An accurate empirical correlation for predicting natural gas compressibility factors

The compressibility factor of natural gas is an important parameter in many gas and petroleum engineering calculations. This study presents a new empirical model for quick calculation of natural gas compressibility factors. The model was derived from 5844 experimental data of compressibility factors for a range of pseudo reduced pressures from 0.01 to 15 and pseudo reduced temperatures from 1 to 3. The accuracy of the new empirical correlation has been compared with commonly used existing methods. The comparison indicates the superiority of the new empirical model over the other methods used to calculate compressibility factor of natural gas with average absolute relative deviation percent （AARD%） of 0.6535.

Study on compressibility of traffic flow

In order to describe the compressibility of traffic flows and determine the compression factors, the Mach number of gas dynamics is introduced, and the concept and the formula of the compression factor are obtained. According to the concept of the compression factor and its differential equation, a stop-wave model is built. The theoretical value and the observed one are obtained by the survey data in Changchun city. The relative error between the two values is 20. 3%. The accuracy is improved 39% compared with the result from the traditional stop-wave model. The results show that the traffic flow is compressible, and the methods of research on gas compressibility is also applicable to the traffic flow. The stop-wave model obtained by the compression factor can better describe the phenomenon of the stop wave at a signalized intersection when compared with the traditional stop-wave model.

Electron G-Factor Anomaly and the Charge Thickness

The electron g-factor relates the magnetic moment to the spin angular momentum. It was originally theoretically calculated to have a value of exactly 2. Experiments yielded a value of 2 plus a very small fraction, referred to as the g-factor anomaly. This anomaly has been calculated theoretically as a power series of the fine structure constant. This document shows that the anomaly is the result of the electron charge thickness. If the thickness were to be zero, g = 2 exactly, and there would be no anomaly. As the thickness increases, the anomaly increases. An equation relating the g-factor and the surface charge thickness is presented. The thickness is calculated to be 0.23% of the electron radius. The cause of the anomaly is very clear, but why is the charge thickness greater than zero? Using the model of the interior structure of the electron previously proposed by the author, it is shown that the non-zero thickness, and thus the g-factor anomaly, are due to the proposed positive charge at the electron center and compressibility of the electron material. The author’s previous publication proposes a theory for splitting the electron into three equal charges when subjected to a strong external magnetic field. That theory is revised in this document, and the result is an error reduced to 0.4% in the polar angle where the splits occur and a reduced magnetic field required to cause the splits.

A novel correlation approach for prediction of natural gas compressibility factor

Gas compressibility factor （z-Factor） is one of the most important parameters in upstream and downstream calculations of petroleum industries.The importance of z-Factor cannot be overemphasized in oil and gas engineering calculations.The experimental measurements,Equations of State （EoS） and empirical correlations are the most common sources of z-Factor calculations.There are more than twenty correlations available with two variables for calculating the z-Factor from fitting in an EoS or just through fitting techniques.However,these correlations are too complex,which require initial value and more complicated and longer computations or have magnitude error.The purpose of this study is to develop a new accurate correlation to rapidly estimate z-Factor.Result of this correlation is compared with large scale of database and experimental data also.Proposed correlation has 1.660 of Absolute Percent Relative Error （EABS） versus Standing and Katz chart and has also 3.221 of EABS versus experimental data.The output of this correlation can be directly assumed or be used as an initial value of other implicit correlations.This correlation is valid for gas coefficient of isothermal compressibility （cg） calculations also.

Rapidly Estimating Natural Gas Compressibility Factor

Natural gases containing sour components exhibit different gas compressibility factor （Z） behavior than do sweet gases. Therefore, a new accurate method should be developed to account for these differences. Several methods are available today for calculating the Z-factor from an equation of state. However, these equations are more complex than the foregoing correlations, involving a large number of parameters, which require more complicated and longer computations. The aim of this study is to develop a simplified calculation method for a rapid estimating Z-factor for sour natural gases containing as much as 90% total acid gas. In this article, two new correlations are first presented for calculating the pseudo- critical pressure and temperature of the gas mixture as a function of the gas specific gravity. Then, a simple correlation on the basis of the standard gas compressibility factor chart is introduced for a quick estimation of sweet gases＇ compressibility factor as a function of reduced pressure and temperature. Finally, a new corrective term related to the mole fractions of carbon dioxide and hydrogen sulfide is developed.

An efficient correlation for calculating compressibility factor of natural gases

Compressibility factor （z-factor） values of natural gases are necessary in most petroleum engineering calculations.Necessity arises when there are few available experimental data for the required composition,pressure and temperature conditions.One of the most common methods of calculating z-factor values is empirical correlation.Firstly,a new correlation based on the famous Standing-Katz （S-K） Chart is presented to predict z-factor values.The advantage of this correlation is that it is explicit in z and thus does not require an iterative solution as is required by other methods.Secondly,the comparison between new one and other correlations is carried out and the results indicate the superiority of the new correlation over the other correlations used to calculate z-factor.

