Numerical Modeling and Spatial Moment Analysis of Solute Mobility and Spreading in a Coupled Fracture-Skin-Matrix System

This study deals with transport of solutes through a saturated sub-surface rock formation with well-defined horizontal parallel fractures. For this purpose, a simplified conceptual model consisting of a single fracture and its associated rock-matrix is considered in the presence of a fracture-skin in order to study the mobility and mixing of solutes along the fracture. In this paper, a coupled fracture-skin-matrix system is modeled numerically using finite difference method in a pseudo two-dimensional domain with a constant continuous source at fracture inlet. Flow and transport processes are considered parallel to the fracture axis, while the transport processes in fracture-skin as well as in rock-matrix are considered perpendicular to the fracture axis. Having obtained the concentration distribution along the fracture, method of spatial moments is employed to study the mobility and spreading of solutes. Sensitivity analyses have been done to understand the effect of various fracture-skin parameters like porosity, thickness, and diffusion coefficient. Further, the influence of non-linear sorption and radioactive decaying of solutes are carried out for different sorption intensities and decay constants. Results suggest that the presence of fracture-skin significantly influences the mobility and spreading of solutes along the fracture in comparison with a coupled fracture-matrix system without fracture-skin.     

http://www.sciencedirect.com/science/article/pii/S1674987112000369

A numerical model is developed for describing the transport of virus in a fracture-matrix coupled system with fracture-skin.An advective dispersive virus transport equation,including firstorder sorption and inactivation constant is used for simulating the movement of viruses.Implicit finite-difference numerical technique is used to solve the coupled non-linear governing equations for the triple continuum model consisting of fracture,fracture-skin and the rock-matrix.A varying grid is adopted at the fracture and fracture-skin interface to capture the mass transfer.Sensitivity analysis was performed to investigate the effect of various properties of the fracture-skin as well as viruses on the virus concentration in the fractured formation with fracture-skin.Simulation results suggest that the virus concentration in the fracture decreases with increment in the fracture-skin porosity,fracture-skin diffusion coefficient,mass transfer coefficient,inactivation constant and sorption distribution coefficient, and with reduction in the fracture aperture.     

http://www.sciencedirect.com/science/article/pii/S1674987111001277

A numerical model is developed for investigating the evolution of fracture permeability in a coupled fracture-matrix system in the presence of fracture-skin with simultaneous colloidal and bacterial tr...     

基于电阻率法的充填裂隙-基质中盐热运移试验研究

为探究盐、热示踪剂在裂隙-基质中示踪的有效性,设计了充填裂隙-基质试验模型,开展了不同示踪剂下的试验,结合不同测点的实时动态电阻率监测数据,研究充填裂隙-基质中示踪剂运移过程,并讨论基于电阻率法的盐、热示踪的有效性结果表明：（1）电阻率法可以揭示3种不同示踪剂注入充填裂隙-基质系统的过程以及裂隙-基质系统中裂隙的存在;（2）盐热示踪剂下裂隙与基质内的体积电导率变化率差异最为显著;（3）质量浓度与体积电导率拟合效果要优于温度与体积电导率拟合效果。这说明了基于电阻率法的示踪剂对刻画裂隙-基质中裂隙与基质位置的有效性,且盐热联合示踪剂效果最好。数据成果对野外电法勘探裂隙位置及其他非均质地层构造研究具有一定的参考价值。     

A 2D coupled hydro-thermal model for the combined finite-discrete element method

Based on the combined finite-discrete element method (FDEM), a two-dimensional coupled hydro-thermal model is proposed. This model can simulate fluid flow and heat transfer in rock masses with arbitrary complex fracture networks. The model consists of three parts: a heat conduction model of the rock matrix, a heat-transfer model of the fluid in the fracture (including the heat conduction and convection of fluid), and a heat exchange model between the fluid and rock at the fracture surface. Three examples with analytical solutions are given to verify the correctness of the coupled model. Finally, the coupled model is applied to hydro-thermal coupling simulations of a rock mass with a fracture network. The temperature field evolution, the effect of thermal conductivity of the rock matrix thermal conductivity and the fracture aperture on the outlet temperature are studied. The coupled model presented in this paper will enable the application of FDEM to study rock rupture driven by the effect of hydro-thermo-mechanical coupling in geomaterials such as in geothermal systems, petroleum engineering, environmental engineering and nuclear waste geological storage.

