等曲率井中有重钻柱屈曲的非线性有限元分析

建立了等曲率井中有重钻柱屈曲的平衡方程及对应的泛函表达式,用有限元法对等曲率井 中有重钻柱屈曲过程进行了分析,给出了钻柱正弦屈曲和螺旋屈曲临界载荷的定义. 力学模 型中考虑了重力、钻柱上端井斜角和井眼轨迹曲率半径对屈曲的影响. 分析结果表明：载荷 增大时,钻柱的下端先出现局部屈曲,随后屈曲向钻柱上部扩展,导致钻柱发生整体屈曲, 屈曲位移、井壁约束力线密度和钻柱弯矩都呈周期性变化;重力对等曲率井中钻柱的屈曲有 较强的抑制作用,其影响不可忽略;井眼轨迹曲率半径越小,钻柱上端井斜角越大则对钻柱 屈曲的抑制作用越强.     

Unsteady Flow to Wells Partially Penetrating in Two-Layered Aquifers

The unsteady flow of water to well in a layered aquifer with an interlayer flow is examined in this paper. The system studied comprises an aquifer consisting of two productive layers of finite thickness that are in a perfect hydraulic contact and a well which partially penetrates in one of the layers. Each layer is assumed to be homogeneous and isotropic and the water contained in the aquifer is of identical physical properties and small compressibility.The analytical solutions are derived for the case when the system is characterised by equality of hydraulic diffusivity of layers. These solutions give the results accurate enough for practical applications and allow to estimate the effects of partial penetration and contrast in parameters of formation on distribution of the flow potential both at large distances from wells and at the wells.The obtained solutions also provide a basis for predicting the interlayer flow arising from the performance of a pumping well as well as between a pair of wells which have an open interval located in different layers of the aquifer. Two cases have been analysed: (1) a pumping pair of wells which is used to prevent water inflow to the productive well, and (2) a pumping-injection pair of wells providing the demanded mixing of water from adjacent layers. Some examples of flow patterns and specially computed diagrams are given to illustrate the operation of such systems.     

垂直井筒井液携砂流动规律研究及其在油井生产中的应用

借助自建的实验装置，研究了油井出砂砂粒在流体中的沉降规律，以此为基础提出了井液携砂能力计算模型，然后将这一研究结果与常规有杆泵抽油井生产参数设计方法相结合，提出了有杆泵抽油系统在携砂生产条件下的参数设计方法。     

污染区对部分打开井井底压力响应的影响

钻井造成的污染区对部分打开井的影响不同于裸眼井. 为了分析污染区对部分打开井井底压力响应的影响,建立了一种部分打开井的二维轴对称渗流模型,模型考虑了真实的污染区以及储层渗透率各向异性特征.利用有限元数值方法对模型进行求解,获得了部分打开井的井底压力响应及储层压力分布. 根据压力响应及压力分布特征,将部分打开井的压力响应过程划分为5 个流动阶段,其中早期局部径向流动和椭球流动是该类井最典型的特征. 对污染区的影响分析表明:传统方法中的表皮系数S 并不等于污染区引起的机械表皮系数S_d;无量纲井筒储存系数不能与机械表皮系数组合. 修正了传统方法中部分打开井的井底压力公式,验证了部分打开井的总表皮计算公式,为该类井的井底压力响应解释及产能预测提供理论指导.      

Scaling Immiscible Displacements in Porous Media with Horizontal Wells

Despite the increase in horizontal well applications, scaling fluid displacement in porous medium with horizontal wells is yet to be fully investigated. Determining the conditions under which horizontal wells may lead to better oil recovery is of great importance to the petroleum industry. In this paper, a numerical sensitivity study was performed for several well configurations. The study is performed in order to reveal the functional relationships between the scaling groups governing the displacement and the performance of immiscible displacements in homogeneous reservoirs produced by horizontal wells. These relationships can be used as a quick prediction tool for the fractional oil recovery for any combinations of the scaling groups, thus eliminating the need for the expensive fine-mesh simulations. In addition, they provide the condition under which a horizontal well configuration may yield better recovery performance. These results have potential applications in modeling immiscible displacements and in the scaling of laboratory displacements to field conditions.     