Experimental determination and prediction of the compressibility factor of high CO_2 content natural gas with and without water vapor

In order to study the effect of different CO2 contents on gas compressibility factor（Z-factor）,the JEFRI-PVT apparatus has been used to measure the Z-factor of dry natural gas with CO2 content range from 10.74 to 70.42 mol%at the temperature range from 301.2 to 407.3 K and pressure range from 7 to 44 MPa.The results show that Z-factor decreases with increasing CO2 content in natural gas at constant temperature and increases with increasing temperature for natural gas with the same CO2 content.In addition,the Z-factor of water-saturated natural gas with high CO2 content has been measured.A comparison of the Z-factor between natural gas with and without saturated water vapor indicates that the former shows a higher Z-factor than the latter.Furthermore,Peng-Robinson,Hall-Yarborough,and Soave-Benedict-Webb- Rubin equations of state（EoS）are used for the calculation of Z-factor of high CO2 content natural gas with and without water vapor.The optimal binary interaction parameters（BIP）for PR EoS are presented.The measured Z-factor is compared with the calculated Z-factor based on three models,which shows that PR EoS combined with van der Waals mixing rule for gas without water and Huron-Vidal mixing rule for water-saturated gas,are in good agreement with the experimental data.

Orthokeratology with increased compression factor in adolescent myopia control:a 2-year prospective randomized clinical trial

AIM:To explore the long-term efficacy,safety,and optical mechanism of orthokeratology with increased compression factor in adolescent myopia control.METHODS:A prospective,double-masked,and randomized clinical trial was performed from May 2016 to June 2020.Subjects aged between 8 and 16y,with myopia(-5.00 to-1.00 D),low astigmatism(≥-1.50 D)and anisometropia(≤1.00 D),were stratified into low(-2.75 to-1.00 D)and moderate(-5.00 to-3.00 D)myopia groups.Then they were randomly assigned to wear either increased compression factor(ICF;1.75 D)orthokeratology or conventional compression factor(CCF;0.75 D)orthokeratology.The data were recorded including axial length(AL),spherical equivalent(SE),best corrected visual acuity(BCVA),near visual acuity(NVA),corneal staining(using Efron grading scales),corneal hysteresis(CH),corneal resistance factor(CRF),higher-order aberrations(HOAs,expressed as root mean square,RMS_(h)),and subfoveal choroidal thickness(SFCh T)in the 2-year followup period.Pearson's correlation coefficient was conducted to analyze the association between the changes in AL and RMS_(h),SFCh T.RESULTS:At the 2-year visit,there were no statistical differences in all the parameters between the ICF group and the CCF group in low myopia subjects(P>0.05).For the moderate myopia subjects,the ICF group had shorter AL elongation(0.23±0.08 vs 0.30±0.11 mm,P=0.015),higher RMS_(h)(1.94±0.50 vs 1.65±0.51μm,P=0.041),and higher SFCh T(279.04±35.72 vs 254.08±29.60μm,P=0.008)than those in CCF group.The change in AL was negatively correlated with RMS_(h)(r=-0.687,P<0.001)and SFCh T(r=-0.464,P=0.013).CONCLUSION:ICF orthokeratology can control the progression of moderate myopia more effectively,which might be related to greater RMS_(h) and SFCh T.

Sliding-Mode PID Control of UAV Based on Particle Swarm Parameter Tuning

Due to the coupled motion between the rotor unmanned aerial vehicle(UAV)and the manipulator,the underactuation characteristics of the system itself,and the influence of external uncertainties,the stability of the rotor UAV’s manipulator control system is difficult to control.Based on the dynamic model of the rotor UAV,the stability of the whole UAV manipulator control system is improved by using the piecewise cost function,the compression factor particle swarm optimization(PSO)algorithm and the sliding mode PID to establish the sliding mode PID control stability method based on the PSO.Compared with the sliding mode PID control method,this method solves the serious buffeting problem in the sliding mode control,reduces the influence of the external disturbance and realizes the attitude stabilization control of the UAV manipulator quickly and accurately,thus shortens the system adjustment time and improves the anti-interference ability.

Monte Carlo Simulations of Density Profiles for Hard-Sphere Chain Fluids Confined Between Surfaces

Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurational-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurational entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various equations of state of HSCFs by different authors.

OUT-OF-PLANE COMPRESSIVE PROPERTIES OF HEXAGONAL PAPER HONEYCOMBS

The compressive behaviour of paper honeycombs is studied by means of an experimental analysis. Experiment results show how geometry aspects of hexagonal paper honeycombs, e.g. the height of paper honeycomb, the thickness and length of honeycomb cell-wall, the drawing ratio of hexagonal honeycomb, affect the compressive properties of the paper honeycombs. It is in good agreement with the theory model. The constraint factor K of the critical buckling stress is mainly determined by the length of honeycomb cell-wail. It can be described as K=1.54 for B type paper honeycombs and K=3.32 for D type paper honeycombs. The plateau stress is the power exponent function of the thickness to length ratio of honeycomb cell-wall, and the experiment results show that the constant is 13.2 and the power exponent is 1.77. The research results can be used to characterize and improve efficiently the compressive properties of paper honeycombs.

