An insight into the role of the association equations of states in gas hydrate modeling:a review

Encouraged by the wide spectrum of novel applications of gas hydrates,e.g.,energy recovery,gas separation,gas storage,gas transportation,water desalination,and hydrogen hydrate as a green energy resource,as well as CO2 capturing,many scientists have focused their attention on investigating this important phenomenon.Of course,from an engineering viewpoint,the mathematical modeling of gas hydrates is of paramount importance,as anticipation of gas hydrate stability conditions is effective in the design and control of industrial processes.Overall,the thermodynamic modeling of gas hydrate can be tackled as an equilibration of three phases,i.e.,liquid,gas,and solid hydrate.The inseparable component in all hydrate systems,water,is highly polar and non-ideal,necessitating the use of more advanced equation of states(EoSs) that take into account more intermolecular forces for thermodynamic modeling of these systems.Motivated by the ever-increasing number of publications on this topic,this study aims to review the application of associating EoSs for the thermodynamic modeling of gas hydrates.Three most important hydrate-based models available in the literature including the van der Waals-Platteeuw(vdW-P) model,Chen-Guo model,and Klauda-Sandler model coupled with and SAFT EoSs were investigated and compared with cubic EoSs.It was concluded that the CPA and SAFT EoSs gave very accurate results for hydrate systems as they take into account the association interactions,which are very crucial in gas hydrate systems in which water,methanol,glycols,and other types of associating compounds are available.Moreover,it was concluded that the CPA EoS is easier to use than the SAFT-type EoSs and our suggestion for the gas hydrate systems is the CPA EoS.

A four parameter cubic equation of state with temperature dependent covolume parameter

A four-parameter, Ghoderao–Dalvi–Narayan 2 cubic equation of state(GDN2 CEOS), is presented which incorporates the following: 1. The experimental value of the critical compressibility factor has been used as a fixed input parameter for calculations;2. All the parameters(a, b, c, d) of CEOS are temperature dependent functions in the subcritical region and are temperature independent functions in the supercritical region and;3. A new α function is introduced with two compound specific parameters which are estimated by matching saturated vapor pressure at two fixed temperature points Tr= 0.5, 0.7. Our formalism enables us to cast three of the four parameters of the CEOS as a function of the remaining parameter. The proposed CEOS is used to predict properties of 334 pure compounds, including saturated vapor pressure and liquid density, compressed liquid density, heat capacities at the constant pressure and volume, enthalpy of vaporization, sound velocity. To calculate thermodynamic properties of a pure compound, the present CEOS require the critical temperature, the critical pressure, the Pitzer’s acentric factor, the critical compressibility factor, and two parameters of the alpha function. The saturated liquid density predictions for pure fluids are very accurate when compared with GDN1(Ghoderao–Dalvi–Narayan 1),MPR(Modified Peng–Robinson), and PT(Patel–Teja) equations of state. Unlike MPR EOS, the proposed temperature dependent covolume parameter b in the present work satisfies all the constraints mentioned in the literature to avoid thermodynamic inconsistencies at the extreme temperature and pressure. Using van der Waals one-fluid mixing rule, the present CEOS is further used to predict bubble pressure and the vapor mole fraction of binary mixtures.

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.

CUBIC CHAIN-OF-ROTATORS EQUATION OF STATE——LOCAL COMPOSITION VERSION

For further improving the representation of mixture VLE data,the local composition version of CCORequation of state has been developed and tested on 42 sets low-pressure and high-pressure as well as polarand nonpolar VLE data.The data reduction results were compared with conventional quadratic mixing ruleand activity coefficient method.The comparison with quadratic mixing rule showed that the local composition version significantly im-proved the data fitting of polar systems,especially for those highly nonideal mixtures where quadratic mixingrule failed to fit satisfactorily.The comparison with the well-known activity coefficient method——Hayden-O’Connell-Wilson model,indicated that this new version gave,in general,better fit to those low-pressure strongly polar systems,which traditionally has to be treated by activity coefficient approach.

