Krylov subspace projection method and its application on oil reservoir simulation

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弹塑性变形油藏中多相渗流的数值模拟

基于流固耦合力学理论,建立了弹性变形油藏中多相渗流的数学模型,该模型考虑了渗流与变形的耦合作用,以及注采交变载荷作下油藏多孔介质的弹性变形特征,给出了耦合数值模拟方法和算例。     

A coupled model for multiphase fluid flow and sedimentation deformation in oil reservoir and its numerical simulation

A mathematical model for coupled multiphase fluid flow and sedimentation deformation is developed based on fluid-solid interaction mechanism. A finite difference-finite element numerical approach is presented. The results of an example show that the fluid-solid coupled effect has great influence on multiphase fluid flow and reservoir recovery performances, and the coupled model has practical significance for oilfield development.     

Simulation of the thermal recovery process in a layered reservoir

The thermohydrodynamic interaction of the layers in a layered oil reservoir in the presence on in situ combustion is considered.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 122–128, May–June, 1994.     

爆炸驱动液体分层现象和液滴尺寸模拟

爆炸驱动液体介质外界面的分散和破碎是气溶胶云团形成的重要过程。采用基于维数分裂的欧拉程序和Youngs混合界面处理方法,对中心药爆炸驱动甘油和水介质流场的液体分层现象进行了数值模拟。结合试验结果推断提出了液滴形成过程的三种并存机制:外层射流破碎、内层R-T失稳和中间液层"空化"破碎,分别建立了不同液层破碎液滴的尺寸模拟方法。对比给出抛撒甘油和水装置初级液滴的尺寸分布及最外层理论射流量。     

河道砂油藏的自适应非均匀网格粗化算法

以河道砂的观测深度为确定性数据，由贝叶斯理论通过随机楚模的方法楚立横截面为抛物线形状的河道砂油藏边界面，并将渗透率自适应网格技术应用于河道砂油藏的网格粗化算法中。在渗透率或孔隙度交化异常区域自动采用精细网格，用直接解法求解渗透率或孔隙度交化异常区域的压强分布，而在其他区域采用不均匀网格粗化方法计算，印在流体流速大的区域采用精细网格。用本文方法计算了河道砂油藏的压强分布，结果表明河道砂油藏的三维不均匀自适应网格粗化算法的解在渗透率或孔隙度异常区的压强分布规律更逼近采用精细网格的解，在其他区域压强分布规律非常逼近粗化算法的解，但计算的速度比采用精细网格提高了100多倍。     

Natural-convection heat transfer in a nonuniform finite annulus with concentric heat source

In this paper, the mechanisms of natural-convection heat transfer inside a nonuniform finite annulus have been numerically investigated. The system is actually a streamlined, water-filled latex balloon with a coaxial cylindrical heating element. The balloon can be applied as a local hyperthermia treatment device for the removal of undesirable tissue if sufficiently high temperatures and preferably uniform surface heat fluxes can be maintained. A validated control-volume-based method has been employed to solve the coupled transient three-dimensional transport equations for laminar free convection. The effects of heat-source temperature distributions and device orientations on the heat transfer have been studied. Possible design improvements of this device are discussed.     

Simulation of micellar-polymericwater-flooding in a system of wells

A mathematical model of the time-dependent two-dimensional flow of a two-phase multicomponent incompressible fluid through a porous medium is proposed for the micellar-polymeric flooding of oil reservoirs. The oil displacement process is investigated numerically using an implicit first-order-accurate upwind scheme with integration over the nonlinearity on a uniform grid under the assumption of plane-radial motion in the neighborhood of the wells. The influence of the nonuniform permeability of the porous medium on the efficiency of the proposed method of improving oil recovery is analyzed using a five-point slug injection scheme.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 124–132. Original Russian Text Copyright © 2004 by Inogamov and Khabeev.     

The exact analytical solutions to the new model of reservoir filtration problem

The present study has obtained the new model of the reservoir filtration problemby taking into account the effect of wellbore storage and skin and by making use ofthe coupled equations of doubled porous media filtration and consequently has got,through various forms of limits,the exact analytical solutions of the three commonreservoirs(fissure,homogeneous and the two-layered)pressure distribution under theconditions of three boundaries,i.e.,infinite boundary,sealed finite boundary and thefinite boundary at constant pressures.     

