A fully coupled thermo-hydro-mechanical model for unsaturated porous media

In examining potential host rocks for such purposes as the disposal of high-level radioactive wastes,it is important to understand the coupled thermo-hydro-mechanical（THM） behavior of a porous medium.A rigorous and fully unified coupled thermo-hydro-mechanical model for unsaturated porous media is required to simulate the complex coupling mechanisms involved.Based on modified Darcy＇s and Fourier＇s laws,equations of mechanical equilibrium,mass conservation and energy conservation are derived by introducing void ratio and volumetric liquid water content into the model.The newly derived model takes into account the effects of temperature on the dynamic viscosity of liquid water and void ratio,the influence of liquid flow on temperature gradient（thermo-osmosis）,the influence on mass and heat conservation equations,and the influence of heat flow on water pressure gradient and thermal convection.The new coupled THM constitutive model is constructed by a finite element program and is used to simulate the coupled behavior of a tunnel during excavation,ventilation and concrete lining stages.Oil and gas engineering,underground disposal of nuclear waste and tunnel engineering may be benefited from the development of the new model.

Coupled thermo-hydro-mechanical modeling of frost heave and water migration during artificial freezing of soils for mineshaft sinking

Artificial freezing of water-bearing soil layers composing a sedimentary deposit can induce frost heave and water migration that affect the natural stress-strain state of the soil layers and freezing process.In the present paper,a thermo-hydro-mechanical(THM)model for freezing of water-saturated soil is proposed to study the effects of frost heave and water migration in frozen soils on the formation of a frozen wall and subsequent excavation activity for sinking a vertical shaft.The governing equations of the model are formulated relative to porosity,temperature,and displacement which are considered as primary variables.The relationship between temperature,pore water,and ice pressure in frozen soil is established by the Clausius-Clapeyron equation,whereas the interaction between the stress-strain behavior and changes in porosity and pore pressure is described with the poromechanics theory.Moreover,constitutive relations for additional mechanical deformation are incorporated to describe volumetric expansion of soil during freezing as well as creep strain of soil in the frozen state.The ability of the proposed model to capture the frost heave of frozen soil is demonstrated by a comparison between numerical results and experimental data given by a one-sided freezing test.Also to validate the model in other freezing conditions,a radial freezing experiment is performed.After the validation procedure,the model is applied to numerical simulation of artificial freezing of silt and sand layers for shaft sinking at Petrikov potash mine in Belarus.Comparison of calculated temperature with thermal monitoring data during active freezing stage is presented.Numerical analysis of deformation of unsupported sidewall of a shaft inside the frozen wall is conducted to account for the change in natural stress-strain state of soil layers induced by artificial freezing.

Coupled thermo-hydro-mechanical simulation of CO2 enhanced gas recovery with an extended equation of state module for TOUGH2MP-FLAC3D

As one of the most important ways to reduce the greenhouse gas emission,carbon dioxide（CO2）enhanced gas recovery（CO2-EGR） is attractive since the gas recovery can be enhanced simultaneously with CO2sequestration.Based on the existing equation of state（EOS） module of TOUGH2 MP,extEOS7C is developed to calculate the phase partition of H2O-CO2-CH4-NaCl mixtures accurately with consideration of dissolved NaCI and brine properties at high pressure and temperature conditions.Verifications show that it can be applied up to the pressure of 100 MPa and temperature of 150℃.The module was implemented in the linked simulator TOUGH2MP-FLAC3 D for the coupled hydro-mechanical simulations.A simplified three-dimensional（3D）1/4 model（2.2 km×1 km×1 km） which consists of the whole reservoir,caprock and baserock was generated based on the geological conditions of a gas field in the North German Basin.The simulation results show that,under an injection rate of 200,000 t/yr and production rate of 200,000 sm3/d,CO2breakthrough occurred in the case with the initial reservoir pressure of 5 MPa but did not occur in the case of 42 MPa.Under low pressure conditions,the pressure driven horizontal transport is the dominant process;while under high pressure conditions,the density driven vertical flow is dominant.Under the considered conditions,the CO2-EGR caused only small pressure changes.The largest pore pressure increase（2 MPa） and uplift（7 mm） occurred at the caprock bottom induced by only CO2injection.The caprock had still the primary stress state and its integrity was not affected.The formation water salinity and temperature variations of ±20℃ had small influences on the CO2-EGR process.In order to slow down the breakthrough,it is suggested that CO2-EGR should be carried out before the reservoir pressure drops below the critical pressure of CO2.

