On the retrograde condensation behavior of lean natural gas

The occurrence of liquid dropout in natural gas pipelines may cause operational problems during storage, transport, and processing. Therefore, the availability of a model that accurately predicts the amount of liquid formed is of great importance for the natural gas industry. The objective of this study is to develop a thermodynamic model for the accurate prediction of the amount of liquid formed in natural gas pipelines at transportation conditions. As input, the model requires an accurate gas analysis. A modified Peng-Robinson equation of state was selected for the phase equilibrium calculations. Interaction parameters were optimized from experimental data at conditions of practical interest, i.e., at pressures 10 < p < 70 bar and at temperatures 250 < T < 290 K. For a number of keysystems, the interaction parameters were calculated from new accurate solubility data of heavy hydrocarbons in some of the main constituents of natural gas like methane and nitrogen. Also, an extensive experimental program was carried out to study the influence of minute amounts of nitrogen, ethane and carbon dioxide in methane on the solubility behavior of decane in these gas mixtures. From a sensitivity analysis, it could be concluded that the liquid dropout is influenced mainly by the concentration and characterization of C₇-C₁₃ fractions. In this work, two characterization procedures to represent these fractions are compared. For two types of lean natural gas, the model predictions are compared with field measurement data, recently supplied by the Dutch natural gas industry.Invited paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

A review of experimental methods for solid solubility determination in cryogenic systems

Over the past years, there have been a number of serious explosions in air industry, which have resulted in workers injuries and fatalities. At the same time, there has been an increase in the use of air separation products for industrial activities.The quality of air entering an air separation plant is of crucial importance for its safe and reliable operation and the interest in the solubility data of solids in cryogenic liquid solvents is closely connected to the problem of impurities accumulation in the process plant and storage tanks. Such accumulations, especially in liquid oxygen, may cause fouling and blockage in heat exchangers and pipelines and they may eventually cause serious explosions. For this reason the air contaminants composition in liquid oxygen must be determined with great precision.This paper aims at reviewing experimental methods for determining the solubility of solid compounds that may be present in the cryogenic liquefaction processing of air distillation. A review of the literature data on solubility of solids in liquid oxygen and nitrogen is included as well.Emphasis is given to the difficulties in setting-up measuring apparatuses working at extreme conditions, i.e. low compositions and low temperatures.     

Band gaps of elastic waves in 1-D phononic crystal with dipolar gradient elasticity

The dispersive relations of Bloch waves in the periodic laminated structure formed by periodically repeating of two different gradient elastic solids are studied in this paper. First, the various wave modes in the gradient elastic solid, which are different from those in the classical elastic solid, are formulated. Apart from the dispersive P wave and SV wave, there are two evanescent waves, which become the P type and S type surface waves at the interface of two different gradient elastic solids. Next, the continuity conditions of displacement vector, the normal derivative of the displacement vector and the monopolar and dipolar tractions across the interface between two different gradient elastic solids are used to derive the transfer matrix of the state vector in a typical single cell. At last, the Bloch theorem of Bloch waves in the periodical structure is used to give the dispersive equation. The in-plane Bloch waves and the anti-plane Bloch waves are both considered in the present work. The oblique propagation situation and the normal propagation situation are also considered, respectively. The numerical results are obtained by solving the dispersive equation. The influences of two microstructure parameters of the gradient elastic solid and the microstructure parameter ratio of two different gradient elastic solids on the dispersive relation are discussed based on the numerical results.     

High-pressure phase equilibria in binary and ternary mixtures with one near- or supercritical and one high-molecular component. New insights for application and theory

In this work we report on two different high-pressure phase equilibria. The first is the solubility of a low-volatile solid in a supercritical phase. These are two anthraquinone dyes 1,4-bis-(hexadecylamino)-9,10-anthraquinone and 1,4-bis-(dodecylamino)-9, 10-anthraquinone dissolved in CO₂ and N₂O. Secondly, the partition of an infinitely diluted high-molecular biocompound between coexisting high-pressure liquid phases in a ternary system consisting of a nearcritical gas, water, and an organic solvent, that is a fully miscible with water at standard conditions, is investigated. The high-molecular compounds are two cardiac glycosides digoxin and digitoxin, which occur in the foxglove plant. The corresponding ternary phase-forming system consists of CO₂, water, and 1-propanol. The binary solubilities are determined within 310 and 340 K and up to 180 MPa where retrograde solubility is observed. The partitioning experiments are done at 313 and 333 K and at pressures, where a three-phase liquid-liquid-gas equilibrium with one water-like and one propanol-like phase exists. Experimental data are listed and discussed. Additionally, the correlation of the solubility data with a recently developed Carnahan-Starling-van der Waals type equation of state extended for the nearcritical region are discussed. The partitioning data with a hybrid model that combines the Peng-Robinson equation of state with an excess Gibbs energy approach based on UNIQUAC are outlined briefly and the results interpreted.     

