致密砂岩垂直裂缝井CO2混相驱试井模型研究

向地层注入CO2可以有效地提高致密砂岩原油采收率,常规的试井解释数学模型不能满足致密砂岩无限导流垂直裂缝井CO2混相驱试井解释的需求．因此,基于渗流力学基本原理建立考虑应力敏感影响的无限导流垂直裂缝井CO2混相驱试井解释数学模型,利用Laplace变换、摄动变换和Stehfest数值反演的方法进行求解,编程绘制典型特征曲线并进行敏感性分析．研究表明：该模型典型特征曲线共划分为八个流动阶段．由于应力敏感效应的影响,径向流阶段内、外区压力导数曲线不再是0.5和0.5M13水平线,而是呈“上翘”的曲线,并且应力敏感系数越大,曲线“上翘”越明显;混相区压力导数曲线符合幂律型变化指数规律且高于(1-n)/(3-n)斜率直线;内区、混相区半径和M12的变化都会使得外区压力曲线升高;通过该模型可以有效地对致密砂岩压裂井CO2混相驱试井资料进行解释．     

Injection of Acid Gas Mixtures in Sour Oil Reservoirs: Analysis of Near-Wellbore Processes with Coupled Modelling of Well and Reservoir Flow

The reinjection of sour or acid gas mixtures is often required for the exploitation of hydrocarbon reservoirs containing remarkable amounts of acid gases (H₂S and CO₂) to reduce the environmental impact of field exploitation and provide pressure support for enhanced oil recovery (EOR) purposes. Sour and acid gas injection in geological structures can be modelled with TMGAS, a new Equation of State (EOS) module for the TOUGH2 reservoir simulator. TMGAS can simulate the two-phase behaviour of NaCl-dominated brines in equilibrium with a non-aqueous (NA) phase, made up of inorganic gases such as CO₂ and H₂S and hydrocarbons (pure as well as pseudo-components), up to the high pressures (~100 MPa) and temperatures (~200°C) found in deep sedimentary basins. This study is focused on the near-wellbore processes driven by the injection of an acid gas mixture in a hypothetical high-pressure, under-saturated sour oil reservoir at a well-sector scale and at conditions for which the injected gas is fully miscible with the oil. Relevant-coupled processes are simulated, including the displacement of oil originally in place, the evaporation of connate brine, the salt concentration and consequent halite precipitation, as well as non-isothermal effects generated by the injection of the acid gas mixture at temperatures lower than initial reservoir temperature. Non-isothermal effects are studied by modelling in a coupled way wellbore and reservoir flow with a modified version of the TOUGH2 reservoir simulator. The described approach is limited to single-phase wellbore flow conditions occurring when injecting sour, acid or greenhouse gas mixtures in high-pressure geological structures.     

Modal Analysis of a Rectangular Piezoceramic Plate with Cross Polarization

An in-depth stress analysis of a piezoceramic plate is carried out using complex-variable theory and an experimental method. The first eight modes in the spectrum of planar vibrations of the rectangular piezoceramic transformer are identified. It is particularly established that the transformation ratios in the first and second and in the third and sixth longitudinal modes are practically equal     

共和干热岩地热井GR2井区三维地应力场反演分析

GR2 地热井位于共和恰卜恰镇，干热岩地热井井深达到4000 米，大深度井区极大增加了反演的难度．井区附近20 千米内无大型构造，附近地应力场的主要影响因素为板块构造应力和自重应力．由于井中未进行三维地应力场测井工作，所以我们以地面地应力调查结果和震源机制解反演结果为依据，基于MIDAS GTS 和大比例尺高清卫星云图建立有限元数值模型，使用改进的边界法进行反演计算，最终预估了井中地应力场分布特征．对于后续的井网布置以及干热岩井场开采具有重要意义．     

变截面电磁波导的辛分析

电磁波导的求解可将基本方程导向Hamilton体系、辛几何的形式。横向的电场和磁场构成了对偶向量。辛体系便于处理不同介质波导的界面连接条件。正则对偶方程、分离变量法、Hamilton算子矩阵本征值问题、共轭辛正交归一关系、本征解的展开定理等整套理论,可以适用于多种波导的课题,有利于不同截面的波导连接、以及与共振腔的连接等。本文分析了两段不同材料不同截面对接的平面波导作为例题,表明辛体系用于波导的分析是有力的。     

Pressure Transient Analysis for Multi-stage Fractured Horizontal Wells in Shale Gas Reservoirs

This article presents the PTA on the multi-stage fractured horizontal well in shale gas reservoirs incorporating desorption and diffusive flow in the matrix. Currently, most PTA models are simply based on Darcy flow both in natural fractures and matrix without considering the mechanisms of desorption and diffusion in shale matrix. Source function and Laplace transform with the numerical discrete method are employed to solve the mathematical model. The solution is presented in the Laplace domain so that the wellbore storage effect and skin factor can be easily incorporated by convolution. Type curves are plotted with Stehfest algorithm and different flow regimes are identified. The presented model could be used to interpret pressure signals more accurately for shale gas reservoirs.     