     

菜芜市冷家庄地热田地质特征浅析

莱芜市冷家庄地热田地热资源类型属层状兼带状,热源为高庄一冷家庄断裂沟通导热,盖层是第四系、古近系、石炭-二叠系。热储层为奥陶纪灰岩,该热储层顶板埋深2100m左右,热储层厚度由南向北逐渐增大,地热流体中富含氟、锶、偏硅酸等微量元素,为结垢非常严重,锅垢很多的腐蚀性水。经计算,奥陶纪热储层单井可采资源量为7．83×10^5m^3／a。     

Seepage-heat transfer coupling process of low temperature return water injected into geothermal reservoir in carbonate rocks in Xian County,China

Fracture seepage and heat transfer in the geothermal reservoir of carbonate rocks after the reinjection of low temperature geothermal return water is a complex coupling process,which is also the frontier of geothermal production and reinjection research. Based on the research of cascade comprehensive development of geothermal resources in Beijing-Tianjin-Hebei (Xian County),the carbonate geothermal reservoir of Wumishan formation in the geothermal field in Xian County is investigated. With the development of the discrete fracture network model and the coupling model of seepage and heat transfer,the numerical solution of seepage field and temperature field with known fracture network is reached using the finite element software COMSOL,and the coupling process of seepage flow and heat in carbonate rocks is revealed. The results show that the distribution of temperature field of fractured rocks in geothermal reservoir of carbonate rocks has strong non-uniformity and anisotropy. The fracture network is interpenetrated,which constitutes the dominant channel of water conduction,and along which the fissure water moves rapidly. Under the influence of convective heat transfer and conductive heat transfer,one of the main factors to be considered in the study of thermal breakthrough is to make the cold front move forward rapidly. When the reinjection and production process continues for a long time and the temperature of the geothermal reservoir on the pumping side drops to a low level,the temperature of bedrocks is still relatively high and continues to supply heat to the fissure water,so that the temperature of the thermal reservoir on the pumping side will not decrease rapidly to the water temperature at the inlet of reinjection,but will gradually decrease after a long period of time,showing an obvious long tail effect. The distribution of fractures will affect the process of seepage and heat transfer in carbonate reservoirs,which should be considered in the study of fluid thermal coupling in carbonate reservoirs.     

Thermo-hydro-mechanical modeling of fracturing porous media with two-phase fluid flow using X-FEM technique

In this paper, a fully coupled thermo-hydro-mechanical model is presented for two-phase fluid flow and heat transfer in fractured/fracturing porous media using the extended finite element method. In the fractured porous medium, the traction, heat, and mass transfer between the fracture space and the surrounding media are coupled. The wetting and nonwetting fluid phases are water and gas, which are assumed to be immiscible, and no phase-change is considered. The system of coupled equations consists of the linear momentum balance of solid phase, wetting and nonwetting fluid continuities, and thermal energy conservation. The main variables used to solve the system of equations are solid phase displacement, wetting fluid pressure, capillary pressure, and temperature. The fracture is assumed to impose the strong discontinuity in the displacement field and weak discontinuities in the fluid pressure, capillary pressure, and temperature fields. The mode I fracture propagation is employed using a cohesive fracture model. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm. It is shown that the effect of thermal expansion on the effective stress can influence the rate of fracture propagation and the injection pressure in hydraulic fracturing process. Moreover, the effect of thermal loading is investigated properly on fracture opening and fluids flow in unsaturated porous media, and the convective heat transfer within the fracture is captured successfully. It is shown how the proposed computational model is capable of modeling the fully coupled thermal fracture propagation in unsaturated porous media.     

A three‐dimensional integral equation model for calculating poro‐ and thermoelastic stresses induced by cold water injection into a geothermal reservoir

