Performance of multi-stage fractured horizontal wells with stimulated reservoir volume in tight gas reservoirs considering anomalous diffusion

Horizontal well combined with volume fracturing technology has been extensively employed in the development of tight gas reservoirs. The disordered distribution of the induced and natural fractures in the reservoirs leads to the existence of the anomalous diffusion, so the conventional Darcy law has some limitations in describing the fluid flow under this circumstance. This paper introduces the fractional Darcy law to take into account the effect of the anomalous diffusion and then extends the conventional model of the multi-stage fractured horizontal (MSFH) well with the presence of the stimulated reservoir volume (SRV). The generated point source model for dual-porosity composite system includes the fractional calculus and its solution in Laplace space is derived. The superposition principle and the numerical discrete method are applied to obtain the solution for the MSFH well with SRV. Stehfest inversion method is used to transform the pseudo-pressure and production rate from Laplace space to real space. Type curves for pseudo-pressure and production rate are presented and analyzed. The influence of the relevant parameters on pseudo-pressure behavior and production rate decline is discussed in detail. The proposed model enriches the flow models of the MSFH well with SRV and can be used to more accurately interpret and forecast the transient pressure and transient rate.     

水平井压裂储层应力场分布模拟方法

在研究分析水力压裂对储层岩石力学特性参数影响的基础上,提出一种压力储层应力场分布模拟计算方法。通过建立水平井储层原地应力场模型和水力压裂产生人工裂缝诱导应力场模型,并且利用实际的水力压裂测井参数对储层原地应力场和压裂产生裂缝诱导应力场分布进行了模拟计算。模拟计算结果表明,压裂产生人工裂缝会对储层应力场分布造成很大影响;压裂后储层应力主要在裂缝周围得到积累,并且距离裂缝越远,应力值积累越少;压裂生成裂缝长度也会影响储层应力场分布,裂缝越长,裂缝诱导应力场减小越慢。     

Pressure transient analysis of multi-fractured horizontal wells in tight oil reservoirs with consideration of stress sensitivity

Multi-fractured horizontal well (MFHW) is an effective technique to develop unconventional reservoirs. Complex fracture network around the well and hydraulic fractures is formed during the fracturing process. Fracture network and hydraulic fractures are the main seepage channel which is sensitivity to the effective stress. However, most of the existing models do not take the effect of stress sensitivity into account. In this study, a new analytical model was established for MFHW in tight oil reservoirs based on the trilinear flow model. Fractal porosity and permeability were employed to describe the heterogeneous distribution of the complex fracture network, and the stress sensitivity of fracture was considered in the model. The Pedrosa substitution and perturbation method were applied to eliminate the nonlinearity of the model. By using the Laplace transformation method, the analytical solutions in Laplace domain were obtained. Then, validations were performed to show that the model is valid. Finally, sensitivity analysis was discussed. The presented model provides a new approach to the estimation of fracturing effect and can be also utilized for recognizing formation properties of tight oil reservoirs.     

高含硫气藏非稳态水平井产量预测模型研究

元素硫从含硫天然气中析出沉降会影响流体流动,常规的水平井产量预测模型无法用于高含硫气藏水平井非稳态产量预测。本文基于非稳态椭圆流理论,耦合基质内的椭圆流动和裂缝内的非达西流动,考虑元素硫沉积及缝间干扰效应的影响,建立了适用于酸化水平井与酸压水平井的非稳态产量预测模型。分析了硫沉积对渗透率、孔隙度的影响,计算了不同裂缝参数对产能的影响,该模型适用于变井底流压生产条件。计算结果表明：科学准确的元素硫溶解度模型能较好地预测高含硫气藏水平井产量。酸压改造后缝间干扰现象会降低气井产能,且随着时间逐渐增强。硫沉积会降低储层渗透率和孔隙度,使得产量下降。增大裂缝导流能力,增加裂缝半长或者裂缝数量都能有效提高水平井产量,与裂缝导流能力相比,裂缝半长和裂缝数量对产量的影响更大。     

Production rate analysis of multiple-fractured horizontal wells in shale gas reservoirs by a trilinear flow model