气体钻水平井环空冲蚀能量分析

在建立水平井流动方程的基础上,通过气固两相流动基本数学模型的求解数值模拟不同工况条件下的气固混合物冲蚀能量,得出了冲蚀能量的变化规律。算例数值模拟显示:环空速度剖面主要由注气量大小决定,机械钻速的影响不大;相同注气量条件下,机械钻速降低与井下岩屑浓度等比例下降;注气量的增加能提高井眼净化程度,但不如降低机械钻速效果明显;环空总冲蚀能中气体冲蚀能量占绝对主要地位,岩屑冲蚀能量只占极小部分,在相同注气量条件下总冲蚀能量基本相同;岩屑冲蚀能量主要取决于机械钻速,机械钻速越大井底产生岩屑越多冲蚀能力越强,相同机械钻速条件下,较大注气量能提供较大岩屑运移速度,提高了岩屑冲蚀能量。     

Mathematical Treatment of Point Sources in a Flow Through Porous Media Governed by Darcy's Law

We consider stationary air flow in a porous medium caused by extraction wells and governed by Darcy's law. Point sinks are described by Dirac functions. We distinguish two different situations: locally continuous and discontinuous conductivity near the wells. In both cases, well-posedness is proved. We propose a finite-element scheme in the general case and show the convergence of the approximated solution to the exact one.     

气体钻水平井井径扩大环空流动特征的数值模拟

由于气体钻水平井中岩屑受力状态与直井有很大不同,特另0是遇到井径扩大,更是携岩的关键点。因此,在分析了气体钻水平并岩屑运移特点以及建立环空连续性方程和动能方程的基础上,以实际并为例考虑了不同井径扩大率,数值模拟了其扩径段气固两相的流动状态,包括气固速度、岩屑浓度、压力分布等。研究结果表明：气体在经历扩径段时环空压力有个降落又回升的过程,随着井眼扩径系数的增大,压力下降又回升,所经历的长度会逐渐增长;扩径系数大于一定值时,扩径变径处存在一定区域的零流动区;扩径系数越大,低速区和回流区就越大越长,扩径下部区域越容易堆积岩屑,填充井眼。     

Using the Sequential Self-calibration Method and Genetic Algorithm Method to Optimally Design Tracer Test to Estimate Conductivity Distribution

A gradient-based inverse method – the sequential self-calibrated method – is combined with a genetic algorithm method to search the optimal design scheme for a tracer test. The sequential self-calibrated method is developed for estimating conductivity distribution in a study domain conditioning on tracer test data. To improve the calculation efficiency, a fast streamline-based approach is used to compute the derivative of concentration with respect to the changes of hydraulic conductivity. Performance of the sequential self-calibrated method has been studied using a synthetic aquifer having a sandwich-like geologic structure where hypothetical tracer tests are conducted. The study results indicate that the locations and number of sampling wells will significantly affect accuracy in the estimates. To maximize estimating accuracy in the sequential self-calibrated method for a fixed number of sampling wells, a genetic algorithm method is applied to search the optimal locations for sampling wells. The results indicate that the optimal sampling well locations depend on the apparent geologic structure and the difference in conductivity values for the various regions. For the sandwich-like structure, when the difference between conductivity values in the two separate regions is large enough, the optimal locations for the sampling wells will be fixed, regardless of conductivity values. The study results also show that based on the optimal sampling-well scheme, estimating accuracy will increase as the number of sampling wells increases, even though the rate of increasing accuracy slows as the number of wells increases.     

防止热采井套管热破坏的预膨胀固井技术

热力采油是开采稠油的最广泛、效益较高的方法.实践表明,注蒸汽稠油井如果用常规方法固井,那么在通常的注汽温度下,套管都因热应力而产生屈服变形.文中提出了防止热采井套管热破坏的预膨胀固井技术,即在注水泥结束但没有凝固时,将油层套管预热和向油层套管施加内压强,使套管膨胀;水泥在套管膨胀的条件下凝固.计算表明,采用预膨胀固井技术后,热采井在整个生产周期内,套管不但不屈服,而且还有较大的安全系数.室内实验证明,注汽后,采用预膨胀固井的套管的塑性变形量远小于常规固井的套管的塑性变形量.此项技术可能成为延长热采井套管使用寿命的重要手段.     