Optimization of cryogenic carbon dioxide capture from natural gas

Cryogenic carbon dioxide removal from natural gas requires accurate thermodynamic phase study of the natural gas mixture and individual components. Thermodynamic data generation of carbon dioxide‐methane mixture having 90 % carbon dioxide for cryogenic carbon dioxide capture from natural gas using Peng Robinson equation of state is discussed in this research work. Golden section search technique along with Eureqa optimizing tool is then used to optimize the pressure‐temperature conditions for the cryogenic carbon dioxide capture in the solid‐vapour two‐phase region. Cost optimization is done for the carbon dioxide capture system at atmospheric pressure and 20 bar. Temperature ranges for optimization were obtained from the predicted thermodynamic data for the mixture. The optimum temperatures obtained in this research work for the cryogenic carbon dioxide capture at atmospheric pressure and the 20 bar are ?103.8 °C and ?60.90 °C respectively. For atmospheric pressure at ?103.8 °C the worth of methane, carbon dioxide, and energy is 114 $/h, 9 $/h, and 53 $/h respectively, while at 20 bar and ?60.9 °C the worth of carbon dioxide, methane, and the energy are found to be 129 $/h, 46 $/h, 52 $/h, respectively.     

Phase Behavior Modeling of Asphaltene Precipitation for Heavy Crudes: A Promising Tool Along with Experimental Data

Thermodynamic modeling is known as a promising tool for phase behavior modeling of asphaltene precipitation under different conditions such as pressure depletion and CO₂ injection. In this work, a thermodynamic approach is used for modeling the phase behavior of asphaltene precipitation. The precipitated asphaltene phase is represented by an improved solid model, while the oil and gas phases are modeled with an equation of state. The PR-EOS was used to perform flash calculations. Then, the onset point and the amount of precipitated asphaltene were predicted. A computer code based on an improved solid model has been developed and used for predicting asphaltene precipitation data for one of Iranian heavy crudes, under pressure depletion and CO₂ injection conditions. A significant improvement has been observed in predicting the asphaltene precipitation data under gas injection conditions. Especially for the maximum value of asphaltene precipitation and for the trend of the curve after the peak point, good agreement was observed. For gas injection conditions, comparison of the thermodynamic micellization model and the improved solid model showed that the thermodynamic micellization model cannot predict the maximum of precipitation as well as the improved solid model. The non-isothermal improved solid model has been used for predicting asphaltene precipitation data under pressure depletion conditions. The pressure depletion tests were done at different levels of temperature and pressure, and the parameters of a non-isothermal model were tuned using three onset pressures at three different temperatures for the considered crude. The results showed that the model is highly sensitive to the amount of solid molar volume along with the interaction coefficient parameter between the asphaltene component and light hydrocarbon components. Using a non-isothermal improved solid model, the asphaltene phase envelope was developed. It has been revealed that at high temperatures, an increase in the temperature results in a lower amount of asphaltene precipitation and also it causes the convergence of lower and upper boundaries of the asphaltene phase envelope. This work illustrates successful application of a non-isothermal improved solid model for developing the asphaltene phase envelope of heavy crude which can be helpful for monitoring and controlling of asphaltene precipitation through the wellbore and surface facilities during heavy oil production.     

Forced torsional oscillations of multilayered solids

A new approach is proposed for obtaining the dynamic elastic response of a multilayered elastic solid caused by a forced torsional oscillation inside the solid. The elastodynamic Green’s function of the center of rotation and a point load method are used to solve the problem. The solution of the center of rotation for multilayered solids is obtained by solving a set of simultaneous linear algebraic equations using the boundary conditions for the singularity and for the layer interfaces. The solution of the forced torsional oscillation is formulated by integrating the Green’s function over the contact area with unknown surface traction. The dual integral equations of the unknown surface traction are established by considering the boundary conditions on the contact surface of the multilayered solid, which can be converted into a Fredholm integral equation of the second kind and solved numerically.     