Most multiple-fractured horizontal wells experience long-term linear flow due to the ultralow permeability of shale gas reservoirs. Considering the existence of natural fractures caused by compression and shear stresses during the process of tectonic movement or the expansion of high-pressure gas, a shale gas reservoir can be more appropriately described by dual-porosity medium. Based on the assumption of slab dual-porosity, this paper uses the trilinear flow model to simulate the transient production behavior of multiple-fractured horizontal wells in shale gas reservoirs, which takes the desorption of adsorbed gas, Knudsen diffusion and gas slippage flow in the shale matrix into consideration. Production decline curves are plotted with the Stehfest numerical inversion algorithm, and sensitivity analysis is done to identify the most influential reservoir and hydraulic fracture parameters. It was found that the density and permeability of the natural fracture network are the most important parameters affecting the production dynamics of multiple-fractured horizontal wells in shale gas reservoirs. The higher the density and permeability of the natural fractures are, the shorter the time is required to exploit the same amount of reserve, which means a faster investment payoff period. The analytical model presented in this paper can provide some insight into the reserve evaluation and production prediction for shale gas reservoirs.     

低勘探程度区煤系致密气水平井地质导向技术及应用

在二维地震区、井控程度低及曲流河三角洲前缘沉积等复杂岩性储层中,实施水平井储层钻遇率较低。三维地质模型迭代更新与地质–工程一体化相结合的水平井地质导向技术应用逐渐广泛。鄂尔多斯盆地东南缘上古生界煤系发育山西组山₂ 3亚段北岔沟砂岩等多套致密砂岩储层,其中,大宁–吉县区块砂岩层厚度较薄、纵向岩性复杂、横向变化快、微幅构造发育,基本无出发井且末端井较远(大于1 500 m),水平井导向难度大。为了提高低勘探程度区水平井钻探效果,通过标志层识别与厘定、煤岩层对比、资料精准分析与补充、储层顶底特征识别等方法开展研究。首先,总结研究区煤层与炭质泥岩的快速区分方法,解决现场岩性识别困难的难题,构建研究区地层格架;而后,基于测井、地震、地质多种资料的地层精细对比,厘定1个Ⅰ级标志层及3个Ⅱ级标志层,在山₂ 3亚段进一步确定2个Ⅱ级标志层。最后,提出着陆点控制技术、水平段钻遇率提高技术与钻头出层判断方法,形成了三角洲前缘亚相储层水平井地质导向技术。将该技术应用于DJ-P37井区,累计完钻34口,平均砂岩钻遇率78.30%,取得了良好的钻探效果,可为类似区域煤系水平井钻进提供技术借鉴。      

低渗致密气井分类评价方法研究 ——以子洲气田为例

由于子洲气田低渗致密气储层地质情况复杂,储层物性差异大,造成子洲气田各井的产量、压力等生产特征不同。为了更好地指导低渗致密气井高效合理的开发,需要基于各井的静态特征和动态规律,对其进行合理的分类。采用储能系数和地层系数两个储层物性参数,作为静态评价指标;采用稳产期累产气量、稳产期日均产气量、平均日产气和单位压降产气量四个动态参数,作为动态评价指标。创造性地提出依据各评价指标频率分布直方图的特征,对气井进行各指标分级。基于正交矩阵的思路,建立了动静结合的低渗致密气井分类评价方法,最终形成了静-动结合的气井分类结果：子洲气田152口低渗致密气井中I类井（储层物性好,实际产量高）占11.2%、II类井（储层物性较差,实际产量高）占8.5%、III类井（储层物性好,实际产量低）占30.3%、IV类井（储层物性差,实际产量低）占50.0%。其中,III类井是今后生产开发的研究重点,明确III类井的范围,可为将来措施提产指明方向。建立的动静结合低渗致密气井分类评价方法,可为类似区块低渗致密气井的分类提供借鉴。     

