A novel parameter extraction method with rational functions is presented for the 2-πequivalent circuit model of RF CMOS spiral inductors. The final S-parameters simulated by the circuit model closely match experiment...A novel parameter extraction method with rational functions is presented for the 2-πequivalent circuit model of RF CMOS spiral inductors. The final S-parameters simulated by the circuit model closely match experimental data. The extraction strategy is straightforward and can be easily implemented as a CAD tool to model spiral inductors. The resulting circuit models will be very useful for RF circuit designers.展开更多
A hybrid Lagrangian - Eulerian （HLE） method is developed for sea ice dynamics, which combines the high computational efficiency of finite difference method （FDM） with the high numerical accuracy of smoothed partic...A hybrid Lagrangian - Eulerian （HLE） method is developed for sea ice dynamics, which combines the high computational efficiency of finite difference method （FDM） with the high numerical accuracy of smoothed particle hydrodynamics （SPH）. In this HLE model, the sea ice cover is represented by a group of Lagrangian ice particles with their own thicknesses and concentrations. These ice variables are interpolated to the Eularian gird nodes using the Gaussian interpolation function. The FDM is used to determine the ice velocities at Eulerian grid nodes, and the velocities of Lagrangian ice particles are interpolated from these grid velocities with the Gaussian function also. The thicknesses and concentrations of ice particles are determined based on their new locations. With the HLE numerical model, the ice ridging process in a rectangular basin is simulated, and the simulated results are validated with the analytical solution. This method is also applied to the simulation of sea ice dynamics in a vortex wind field. At last, this HLE model is applied to the Bohai Sea, and the simulated concentration, thickness and velocity match the satellite images and the field observed data well.展开更多
盾构施工过程中土体大部分区域处于小应变状态,与常用的本构模型的土体性质有所不同。因此,为研究济南济泺路穿黄隧道区域内典型粉质黏土的的静动力行为特性及工程适用性,通过室内基础土工试验、侧限固结试验、标准三轴固结试验以及动...盾构施工过程中土体大部分区域处于小应变状态,与常用的本构模型的土体性质有所不同。因此,为研究济南济泺路穿黄隧道区域内典型粉质黏土的的静动力行为特性及工程适用性,通过室内基础土工试验、侧限固结试验、标准三轴固结试验以及动三轴试验,确定了粉质黏土基本物理性质参数以及切线刚度E_(oed)^(ref)、割线模量E_(50)^(ref)、卸载/重加载参考刚度E_(ur)^(ref),并将所得参数应用于济南济泺路穿黄隧道工程下穿北岸大堤沉降分析中,同时通过对比应用硬化土小应变硬化(hardening soil model with small strain stiffness,HSS)本构模型、摩尔库伦(M-C)本构模型的模拟结果与现场实测结果,验证了HSS本构模型在该地区变形分析中的准确性。结果表明:围压一定时,该地区粉质黏土试样竖向应变以塑性应变为主,且随动应力的增加,土体达到稳定所需时间越长;循环荷载一定时,增大土体围压可提高土体的稳定性;基于室内试验获取的HSS本构模型参数模拟的济南济泺路穿黄隧道下穿大堤工程地层变形结果与现场实测值吻合良好,验证了基于所提出的室内试验获取岩土小应变相关参数方法的适用性。研究成果可以丰富济南黄河地区粉质黏土地层参数研究,并为该地区岩土工程数值模拟分析的本构模型与地层参数选取提供参考。展开更多
Different phenomenological equations based on plasticity, primary creep （as a viscoplastic mechanism）, secondary creep （as another viscoplastic mechanism） and different combinations of these equations are presente...Different phenomenological equations based on plasticity, primary creep （as a viscoplastic mechanism）, secondary creep （as another viscoplastic mechanism） and different combinations of these equations are presented and used to describe the material inelastic deformation in uniaxial test. Agreement of the models with experimental results and with the theoretical concepts and physical realities is the criterion of choosing the most appropriate formulation for uniaxial test. A model is thus proposed in which plastic deformation, primary creep and secondary creep contribute to the inelastic deformation. However, it is believed that the hardening parameter is composed of plastic and primary creep parts. Accordingly, the axial plastic strain in a uniaxial test may no longer be considered as the hardening parameter. Therefore, a proportionality concept is proposed to calculate the plastic contribution of deformation.展开更多
A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S...A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.展开更多
A periodic packing mode of trickle-bed reactor (TBR) for the gas limited reaction was proposed. Hy-drogenation of 2-ethylanthraquinone over Pd/Al2O3 in a laboratory-scale TBR was taken as a test reaction for determini...A periodic packing mode of trickle-bed reactor (TBR) for the gas limited reaction was proposed. Hy-drogenation of 2-ethylanthraquinone over Pd/Al2O3 in a laboratory-scale TBR was taken as a test reaction for determining whether the periodic packing mode is advantageous. The effects of operating conditions and packing type on TBR performance were experimentally examined to demonstrate the cause-effect relationships. A mathe-matic model of TBR considering axial dispersion and fractional wetting was developed to quantitatively illuminate the reason of performance enhancement.展开更多
