Simulation of Pressure Transient Behavior for Asymmetrically Finite-Conductivity Fractured Wells in Coal Reservoirs

Based on Fick’s law in matrix and Darcy flow in cleats and hydraulic fractures, a new semi-analytical model considering the effects of boundary conditions was presented to investigate pressure transient behavior for asymmetrically fractured wells in coal reservoirs. The new model is more accurate than previous model proposed by Anbarci and Ertekin, SPE annual technical conference and exhibition, New Orleans, 27–30 Sept 1998 because new model is expressed in the form of integral expressions and is validated well through numerical simulation. (1) In this paper, the effects of parameters including fracture conductivity, coal reservoir porosity and permeability, fracture asymmetry factor, sorption time constant, fracture half-length, and coalbed methane (CBM) viscosity on bottomhole pressure behavior were discussed in detail. (2) Type curves were established to analyze both transient pressure behavior and flow characteristics in CBM reservoir. According to the characteristics of dimensionless pseudo pressure derivative curves, the process of the flow for fractured CBM wells was divided into six sub-stages. (3) This paper showed the comparison of transient steady state and pseudo steady state models. (4) The effects of parameters including transfer coefficient, wellbore storage coefficient, storage coefficient of cleat, fracture conductivity, fracture asymmetry factor, and rate coefficient on the shape of type curves were also discussed in detail, indicating that it is necessary to keep a bigger fracture conductivity and fracture symmetry for enhancing well production and reducing pressure depletion during the hydraulic fracturing design.     

页岩水力压裂的关键力学问题

页岩气是指以吸附和游离时而还有流体相的形态状态赋存于泥页岩中的非常规天然气。页岩气开采成为我国绿色能源开发的新领域。尽管北美页岩气革命取得了成功,但目前仍仅有预期产量5~15%的油气采收率,问题出在什么地方？水力压裂被认为是提高采收率的关键一环,但水力压裂过程中复杂缝网的形成和力学控制机理尚不清楚,这给力学家提出了巨大的挑战和机遇。结合本课题组近期研究成果,本文从理论、计算和实验三个方面对页岩水力压裂中的关键基础力学问题进行介绍和总结。主要内容包括发展页岩人工裂缝扩展的大型物理模型实验,建立页岩本构模型和断裂力学理论,发展耦合断裂力学和流体力学的裂缝网扩展数值模拟方法。页岩水力压裂研究对发展断裂力学的实验技术、理论模型和数值模拟方法起到推动作用,对提高我国页岩气高效开采技术具有重要意义。     

岩体中饱和渗流应力耦合模型研究进展

在大坝渗流与控制、各种水工隧洞和交通隧道以及地下各种洞室开挖、采矿工程与油藏开采中的水力劈裂、 岩坡和坝基的稳定性研究等领域中经常会遇到岩体的饱和渗流应力耦合问题.本文对这些领域中的渗流应力耦合问题分为6种力学模型: 等效连续介质模型、 裂隙网络模型、 双重介质模型、 断裂力学模型、 连续损伤力学模型和统计模型.前3种主要从经典的黏弹塑性本构着手考虑, 着重对渗流场的处理, 后3种则是从考虑岩体在耦合作用下发生损伤破裂行为方面切入, 着重于岩体结构内部发生质的改变带来的更加复杂的耦合效应.对这些模型进行了详细的介绍, 指出了这些模型的优缺点与适用范围, 给出了一些有代表性的研究成果, 并对该研究领域中未来的研究方向进行了展望.     

页岩气高效开采的可压裂度和射孔簇间距预测

页岩储层的可压裂性是影响页岩气产量的关键因素. 本文基于断裂力学理论, 以高围压下岩石层理弱面的剪切破坏为主要研究对象, 依据岩石抗拉强度和层理弱面抗剪强度的比值关系, 首先提出了可压裂度的概念, 给出了无量纲的定性曲线图, 涵盖了岩石脆性矿物质含量, 粘性主导和韧性主导裂缝尖端流体压强、射孔簇分布间距的综合地质与工程因素. 接着提出了一种新的表征高围压下页岩可压裂度的无量纲参数, 在保证达到充分解吸附的最小压裂间距前提下, 依据该参数可计算水平井压裂中的射孔簇间距, 可作为工程参考指标. 本文将断裂力学理论结合水力压裂高效开采页岩气工程, 具有力学理论意义和工程应用前景.      

