Measurement and Modelling of Gas Condensate Flow Around Rock Perforation

In the petroleum production industry wells are mostly cased and perforated in the producing formation. Perforation characteristics such as size, length, number of perforation tunnels and their arrangements as well as fluid and rock properties determine fluid flow behaviour in the wellbore region, hence, well productivity. Flow of gas and condensate around a perforation tunnel (including the damaged zone) has been studied by performing steady-state core experiments and simulating the results numerically, using a finite element modelling approach. The model allows for the changes in fluid properties and accounts for the coupling of the two phases and the inertial effect using a fractional flow based correlation. The results indicated that different sets of thickness-permeability (h−k) values obtained from matching single-phase flow performance could be assigned to the damaged zone around perforation to represent the two-phase flow performance. The status of the tip of the perforation for two extreme cases of totally closed and fully open was investigated and found to have a minimal effect on the performance of the system.     

Acoustic sounding of perforated wellbores by short waves

The reflection and transmission of harmonic waves and waves of finite duration through the boundary of the perforated zone of a cased wellbore filled with a fluid are studied. A model of the plane fluid flow in the well (in a quasi-one-dimensional approximation) and filtration absorption of the fluid by the porous medium surrounding the well is proposed. The effect of the quality of the perforation (length of perforation tunnels) on the evolution of the waves reflected from the boundary of the perforated zone of the well is studied.     

The study of the induction of subsonic wind tunnels with an axisymmetric working part

For the case of small perturbations of the velocity on the boundary of the flow and arbitrary degree of perforation of the wall of the wind tunnel which is constant along its length, a solution has been found for the axisymmetric boundary-value problem of subsonic flow around a thin body of revolution in perforated boundaries. The boundary condition connects the tangential component of the perturbed velocity and the component normal to the wall, and has a general form for the whole boundary. From the solution obtained, the optimum degree of perforation of the wall is found for which distortion of the pressure coefficient on the surface of the model is a minimum in comparison with the unbounded flow round the body. The questions of the induction of the walls of the working part of the wind tunnel, the formulation of the boundary condition, and the determination of the corrections to the aerodynamic characteristics of the model are considered in a number of studies [1–5]. Lately a promising method was been worked out for reducing the influence of the walls directly in the process of experiment by regulating the parameters of the gas near the boundary in such a way that they correspond to the parameters in flow round the same body by an unbounded flow [3, 5]. However, the design properties of many working tunnels do not permit this method to be applied. The induction of such tunnels as these can be reduced only by the choice of an optimum degree of perforation of the walls. In the articles [6–8] there is a study of the effect of perforated boundaries on the flow round a profile, the degree of perforation in [7] being assumed to be small.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–154, January–February, 1985.The author is grateful to V. M. Neiland for his constant attention to the study and for discussion of the results.     

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.     

Drag reduction by reconfiguration of a poroelastic system

Because of their flexibility, trees and other plants deform with great amplitude (reconfigure) when subjected to fluid flow. Hence the drag they encounter does not grow with the square of the flow velocity as it would on a classical bluff body, but rather in a less pronounced way. The reconfiguration of actual plants has been studied abundantly in wind tunnels and hydraulic canals, and recently a theoretical understanding of reconfiguration has been brought by combining modelling and experimentation on simple systems such as filaments and flat plates. These simple systems have a significant difference with actual plants in the fact that they are not porous: fluid only flows around them, not through them. We present experimentation and modelling of the reconfiguration of a poroelastic system. Proper scaling of the drag and the fluid loading allows comparing the reconfiguration regimes of porous systems to those of geometrically simple systems. Through theoretical modelling, it is found that porosity affects the scaling of the drag with flow velocity. For high porosity systems, the scaling is the same as for isolated filaments while at low porosity, the scaling is constant for a large range of porosity values. The scalings for the extreme values of porosity are also obtained through dimensional analysis.     

