Productivity analysis of horizontal wells intercepted by multiple finite-conductivity fractures

Horizontal wells in the anisotropic reservoirs can be stimulated by hydraulic fracturing in order to create multiple finite-conductivity vertical fractures. Several methods for evaluating the productivity of the horizontal wells have been presented in the literature. With such methods, however, it is still difficult to obtain an accurate result. This paper firstly presents the dimensionless conductivity theory of vertical fractures. Then models for calculating the equivalent wellbore radius and the skin factor due to flow convergence to the well bore are proposed after analyzing the steady-state flow in porous reservoirs. By applying the superposition principle to the pressure drop, a new method for evaluating the productivity of horizontal wells intercepted by multiple finite-conductivity fractures is developed. The influence of fracture conductivity and fracture half length on the horizontal well productivity is quantitatively analyzed with a synthetic case. Optimum fracture number and fracture space are further discussed in this study. The results prove that the method outlined here should be useful to design optimum fracturing of horizontal wells.

Pressure transient analysis of a finite-conductivity multiple fractured horizontal well in linear composite gas reservoirs

Faulted gas reservoirs are very common in reality,where some linear leaky faults divide the gas reservoir into several reservoir regions with distinct physical properties.This kind of gas reservoirs is also known as linear composite(LC)gas reservoirs.Although some analytical/semi-analytical models have been proposed to investigate pressure behaviors of producing wells in LC reservoirs based on the linear composite ideas,almost all of them focus on vertical wells and studies on multiple fractured horizontal wells are rare.After the pressure wave arrives at the leaky fault,pressure behaviors of multiple fractured horizontal wells will be affected by the leaky faults.Understanding the effect of leaky faults on pressure behaviors of multiple fractured horizontal wells is critical to the development design.Therefore,a semi-analytical model of finite-conductivity multiple fractured horizontal(FCMFH)wells in LC gas reservoirs is established based on Laplace-space superposition principle and fracture discrete method.The proposed model is validated against commercial numerical simulator.Type curves are obtained to study pressure characteristics and identify flow regimes.The effects of some parameters on type curves are discussed.The proposed model will have a profound effect on developing analytical/semi-analytical models for other complex well types in LC gas reservoirs.

New approach for the treatment of vertical root fracture of teeth:A case report and review of literature

BACKGROUND Vertical root fracture(VRF)is one of the most common reasons for tooth extraction,although various methods have been applied for saving teeth with VRF.CASE SUMMARY This case report describes a woman who had a sinus tract on the labial gingiva of the left maxillary central incisor for past two months.Periodontal probing revealed an 8–10 mm deep,narrow,isolated pocket on the palatal side of the tooth.Clinical and radiographic examination confirmed a longitudinal root fracture.A new approach using a combination of resin and iRoot BP Plus through intentional replantation was used for the treatment of the tooth.At one-year follow-up,the tooth remained asymptomatic with normal periodontal probing depth,and radiographic images showed almost normal bone and periodontal structures around the root.CONCLUSION This new approach may be developed as an effective method for saving teeth with VRF.

The biomechanical role of periodontal ligament in bonded and replanted vertically fractured teeth under cyclic biting forces

After teeth are replanted,there are two possible healing responses：periodontal ligament healing or ankylosis with subsequent replacement resorption.The purpose of this study was to compare the fatigue resistance of vertically fractured teeth after bonding the fragments under conditions simulating both healing modes.Thirty-two human premolars were vertically fractured and the fragments were bonded together with Super-Bond C＆B.They were then randomly distributed into four groups（BP,CP,CA,BA）.The BP and CP groups were used to investigate the periodontal ligament healing mode whilst the BA and CA groups simulated ankylosis.All teeth had root canal treatment performed.Metal crowns were constructed for the CP and CA groups.The BP and BA groups only had composite resin restorations in the access cavities.All specimens were subjected to a 260 N load at 4 Hz until failure of the bond or until 2 x 106 cycles had been reached if no fracture occurred.Cracks were detected by stereomicroscope imaging and also assessed via dye penetration tests.Finally,interfaces of the resin luting agent were examined by scanning electron microscope.The results confirmed that the fatigue resistance was higher in the groups with simulated periodontal ligament healing.Periodontal reattachment showed important biomechanical role in bonded and replanted vertically fractured teeth.