Modeling of Coal Fine Migration During CBM Production in High-Rank Coal

During CBM (coalbed methane) production, the interaction of coal fracture surface with water flow commonly generates and starts coal fine flow. Part of flowing coal fines deposit in coal fracture system due to water production reduction and methane production increase. The fine sedimentation results in the reduction of coal permeability and well productivity. Despite the increasing awareness of the importance of fine migration, limited research has been carried out on the flow model of coal fine coupled with water and gas. In this paper, a flow model of coal fine is established coupled with water and gas flow, taking coal fine generation, migration and sedimentation process into consideration. Then, case simulations are conducted to illustrate effects of water production schedule, permeability performance and gas content on production performance in flow model. The simulation results indicate that methane rate with the lowest initial water rate is observed to have the highest production in late production period. This is mainly due to the reason that the low water flow cannot generate and start the flow of coal fine. Further, the case with high initial water production has faster gas and water flow rate, thus higher coal fine generation rates, which can improve well productivity at earlier production period. As water production declines quickly, both permeability and production performance decrease, which leads to the loss of well productivity. Meanwhile, higher gas content will lead to a faster water production decline at late production period. This indicates that a portion of coal fines plugged in the fracture as water production deceases and the CBM reservoir with high gas content should not adopt a high initial water production schedule.     

Dynamic production prediction and parameter identification for gas well with vertical fracture

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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.      

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。     

Numerical well test for well with finite conductivity vertical fracture in coalbed

A new well test model is developed for the hydraulic fractured well in coalbed by considering the following aspects： methane desorption phenomena, finite conductivity vertical fractures, and asymmetry of the fracture about the well. A new parameter is introduced to describe the storage of the fracture, which is named as a combined fracture storage. Another new concept called the fracture asymmetry coefficient is used to define the asymmetry of the fracture about the well. Finite element method （FEM） is used to solve the new mathematical model. The well test type curves and pressure fields are obtained and analyzed. The effects of the combined fracture storage, desorption factor, fracture conductivity, and fracture asymmetry coefficient on the well test type curves are discussed in detail. In order to verify the new model, a set of field well test data is analyzed.     

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。     

基于混合方法的二维水力压裂数值模拟

水力压裂在页岩气开采中被广泛使用,采用数值方法研究压裂机理具有重要意义.基于连续-非连续单元法(CDEM) 和中心型有限体积法(FVM),提出解决水力压裂流固耦合问题的二维混合数值计算模型.该混合模型中,使用CDEM 求解应力场和裂缝扩展过程,使用FVM 求解裂隙渗流场.应力场裂缝扩展和渗流场均使用显式迭代求解, 并通过相互之间数据交换实现流固耦合.通过与KGD 理论模型进行对比, 验证数值模型的正确性.通过与颗粒离散元数值结果进行对比,验证数值模型的有效性.通过计算复杂缝网压裂模型,研究水力压裂机理,并说明该数值模型在水力压裂模拟中具有很好的前景.      

Experimental Method to Simulate Coal Fines Migration and Coal Fines Aggregation Prevention in the Hydraulic Fracture

A simple and effective experimental method is proposed to simulate coal fines migration through the proppant pack; such migration inevitably occurs during the process of fracturing fluid flowback or dewatering and gas production in coalbed methane (CBM) reservoirs. The damage to conductivity caused by coal fines migration in the pack and the factors affecting such migration are analyzed. A dispersion agent of coal fines applicable to hydraulic fracturing in CBM is optimized, consequently solving the problem of coal fines aggregation and retention in the proppant pack. Discharging coal fines with water or water-based fracturing fluid from the proppant pack can be difficult because of the adsorption and hydrophobicity of coal fines. Thus, coal fines are likely to aggregate and be retained in the proppant pack, thereby resulting in pore throat plugging, which causes serious damage to fracture conductivity. Two percent coal fines can reduce propped fracture conductivity by 24.4 %. The mobility and retention of coal fines in the proppant pack are affected by proppant size, proppant type, flowback rate, and coal fines property. When flowback rate exceeds the critical value, coal fines can be discharged from the pack, consequently reducing damage to propped fracture conductivity. More importantly, the steady discharging of coal fines requires steady dewatering and gas production to avoid flow shock, which causes pressure disturbance to drive coal fines in a remote formation. The optimized dispersant FSJ-02 employed in this paper can effectively change the wettability and surface potential of coal fines to improve their suspension and dispersion in water-based fracturing fluid. The recovery rate of coal fines increased by 31.5 %, whereas conductivity increased by 13.3 %.     

围压下泥岩断裂韧性测试与解释方法

根据围压条件下的断裂力学理论 ,采用双翼裂纹厚壁圆筒 ,对泥岩进行了不同围压和不同泥质含量条件下的人工岩样断裂韧性测试。建立了有限元方法解释断裂韧性的数值模型。在进行大量实验测试的基础上 ,通过回归分析表明 ,断裂韧性与围压、泥质含量有较好的线性统计关系。解决了水力压裂设计中断裂韧性参数的准确获取问题 ,有利于提高压裂设计、预测的精度     