Interaction of a die with a layered elastic foundation

Plane and axisymmetric contact problems for a three-layer elastic half-space are considered. The plane problem is reduced to a singular integral equation of the first kind whose approximate solution is obtained by a modified Multhopp-Kalandiya method of collocation. The axisymmetric problem is reduced to an integral Fredholm equation of the second kind whose approximate solution is obtained by a specially developed method of collocation over the nodes of the Legendre polynomial. An axisymmetric contact problem for an transversely isotropic layer completely adherent to an elastic isotropic half-space is also considered. Examples of calculating the characteristic integral quantities are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 165–175, May–June, 2006.     

利用改进的ADI方法实现单机千万节点的油水两相渗流数值模拟

针对实际油藏的非均质分布特征及其复杂的边界条件,本文通过引入迭代参数的压缩因子和放大因子,对现有的交替方向迭代法(ADI)进行改进,提出一种适用于大规模油藏数值模拟的新算法．改进的ADI 方法计算精度可靠,且与现有的算法相比计算效率有所提高．更为关键的是,ADI 算法将求解三维压力方程的七对角矩阵分解为三个方向的三对角矩阵依次迭代求解,所需的运算存储量大幅减少,最大的计算规模有了大幅的提升．使用改进的ADI 方法,在单机上成功实现了千万节点的油水两相渗流数值模拟．计算实例表明,在同等单机硬件条件下,改进ADI 算法的最大计算规模是现有算法的1.7 倍以上．     

基于离散缝洞网络模型的缝洞型油藏混合多尺度有限元数值模拟

针对缝洞型油藏具有多尺度特征,基于离散缝洞网络模型,建立了Darcy/Stokes-Brinkman多尺度耦合数学模型,采用多尺度混合有限元方法,对缝洞型油藏的流体流动问题进行了研究。阐述了多尺度混合有限元方法的基本原理,推导得到了Darcy/Stokes-Brinkman多尺度模型的多尺度混合有限元计算格式。数值计算结果表明,在大尺度模型上进行计算能够捕捉到小尺度上的流动特征;相对于传统有限元,多尺度混合有限元能够捕捉小尺度上的非均质特征而具有更高的计算精度,在保证计算精度的同时能够减少计算量。     

Formation of a gas hydrate due to injection of a cold gas into a porous reservoir partly saturated by water

Specific features of formation of gas hydrates due to injection of a gas into a porous medium initially filled by a gas and water are considered. Self-similar solutions of an axisymmetric problem, which describe the distributions of the basic parameters in the reservoir, are constructed. The existence of solutions is demonstrated, which predict gas hydrate formation both on the frontal surface and in the volume zone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 137–150, May–June, 2008.     

Numerical simulation of pore-scale flow in chemical flooding process

Chemical flooding is one of the effective technologies to increase oil recovery of petroleum reservoirs after water flooding. Above the scale of representative elementary volume (REV), phenomenological modeling and numerical simulations of chemical flooding have been reported in literatures, but the studies alike are rarely conducted at the pore-scale, at which the effects of physicochemical hydrodynamics are hardly resolved either by experimental observations or by traditional continuum-based simulations. In this paper, dissipative particle dynamics (DPD), one of mesoscopic fluid particle methods, is introduced to simulate the pore-scale flow in chemical flooding processes. The theoretical background, mathematical formulation and numerical approach of DPD are presented. The plane Poiseuille flow is used to illustrate the accuracy of the DPD simulation, and then the processes of polymer flooding through an oil-wet throat and a water-wet throat are studies, respectively. The selected parameters of those simulations are given in details. These preliminary results show the potential of this novel method for modeling the physicochemical hydrodynamics at the pore scale in the area of chemical enhanced oil recovery.     

Numerical research on shock propagation down a tube of changing area with a nonuniform steady flow

In this paper, the random choice method (RCM) with an operator-splitting technique is applied to the numerical simulation of shock propagation down a tube of changing area with a nonuniform steady flow and the flow properties behind the shock. The change rules of the shock strength and flow properties behind it are obtained, and the results are analysed.     

