Weakly nonlinear stability analysis of triple diffusive convection in a Maxwell fluid saturated porous layer

The weakly nonlinear stability of the triple diffusive convection in a Maxwell fluid saturated porous layer is investigated. In some cases, disconnected oscillatory neutral curves ave found to exist, indicating that three critical thermal Darcy-Rayleigh numbers are required to specify the linear instability criteria. However, another distinguishing feature predicted from that of Newtonian fluids is the impossibility of quasi-periodic bifurcation from the rest state. Besides, the co-dimensional two bifurcation points are located in the Darcy-Prandtl number and the stress relaxation parameter plane. It is observed that the value of the stress relaxation parameter defining the crossover between stationary and oscillatory bifurcations decreases when the Darcy-Prandtl number increases. A cubic Landau equation is derived based on the weakly nonlinear stability analysis. It is found that the bifurcating oscillatory solution is either supercritical or subcritical, depending on the choice of the physical parameters. Heat and mass transfers are estimated in terms of time and area-averaged Nusselt numbers.

Rate decline analysis of multiple fractured horizontal well in shale reservoir with triple continuum

Multiple fractured horizontal well(MFHW) is widely applied in the development of shale gas. To investigate the gas flow characteristics in shale, based on a new dual mechanism triple continuum model, an analytical solution for MFHW surrounded by stimulated reservoir volume(SRV) was presented. Pressure and pressure derivative curves were used to identify the characteristics of flow regimes in shale. Blasingame type curves were established to evaluate the effects of sensitive parameters on rate decline curves, which indicates that the whole flow regimes could be divided into transient flow, feeding flow, and pseudo steady state flow. In feeding flow regime, the production of gas well is gradually fed by adsorbed gases in sub matrix, and free gases in matrix. The proportion of different gas sources to well production is determined by such parameters as storability ratios of triple continuum, transmissibility coefficients controlled by dual flow mechanism and fracture conductivity.

Isothermal section of Mg-Nd-Gd ternary system at 723 K

An isothermal section of the Mg-Nd-Gd ternary system at 723 K was established by diffusion triple technique and electron probe microanalysis （EPMA）. Mg3Gd and Mg3Nd form a continuous solid solution （Gd,Nd）3Mg, and a continuous solid solution （Gd,Nd）Mg is also formed between MgGd and MgNd. Mg7Gd, Mg5Gd, Mg2Gd, Mg41Nd5, （Gd,Nd）3Mg and （Gd,Nd）Mg are found in the ternary system. In these intermetallic phases, Mg7Gd has been reported to be a metastable phase in previous literatures. The solubilities of Mg, Gd and Nd in all the phases were detected. Furthermore, four three-phase equilibria, α（Mg）＋Mg7Gd＋Mg41Nd5, Mg7Gd＋Mg5Gd＋Mg41Nd5, Mg5Gd＋Mg41Nd5＋（Gd,Nd）3Mg and （Gd,Nd）3Mg＋（Gd,Nd）Mg＋Mg2Gd, were identified in the isothermal section.

Isothermal section of Al-Ti-Zr ternary system at 1073 K

Through alloy sampling combined with diffusion triple technique, phase equilibria in Al-Ti-Zr ternary system at 1073 Kwere experimentally determined with electron probe microanalysis （EPMA）. Experimental results show that there is a solid solutionβ（Ti,Zr） which dissolves Al up to 16.3% （mole fraction）. Ti and Zr can substitute each other in most Ti-Al and Al-Zr binaryintermediate phases to a certain degree while the maximum solubility of Zr in Ti3Al and TiAl reaches up to 17.9% and 4.0% （molefraction）, respectively. The isothermal section consists of 16 single-phased regions, 27 two-phased regions and 14 three-phasedregions. No ternary phase was detected.

Phase equilibria in Ti-Ni-Pt ternary system

Phase equilibria in Ti?Ni?Pt ternary system have been experimentally determined through diffusion triple technique combined with alloy samples approach.Assisted with electron probe microanalysis(EPMA)and X-ray diffraction(XRD)techniques,isothermal sections at 1073 and 1173 K of this system were constructed and existence of ternary phase Ti2(Ni,Pt)3 was confirmed.In addition,binary compounds Ti3Pt5 and TiPt3-were found to be stable at 1073 and 1173 K,and remarkable ternary solubility in some binary compounds was detected,e.g.,solubility of Pt in TiNi can be up to about 36%(molar fraction)at 1073 K and 40%(molar fraction)at 1173 K.Furthermore,a ternary invariant transition reaction TiNi3+Ti3Pt5→Ti2(Ni,Pt)3+TiPt3+at a temperature between 1073 and 1173 K was deduced.