MODEL AND METHOD OF WELL TEST ANALYSIS FORWELLS WITH VERTICAL FRACTURE

Based on the flow mechanism of hydraulic fractured wells, through integrating linear-flow model and effective well-radius model, a new model of well test analysis for wells with vertical fracture was established. In the model, wellbore storage, the damage in the wall of fracture and all kinds of boundary conditions are considered. The model is concise in form, has intact curves and computes fast, which may meet the demand of real-time computation and fast responded well test interpretation. A new method to determine effective well radius was presented, and the correlation between effective well radius and the fracture length, fracture conductivity, skin factor of fracture was given. Matching flow rate or pressure tested, the optimization model that identified formation and fracture parameters was set up. The automatic matching method was presented by synthetically using step by step linear least square method and sequential quadratic programming. At last, the application was also discussed. Application shows that all of these results can analyze and evaluate the fracturing treatment quality scientifically and rationally, instruct and modify the design of fracturing and improve fracturing design level.

A new method to calculate the productivity index for vertical fractured well of tight gas reservoir

Generally the irreducible water saturation of low permeability gas reservoir is quite high which leads to the permeability stress sensibility and threshold pressure gradient. Under the assumption that permeability varies with experimental law of the pseudo pressure drop, according to concepts of perturbable ellipses and equivalent developing regulations, the calculation method of stable production of hydraulically fractured gas well in low permeability reservoirs is investigated with threshold pressure. And productivity curve is drawn and analyzed. The result shows that, permeability modulus and threshold pressure have effect on production of fractured gas well. The higher the permeability modulus and the threshold pressure, the lower the production is. Therefore, the impact of stress sensitive and threshold pressure must he considered when analyzing the productivity of vertical fracture well in low permeability gas reservoir.

External fixator with lumbopelvic distraction spondylodesis for vertically unstable pelvic fracture

Objective To evaluate the clinical outcomes of external fixator with lumbopelvic distraction spondylodesis in treatment of vertically unstable pelvic fractures.Methods From January 2008 to March 2009,9 patients(4 males and 5 females)

Transient pressure analysis of polymer flooding fractured wells with oil-water two-phase flow

The oil-water two-phase flow pressure-transient analysis model for polymer flooding fractured well is established by considering the comprehensive effects of polymer shear thinning,shear thickening,convection,diffusion,adsorption retention,inaccessible pore volume and effective permeability reduction.The finite volume difference and Newton iteration methods are applied to solve the model,and the effects of fracture conductivity coefficient,injected polymer mass concentration,initial polymer mass concentration and water saturation on the well-test type curves of polymer flooding fractured wells are discussed.The results show that with the increase of fracture conductivity coefficient,the pressure conduction becomes faster and the pressure drop becomes smaller,so the pressure curve of transitional flow goes downward,the duration of bilinear flow becomes shorter,and the linear flow appears earlier and lasts longer.As the injected polymer mass concentration increases,the effective water phase viscosity increases,and the pressure loss increases,so the pressure and pressure derivative curves go upward,and the bilinear flow segment becomes shorter.As the initial polymer mass concentration increases,the effective water phase viscosity increases,so the pressure curve after the wellbore storage segment moves upward as a whole.As the water saturation increases,the relative permeability of water increases,the relative permeability of oil decreases,the total oil-water two-phase mobility becomes larger,and the pressure loss is reduced,so the pressure curve after the wellbore storage segment moves downward as a whole.The reliability and practicability of this new model are verified by the comparison of the results from simplified model and commercial well test software,and the actual well test data.