基于响应面方法的桁架截面敏度分析和优化

把响应面方法引入桁架截面优化中,将应力和位移约束近似表达为桁架截面倒变量的线性函数。为拟合响应面,基于中心复合和单纯形试验设计方法开发了中心对称和拟单纯形试验设计两种方法,既可保证约束近似精度,又降低了结构分析计算量。对于桁架结构重量目标函数,直接推出倒变量的二阶形式,以桁架重量最小为目标的优化问题构造为标准的二次规划模型。将响应面方法计算的位移对设计变量的敏度与莫尔积分方法的近似显式进行了对比。以MSC.Patran为平台的数值算例表明:结合响应面方法,应用序列二次规划对问题进行寻优,其收敛精度及稳定性都可获得保障。     

The Flow Analysis of Viscoelastic Fluid with Fractional Order Derivative in Horizontal Well

The fractional calculus approach is introduced into the seepage mechanics. A three-dimensional relaxation model of viscoelastic fluid is built. The models based on four boundary conditions of exact solution in Laplace space for some unsteady flows in an infinite reservoir is obtained by using the Laplace transform and Fourier sine and cosine integral transform. The pressure transient behavior of non-Newtonian viscoelastic fluid is studied by using Stehfest method of the numerical Laplace transform inversion and Gauss–Laguerre numerical integral formulae. The viscoelastic fluid is very sensitive to the order of the fractional derivative. The change rules of pressure are discussed when the parameters of the models change. The plots of type pressure curves are given, and the results can be provided to theoretical basis and well-test method for oil field.     

Relative Permeability of Gas for Unconventional Reservoirs

Relative permeability of gas gains great significance in exploring unconventional gas. This paper developed a universal relative permeability model of gas, which is applicable for unconventional gas reservoirs such as coal, tight sandstone and shale. The model consists of the absolute relative permeability of gas and the gas slippage permeability. In the proposed model, the effects of water saturation and mean pore pressure on gas slippage permeability are taken into account. Subsequently, the evaluation of the model with existing model is done and then the validation of the model is made with data of tight sandstones, coals and shales from published literatures. The modeling results illustrate that a strong power-law relationship between relative permeability of gas and water saturation and the contribution of gas slippage permeability to relative permeability is determined by water saturation and mean pore pressure simultaneously. Furthermore, a sensitivity analysis of the impact of the parameters in the model is conducted and their effects are discussed.     

同轴交叉射流的轴线速度

研究了射流交叉角度和密度比对同轴交叉射流流场的影响。基于动量守恒原理,提出了考虑径向流动和密度差别的同轴交叉射流的当量直径和当量速度。当量速度与Dual PDA的实验结果较为吻合。该法可较好地描述射流交叉角度、密度比对轴线上轴向速度的影响。     

Calculation of Groundwater Flows in Coastal Pressurized Reservoirs

A model of a fresh groundwater flow through a rectangular horizontal pressurized reservoir toward a salt-water sea (basin, reservoir, trench, etc.) is examined within the framework of two-dimensional steady-state flow theory. In order to study the model, a mixed multi-parameter boundary value problem of the theory of analytic functions is formulated and solved using the Polubarinova-Kochina method. The structure and the characteristic features of the simulated process and the effect of all the determining physical parameters of the model on the nature of the flow are analyzed using the analytic dependences obtained and numerical calculations. An approximate hydraulic solution of the problem is compared with the exact solution obtained.     

The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics

This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator.

