A Finite Element Computational Method for Gas Hydrate. Part I: Theory

A finite element scheme is presented to model the dissociation of gas hydrates in porous media by hot water injection. We show a complete derivation of the finite element formulation, including the associated mass and energy conservation equations capable of performing transient analysis of both conductive and convective heat transfer for gas and liquid flow in porous media. The scheme also includes the latent heat effect to accommodate the change of phase due to melting of hydrate. In the companion paper, Part II, this method is successfully applied to hydrate reservoirs.     

A Finite Element Computational Method for Gas Hydrate. Part I: Theory

Abstract

A finite element scheme is presented to model the dissociation of gas hydrates in porous media by hot water injection. We show a complete derivation of the finite element formulation, including the associated mass and energy conservation equations capable of performing transient analysis of both conductive and convective heat transfer for gas and liquid flow in porous media. The scheme also includes the latent heat effect to accommodate the change of phase due to melting of hydrate. In the companion paper, Part II, this method is successfully applied to hydrate reservoirs.     

计算流体力学方法模拟规整填料塔内流体流动行为的研究进展

对采用计算流体力学(CFD)方法模拟规整填料塔内流体流动行为的研究进展进行了综述,分别介绍了单相流模型和两相流模型。单相流模型可预测气相或液相在规整填料塔内轴向、径向的扩散行为及气相的压头损失等;两相流模型主要研究规整填料塔内气液相流动行为,利用该模型可计算液体在规整填料表面的流动过程及气液相间的传质行为,其模拟结果比单相流模拟更接近实际。随流体力学学科和计算机技术及现代测量技术的进一步发展,将会促进CFD技术在化工过程中的应用。     

A control volume based finite element method for simulating incompressible two-phase flow in heterogeneous porous media and its application to reservoir engineering

Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.     

考虑高速非达西效应的油水相对渗透率计算模型

油水相对渗透率是描述储层多孔介质油水渗流的重要参数,高产的高孔高渗油藏在近井地带可能会发生单相或两相的非达西渗流,以致于在常规条件下得出的相渗曲线并不能准确地表达该类油藏的渗流特征,导致产能评价及预测不合理。通过考虑高孔高渗储层多孔介质的油水渗流特征,建立了考虑高速非达西效应的高孔高渗油藏非稳态油水相对渗透率计算模型,进行了非稳态油水相对渗透率实验,计算了不同油相或水相非达西系数对油水相对渗透率曲线的影响,最后数模分析了高速非达西效应对高孔高渗油藏的影响。研究表明,水相对油水相对渗透率曲线的影响较为显著,非达西效应的影响在油水相渗曲线的两端更为明显。两相高速非达西效应虽然降低了油藏的总体产液量,但是抑制了产水,增加了产油量,与单相高速非达西效应相比,两相高速非达西效应对油田生产并不一定具有负面作用。     

Steady boundary layer slip flow and heat transfer over a flat porous plate embedded in a porous media

A mathematical model is presented for analyzing the boundary layer forced convective flow and heat transfer of an incompressible fluid past a porous plate embedded in a Darcy porous medium. Velocity and thermal slips are considered instead of no-slip conditions at the boundary. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. In case of porous plate, fluid velocity increases whereas non-dimensional temperature decreases for increasing values of suction parameter but it increases with increasing blowing parameter. Our analysis reveals that the increase of velocity slip parameter reduces the momentum boundary layer thickness and also enhances the heat transfer from the plate. On the other hand, heat transfer decreases with thermal slip parameter.     

A Finite Element Computational Method for Gas Hydrate. Part II: Application

A finite element model has been applied to the dissociation of gas hydrates in porous media by hot water injection. In the first step, it was applied to calculate the temperature and saturation profiles for a two-phase convective heat transfer case. The second step involved hydrate thawing calculations with release of water and gas. Realistic results were obtained in predicting the temperature, pressure, and water saturation profiles in the hydrate medium with respect to time, when subjected to hot water injection at high pressure in a wellbore. Furthermore, the thaw front progression calculated by this scheme exhibits stable and satisfactory behavior with respect to time.     

Wettability and Its Effects on Oil Recovery in Fractured and Conventional Reservoirs

Abstract

The lattice Boltzmann method is a relatively new simulation technique of computational fluid dynamic class. Its several advantages such as dealing with complex boundary and incorporating of microscopic interaction make it an alternative and promising numerical scheme for simulating fluid flow in porous media. Three lattice Boltzmann equation models are introduced and used for calculating permeability of a 2D porous media. Analytical solutions of Poiseuille flow between infinite parallel plates is used for validating lattice Boltzmann equation models. In the numerical simulations the effects of grid resolution and viscosity on the predicted permeability are checked.     