页岩油藏多段水平井压后关井阶段压力扩散数学模型研究

多段多簇水平井压裂技术作为页岩油藏的重要开发手段已经得到了广泛认同,压后关井能充分发挥渗吸的作用,提高单井压后产量,但目前压裂液渗吸作用区域一直是困扰油藏工程师的重要难题。本文以陇东页岩油藏多段压裂井为研究对象,基于物质平衡原理,利用渗流力学和岩石力学理论,建立了压裂施工过程中和压后关井过程中流体压力扩散数学模型,研究了压力扩散和压裂液波及体积随时间的变化关系。结果表明：压裂液波及体积随关井时间的增加逐渐增加,但增加的幅度会逐渐降低。储层渗透率越小,孔隙度越大,压裂施工时间越长,关井阶段井底压力越高,地层能量越高。该结果可为页岩油藏最佳关井时间的确定提供理论支持。     

海上某气田悬空侧钻水平分支井技术及应用

E海低孔渗气田储量占总储量的93%,提高低渗透、特低渗透气田开采率,已经成为油气田勘探开发的重要课题。水平分支井技术成为提高低渗透、特低渗透气田开采率的重要手段,使用水平分支井技术提高气田开采率在国内外油气田开发已有先例且效果显著。水平分支井技术,是水平井和侧钻井等多种钻井技术的融合,是当今石油开采工业的热门技术,已在海油E海域多个油气田应用,是实现低渗气田高效开发的重要技术手段。因此,深入研究总结水平井分支井钻井技术意义重大。本文针对水平分支井侧钻技术,深入分析并结合X气田水平分支井现场实钻情况,总结出水平分支井在该区块现场应用的关键,为以后水平分支井在低渗油气田的推广和应用提供借鉴。     

非常规油气致密储集层微观结构研究进展*

致密储集层储集性能差, 孔喉以纳米级为主, 孔喉连通复杂。中国南方高过成熟海相页岩有机质纳米孔与粒内孔大小约为20～890 nm;陆相泥页岩孔喉类型为有机质孔与基质孔, 主体介于30～200 nm之间;致密砂岩微米级孔喉为粒间溶孔、颗粒溶蚀孔与微裂缝, 主体介于10～200μm之间, 纳米级孔隙大小介于70～400 nm之间, 以原生粒间孔与自生矿物晶间孔为主;致密灰岩孔喉类型有方解石粒内溶孔、粒间溶孔与微裂缝, 大小介于50～500 nm之间。页岩微孔喉总体随热演化程度增高呈先减少后增加趋势, 致密含油砂岩中油气赋存有4种状态, 粒间微孔为油气赋存最有利位置。针对非常规油气储集层独特特征, 仍需在仪器研发、技术方法与评价参数等方面加强研究探索。     

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.     

A model for gas pressure in layered landfills with horizontal gas collection systems

The recovery and emission of landfill gas (LFG) is an important topic in landfill management. To produce an effective engineering design for an LFG collection system, designers must understand the migration of gas from the waste body to horizontal extraction wells. This paper develops a two-dimensional analytical solution to enable the study of the gas pressure distribution, well pressure and recovery efficiency in layered landfills with horizontal wells. A horizontal layered structure is used to accommodate the non-homogeneity of various municipal solid waste (MSW) aspects with respect to depth, including gas generation, permeability and temperature. The governing equations, subject to boundary and continuity conditions, are solved by using separation of variables and double finite integral transforms. The solution was verified against another analytical solution and a numerical simulation. Subsequently, a sensitivity analysis of single-well model parameters is performed to optimize a double-well system. The results show that a landfill with horizontal collection systems cannot be assumed to be one dimensional with increasing well spacing. Additionally, both the operational vacuum and maximum gas pressure can be reduced through the design of a double- or multiple-well system. Therefore, the proposed solution can be used for the verification of more complex models and the preliminary design of a horizontal well system.     

