Phase Transition Front Research Articles

Bifurcations and Stability of Phase Transition Fronts in Geothermal Reservoirs

Bifurcations and Stability of Phase Transition Fronts in Geothermal Reservoirs

Modeling heat and mass transfer during artificial ground freezing considering the influence of water seepage

In the system of artificial ground freezing under water seepage, the dynamic liquid–ice phase equilibrium relationship considering the contribution of water seepage pressure was established based on the classical thermodynamics fundamentals. The freezing characteristic function was represented by combining the Young–Laplace law with van Genuchten model. A thermal-hydraulic model of saturated porous media considering dynamic liquid–ice phase equilibrium was established and validated thorough laboratory tests under various seepage velocities. The temperature field evolution laws of sand, silty and clay grounds were studied based on the thermal-hydraulic model. The temperature field development laws of primary side tunnel of subway cross passages in silty-clay layer were analyzed by applying the thermal-hydraulic model. The relationship between water seepage pressure and the decrease of water freezing point temperature was obtained according to the dynamic liquid–ice phase equilibrium. Compared with the simulation results of considering static liquid–ice phase equilibrium relationship, considering the dynamic liquid–ice phase equilibrium relationship changes the distribution of water-ice phase transition front and has significant influence on the temperature evolution in silty ground. However, that influence in sand ground and clay ground is insignificant because of the relatively lower water seepage pressure in sand ground and poor thermal conductivity in clay ground. Due to the cold energy accumulation bring by water seepage, the freezing rate in the downstream of freezing pipes is faster than that in the upstream of freezing pipes. This effects are exacerbated by lower decrease of water freezing point temperature caused by minor water seepage pressure in the downstream of freezing pipes. Four representative temperature measured points were selected to acquire the relationship between simulation and on-site temperatures. It was observed that the trends of simulation results reflect the tunnel freezing process well.

Rheology of fibrous gels under compression

A number of biological tissues and synthetic gels consist of a fibrous network infused with liquid. There have been a few experimental studies of the rheological properties of such gels under applied compressive strain. Their results suggest that a plot of rheological moduli as a function of applied compressive strain has a long plateau flanked by a steeply increasing curve for large compressive strains and a slowly decreasing curve for small strains. In this paper we explain these trends in rheological properties using a chemo-elastic model characterized by a double-well strain energy function for the underlying fibrous network. The wells correspond to rarefied and densified phases of the fibrous network at low and high strains, respectively. These phases can co-exist across a movable transition front in the gel in order to accommodate overall applied compression. We find that the rheological properties of fibrous gels share similarities with a Kelvin–Voigt visco-elastic solid. The storage modulus has its origins in the elasticity of the fibrous network, while the loss modulus is determined by the dissipation caused by liquid flow through pores. The rheological properties can depend on the number of phase transition fronts present in a compressed sample. Our analysis may explain the dependence of storage and loss moduli of fibrin gels on the loading history. We also point to the need for combining rheological measurements on gels with a microstructural analysis that could shed light on various dissipation mechanisms.

Shock-induced plasticity and phase transformation in single crystal magnesium: an interatomic potential and non-equilibrium molecular dynamics simulations

An effective and reliable Finnis–Sinclair (FS) type potential is developed for large-scale molecular dynamics (MD) simulations of plasticity and phase transition of magnesium (Mg) single crystals under high-pressure shock loading. The shock-wave profiles exhibit a split elastic–inelastic wave in the [0001]HCP shock orientation and a three-wave structure in the [10-10]HCP and [-12-10]HCP directions, namely, an elastic precursor, a followed plastic front, and a phase-transition front. The shock Hugoniot of the particle velocity (U p) vs the shock velocity (U s) of Mg single crystals in three shock directions under low shock strength reveals apparent anisotropy, which vanishes with increasing shock strength. For the [0001]HCP shock direction, the amorphization caused by strong atomic strain plays an important role in the phase transition and allows for the phase transition from an isotropic stressed state to the product phase. The reorientation in the shock directions [10-10]HCP and [-12-10]HCP, as the primary plasticity deformation, leads to the compressed hexagonal close-packed (HCP) phase and reduces the phase-transition threshold pressure. The phase-transition pathway in the shock direction [0001]HCP includes a preferential contraction strain along the [0001]HCP direction, a tension along [-12-10]HCP direction, an effective contraction and shear along the [10-10]HCP direction. For the [10-10]HCP and [-12-10]HCP shock directions, the phase-transition pathway consists of two steps: a reorientation and the subsequent transition from the reorientation hexagonal close-packed phase (RHCP) to the body-centered cubic (BCC). The orientation relationships between HCP and BCC are (0001)HCP ⟨-12-10⟩HCP // {110}BCC ⟨001⟩BCC. Due to different slipping directions during the phase transition, three variants of the product phase are observed in the shocked samples, accompanied by three kinds of typical coherent twin-grain boundaries between the variants. The results indicate that the highly concentrated shear stress leads to the crystal lattice instability in the elastic precursor, and the plasticity or the phase transition relaxed the shear stress.

