Transient gas flow around boreholes

We present numerical solutions and analytical approximate solutions to problems of gas flow in porous media arising in the modelling of outbursts in coal mines and the efficient recovery of methane from coal seams.     

分形理论在煤层气非平衡吸附模型中的应用

传统的煤层气动力学模型均是建立在欧几里得几何基础上的,难以描述煤层孔隙结构的复杂性及形状的不规则性。本文以分形理论为基础,通过引入分形维数来刻画煤层孔隙结构的复杂性并考虑煤层的吸附特性、双重介质特征及介质的变形,建立基于Fick第二定律的分形介质煤层气非稳态渗流数学模型。由于流动方程的强非线性,结合各类边界条件用正则摄动法和Laplace变换得到模型在拉氏空间上的近似解析解,再利用Laplace数值反演求得实空间上的数值解。对参数进行敏感性分析并绘制了典型压力曲线,这些结果为煤层气开采提供了理论依据和试井方法。     

THE ANALYTIC RESOLUTIONS AND APPLICATIONS OF THE NON－LINEAR SEEPAGE FLOW EQUATIONS OF COAL INFUSION

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煤层气三孔双渗流动模型及压力分析

通过对美国Antrim页岩气藏及一些别的低阶煤层的研究表明,在基质颗粒中也有相当一部分自由气存在。本文建立了低阶煤层中单相煤层气三孔双渗流动的试井模型,并获得了模型在拉氏空间上的解析解以及模型的数值解,讨论了储层外边界条件、弹性储容比、窜流系数以及吸附系数等参数对于压力动态响应的影响。结果表明：外边界条件决定着早期过渡段出现的早晚;窜流系数和弹性储容比影响窜流阶段出现的早晚;而吸附系数对晚期过渡段影响明显。     

Mathematical Model of Coalbed Gas Flow with Klinkenberg Effects in Multi-Physical Fields and its Analytic Solution

The deep-mining coal seam impacted by high in situ stress, where Klinkenberg effects for gas flow were very obvious due to low gas permeability, could be regarded as a porous and tight gas-bearing media. Moreover, the Klinkenberg effects had a significant effect on gas flow behavior of deep-mining coal seam. Based on the gas flow properties of deep-mining coal seams affected by in situ stress field, geothermal temperature field and geo-electric field, a new mathematical model of coalbed gas flow, which reflected the impact of Klinkenberg effects on coalbed gas flow properties in multi-physical fields, was developed by establishing the flow equation, state equation, and continuity equation and content equation of coalbed gas. The analytic solution was derived for the model of one-dimensional steady coalbed gas flow with Klinkenberg effects affected by in situ stress field and geothermal temperature field, and a sensitivity analysis of its physical parameters was carried out by comparing available analytic solutions and the measured values. The results show that the analytic solutions of this model of coalbed gas flow with Klinkenberg effects are closer to the measured values compared to those without Klinkenberg effects, and this model can reflect more accurately gas flow of deep-mining coal seams. Moreover, the analytic solution of this model is more sensitive to the change of Klinkenberg factor b and temperature grad G than depth h.     

岩石深孔爆破对邻近煤层的动应力作用

为解决松软煤体爆破孔成形困难导致深孔预裂爆破技术无法应用的问题,选择在运输巷底板距煤 层较近的岩石中进行爆破,利用数值模拟方法进行了相关理论探讨。分析了煤岩介质和单煤体介质中布孔的 差异,建立了单煤体和煤岩体深孔预裂爆破的5个数值计算模型。研究了单煤体和煤岩介质爆破孔与抽放孔 连心线上有效应力随距离的变化,从岩孔爆破传播到煤层其应力衰减的程度较单煤层中大得多,但在靠近抽 放孔附近煤层,二者的差距变小。抽放孔轴线方向所受有效应力的大小是决定爆破效果的重要因素,煤岩介 质中爆破孔与抽放孔间距为2.0m 时,抽放孔轴线方向上的平均有效应力与单煤层中爆破孔与抽放孔间距 为3.0m 时的相当,可作为实现岩孔爆破效果的布孔参数。     

王营子矿煤层中水—煤层气两相流体渗流规律的研究

本文通过在实验室中自行设计的装置,测定了阜新王营子矿煤层中水、煤层气共同流动时的两相流体的流量、渗透率及随水的饱合度变化关系,并根据这种数据模拟出了该煤层反映水、煤层气渗透基本规律的数学关系式,从而为它的煤层气开采提供了理论依据。     