基于物质平衡反演法的致密砂岩气藏地层压力计算

压力是气藏的“灵魂”,地层压力是评价气井产能,分析气藏潜力的基础。然而,受到资料完整程度、方法适用条件等因素的限制,大部分气井无法准确获取地层压力。为了评价致密砂岩气藏地层压力,基于少量压力监测资料,采用数学反演思维,提出物质平衡反演法。首先,利用拟稳定流动状态下气井生产数据,拟合Blasingame图版,计算气井动态储量。而后,通过动态储量及一个测压数据进行反演,建立物质平衡方程,代入累产气量,评价地层压力,最后,以大宁–吉县区块致密砂岩气井为例,进行地层压力计算。结果表明:(1) 物质平衡反演法仅需一个测压点,可以评价气井的地层压力变化。(2) 气井原始地层压力差异大,单井地层压力变化复杂,存在多个压力系统。(3) 压力系统不一致与储层非均质性强有关。研究结果对于致密气单井压力计算和致密气藏压力评价提供了可靠的方法,为致密气藏开发方案调整和效益开发奠定了基础。      

Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method

The scaled boundary finite‐element method, a semi‐analytical computational scheme primarily developed for dynamic stiffness of unbounded domains, is applied to the analysis of unsteady seepage flow problems. This method is based on the finite‐element technology and gains the advantages of the boundary element method as well. Only boundary of the domain is discretized, no fundamental solution is required and singularity problems can be modeled rigorously. Anisotropic and non‐homogeneous materials satisfying similarity are modeled with no additional efforts. In this study, firstly, formulation of the method for the transient seepage flow problems is derived followed by its solution procedures. The accuracy, simplicity and applicability of the method are demonstrated via four numerical examples of transient seepage flow – three of them are available in the literature. Homogenous, non‐homogenous, isotropic and anisotropic material properties are considered to show the versatility of the technique. Excellent agreement with the finite‐element method is observed. The method out‐performs the finite‐element method in modeling singularity points. Copyright © 2014 John Wiley & Sons, Ltd.     

水平井网状裂缝储层双侧向响应特性研究

网状裂缝型储层具有良好的油气储集能力且广泛存在。双侧向测井能够有效地识别裂缝。采用三维有限元素法对水平井网状裂缝型储层的双侧向响应进行数值模拟,并重点对网状裂缝中流体电阻率、基岩电阻率及裂缝倾角等因素变化所引起的响应特性进行了研究。数值结果分析表明,随着裂缝中流体电阻率增加,视电阻率值相应增加,但增加幅度不大;随着基岩电阻率的增加,视电阻也会随着增加,当基岩电阻率较小时,基岩电阻率的影响会降低;两组裂缝为低角度裂缝时,形成的网状裂缝对电流的阻碍能力较强。所得结论可为水平井网状裂缝型储层测井评价提供理论参考。     

Some applications of the boundary element method in geomechanics

This paper presents the complete formulation for the application of the Boundary Element Method to solve non-tension material problems. The formulation is based on including an extra term due to an initial stress field into the boundary integral statement. This is then used to iterate the solution until a state of non-tension is achieved. The resulting iteration process is very simple to apply and basically consists only of a single matrix–vector product. The applications show that accurate resultscan be obtained for boundary discretizations involving a small number of unknowns. Whenever possible, results are compared with analytical solutions or finite elements.     

Seepage analysis in a zoned anisotropic medium by the boundary element method

A simple and effective extension to the boundary element method for solving Laplace'S equation (?²u = 0) for boundary value problems is presented to solve steady confined and (or) steady unconfined seepage problems in zoned anisotropic mediums. Sample problems indicating the accuracy of results are given.     

Land subsidence due to gas/oil production in inhomogeneous transversally anisotropic half-space by a boundary element method

In a previous paper¹ the authors have developed and implemented a new boundary element (BE) model to simulate and predict land subsidence occurring over three-dimensional gas/oil fields in a homogeneous and isotropic half-space. The approach relies on Betti's reciprocal theorem and makes use of the classical fundamental solution of Boussinesq in the framework of the theory of linear poroelasticity. The BE method is here extended to inhomogeneous, transversally anisotropic soils by the aid of a two-dimensional finite element (FE) model which provides a fundamental numerical solution for the actual multi-layer setting of the subsurface system. The new FE–BE approach is then used to simulate the subsidence caused by gas production over the deep reservoir of Campo Ravenna Terra, Ravenna (Italy) from 1950 to 1980. The results compare very favourably with the outcome from a full more expensive three-dimensional FE model of the same occurrence.