Calculation of the compressibility factor of natural gases based on the calorific value and the specific gravity

The measurement of large volume flows of natural gas in transmission lines requires an accurate equation of state for pressures up to about 12 MPa and in the temperature range from 265 to 335 K. If a detailed analysis of the gas mixture is available, one of the possibilities is to use the virial equation of state. However, such a gas analysis is time-consuming and expensive and, therefore, not always practical. We have developed a new equation which is based on the virial equation but requires limited input data. In general, for any given natural gas, the gross calorific value, the specific gravity, and the mole fractions of nitrogen and carbon dioxide are known. It will be shown that a knowledge of three of these four quantities is sufficient for an accurate prediction of the compressibility factor of the natural gas.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Vehicular applications of solid sorbents for natural gas storage

The state of the art of vehicular applications of solid sorbents for storage of natural gas is analyzed. Experimental data on methane sorption by activated carbon fiber at temperatures from −40 to +40°C and pressures up to 4 MPa are reported. Owing to the sorbent application the gas cylinder used provides a decrease in the working pressure and an increase in the volume density of storage as compared to systems based on compressed natural gas.     

The convection heat transfer coefficient in a Circulating Fluidized Bed (CFB)

Circulating Fluidized Beds are increasingly used in gas–solid and gas–catalytic reactions. A recent development involves their use in physical gas–solid processes such as drying, VOC adsorption or solar energy capture and storage. The heat transfer from the wall of the CFB to the flowing gas–solid suspension is the major design parameter, and was studied for different powders at different operating conditions as determined by the gas velocity and solids circulation flux. Measured values of the heat transfer coefficients are discussed, and compared with empirical predictions of Molodtsof–Muzyka, and Gorliz–Grace. Whereas Gorliz–Grace predicts heat transfer coefficients correctly within a narrow range of operating conditions only, the Molodtsof–Muzyka approach can be simplified into a linear relationship.     

Theoretical and experimental study of the aluminization of iron and steel in the pack and in the gas phase

A theoretical model which combines gaseous transport and solid state diffusion with the multicomponent equilibria at the gas-pack and gas-coating interfaces was used to study the pack aluminization of iron and steel. It allows the surface composition and the growth rate to be calculated. For a given activator they depend on the temperature and the aluminium activity in the pack. A good agreement is obtained between the theoretical predictions and the experimental results when the parts to be treated are embedded in the pack. Theoretical predictions for deposition in the gas phase, onto substrates out of contact with the pack, can be qualitatively deduced, and the conditions for obtaining uniform coatings in the gas phase are pointed out.     

An Eulerian particle level set method for compressible deforming solids with arbitrary EOS

In this study, an Eulerian, finite‐volume method is developed for the numerical simulation of elastic–plastic response of compressible solid materials with arbitrary equation of state (EOS) under impact loading. The governing equations of mass, momentum, and energy along with evolution equations for deviatoric stresses are solved in Eulerian conservation law form. Since the position of material boundaries is determined implicitly by Eulerian schemes, the solution procedure is split into two separate subproblems, which are solved sequentially at each time step. First, the conserved variables are evolved in time with appropriate boundary conditions at the material interfaces. In the present work a fourth‐order central weighted essentially non‐oscillatory shock‐capturing method that was developed for gas dynamics has been extended to high strain rate solids problems. In this method fluxes are determined on a staggered grid at places where solution is smooth. As a result, the method does not rely on the solution of Riemann problems but enjoys the flexibility of using any type of EOS. Boundary conditions at material interfaces are also treated by a special ghost cell approach. Then in the second subproblem, the position of material interfaces is advanced to the new time using a particle level set method. A fifth‐order Godunov‐type central scheme is used to solve the Hamilton–Jacobi equation of level sets in two space dimensions. The capabilities of the proposed method are evaluated at the end by comparing numerical results with the experimental results and the reported benchmark solutions for the Taylor rod impact, spherical groove jetting, and void collapse problems. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear Wave Simulation on a Surface of Liquid Film Entrained by Turbulent Gas Flow at Weightlessness

The article considers the joint flow of a liquid film entrained by turbulent gas. Since liquid velocity is small in comparison with gas velocity, the problem is reduced to the calculation of pressure and shear stresses produced by the gas flowing over a wavy wall with small amplitude. Further, these data are used at the boundary conditions, when the flow of a liquid film is considered separately. As a result, we obtain a new system of equations for modeling the dynamics of long-wave perturbations on the surface of a viscous liquid film entrained by turbulent gas at microgravity. At small Reynolds numbers typical to the condition of microgravity, it was proved that this system is reduced to one evolution equation for the film thickness. Some numerical solutions of this equation have been received in this work.     

