Modeling Water Leak-off Behavior in Hydraulically Fractured Gas Shale under Multi-mechanism Dominated Conditions

Fracturing-fluid leak-off in fractured gas shale is a complex process involving multiple pore/fluid transports and interactions. However, water leak-off behavior has not been modeled comprehensively by considering the multi-pores and multi-mechanisms in shale with existing simulators. In this paper, we present the development of a comprehensive multi-mechanistic, multi-porosity, and multi-permeability water/gas flow model that uses experimentally determined formation properties to simulate the fracturing-fluid leak-off of hydraulically fractured shale gas wells. The multi-mechanistic model takes into account water transport driven by hydraulic convection, capillary and osmosis, gas transport caused by hydraulic convection, and salt ion transport caused by advection and diffusion. The multi-porosity includes hydraulic fracture millipores, organic nanopores, clay nanopores, and other inorganic micropores. The multi-permeability model accounts for all the important processes in shale system, including gas adsorption on the organics’ surface, multi-mechanistic clay/other inorganic mineral mass transfer, inorganic mineral/hydraulic fracture mass transfer, and injection from a hydraulically fractured wellbore. The dynamic water saturation and pressure profiles within clay and other inorganic matrices are compared, revealing the leak-off behavior of water in rock media with different physicochemical properties. In sensitivity analyses, cases with different clay membrane efficiency, volume proportion of source rock, connate water salinity, and saturation are considered. The impacts of shale properties on water fluxes through wellbore, hydraulic fracture and matrix, and the total injection and leak-off volumes of the well during the treatment of hydraulic fracturing are investigated. Results show that physicochemical properties in both organic and inorganic matrices affect the water leak-off behavior.     

Anisotropic porochemoelectroelastic Mandel's problem solutions for applications in reservoir modeling and laboratory characterization

The porochemoelectroelastic analytical models have been used to describe the response of chemically active and electrically charged saturated porous media such as clay soils, shales, and biological tissues. In this work, the porochemoelectroelastic theory is applied to derive the solution for stress, pore pressure, strain, and displacement of the Mandel's problem for orthotropic charged saturated porous media. Numerical examples are given to demonstrate applications of the present solutions to laboratory characterization and hydraulic fracturing analysis of shale formation. The analysis shows that ignoring either the porochemoelectroelastic effects or the material anisotropy can leads to inaccurate prediction of the pore pressure and effective stress distributions in the shale sample or formations during these processes.     

A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs

The pore and pore-throat sizes of shale and tight rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary layer effect on fluid flow in tight rocks has been investigated through laboratory work on capillary tubes. It is observed that low permeability is associated with large boundary layer effect on fluid flow. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley–Leverett-type analytical solution is derived with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multidimensional porous and fractured tight oil reservoirs. Finally, the numerical studies on an actual field example in China demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations.     

Fully Coupled THMC Modeling of Wellbore Stability with Thermal and Solute Convection Considered

Wellbore stability analysis is an important topic in petroleum geomechanics. Analytical and numerical analysis of wellbore stability involves the study of interactions among pressure, temperature and chemical changes, and the mechanical response of the rock, a coupled thermal–hydraulic–mechanical–chemical (THMC) process. Thermal and solute convection have usually been overlooked in numerical models. This is appropriate for shales with extremely low permeability, but for shales with intermediate and high permeability (e.g., shale with a disseminated microfissure network), thermal and solute convection should be considered. The challenge of considering advection lies in the numerical oscillation encountered when implementing the traditional Galerkin finite element approach for transient advection–diffusion problems. In this article, we present a fully coupled THMC model to analyze the stress, pressure, temperature, and solute concentration changes around a wellbore. In order to overcome spurious spatial temperature oscillations in the convection-dominated thermal advection–diffusion problem, we place the transient problem into an advection– diffusion-reaction problem framework, which is then efficiently addressed by a stabilized finite element approach, the subgrid scale/gradient subgrid scale method (SGS/GSGS).     