THM Coupled Modeling in Near Field of an Assumed HLW Deep Geological Disposal Repository

One of the most suitable ways under study for the disposal of high-level radioactive waste (HLW) is isolation in deep geological repositories. It is very important to research the thermo-hydro- mechanical (THM) coupled processes associated with an HLW disposal repository. Non-linear coupled equations, which are used to describe the THM coupled process and are suited to saturated-unsaturated porous media, are presented in this paper. A numerical method to solve these equations is put forward, and a finite element code is developed. This code is suited to the plane strain or axis-symmetry problem. Then this code is used to simulate the THM coupled process in the near field of an ideal disposal repository. The temperature vs. time, hydraulic head vs. time and stress vs. time results show that, in this assumed condition, the impact of temperature is very long (over 10 000 a) and the impact of the water head is short (about 90 d). Since the stress is induced by temperature and hydraulic head in this condition, the impact time of stress is the same as that of temperature. The results show that THM coupled processes are very important in the safety analysis of an HLW deep geological disposal repository.

Comparison of numerical codes for coupled thermo-hydro-mechanical simulations of fractured media

Geo-energy and geo-engineering applications,such as improved oil recovery(IOR),geologic carbon storage,and enhanced geothermal systems(EGSs),involve coupled thermo-hydro-mechanical(THM)processes that result from fluid injection and production.In some cases,reservoirs are highly fractured and the geomechanical response is controlled by fractures.Therefore,fractures should explicitly be included into numerical models to realistically simulate the THM responses of the subsurface.In this study,we perform coupled THM numerical simulations of water injection into naturally fractured reservoirs(NFRs)using CODE_BRIGHT and TOUGH-UDEC codes.CODE_BRIGHT is a finite element method(FEM)code that performs fully coupled THM analysis in geological media and TOUGH-UDEC sequentially solves coupled THM processes by combining a finite volume method(FVM)code that solves nonisothermal multiphase flow(TOUGH2)with a distinct element method(DEM)code that solves the mechanical problem(UDEC).First,we validate the two codes against a semi-analytical solution for water injection into a single deformable fracture considering variable permeability based on the cubic law.Then,we compare simulation results of the two codes in an idealized conceptual model that includes one horizontal fracture and in a more realistic model with multiple fractures.Each code models fractures differently.UDEC calculates fracture deformation from the fracture normal and shear stiffnesses,while CODE_BRIGHT treats fractures as equivalent porous media and uses the equivalent Young’s modulus and Poisson’s ratio of the fracture.Finally,we obtain comparable results of pressure,temperature,stress and displacement distributions and evolutions for the single horizontal fracture model.Despite some similarities,the two codes provide increasingly different results as model complexity increases.These differences highlight the challenging task of accurately modeling coupled THM processes in fractured media given their high nonlinearity.

Numerical thermo-hydro-mechanical modeling of compacted bentonite in China-mock-up test for deep geological disposal

The China-mock-up test is to evaluate the performance of the compacted Gaomiaozi （GMZ） bentonite under coupled thermo-hydro-mechanical （THM） conditions in deep geological disposal. A numerical study of the test is conducted in this paper. The principal THM characteristics of the bentonite are presented at first. A THM model is then presented to tackle the complex coupling behavior of the bentonite. The model of Alonso-Gens is incorporated to reproduce the mechanical behavior of the bentonite under unsaturated conditions. With the proposed model, numerical simulations of the China-mock-up test are carried out by using the code of LAGAMINE. The time variations associated with the temperature, degree of saturation, suction and swelling pressure of the compacted bentonite are studied. The results suggest that the proposed model is able to reproduce the mechanical behavior of the bentonite, and to predict moisture motion under coupled THM conditions.