EQUATIONS OF STATE FOR HARD-SPHERE CHAIN FLUIDS AND SQUARE-WELL CHAIN FLUIDS

Based on the statistical theory for chemical association,equations of state for hard-spherechain fluids(HSCFs)and square-well chain fluids(SWCFs)can be derived through the n-particlecavity correlation function(CCF)of the corresponding reference system,where n is the chain lengthor the number of segments of a chain molecule.The reference system is a fluid composed of only cor-responding monomers.In this work,the n-particle CCF is approximated by a product of effectivetwo-particle CCFs which accounts for correlations in nearest-neighbour and next-to-nearest-neighboursegment pairs.The CCFs for SWCFs may be expressed by a product of the corresponding functionfor HSCFs and a perturbation term originated from the square-well attractive potential.All these ef-fective two-particle CCFs and perturbation terms are density dependent.The dependence is determinedmainly by using computer-simulation results.The obtained equations can excellently describecompressibility factors and second Virial coefficients for

A New General Equation of State

A new general equation of state is presented, which can be used to express not only common cubic equations of state, but also quartic equations of state and so on. Main advantage of the new equation over the previous general equations is that it is in simple form, and is easy to manipulate mathematically.

CPA方程计算醇、水的比热容性质

针对立方型附加缔合项(CPA)状态方程(EoS)对比热容的计算精度不高的问题,采用11种包含不同性质的参数计算方法研究了CPA方程对极性缔合流体甲醇、乙醇、水比热容的计算精度。计算结果表明:不考虑比热容时,CPA方程的参数计算必须考虑蒸汽压性质,且蒸汽压计算精度越高,方程对液相比热容的预测精度越高;在参数计算中加入比热容后,CPA方程无法同时准确描述所有比热容性质,其中对液相比定压热容的计算精度最高;在参数计算过程中比热容性质只考虑液相比定压热容时,方程对蒸汽压、各相密度及液相比定压热容的平均绝对相对偏差都在3%及以内。

基于立方型气体状态方程的激波风洞准一维流动数值研究

采用基于立方型气体状态方程的准一维流动数值模拟方法研究了反射式高焓激波风洞的真实气体流动,重点关注了高压真实气体效应对风洞全场流动时空结构和驻室区气流参数的影响,并以理论分析揭示了高压真实气体效应对激波管内流动的作用机理。研究表明:对于以冷高压气体驱动的激波风洞,使用考虑分子体积和分子间作用力的真实气体状态方程能够更准确地描述气体的状态和风洞内的流动状况。高压真实气体效应主要在冷驱动气体中发生作用,其作用效果主要是使当地声速增大,从而使得入射稀疏波和反射稀疏波的传播速度加快;另一方面,高压气体效应在高温气体效应较显著的被驱动气体中作用微弱,且对激波管产生激波的强度和激波后的流动状态影响甚微。稀疏波的加快传播改变了激波管波系的相干时空关系。提前抵达的稀疏波可在一定情况下侵蚀激波风洞的有效试验时间。对于所测试的激波风洞构型,在150 MPa氢气驱动110 kPa氮气的工况下,高压效应导致的有效试验时间缩短约38%。适当加长驱动段长度和采用高温气体驱动均可有效减弱高压真实气体效应的影响。

使用立方型状态方程求氢氮混合气在不同温度下的配制压力

利用立方型状态方程(P-R方程)、Prausnitz等建议的混合规则,计算出配制同一比例混合气在不同充装温度下,所需要各组分充装压力。

Enhancing asphaltene precipitation modeling by cubic-PR solid model using thermodynamic correlations and averaging techniques

Cubic equation-of-state solid models are one of the most widely used models to predict asphaltene precipitation behavior.Thermodynamic parameters are needed to model precipitation under different pressures and temperatures and are usually obtained through tuning with multi asphaltene onset experiments.For the purpose of enhancing the cubic Peng–Robinson solid model and reducing its dependency on asphaltene experiments,this paper tests the use of aromatics and waxes correlations to obtain these thermodynamic parameters.In addition,weighted averages between both correlations are introduced.The averaging is based on reported saturates,aromatics,resins,asphaltene(SARA)fractions,and wax content.All the methods are tested on four oil samples,with previously published data,covering precipitation and onset experiments.The proposed wax-asphaltene average showed the best match with experimental data,followed by a SARA-weighted average.This new addition enhances the model predictability and agrees with the general molecular structure of asphaltene molecules.

