Heat and mass transfer in unsaturated porous media with solid–liquid change

 A model on heat and mass transfer in unsaturated porous media with solid/liquid phase change was developed with extending the three-variable model previously proposed. The movement of air phase and its effect on the motion of water is considered. The model has been checked with comparison of the experimental results of the temperature distribution for two dimensional freezing process. The evolution of air pressure, water and ice saturation were predicted by solving the governing equations. The ice segregation and moisture movement toward the front of freezing were numerically simulated. Received on 8 December 1999     

Self-similar solution of a problem of freezing of finely dispersed soils with allowance for moisture migration in thawed and frozen zones

Heat transfer in freezing and thawing soils is accompanied by various processes among which phase transition of moisture and mass transfer should be distinguished in both the thawed and the frozen zones. Their consequence is the formation of ice schlieren and the swelling associated with this. In developing the methods of calculation of moisture migration it was assumed (see, for example, [1, 2]) that the mass transfer occurs only in the thawed part of the soil and is realized predominantly in the liquid phase through the diffusion-film mechanism. It was assumed that the phase conversion of water into ice occurs wholly on the phase interface (the Stefan formulation) and at the same time supplementary conditions for the moisture function are specified on it. Not all these assumptions are valid. In particular, the marked redistribution of moisture in the frozen zone is an important factor in the freezing of moist rocks [3, 4]. This last is also observed in the thawing of dispersed rocks and in frozen samples which are under the influence of a temperature gradient. These phenomena were modeled in [5, 7] on the basis of a single mathematical model which describes the conductive heat transfer, the moisture transfer in thawed and frozen zones, the phase transition of moisture in the temperature range, and the kinetic relaxation effects of moisture crystallization and ice melting. Analysis of the solutions obtained by means of a finite difference method showed that the proposed method of calculation gives results near the experiment. The present paper is devoted to a further study of the model indicated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 113–120, March–April, 1986.     

冻土力学的研究进展与思考

从冻结土的宏观力学性质,正冻土中的水、热迁移理论,正 冻土的水热力耦合模型四个方面分析综述了国内外冻土力学的发展 历史、研究现状与我国冻土力学研究中存在的问题,指出：（1）当 前冻土力学的研究内容应该从对冻结土的宏观强度与变形性质向更 切合实际工程需要的正冻土、正融土微、细观热、力学耦合性质方 面深化;（2）冻土力学的研究思路应该从对土样纯力学量的试验研 究向土样组构、级配、含水量、饱和度等土性指标在不同负温下对 土样颗粒排列与胶结特性的强度、变形影响机理方面转移;（3）冻 土力学的研究对象也应该从室内冻结试验的研究向具有各种不同水 热交换边界条件与水热迁移内在规律的冻土体发展。     

黄土斜(边)坡表层冻结效应及其稳定响应

中国黄土分布于季节性冻土区,年复一年的冻融作用对具有特殊结构黄土斜(边)坡的稳定性有很大影响,促发了大量黄土斜(边)坡灾害,制约着地区经济发展。深入研究冻融作用机理,对减轻黄土斜(边)坡灾害有重要的理论和现实意义。针对黄土斜(边)坡灾害及冻融作用特点,利用表层冻结温度场数值模拟、冻结前后地下水聚集模型分析及实例验证分析等方法、手段,揭示边坡表层土体冻结过程、坡体内地下水集聚过程,探讨黄土斜(边)坡表层冻结效应及其稳定响应。结果是: (1)表层冻结作用由表及里进行,大约在冻结3个月后达到当地最大冻深; (2)以简化的地下水聚集模型分析,推导得到坡体内地下水浸润线方程; (3)冻结滞水作用可使黄土斜(边)坡稳定性降低约25%。     

