High Velocity Flow in and Around Long Perforation Tunnels

In oil industries, wells are mostly cased and perforated rather than completing the producing formation as open-hole. This study concentrates on the steady-state flow behaviour of a single-phase fluid in and around perforated completion tunnels (up to 50 inches long) including inertial effects (Non-Darcy flow). It is shown that the pressure drop inside long perforated tunnels under high flow velocity conditions is negligible compared to that around the perforated region within the porous medium. The results also indicate that the impact of perforation parameters varies with increasing fluid velocity but approaches an asymptotic value at very high flow velocity. The perforation length is the most important parameter whereas perforation radius, rock and fluid properties have little impact on the perforation performance.     

THE PERFORATION PARAMETER OPTIMIZATION FOR MULTI FRACTURE INITIATION IN HYDRAULIC FRACTURING

针对复杂地质近井筒多裂缝起裂的难题, 结合岩体力学与损伤力学相关理论, 建立了近井筒地层流固——损伤力学模型, 采用数值求解获得了射孔壁面的应力及损伤状态, 计算表明:初始地应力最小值越小, 地层的起裂压力越低;射孔方位角越小, 起裂压力越低. 随着射孔方位角增大, 近井筒微裂缝为45° 夹角的拐折裂缝, 起裂压力增大, 基于此, 对于正断层及顺滑断层地应力类型, 取射孔方位角小于30°, 螺旋射孔夹角30°或45°, 对于逆断层地应力类型, 螺旋射孔夹角取45°, 可有效地实现多裂缝起裂.     

INVESTIGATION ON THE ATTENUATION OF A ROTATING LIQUID MOTION IN A CYLINDER WITH BOUNDARY RESISTANCE

为了分析圆柱形容器内同步旋转液面在边界阻力作用下的衰减机理，采用层流摩阻与湍流摩阻的理论模型和实验测试的方法对同步旋转液面在边壁阻力作用下的衰减规律进行了研究. 通过分析壁面阻力的特性，采用当量湿周对圆柱形容器中旋转液体运动的能量损失进行模拟，建立了壁面糙率、旋转半径，静水深度和液体旋转速度之间的本构方程. 通过对圆柱容器中的同步旋转液面在边界阻力作用下的层流和湍流形态的衰减过程进行实验测试，验证了理论模型的正确性. 基于验证后的理论方法，获得了圆柱容器中旋转液体的角速度、高度等随时间的变化过程，分析了摩阻形态、糙率和直径对旋转液面衰减过程的影响. 结果表明，边壁糙率和容器半径是决定旋转液面的衰减过程主要因素，边壁糙率越大液体旋转速度衰减越快，圆柱形容器半径越大液体旋转的衰减越慢.     

A numerical and experimental study to evaluate performance of vascularized cooling plates

The present paper reports on a numerical simulation and experimental validation of fluid flow and conjugate heat transfer characteristics of new vascular channels, whose cross-sections are semi-circular. The numerical analysis covers the Reynolds number range of 30−2000, with a cooling channel volume fraction of 0.04, pressure drop range of 30−10⁵ Pa. Six flow configurations were considered: first, second, and third constructal structures with optimized hydraulic diameters and non-optimized hydraulic diameter for each system size 10 × 10, 20 × 20, and 50 × 50, respectively. The numerical results of the proposed vascular channels show that the channel configurations of the optimized constructs show much lower flow resistance and temperature distribution than those of the non-optimized constructs. It is also shown that the power component in the power-law relationship between mass flow rate and pressure drop decreases as the system size and mass flow rates increase. The numerical results are validated by experimental data, and with the two exhibiting excellent agreement in all cases. The validation study against the experimental data shows that the presented numerical model is a reliable tool for predicting the performance of cooling plates under practical operating conditions and for the design of self healing or cooling system.     