Thermo-hydro-mechanical modeling of fault discontinuities using zero-thickness interface element

In this paper,a coupled thermo-hydro-mechanical(THM)simulation in a faulted deformable porous medium is presented.This model involves solving the mass conservation,linear momentum balance,and energy balance equations which are derived from the Biot’s consolidation theory.Fluid pore pressure,solid displacement,and temperature are chosen as initial variables in these equations,and the finite element method in combination with the interface element is used for spatial discretization of continuous and discontinuities(fault)parts of the medium to solve the equations.The main purpose of this study is providing precise formulations,applicability,and ability of the triple-node zero-thickness interface element in THM modeling of faults.It should be noted that the system of equations is solved using a computer code written in Matlab program.In order to verify the developed method,simulations of index problems such as Mandel’s problem,and coupled modeling of a faulted porous medium and a faulted aquifer are presented.The modeling results obtained from the developed method show a very good agreement with those by other modeling methods,which indicates its accuracy.

Rheological numerical simulation for thermo-hydro-mechanical coupling analysis for rock mass

Under the environment of seepage field, stress field and temperature field interaction and influence, the three fields will not only produce coupling effect, but also have deformation with time due to the rheological behavior of rock mass. In the paper, based on the fundamental theories of rock mass coupling theory and rheological mechanics, the rheological model for fully coupled thermo-hydro-mechanical analysis for rock mass was set up, and the corresponding constitutive relationship, the conservation equation of mass and the conservation equation of energy were given, and the finite element formulas were derived for coupling analysis of rock mass. During establishing governing equations, rock mass was assumed approximately as macro-equivalent continuum medium. The obtained rheological numerical model for fully coupled thermo-hydro-mechanical analysis can be used for analyzing and predicting the long-term stability of underground caverns and slope engineering under the condition of thermo-hydro-mechanical coupling with rheological deformation.

Two-phase flow thermo-hydro-mechanical modeling for a water flooding field case

Simulation of subsurface energy system involves multi-physical processes such as thermal,hydraulical,and mechanical(THM)processes,and requires a so-called THM coupled modeling approach.THM coupled modeling is commonly performed in geothermal energy production.However,for hydrocarbon extraction,we need to consider multiphase flow additionally.In this paper,we describe a three-dimensional numerical model of non-isothermal two-phase flow in the deformable porous medium by integrating governing equations of two-phase mixture in the porous media flow in the reservoir.To account for inter-woven impacts in subsurface condi-tions,we introduced a temperature-dependent fluid viscosity and a fluid density along with a strain-dependent reservoir permeability.Subsequently,we performed numerical experiments of a ten-year water flooding pro-cess employing the open-source parallelized code,OpenGeoSys.We considered different well patterns with colder water injection in realistic scenarios.Our results demonstrate that our model can simulate complex interactions of temperature,pore pressure,subsurface stress and water saturation simultaneously to evaluate the recovery per-formance.High temperature can promote fluid flow while cold water injection under non-isothermal conditions causes the normal stress reduction by significant thermal stress.Under different well patterns the displacement efficiency will be changed by the relative location between injection and production wells.This finding has provided the important reference for fluid flow and induced stress evolution during hydrocarbon exploitation under the environment of large reservoir depth and high temperature.

Thermal-hydro-mechanical coupling damage model of brittle rock

Based on fluid mechanics, thermodynamics and damage mechanics, thermal-hydro-mechanical （THM） coupling damage model of brittle rock is established by analyzing THM coupling mechanism, where THM coupling damage variable DTHM is dominated by TH coupling damage variable DTH, TM coupling damage variable DTM and HM coupling damage variable DHM, and DTH is firstly expressed in term of dimensionless total thermal conductivity of the water Nu. Permeability test, uni-axial compression test and THM coupling test are conducted to measure the permeability, elastic modulus and THM coupling stress-strain curves of brittle rock. The tested values of THM coupling elastic modulus E＇HM are in good agreement with the predicted values of THM coupling elastic modulus ETHM, which can verify the newly established THM coupling damage model.