温度对季节性冻土水分迁移的影响研究

寒区季节性冻土冻胀性质对工程实际影响很大。为了了解温度对水分迁移现象的影响,本文通过地温测试仪对野外不同深度处的土层温度进行测量,并在不同时间相应深度取土样,测其含水率,通过比较不同时间不同深度处的含水率的变化情况来分析温度变化对水分迁移现象的影响。在气温回升之前,当地表温度降低时,温度随深度的降低而升高; 随着地表温度不断降低,各深度处的温度也不断下降,温度梯度增加,各深度处地层的含水率变化大,即温度梯度的增加促进了季节性冻土区水分迁移现象的发生。     

Approximate solution for the temperature field of 1-D soil freezing process in a semi-infinite region

Unfrozen liquid water always exists in the humid soil system below freezing point, and the amount of the unfrozen water decreases continuously with the temperature decreasing. This phenomenon is a special characteristic for the freezing of the humid soil system. The temperature field of 1-D soil freezing process in a semi-infinite region has been studied. The problem is a Stefan-like problem. After the continuous phase change process of soil water is divided into a finite number of substeps, the Stefan problem of a multi-phase material is obtained. A similarity solution is found and determined. In order to get the right solution of the nonlinear equations, a variable substitution technique is introduced. The approximate solution is verified by the numerical results of the continuous phase change model of soil freezing process. Finally, for practical purpose, the advancing factor of the freezing front and the mean squared error of the temperature caused by the measurement errors are defined. Computational examples concerning the effect of different parameters on the advancing factor of the freezing front and the effect of the measurement errors on the accuracy of the solution are presented and discussed.     

基于邓肯-张的冻结粉质粘土本构模型试验研究

为研究冻结粉质粘土强度和变形特性,以沈阳地铁DK11+395联络通道处人工冻结粉质粘土为研究对象,通过冻土三轴剪切试验,研究了不同试验条件下冻结粉质粘土的强度和变形特性。试验结果表明：围压、温度和试件初始含水量是影响冻结粉质粘土强度和变形的主要因素。冻结粉质粘土偏应力-应变曲线呈应变硬化型,其破坏强度和切线弹性模量随围压和试件初始含水量的增加而增大,随温度的升高而减小,破坏偏应力比Rf取值在0.79~0.96之间。基于试验数据建立了以上述三因素为影响因子的冻结粉质粘土Duncan-Chang模型。通过回归分析,建立了模型参数a和b与围压、初始含水量和温度之间的线性回归公式。将依据模型计算的偏应力-应变曲线与对比试验曲线相比较,发现两者具有较好的吻合程度,说明建立的模型能够准确反映围压、初始含水量和温度等条件对冻结粉质粘土强度和变形的影响规律。上述研究成果为冻结粉质粘土强度和变形特性的研究提供了参考,为人工冻结法施工提供了指导,具有重要的理论意义和工程应用价值。     

基于WOA-BP神经网络的超低温冻土抗压强度预测模型研究

为获得超低温冻土抗压强度预测模型, 探究超低温状态下冻土的物理性质及力学性质的变化, 对含水率19%, 22%, 25%和28%的低液限黏土土样进行?180 °C ~ ?10 °C的单轴压缩强度试验, 并测量?80 °C ~ ?10 °C土样的未冻水含量, 建立基于WOA-BP神经网络和BP神经网络的预测模型, 探究含水率、温度、未冻水含量与超低温冻土抗压强度关系. 预测结果表明: 含水率、温度、未冻水含量与超低温冻土抗压强度存在复杂的非线性关系, 特别是在?180 °C ~ ?80 °C区间内, 现有的线性拟合公式已无法准确预测该区间内冻土抗压强度; 基于WOA-BP神经网络预测模型的整体预测效果较好, 其绝对误差平均值为1.167 MPa, 相对误差平均值为7.62%, BP神经网络预测模型的绝对误差平均值为8.462 MPa, 相对误差平均值为47.99%. 基于鲸鱼优化算法的BP神经网络预测模型预测误差明显小于BP神经网络预测模型及线性拟合值, 更接近实测值. 该预测模型具有较高精确度, 能有效解决超低温冻土抗压强度与其影响因素间复杂的非线性关系, 可为人工冻结技术在地层应急工程中的应用提供参考.      