THE FLOW RESISTANCE CHARACTERISTICS OF PERFORATED LINER DUCTS

利用计算流体力学方法对穿孔壁面通道内部流动进行了数值模拟,分析了其流动沿程摩擦阻力特性。计算中,假设流体不通过小孔进出穿孔壁面背后的吸声材料。经实验对比,采用Realizable k--" 湍流模型结合增强型壁面函数,可获得比较理想的计算结果,数值模拟与实验测量的压损值相对偏差在10% 以内。对于穿孔壁面通道流动阻力计算,提出了等效粗糙度概念,结合达西公式、克罗布鲁克公式计算获得了等效粗糙度数值。研究了穿孔板小孔孔径、穿孔率对等效粗糙度的影响,发现等效粗糙度与孔径成二次方关系、与穿孔率成线性关系。     

Possibility of determining the quality of well perforation by local acoustic probing

A theoretical problem of local acoustic probing of a perforated segment of the well is considered. The effect of porosity and permeability of the porous medium surrounding the well and the quality of perforation (porosity, length, and radius of perforation channels) on the velocity and the coefficient of decay of harmonic waves and on the evolution of finite-duration waves propagating in the perforated segment is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 52–57, January–February, 2009.     

A study of the perforation of stiffened plates by rigid projectiles

In the present paper, a four-stage perforation model that accurately predicts the residual velocity is developed by adopting an energy method. The four stages are plug formation, dishing formation, petal formation and projectile exit. In addition, some important experimental results are presented and analyzed to validate the present perforation model. In the experiments, high speed camera system is used to record the perforation process. Observations on target damage and measurements of initial velocities and residual velocities with the aid of the system are presented. Numerical simulations are carried out for projectiles against single and layered plates adopted in the experiments. The perforation process is studied and the deformation and failure modes are obtained. The predictions of numerical simulations and analytical model are found in reasonably good agreement with those of experiments, and can be used to predict the ballistic limit and residual velocity of stiffened plates perforated by rigid projectiles.     

Self-sustained oscillations of shear flow past a slotted plate coupled with cavity resonance

Shear flow past a slotted plate configuration can give rise to highly coherent, self-sustained oscillations when coupling occurs with a resonant mode of an adjacent cavity. The distinctive feature of these oscillations is that the wavelength of the coherent instability along the plate is of the order of the plate length. This observation is in contrast to previous investigations of flow past perforated or slotted surfaces, where the instability scales on the diameter of the perforation or the gap length of a slot. The present oscillations occur even when the inflow boundary layer is turbulent and an inflectional form of the shear flow cannot develop along the cavity opening, due to the presence of the slotted plate. Instigation of a resonant mode of the cavity, in conjunction with an inherent instability of the shear flow along the plate, gives rise to ordered clusters of instantaneous vorticity and instantaneous velocity correlation. During the oscillation, ejection of flow occurs from the cavity to the region of the shear flow; this ejection is in accord with the convection of the large-scale cluster of vorticity along the slotted plate. This oscillation can be effectively detuned by adjusting the inflow velocity, such that the inherent instability of the shear flow past the slotted plate is no longer coincident with the resonant frequency of the cavity. Certain features of this self-sustained oscillation are directly analogous to recent findings of oscillations due to shear flow past a perforated plate bounded by a cavity, but in the absence of cavity resonance effects.     

Slow motion of a permeable sphere in a viscous fluid

Flow of a viscous fluid past a permeable sphere is investigated in the Stokes approximation. An example of such a flow is flow past a perforated or meshed spherical surface. The elements of the sphere contain rigid impermeable sections and openings through which the fluid can flow. The interaction of the sphere with the flow is described by two drag coefficients, which established the connection between the flow velocity of the fluid at the sphere and the stress tensor on it. The dependence of the flow pattern and also the drag and flow rate of the fluid on these coefficients is investigated. In special cases, the obtained solution describes flow past solid and liquid spheres.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 165–167, September–October, 1982.     