An evaluation method of volume fracturing effects for vertical wells in low permeability reservoirs

To evaluate the fracturing effect and dynamic change process after volume fracturing with vertical wells in low permeability oil reservoirs, an oil-water two-phase flow model and a well model are built. On this basis, an evaluation method of fracturing effect based on production data and fracturing fluid backflow data is established, and the method is used to analyze some field cases. The vicinity area of main fracture after fracturing is divided into different stimulated regions. The permeability and area of different regions are used to characterize the stimulation strength and scale of the fracture network. The conductivity of stimulated region is defined as the product of the permeability and area of the stimulated region. Through parameter sensitivity analysis, it is found that half-length of the fracture and the permeability of the core area mainly affect the flow law near the well, that is, the early stage of production;while matrix permeability mainly affects the flow law at the far end of the fracture. Taking a typical old well in Changqing Oilfield as an example, the fracturing effect and its changes after two rounds of volume fracturing in this well are evaluated. It is found that with the increase of production time after the first volume fracturing, the permeability and conductivity of stimulated area gradually decreased, and the fracturing effect gradually decreased until disappeared;after the second volume fracturing, the permeability and conductivity of stimulated area increased significantly again.

2.5D boundary element simulation of wave propagation in a vertical fluid-filled borehole with irregular shape

In this paper, a boundary element formulation in the wave-number space domain for solving the wave equation for a borehole with arbitrary shape in acoustic logging problems is presented. The problem is treated as a two-dimensional medium with the discrete wave- number method in the vertical direction. The method is validated by comparing the results obtained by this method with those obtained by the finite-difference method. The method is used to study the effect on wave propagation in a vertical borehole of a vertical fracture. For a monopole source, the dispersion curves for Stoneley waves yield three branches. For dipole and quadrupole sources, different orientations of the source yield different results. When the dipole source is orthogonal to the fracture, the dispersion curve is similar to that of the open hole, while the curves are quite different when the source is parallel to the fracture. These characteristics enable us to determine the orientation of the vertical fracture.

Integration of Electrical Resistivity and Electromagnetic Radiation Methods for Fracture Flow System Detection

An electrical resistivity and electromagnetic emission survey was carried out involving the use of vertical electrical soundings (VES) and natural pulse electromagnetic field of the earth (NPEMFE). The use of this new methodology managed to detect the fracture flow system rupture zones in the underground, also answered the questions about the deferent subsurface water bodies. The present study focuses on Marsaba-Feshcha sub-basin in the northeast of the Dead Sea. Due to the scarcity of boreholes in the study area, several geophysical methods were implanted. The combination of these two methods (VES and NPEMFE) with the field observations and East-West transversal faults with the coordination (624437/242888) was determined, cutting through the anticlines with their mainly impervious cores with fracture length of >400 m. These transversal faults saddle inside Nabi Musa syncline (Boqea syncline), leading to a hydraulic connection between the Lower and the Upper Aquifer. Due to the identified transversal fault, the water of the Upper and Lower Aquifer mixed and emerged as springs at Ein Feshcha group.

A new model for predicting hydraulic fracture penetration or termination at an orthogonal interface between dissimilar formations

Vertical height growth of hydraulic fractures(HFs)can unexpectedly penetrate a stratigraphic interface and propagate into neighboring layers,thereby resulting in low gas-production efficiency and high risk of groundwater contamination or fault reactivation.Understanding of hydraulic fracture behavior at the interface is of pivotal importance for the successful development of layered reservoirs.In this paper,a twodimensional analytical model was developed to examine HF penetration and termination behavior at an orthogonal interface between two dissimilar materials.This model involves changes in the stress singularity ahead of the HF tip,which may alter at the formation interface due to material heterogeneity.Three critical stress conditions were considered to assess possible fracture behavior(i.e.,crossing,slippage,and opening)at the interface.Then,this model was verified by comparing its theoretical predictions to numerical simulations and three independent experiments.Good agreement with the simulation results and experimental data was observed,which shows the validity and reliability of this model.Finally,a parametric study was conducted to investigate the effects of key formation parameters(elastic modulus,Poisson’s ratio,and fracture toughness)between adjacent layers.These results indicate that the variation in the introduced parameters can limit or promote vertical HF growth by redistributing the induced normal and shear stresses at the interface.Among the three studied parameters,Poisson’s ratio has the least influence on the formation interface.When the fracture toughness and elastic modulus of the bounding layer are larger than those of the pay zone layer,the influence of fracture toughness will dominate the HF behavior at the interface;otherwise,the HF behavior will more likely be influenced by elastic modulus.