Joints in unsaturated rocks:Thermo-hydro-mechanical formulation and constitutive behaviour

A formulation for the coupled analysis of thermo-hydro-mechanical （THM） problems in joints is first presented. The work involves the establishment of equilibrium and mass and energy balance equations. Balance equations were formulated taking into account two phases： water and air. The joint element developed was implemented in a general purpose finite element computer code for THM analysis of porous media （Code_Bright）. The program was then used to study a number of cases ranging from laboratory tests to large scale in situ tests. A numerical simulation of coupled hydraulic shear tests of rough granite joints is first presented. The tests as well as the model show the coupling between permeability and the deformation of thejoints. The experimental investigation was focused on the effects of suction on the mechanical behaviour of rock joints. Laboratory tests were performed in a direct shear cell equipped with suction control. Suction was imposed using a vapour forced convection circuit connected to the cell and controlled by an air pump. Artificial joints of Lilla claystone were prepared.Joint roughness of varying intensity was created by carving the surfaces in contact in such a manner that rock ridges of different tip angles were formed. These angles ranged from 0° （smooth joint） to 45° （very rough joint profile）. The geometric profiles of the two surfaces in contact were initially positioned in a ＂matching＂ situation. Several tests were performed for different values of suctions （200, 100, and 20 MPa） and for different values of vertical stresses （30, 60, and 150 kPa）. A constitutive model including the effects of suction and joint roughness is proposed to simulate the unsaturated behaviour of rock joints. The new constitutive law was incorporated in the code and experimental results were numerically simulated.

Parametric study of thermo-hydro-mechanical response of claystone with consideration of steel corrosion

In this paper,the thermo-hydro-mechanical(THM)response of claystone is studied via a series of parametric studies,considering the evolution of mechanical properties and deformation behavior of corroded steel.The numerical simulations are performed by using a coupled THM finite element code and two different constitutive models:a visco-elastoplastic model for geological formation and a von Mises type model for steel liner.The mechanical properties and deformation behavior of corroded steel are described in a conceptual model.Finally,a disposal tunnel supported by a steel liner is studied and a series of parametric studies is defined to demonstrate the corrosion effects of steel liner on the THM response of the claystone.The comparison of different numerical calculations exhibits that the volumetric expansion related to corrosion products has an important impact on the stress and displacement fields in the claystone surrounding the disposal tunnel.However,the evolutions of temperature and liquid pressure in the claystone are essentially controlled by its THM properties and independent of the steel corrosion.

Thermal-hydro-mechanical coupled analysis of unsaturated frostsusceptible soils

Damage caused by frost heave leads to costly maintenance in cold regions, like Hokkaido, Japan. Therefore, thestudy of the frost mechanism with experimental and numerical methods has been of great interest. Numerousmodels have been developed to describe the freezing process of saturated soil, which differs from the partiallysaturated conditions in the field. In fact, most subsurface soils are unsaturated. The freezing process of partiallysaturated soils is more complex than saturated soils, as the governing equations show strongly nonlinear characteristics. This study proposes a thermo-hydro-mechanical coupled model considering the heat transfer, waterinfiltration, and deformation of partially saturated soil to reproduce the freezing process of partially saturatedfrost susceptible soils distributed in Hokkaido. This model better considers the water-ice phase change and soilfreezing characteristic curve (SFCC) during freezing under field conditions. The results from the multiphysicssimulations agree well with the frost heave and water migration data from frost heave tests of Touryo soil andFujinomori soil. In addition, this study discussed the influence of the various factors on frost heave amount,including temperature gradients, overburden pressures, water supply conditions, cooling rates, and initial saturation. The simulation results indicate that the frost heave ratio is proportional to the initial degree of saturationand is inversely proportional to the cooling rate and overburden pressure.Moreover, simulation under the open system generates much more frost heave than under the closed system.Finally, the main features of the proposed model are revealed by simulating a closed-system frost heave test. Thesimulation results indicate that the proposed model adequately captures the coupling characteristics of water andice redistribution, temperature development, hydraulic conductivity, and suction in the freezing process. Togetherwith the decreased hydraulic conductivity, the increased suction controls the water flow in the freezing zone. Theinflow water driven by cryogenic suction gradient feeds the ice formation, leads to a rapid increase in total watercontent, expanding the voids that exceed the initial porosity and contributing to the frost heave.

