肝脏中生物流体流动的多重介质渗流模型和数值模拟

本文采用生物渗流理论，建立了肝脏内不同生物流体流动的多重介质渗流模型，采用有限元法求解这种特殊的渗流问题，根据数值计算结果揭示了肝内血液、组织液以及胆汁等的流动规律，并探讨了肝脏血流动力学的一些问题。论文将肝脏内部与生物代谢功能有关的肝血窦和窦周间隙当作两重并存的多孔介质，血液在肝血窦中，以及组织液在窦周间隙中的流动均当作渗流处理，通过Starling公式考虑了两重介质之间的流量交换，从而建立了肝血窦-窦周间隙的双重介质模型。针对肝脏胆汁分泌功能，将肝脏内密布的毛血肝管网当作多孔介质，以受静压及渗透压驱动的流体跨壁流动表示肝汁从肝细胞向毛细肝管的分泌，肝汁在毛细胆管网中的流动作为渗流处理，从而建立了肝汁分泌与输运的双重介质模型。采用有限元法求解了生物流体的双重介质渗流问题，针对非牛顿渗流和两重介质的相互作用，本文发展了一种嵌套迭代方法，即采用直接迭代求解血液在肝血窦中的非线性渗流，采用交替迭代解决双重介质渗流中由跨壁流支引起的相互流体交换，直接迭代嵌套于交替迭代中。这种算法比较有效的解决了包含非牛顿渗流的双重介质渗流问题。根据生物多孔介质中微细管系统的构筑方式以及不同微细管系统之间的联系方式，论文提出将生物多孔介质划分为分级多孔介质和多重多孔介质两种主要类型。基于多相混合物的平均化的理论，论文推导了双重多孔介质中的动量守恒方程、质量守恒方程以及相应的渗流方程，建立了双重多孔介质渗流的平均化模型。基于分级多孔介质渗流的理论，论文将脏器中的血管树按管径分为不同级别的多孔介质，各级血管中和血液流动均作为渗流处理，从而提出了计算脏器整体血流的一种渗流方法。采用这种方法，在论文提出的肝血窦 - 窦周间隙双重介质渗流流模型的基础之上，初步研究了肝脏门静脉系统的血液动力学规律。采用本文提出的肝血窦 - 窦周间隙双重介质模型和胆汁分泌 - 流动的双重介质模型，得到了血液、组织液和胆汁在肝小叶中的压力分布和速度分布，并分析了肝血窦壁的跨壁流动模式，胆汁流量的影响因素，以及窦周间隙中组织液流量与肝血窦中血液流动及肝血窦壁渗透系数等因素的关系，揭示了肝脏内血液、组织液及胆汁等生物流体流动的一般规律。

Numerical Solutions for the Transient Flow in the Homogenous Closed Circle Reservoirs

There are many fault block fields in China. A fault block field consists of fault pools. The small fault pools can be viewed as the closed circle reservoirs in some case. In order to know the pressure change of the developed formation and provide the formation data for developing the fault block fields reasonably, the transient flow should be researched. In this paper, we use the automatic mesh generation technology and the finite element method to solve the transient flow problem for the well located in the closed circle reservoir, especially for the well located in an arbitrary position in the closed circle reservoir. The pressure diffusion process is visualized and the well-location factor concept is first proposed in this paper. The typical curves of pressure vs time for the well with different well-location factors are presented. By comparing numerical results with the analytical solutions of the well located in the center of the closed circle reservoir, the numerical method is verified.

Numerical Study On Transient Flow In The Deep Naturally Fractured Reservoir With High Pressure

According to the experimental results and the characteristics of the pressure-sensitive fractured formation, a transient flow model is developed for the deep naturally-fractured reservoirs with different outer boundary conditions. The finite element equations for the model are derived. After generating the unstructured grids in the solution regions, the finite element method is used to calculate the pressure type curves for the pressure-sensitive fractured reservoir with different outer boundaries, such as the infinite boundary, circle boundary and combined linear boundaries, and the characteristics of the type curves are comparatively analyzed. The effects on the pressure curves caused by pressure sensitivity module and the effective radius combined parameter are determined, and the method for calculating the pressure-sensitive reservoir parameters is introduced. By analyzing the real field case in the high temperature and pressure reservoir, the perfect results show that the transient flow model for the pressure-sensitive fractured reservoir in this paper is correct.