Soil-rock mixture （SRM） is a unique type of geomaterial characterized by a heterogeneous composition and a complicated structure. It is intractable for the continuum-based soil and rock mechanics theories to accurat...Soil-rock mixture （SRM） is a unique type of geomaterial characterized by a heterogeneous composition and a complicated structure. It is intractable for the continuum-based soil and rock mechanics theories to accurately characterize and predict the SRM＇s mechanical properties. This study reports a novel numerical method incorporating microfocus computed tomography and PFC3D codes to probe the deformation and failure processes of SRM. The three-dimensional （3D） PFC models that represent the SRM＇s complex structures were built. By simulating the entire failure process in PFC3D, the SRM＇s strength, elastic modulus and crack growth were obtained. The influence of rock ratios on the SRM＇s strength, deformation and failure processes, as well as its internal mesoscale mechanism, were analyzed. By comparing simulation results with experimental data, it was verified that the 3D PFC models were in good agreement with SRM＇s real structure and the SRM＇s compression process, deformation and failure patterns; its intrinsic mesomechanism can be effectively analyzed based on such 3D PFC models.展开更多
The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformatio...The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement＇s mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.展开更多
Deepwater oil and gas projects embody high risks from geology and engineering aspects, which exert substantial influence on project valuation. But the uncer- tainties may be converted to additional value to the projec...Deepwater oil and gas projects embody high risks from geology and engineering aspects, which exert substantial influence on project valuation. But the uncer- tainties may be converted to additional value to the projects in the case of flexible management. Given the flexibility of project management, this paper extends the classical real options model to a multi-factor model which contains oil price, geology, and engineering uncertainties. It then gives an application example of the new model to evaluate deepwater oil and gas projects with a numerical analytical method. Compared with other methods and models, this multi-factor real options model contains more project information. It reflects the potential value deriving not only from oil price variation but also from geology and engi- neering uncertainties, which provides more accurate and reliable valuation information for decision makers.展开更多
This paper describes a quasi 3-D finite element model of the groundwater flow in two -aquifer system which is constructed from a sequence of aquifer flow equations coupled by leakage terms representing flow through th...This paper describes a quasi 3-D finite element model of the groundwater flow in two -aquifer system which is constructed from a sequence of aquifer flow equations coupled by leakage terms representing flow through the aquitard . It is applied to evaluate the maximum rate of groundwater resources exploited from the coastal aquifer without seawater intrusion . The main task in this model is to determine the drainage boundary of the aquifer extending under the sea . The information of the boundary can be obtained from the fluctuations of the groundwater level caused by sea-tide fluctuations . A new idea, Equivalent Drainage Boundary (EDB), is proposed and the corresponding methods , determining the EDB, are developed with tidal fluctuations data observed in boreholes . The quasi 3-D model and the methods determining EDB have been applied to the aquifer system of Beihai peninsula , Guangxi Autonomous Region of China for calculating the available groundwater resources .展开更多