基于多孔介质加氢裂化反应器多相流数值模拟

采用欧拉多相流模型,通过建立多孔介质能量守恒模型、热量传递模型和质量传递模型,对加氢裂化反应器内的多相流动、传热和传质进行了数值模拟计算,得到了反应器内多孔介质床层的速度场、温度场、浓度场和压力分布。结果表明,多相流模型的选取、传热传质模型的建立、油品物性的计算和边界条件的设置能够较准确地描述三相流动状态及其分布状态。反应器入口处的流动状况将直接向内部传递,壁面流随流动而发展,其宏观描述为：在出口床层处径向体积分率曲线出现拐点,进而使流体在催化剂床层径向和轴向分布不均匀,气化率得到提升。为了获得反应介质与催化剂充分混合的流体分布状态,有效利用催化剂,反应器入口处的流动状态必须得到优化。     

A Finite Element Computational Method for Gas Hydrate. Part II: Application

Abstract

A finite element model has been applied to the dissociation of gas hydrates in porous media by hot water injection. In the first step, it was applied to calculate the temperature and saturation profiles for a two-phase convective heat transfer case. The second step involved hydrate thawing calculations with release of water and gas. Realistic results were obtained in predicting the temperature, pressure, and water saturation profiles in the hydrate medium with respect to time, when subjected to hot water injection at high pressure in a wellbore. Furthermore, the thaw front progression calculated by this scheme exhibits stable and satisfactory behavior with respect to time.     

模拟深水井筒中流速对传热影响的实验研究

为研究深水低温环境下油气开发过程中井筒内的传热规律,提高深水低温环境井筒内温度的计算精度,以深水油气流动模拟实验系统中的低温冷却传热实验装置为平台,进行了模拟深水低温环境下的冷却传热实验和气液两相流传热实验。根据对流传热准则方程,数据回归得到深水低温情况下的模拟井筒内对流传热关系式。实验结果表明,在模拟深水低温环境下,流体管内对流传热系数主要受流速的影响,且层流时流速对传热的影响更明显;气液两相流时,不同流型管内对流传热系数不同的根本原因是各流型流动结构不同,液体流速是影响传热的主要因素。     

Vorticity-based coarse grid generation for upscaling two-phase displacements in porous media

Coarse grid generation from finely gridded geological model is a main step in reservoir simulation. Coarse grid generation algorithms aim at optimizing size, number and location of the grid blocks by identifying the important geological and flow features which control flow in porous media. By optimizing coarse grid structure we can improve accuracy of the coarse scale simulation results to reproduce fine grid behavior. A number of techniques have been proposed in the literature. We present a novel coarse grid generation procedure based on vorticity preservation between fine and coarse grids. In the procedure, the coarse grid mesh tries to capture variations in both permeability and fluid velocity using a single physical quantity — “vorticity” which is extracted from single-phase flow simulation. One essential element in the procedure is that the improved coarse grid (ICG) has minimum single-phase vorticity error with respect to the fine grid vorticity. Our numerical investigations on modeling two-phase flow demonstrate that the ICG represents fine grid flow behavior very closely. In addition, our analyses show that the use of single-phase vorticity has only a minor impact on the ICG generation, and its performance is not affected by two-phase flow parameters such as mobility ratio.     

A New Approach for Specifying Imbibition Face Boundary Condition in Countercurrent Spontaneous Imbibition

Abstract

Countercurrent spontaneous imbibition is one of the basic processes in two-phase fluid flow in fractured porous media. Many researchers have studied modeling of this phenomenon and analytical and numerical solutions have been presented. Specifying the imbibition face (open face) wetting phase saturation, which acts as a boundary condition, has been one of the main challenges in this area. There is no method to specify the imbibition face boundary condition satisfactorily. In this study a new logical method is introduced to determine the open face boundary condition that is satisfactorily close to experimental results. This method considers different aspects of the process of countercurrent spontaneous imbibition and, based on formulation and effective forces in this process, three pieces of evidence are presented to prove that the wetting phase saturation at the imbibition face is a value that leads to maximum wetting phase and nonwetting phase flow with respect to saturation. Because flow rates in this process are a function of saturation and gradient of saturation with respect to location, the maximum wetting and nonwetting phase flow with respect to only saturation would not lead to maximum reachable flow rates for the process.     

An extended Krylov subspace method to simulate single-phase fluid flow phenomena in axisymmetric and anisotropic porous media

We develop and validate a novel numerical algorithm for the simulation of axisymmetric single-phase fluid flow phenomena in porous and permeable media. In this new algorithm, the two-dimensional parabolic partial differential equation for fluid flow is transformed into an explicit finite-difference operator problem. The latter is solved by making use of an extended Krylov subspace method (EKSM) constructed with both positive and inverse powers of the finite-difference operator. A significant advantage of the method of solution presented in this paper is that simulations of pressure can be obtained at a multitude of times with practically the same efficiency as that of a single-time simulation. Moreover, the usage of inverse powers of the finite-difference operator provides a substantial increase in efficiency with respect to that of standard Krylov subspace methods. Tests of numerical performance with respect to analytical solutions for point and line sources validate the accuracy of the developed method of solution. We also validate the algorithm by making comparisons between analytical and numerical solutions in the Laplace transform domain. Additional tests of accuracy and efficiency are performed against a commercial simulator for spatially complex and anisotropic models of permeable media.     