Coal Permeability Evolution and Gas Migration Under Non-equilibrium State

Laboratory test of coal permeability is generally conducted under the condition of gas adsorption equilibrium, and the results contribute to an understanding of gas migration in the original coal seams. However, gas flow under the state of non-equilibrium, accompanied by gas adsorption and desorption, is more common in coalbed methane (CBM) recovery and \(\hbox {CO}_{2}\) geological sequestration sites. Therefore, research on gas migration under the non-equilibrium state has a greater significance with regard to CBM recovery and \(\hbox {CO}_{2}\) geological sequestration. However, most permeability models, in which only one gas pressure has been considered, cannot be used to study gas flow under the non-equilibrium state. In this study, a new mathematical model, which includes both fracture gas pressure and matrix gas pressure, and couples the gas flow with the coal deformation, has been developed and verified. With the developed model, the spatial and temporal evolution of gas flow field during gas adsorption and desorption phases has been explored. The results show that the gas pressures present nonlinear distributions in the coal core, and the matrix gas pressure is generally lower than the fracture gas pressure during adsorption, but higher than the fracture gas pressure during desorption. For gas flow during adsorption, the main factor controlling permeability varies at different points. At the initial time, the permeability is dominated by the effective stress, and at the later time, the permeability in the part close to the gas inlet is mainly controlled by the matrix swelling, whereas that in the part close to the gas outlet is still dominated by the effective stress. For gas flow during desorption, from the gas inlet to the gas outlet, the permeability deceases at the initial time, and when the time is greater than 10,000 s, it shows a decreasing and then an increasing trend. The reason is that at the initial time, the permeability is dominated by the increased effective stress caused by the sharp decrease of the fracture gas pressure. Later, desorption of the adsorbed gas results in matrix shrinkage, which further leads to an increase of the permeability.     

基于分形理论的煤层气非达西流动分析

在考虑了煤层的分形特征和启动压力梯度影响的基础上,建立了无限大煤层中气体低速非达西流动的数学模型,并求得了量纲为一的井底压力的Laplace空间解析解,并根据数值求解结果绘制了典型的井底压力动态曲线。研究结果表明:在定产量生产的情况下,分形维数和量纲为一的启动压力梯度对早期井底压力动态无显著影响;在生产的中后期,由于受二者的影响,压力导数曲线上的径向流水平直线段消失;量纲为一的井储系数的影响主要表现在续流阶段,而吸附系数则主要影响煤基质向裂隙扩散的过渡阶段。     

Characteristics of Seepage and Diffusion in Gas Drainage and Its Application for Enhancing the gas utilization rate

Although gas drainage technology has greatly developed, gas concentration and utilization rates are still very low, resulting in substantial quantities of low concentration gas emissions in coal mine. To study the roles of suction pressure on gas drainage, a mathematical model is developed in this study for coupled gas migration and coal deformation based on a dual-porosity medium. The simulation results reveal the initial gas production is mainly contributed by the seepage in the fracture, and then the dominating factor rapidly transitions to diffusion which provides relatively stable gas production in most drainage time. In addition, the increase in gas production is tiny while the gas concentration clearly decreases because of air leakage as the suction pressure increases. Therefore, a concentration-based suction pressure regulating method is proposed to extend the time period of effective gas drainage and increase the gas utilization rate through adjusting the suction pressure of the bedding borehole. Field tests were performed to constrain the gas drainage process under different suction pressures, and the results gained verify the effectiveness and applicability of this method. This study proves that the concentration-based suction pressure regulating method may be a promising technology to realize safe, economical and efficient underground gas drainage in coal mines in the future.

     

含瓦斯煤单轴压缩的尺度效应实验研究

含瓦斯煤与其它岩石类材料一样,在力学特性等方面具有尺度效应。利用特制的饱和加压装置和电子万能试验机,对不同尺度、不同饱和瓦斯压力下的煤样进行了单轴压缩试验,探讨了煤样变形破坏及强度特性的变化规律。分析表明,煤样抗压强度、弹性模量随瓦斯压力的增大而减小,抗压强度随高径比的增加明显减小,弹性模量随高径比的增加略有提高。利用Weibull模型和线弹性强化理论对含瓦斯煤产生尺度效应的原因进行了合理地解释,为含瓦斯煤样尺度效应在强度表征等方面的深入研究提供了新的实验和理论依据。     

突出煤层深孔控制爆破时控制孔的作用

为进行煤层深孔爆破应力传播和有关控制孔作用的研究,以松藻煤电公司实际采用的爆破、炸药和煤层参数为基础,利用三维数值模拟方法,建立煤层长柱状药包爆破数值计算模型。分析了松软煤介质深孔爆破在有控制孔时应力波传播的特点和因爆破作用的抽放影响区域。研究表明:在距爆破孔10 m范围内,有控制孔的孔壁平均有效应力较没有控制孔相同条件下高48%~66%.并随着与爆破孔距离的增加,尽管煤体所受有效应力衰减,但有控制孔的平均有效应力值较无控制孔的比率增大。上述研究结果与现场爆破前后实际取得的瓦斯抽放数据相比基本吻合,证明了爆破前预先设置控制孔的必要性。     