页岩储层体积压裂的地应力变化研究

页岩储层属于致密超低渗透储层,需改造形成复杂缝网才有经济产能.体积压裂是页岩储层增产改造的主要措施,而地应力场特别是水平主应力差值是体积压裂的关键控制因素. 理论研究表明:(1)当初始两向水平主应力差较小时,容易形成缝网,反之不易产生缝网;(2)人工裂缝的形成能够改变地层初始应力场. 因此应在前人研究的基础上优化设计压裂方式,以克服和翻转初始水平主应力差值,产生体积缝网.基于此,建立了页岩气藏水平井体积压裂数值模型,模型中采用多孔介质流固耦合单元模拟页岩基质的行为,采用带有孔压的"cohesive"单元描述水力裂缝的性质,模型对"Texas Two-Step" 压裂方法进行了数值模拟,模拟结果得到了压裂过程中地层应力场的分布及其变化,模拟结果和解析公式计算结果吻合良好.模拟结果表明:(1)裂缝的产生减弱了地层应力场的各向异性;(2 对于低水平应力差页岩储层,采用"Texas Two-Step"压裂方法可以产生缝网. 对于采用"Texas Two-Step"压裂方法无法产生缝网的高应力差页岩储层,提出了三次应力"共振" 和四次应力"共振" 压裂方法并进行了数值模拟,模拟结果得到了压裂过程中页岩储层应力场的分布及其变化,得到了缝网形成的区域,模拟结果表明:(1)对于高应力差页岩储层,采用"Texas Two-Step" 压裂方法无法产生缝网;(2)对于高应力差页岩储层,三次应力"共振" 和四次应力"共振"压裂方法是有效的体积压裂缝网形成的方法.      

钻井完井液浸泡弱化页岩脆性机制

页岩脆性是页岩地层钻井、水力压裂设计的关键参数之一,目前针对钻井过程中工作液浸泡对页岩脆性的影响还未引起关注.通过开展钻井完井液浸泡前后页岩三轴力学实验,利用脆性评价模型分析了页岩脆性变化特征.结果表明,延长组页岩脆性强于龙马溪组页岩;油基和水基钻井完井液浸泡均能导致页岩脆性降低,且油基钻井完井液浸泡后的页岩脆性降低幅度更大;龙马溪组页岩浸泡后脆性减弱幅度较延长组页岩大.页岩脆性弱化机制包括:(1)由层理面胶结强度不同引起的脆性强弱差异;(2)由毛管自吸作用导致的高孔压、高应力强度因子、低临界断裂韧性;(3)由碱液侵蚀导致的页岩溶蚀孔形成及矿物颗粒碎裂;(4)由黏土矿物水化膨胀产生的膨胀应力;(5)由钻井完井液滤液润滑导致的页岩破裂面摩擦系数降低.延长组页岩层理面强度较龙马溪组页岩低,导致延长组页岩脆性强于龙马溪组页岩.其次,和水基钻井完井液相比,油基钻井完井液具有更大的自吸量、更高的pH值、更强的润滑性,因此,油基钻井完井液浸泡降低页岩脆性幅度更大.另外,由于龙马溪组页岩具有更小的润湿角、更强的毛管自吸和碱液侵蚀作用,相同浸泡条件下,龙马溪组页岩脆性降低幅度更大.本研究可为页岩地层钻井液性能优化、井壁稳定控制、水力压裂设计等提供理论指导.      

饱和多孔介质化学-热-弹性模型及应用

本文基于热局部非平衡(LTNE)条件和加权平均温度概念,并假设孔隙流体由溶质和溶剂两组元组成,对页岩（饱和多孔介质）,推导给出了一种LTNE条件下的化学-热-弹性模型,同时讨论了耦合方程组的解耦求解问题．作为模型的应用,考虑无限大平面含一圆形孔的情况,研究了冷/热对流以及溶质摩尔分数突变边界条件下圆孔附近的孔隙压力和化-热应力问题,用Laplace变换得到了平面轴对称情况下有关力学变量的表达式．数值分析了圆孔边界上冷/热对流的Biot数和溶质摩尔分数改变量对圆孔附近孔隙压力和化-热应力的影响．结果表明：在Biot数为中等值(1~5)范围内,LTNE效应是非常明显的;化学作用对孔隙压力和固相应力的影响不可忽视．     