水力压裂解析模型裂缝扩展参数敏感性分析

水力压裂形成复杂裂缝网络是致密储层油气开采的重要技术,掌握水压裂缝扩展机理是控制压裂行为和优化压裂效果的关键．水压裂缝动态扩展行为涉及储层岩体、注入压裂液、压裂实施工艺等方面,其中水力压裂扩展时间、压裂液流体动力粘度系数、压裂液流体注入流速、储层岩石剪切模量成为决定裂缝扩展长度和裂缝开度的重要因素．本研究采用KGD、PKN两类等高解析模型对主控因素的参数敏感性进行分析,直观、快速、可靠地获得水压裂缝扩展长度、张开度动态演化行为的量化数值．研究发现,压裂持续开展过程中水压裂缝扩展长度呈线性增长、开度逐渐趋于稳定,高流体动力粘度导致裂缝难扩展、形成较大裂缝开度,通过增加压裂液流体注入流速可同时增加裂缝扩展长度和开度,较高的岩石剪切模量将降低水压裂缝的开度．通过对比两类解析模型在不同参数下的水压裂缝扩展结果,分析压裂参数与裂缝扩展的相关性和敏感系数,讨论水力压裂解析模型的裂缝扩展参数敏感性．     

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.      

不同围压作用下非均匀岩石水压致裂过程的数值模拟

从岩石细观非均匀性的特点出发，提出一个描述非均匀材料渗流和破裂相互作用的数值模型。在这个数值模型中，单元的力学、水力学性质根据统计分布而变化，以体现材料的随机不均质性，材料在开裂破坏过程中流体压力传递通过单元渗流，损伤耦合迭代来实现。算例表明，该模型能较好地模拟出岩石类材料在水力压裂作用下，微结构非均匀分布和不同围压比对破裂模式、失稳压力的影响，非均匀性导致试件的开裂压力、失稳压力明显不同，裂纹扩展路径不规则发展，模拟结果和实验结果较为一致。     

MODEL AND METHOD OF WELL TEST ANALYSIS FOR WELLS WITH VERTICAL FRACTURE

NomenclatureB———volumecoefficientofformationfluid,dimensionless;C———wellborestoragecoefficient,m3 MPa;Cft ———comprehensivecompressioncoefficientoffluidinfracture ,1 MPa;Ct ———comprehensivecompressioncoefficientofformationfluid,1 MPa ;h———heightofformation ,m ;K———formationpermeability ,μm2 ;Kf ———fracturepermeability ,μm2 ;KfWf ———fractureconductivity ,μm2 ·cm ;Lf ———halfoffracturelength,m ;N———thetotalnumberofselectedtimepoint,dimensionless;P———for…     

页岩气高效开采中钻井完井和水力压裂的关键力学问题

本文研究了在页岩气高效开采中钻井完井和水力压裂缝网改造的关键力学问题. 提出了页岩多孔弹性介质的本构、强度和断裂韧性的各向异性模型, 指出了微观均匀假设与微观各向同性假设在页岩多孔弹性本构中的简化应用, 给出了横观各向同性多孔弹性岩石材料常数的简化测量方案, 讨论了基于修正的能量最大释放率下裂纹扩展的弱面模型, 提出了裂纹扩展禁止区现象. 阐述了钻井完井过程中的多孔弹性介质井壁稳定性和剪切破坏的时间效应, 提供了多种破坏模式下井壁许可压力范围的显式表达式, 并与传统广义胡克定律得到结果对比. 给出了水平井水力压裂缝网改造技术, 包含水力压裂的大物模实验技术、水力压裂过程中基于扩展有限元与有限体积法的耦合流体/固体/裂缝扩展的数值模拟方法, 并与黏性主导的水力压裂解析解结果对比, 针对性分析了川渝地区的水力压裂施工现场实践应用问题. 建立了基于数据驱动的页岩气采收率预测方法, 指出了机器学习中极限梯度爬升法在小数据集情况下的有效性.      

Phenomenological approach to simulating hydraulic fracturing of a stratum

A mathematical model for hydraulic fracturing is proposed. The model is based on the presentation of the fractured portion of the stratum adjacent to the well as a heterogeneous fractured porous medium. Assumptions usually used in the theory of elastic flow are applied. Formulas for determining the size of the hydraulic fracturing zone and the degree of fracture opening under conditions of relative equilibrium are derived.     

Model of stepwise propagation of the tip of a hydraulic fracture in the absence of filtration

Quasi-static stepwise propagation of a hydraulic fracture in rock with a regular structure in the absence of filtration is considered. It is proposed to use a brittle fracture diagram taking into account the hydraulic fracturing fluid pressure and the confining pressure. Fracture curves describing the brittle rock fracture where the hydraulic fracturing fluid partially fills the fracture are constructed and used to predicted the possibility of stepwise propagation of hydraulic fracturing in the case where the fluid gradually flows into the fracturing crack. The regularity of the structure of the brittle rocks fracture is estimated from the results of two full-scale experiments: the critical stress intensity factor and the tensile strength limit of the rock. Experiments on pulsed loading of polymethylmethacrylate samples with stepwise crack propagation along concentric circular arcs were performed. The results of the experiments are consistent with theoretical predictions.