Effect of Freeze Pipe Eccentricity in Selective Artificial Ground Freezing Applications

Abstract Building concentric tubes is one of biggest practical challenges in the construction of freeze-pipes of selective artificial ground freezing (S-AGF) applications for underground mines. In this study, the influence of tubes eccentricity on phase-front expansion (i.e., expansion of the frozen body) and energy consumption of S-AGF systems is analyzed. A 1 + 1D semi-conjugate model that solves two-phase transient energy conservation equation is derived based on the enthalpy method. The 1 + 1D model is first validated against experimental data and then verified with a fully conjugate model from our previous work. After that, the 1 + 1D model is extended to a field-scale of typical underground mines to examine the effect of freeze-pipe eccentricity. The results show that concentric freeze-pipes form the desired frozen ground volume 17% faster than eccentric freeze-pipes. Also, the geometrical profile of the phase-transition front of the frozen ground is found to be significantly influenced by the freeze-pipe eccentricity. Furthermore, in the passive zone, where S-AGF coolants are isolated from the ground to reduce energy consumption, freeze-pipe eccentricity can increase the coolant heat gain by 20%. This percentage can increase up to 200% if radiation heat transfer is minimized.

Reduction of plane-radial freezing - thawing problems to plane-parallel ones

Construction in northern conditions is complicated by the processes of seasonal freezing and thawing of soils. This factor is of particular importance in the area of permafrost distribution. The paper deals with the problems that arise when laying communication networks. Any engineering solution must be justified by a heat engineering calculation. In one case, it is necessary to exclude the thawing of water or sewer networks, in the other case – to prevent the destructive effect of the heating main on the permafrost soil. The most common mathematical model of the heat transfer process in the presence of phase transitions is the Stefan problem. When calculating the processes of freezing-thawing near the pipes of communications, it is rational to set the problem in cylindrical coordinates, using the property of plane-radial symmetry. But the Stefan problem has an exact solution only in Cartesian coordinates, for the case of plane-parallel symmetry. For this case, many approximate dependencies are also obtained. The paper presents a method that allows using the results of solving the plane-parallel Stefan problem to solve the plane-radial problem with the same values of the input parameters. Approximate values of the coordinate of the phase transition front as a function of time for the plane-parallel and plane-radial areas are obtained using the method of sequential change of stationary states. A one-to-one relationship is established between the obtained values. If there is a solution obtained by any method for a plane-parallel area, and then using this dependence, it can be applied to a plane-radial area. This technique is suitable not only for the Stefan problem, but also for many nonlinear heat conduction problems. The results given in the paper are of practical importance: using the above method, almost any solution obtained for one type of symmetry directly extends to other types of symmetry.

МОДЕЛЮВАННЯ ПОВЕДІНКИ СТРИЖНЯ З ТРИЛІНІЙНОГО ДВОФАЗНОГО МАТЕРІАЛУ З УРАХУВАННЯМ ТЕМПЕРАТУРИ

В роботі сформульовано феноменологічну модель для опису властивостей сплавів із пам’яттю форм та пам’яттю в точці зміни температури. Встановлено, що класичні матеріальні діаграми – це конверт певного сімейства матеріальних діаграм, побудований за певнимизаконами зміни швидкості та розриву фронту деформації. Для використання феноменологічної моделі з метою дослідження двофазних матеріалів з різними модулями пружності розв’язано додаткову задачу, яка пов’язана з розбудовою миттєвої термомеханічної поверхні. В роботі проведено числове дослідження, як результат показано типову залежність для швидкості розповсюдження фазового переходу від часу. Графік залежності має три ділянки. На першій ділянці швидкість дорівнює нулю, а на третій – досягає постійного значення. Між ними міститься ділянка зі змінною швидкістю. В результаті обчислення дотичного модуля на кожному кроці інтегрування за часом інтегральна діаграма матеріалу, побудована в роботі, теж має три характерні ділянки.