Cylindrical cavity expansion and contraction in pressure sensitive geomaterials

Summary A broad class of plane-strain axially-symmetric deformation patterns in geomaterials is studied within the framework of large strain pressure-sensitive plasticity. Invariant, non-associated deformationtype theories are formulated for the Mohr-Coulomb (M-C) and Drucker-Prager (D-P) solids with arbitrary hardening and accounting for an initial hydrostatic state of stress. With the M-C model we arrive at a single first order differential equation, while for the D-P solid an algebraic constraint supplements the governing differential equation. The analysis centers on the effective stress as the independent variable. A simplified treatment is given for the cavitation limit and some useful relations are derived for thin walled cylinders. The theory is applied to the triaxial calibration test for Castlegate sandstone and then used to simulate the hole closure problem. Numerical examples are provided for the case of a cavity embedded in an infinite medium subjected to external or internal pressure. Results for the D-P inner cone model were found to be in close agreement with those obtained from the M-C model.     

The density and thermal conductivity of solid nitrogen and carbon dioxide

The density and thermal conductivity of solid nitrogen and carbon dioxide have been measured. The solids were condensed from the gas phase under cryopumping conditions over a wide range of deposition rates and temperatures. The density and thermal conductivity of solid nitrogen increased with increasing deposition rate and temperature but carbon dioxide showed different behaviour. At a deposition rate of 400 mg s^?1 m^?2 and a temperature of 108 K the density and thermal conductivity fell sharply, the density reaching a value which was only 20% of that of the bulk crystals.     

陶瓷膜过滤微米级颗粒悬浮液操作条件的影响

测定不同操作条件下陶瓷膜过滤微米级颗粒悬浮液的渗透能量数据,并与决定膜污染柚是的ｄｐ／ｄｍ的结合进行分析,确定了操作条件对微炫有颗粒悬浮液微滤过程的影响,获得了陶瓷膜微滤微米级颗粒悬浮液过程中操作条件方法。为促进陶瓷膜在涉及微米级颗粒悬浮液分离领域中的应用尊定基础。     

A gas phase analysis technique applied to in-situ studies of gas–solid interactions

An ultrahigh vacuum technique using mass spectrometry for in-situ investigations of gas–solid interactions is described in this paper. Examples of chemical reactions (oxidation, hydration) between solids and gas mixtures, dissociation of gases on solid surfaces, outgassing of solid materials and permeation of gases through membranes are discussed where the experimental arrangement is explained in detail. This Gas Phase Analysis (GPA) technique can be used at temperatures from room temperature to 1200 °C and at pressures up to 1 atm. Aspects related to sample preparation, isotopic gas mixture selection, data acquisition, calibration and interpretation of the experimental data are also addressed.     

Statistical mechanical description of supercritical fluid extraction and retrograde condensation

The phenomena of supercritical fluid extraction (SFE) and its reverse effect, which is known as retrograde condensation (RC), have found new and important applications in industrial separation of chemical compounds and recovery and processing of natural products and fossil fuels. Full-scale industrial utilization of SFE/RC processes requires knowledge about thermodynamic and transport characteristics of the asymmetric mixtures involved and the development of predictive modeling and correlation techniques for performance of the SFE/RC system under consideration. In this report, through the application of statistical mechanical techniques, the reasons for the lack of accuracy of existing predictive approaches are described and they are improved. It is demonstrated that these techniques also allow us to study the effect of mixed supercritical solvents on the solubility of heavy solutes (solids) at different compositions of the solvents, pressures, and temperatures. Fluid phase equilibrium algorithms based on the conformal solution van der Waals mixing rules and different equations of state are presented for the prediction of solubilities of heavy liquid in supercritical gases. It is shown that the Peng-Robinson equation of state based on conformal solution theory can predict solubilites of heavy liquid in supercritical gases more accurately than the van der Waals and Redlich-Kwong equations of state.     

Steam Solubilities for Combustion Turbine Steam Cooling

Steam cooling of combustion turbine parts provides significant advantages over air cooling. Steam potentially carries dissolved salts that can deposit on the cooled parts and cause corrosion. By maintaining the salt concentration below its solubility limit in the steam, deposition of salts may be avoided. A literature survey reveals that only sodium chloride and silica have adequate data for reasonable extrapolation to the steam cooling conditions. Estimates of steam solubility of sodium sulfate and sodium phosphate used liquid–vapor distribution coefficients for a solubility at saturation and sodium chloride as a model compound to extrapolate the solubility to other conditions. Copper oxide data were also insufficient to predict steam solubilities with confidence. The large potential errors in the sodium phosphate and sodium sulfate solubility estimates may add considerable cost to the water treatment system. Accurate experimental values for sodium sulfate and sodium phosphate solubilities in steam are needed.     

Equation of state of a solid with fractal structure

Expressions for the characteristic frequency and free energy and the generalized equation of state for a solid possessing a fixed fractal structure are obtained within the framework of the Debye model. The equation of state involves the Grüneisen parameter. Conditions under which the fractal structure of solids is significant are discussed.