At present, shallow gases have received much attention due to low cost in exploration and production. Low-mature gases, as one significant origin to shallow gas, turns to be an important research topic. The present un...At present, shallow gases have received much attention due to low cost in exploration and production. Low-mature gases, as one significant origin to shallow gas, turns to be an important research topic. The present understanding of low-mature gases is confined within some geological cases, and few laboratory studies have been reported. Therefore, the potential and characters of low- mature gases are not clear up to now. Here, two premature samples （one coal and the other shale） were pyrolyzed in a gold confined system. The gaseous components including hydrocarbon gases and non-hydrocarbon gases were analyzed. Based on kinetic modeling, the formation of low-mature gases was modeled. The results showed that during low mature stage, about 178 mL/gTOC gas was generated from the shale and 100 mL/gTOC from the coal. Two third to three fourth of the generated gases are non-hydrocarbon gases such as H2S and CO2. The total yields of C1-5 for the two samples are almost the same, 30-40 mL/gTOC, but individual gaseous hydrocarbon is different. The shale has much lower C1 but higher C2-5, whereas the coal has higher C1 but lower C2-5. Hydrocarbon gases formed during low-mature stage are very wet. The stable carbon isotope ratios of methane range from -40‰ to -50‰ （PDB）, in good consistence with empiric criterion for low-mature gases summed up by the previous researchers. The generation characters suggest that the low-mature gases could be accumulated to form an economic gas reservoir, but most of them occur only as associated gases.展开更多
It is still a challenging task to accurately and temperature-continuously express the thermodynamic properties and phase equilibrium behaviors of the salt-lake brine with multi-component,multitemperature and high conc...It is still a challenging task to accurately and temperature-continuously express the thermodynamic properties and phase equilibrium behaviors of the salt-lake brine with multi-component,multitemperature and high concentration.The essential subsystem of sulfate type brine,aqueous Li^(+)-Na^(+)-K^(+)-SO_(4)^(2-) and its subsystems across a temperature range from 250 K to 643 K are investigated with the improved comprehensive thermodynamic model.Liquid parameters(Δg_(IJ),Δh_(IJ),and ΔC_(p,IJ))associated with the contributions of Gibbs energy,enthalpy,and heat capacity to the binary interaction parameters,i.e.the temperature coefficients of eNRTL parameters formulated with a Gibbs Helmholtz expression,are determined via multi-objective optimization method.The solid constantsΔ_(f)G_(k)°^((298.15))andΔ_(f)H_(k)°^((298.15))of11 solid species occurred in the quaternary system are rebuilt from multi-temperature solubilities.The modeling results show the accurate representation of(1)solution properties and binary phase diagram at temperature ranges from eutectic points to 643 K;(2)isothermal phase diagrams for Li_(2)SO_(4)-Na_(2)SO_(4)-H_(2)O,Li_(2)SO_(4)-K_(2)SO_(4)-H_(2)O and Na_(2)SO_(4)-K_(2)SO_(4)-H_(2)O ternary systems.The predicted results of complete structure and polythermal phase diagram of ternary systems and the isothermal phase diagrams of quaternary system excellently match with the experimental data.展开更多
In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-d...In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.展开更多
文摘A novel parameter extraction method with rational functions is presented for the 2-πequivalent circuit model of RF CMOS spiral inductors. The final S-parameters simulated by the circuit model closely match experimental data. The extraction strategy is straightforward and can be easily implemented as a CAD tool to model spiral inductors. The resulting circuit models will be very useful for RF circuit designers.
基金The study was supported by the National Natural Science Foundation of China under contract No.10772041the State 0ceamic Administration Key Laboratory for Ploar Science of China under contract No.KP 2007004.
文摘A hybrid Lagrangian - Eulerian （HLE） method is developed for sea ice dynamics, which combines the high computational efficiency of finite difference method （FDM） with the high numerical accuracy of smoothed particle hydrodynamics （SPH）. In this HLE model, the sea ice cover is represented by a group of Lagrangian ice particles with their own thicknesses and concentrations. These ice variables are interpolated to the Eularian gird nodes using the Gaussian interpolation function. The FDM is used to determine the ice velocities at Eulerian grid nodes, and the velocities of Lagrangian ice particles are interpolated from these grid velocities with the Gaussian function also. The thicknesses and concentrations of ice particles are determined based on their new locations. With the HLE numerical model, the ice ridging process in a rectangular basin is simulated, and the simulated results are validated with the analytical solution. This method is also applied to the simulation of sea ice dynamics in a vortex wind field. At last, this HLE model is applied to the Bohai Sea, and the simulated concentration, thickness and velocity match the satellite images and the field observed data well.