Stochastic and upscaled analytical modeling of fines migration in porous media induced by low-salinity water injection

Fines migration induced by injection of low-salinity water(LSW) into porous media can lead to severe pore plugging and consequent permeability reduction. The deepbed filtration(DBF) theory is used to model the aforementioned phenomenon, which allows us to predict the effluent concentration history and the distribution profile of entrapped particles. However, the previous models fail to consider the movement of the waterflood front. In this study, we derive a stochastic model for fines migration during LSW flooding, in which the Rankine-Hugoniot condition is used to calculate the concentration of detached particles behind and ahead of the moving water front. A downscaling procedure is developed to determine the evolution of pore-size distribution from the exact solution of a large-scale equation system. To validate the proposed model,the obtained exact solutions are used to treat the laboratory data of LSW flooding in artificial soil-packed columns. The tuning results show that the proposed model yields a considerably higher value of the coefficient of determination, compared with the previous models, indicating that the new model can successfully capture the effect of the moving water front on fines migration and precisely match the effluent history of the detached particles.     

Mathematical model of water-steam phase transitions in hydrothermal reservoirs

The problem of steam production from a water-saturated hydrothermal reservoir is considered. It is shown that the introduction of a evaporation surface separating the gas and liquid phases leads to superheating of the water in a zone ahead of the front. This contradiction is removed by introducing of an extended phase transitions zone between the single-phase zones. In this case the problem contains two unknown moving boundaries considered as surfaces of discontinuity of the moisture content.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 98–105, November–December, 1994.     

Numerical and experimental investigation of variable phase transformation number effect in porous media during freezing process

A model is proposed to investigate heat and moisture transfer in porous media during freezing process based on Luikov’s model by considering the effect of variation of phase transformation number, ε. This parameter has been mostly used as a constant by researchers. Three-dimensional Luikov’s equations are considered and solved numerically. The model is compared with obtained experimental data. It is shown that the effect of variable phase transformation number is noticeable in heat and moisture transfer process.     

冻土水热力耦合作用的数学模型及数值模拟

将冻土体视为空间弹性体,提出了土体在冻结过程中水分场、温度场、应力场三场耦合的一般数学模型,并给出了相应的离散方程及其解法,最后给出了数值算例,并与实测值比较,证明了该模型和算法的正确性。     

Freezing and thawing porous media: experimental study with a dielectric capacitive method

A capacitive sensor-based apparatus has been used to study the ice/water phase change in consolidated porous media subjected to freezing and thawing. This technique relies on the dielectric properties of water, ice, air, and the mineral substrate in the radio-frequency range. It gives directly the freezing and thawing temperature depressions and indirectly provides an estimation of pore size distribution through the Gibbs–Thomson relation. It also holds good promise for evaluating the amount of liquid water in frozen porous media by combining drying and freezing tests. To cite this article: T. Fen-Chong, A. Fabbri, C. R. Mecanique 333 (2005).     

A model of a casting

A model of a casting is presented which describes the freezing of a mushy zone, growing with a dynamically calculated undercooling at the dendrite tips. Equiaxed grains are introduced ahead of a columnar front. The model resembles a combination of the Stefan and mushy zone problems.     

Heating zone dynamics in in situ combustion

The integrodifferential equation of the quasisteady regime of a moving in situ combustion front is obtained and its exact solution is constructed in a particular case; the possibility of the heat generated at the combustion front being projected into the region ahead of the front is analyzed and the heating zone dynamics in the reservoir and the surrounding rock are investigated. In a number of studies of in situ combustion it is assumed that an increase in the water-air factor or, what amounts to the same thing, an increase in convection velocity in the reservoir leads to the total transfer of the heat into the region ahead of the combustion front [1–3]. In [3] the area of the heating zone ahead of the combustion front was calculated in accordance with the Marx-Longenheim model [4]. Below, on the basis of exact solutions of model problems it is shown that in the case of quasisteady Newtonian heat transfer between the surrounding medium, when the latter is assumed to be a thermal reservoir, i.e., maintain a constant temperature, this projection of heat is possible if the convection velocity exceeds the velocity of the combustion front. In the case of unsteady heat transfer in accordance with the Leverrier model there is no total projection of heat into the region in question; in the steady-state regime a limited heating zone, proportional in depth to the square of the difference of the convection and combustion front velocities, is formed ahead of the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 166–172, July–August, 1987.The author wishes to thank V. M. Entov for his valuable advice and useful discussions.     