Constitutive unsaturated hydro-mechanical model based on modified mixture theory with consideration of hydration swelling

This paper has extended modified mixture theory with consideration of hydration swelling in unsaturated rock. By using non-equilibrium thermodynamics and Biot elasticity, a fully coupled formulation including hydration swelling term is derived. Standard arguments of non-equilibrium thermodynamics are used to derive the Darcy’s law for unsaturated flow. Helmholtz free energy has been used to give the relationship between the stress and pore pressure. The chemical potential of water in pore space and clay platelets has been included in the analysis of water sensitive materials such as shale. Finally, a simple numerical example has been presented for illustrative purpose, the results show that the swelling parameter has a strong influence on stress and strain.     

Liquid crystal model of vesicle deformation in alternating electric fields

Considering the effects of osmotic pressure, elastic bending, Maxwell pressure, surface tension, as well as flexo-electric and dielectric properties of phospholipid membrane, the shape equation for sphere vesicle in alternation (AC) electric field is derived based on the liquid crystal model by minimizing the free energy due to coupled mechanical and AC electrical fields. Besides the effect of elastic bending, the influence of osmotic pressure and surface tension on the frequency dependent behavior of vesicle membrane in AC electric field is also discussed. Our theoretical results for membrane deformation are consistent with corresponding experiments. The present model provides the possibility to further disclose the frequency-depended behavior of biological cells in the coupled AC electric and different mechanical fields.     

Parameter Determination Using 3D FIB-SEM Images for Development of Effective Model of Shale Gas Flow in Nanoscale Pore Clusters

A large amount of nano-pores exists in pore clusters in shale gas reservoirs. In addition to the multiple transport regimes that occur on the nanoscale, the pore space is another major factor that significantly affects the shale gas recoverability. An investigation of the pore-scale shale gas flow is therefore important, and the results can be used to develop an effective cluster-scale pore network model for the convenient examination of the process efficiency. Focused ion beam scanning electron microscope imaging, which enables the acquisition of nanometre-resolution images that facilitate nano-pore identification, was used in conjunction with a high-precision pore network extraction algorithm to generate the equivalent pore network for the simulation of Darcy and shale gas flows through the pores. The characteristic parameters of the pores and the gas transport features were determined and analysed to obtain a deeper understanding of shale gas flow through nanoscale pore clusters, such as the importance of the throat flux–radius distribution and the variation of the tortuosity with pressure. The best parameter scheme for the proposed effective model of shale gas flow was selected out of three derived schemes based on the pore-scale prediction results. The model is applicable to pore-scale to cluster-scale shale gas flows and can be used to avoid the multiple-solution problems in the study of gas flows. It affords a foundation for further study to develop models for shale gas flows on larger scales.     

Thermo-Osmosis Effect in Saturated Porous Medium

In this paper, the thermo-poroelasticity theory is used to investigate the quasi-static response of temperatures, pore pressure, stress, displacement, and fluid flux around a cylindrical borehole subjected to impact thermal and mechanical loadings in an infinite saturated poroelastic medium. It has been reported in literatures that coupled flow known as thermo-osmosis by which flux is driven by temperature gradient, can significantly change the fluid flux in clay, argillaceous and many other porous materials whose permeability coefficients are very small. This study presents a mathematical model to investigate the coupled effect of thermo-osmosis in saturated porous medium. The energy balance equations presented here fulfill local thermal non-equilibrium condition (LTNE) which is different from the local thermal equilibrium transfer theory, accounting for that temperatures of solid and fluid phases are not the same and governed by different heat transfer equations. Analytical solutions of temperatures, pore pressure, stress, displacement, and fluid flux are obtained in Laplace transform space. Numerical results for a typical clay are used to investigate the effect of thermo-osmosis. The effects of LTNE on temperatures, pore pressure, and stress are also studied in this paper.     