Extension of Compressibility-Route Cubic Equations of State and the Radial Distribution Functions at Contact to Multi-Component Hard-Sphere Mixtures

The equation of state(EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory(PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid.The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact(RDFC) of mixtures.The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.

Measurement and Correlation of Solid Drugs Solubility in Supercritical Systems

A dynamic experimental set-up was utilized to measure ibuprofen solubility in supercritical CO2 at the pressure range of 8-13 MPa and the temperatures of 308, 313 and 318 K. Mole fraction values varied from 0.015＆#215;10^-3 to 3.261＆#215;10^-3 and correlated by using seven different semi empirical equations of state （Bartle, Modi-fied Bartle, Mendez-Teja, Modified Mendez-Teja, Kumar-Johnson, Sung-shim and Gordillo） as well as seven cubic equations of state （van der Waals, Redlich-Kwong, Soave-Redlich-Kwong, Peng-Robinson, Stryjek-Vera, Patel-Teja-Valderana and Pazuki）. Single and twin-parametric van der Walls mixing rules （vdW1, vdW2） were ap-plied in order to estimate the supercritical solution properties. The physicochemical properties were also obtained using Joback, Lydersen and Ambrose methods. Absolute average relatives deviation （AARD） were calculated and compared for all the correlating systems. Results showed that among the cubic equations of state （EOSs） the Pazuki equation （AARD=19.85% using vdW1 and AARD=8.79% using vdW2） and SRK equation （AARD=19.20%using vdW1 and AARD=10.03%using vdW2） predicted the ibuprofen solubility in supercritical CO2 with the least error in comparison to the others. Among the semi-empirical EOSs the most desirable deviation （AARD〈10%） was obtained by using Modified Bartle and Modified Mendez-Teja equations in all the studied temperatures.

Sensitivity Analysis of Computations of the Vapor-Liquid Equilibria of Methane + Methanol or Glycols at Gas Hydrate Formation Conditions

The Soave-Redlich-Kwong (SRK-EOS) and Peng-Robinson (PR-EOS) equations of state are used often to describe the behavior of pure substances and mixtures despite difficulties in handling substances, like water, with high polarity and hydrogen bonding. They were employed in studying the binary vapor-liquid equilibria (VLE) of methane + methanol, monoethylene glycol (MEG), and triethylene glycol (TEG). These liquids are used to inhibit the formation of gas hydrates. The investigation focused on the conditions at which methane-water clathrates can form 283.89?K to 323.56?K and 5.01?MPa to 18.48?MPa. The pressure of methane in methanol is overestimated by a factor of two by either the SRK-EOS or the PR-EOS. In the methane + MEG system, the predicted pressures for both equations of state are generally less than experimental pressure except for the highest concentration of methane in MEG calculated by the SRK-EOS. In the methane + TEG system, the predictions of both models are close and trend similarly. Because of the comparative lack of extensive experimental methane + TEG data, the similarity of the methane + TEG computed results can be used as a basis for further study of this system experimentally.

Modeling and Numerical Simulation of Ammonia Synthesis Reactors Using Compositional Approach

Ammonia synthesis reactors operate in conditions of high pressure and high temperature. Consequently, the flow inside these reactors always presents interaction between components in the feed mixture. A modeling accounts these interactions with pressure, temperature and the molar fraction is essential to converter simulation more realistic. The compositional approach based on cubic equations of state provides the influences of the component of a gas mixture using mixing rules and binary interaction parameters. This multicomponent description makes the model more robust and reliable for properties mixture prediction. In this work, two models of ammonia synthesis reactors were simulated: adiabatic and autothermal. The fitted expression of Singh and Saraf was used. The adiabatic reactor model presented a maximum relative error of 1.6% in temperature and 11.4% in conversion while the autothermal reactor model presents a maximum error of 2.7% in temperature, when compared to plant data. Furthermore, a sensitivity analysis in input variables of both converter models was performed to predict operational limits and performance of the Models for Ammonia Reactor Simulation (MARS).