A study of the perforation of stiffened plates by rigid projectiles

In the present paper, a four-stage perforation model that accurately predicts the residual velocity is developed by adopting an energy method. The four stages are plug formation, dishing formation, petal formation and projectile exit. In addition, some important experimental results are presented and analyzed to validate the present perforation model. In the experiments, high speed camera system is used to record the perforation process. Observations on target damage and measurements of initial velocities and residual velocities with the aid of the system are presented. Numerical simulations are carried out for projectiles against single and layered plates adopted in the experiments. The perforation process is studied and the deformation and failure modes are obtained. The predictions of numerical simulations and analytical model are found in reasonably good agreement with those of experiments, and can be used to predict the ballistic limit and residual velocity of stiffened plates perforated by rigid projectiles. The project supported by the National Natural Science Foundation of China (90305018) The English text was polished by Yunming Chen     

Unsteady flow of an incompressible viscous fluid around a deformable spherical body

An unsteady flow of a viscous incompressible fluid around a deformable spherical body is considered in the approximation of low Reynolds numbers with a predetermined flow velocity. The hydrodynamic impact of the flow incoming onto the body is determined with allowance for small radial displacements of the body surface. The effect of spherical body surface deformation on the magnitude of the incoming flow impact force is taken into account, in particular, the dependence of small radial displacements of the body surface on the time is found, which makes it possible to minimize the physical impact of the incident flow.     

Flow structure around perforated cylinders in shallow water

The experimental investigations were carried out in order to have detailed information on the flow structure around perforated cylinders using high-image density Particle Image Velocimetry technique in shallow water flow. The depth-averaged free-stream velocity was kept constant as U_∞=100 mm/s corresponding to the Reynolds number of Re=10 000 based on the perforated cylinder diameter. In order to analyze the effect of porosity, β on the flow structure, the porosities in the range of 0.1≤β≤0.8 with an increment of 0.1 were used and the results were compared with the bare cylinder case by means of velocity and vorticity contours, turbulent kinetic energy, Reynolds shear stress and streamline topologies. It was concluded that the porosity, β had a substantial effect on the control of large-scale vortical structures downstream of the cylinder in which the shear layers were elongated, fluctuations were significantly attenuated and formation of Karman Vortex Street was successfully prevented by the use of perforated cylinders.     

Numerical computation of a three-dimensional vortex sheet in a swirl flow

We consider an incompressible and inviscid fluid flow, called “swirl flow” that rotates around a certain axis in three-dimensional space. We investigate numerically the dynamics of a three-dimensional vortex sheet which is defined as a surface across which the velocity field of the swirl flow changes discontinuously. The vortex method and a fast summation method are implemented on a parallel computer. These numerical methods make it possible to compute the evolution of the vortex sheet for a long time and to describe the complex dynamics of the sheet.     

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。     

Forced convective heat transfer enhancement with perforated pin fins

Increasing miniaturization of high speed multi-functional electronics demands ever more stringent thermal management. The present work investigates experimentally and numerically the use of staggered perforated pin fins to enhance the rate of heat transfer in these devices. In particular, the effects of the number of perforations and the diameter of perforation on each pin are studied. The results show that the Nusselt number for the perforated pins is 45 % higher than that for the conventional solid pins and it increases with the number of perforation. Pressure drop with perforated pins is also reduced by 18 % when compared with that for solid pins. Perforations produce recirculations in the x–y as well as the x–z planes downstream of the pins which effectively increase convective heat transfer. However, thermal dissipation decreases significantly when the ratio of pin diameter to perforation diameter exceeds 0.375. This is due to both a reduction in the number of perforation per pin and the decrease in the axial heat conduction along the pin.     