Chemo-Mechanical Consolidation of Clays: Analytical Solutions for a Linearized One-Dimensional Problem

Consolidation (and swelling) of clayey soils caused by change in chemistry of pore fluid is addressed. Such phenomena are caused by changes in the concentration of various species in the solution and result primarily from a stress-independent deformation of individual clusters, and from a mechanical weakening or strengthening of the clay solid matrix in the presence of stress. Second, transport of chemicals that involves concentration gradients induces additional driving forces of osmotic consolidation due to semipermeable membrane nature of clay. In this paper an extension of Terzaghi's model of the mechanical consolidation to incorporate chemical loading of soil is proposed. A linearized model is used to solve analytically two one-dimensional problems of consolidation of a homogeneous layer simulating a landfill liner with drained or undrained boundaries. The numerical results show a strong dependence of distribution of pore pressure on the chemical load and chemically induced settlements of soil to be comparable to the mechanical ones.     

ANALYSIS OF THE WELLBORE STABILITY BASED ON PLASTIC DAMAGE THEORY IN SOFT SHALE FORMATION

软泥页岩在地层高压、流体环境下独有的力学变形特性一直是井壁稳定性控制工程领域的研究热点。针对软泥页岩低强度、高塑性的特点,考虑孔隙渗流、塑性损伤引起的渗透率变化等因素,建立了渗流-- 应力耦合形式的井壁稳定性评价数值模型,研究了流体渗流、泥浆压力、水平应力差的影响。结果表明,对过平衡钻井,当泥浆压力超过地层孔隙压力10% 时,渗流-- 应力耦合效应导致井壁塑性损伤区扩大至少65%,需予以考虑。水平应力差的增大会促进井壁塑性损伤区向最小水平主应力方向集中,且损伤区深度增大。     

Analysis of hydrodynamic and thermal dispersion in porous media by means of a local approach

A pore scale analysis is implemented in this numerical study to investigate the behavior of microscopic inertia and thermal dispersion in a porous medium with a periodic structure. The macroscopic characteristics of the transport phenomena are evaluated with an averaging technique of the controlling variables at a pore scale level in an elementary cell of the porous structure. The Darcy–Forchheimer model describes the fluid motion through the porous medium while the continuity and Navier–Stokes equations are applied within the unit cell. An average energy equation is employed for the thermal part of the porous medium. The macroscopic pressure loss is computed in order to evaluate the dominant microscopic inertial effects. Local fluctuations of velocity and temperature at the pore scale are instrumental in the quantification of the thermal dispersion through the total effective thermal diffusivity. The numerical results demonstrate that microscopic inertia contributes significantly to the magnitude of the macroscopic pressure loss, in some instances with as much as 70%. Depending on the nature of the porous medium, the thermal dispersion may have a marked bearing on the heat transfer, particularly in the streamwise direction for a highly conducting fluid and certain values of the Peclet number.     

页岩气藏压裂缝网扩展数值模拟

为探究页岩气藏水力压裂复杂裂缝网络的形成机理,开展了缝网扩展的数值模拟研究.考虑应力阴影和天然裂缝作用,建立了井筒和裂缝中流体流动模型,利用位移不连续方法求解应力与位移不连续量,然后构建了压力与裂缝宽度的迭代方程,并采用牛顿迭代法求解.通过比较数值解经典模型解析解,验证了模型和迭代解法的正确性.多簇裂缝同步扩展时裂缝间距越小,压裂液分配到各条裂缝越不均匀,靠近井筒跟部的裂缝的分流量越大,从而裂缝宽度越大;考虑天然裂缝作用时,逼近角越小或者应力各向异性越弱,水力裂缝越容易发生转向扩展,裂缝网络越复杂.      

Pore Size of Shale Based on Acyclic Pore Model

The transport properties inside a nanosize conduit, such as viscosity and density, deviate from those reported at unconfined conditions with an identical pressure and temperature. The deviation from the nominal value is well studied for the simple topology in nanofluidics. A straight circular tube is an example of a simple topology. The pore space inside the matrix of a shale formation is also a nanofluidic system, because its characteristic size is smaller than or equal to 100 nm, but it includes a complex structure. With this in mind, we determine the pore-throat and pore-body size distributions of different shales whose data are available in the literature. The main objective is to quantitatively distinguish the two sizes, whose importance is overlooked in the study of shale formations. The pore-throat size distribution is determined from mercury injection capillary pressure measurements, and the pore-body size distribution is derived from nitrogen adsorption–desorption. The acyclic pore model, which is physically representative of the pore space at the core scale, allows us to interpret the petrophysical measurements. Our study of different shales shows that the average pore-body size is usually larger than 20 nm; thus, there is no need to account for the pore proximity (confinement). The pore-throat size distributions of different shales usually fall below 20 nm, which entails the modification of a transport property that is relevant to the formation resistance against the flow.     