文摘盾构施工过程中土体大部分区域处于小应变状态,与常用的本构模型的土体性质有所不同。因此,为研究济南济泺路穿黄隧道区域内典型粉质黏土的的静动力行为特性及工程适用性,通过室内基础土工试验、侧限固结试验、标准三轴固结试验以及动三轴试验,确定了粉质黏土基本物理性质参数以及切线刚度E_(oed)^(ref)、割线模量E_(50)^(ref)、卸载/重加载参考刚度E_(ur)^(ref),并将所得参数应用于济南济泺路穿黄隧道工程下穿北岸大堤沉降分析中,同时通过对比应用硬化土小应变硬化(hardening soil model with small strain stiffness,HSS)本构模型、摩尔库伦(M-C)本构模型的模拟结果与现场实测结果,验证了HSS本构模型在该地区变形分析中的准确性。结果表明:围压一定时,该地区粉质黏土试样竖向应变以塑性应变为主,且随动应力的增加,土体达到稳定所需时间越长;循环荷载一定时,增大土体围压可提高土体的稳定性;基于室内试验获取的HSS本构模型参数模拟的济南济泺路穿黄隧道下穿大堤工程地层变形结果与现场实测值吻合良好,验证了基于所提出的室内试验获取岩土小应变相关参数方法的适用性。研究成果可以丰富济南黄河地区粉质黏土地层参数研究,并为该地区岩土工程数值模拟分析的本构模型与地层参数选取提供参考。
文摘Different phenomenological equations based on plasticity, primary creep （as a viscoplastic mechanism）, secondary creep （as another viscoplastic mechanism） and different combinations of these equations are presented and used to describe the material inelastic deformation in uniaxial test. Agreement of the models with experimental results and with the theoretical concepts and physical realities is the criterion of choosing the most appropriate formulation for uniaxial test. A model is thus proposed in which plastic deformation, primary creep and secondary creep contribute to the inelastic deformation. However, it is believed that the hardening parameter is composed of plastic and primary creep parts. Accordingly, the axial plastic strain in a uniaxial test may no longer be considered as the hardening parameter. Therefore, a proportionality concept is proposed to calculate the plastic contribution of deformation.
基金supported by the National Natural Science Foundation of China (10872195)
文摘A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.
基金the State Key Development Program for Basic Research of China (No. G2000048005) the SINOPEC (No.X503023).
文摘A periodic packing mode of trickle-bed reactor (TBR) for the gas limited reaction was proposed. Hy-drogenation of 2-ethylanthraquinone over Pd/Al2O3 in a laboratory-scale TBR was taken as a test reaction for determining whether the periodic packing mode is advantageous. The effects of operating conditions and packing type on TBR performance were experimentally examined to demonstrate the cause-effect relationships. A mathe-matic model of TBR considering axial dispersion and fractional wetting was developed to quantitatively illuminate the reason of performance enhancement.
基金Acknowledgements The authors gratefully acknowledge the financial support from the State Key Research Development Program of China （Grant No. 2016YFC0600705）, the National Natural Science Foundation of China （Grant Nos. 51674251, 51727807, 51374213）, the National Natural Science Foundation for Distinguished Young Scholars of China （Grant No. 51125017）, the Fund for Creative Research and Development Group Program of Jiangsu Province （Grant No. 2014-27）, and the Priority Academic Program Development of Jiangsu Higher Education Institutions （Grant No. PAPD2014）, and an open project sponsored by the State Key Labo- ratory for Geomechanics and Deep Underground Engineering （Grant SKLGDUE K1318） for their financial support.
文摘Soil-rock mixture （SRM） is a unique type of geomaterial characterized by a heterogeneous composition and a complicated structure. It is intractable for the continuum-based soil and rock mechanics theories to accurately characterize and predict the SRM＇s mechanical properties. This study reports a novel numerical method incorporating microfocus computed tomography and PFC3D codes to probe the deformation and failure processes of SRM. The three-dimensional （3D） PFC models that represent the SRM＇s complex structures were built. By simulating the entire failure process in PFC3D, the SRM＇s strength, elastic modulus and crack growth were obtained. The influence of rock ratios on the SRM＇s strength, deformation and failure processes, as well as its internal mesoscale mechanism, were analyzed. By comparing simulation results with experimental data, it was verified that the 3D PFC models were in good agreement with SRM＇s real structure and the SRM＇s compression process, deformation and failure patterns; its intrinsic mesomechanism can be effectively analyzed based on such 3D PFC models.
基金Supported by National Natural Science Foundation of China(Grant No.51375424)
文摘The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement＇s mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.
基金supported from the National Science and Technology Major Project under Grant No.2011ZX05030
文摘Deepwater oil and gas projects embody high risks from geology and engineering aspects, which exert substantial influence on project valuation. But the uncer- tainties may be converted to additional value to the projects in the case of flexible management. Given the flexibility of project management, this paper extends the classical real options model to a multi-factor model which contains oil price, geology, and engineering uncertainties. It then gives an application example of the new model to evaluate deepwater oil and gas projects with a numerical analytical method. Compared with other methods and models, this multi-factor real options model contains more project information. It reflects the potential value deriving not only from oil price variation but also from geology and engi- neering uncertainties, which provides more accurate and reliable valuation information for decision makers.