Poro‐mechanical and thermo‐mechanical processes change the fracture aperture and thus affect the water flow pattern in the fracture during the cold water injection into enhanced geothermal systems (EGS). In addition, the stresses generated by these processes contribute to the phenomenon of reservoir seismicity. In this paper, we present a three‐dimensional (3D) partially coupled poro‐thermoelastic model to investigate the poroelastic and thermoelastic effects of cold water injection in EGS. In the model, the lubrication fluid flow and the convective heat transfer in the fracture are modeled by the finite element method, while the pore fluid diffusion and heat conductive transfer in the reservoir matrix are assumed to be 3D and modeled by the boundary integral equation method without the need to discretize the reservoir. The stresses at the fracture surface and in the reservoir matrix are obtained from the numerical model and can be used to assess the variation of in situ stress and induced seismicty with injection/extraction. Application of the model shows that rock cooling induces large tensile stresses and increases fracture conductivity, whereas the rock dilation caused by fluid leakoff decreases fracture aperture and increases compressive total stresses around the injection zone. However, increases in pore pressure reduce the effective stresses and can contribute to rock failure, fracture slip, and microseismic activity. Copyright © 2009 John Wiley & Sons, Ltd.     

A fully coupled numerical modeling to investigate the role of rock thermo-mechanical properties on reservoir uplifting in steam assisted gravity drainage

One of the crucial consequences of steam assisted gravity drainage (SAGD) process is abnormal reservoir uplifting under thermal steam injection, which can significantly influence the reservoir rock deformation, specifically thin bed reservoirs and causes intensive failures and fractures into the cap rock formations. A thorough understanding of the influences of rock thermo-mechanical properties on reservoir uplifting plays an important role in preventing those aforementioned failures within design and optimization process in SAGD. In addition, coupling of reservoir porous medium and flowing of specific fluid with temperature as an additional degree of freedom with initial pore pressure and in-situ stress condition, are also very challenging parts of geomechanical coupled simulation which would be clearly explained. Thus, a fully coupled thermo-poro-elastic geomechanical model with finite element codes was performed in ABAQUS to investigate the role of rock thermo-mechanical parameters on reservoir vertical uplift during steam injection. It is clearly observed that, any increase in rock thermo-mechanical properties specifically rock’s thermal properties such as specific heat, thermal expansion, and formation’s thermal conductivity, have significant influences on reservoir uplift. So by coupling the temperature as an additional degree of freedom with the coupled pore-fluid stress and diffusion finite element model of SAGD process, the more realistic simulation will be conducted; hence, the errors related to not having heat as an additional degree of freedom will be diminished. In addition, Young’s modulus and specific heat are the rock thermo-mechanical parameters which have the maximum and minimum effects on the reservoir uplift, respectively.     

分布热源作用下单裂隙岩体三维水流-传热的半解析计算方法

针对高放射性核废物地下处置库近场饱和裂隙岩体环境,提出一种由分布热源、饱和单裂隙和两侧无限大岩石构成的三维水流-传热简化模型,建立了控制微分方程和基于拉氏变换域格林函数的积分方程;采用矩形单元把裂隙面域离散化,利用极坐标下的解析方法计算包含奇点的单元积分,利用数值方法计算分布热源和不包含奇点的单元积分,建立拉氏变换域的线性代数方程组,求解后,利用拉氏数值逆变换,计算任意时刻裂隙水和岩石的温度分布。对两个无内热源、流场确定的计算模型进行了计算,与仅考虑岩石沿裂隙面法向一维热传导的解析解进行了对比。计算分析了分布热源作用下饱和单裂隙岩体的三维水流-传热特征及其对裂隙水流速、岩石热传导系数和热源热流集度的敏感度。计算结果表明：与直接采用高斯数值积分相比,提出的解析法奇异积分精度较高;就裂隙水温度而言,单裂隙岩体三维水流-传热半解析计算方法与解析法得到的结果基本一致,但由于半解析计算方法考虑了岩石的三维热传导,使得裂隙水的上游温度较低,而下游温度较高;无分布热源作用时,岩石热传导系数越大,裂隙水温度越低;裂隙水流速越大,裂隙进水温度对裂隙水和岩石温度分布的影响越明显;由于受到裂隙水流动传热的作用,分布热源对裂隙水温度和岩石温度的影响在裂隙水流的下游区域比较显著。     