Development of conjugate reduced-order models for selective artificial ground freezing: Thermal and computational analysis

Selective artificial ground freezing (S-AGF) applications usually extend to very deep levels (more than 400 meters); numerical modeling of such large AGF applications encounters two main issues: (i) Predicting the variable heat extraction capacity along the freeze-pipe depth and (ii) the extremely long computational time. In this paper, we develop novel semi-conjugate reduced-order models that accurately predict heat extraction along the freeze-pipe while substantially reducing the computational time. In regards to the thermal modeling novelty, the freeze-pipe boundary condition of S-AGF is mathematically derived considering the development of the coolant flow temperature and boundary layer. As for the computational novelty, fast semi-conjugate reduced-order algorithms are developed for S-AGF, with the optional incorporation of analytical solutions and spatial correction. The models are validated against experimental data and verified with established fully-conjugate models. The thermal results demonstrate that the phase transition front profile of the frozen ground is primarily shaped by the thermal development of the flow. On the other hand, the computational results reveal that the computational time of the reduced-order algorithms is decreased by more than 99%, as compared with the established models. In short, our proposed reduced-order models are proven to be reliable and computationally efficient, which shows potential for practical field application.

Numerical study of the combustion of a flat layer of methane gas hydrate

In the work in a flat-one-dimensional formulation, a mathematical model and the results of modeling the combustion process of a gas hydrate as a result of its ignition with a mixture of methane and an oxidizer are presented. It was assumed that the rate constant of a chemical reaction depends on temperature according to the Arrhenius law. The solution was carried out by a numerical method based on the method of catching the phase transition front into the nodes of the spatial grid. On the basis of the obtained solutions, the distributions of the main parameters of the system, as well as the dependences of the highest temperature of the gas mixture and the rate of decomposition on time, were constructed.

Superheating of water and morphological instability of the boiling front moving in the low-permeability rock

We explore the decompression and associated boiling front motion through permeable rock. The regime of the front movement with constant speed is studied. The range of parameters is defined when the water ahead of the phase transition front is in an superheated state. The dispersion equation was obtained using the normal mode method and the flow stability was studied. In the parameter domain, neutral stability diagrams are presented and a comparison is made with the domains of existence of solutions with water superheating ahead of the front. We show that the occurrence of instability of the boiling front is always preceded by the transition of the water ahead of the front to a superheated state.

Dynamic thermo-mechanical behaviors of SME TiNi alloys subjected to shock loading

Dynamic thermo-mechanical coupling behaviors of shape memory TiNi alloy in the strain rate ranging from 300 s−1 to 2000 s−1 are investigated by the split Hopkinson pressure bar (SHPB) device with an infrared (IR) detection system. In stress–strain space, dynamic response shows a strong strain hardening property, however, in stress–temperature space, transformation path is particularly sensitive to the strain rate. The corresponding temperature evolution measured synchronously shows that local temperature increased associated with the forward phase transition, and it would keep the loading maximum value unchanged or decreased for unloading, depending on the strain rate. Besides, local temperature evolution was consistent with the transformation stress and its values at different points are the same. Temperature evolution and transformation deformation mechanism is then analyzed by a simple one-dimensional model. The results show that latent heat and dissipated energy are responsible for temperature variation. Furthermore, the temperature evolution with strain rate reveals that with the increase of strain rate, the phase transformation deformation mechanism undergoes a transformation from phase transition fronts propagation during lower strain rates to combination of local nucleation and front propagation during middle strain rate and to uniform nucleations during higher strain rates. The results are helpful for a passive shape memory alloy (SMA) micro-valve design.

Comparative Analysis of the Occurrence of Water Superheating and Instability of the Boiling Front in a Porous Medium

The stability of the boiling front propagating at a constant rate in a geothermal reservoir is studied by the normal mode method. On the parameter plane, domains corresponding to the instability and water superheating ahead of the front are determined. It is found that instability of the phase transition front is always preceded by the transition of the water to a metastable state.

Investigation of the influence of medium and microwave radiation parameters on the dynamics of decomposition of gas hydrate

The paper considers the problem of dissociation of methane gas hydrate saturating a porous medium of finite extent under the action of an external radiation source. The mathematical model includes the equations of continuity, heat inflow, and Darcy’s law, and is supplemented by the conditions of mass and heat balance on the discontinuity surface. In this case, we consider the case when the left boundary of a porous system is impervious to gas and heat flows, and the power of the source depends inversely on the coordinate of the phase transition front. Based on a computational algorithm developed using the method of catching the front in the grid node, the influence of the initial parameters of the reservoir on the maximum temperatures and pressures implemented in the system is studied. The influence of the power of the radiation source and the volume content of gas hydrate in the system on the intensity of its decomposition is also considered.