Multiphase Flow Fields in In-situ Air Sparging and its Effect on Remediation

In-situ air sparging (IAS) is used for the clean-up of soil and groundwater that are contaminated with volatile organic compounds in relatively permeable subsurface environments. In this study, we investigated the secondary groundwater and gas flow fields that develop in the vicinity of single and multiple air sparging wells. The purpose is to evaluate their effects on contaminant plume migration and thus, remediation. Governing equations describing multiphase flow and contaminant transport in a three-dimensional domain were formulated and solved using the Galerkin finite element technique. Trichloroethylene was selected as a target contaminant. The increase in air injection contributed to an increase in the size of the IAS cone of influence and the gas saturation levels within the cone. This reduced the groundwater velocity within the cone and increased the zone of detour of groundwater around the air sparging wells. This outcome was quantified and compared under several IAS operations. Different soil permeability characteristics also affected the groundwater and gas flow patterns, and this impacted the remedial performance of the IAS system. Under high ambient groundwater velocity, an air sparging system that uses a single injection well caused the detour of contaminant plumes around injection wells, regardless of air injection rates, and failed to meet the remedial goal specified here. This system was successful for relatively low ambient groundwater velocity environments used here. An IAS system with multiple injection wells was effective in capturing and remediating the detoured contaminant plume, and showed superior performance when compared to a single injection well IAS system. Using IAS simulation, we also analyzed the impact of injection rates on site remediation using single or multiple wells. Design criteria that are based on the results of this study would be useful in enhancing the performance of the IAS systems.     

Effective-Well Method for Matching and Predicting Oil Production

Decline curve analysis (DCA) is a traditional method for production prediction, which is still being used because it works in many cases and it is relatively simple to apply. However, DCA methods can neither match nor predict the fluctuating oil production during the early period when applied to entire reservoirs. The change in oil production may be because of variation in production conditions or the number of injection/production wells. In this study, we focused on the latter problem, change in the number of production wells. Obviously, there would be a significant oil production boost during a specific time period if more oil wells are drilled. The traditional DCA approach cannot match the increase in oil production due to the increase in the number of oil production wells. We have developed a method to match the oil production of entire reservoirs for the life span by considering the change in the number of production wells. The main idea of this approach came from the concept of effective wells. We applied this approach in several sandstone oil reservoirs with different permeabilities. The proposed effective-well model could match the oil production data in different reservoirs, even during the early period of production when the oil production rate change with time because of the variation in the number of producers. Comparison with the existing models (exponential, hyperbolic model, and harmonic models) was made and the results showed the proposed approach had the best fit to the production history in the cases studied.     

Effect of Well Orientation (Vertical vs. Horizontal) and Well Length on the Injection of CO<Subscript>2</Subscript> in Deep Saline Aquifers

Simulations of CO₂ injection into confined saline aquifers were conducted for both vertical and horizontal injection wells. The metrics used in quantifying the performances of different injection scenarios included changes in pressure near the injection well, mass of CO₂ dissolved into brine (solubility trapping), and storage efficiency, all evaluated with an assumed injection period of 50 years. Metrics were quantified as functions of well length, well orientation, CO₂ injection rate, and formation anisotropy (ratio of vertical to horizontal conductivity). When equal well lengths are compared, there is not a significant difference between the predicted performances of horizontal and vertical wells. However, the length of a horizontal well may exceed the length of a vertical well because the length of the horizontal well is not constrained to the vertical thickness of the geologic formation. Simulations show that, as the length of the horizontal well is allowed to increase, the geologic formation can receive a significantly higher CO₂ injection rate without exceeding a maximum allowable pressure. This result is observed in both isotropic and anisotropic formations, and suggests that horizontal wells may be advantageous under pressure-limited conditions. However, the use of horizontal wells does not significantly improve the storage efficiency, and under strongly anisotropic conditions, a vertical well provides higher storage efficiency than a horizontal well. We conclude that horizontal wells may be preferable if the goal is to sequester a large amount of CO₂ in a short period of time, but do not offer a significant advantage in terms of long-term capacity of a potential repository.     

