The pressure compensation technology of deep-sea sampling based on the real gas state equation

Compressed gas is usually used for the pressure compensation of the deep-sea pressure-maintaining sampler.The pressure and volume of the recovered fluid sample are highly related to the precharged gas. To better understand the behavior of the gas under high pressure, we present a new real gas state equation based on the compression factor Z which was derived from experimental data. Then theoretical calculation method of the pressure and volume of the sample was introduced based on this empirical gas state equation. Finally, the proposed calculation method was well verified by the high-pressure vessel experiment of the sampler under 115 MPa.

A New Alpha-function for the Peng-Robinson Equation of State： Application to Natural Gas

Cubic equations of state(EOSs) are simple and easy at calculation. One way of improving the accuracy of a cubic EOS is through the modification of temperature-dependent energy parameter by using alpha-function.The industrial applications of natural gas are very wide and as a result, prediction of thermodynamic properties and phase behavior of natural gas is an important part of design for such processes. In this work we develop a newα-function for the Peng-Robinson(PR) EOS with the parameters optimized especially for natural gas components.The parameters are generalized as a linear function of acentric factor. The results are compared to the predictions from original PR EOS and other α-functions in literature. It is shown that the new α-function presents a good accuracy with the average deviation of 1.42% for natural gas components.

EQUATION OF STATE BASED HYDRATE MODEL FOR NATURAL GAS SYSTEMS CONTAINING BRINE AND POLAR INHIBITOR

A new thermodynamic model for gas hydrates was established by combining the modified Patel-Teja equation of state proposed for aqueous electrolyte systems and the simplified Holder -John multi -shell hydrate model. The new hydrate model is capable of predicting the hydrate formation/dissociation conditions of natural gas systems containing pure water/formation water (brine) and polar inhibitor without using activity coefficient model. Extensive test results indicate very encouraging results.

PREDICTION OF THE PHASE BEHAVIOR OF GAS CONDENSATES USING PATEL-TEJA EQUATION OF STATE AND GAMMA DISTRIBUTION FUNCTION

The three-parameter Petal-Teja equation of state coupled with a characterization proceduref0r C7+-fraction based on gamma distribution function was employed to predict the phase behaviorof eight gas condensates.The lumping of the subdivided single carbon number（SCN）hydrocarbons inthe plus-fraction and the choice of empirical correlations for calculating the critical properties andacentric factor of SCN hydrocarbons were discussed.

A Modified Peng-Robinson Equation State for Prediction of Gas Adsorption Isotherm

This research proposes a modified two-dimensional Peng-Robinson equation model to predict adsorption isotherm in adsorbate-adsorbent systems. The parameters of the proposed model are calculated by using the optimization of experimental data for the different single gas adsorption systems at various temperatures. The experimental adsorption equilibrium data of adsorbate-adsorbent systems was compared with the calculated results in our proposed model and the two-dimensional Hill-deBoer equation model. The proposed model as indicated in the results shows a better prediction of the experimental results compared with two others.

Coupled thermo-hydro-mechanical simulation of CO2 enhanced gas recovery with an extended equation of state module for TOUGH2MP-FLAC3D

As one of the most important ways to reduce the greenhouse gas emission,carbon dioxide（CO2）enhanced gas recovery（CO2-EGR） is attractive since the gas recovery can be enhanced simultaneously with CO2sequestration.Based on the existing equation of state（EOS） module of TOUGH2 MP,extEOS7C is developed to calculate the phase partition of H2O-CO2-CH4-NaCl mixtures accurately with consideration of dissolved NaCI and brine properties at high pressure and temperature conditions.Verifications show that it can be applied up to the pressure of 100 MPa and temperature of 150℃.The module was implemented in the linked simulator TOUGH2MP-FLAC3 D for the coupled hydro-mechanical simulations.A simplified three-dimensional（3D）1/4 model（2.2 km×1 km×1 km） which consists of the whole reservoir,caprock and baserock was generated based on the geological conditions of a gas field in the North German Basin.The simulation results show that,under an injection rate of 200,000 t/yr and production rate of 200,000 sm3/d,CO2breakthrough occurred in the case with the initial reservoir pressure of 5 MPa but did not occur in the case of 42 MPa.Under low pressure conditions,the pressure driven horizontal transport is the dominant process;while under high pressure conditions,the density driven vertical flow is dominant.Under the considered conditions,the CO2-EGR caused only small pressure changes.The largest pore pressure increase（2 MPa） and uplift（7 mm） occurred at the caprock bottom induced by only CO2injection.The caprock had still the primary stress state and its integrity was not affected.The formation water salinity and temperature variations of ±20℃ had small influences on the CO2-EGR process.In order to slow down the breakthrough,it is suggested that CO2-EGR should be carried out before the reservoir pressure drops below the critical pressure of CO2.

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.