工程尺度缓冲材料热-水-力多场耦合数值模拟研究

缓冲材料作为填充在废物罐与地质体之间重要的人工屏障,对高放废物处置库的长期安全至关重要。以工程尺度缓冲材料热-水-力多场耦合大型模型试验系统(China-Mock-up)为研究对象,采用有限元数值模拟软件LAGAMINE,考虑试验过程中复杂的边界条件与材料属性,实现了近5 a试验数据的定量模拟。模拟结果可准确预测试验系统内部不同特征点温度随室温周期性波动及线性增长这一动态变化规律;能够较好反映不同特征点相对湿度随时间的行为演化趋势,在加热器附近区域呈现出先干燥后饱和的现象,远离加热器区域则逐渐增大;模拟的总应力与实测试验数据间表现较好地一致性,能够反映试验台架内部不同特征点的总应力随时间逐渐增大这一演化过程。揭示了多场耦合条件下缓冲材料(膨润土)温度、湿度及应力的相互作用关系,为深入认识处置库环境下缓冲材料行为演化特征提供了重要的参考依据。

Effects of fracture evolution and non-Darcy flow on the thermal performance of enhanced geothermal system in 3D complex fractured rock

In fractured geothermal reservoirs,the fracture networks and internal fluid flow behaviors can significantly impact the thermal performance.In this study,we proposed a non-Darcy rough discrete fracture network(NR-DFN)model that can simultaneously consider the fracture evolution and non-Darcy flow dynamics in studying the thermo-hydro-mechanical(THM)coupling processes for heat extraction in geothermal reservoir.We further employed the model on the Habanero enhanced geothermal systems(EGS)project located in Australia.First,our findings illustrate a clear spatial-temporal variation in the thermal stress and pressure perturbations,as well as uneven spatial distribution of shear failure in 3D fracture networks.Activated shear failure is mainly concentrated in the first fracture cluster.Secondly,channeling flow have also been observed in DFNs during heat extraction and are further intensified by the expansion of fractures driven by thermal stresses.Moreover,the combined effect of non-Darcy flow and fracture evolution triggers a rapid decline in the resulting heat rate and temperature.The NR-DFN model framework and the Habanero EGS's results illustrate the importance of both fracture evolution and non-Darcy flow on the efficiency of EGS production and have the potential to promote the development of more sustainable and efficient EGS operations for stakeholders.

单向冻结时开放条件下饱和砂岩冻胀试验及THM耦合冻胀模型

为研究寒区岩石在梯度温度场中补水条件下的冻胀变形规律,进行了单向冻结时开放条件下饱和砂岩冻胀试验。试验结果表明,单向冻结时开放条件下饱和岩石冻胀过程中,沿冻结方向的冻胀位移变化过程可分为冷缩阶段、原位冻胀阶段、分凝冻胀阶段3个阶段。分凝冻胀阶段冻结锋面趋于稳定,冻胀变形持续增长,与时间基本呈线性关系。此外,分凝冻胀阶段补水量换算的迁移水分凝冻胀位移与冻结方向冻胀位移比较接近。随着平均温度梯度增大,分凝冻胀变形速率增大,且分凝冰位置与平均温度梯度线性相关。然后,建立了考虑孔隙水原位冻胀与迁移水分凝冻胀的THM耦合冻胀模型。模型中,孔隙水原位冻胀计算基于未冻水含量,并引入约束系数表征岩石骨架对孔隙水冻胀约束程度;迁移水分凝冻胀计算基于分凝势理论,水分迁移速率与冻结缘处的温度梯度成正比。模型计算结果与试验结果对比表明,建立的THM耦合冻胀模型能够比较准确地计算单向冻结时开放条件下饱和岩石冻胀位移,并能够模拟出分凝冻胀时分凝冰层引起的位移突变及分凝冰位置,可用于寒区冻胀敏感性岩石开放条件下冻胀变形计算。