Discontinuity-driven mesh alignment for evolving discontinuities in elastic solids

A special mesh adaptation technique and a precise discontinuity tracking are presented for an accurate, efficient, and robust adaptive-mesh computational procedure for one-dimensional hyperbolic systems of conservation laws, with particular reference to problems with evolving discontinuities in solids. The main advantage of the adaptive technique is its ability to preserve the modified mesh as close to the original fixed mesh as possible. The constructed method is applied to the martensitic phase-transition front propagation in solids.

Critical Evolution of Finite Perturbations of a Water Evaporation Surface in Porous Media

It is shown that the approximate steady-state solutions, which satisfy the model dissipative equation that describes the process of water evaporation in the neighborhood of the instability threshold of a phase transition interface, determine localized damped finite-amplitude perturbations when a certain condition is fulfilled. These steady-state solutions can be used for forecasting the scenario of the development of a perturbation with sufficient accuracy if this perturbation has no common points with any steady-state solution. If the initial position of the phase transition front is located between the spectrally stable solution and any of the steady-state solutions, this front damps. If the initial position of the front is located above at least one of the spectrally unstable steady-state solutions, then the solution is catastrophically restructured.

Natural Convection in Water-Saturated Rock Mass under Artificial Freezing

The authors study theoretically the non-isometric natural convection of pore water in rock mass subjected to artificial ground freezing. The mathematical model is developed for a permeable water-saturated layer of rocks under artificial freezing. The model assumptions allowed transition to a two-dimension axially symmetric model. The numerical computation gives critical Rayleigh number values such that natural convection of pore water has a significant influence on temperature and position of phase transition front. Three possible convection regimes of pore water are determined as function of alternating-sign ability of thermal expansion factor.

X-FEM: An efficient algorithm for simulation of phase transition during prostate cryosurgery

Cryosurgery is a surgical technique to ablate abnormal tumor tissues with the help of extreme cold using cryogens such as liquid nitrogen, solid carbon dioxide, argon etc. This therapy may be used as a primary treatment for early prostate cancers effectively. During the process of freezing in cryosurgery, a phase transition occurs between the frozen tumor tissues and unfrozen surrounding tissues. The present study aims to showcase the efficiency of fixed grid X-FEM to numerically simulate the evolving phase transition front with time which further illustrates location & dimensions of ice ball generated after freezing. It has been observed that X-FEM with a fixed mesh is capable to capture phase transitions front and temperature fields accurately while traditional form of FEM requires adaptive re-meshing at each time step. From physician point of view, obtained temperature fields are really important to decide the extent of freezing, location of different cryoprobes, and numbers of cryoprobes to be used for a successful treatment.

Analytical solution of the problem of hydrate formation in a porous medium with a temperature jump at the phase transition front

The results of theoretical study of the methane hydrate formation during the hydrocarbon gas injection into a porous reservoir initially saturated with methane and water are presented. In the axisymmetric approximation, mathematical model with a stepwise temperature distribution in the reservoir is considered. For this case, an approximate analytical solution is constructed with a temperature jump at the gas hydrate formation front in the form of an explicit functional dependence of the self-similar coordinate of this boundary on the parameters of a porous medium and an injected gas.

The effect of cryogenic suction on the monitoring data of ice barrier formation in a porous water-saturated soil

Artificial ice wall formation is one of the most frequently used techniques for waterproofing of mineshafts constructed in water-saturated rock massifs. In this work, we have developed a complex monitoring system for control of formation of ice. The system includes hydro-observation and temperature monitoring wells combined with simulation module. At the beginning of the monitoring process, we observed contradictory indications of ice wall closing moment by hydro-observation and temperature monitoring subsystems. To explain this effect we introduced in the simulation module two models of ground freezing, which consider the key effects observed under the phase transition in a saturated soil. There are existing of nonequilibrium moisture content in the soil at negative temperatures, kinetic peculiarities of water-ice transition in a porous medium and redistribution of moisture in partially saturated soil. Based on the detail simulation model we have shown that moisture content inside the closed ice wall can decrease due to water migration towards the phase transition front, which, consequently, slows down the water level in hydro-observation wells.

Application of the Fokker-Planck Kolmogorov equation to determining the mean value of nucleons generated by the direct ejection process

The statistical description of the process of direct nucleon ejection is the subject of this paper. This description is based on the generalized Fokker-Planck-Kolmogorov equation. The basic proposal is this: deterministic equations and their solutions have the mean values of the stochastic model of the ablation problem. The problem of deformation of the phase transition front is considered. The study is carried out by using the introduced stability position for the dispersion of solutions for mean values. The result of the study is the conclusion that the influence of the Markov diffusion coefficient leads to distortion of the original shape of the boundary phase transition front. The effect of the initial aspiration to resist changing the shape of the phase transition front was found.