New insight into prediction of phase behavior of natural gas hydrate by different cubic equations of state coupled with various mixing rules

Progress in hydrate thermodynamic study necessitates robust and fast models to be incorporated in reservoir simulation softwares. However, numerous models presented in the literature makes selection of the best,proper predictive model a cumbersome task. It is of industrial interest to make use of cubic equations of state(EOS) for modeling hydrate equilibria. In this regard, this study focuses on evaluation of three common EOSs including Peng–Robinson, Soave–Redlich–Kwong and Valderrama–Patel–Teja coupled with van der Waals and Platteeuw theory to predict hydrate P–T equilibrium of a real natural gas sample. Each EOS was accompanied with three mixing rules, including van der Waals(vd W),Avlonitis non-density dependent(ANDD) and general nonquadratic(GNQ). The prediction of cubic EOSs was in sufficient agreement with experimental data and with overall AARD% of less than unity. In addition, PR plus ANDD proved to be the most accurate model in this study for prediction of hydrate equilibria with AARD% of 0.166.It was observed that the accuracy of cubic EOSs studied in this paper depends on mixing rule coupled with them,especially at high-pressure conditions. Lastly, the present study does not include any adjustable parameter to be correlated with hydrate phase equilibrium data.

A Theoretical Study on Energy of a Gaseous System Vis-a-Vis Mass and Temperature

To study various properties of a gas has been a subject of rational curiosity in pneumatic sciences. A gaseous system, in general, is studied by using four measurable parameters namely, the pressure, volume, number of moles and temperature. In the present work, an attempt is made to study the variation of energy of an ideal gas with the two measurable parameters, the mass and temperature of the gas. Using the well known ideal gas equation, PV = nRT where symbols have their usual meanings and some simple mathematical operations widely used in physics, chemistry and mathematics in a transparent manner, an equation of state relating the three variables, the energy, mass and temperature of an ideal gas is obtained. It is found that energy of an ideal gas is equal to the product of mass and temperature of the gas. This gives a direct relationship between the energy, mass and temperature of the gas. Out of the three variables, the energy, mass and temperature of an ideal gas, if one of the parameters is held constant, the other two variables can be measured. At a constant temperature, when the power or energy is stabilized, the increase in the mass of the gas may affect the new works and an engine can therefore be prevented from overheating.

GC-MCSPT-A MODIFIED HARD-SPHERE THREE-PARAMETER EQUATION OF STATE WITH GROUP MODEL FOR VLE PREDICTION

The mixing rule for a new group-contribution equation of state was proposed by combining the excess Gibbs energy model with the modified Hard-Sphere Three-Parameter Equation of State designated as the MCSPT equation. Low-and high-pressure vapor-liquid equilibria of 28 binary and 9 ternary systems containing strongly polar substances were predicted by using the interaction parameters of the original and modified UNIFAC model. Predicted results have shown that the proposed GO-MCSPT equation has an extensive applicability with satisfactory accuracy.

A modified equation of state for Xe at high pressures by molecular dynamics simulation

The exact equation of state （EOS） for the fission gas Xe is necessary for the accurate prediction of the fission gas behavior in uranium dioxide nuclear fuel, However, the comparison with the experimental data indicates that the applicable pressure ranges of existing EOS for Xe published in the literature cannot cover the overpressure of the rim fission gas bubble at the typical UO2 fuel pellet rim structure. Based on the interatomic potential of Xe, the pressure-volume-temperature data are calculated by the molecular dynamics （MD） simulation. The results indicate that the data of MD simulation with Ross and McMahan＇s potential [M. Ross and A. K. McMahan 1980 Phys. Rev. B 21 1658] are in good agreement with the experimental data. A preferable EOS for Xe is proposed based on the MD simulation. The comparison with the MD simulation data shows that the proposed EOS can be applied at pressures up to 550 MPa and 3 GPa and temperatures 900 K and 1373 K respectively. The applicable pressure range of this EOS is wider than those of the other existing EOS for Xe published in the literature.

Influence of Different Equations of State on Simulation Results of Supercritical CO_(2) Centrifugal Compressor

Supercritical CO_(2)(SCO_(2))Brayton cycle has received more and more attention in the field of power generation due to its high cycle efficiency and compact structure.SCO_(2) compressor is the core component of the cycle,and the improvement of its performance is the key to improving the efficiency of the entire cycle.However,the operation of the SCO_(2) compressor near the critical point has brought many design and operation problems.Based on the Reynolds Averaged Navier-Stokes(RANS)model,the performance and flow field of SCO_(2) centrifugal compressors based on different CO_(2) working fluid models are numerically investigated in this paper.The stability and convergence of the compressor steady-state simulation are also discussed.The results show that the fluid based on the Span-Wanger(SW)equation can obtain a more ideal compressor performance curve and capture a more accurate flow field structure,while the CO_(2) ideal gas is not suitable for the calculation of SCO_(2) centrifugal compressors.But its flow field can be used as the initial flow field for numerical calculation of centrifugal compressor based on CO_(2) real gas.