     

具有井简储集的变形介质双渗模型的压力分析

为更好地研究碳酸盐油藏和低渗油的渗流问题，引入渗透率模数，考虑应力敏感地层中介质的变形，介质的双孔隙度、双渗秀率特征，同时考虑井筒储集的影响，建立新的数学模型。渗透率依赖于孔隙压力变化的流动方程是强非线性的，模型采用Douglas—Jones预估-校正法获得了无限大地层及有界封闭地层的数值解，形成了新的理论图版，并利用这些图版对模型中的有关参数进行了敏感性分析。     

具有井筒储集的变形介质双渗模型的压力分析

为更好地研究碳酸盐油藏和低渗油的渗流问题,引入渗透率模数,考虑应力敏感地层中介质的变形,介质的双孔隙度、双渗秀率特征,同时考虑井筒储集的影响,建立新的数学模型。渗透率依赖于孔隙压力变化的流动方程是强非线性的,模型采用Douglas-Jones预估-校正法获得了无限大地层及有界封闭地层的数值解,形成了新的理论图版,并利用这些图版对模型中的有关参数进行了敏感性分析。     

WAG Displacements of Oil-Condensates Accounting for Hydrocarbon Ganglia

During two-phase flow in porous media, non-wetting phase is present simultaneously in states of mobile connected continuum and of trapped isolated ganglia. Mass exchange between these two parts of non-wetting phase is going on by dissolution and diffusion of component in the wetting phase, so, compositions of non-wetting phase in both parts are different. Nevertheless, the traditional mathematical model for two-phase multicomponent transport in porous media assumes the homogeneous distribution of each component in the overall non-wetting phase. New governing equations honouring ganglia of non-wetting phase are derived. They are successfully verified by a number of laboratory tests. Analytical model is developed for miscible water-alternate-gas (WAG) displacement of oil-condensates. The modelling shows that the significant amount of oil-condensate is left in porous media after miscible WAG, while the traditional model predicts that the miscible displacement results in the total sweep.     

Vertical Permeability Distribution of Reservoirs with Impermeable Barriers

The presence of impermeable horizontal barriers (such as shales) in a reservoir is known to have a significant effect on its vertical permeability. Since calculation of an effective vertical permeability of such a reservoir is important, approximation of the distribution of vertical permeability may also be useful for analysis of the two-phase vertical flow of buoyant fluid, such as may occur in the subsurface injection of carbon dioxide into saline formations. In this situation, the maximum likely vertical permeability of a reservoir with impermeable barriers, which could be estimated from the probability distribution of the vertical permeability, is a more useful metric than an overall effective value for the vertical permeability due to its presumed relationship to breakthrough time. In this article, we derive expressions for the mean and variance of the vertical permeability of both two and three-dimensional reservoirs using the statistical streamline method of Begg and King (Paper No. 13529, 1985), and calculate the probability distribution of the vertical permeability of a reservoir with impermeable barriers. In addition, we also provide a simple statistical analysis of the presence of high vertical permeability regions in the reservoir, which may be of importance in coarse-scale simulations of vertical migration.     

Compressed Air Flow within Aquifer Reservoirs of CAES Plants

A model on the air flow within aquifer reservoirs of Compressed Air Energy Storage (CAES) plants was developed. The design of such CAES plants requires knowledge of the reservoir air pressure distribution during both the charging and discharging phases. Also, it must assure air/water interface stability to prevent water suction during discharge. An approximate analytical solution for the pressure variations within the anisotropic reservoir porous space was developed, subject to the Darcy equation and for conditions of partially penetrating wells. Sensitivity analyses were conducted to identify the dominant parameters affecting the well pressure and the critical flow rate (water suction threshold). It is demonstrated that water coning is a factor that could severely limit the discharge air flow rate. A significant diminishment of that limitation and reduction of the pressure fluctuation can be achieved by enlargement of the air layer height and discharge period. Likewise, aquifers with larger horizontal permeability impose less restrictive critical flows. A conclusion on the preferred screen length could not be merely drawn from technological considerations, but should also involve important economic aspects.     

Equivalent Fracture Network Permeability of Multilayer-Complex Naturally Fractured Reservoirs