页岩气高效开采的力学问题与挑战

页岩气是指赋存于富含有机质泥页岩中以吸附和游离状态为主要存在方式的天然气,中国资源量丰富,地域分布广泛.页岩气开采能缓解我国常规油气产量不足、煤化石燃料引起环境污染等问题,已成为中国绿色能源开发的重要领域.尽管北美页岩气"革命"取得了成功,目前也仅有预期产量5%～15%的采收率.与北美地区相比,中国页岩气埋藏深,赋存条件差,自然丰度低,因此,高效开采面临更多的困难和挑战.近年来,围绕国家重大能源战略需求,瞄准技术发展前沿,学术界和工业界联合对页岩气高效开采的关键科学和技术问题展开研究.本文结合近三年四川、重庆地区的页岩气试验区块遇到的新问题,针对中国未来3 500 m以下深部开采的新挑战,如地质沉积、裂缝发育构造不同、上覆压力增加、水平应力场变化等新问题,介绍和总结了目前中国页岩气高效开采面临的力学科学问题,主要包括多重耦合下的安全优质钻完井力学理论和方法、水力压裂体积改造和多尺度缝网形成机制、多尺度渗流力学特性与解吸附机理等."深部页岩气高效开采"的研究面向国家重大能源需求,科学意义重大,工程背景明确,需要工程力学、石油工程、地球物理、化学工程和环境工程等多学科专家合作,开展理论研究、物理模拟、数值模拟及现场试验等综合应用基础研究,取得高效开采页岩油气理论与技术的突破.学科交叉是研究页岩气高效开采问题、突破技术瓶颈的桥梁,只有力学与石油工程、地球科学等学科实现深度交叉融合,才能更加有效地推动页岩油气等非常规油气资源的开发.     

Entropy analysis in electrical magnetohydrodynamic(MHD) flow of nanofluid with effects of thermal radiation,viscous dissipation,and chemical reaction

The unsteady mixed convection flow of electrical conducting nanofluid and heat transfer due to a permeable linear stretching sheet with the combined effects of an electric field, magnetic field, thermal radiation, viscous dissipation, and chemical reaction have been investigated. A similarity transformation is used to transform the constitutive equations into a system of nonlinear ordinary differential equations.The resultant system of equations is then solved numerically using implicit finite difference method.The velocity, temperature, concentration, entropy generation, and Bejan number are obtained with the dependence of different emerging parameters examined. It is noticed that the velocity is more sensible with high values of electric field and diminished with a magnetic field. The radiative heat transfer and viscous dissipation enhance the heat conduction in the system. Moreover, the impact of mixed convection parameter and Buoyancy ratio parameter on Bejan number profile has reverse effects. A chemical reaction reduced the nanoparticle concentration for higher values.     

油页岩原位注热开采储层有效热解区变化规律分析

针对油页岩原位注热开采过程中储层有效热解区变化规律不清,实际热解效果无法准确判断难题,采用数值模拟方法,以抚顺油页岩储层为研究对象,建立了油页岩原位注热开采热流固耦合力学模型,与前人结果对比,验证了模型可靠性。重点考察水力压裂裂缝通道短路问题,分析得到了油页岩原位注热开采过程中储层有效热解区、储层有效热解区中地应力、注汽压力及沉降量随注热时间变化规律。结果表明,过热蒸汽沿水力压裂裂缝流动不会出现裂缝通道短路现象,过热蒸汽可通过水力压裂裂缝加速油页岩储层热解;采用过热蒸汽对流加热油页岩储层效率高,只需1年能使96%的油页岩储层达到热解所需温度;油页岩储层有效热解区中部形成应力集中区,最大地应力为21.6 MPa;热解后靠近注热井处岩层发生沉降,热解2年后最大沉降量达0.85 m。所得结论对现场油页岩原位注热开采有参考意义。