煤层气在非饱和水流阶段的非定常渗流摄动解

煤层甲烷由煤层的割理裂隙系统流入生产井一般经历：单相水流、非饱和流和气、水两相饱和流三个阶段，在非饱和流阶段，储层压力降至临界解吸压力之后，储存在煤基质中的吸附气体少量被解吸出来形成互不连续的气泡并阻止水的流动，含气量尚未达到饱和程度。同时煤层甲烷运移包含渗流场、变形场和应力场的动态耦合过程。本文考虑渗流过程中水-气两相不溶混流体与固体耦合作用，建立了非饱和水流阶段非定常渗流问题的流固耦合数学模型，对该强非线性一维数学模型采用摄动法和积分变换法进行解析求解，并讨论了其压力动态特性，分析了压力随饱和度S及时间t变化的规律和气相及耦合作用的影响，这些研究对煤层气、石油和天然气的开采等地下工程领域具有一定的指导意义。     

TRANSIENT WELL TEST MODEL FOR THE WELL WITH GAS AND WATER DISTRIBUTED IN COALBED

煤层气是一种高效清洁的非常规天然气资源,其开采过程是一个排水降压采气的过程. 由于煤层气主要是以吸附态的形式存在于煤层中,当煤层压力降低到临界解吸压力以下时煤层气从煤层中解吸出来并与水一起采出,因此煤层中流体是气水两相分布的. 本文根据煤层气藏排采过程中的解吸特征,通过考虑气水两相分布的渗透率关系,提出了一种与解吸区域大小相关的煤层气井不稳定试井模型. 该模型较好地描述了煤层气排采过程中煤层内气水的流动状态,采用分区模式对气水两相进行描述. 通过有限体积方法求解了所建立的试井模型,计算得到了煤层气井气水两相分布不稳定试井理论曲线,分析了煤层气解吸系数、解吸复合半径、气水饱和度分布等对试井理论曲线的影响.     

低渗透煤层气藏中气-水两相不稳定渗流动态分析

针对低渗透煤层渗流问题,考虑启动压力梯度及其引起的动边界和动边界内吸附气解吸作用的渗流模型研究目前仅限于单相流,而更符合实际的气-水两相渗流动边界模型未见报道.本文综合考虑了煤层吸附气的解吸作用、气-水两相渗流、非达西渗流、地层应力敏感等影响因素,进行了低渗透煤层的气-水两相渗流模型研究.采用了试井技术中的"分相处理"方法,修正了两相渗流的综合压缩系数和流度,并基于含气饱和度呈线性递减分布的假设,建立了煤层气藏的气-水两相渗流耦合模型.该数学模型不仅可以描述由于低渗透煤层中渗流存在启动压力梯度而产生的可表征煤层有效动用范围随时间变化的移动边界,还可以描述煤层有效动用范围内吸附气的解吸现象以及吸附气解吸作用所引起的煤层含气饱和度的上升;为了提高模型精度,控制方程还保留了二次压力梯度项.采用了稳定的全隐式有限差分方法进行了模型的数值求解,并验证了数值计算方法的正确性,获得了模型关于瞬时井底压力与压力导数响应的双对数特征曲线,由此分析了各渗流参数的敏感性影响.本文研究结果可为低渗透煤层气藏开发的气-水两相流试井技术提供渗流力学的理论基础.     

甲烷/煤尘复合爆炸火焰的传播特性

为揭示甲烷/煤尘复合爆炸火焰的传播机理,利用气粉两相混合爆炸实验系统,在低于甲烷爆炸下限条件下,采用高速摄影机记录火焰传播图像,通过热电偶采集火焰温度,研究了煤尘种类以及甲烷体积分数对甲烷/煤尘复合火焰传播特性的影响。结果表明:挥发分是衡量煤尘燃烧特性的主导因素;随着煤尘挥发分的升高,燃烧反应增强,火焰传播速度升高,火焰温度升高;挥发分含量差异较小时,水分含量越低,燃烧反应越剧烈;在相同条件下,焦煤的燃烧反应强度最高,其次为长焰煤,最后为褐煤;随着甲烷体积分数的增加,煤尘颗粒的燃烧可由释放挥发分的扩散燃烧转变为气相预混燃烧,燃烧反应增强,火焰传播速度和火焰温度显著升高;热辐射和热对流作用促进煤尘颗粒热解,释放挥发分进行燃烧反应,维持复合火焰的持续传播;随着混合体系中甲烷体积分数的增加,混合爆炸机制由粉尘驱动型爆炸转为气体驱动型爆炸,燃烧反应增强;甲烷/煤尘复合爆炸火焰可由未燃区、预热区、气相燃烧区、多相燃烧区和焦炭燃烧区5部分组成,湍流扰动导致燃烧介质空间分布存在差异,使得燃烧区无规则交错分布。     