文摘This paper describes a quasi 3-D finite element model of the groundwater flow in two -aquifer system which is constructed from a sequence of aquifer flow equations coupled by leakage terms representing flow through the aquitard . It is applied to evaluate the maximum rate of groundwater resources exploited from the coastal aquifer without seawater intrusion . The main task in this model is to determine the drainage boundary of the aquifer extending under the sea . The information of the boundary can be obtained from the fluctuations of the groundwater level caused by sea-tide fluctuations . A new idea, Equivalent Drainage Boundary (EDB), is proposed and the corresponding methods , determining the EDB, are developed with tidal fluctuations data observed in boreholes . The quasi 3-D model and the methods determining EDB have been applied to the aquifer system of Beihai peninsula , Guangxi Autonomous Region of China for calculating the available groundwater resources .
基金supported by the CNPC Project(Grant No.06-01C-01-04)National Natural Science Foundation of China(Grant No.40603014).
文摘At present, shallow gases have received much attention due to low cost in exploration and production. Low-mature gases, as one significant origin to shallow gas, turns to be an important research topic. The present understanding of low-mature gases is confined within some geological cases, and few laboratory studies have been reported. Therefore, the potential and characters of low- mature gases are not clear up to now. Here, two premature samples （one coal and the other shale） were pyrolyzed in a gold confined system. The gaseous components including hydrocarbon gases and non-hydrocarbon gases were analyzed. Based on kinetic modeling, the formation of low-mature gases was modeled. The results showed that during low mature stage, about 178 mL/gTOC gas was generated from the shale and 100 mL/gTOC from the coal. Two third to three fourth of the generated gases are non-hydrocarbon gases such as H2S and CO2. The total yields of C1-5 for the two samples are almost the same, 30-40 mL/gTOC, but individual gaseous hydrocarbon is different. The shale has much lower C1 but higher C2-5, whereas the coal has higher C1 but lower C2-5. Hydrocarbon gases formed during low-mature stage are very wet. The stable carbon isotope ratios of methane range from -40‰ to -50‰ （PDB）, in good consistence with empiric criterion for low-mature gases summed up by the previous researchers. The generation characters suggest that the low-mature gases could be accumulated to form an economic gas reservoir, but most of them occur only as associated gases.
基金financial support of the National Natural Science Foundation of China(U1707602,U1407204)Yangtze Scholars and Innovative Research Team in University of Education of China,the Innovative Research Team of Tianjin Municipal Education Commission(TD125004)。
文摘It is still a challenging task to accurately and temperature-continuously express the thermodynamic properties and phase equilibrium behaviors of the salt-lake brine with multi-component,multitemperature and high concentration.The essential subsystem of sulfate type brine,aqueous Li^(+)-Na^(+)-K^(+)-SO_(4)^(2-) and its subsystems across a temperature range from 250 K to 643 K are investigated with the improved comprehensive thermodynamic model.Liquid parameters(Δg_(IJ),Δh_(IJ),and ΔC_(p,IJ))associated with the contributions of Gibbs energy,enthalpy,and heat capacity to the binary interaction parameters,i.e.the temperature coefficients of eNRTL parameters formulated with a Gibbs Helmholtz expression,are determined via multi-objective optimization method.The solid constantsΔ_(f)G_(k)°^((298.15))andΔ_(f)H_(k)°^((298.15))of11 solid species occurred in the quaternary system are rebuilt from multi-temperature solubilities.The modeling results show the accurate representation of(1)solution properties and binary phase diagram at temperature ranges from eutectic points to 643 K;(2)isothermal phase diagrams for Li_(2)SO_(4)-Na_(2)SO_(4)-H_(2)O,Li_(2)SO_(4)-K_(2)SO_(4)-H_(2)O and Na_(2)SO_(4)-K_(2)SO_(4)-H_(2)O ternary systems.The predicted results of complete structure and polythermal phase diagram of ternary systems and the isothermal phase diagrams of quaternary system excellently match with the experimental data.
基金the National Natural Science Fund(11661058,11761053)Natural Science Fund of Inner Mongolia Autonomous Region(2016MS0102,2017MS0107)+1 种基金Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07)National Undergraduate Innovative Training Project of Inner Mongolia University(201710126026).
文摘In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.