Simulations of THM processes in buffer-rock barriers of high-level waste disposal in an argillaceous formation

The main objective of this paper is to investigate and analyse the thermo-hydro-mechanical（THM） coupling phenomena and their influences on the repository safety.In this paper,the high-level waste（HLW） disposal concept in drifts in clay formation with backfilled bentonite buffer is represented numerically using the CODE BRIGHT developed by the Technical University of Catalonia in Barcelona.The parameters of clay and bentonite used in the simulation are determined by laboratory and in situ experiments.The calculation results are presented to show the hydro-mechanical（HM） processes during the operation phase and the THM processes in the after-closure phase.According to the simulation results,the most probable critical processes for the disposal project have been represented and analyzed.The work also provides an input for additional development regarding the design,assessment and validation of the HLW disposal concept.

A new numerical model of ring shear tester for shear band soil considering friction-induced thermal pressurization

In this study,a new numerical model of ring shear tester for shear band soil of landslide was established.The special feature of this model is that it considers the mechanism of friction-induced thermal pressurization,which is potentially an important cause of high-speed catastrophic landslides.The key to the construction of this numerical ring shear model is to realize the THM(thermo-hydro-mechanical)dynamic coupling of soil particles,which includes the processes of frictional heating,thermal pressurization,and strength softening during shearing of solid particles.All of these are completed by using discrete element method.Based on this new model,the characteristics of shear stress change with shear displacement,as well as the variation of temperature and pore pressure in the specimen,are studied at shear rates of 0.055 m/s,0.06 m/s,0.109 m/s and 1.09 m/s,respectively.The results show that the peak strength and residual strength of specimen are significantly reduced when the mechanism of frictioninduced thermal pressurization is considered.The greater the shear rate is,the higher the temperature as well as the pore pressure is.The effect of shear rate on the shear strength is bidirectional.The simulation results demonstrate that this model can effectively simulate the mechanism of friction-induced thermal pressurization of shear band soil during ring shear process,and the shear strength softening in the process.The new numerical ring shear model established in this study is of great significance for studying the dynamic mechanism of high-speed catastrophic landslides.

工质密度和储层渗透率演化对EGS系统传热效能的影响

工质进入地热储层后的流动和采热问题是典型的热流固(THM)耦合问题。工质的密度、地热储层的渗透率在热开采过程中受THM耦合作用影响,导致地热储层传热效能的变化。为了探究这一变化,基于等效多孔介质模型建立了THM完全耦合的二维有限元模型和计算程序,模拟了增强地热系统(EGS)长期热开采过程,分析了岩石温度、孔压、储层变形的演化规律,研究了密度、渗透率演化对EGS采热性能的影响。结果表明:在温度、地应力、孔压等因素中,温度是稳定开采阶段对流体密度演化和渗透率演化影响最大的因素。但对于最终储层的传热效能而言,密度演化延缓了储层出口温度的冷却速度,提高了净热提取率;而渗透率演化虽然加速了出口温度的冷却,也提高了净热提取率。研究丰富了斜压流体THM耦合模型的应用,为EGS地热开采和储层管理提供了重要参考。

岩石损伤过程中的热-流-力耦合模型及其应用初探

岩石损伤过程热-流-力(THM)耦合问题的研究对于深部采矿等许多工程领域都具有重要的理论意义。以岩石的损伤为主线,在多场耦合分析方程中引入损伤变量,基于质量守恒和能量守恒原理,提出岩体损伤过程中的THM耦合模型。通过把均匀弹性介质THM耦合响应的模拟结果与理论分析结果进行对比,验证了程序及有限元实施的正确性。然后,用该耦合模型进行了不同地应力条件下流固耦合过程的数值模拟,探讨了水压力对于岩石损伤过程的作用机制。数值模拟表明,水压力导致了拉伸损伤范围的扩大和损伤程度的加剧,同时亦对剪切损伤具有抑制作用。