Krachow法缝合联合钢丝垂直间断治疗老年髌骨下极粉碎性骨折的疗效

目的研究Krachow法缝合联合钢丝垂直间断固定治疗老年髌骨下极粉碎性骨折的疗效。方法选取2019年1月至2022年3月收治的102例老年髌骨下极粉碎性骨折患者作为研究对象。按随机数字表法分为两组,观察组51例,采用Krachow法缝合联合钢丝垂直间断固定,对照组51例,采用钢丝垂直间断固定。统计分析两组临床疗效、膝关节活动范围(ROM)、膝关节功能Bostman评分及并发症情况。结果观察组临床疗效优良率为88.24%,对照组优良率为64.71%,差异有统计意义(P<0.05)。观察组膝关节ROM、Bostman评分分别为131.51°±6.80°、(28.65±2.20)分,对照组膝关节ROM、Bostman评分分别为115.87°±5.91°、(23.58±2.51)分,差异有统计意义(P<0.05)。观察组并发症总发生率为9.80%,对照组并发症总发生率为27.45%,差异有统计意义(P<0.05)。结论Krachow法缝合联合钢丝垂直间断固定治疗老年髌骨下极粉碎性骨折复位良好,固定牢靠,对周围软组织影响小,并发症少,有利于膝关节功能恢复。

鄂尔多斯盆地东南地区延长组长6_(3)-长7_(1)低孔低渗储层裂缝特征及其影响因素

研究区长6_(3)-长7_(1)低孔低渗储层天然裂缝发育类型多、成因复杂,为了厘清其裂缝发育特征及其影响因素,通过综合运用野外露头调查、岩心观察及成像测井裂缝识别等方法,系统分析了研究区长6_(3)-长7_(1)裂缝特征及其影响因素。结果表明:研究区长7_(1)较长6_(3)裂缝更发育,裂缝主要发育在细砂岩中,产状以垂直缝和高角度斜交缝为主,多数为未充填缝,裂缝的发育主要受区域应力值、地层岩性、岩石物性、岩层厚度及力学结构面影响。研究成果为该地区低孔低渗储层注水驱油和人工压裂的部署方案提供理论依据与支持。

基于改进粒子群算法的VTI介质裂隙预测

裂隙产生的各向异性在地层介质中广泛存在,基于各向异性的裂隙参数反演和预测在一定程度上能提高裂隙反演的精度和预测的可靠性。本文通过建立基于VTI介质的反射系数方程,引入模拟退火算法中的Metropolis准则设置跳出概率对粒子群标准算法进行改进,实现对VTI介质中纵、横波速度及各向异性参数等属性的反演;并通过各向异性相关的属性、泊松比和泊松速度的联合,实现对裂隙充填物的预测。通过二层模型和Marmousi2模型对算法的稳定性和抗噪性进行测试,论证了方法的可行性;并进一步将方法应用于煤矿实际资料,对裂隙含水性进行预测,论证了方法的有效性。