Modeling naturally fractured reservoirs (NFRs) requires an accurate representation of fracture network permeability (FNP). Conventionally, logs, cores, seismic, and pressure transient tests are used as a data base for this. Our previous attempts showed that a strong correlation exists between the fractal parameters of 2-D fracture networks and their permeability (Jafari and Babadagli, SPE 113618, Western Regional and Pacific Section AAPG joint meeting, 2008; Jafari and Babadagli, SPE Reserv Eval Eng 12(3):455–469, 2009a). We also showed that 1-D well (cores-logs) and 3-D reservoir data (well test) may not be sufficient in FNP mapping and that 2-D (outcrop) characteristics are needed (Jafari and Babadagli, SPE 124077, SPE/EAGE reservoir characterization and simulation conference, 2009b). This paper is an extension of those studies, where only 2-D (single-layer, uniform fracture characteristics in z direction) representations were used. In this paper, we considered a more complex and realistic 3-D network system. Two-dimensional random fractures with known fractal and statistical characteristics were distributed in the x- and y directions. A variation of fracture network characteristics in the z direction was presented by a multilayer system representing three different facieses with different fracture properties. Wells were placed in different locations of the model to collect 1-D fracture density and pressure transient data. In addition, five different fractal and statistical properties of the network of each layer were measured. The equivalent FNP was calculated using a commercial software package as the base case. Using available 1-D, 2-D, and 3-D data, multivariable regression analyses were performed to obtain equivalent FNP correlations for many different fracture network realizations. The derived equations were validated against a new set of synthetic fracture networks, and the conditions at which 1-D, 2-D and 3-D data are sufficient to map FNP were determined. The importance of the inclusion of each data type, i.e., 1-D, 2-D and 3-D, in the correlations was discussed. It was shown that using only 3-D data are insufficient to predict the FNP due to wide spatial heterogeneity of the fracture properties in the reservoir, which cannot be captured from single-well tests. Incorporating all types of data (1-D, 2-D, and 3-D) would result in better prediction. Also, it is recommended that the 2-D data of the most conductive layer in reservoir, which has longer fractures with a higher density, should be incorporated in the correlations.     

Cross transport of energy in fluid streams

Fluids flowing over an unheated cylinder with its axis normal to the flow separate in their wake into a central stream with a total enthalpy lower than the one in the upstream and two outer streams with higher total enthalpies provided the Reynolds number is such that alternate separation of vortices and the formation of a Karmán vortex street occur. Evidence of this was observed in 1940 by low values of the recovery temperature on the downstream side of a cylinder normal to a high velocity air stream. A number of experimental studies by various investigators confirmed the energy separation, established that it was connected with the unsteady character of the vortex formation, and that it was enhanced by the presence of sound waves. Various explanations have been proposed for the mechanisms which lead to this energy separation. The present paper surveys the significant experimental findings and attempts to describe the energy separation effect in physical terms starting with the unsteady energy equation and drawing on recent computer solutions.

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Quertransport von Energie in Fluid-Strömen

Zusammenfassung Flüssigkeiten, die über einen unbeheizten Zylinder senkrecht zu dessen Achse strömen, separieren sich im Nachlauf in einen zentralen Strom mit einer Enthalpie, die niedriger ist, als die im Anströmbereich und in zwei äußere Ströme mit höherer Enthalpie, vorausgesetzt, daß die ReynoldsZahl groß genug ist für die intermittierende Ablösung von Wirbeln und die Ausbildung einer Kármánschen Wirbelstraße. Diese Erscheinung wurde 1940 durch niedrige Werte der Ruhetemperatur stromabwärts eines mit hoher Luftgeschwindigkeit quer angeströmten Zylinders beobachtet. Eine Anzahl von Experimenten, durchgeführt an verschiedenen Stellen, bestätigten die Trennung in Ströme unterschiedlicher Energie, zeigten den Zusammenhang mit dem unstetigen Charakter der Wirbelbindung und gaben Hinweise auf die Stimulation des Phänomens durch Schallwellen.Es wurden verschiedene Erklärungen für diesen Mechanismus vorgeschlagen, der zu einer Energieseparation führt. Der vorliegende Aufsatz gibt einen Überblick über die wichtigsten experimentellen Erkenntnisse und versucht, den Effekt der Trennung in Ströme unterschiedlicher Energie physikalisch zu beschreiben, ausgehend von der instationären Energiegleichung und hinweisend auf neue numerische Lösungen mittels Computer.

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Nomenclature C_p specific heat at constant pressure - f frequency - i enthalpy - i⁰ total enthalpy - k thermal conductivity - Ma Mach number - p static pressure - P_ij viscous pressure tensor - Pr Prandtl number - r recovery factor - Re Reynolds number - S_r energy separation factor - T static or true temperature - T⁰ total temperature - T_r recovery temperature - t time - V amount of velocity - _i velocity components - x_i length components - y coordinate normal to surface Greek symbols shear stress - viscosity Dedicated to Prof. Dr.-Ing. U. Grigull's 75th birthday