C_(6)~C_(10)烷醇的SAFT-VR Mie状态方程参数回归及其热物性研究

统计缔合流体理论(SAFT)状态方程对长链烷醇的热物性研究具有重要意义,而状态方程参数的获取是流体热物性研究的基础。基于SAFT-VRMie状态方程,采用Levenberg-Marquardt算法并结合相平衡、过冷液相密度和声速性质的参数回归策略,获取C_(6)~C_(10)烷醇的状态方程模型参数。进一步评估SAFT-VRMie状态方程对C_(6)~C_(10)烷醇在宽温度和压力范围内的相平衡和热力学偏导特性的预测性能,并与PC-SAFT状态方程进行比较。结果表明,SAFT-VRMie对五种烷醇整体具有更优的饱和蒸气压、饱和液相密度、蒸发焓、过冷液相密度、比定压热容和声速预测性能,平均预测偏差分别为0.74%、0.82%、3.02%、0.54%、2.88%和2.31%。同时,SAFTVR Mie具有可靠的外推预测能力,其对高压声速的预测结果与实验数据具有较好的一致性。此外,SAFT-VR Mie对压力-密度导数的不合理描述是造成声速预测偏差的主要原因。改进分子间单体和缔合相互作用能够有效提高比热容的预测精度,为长链烷醇缔合流体的热物性预测提供更好的理论关联模型。

液体火箭发动机高压混合燃气涡轮绝热功计算方法

在高压补燃循环液体火箭发动机的设计中,涡轮绝热功是影响发动机推力的重要设计参数,其计算的准确性直接影响涡轮设计的有效性。高压下,真实气体效应突出,对绝热功的计算有较大影响,必须考虑其作用。对比分析了Soave-Redlich-Kwong(SRK)、Peng-Robinson(PR)和Redlich-Kwong-Peng-Robinson(RK-PR)3种立方型状态方程描述氧气、甲烷和氢气的热力学性质的准确性。结果表明SRK方程的准确性较高,与NIST数据最大误差不超过2%。高压涡轮燃气为多元混合物,其绝热功的计算应考虑混合规则。假设涡轮等熵膨胀,分别推导了理想气体假设和考虑混合规则下的SRK方程的涡轮绝热功的计算公式,发现理想气体绝热功的计算与真实气体偏差近10%。提出了一种可以在工程上计算各型号发动机高压涡轮绝热功的算法,即利用进出口平均压缩因子计算高压涡轮近似绝热功,该方法与理论方法的最大误差不超过3%。

Phase Equilibrium Calculation of Mixtures: Use of the SAFT-BACK Equation of State for Binary Systems under Elevated Pressure

The statistical associating fluid theory (SAFT) Boublík Alder Chen Kreglewshi(BACK) equation of state is employed to correlate vapor liquid equilibria of 16 binary mixtures composed of supercritical fluids with other fluids at elevated pressures. The van der Waals mixing rules are used and the binary parameters are adjusted to experimental data. The SAFT BACK equation of state provides a better correlation of vapor liquid equilibrium than the original BACK equation. Consequently, the binary parameters computed from the data sets can be used to accurately predict the saturated densities of the vapor and liquid phases.

An Analytic Equation of State Based on SAFT-CP for Binary Non-Polar Alkane Mixtures Across the Critical Point

The description using an analytic equation of state of thermodynamic properties near the critical points of fluids and their mixtures remains a challenging problem in the area of chemical engineering. Based on the statistical associating fluid theory across the critical point (SAFT-CP), an analytic equation of state is established in this work for non-polar mixtures. With two binary parameters, this equation of state can be used to calculate not only vapor-liquid equilibria but also critical properties of binary non-polar alkane mixtures with acceptable deviations.

状态方程研究进展

本文较为详细地介绍了自Van der Waals状态方程以来所发展的若干典型的状态方程,并对各类型的状态方程进行了评价。但到目前为止还没有一种状态方程能对任何物质在很大范围内都是通用的。特别对量子流体及某些强极性物质,任何状态方程都还有困难。当前的办法仍是将若干类状态方程同时并用,在不同场合选择最合适的方程使用。因此本文对于状态方程的详细的综述可以为工程设计及从事这方面研究的人员提供有价值的参考。

计算原油体积系数的状态方程法

在组分分析的基础上,采用立方型状态方程建立了计算原油体积系数的新方法。在不同压力下,对5种原油样品进行了计算。与实验值的对比结果表明,其平均相对误差为0.911%,明显低于石油工程中常用的Standing和Vazquez-Beggs经验公式,表明该方法的计算精度较高。