the elastance-pressure curve is discussed, and explanations for the shape are suggested. After intra-articular pressure in the knee was raised by infusion of paraffin oil the joint was moved through the range of positions from 125 deg extension to 50 deg flexion. Intra-articular pressure did not change across the range 125-110 deg. However, increasing the angle of flexion from 110 to 50 deg resulted in a rise in pressure which became steeper for each volume increment. Increasing intra-articular fluid volume caused a decrease in the total range of movement of the joint. The pressure-volume curves measured at extended angles of 110, 125 and 140 deg, where the starting pressures were subatmospheric, were the same. At flexed joint positions of 80 and 50 deg, where the starting pressures were supra-atmospheric, the pressure-volume curves became steeper with greater flexion. Elastance of the joint tissues increased with flexion. The elastance at each joint angle depended also on the volume or pressure. Significant differences were found to exist between pressure-volume curves for three groups of animals of different weight.(ABSTRACT TRUNCATED AT 400 WORDS)

Mechanical and physical properties of poly(vinylidene fluoride) at high pressures and temperatures

Abstract Stress-strain behavior in tension and compression, Pressure-Volume-Temperature (PVT) relations, and the pressure dependency of transitional behavior, by dielectric technique, of Phase I and Phase II ploy(vinylidene fluoride) (PVDF) have been determined. The result obtained are used in analyzing the complex behavior of piezoelectric and pyroelectric properties of the material at high pressures and temperatures. The Young's modulus(E) of Phase II PVDF increases, at room temperature, monotonically but nonlinearly, with increasing pressure as long as the amorphous material is in the rubbery state. It then takes a step-jump at Pg (5 Kbars) and continues to increase with pressure. However, the yield strength in both tension and compression is observed to be linear functions of pressure. PVT measurements clearly show the glass transion temperature (Tg) at −50°C and the crystal transition (Tc) at 22°C at atmospheric pressure. The Tg of both unoriented and oriented Phase I PVDF increase, in most part, lin...

The effect of pressure on the flow stress of metals

The classical theory of plastic flow of metals assumes that any pressure dependence of yielding is associated with irreversible dilatation through the normality flow rule. Experimental results presented here on iron-based materials and on aluminum show that although the flow stress is a linear function of pressure, the plastic dilatancy is not related by the normality flow rule and is in fact negligible by comparison. The pressure dependence of the flow stresses in these materials results from the effect of pressure on dislocation motion, whereas the observed plastic volume changes are in accord with expected increases due to dislocation generation. Thus, there is no need for the pressure dependency of yielding to be associated with irreversible plastic dilatancy.

Use of the Pressure Bomb for Hydraulic Conductance Studies

Stem sections of alfalfa (Medicago sativa L.) were subjected to forced flows of both water and high molecular weight dextran solutions. In either case, stems responded in accordance with the Ohm's law analogy for flow, i.e., flow was a linear function of pressure, at pressures ranging from 7-0-500 kPa and vacuum from 25-69 kPa. Since conductance values were the same for both pressure and vacuum powered flows, it is possible to extrapolate conductance values determined with a pressure bomb to negative pressure gradients experienced by plants.

Capture and emission of electrons by the resonant state strongly coupled to the lattice inn-InSb

The pressure and temperature dependences of the free-electron capture cross section $\ensuremath{\sigma}$ and the emission rate $\ensuremath{\alpha}$ are determined for the defect level which is resonant at ambient pressure and becomes bound at pressures $p>700$ MPa. Irrespective of the level position, i.e., for the level being resonant as well as bound, both $\ensuremath{\sigma}$ and $\ensuremath{\alpha}$ are thermally activated and their activation energies are the linear functions of pressure. It is found that, during the capture or emission process, the adiabatic potential barrier which originates from the strong defect-lattice coupling cannot be practivally tunneled. It means that the barrier is very extensive and the capture or emission process leads to the drastic rearrangement of the defect center in the crystal lattice.