New Correlative Models to Improve Prediction of Fracture Permeability and Inertial Resistance Coefficient

Presence of fracture roughness and occurrence of nonlinear flow complicate fluid flow through rock fractures. This paper presents a qualitative and quantitative study on the effects of fracture wall surface roughness on flow behavior using direct flow simulation on artificial fractures. Previous studies have highlighted the importance of roughness on linear and nonlinear flow through rock fractures. Therefore, considering fracture roughness to propose models for the linear and nonlinear flow parameters seems to be necessary. In the current report, lattice Boltzmann method is used to numerically simulate fluid flow through different fracture realizations. Flow simulations are conducted over a wide range of pressure gradients through each fracture. It is observed that creeping flow at lower pressure gradients can be described using Darcy’s law, while transition to inertial flow occurs at higher pressure gradients. By detecting the onset of inertial flow and regression analysis on the simulation results with Forchheimer equation, inertial resistance coefficients are determined for each fracture. Fracture permeability values are also determined from Darcy flow as well. According to simulation results through different fractures, two parametric expressions are proposed for permeability and inertial resistance coefficient. The proposed models are validated using 3D numerical simulations and experimental results. The results obtained from these two proposed models are further compared with those obtained from the conventional models. The calculated average absolute relative errors and correlation coefficients indicate that the proposed models, despite their simplicity, present acceptable outcomes; the models are also more accurate compared to the available methods in the literature.     

格子Boltzmann方法模拟多孔介质惯性流的边界条件改进

格子Boltzmann方法可以有效地模拟水动力学问题,边界处理方法的选择对于可靠的模拟计算至关重要.本文基于多松弛时间格子Boltzmann模型开展了不同边界条件下,周期对称性结构和不规则结构中流体流动模拟,阐述了不同边界条件的精度和适用范围. 此外,引入一种混合式边界处理方法来模拟多孔介质惯性流, 结果表明:对于周期性对称结构流动模拟,体力格式边界条件和压力边界处理方法是等效的,两者都能精确地捕捉流体流动特点; 而对于非周期性不规则结构,两种边界处理方法并不等价,体力格式边界条件只适用于周期性结构;由于广义化周期性边界条件忽略了垂直主流方向上流体与固体格点的碰撞作用,同样不适合处理不规则模型;体力-压力混合式边界格式能够用来模拟周期性或非周期性结构流体流动,在模拟多孔介质流体惯性流时,比压力边界条件有更大的应用优势,可以获得更大的雷诺数且能保证计算的准确性.      

页岩气藏压裂水平井试井分析

页岩气藏资源丰富,开发潜力巨大,已成为目前研究的热点.与常规气藏相比,页岩气藏运移机制复杂,流动模式呈非线性,有必要考虑页岩气的吸附解吸,天然微裂缝的应力敏感性,人工裂缝内的非达西流等非线性因素对压裂水平井压力响应的影响. 基于双重介质和离散裂缝混合模型,分别采用Langmuir等温吸附方程描述吸附解吸,渗透率指数模型描述应力敏感,Forchheimer方程描述非达西效应,建立页岩气藏压裂水平井数值试井模型. 运用伽辽金有限元法对模型进行求解.根据试井特征曲线,划分流动阶段,着重分析非线性因素对压力响应的影响.结果表明:页岩气藏压裂水平井存在压裂裂缝线性流、压裂裂缝径向流、地层线性流、系统径向流及封闭边界影响5 种流动阶段.吸附解吸的影响发生窜流之后,Langmuir吸附体积增大,拟压力导数曲线凹槽更加明显,系统径向流出现时间与压力波传播到边界时间均延迟;天然裂缝系统的应力敏感性主要影响试井曲线的晚期段,拟压力和拟压力导数曲线均表现为上翘,应力敏感效应越强,上翘幅度越大;高速非达西效应对早期段影响较大,非达西效应越强,拟压力降幅度越大,试井曲线上翘.与解析解的对比以及矿场实例验证了模型的正确性与适用性.      