Numerical solution of a singularly perturbed elliptichyperbolic partial differential equation on a nonuniform discretization mesh

In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order convergent, uniformly in the small parameter ε, to the solution of problem (1.1). Numerical results are finally provided.     

New model of gas flow problem in multi-layered gas reservoir and application

In this paper,the new model of the real gas filtration problem has been presented multi-layered gas reservoir,when a gas well output and wellbore storage may be variable,and have obtained the exact solutions of pressure distribution for each reservoir bed under three kinds of typical out-boundary conditions.As a special case,according to the new model have also obtained the exact solutions of presssure distribution in homogeneous reservoir and is given important application in gas reservoir development.     

Simulation and application of three-dimensional migration-accumulation of oil resources

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Filtration in a Porous Granular Medium: 1. Simulation of Pore-Scale Particle Deposition and Clogging

This paper presents a numerical model for simulating the pore-scale transport and infiltration of dilute suspensions of particles in a granular porous medium under the action of hydrodynamic and gravitational forces. The formulation solves the Stokes’ flow equations for an incompressible fluid using a fixed grid, multigrid finite difference method and an embedded boundary technique for modeling particle–fluid coupling. The analyses simulate a constant flux of the fluid suspension through a cylindrical model pore. Randomly generated particles are collected within the model pore, initially through contact and attachment at the grain surface (pore wall) and later through mounding close to the pore inlet. Simple correlations have been derived from extensive numerical simulations in order to estimate the volume of filtered particles that accumulate in the pore and the differential pressure needed to maintain a constant flux through the pore. The results show that particle collection efficiency is correlated with the Stokes’ settling velocity and indirectly through the attachment probability with the particle–grain surface roughness. The differential pressure is correlated directly with the maximum mound height and indirectly with particle size and settling velocity that affect mound packing density. Simple modification factors are introduced to account for pore length and dip angle. These parameters are used to characterize pore-scale infiltration processes within larger scale network models of particle transport in granular porous media in a companion paper. Articlenote: Currently at GZA GeoEnvironmental Inc., 1 Edgewater Drive, Norwood, MA 02062, U.S.A.     

Displacement of trapped oil from water-wet reservoir rock

Displacement of oil trapped in water-wet reservoirs was analyzed using percolation theory. The critical capillary number of the CDC (Capillary Desaturation Curve) was be predicted based on the pore structure of the medium. The mobilization and stability theories proposed by Stegemeier were used to correlate oil cluster length to the capillary number needed to mobilize the trapped oil. Under the assumption that all pore chambers have the same size, a procedure was developed using the drainage capillary pressure curve and effective accessibility function to predict the CDC curve for a given medium. The prediction of critical capillary numbers was compared with the experimental data from 32 sandstone samples by Chatzis and Morrow. Also, the CDC curve of one sandstone sample was calculated using the procedure developed in this work and compared with the measured data. Very good agreements were obtained.Nomenclature a average radius of a liquid filament [m] - c constant - D pore throat diameter [m] - D _a advancing diameter of an oil cluster [m] - D _af average flowing diameter of the medium [m] - D _da controlling diameter of the medium [m] - D _r receding diameter of an oil cluster [m] - D _X difficulty index - f ratio of length to average radius of an oil cluster - F _i interfacial forces [N] - F _p force from pressure gradient [N] - g wettability function - k absolute permeability [m²] - l length of an oil cluster [m] - l _m mobile oil cluster length [m] - l _s stable oil cluster length [m] - l _w wavelength [m] - n* relative length of an oil cluster - N _c 1 capillary number defined by Equation (1) - N _c 2 capillary number defined by Equation (2) - P _b probability of oil filling a pore - P _c percolation threshold value - p _c capillary pressure [N/m²] - r radius of a pore [m] - r _e average pore radius [m] - S _n the nonwetting phase saturation - S _or residual oil saturation - S _orn normalized oil saturation - v Darcy flow rate [m/s] - X _t total fraction of pores - X _t ^a accessibility - X _e ^a effective accessibility - (D) pore throat size distribution function - _a advancing contact angle - _r receding contact angle - porosity - density of the liquid [kg/m³] - constant in Equation (4) - dynamic length of an oil cluster [m] - interfacial tension [N/m] - viscosity [N/(m s)] - p pressure gradient [N/m³]