Influencing factor of sinter body strength and its effects on iron ore sintering indexes

Sinter body strength, which reflects the strength of sinter, plays an important role in the improvement of sinter. In this study, the sinter body strengths of iron ores were measured using a microsintering method. The relationship between the chemical composition and sinter body strength was discussed. Moreover, sinter-pot tests were performed. The effects of sinter body strength on the sintering indexes were then elucidated, and the bottom limit of sinter body strength of blending ores was confirmed. In the results, the compressive strengths（CSs） of iron ores are observed to decrease with the increasing of the contents of loss on ignition（LOI）, SiO 2, and Al2O3; however, LOI of less than 3wt% does not substantially influence the CSs of fine ores. In the case of similar mineral composition, the porosity, in particular, the ratio between the number of large pores and the total number of pores, strongly influences the sinter body strength. With an increase of the blending-ore CSs used in sinter-pot tests, the yield, productivity, and tumbler strength increase, and the solid fuel consumption decreases. The CSs of the blending ores only slightly affect the sintering time. The CS bottom limit of the blending ores is 310 N. When the CSs of the blending ores increase by 10%, the yield, productivity, and tumbler index increase by 1.9%, 2.8%, and 2.0%, respectively, and the solid fuel consumption decreases by 1.9%.

Prediction of Volumetric Properties(p-v-T)of Natural Gas Mixtures Using Extended Tao-Mason Equation of State

A statistical-mechanical-based equation of state(EOS)for pure substances,the Tao-Mason equation of state,is successfully extended to prediction of the(p-v-T)properties of fourteen natural gas mixtures at temperatures from 225 K to 483 K and pressures up to 60.5 MPa.This work shows that the Tao-Mason equation of state for multicomponent natural gas is predictable with minimal input information,namely critical temperature,critical pressure,and the Pitzer acentric factor.The calculated results agree well with the experimental data.From a total of 963 data of density and 330 data of compressibility factor for natural gases examined in this work,the average absolute deviations(AAD)are 1.704%and 1.344%,respectively.The present EOS is further assessed through the comparisons with Peng-Robinson(PR)equation of state.For the all of mixtures Tao-Mason(TM)EOS outperforms the PR EOS.

Determination of Critical Parameters of Carbon Dioxide+Butyraldehyde System with Different Compositions

Supercritical carbon dioxide（SC-CO2 ） is considered in green chemistry as a substitute for conventional solvents in chemical reactions due to its environmentally benign character. Recently we have reported the homogeneous hydroformylation of propylene in supercritical carbon dioxide（ SC-CO2 ） , which is an example of this kind of application of carbon dioxide. The determination for the critical parameters of carbon dioxide ＋ butyraldehyde mixtures is necessary for this reaction design which is the focus of the present paper. The critical parameters of the binary systems were determined via the static visual method at a constant volume with the molar fraction of butyraldehyde ranging from 1.0% to 2. 2% and the pressure ranging from 5 to 10 MPa. The experimental results show that the critical pressure and temperature increased with increasing the molar fraction of butyraldehyde. The bubble（dew） temperatures and the bubble （dew） pressures for the binary systems were also determined experimentally. The p-T Figures at different compositions of the binary systems were described. In addition, the critical compressibility factors Zc of the binary systems at different concentrations of n-butyraldehyde were calculated. It was found that the critical compressibility factor values of the binary systems decreased with increasing the molar fraction of n-butyraldehyde in the experimental range.

A Thermodynamic Model for square-well Chain Fluid:Theory and Monte Carlo Simulation

A thermodynamic model for the freely jointed square-well chain fluids was developed based on the thermodynamic perturbation theory of Barker-Henderson, Zhang and Wertheim. In this derivation Zhang’s expressions for square-well monomers improved from Barker-Henderson compressibility approximation were adopted as the reference fluid, and Wertheim’s polymerization method was used to obtain the free energy term due to the bond connectivity. An analytic expression for the Helmholtz free energy of the square-well chain fluids was obtained. The expression without adjustable parameters leads to the thermodynamic consistent predictions of the compressibility factors, residual internal energy and constant-volume heat capacity for dimer, 4-mer, 8-mer and 16-mer square-well fluids. The results are in good agreement with the Monte Carlo simulation. To obtain the MC data of residual internal energy and the constant-volume heat capacity needed, NVT MC simulations were performed for these square-well chain fluids.

Research on Calculation Method of Aerodynamic Parameters of Supersonic Probe Based on Gas Compressibility Factor

The supersonic multi-hole probe is an essential test tool for wind tunnel experiments, which is necessary to develop the basic research of improving the measurement accuracy and expanding the application of the probes.