岩石导热热阻对裂隙对流换热的影响机制

增强型地热系统(EGS)中高温岩石与流体之间的对流换热特征一直以来是干热岩(HDR)研究的重要基础内容。岩石导热热阻对裂隙对流换热特征具有重要影响。为研究其具体影响,综合运用理论解析与数值模拟2种研究方法,通过对解析解讨论以及建立数值模型,研究两平行光滑平板之间的换热规律。结果表明：流体速度、传热边界层充分发展时,局部努塞尔特准数Nu_x为定值,与其他因素无关;局部对流换热系数h_x仅与流体热导率k和裂隙开度e有关,与其他因素无关。上下平板壁面热流恒定时,Nu_x为8.235;温度恒定时,Nu_x为7.54。然后建立多组导热热阻不同的岩石裂隙对流换热数值模型,发现岩石导热热阻增大,温度场进口段延长,对流换热系数h增大。岩石长度显著影响进口段占比,进而影响h的大小。h随着长度增大而减小;当岩石长度足够长时,进口段占比足够小,此时除k与e之外的参数对h基本没影响。并且发现实验室常用岩石长度为100 mm,而典型EGS工程中裂隙长度是米级的,建议室内实验重视岩石长度对裂隙对流换热特征的影响。     

Numerical analysis of thermal effects during carbon dioxide injection with enhanced gas recovery: a theoretical case study for the Altmark gas field

Prediction about reservoir temperature change during carbon dioxide injection requires consideration of all, often subtle, thermal effects. In particular, Joule?CThomson cooling (JTC) and the viscous heat dissipation (VHD) effect are factors that cause flowing fluid temperature to differ from the static formation temperature. In this work, warm-back behavior (thermal recovery after injection completed), as well as JTC and VHD effects, at a multi-layered depleted gas reservoir are demonstrated numerically. OpenGeoSys (OGS) is able to solve coupled partial differential equations for pressure, temperature and mole-fraction of each component of the mixture with a combination of monolithic and staggered approaches. The Galerkin finite element approach is adapted for space discretization of governing equations, whereas for temporal discretization, a generalized implicit single-step scheme is used. For numerical modeling of warm-back behavior, we chose a simplified test case of carbon dioxide injection. This test case is numerically solved by using OGS and FeFlow simulators independently. OGS differs from FeFlow in the capability of representing multi-componential effects on warm-back behavior. We verify both code results by showing the close comparison of shut-in temperature profiles along the injection well. As the JTC cooling rate is inversely proportional to the volumetric heat capacity of the solid matrix, the injection layers are cooled faster as compared to the non-injection layers. The shut-in temperature profiles are showing a significant change in reservoir temperature; hence it is important to account for thermal effects in injection monitoring.     

A numerical study on the long term thermo-poroelastic effects of cold water injection into naturally fractured geothermal reservoirs

The residing fracture system and the prevailing in situ stresses have a significant impact on fluid flow and heat transfer in crystalline rocks. The long term response of fracture systems to changes in effective stresses, in particular the long term geo-mechanical effects of thermal stresses on reservoir characteristics is of particular interest to the geothermal industry.     

Controls on the deep thermal field: implications from 3-D numerical simulations for the geothermal research site Groß Schönebeck

The deep thermal field in sedimentary basins can be affected by convection, conduction or both resulting from the structural inventory, physical properties of geological layers and physical processes taking place therein. For geothermal energy extraction, the controlling factors of the deep thermal field need to be understood to delineate favorable drill sites and exploitation compartments. We use geologically based 3-D finite element simulations to figure out the geologic controls on the thermal field of the geothermal research site Groß Schönebeck located in the E part of the North German Basin. Its target reservoir consists of Permian Rotliegend clastics that compose the lower part of a succession of Late Carboniferous to Cenozoic sediments, subdivided into several aquifers and aquicludes. The sedimentary succession includes a layer of mobilized Upper Permian Zechstein salt which plays a special role for the thermal field due to its high thermal conductivity. Furthermore, the salt is impermeable and due to its rheology decouples the fault systems in the suprasalt units from subsalt layers. Conductive and coupled fluid and heat transport simulations are carried out to assess the relative impact of different heat transfer mechanisms on the temperature distribution. The measured temperatures in 7 wells are used for model validation and show a better fit with models considering fluid and heat transport than with a purely conductive model. Our results suggest that advective and convective heat transport are important heat transfer processes in the suprasalt sediments. In contrast, thermal conduction mainly controls the subsalt layers. With a third simulation, we investigate the influence of a major permeable and of three impermeable faults dissecting the subsalt target reservoir and compare the results to the coupled model where no faults are integrated. The permeable fault may have a local, strong impact on the thermal, pressure and velocity fields whereas the impermeable faults only cause deviations of the pressure field.     