孔眼流入对水平井中流动影响的实验研究

设计并建立了水平井筒变质量流动模拟实验装置。对具有射孔完井的水平井筒变质量流动进行了实验研究,利用先进的数据采集系统获取了大量的实验数据。对水平井井筒单孔眼段流动阻力损失分析可知,流动阻力由三部分组成：管壁摩擦阻力、加速损失和混合损失。对实验数据进行处理得出了混合损失和主流流速与孔眼流速之间的关系。对于一定的主流流速,混合损失随孔眼流速的增大而增大,同时,对于一定的孔眼流速,混合损失随主流流速的增大而增大,此时孔眼的流入对水平井筒中的流动造成的影响比较显著。孔眼的流入增加了井筒中流动的复杂性。对实验数据进行的回归结果表明,在本实验条件和范围内,主流流速和孔眼流速是造成混合损失的主要因素。     

Flow Performance of Perforated Completions

A powerful approximate method for modeling the flow performance of perforated completions under steady-state conditions has been developed. The method is based on the representation of the perforation tunnels surrounding a wellbore by the equivalent elongated ellipsoids. This makes possible an analytical treatment of a 3D problem of steady-state flow in a porous medium with complex multiple production surfaces. The solution is obtained for a vertical wellbore fully penetrating through a horizontal formation in the presence of permeability anisotropy. The perforations are oriented horizontally, arranged in almost arbitrary patterns, repeating along the wellbore, and may have different lengths and shapes. The hydraulic resistances of perforations flowing inside them as well as the crushed zones around them with impaired permeability are neglected. The approximate solution found was verified by comparing the previous analytical/numerical solutions for a small number of perforations. This approach allows one to determine the local skin or the effective wellbore radius for any perforated interval, which can then be integrated into the conventional calculations of well productivity and used for the perforating gun selection during perforation job design.     

A numerical method for accelerating the rate of convergence of the SIMPLE-like algorithm for flow through a thin filter

The control volume, finite difference method and the k-? tubulence model are employed in a numerical simulation of the turbulent fluid flow both outside and inside a blunt cylindrical sampler which houses a paper filter in its chamber. The presence of a paper filter, which has a very large resistance, results in a large pressure drop across the filter and this causes difficulties in making the SIMPLE or the SIMPLEC scheme converge. In order to improve the rate of convergence of the SIMPLE-like algorithm when the resistance of the filter is very large, an average pressure correction formula is proposed. Based on global mass conservation, a line average pressure correction for the paper filter is derived using a modified Darcy law for a porous medium. A combination of this formula and the SIMPLE-like algorithm can rapidly build up the pressure drop across the filter and hence dramatically improve the rate of convergence of the iterative scheme. Comparisons of the convergence histories and the numerical results for the fluid flow when using SIMPLE and SIMPLEC with the average pressure correction method show that the average pressure correction method for dealing with the paper filter significantly accelerates the rate of convergence of the iterative scheme.     

An optimization of a multi-layered plate under ballistic impact

This paper may be the first trial regarding the optimal design of a multi-layered plate under ballistic impact. An optimal design of a multi-layered plate to endure ballistic impact is suggested by using size optimization based on numerical simulations. The NET2D, a Lagrangian explicit time-integration finite element code for impact analyses, is used to find the optimal parameter values. Three different materials such as mild steel and aluminum for a multi-layered plate structure and die steel for the pellet are assumed. In order to consider the effects of strain rate hardening, strain hardening and thermal softening, the Johnson–Cook model is used as the constitutive models for the simulation. Several mesh types of different size and aspect ratio are tried to check the effect of mesh on the solution and to obtain the appropriate mesh density. The measuring domain is selected to reduce the analyzing time without affecting the sensitivity.The response surface method based on the design of experiments is used to obtain the optimal design. The average temperature or the equivalent plastic strain is introduced as a response for the optimization of the impact problem. Furthermore, the perforation criteria with the equivalent plastic strain to determine whether the plate structure is perforated or not is suggested. The optimized thickness of each layer in which perforation does not occur and the strength of multi-layer is maximized is obtained at a constant velocity of a pellet with a designated total thickness.     