Nonlinear Coupled Mathematical Model for Solid Deformation and Gas Seepage in Fractured Media

Based on detailed investigation into the interactional physical mechanism of solid deformations and gas seepage in rock matrix and fracture, a nonlinear coupled mathematical model of solid deformation and gas seepage is put forward and the FEM model is built up to carry out numerical analysis. The coupled interaction laws between solid deformations and gas seepage in rock matrix and fractures has been emphasized in the model, which is a vital progress for coupled mathematical model of solid deformation and gas seepage of rock mass media. As an example, the methane extraction in fractured coal seam has been numerically simulated. By analyzing the simulation results, the law of methane migration and exchange in rock matrix and fractures is interpreted.     

海陆过渡相页岩气藏不稳定渗流数学模型

海陆过渡相页岩常与煤层和砂岩呈互层状产出, 储层连续性较差、横向变化快、非均质性强, 水力压裂技术是其获得经济产量的关键手段. 然而, 目前缺乏有效的海陆过渡相页岩气藏不稳定渗流数学模型, 对其渗流特征分析及储层参数评价不利. 针对这一问题, 首先建立海陆过渡相页岩气藏压裂直井渗流数学模型, 其次采用径向复合模型来反映强非均质性, 采用Langmuir等温吸附方程来描述气体的解吸和吸附, 分别采用双重孔隙模型和边界元模型模拟天然裂缝和水力裂缝, 建立并求解径向非均质的页岩气藏压裂直井不稳定渗流数学模型, 分析海陆过渡相页岩气藏不稳定渗流特征, 并进行数值模拟验证和模型分析应用. 分析结果表明, 海陆过渡相页岩气藏不稳定渗流特征包括流动早期阶段、双线性流、线性流、内区径向流、页岩气解吸、内外过渡段、外区径向流及边界控制阶段. 将本模型应用在海陆过渡相页岩气试井过程中, 实际资料拟合效果较好, 其研究成果可为同类页岩气藏的压裂评价提供一些理论支撑, 具有较好应用前景.      

Flow of Coal-Bed Methane to a Gallery

Coal-seam methane reservoirs have a number of unique feature compared to conventional porous or fractured gas reservoirs. We propose a simplified mathematical model of methane movement in a coal seam taking into account the following features: a relatively regular cleat system, adsorptive methane storage, an extremely slow mechanism of methane release from the coal matrix into cleats and a significant change of permeability due to desorption.Parameters of the model have been combined into a few dimensionless complexes which are estimated to an order of magnitude. The simplicity of the model allows us to fully investigate the influence of each parameter on the production characteristics of the coal seam. We show that the reference time of methane release from the coal matrix into cleats – the parameter which is most poorly investigated – may have a critical influence on the overall methane production.     

A Computational Approach to Determine Average Reservoir Pressure in a Coalbed Methane (CBM) Well Flowing Under Dominant Matrix Shrinkage Effect

Desorption of gas from coal matrix alters the pore volume of fracture network. Consequently, cleat porosity and permeability of reservoir changes as pressure depletes. The method of standard pressure analysis calculations produces incorrect results in the case of coalbed methane reservoirs producing under dominant matrix shrinkage effect. The change in cleat porosity and permeability due to shrinkage of coal matrix following gas desorption with pressure depletion invalidates the underlying assumptions made in the derivation of diffusivity equation. Consequently, equations of pseudo-steady state commonly used in conventional reservoirs no longer remain valid as the porosity and permeability values change with pressure depletion. In this paper, effort has been made to describe pseudo-steady-state flow in coalbed methane reservoirs in the form of a new equation that accounts for pressure dependency of cleat porosity and permeability due to shrinkage of coal matrix. The concept of Al-Hussainy et al. (1966) has been extended to define a new pseudo-pressure function which assimilates within itself the pressure dependence of porosity and permeability Palmer and Mansoori (1998). Equation has been used to relate the cleat porosity with pressure. The equation-based computational method suggested in this paper finds its usefulness in estimating average reservoir pressure for any known flowing bottom hole pressure and thus reducing the frequency of future pressure buildup tests. The new equation is also useful in predicting reservoir pressure under the situation when coal matrix shrinks below desorption pressure. The equation used in the computational method has been validated with the help of numerical simulator CMG-GEM.