不同空心加压螺钉固定方式对股骨颈垂直型骨折的有限元分析

背景:股骨颈骨折线越垂直的股骨颈骨折可能承受更多的剪切力,因此可能容易发生内固定失效、骨不连或股骨头坏死等并发症,目前关于哪种空心钉固定模式是理想的还存在争议。目的:通过有限元分析方法评估不同构型及数目的空心螺钉构型对股骨颈垂直骨折的生物力学差异。方法:收集1名24岁健康男性志愿者的股骨CT数据,导入Mimics软件构建股骨三维几何模型;在Geomagic软件进行模型细化及拟合曲面处理;导入SolidWorks软件,建立股骨颈垂直骨折模型。通过建立3枚正三角构型、3枚倒三角构型、3枚双平面双支撑构型(F方案)、3枚横行构型、4枚菱形构型、4枚Alpha构型6种空心螺钉模型,比较各构型内固定和股骨骨折模型在不同载荷(350,700,1400,2100 N)作用下的应力分布情况及位移峰值。结果与结论:(1)在4种载荷下,螺钉应力情况:双平面双支撑构型(F方案)>横行构型>倒三角构型>正三角构型>Alpha构型>菱形构型,各组螺钉的Von mises应力峰值均集中在靠近断裂线的螺钉处。(2)在4种载荷下,螺钉位移情况:Alpha构型>倒三角构型>正三角构型>双平面双支撑构型(F方案)>菱形构型>横行构型,位移峰值主要集中于空心螺钉头部。(3)在4种载荷下,股骨近端骨块应力情况:双平面双支撑构型(F方案)>横行构型>倒三角构型>Alpha构型>正三角构型>菱形构型,应力峰值主要集中在股骨颈下部。(4)在350 N载荷下,股骨近端骨块位移情况:横行构型>双平面双支撑构型(F方案)>正三角构型>Alpha构型>倒三角构型>菱形构型;在其他3种载荷中,倒三角构型位移峰值均小于菱形构型,位移峰值主要集中于头部;(5)股骨近端骨块断面应力分布中棱形构型最为分散,股骨位移峰值中棱形构型最小;各内固定模型的应力、位移、断裂端位移峰值随载荷的增加而逐渐增大;(6)4枚菱形构型模型对股骨颈垂直骨折内固定的生物力学性能优于其他各组模型,其固定牢靠,骨折端位移值小,应力分散,有助于抵抗剪切力和防止内翻坍塌发生,为骨折愈合创造良好的机械环境。

GuttaFlow Bioseal封闭剂对椭圆形根管抗垂直折裂能力的影响

目的:探讨GuttaFlow Bioseal根管封闭剂对椭圆形根管抗垂直折裂能力的影响。方法:CBCT扫描60颗正畸减数拔除的下颌单根前磨牙,当距离根尖5 mm处颊舌管径大于等于近远中管径2倍时,为符合筛选条件的椭圆形根管。使用Protaper系统将30颗椭圆形根管的离体牙预备至F2,随机分为GuttaFlow Bioseal充填组和iRoot SP充填组,每组分别用热垂直加压法、冷牙胶侧压法及单尖法充填根管。选取5颗离体牙作为阴性对照组。将充填完好的牙根在37℃、100%湿度的恒温箱中保存14天后,垂直放入自聚合丙烯酸树脂圆柱模型中,随后将样本固定于万能试验机的下板,用直径4 mm的球以1 mm/min的速度垂直向下加压,直至出现折裂,用N记载负载值。采用SPSS 29.0软件包对数据进行t检验与单因素方差分析,组间进行LSD分析,显微镜下分析断裂模式。结果:GuttaFlow Bioseal充填组及iRoot SP充填组相比无显著差异(P=0.321),不同组间抗垂直折裂能力存在显著差异(P<0.05)。使用热垂直加压充填法与单尖法时,GuttaFlow Bioseal充填后的样本牙抗垂直折裂能力显著高于iRoot SP,而使用冷侧压充填法时的抗垂直折裂能力显著低于iRoot SP。结论:使用热垂直加压充填法和单尖法充填根管时,GuttaFlow Bioseal有提高牙根抗垂直折裂能力的潜力,但仍需更多临床试验予以验证。