THE INFLUENCE OF THE NEW TECHNOLOGY OF FIXED SURFACE PERFORATION ON CASING STRENGTH1)

用于非常规储层的定面射孔工艺可有效地降低水力裂缝的起裂压力,提高近井筒的泄油面积;但该工艺对套管强度的影响研究较少。本文基于流固耦合理论,建立了地层$\!$-$\!$-$\!$水泥环$\!$-$\!$-$\!$射孔套管的应力耦合模型,退化为裸套管与API标准进行比对,效验了模型,并发现地层约束条件下套管承受内压的能力提高了1.48$\sim$2.16倍,在此基础上,给出了套管尺寸、射孔直径及射孔相位角对套管承压能力的变化规律。计算表明：螺旋射孔方位角为45$^\circ$时,定面射孔间夹角为30$^\circ$时,套管内径越小,套管壁厚越厚,则套管的承压能力越高;相同参数下,定面射孔工艺比螺旋射孔工艺引起的套管承压能力略低。     

Experimental and numerical study of developing turbulent flow and heat transfer in convergent/divergent square ducts

 The work reported in this paper is a systematic experimental and numerical study of friction and heat transfer characteristics of divergent/convergent square ducts with an inclination angle of 1^∘ in the two direction at cross section. The ratio of duct length to average hydraulic diameter is 10. For the comparison purpose, measurement and simulation are also conducted for a square duct with constant cross section area, which equals to the average cross section area of the convergent/divergent duct. In the numerical simulation the flow is modeled as being three-dimensional and fully elliptic by using the body-fitted finite volume method and the kɛ turbulence model. The uniform heat flux boundary condition is specified to simulate the electrical heating used in the experiments. The heat transfer performance of the divergent/convergent ducts is compared with the duct with uniform cross section under three constraints (identical mass flow rate, pumping power and pressure drop). The agreement of the experimental and numerical results is quite good except at the duct inlet. Results show that for the three ducts studied there is a weak secondary flow at the cross section, and the circumference distribution of the local heat transfer coefficient is not uniform, with an appreciable reduction in the four corner regions. In addition, the acceleration/deceleration caused by the cross section variation has a profound effect on the turbulent heat transfer: compared with the duct of constant cross section area, the divergent duct generally shows enhanced heat transfer behavior, while the convergent duct has an appreciable reduction in heat transfer performance. Received on 18 September 2000 / Published online: 29 November 2001     

Numerical and experimental study of an innovative pipeline design in a granular pneumatic-conveying system

During gas–solid mixture conveying in a dense phase, material is conveyed in dunes on the bottom of the pipeline, or as a pulsating moving bed. This phenomenon increases the pressure drop and power consumption. We introduce a new technique to reduce the pressure drop, which is termed the perforated double tube. To validate this new model, the gas–solid flow pattern and pressure drop were studied numerically and experimentally. The power consumption was also studied experimentally. Numerical studies were performed by the Eulerian–Lagrangian approach to predict gas and particle movement in the pipeline. Comparisons between the numerical predictions and the experimental results for the gas–solid flow patterns and pressure drop show good agreement.     

NUMERICAL SIMULATION OF DRAG REDUCTION CAUSED BY PATTERNED WALL

用加入近邻相互作用势的格子玻尔兹曼方法模拟了表面修饰了去润湿性颗粒的二维管道内流体的流动. 结果显示,管壁的粗糙度、修饰颗粒的润湿性、管内压强以及管内流体黏滞性等都是影响管内流体流速的因素. 在一定压强下,管壁修饰疏水性的颗粒可以明显减小阻力,模拟结果也解释了开采地下油藏时存在启动压力梯度的原因.     

RESPONSE OF SPHERICAL SANDWICH STRUCTURE UNDER INNER BLAST LOADING

轻质夹芯结构在能量吸收领域有很广泛的应用。本文采用数值仿真的方法分析了球形密闭夹芯结构在内爆载荷作用下的动态响应。发现与主要靠夹芯层吸能的平板或曲板结构不同,球形密闭夹芯结构的内壁在能量耗散中起关键作用。与相同质量的均质球壳相比,夹芯层可以有效地降低外壁的变形和应力水平。此外,利用理论分析的方法,得出了几何尺寸对球形夹芯结构能量吸收特性的影响。最后指出,在爆炸容器的设计中,如果充分利用球形夹芯结构的内壁进行耗能,可以显著提高结构的抗爆当量。     

A unified theory of turbulent flow

Summary A general theory of turbulent flow is applied to incompressible flow in a circular pipe. The theoretical mean velocity distribution is found to be in good agreement with experiment, but there is some discrepancy in the normal stress distribution. The available pressure drop data are used to estimate the value of the apparent wall velocity as a function of Reynolds number and roughness. It is found that the results can be represented by simple expressions which in turn imply simple expressions for the pressure drop as a function of Reynolds number and roughness. However, it has not been possible to derive these results from fundamental considerations. The basis of Reynolds analogy and the application of the theory to channel flow are also discussed.     