Water filtration to partially penetrating wells in a two-layer confined stratum

Water filtration to partially penetrating wells in a uniform confined stratum has been extensively studied recently. Considerably less study has been made of filtration to partially penetrating wells in layered strata, which are frequently encountered in practice. Some particular cases of this problem were considered in [1–4], and its most complete solution was given in [4]. However, this solution is presented in a general form which is difficult to apply in practice.In the following we present the solution of the water filtration problem to partially penetrating wells in a two-layer confined stratum for the cases of the operating portion of the well located in both the upper and lower stratum layers. The problem is solved by the method developed in [5, 6], where the potential of a point sink is first found, and then the potential of a line sink of intensity q is found, which is then used as the operating portion of the well.Applying to the resulting solutions the known method of filtration resistances, approximate relations are presented for the final calculations.     

Interaction between bending and mobile charges in a piezoelectric semiconductor bimorph

We study the bending of a two-layer piezoelectric semiconductor plate (bimorph). The macroscopic theory of piezoelectric semiconductors is employed. A set of two-dimensional plate equations is derived from the three-dimensional equations. The plate equations exhibit direct couplings among bending, electric polarization along the plate thickness, and mobile charges. In the case of pure bending, a combination of physical and geometric parameters is identified which characterizes the strength of the interaction between the mechanical load and the distribution of mobile charges. In the bending of a rectangular plate under a distributed transverse mechanical load, it is shown that mobile charge distributions and potential barriers/wells develop in the plate. When the mechanical load is local and self-balanced, the induced carrier distributions and potential barriers/wells are also localized near the loading area. The results are fundamentally useful for mechanically manipulating mobile charges in piezoelectric semiconductor devices.     

边界元理论在复杂外边界油藏水平井渗流中的应用

受构造作用的影响,实际油藏的外边界往往是复杂多样的.本文从渗流理论出发建立了复杂外边界油藏水平井渗流数学模型,并采用Lord Kelvin点源解、贝塞尔函数积分和泊松叠加公式等方法求解了复杂外边界油藏水平井的边界元基本解,利用边界元的理论建立了复杂外边界油藏水平井井底压力响应数学模型.通过计算得到了无因次压力和压力导数双对数理论图版,并在其基础上分析了复杂外边界油藏水平井渗流特征及其影响因素.     

井筒气液两相流对致密气压裂水平井试井的影响

多段压裂水平井技术是目前开采致密气最常用的方法之一,在致密气压裂水平井试井测试中常常伴随着一定的产水量,井筒气液两相流会增加井筒流体的流动阻力,加大井筒流体流动对试井解释的影响.为了明确井筒气液两相流对致密气藏压裂水平井试井的影响,提高产水致密气压裂水平井的试井解释精度,建立了一种井筒气液两相流与地层渗流耦合的试井模型,采用数值方法对模型进行求解,获得了考虑井筒气液两相流的压裂水平井试井理论曲线、压力场分布及裂缝产量分布.研究结果表明:井筒气液两相流会增加试井理论曲线中压力和压力导数值,造成靠近入窗点的压力扩散要快于远离入窗点的压力扩散,引起靠近入窗点的裂缝产量要高于远离入窗点的裂缝产量.现场实例分析进一步说明,不考虑井筒两相流可能会对产水压裂水平井的试井解释结果产生很大误差,主要表现为水平井筒假设为无限大导流能力会使得拟合得到的表皮系数偏大,将测试点视为入窗点会使得拟合得到的原始地层压力偏小.所建立的考虑井筒两相流的压裂水平井试井模型为产水致密气井试井资料的正确解释提供了重要技术保障.      

Stator well flows in axial compressors

This paper reports a study of the flow conditions in spaces often found beneath the stationary blades of modern compressors – stator wells. The design of the stator wells in a modern high-pressure turbofan can be a limiting factor. This study shows good comparison with existing experimental data upon the pressures and velocities in related geometries. The deleterious effects upon machine performance of the flows between the stator well and the mainstream are considered. The purpose of this paper is to show that these effects, especially seal leakage, can be reduced by the incorporation of fins on the rotating component of the downstream well. This works by increasing the tangential velocity in this region, so reducing the pressure there and thus the inter-well leakage for a given radial clearance in the intermediate labyrinth seal and hence the outflow into the mainstream from the upstream well.