稠油油藏中含内热源多孔介质的传热研究

立足于稠油热采技术,通过研究分析储层中含内热源多孔介质的传热机理,建立相应的传热计算模型,给出稠油油藏多孔介质在内热源作用下的温度分布,从而了解温度对油层中原油(尤其是稠油)性质的影响。文中以火烧油层工艺为例,考虑了由生产井注入空气与油层(即含内热源多孔介质)中原油的燃烧放热反应这一因素。运用了数理方程、渗流力学、采油工程等方面的知识,建立了含内热源多孔介质一维传热模型,并对所建立的一维传热微分方程进行求解,得到油层多孔介质在内热源作用下的温度场分布。研究油层多孔介质内部温度场分布对原油开采有重要指导意义。     

Influence of hydrodynamic forces and interfacial momentum transfer on the flow of two immiscible phases

Conventional theory regarding immiscible two-phase flow neglects the effect that hydrodynamic forces and interfacial momentum transfer have on flow through porous media. The significance of such neglect is explored by estimating the relative error incurred when these effects are neglected. It is shown, by investigating several one-dimensional problems, that relative errors of about 1% are incurred by neglecting the effect of the hydrodynamic forces, whereas errors of about 40% are introduced when viscous coupling across fluid–fluid interfaces is neglected.     

正交非线性渗流控制方程

用矢量场论知识,将由福希海默方程等价转化而来的渗流速度关于压强梯度的显式函数代入流体渗流连续方程,对所得方程进行先展开后化简运算,得到正交高速非线性渗流控制方程。正交高速非线性渗流控制方程和正交低速非线性渗流控制方程统称正交非线性渗流控制方程。面对繁琐的正交非线性渗流控制方程,在求其符号解举步维艰的情况下运用矢量场论和微分几何知识对正交非线性渗流进行了流场几何分析,得出新的认识,即“曲渗定理:共形映射不适用于除直流场外的正交非线性渗流场。”为了绕过求正交非线性渗流控制方程符号解过程中的边界条件,应用复势公式和“平面稳态流速场运动学通式”中的度量张量公式,将笛卡尔坐标系内的正交非线性渗流控制方程转换成了既定问题相应势流坐标系内的正交非线性渗流控制方程。鉴于势流坐标系内的正交非线性渗流控制方程依然繁琐,即其曲流场符号解难以直接求得,建议先探寻能间接获得正交非线性渗流场函数的某种未知映射。     

Analytical Analysis for Mass Transfer in a Fractured Porous Medium

The aim was to analyze the transient behavior of mass transfer in a fractured porous medium. The jump condition that applies between the two regions (porous media and fracture) considers a transient term with an adjustable parameter (γ). In order to know more about the γ parameter, the problem under consideration in this work is the adsorption in a porous medium adjacent to a fluid (acts as fracture). The analytical solution for the concentrations in the porous media and in the homogeneous flow coupled by a jump condition with accumulation effects was obtained using the Laplace method.     

饱和孔隙流体作用下甲烷水合物降压分解机制及实验研究

水合物地层中常含有饱和的孔隙流体,饱和孔隙流体的存在改变了水合物藏的传热及传质特性。通过实验模拟了饱和孔隙流体下多孔介质尺寸、分解温度、压降和注入流体类型对水合物的降压分解过程中产气速率的影响。结果表明：饱和孔隙流体下,产气速率受多孔介质尺寸、压降和注入流体类型影响较大,而受分解温度影响较小。实验范围内,水合物在大压降和小尺寸介质中分解更快速。水合物分解初始阶段,分解速率随着流体盐度的增加而增大;在中后阶段,分解速率随流体盐度的增加而降低。气体扩散阻力因盐溶液水化离子氛存在而增加并进一步阻碍水合物的分解。实际水合物藏开采过程中可通过增大压降和降低溶液盐度来解决该问题。     

折流板换热器的流场数值模拟与结构优化

基于多孔介质与分布阻力的概念,采用FLUENT软件对单弓形折流板换热器的壳程流场进行了三维数值模拟,模拟结果与实验结果吻合较好。在此基础上针对折流板换热器壳程压降大、能耗高,存在传热死区等的缺点提出了壳程流场的改进方案,即在增加折流板缺口高度的同时,再加入2块分隔板。通过数值模拟可以看到壳程流场改进后不仅具有压降低、场协同性能好、基本无传热死区等特点,而且在一定程度还提高了管束抗流体诱导振动的性能。