Flow and heat transfer performance of a mini-channel radiator with cylinder disturbed flow

Mini-channel heat sinks have relatively low Nusselt number due to small Reynolds number. For heat transfer enhancement purpose, a mini-channel radiator with cylinder disturbed flow was proposed. The disturbed flow was created by a circular cylinder placed horizontally in front of channels entrance. The performance of heat transfer and pressure drop with/without disturbed flow was studied experimentally. It was found that the friction factor of mini-channel flow was larger than that of the macro-channel flow due to larger surface roughness, and the pressure drop caused by cylinder disturbed flow was less than 5%. It also concluded that the average Nusselt number increases with augment of Reynolds and Prandtl number. The Nusselt number correlations as the function of the Reynolds and Prandtl number were given for evaluation the heat removal performance of similar heat radiators. There is an inflexion point in the empirical formulas when the channel length equals to the thermal entrance length. For the mini-channels heat radiators with disturbed flow, the inflexion Reynolds number is larger than that of without disturbed flow. Due to the flow pulsing caused by circular cylinder placed in front of channels entrance, the thermal entrance length increases. On the other hand, for both mini-channels with or without disturbed flow, the thermal resistance increases with the decrease of pressure drop.     

聚能射流侵彻页岩储层损伤裂隙形成机制

为研究药型罩对聚能射孔弹侵彻页岩储层的射孔和损伤致裂效果的影响机理,建立了射孔弹-空气-页岩三维模型,设置药型罩的锥角分别为50°、60°、70°和80°,壁厚分别为0.5、1.0和1.5 mm,材料分别为铜、钢、钛和钨。利用ANSYS/LS-DYNA软件进行数值计算,分别从射流速度与形态、页岩射孔效果及页岩孔裂隙形成规律特征等进行系统性分析。研究结果表明：在射孔弹结构中,随着药型罩锥角的减小,射流速度提高、杵体速度降低、侵彻深度增大同时开孔孔径减小。在一定范围内,适当减小药型罩的壁厚,可以提高射流速度、减小杵体质量、增大侵彻深度和开孔倾斜度。药型罩材料对射流速度、杵体结构和页岩射孔效果均有显著影响,其中钨药型罩射孔弹的侵彻深度最大但开孔孔径最小,钛药型罩射孔弹的侵彻深度最小但开孔倾斜度最大,铜比钢药型罩射孔弹的侵彻深度略大但开孔孔径略小。通过研究不同对照组的页岩孔裂隙形成规律特征发现,页岩孔裂隙发育主要发生在杵体对页岩的再扩孔阶段,减小射流初始扩孔孔径、增大杵体直径、提高杵体速度,可以促进页岩孔裂隙发育程度。     

Y型微通道两相流内部流动特性刘

利用显微粒子图像测速技术、高速度数码显微系统及数值模拟方法研究了Y 型微通道内液滴的形成. 主要考虑了Y 型角度（45°,90°,135°,180°）、两相流量大小等因素的影响. 发现在挤压机制中,Y 型微通道内分散相液滴的形成主要受到来自连续相的剪切作用,Y 型角度越小,分散相所受到的剪切作用越大. 在液滴生成过程中,连续相速度剖面呈非对称抛物线型分布. 当Y 型角度小于180°时,角度的变化对液滴直径大小影响较小,但角度的减小会加快液滴的生成时间. 当Y 型角度为180°时,生成的液滴体积最大且生成时间最长. 毛细数对液滴直径和生成时间的变化同时产生影响,连续相毛细数的增大使得连续相在两相交汇位置处对分散相的作用力更集中,导致分散相更易破裂.