Study on the mechanism of interaction for coal and methane gas

Although two moulds for methane gas in coal with the free state and adsorption state have been popularly considered, the derivation between the real methane gas state equation in coal and the perfect gas state equation has been fuzzily considered and the mechanism of interaction for coal aromatics and methane gas molecules has not been understood. Then these problems have been discussed in this paper applied the principle of statistical thermo mechanics and quantum chemistry as well as based on the numerical calculating of experiential data in quantum chemistry. Therefore, it is revealed by research results that the experience state equation for real methane gas in coal, which is put forward in this paper, is closer to actual situation and the interaction process for methane gas adsorption on the surface of coal aromatics can be formulated by Morse potential function. Furthermore it is most stable through this research that the structural mould for methane gas molecule adsorption on the surface of coal nuclear with one gas molecule on top of another aromatics in regular triangle cone has been understood, and it is a physical adsorption for methane gas adsorption with single layer molecule on the surface of coal nuclear.

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.

MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID

This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn（n = 2,3）. One of the important features is that the metric spaces H（1）, H（2）, and H（4） we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ（4） H（i） （i = 1, 2, 4） is found, and the existence of maximal （universal） attractors in Hδ（i） （i = 1.2.4） is established.

A Numerical Simulation of Air Flow in the Human Respiratory System Based on Lung Model

The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airways of human lungs is considered. The basis of a lumped parameter model or a transport equation is modeled during the inspiration process, when oxygen enters into the human lung channel. The quantitative measurements of oxygen are detached and the model equation is solved numerically by explicit finite difference schemes. Numerical simulations were made for natural breathing conditions or normal breathing conditions. The respiratory flow results for the resting conditions are found strongly dependent on the AD effect with some contribution of the unsteadiness effect. The contour of the flow rate region is labeled and AD effects are compared with the variation of small intervals of time for a constant velocity when breathing is interrupted for a negligible moment.

Gas condensate reservoirs: Characterization and calculation of dew-point pressure

A large data bank of more than 700 gas-condensate samples collected from literature and experiments was established.On this basis,empirical correlations and equations of state commonly used to calculate dew-point pressure(DPP)were evaluated.A new model for estimating DPP was proposed.All the empirical correlations and the Peng-Robinson state equation were compared,and sensitivity of parameters was analyzed.The current standards used to identify gas condensate were evaluated and found to be not accurate enough.The Peng-Robinson state equation has no unique solution and is affected by multiple factors such as the characterization of C7+components and the splitting scheme.The Nemeth-Kennedy correlation has the highest accuracy when applied to the data bank established in this study,followed by Elsharkawy correlation and Godwin correlation.While Shokir correlation cannot be used for samples without C7+components,it is therefore the lowest in accuracy.The newly proposed model has an average absolute error,root mean square error and coefficient of determination of 7.5%,588,and 0.87,respectively,and is better than the above four correlations statistically.The proposed model proved to be more accurate and valid when compared to experimental results and simulation with the Peng-Robinson state equation.

On the Definition of State Variables for an Internal State Variable Constitutive Model Describing Metal Deformation

The quest for an internal state variable constitutive model describing metal deformation is reviewed. First, analogy is drawn between a deformation model and the Ideal Gas Law. The use of strain as a variable in deformation models is discussed, and whether strain serves as an internal state variable is considered. A simple experiment that demonstrated path dependence in copper is described. The importance of defining appropriate internal state variables for a constitutive law relates to the ability to accurately model temperature and strain-rate dependencies in deformation simulations.

The Performance of EOS Models in the Prediction of Vapor-Liquid Equilibria in Asymmetric Natural Gas Mixtures

The aim of this work is to apply cubic equations of state(EOS)to vapor-liquid equilibriacalculations of gas-heavy hydrocarbon systems,which are asymmetric in molecular size and areusually found in natural gases.Investigation has been done to test the validity of the original PSRKand the cubic simplified perturbed hard-chain(CSPhC)models for global phase diagrams.Thecalculation results show that both equations overpredict vapor pressure in the near critical region.In the prediction of the solubilities of high molecular weight(MW)hydrocarbons in the naturalgas,the PSRK model gives good agreement for the dew point pressure-vapor composition diagrams.Adjustment of the pure component parameters of the CSPHC EOS for heavy components to fit thevapor-liquid equilibrium(VLE)data has been proved to give significant promoting in predictionaccuracy.However,further improvement of a van der Waals EOS,such as SRK,PT and DG modelsfor the asymmetric systems by adjusting the three pure component properties,T_c, p_c and ?

Modeling and Simulation of Real Gas Flow in a Pipeline

In this paper, a mathematical model that describes the flow of gas in a pipe is formulated. The model is simplified by making some assumptions. It is considered that the natural gas flowing in a long horizontal pipe, no heat source occurs inside the volume, transfer of heat due to heat conduction is dominated by heat exchange with the surrounding. The flow equations are coupled with equation of state. Different types of equations of state, ranging from the simple Ideal gas law to the more complex equation of state Benedict Webb Rubin Starling (BWRS), are considered. The flow equations are solved numerically using the Godunov scheme with Roe solver. Some numerical results are also presented.