根管治疗后隐匿性牙根纵裂特征的体外及micro-CT研究

目的:收集根管治疗后隐匿性牙根纵裂牙(subtle vertical root fracture, SVRF),对其进行裂纹特征体外观察及micro-CT扫描,探索其裂纹特征并探讨其发生发展过程。方法:收集我院2021年10月~2023年10月拔除的根管治疗后SVRF患牙共计21颗,收集SVRF患牙的牙位及裂纹发生的牙根位。在直视或透照法下观察裂纹数目,以根管为中心,颊、舌、近中、远中分别计算,以及裂纹纵向长度根据裂纹是否累及釉牙骨质界及根尖区分为4类。使用micro-CT扫描并评价裂纹是否累及根管,裂纹在轴位图像上的方向(颊舌,近远中向),并在裂纹最宽层面进行裂纹宽度测量,将裂纹最宽处在牙根上的分布分为根上部、根中部及根下部。结果:本研究共收集21颗SVRF患牙,累及24个牙根,其中17个牙根为完全性裂纹,7个为不完全性裂纹,共计41条裂纹。上颌前磨牙牙根及下颌磨牙近中根为发生牙根纵裂最多的牙根,且这些牙根均表现为颊舌/腭向扁根并分为颊舌/腭向双根管。所有裂纹均为颊舌/腭向,均累及根中区及根管内壁。裂纹最大宽度无论是在牙根上的纵向分布还是在水平面上的分布都没有明显的规律。结论:根管治疗后SVRF的裂纹均累及根中区,均由根管壁向根面延伸,裂纹宽度无明显规律;推测根中区的根管内壁为牙根纵裂发生的起始部位;裂纹扩展的过程具有无序性和多样性。

水平井水力压裂裂缝扩展诱发垂直邻井光纤应变演化特征

水力压裂过程中很难准确获取裂缝高度扩展信息,利用分布式光纤可准确评价裂缝扩展信息。采用有限元耦合内聚力单元方法,建立水平井水力压裂裂缝扩展诱发垂直邻井光纤应变的正演模型,进行垂直邻井光纤应变数值模拟,分析光纤应变演化特征;根据压裂施工参数及垂直邻井光纤布设位置,判定水力压裂裂缝的光纤有效监测范围;利用大型真三轴压裂实验与分布式光纤感测设备,进行光纤实时监测水平井水力压裂物理实验。结果表明:裂缝高度扩展诱发光纤应变演化分为应变增强、张应变扩展、应变直线状汇聚及应变弱化4个阶段,光纤应变演化特征表现为中间部分出现张应变汇聚带,两侧出现压应变汇聚带。当水力压裂裂缝在光纤有效监测范围内时,垂直邻井光纤可有效监测裂缝高度扩展情况。垂直邻井的光纤应变演化结果与光纤应变正演模计算结果验证正演模型的正确性。利用裂缝高度扩展诱发垂直邻井光纤应变演化特征可评价裂缝高度扩展状态,为油田压裂设计提供参考。

沁水盆地柿庄北区块水平井开发方式地质适应性分析

针对柿庄北区块直井表现出达产率低、产量下降快、产能差异大的生产特征,通过对柿庄北区块43口探井、397口开发井进行详细剖析,并与潘河、柿庄南区块地质条件进行了对比分析。结果表明,埋深大、低渗透、煤体结构分布复杂是制约柿庄北区块开发关键地质问题。为了进一步明确柿庄北储层渗透低原因,对柿庄北、潘河、杨家坡区块煤心进行数字岩心扫描,发现柿庄北区块相对潘河、杨家坡区块储层孔裂隙数量都发育最少且孔裂隙连通性最差,并明确煤层演化过程是形成孔裂隙差异的关键因素。此外,结合地质剖析,开展了地质—工程一体化分析,明确直井压裂这种点状开发方式的不适应性,提出水平井开发方式适应埋深增大、煤体结构分布复杂、微观孔裂隙连通性较差的储层特征,并在柿庄北一体化二期显示出较好产气潜力。