工质变物性对EGS热开采过程影响的数值模拟

增强型地热系统(EGS)热开采过程中循环工质的温度和压力会经历较大范围的变化,这会造成循环工质的热物性变化,从而影响流体工质的输运和岩石-流体热交换;数值模拟EGS热开采过程,预测EGS的寿命、出力等性能指标有必要考虑循环工质的热物性变化.笔者在EGS热开采过程三维数值模拟中考虑水和超临界二氧化碳的变物性,实现了热流双向耦合.针对水EGS分析了各物性变化对EGS采热性能的影响,并对变物性条件的水和超临界二氧化碳EGS的采热性能进行了对比研究.结果表明:工质在密度影响下开采寿命为9.0 a在密度和比定压热容共同影响下的开采寿命为7.5 a,说明密度和比定压热容越大则EGS开采寿命越短;在黏度系数影响下的开采寿命为18.0 a,说明黏度系数越大则EGS开采寿命越长;导热系数则对EGS采热性能无明显影响.注入压力一定的条件下以水为工质的EGS具有较长寿命,但相同时刻的质量流率和热开采率低于以临界二氧化碳为工质的EGS.     

FDEM-TH3D: A three-dimensional coupled hydrothermal model for fractured rock

This paper proposes a three-dimensional coupled hydrothermal model for fractured rock based on the finite-discrete element method to simulate fluid flow and heat transport. The 3D coupled hydrothermal model is composed of three main parts: a heat conduction model for the rock matrix, a heat transfer model for the fluid in the fractures (including heat conduction and heat convection), and a heat exchange model between the rock matrix and the fluid in the fractures. Four examples with analytical solutions are provided to verify the model. A heat exchange experiment of circulating water in a cylindrical granite sample with one fracture is simulated. The simulation results agree well with the experimental results. The effects of the fracture aperture, fluid viscosity, and pressure difference on the heat exchange between the fluid and rock are studied. Finally, an application concerned with heat transport and fluid flow in fractured rock is presented. The simulation results indicate that the 3D fully coupled hydrothermal model can capture the fluid flow and temperature evolution of rocks and fluids.     

松辽盆地增强型地热系统(EGS)地热能开发热-水动力耦合过程

增强型地热系统地热能开发涉及到热和水动力的耦合,对应的温度和压力场时空变化特征是评价地热开发效果的关键问题。基于松辽盆地徐家围子深部地质条件,采用TOUGH2进行了地热能开发过程中裂隙-孔隙介质系统中温度和压力变化的数值模拟,分析了不同埋深水平情况下地热能开发的差别,研究了孔隙基质和裂隙介质的渗透率和孔隙度、岩石导热系数、井径、注入压力、注入温度及裂隙周围基质因素对地热能开发的影响。结果表明：采用定压力开发时生产井抽出控制整个区域的压力分布,压力梯度在注入井区域较大,并随着开发的进行,注入井的注入对压力的影响逐渐增大;温度由注入井到生产井逐渐增大,并随着开发的进行温度降低范围逐渐向生产井扩大;质量和热提取速率随时间逐渐减小。不同埋深位置的模拟结果显示,埋深大的温度相对较高,水的流动性较强,质量和热提取速率较高,压力和温度变化幅度均较大。裂隙系统的渗透率、注入井/生产井压力和注入温度、井径对深部地热开采过程中的压力和温度影响较大,从而影响热的提取效率;而孔隙基质的渗透率和孔隙度、裂隙介质的裂隙度和岩石的热传导系数的影响并不明显。     

水平井水力压裂影响参数的数值模拟

水力压裂是低渗油气藏的主要开发手段,传统数值模型所得到的基质-裂缝窜流量以及断裂参数精度不足.为此以流固耦合理论与断裂力学相结合的压裂模型为基础,模拟了水力裂缝扩展过程.在模型中分别引入离散裂缝模型和广义J积分计算基质-裂缝流量交换和断裂参数,并采用动态网格技术对裂缝尖端进行局部加密,以提高模拟的效率和精度.模型计算结果显示,影响水力压裂过程的主要参数中:基质渗透率和压裂液粘度主要影响水力裂缝的最终形态;岩石弹性模量影响裂缝宽度.对压裂车而言,最高工作压力一般都能够满足压裂增产需求,其最大输出功率和最大输出流量是限制压裂能力的主要因素.