Time resolved measurements of the flow generated by suction feeding fish

The majority of aquatic vertebrates are suction feeders: by rapidly expanding the mouth cavity they generate a fluid flow outside of their head in order to draw prey into their mouth. In addition to the biological relevance, the generated flow field is interesting fluid mechanically as it incorporates high velocities, is localized in front of the mouth, and is unsteady, typically lasting between 10 and 50 ms. Using manometry and high-speed particle image velocimetry, this is the first study to quantify pressure within and outside the mouth of a feeding fish while simultaneously measuring the velocity field outside the mouth. Measurements with a high temporal (2 ms) and spatial (<1 mm) resolution were made for several feeding events of a single largemouth bass (Micropterus salmoides). General properties of the flow were evaluated, including the transient velocity field, its relationship to pressure within the mouth and pressure at the prey. We find that throughout the feeding event a relationship exists for the magnitude of fluid speed as a function of distance from the predator mouth that is based on scaling the velocity field according to the size of the mouth opening and the magnitude of fluid speed at the mouth. The velocity field is concentrated within an area extending approximately one mouth diameter from the fish and the generated pressure field is even more local to the mouth aperture. Although peak suction pressures measured inside the mouth were slightly larger than those that were predicted using the equations of motion, we find that these equations give a very accurate prediction of the timing of peak pressure, so long as the unsteady nature of the flow is included.     

双周期加筋微穿孔板的振动响应及声透射的研究

本文主要研究了水下无穷大双周期加筋微穿孔薄板,在平面声波斜入射下的振动响应和声透射,并提出了一种半解析半数值的计算方法。利用微穿孔板的声阻抗以及薄板表面的振速边界条件,建立了加筋穿孔薄板的振动方程,并根据傅立叶变换及空间波数法将振动位移表达为波数分量的迭加形式。采用数值计算的方法对波数分量进行求解并通过傅里叶逆变换,最终得到了双周期加筋穿孔薄板的振动响应及透射系数。通过与Takahashi穿孔板声压结果的对比,证明了本方法的正确性。在算例中,分析了加强筋及穿孔率对薄板结构的振动和声透射的影响。     

Semi-theoretical analyses of the concrete plate perforated by a rigid projectile

Based on the three-stage perforation model, a semi-theoretical analysis is conducted for the ballistic performances of a rigid kinetic projectile impacting on concrete plates. By introducing the projectile resistance coefficients, dimensionless formulae are proposed for depth of penetration (DOP), perforation limit thickness, ballistic limit velocity, residual velocity and perforation ratio, with the projectile nosed geometries and projectile-target interfacial friction taken into account. Based on the proposed formula for DOP and lots of penetration tests data of normal and high strength concrete targets, a new expression is obtained for target strength parameter. By comparisons between the results of the proposed formulae and existing empirical formulae and large amount of projectile penetration or perforation tests data for monolithic and segmented concrete targets, the validations of the proposed formulae are verified. It is found that the projectile-target interfacial friction can be neglected in the predictions of characteristic ballistic parameters. The dimensionless DOP for low-to-mid speed impacts of non-flat nosed projectiles increases almost linearly with the impact factor by a coefficient of 2/(πS). The anti-perforation ability of the multilayered concrete plates is dependent on both the target plate thickness and the projectile impact velocity. The variation range of the perforation ratio is 1–3.5 for concrete targets.     

Numerical prediction of turbulent flow in a conical diffuser usingk-ε model

Fully developed incompressible turbulent flow in a conical diffuser having a total divergence angle of 8° and an area ratio of 4∶1 has been simulated by ak-ε turbulence model with high Reynolds number and adverse pressure gradient. The research has been done for pipe entry Reynolds numbers of 1.16×10⁵ and 2.93×10⁵. The mean flow velocity and turbulence energy are predicted successfully and the advantage of Boundary Fit Coordinates approach is discussed. Furthermore, thek-ε turbulence model is applied to a flow in a conical diffuser having a total divergence angle of 30° with a perforated screen. A simplified mathematical model, where only the pressure drop is considered, has been used for describing the effect of the perforated screen. The optimum combination of the resistance coefficient and the location of the perforated screen is predicted for high diffuser efficiency or the uniform velocity distribution.