多圈管冻结模型试验水热力分析研究

人工多圈管冻结过程中的温度场、应力场及水分场的相互作用,是一个非线性多场耦合问题,影响因素多. 本文以淮南顾北矿作为模型设计原型,通过模型试验对多圈管冻结土体过程的温度场、应力场及水分场变化进行研究,获得了冻结温度场、冻结压力及含水量随冻结时间的变化规律,其成果对建立水热力耦合数学模型提供可靠依据并能更好的指导矿井工程实践.     

Influence of root resistivity on plant water uptake mechanism,Part II: analytical solutions for low/moderate soil-root conductivity ratio

A one-dimensional approximate analytical model, which preserves the main features of soil-crop-atmospheric hydrodynamics, has been suggested for plant roots of low soil-root conductivity ratio (SRCR). The proposed approach involves physically based concepts, such as mass balance equation, Darcy’s law, and related water uptake and plant transpiration functions. Two main assumptions have been made to derive the analytical solution: (1) gravitational flow is adopted and (2) the uniform soil moisture distribution within the root water activity zone is supposed. The mass balance equation in its integral form is solved by the method of characteristics. This leads to the two functional equations for soil pressure head and root potential, which can be solved simultaneously by using common software. The model has been further verified against the numerical one. The model represents a reasonable compromise between the complicated mechanism of unsaturated water flow with root water uptake (RWU) and still insufficient knowledge of the soil-plant-atmospheric continuum. It is able to account for temporal fluctuations in root activity zone and provides a relatively simple algorithm for investigation of RWU-mechanism. Besides the theoretical and applicative importance, this flow model yields water and velocity distributions within soil profile, and, thereby, constitutes a preliminary step toward solution of contaminant transport problems in vadose zone. Deceased     

Crystallization,pore relaxation and micro-cryosuction in cohesive porous materials

A poro-elastic analysis is undertaken to account for the pressure time history of water-infiltrated pores within a material subjected to freezing. The thermodynamic-mechanical equilibrium of undercooled water and ice crystal, and Poiseuille-like flow through the connection channels, combine to reveal three successive mechanisms: in-pore crystallization, in-pore partial melting and a micro-cryosuction process, driving liquid water from the yet unfrozen pores to the frozen sites. The model turns out to be apt to predict the macroscopic relaxation process observed at the onset of crystallization as reported in the literature for cement-based materials. To cite this article: O. Coussy, T. Fen-Chong, C. R. Mecanique 333 (2005).     

Self-similar solution of the thawing soil problem

A mathematical model of phase transitions in frozen soils containing unfrozen water is proposed. It is shown that phase transitions in frozen soils always occupy an extended zone. The problem of the interaction of frozen rock with a salt solution is solved on the assumption that the interface between the solution and the frozen rock is permeable both for the liquid and for the dissolved impurity. This problem arises, for example, in drilling wells in frozen ground, when the circulating drilling solution is an aqueous salt solution [7]. A series of natural processes is based on the interaction between groundwaters having different, possibly negative, temperatures and different degrees of mineralization and the surrounding frozen rock [8] and on the thawing of the frozen bed of northern seas in contact with saline seawater [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 136–142, November–December, 1988.     

Nonlinear problem of unsaturated frozen soil thawing in the presence of capillary forces

The problem of ice melting in unsaturated frozen soil in the presence of the capillary pressure in the water-air zone is formulated. The complete system of boundary conditions on the phase transition front is derived. For solving the nonlinear problem a numerical method is proposed. The dependence of the water saturation distribution on the form of the Leverett function, the capillary pressure, and the external pressure and temperature gradients is investigated. In the limiting case of saturated frozen soil the numerical and analytical solutions are compared.