Determination of phase equilibria in the Ni-Ta-Zr system at 1223 K

The phase equilibrium relations of the ternary Ni-Ta-Zr system at 1223 K wereinvestigated by means of diffusion triple and electron probe microanalysis (EPMA) techniques. Twoternary compounds were found and a series of tie lines and tie triangles have been determined. Themaximum solubility of Ta in NiZr_2 is about 13.5% (atom fraction). The corresponding tentativeisothermal section at this temperature was constructed based on current experimental information.

DETERMINATION OF ISOTHERMAL SECTION OF Fe-Ni-Zr TERNARY SYSTEM AT 1198K

The isothermal section of Fe-Ni-Zr ternary system at 1198K was experimentally determined using diffusion triple technique together with scanning electron microscopy （SEM） and electron probe microanalysis （EPMA ）. The results indicate that there are seven binary intermetallic phases, Fe2Zr, FeZr2, Nir2, NiZr, Ni10Zr7, Ni7Zr2 and Ni5Nr, found in the temary system, the binary compounds NiZr2 and FeZr2 show a homogeneity range and form a continuous solid solution, namely （Fe, Ni）Zr2 Five three-phase sections, γ（Fe,Ni） ＋ Ni3Zr2 ＋ Ni5Zr,γ（Fe, Ni） ＋ Ni7Zr2 ＋ Ni10Zr7, γ（Fe,Ni） ＋ Fe2Zr ＋ Ni10Zr7, （Fe,Ni）Zr2 ＋ Fe2Zr ＋ Nil0Zr7, and （Fe,Ni）Zr2 ＋ NiZr ＋ Ni10Zr7, exist in the isothermal section. No ternary compound is observed.

Determination of isothermal sections of the Co-Nb-Ni and Ni-Mo-Re ternary systems

The isothermal sections of the Co-Nb-Ni ternary system at 1373 K and the Ni-Mo-Re ternary system at 1473 K were determined by means of diffusion triple and electron probe microanalysis（EPMA）.The results indicate that there are three three-phase regions found in the Co-Nb-Ni ternary system at 1373 K：（Ni,Co） ＋ NbCo3 ＋ Ni3Nb,NbCo3 ＋ NbCo2 ＋ Ni3Nb,and NbCo2 ＋ μ ＋ Ni3Nb;and four three-phase regions found in the Ni-Mo-Re ternary system at 1473 K：Re ＋ Ni ＋ χ,Ni ＋ NiMo ＋ σ,σ ＋ χ ＋ Ni,and σ ＋ Mo ＋ NiMo.No ternary compound is observed in the two isothermal sections.The isothermal sections are contrasted with the previous study.

Miscibility Gap in the Fe-Cu-Ni System at 1173 K

The isothermal section of the Fe-Cu-Ni ternary system at 1173 K was determined by microprobe analysis and diffusion triple technique. The experimental results show that this isothermal section only contains a miscibility gap region,and the maximal Ni content in the miscibility gap is 44.7 at.-%Ni.

Determination of isothermal section of Ni-Re-Hf ternary system at 1173 K

The phase equilibriua in the Ni Re Hf ternary system at 1173K were investigated by means of diffusion triple technique and electron microprobe analysis(EMPA). The experimental results indicate that two ternary intermetallics (α and β) and five binary intermetallics (Ni 3Hf, Ni 10 Hf 7, Ni 11 Hf 9, NiHf and NiHf 2) exist in the Ni Re Hf system at 1?173 K. A tentative isothermal section of this system at 1?173 K was constructed on the basis of experimental results. The isothermal section consists of nine three phase regions, five of which are supported by the experimental data.

Determination of isothermal section of Ag-Ti-Zr ternary system at 1 023 K

The isothermal section of Ag-Ti-Zr ternary system at 1023 K was determined by diffusion triple and electron probe microanalysis. The results indicate that four binary intermetallic phases of AgTi, AgTi2, AgZr and AgZr2 are found in Ag-Ti-Zr ternary system at 1 023 K. AgZr2 and AgTi2 form a continuous solid solution, namely Ag(Ti,Zr)2. Four three-phase regions: AgTi +AgZr + Ag, AgTi +AgZr + Ag (Ti, Zr)2, α-Zr +β(Ti, Zr) + Ag (Ti, Zr) 2 and α-Ti +β(Ti, Zr) + Ag (Ti, Zr)2 exist in the isothermal section. No ternary compound is observed.