Hydrogeochemistry of formation water in relation to overpressures and fluid flow in the Qikou Depression of the Bohai bay basin, China

The Qikou Depression is the largest hydrocarbon bearing depression in the western part of the Bohai bay basin, dominated by fan delta and lacustrine strata with volcanic and volcaniclastic rocks. In this study, the formation pressures and hydrochemistry of the formation water in the Qikou depression are investigated. It is found that a significant overpressure occurs in the Dongying (Ed) Formation and the first member (Est), the second member (Es2), the third member (Es3) of the Shahejie Formation. The pressure coefficients commonly range from 1.2 to 1.6 with the highest pressure coefficient being 1.7. The analysis of hydrochemistry data shows that the whole depression is dominated by NaHCO3 water type. The concentration of total dissolved solid (TDS) ranges from 2.13 to 53.16 g/L and shows a distinct vertical variation of salinity and ion ratios. High salinity water (TDS> 10 g/L) occurs below a depth of 2500 m, which coincides with the presence of the overpressured system. However, the increasing trend of TDS is diminished below 3500 m because the generation of organic acids in Qikou Depression is inhibited in the presence of overpressure. The analysis of the relationship among different ions indicates that the present-day characteristics of the formation water result from the albitization of feldspar and the dissolution of sodium-rich silicate minerals and halite in the different hydrochemical and pressure systems. (C) 2009 Elsevier B.V. All rights reserved.

Transient Flows in Low Permeability Porous Media with Composite Start-Up Pressure Gradient

A new mathematical model for the transient flow in the composite low permeability is established. It is solved by FEM with different boundary conditions such as infinite, circular closed and constant pressure boundary conditions. The typical curves for transient wellbore pressure have been presented. It is shown that the pressure and pressure derivative curves with composite start-up pressure gradients have different slopes which are depended on the start-up pressure gradients and the mobility radios in different regions. The boundary effects are the same as the normal reservoirs without start-up pressure gradients. The study provides a new tool to analyze the transient pressure test data in the low permeability reservoir.

Permeability of Fractal Porous Media by Monte Carlo Simulations

The permeability of the fractal porous media is simulated by Monte Carlo technique in this work. Based oil the fractal character of pore size distribution in porous media, the probability models for pore diameter and for permeability are derived. Taking the bi-dispersed fractal porous media as examples, the permeability calculations are performed by the present Monte Carlo method. The results show that the present simulations present a good agreement compared with the existing fractal analytical solution in the general interested porosity range. The proposed simulation method may have the potential in prediction of other transport properties (such as thermal conductivity, dispersion conductivity and electrical conductivity) in fractal porous media, both saturated and unsaturated.

Fractal dimensions for unsaturated porous media

The analytical expressions of the fractal dimensions for wetting and non-wetting phases for unsaturated porous media are derived and are found to be a function of porosity, maximum and minimum pore sizes as well as saturation. There is no empirical constant in the proposed fractal dimensions. It is also found that the fractal dimensions increase with porosity of a medium and are meaningful only in a certain range of saturation S-w, i.e. S-w > S-min for wetting phase and S-w < S-max for non-wetting phase at a given porosity, based on real porous media for requirements from both fractal theory and experimental observations. The present analysis of the fractal dimensions is verified to be consistent with the existing experimental observations and it makes possible to analyze the transport properties such as permeability, thermal dispersion in unsaturated porous media by fractal theory and technique.

Three-Dimensional Linear Instability Analysis of Thermocapillary Return Flow on a Porous Plane

A three-dimensional linear instability analysis of thermocapillary convection in a fluid-porous double layer system, imposed by a horizontal temperature gradient, is performed. The basic motion of fluid is the surface-tension-driven return flow, and the movement of fluid in the porous layer is governed by Darcy's law. The slippery effect of velocity at the fluid-porous interface has been taken into account, and the influence of this velocity slippage on the instability characteristic of the system is emphasized. The new behavior of the thermocapillary convection instability has been found and discussed through the figures of the spectrum.

Kramers Escape Rate in Nonlinear Diffusive Media

In this paper, we study nonlinear Kramers problem by investigating overdamped systems ruled by the one-dimensional nonlinear Fokker-Planck equation. We obtain an analytic expression for the Kramers escape rate under quasistationary conditions by employing

Thermocapillary flow in an annular liquid layer painted on a moving fiber

In the present paper, a theoretical model is studied on the flow in the liquid annular film, which is ejected from a vessel with relatively higher temperature and painted on the moving solid fiber. A temperature gradient, driving a thermocapillary flow, is formed on the free surface because of the heat transfer from the liquid with relatively higher temperature to the environmental gas with relatively lower temperature. The thermocapillary flow may change the radii profile of the liquid film. This process analyzed is based on the approximations of lubrication theory and perturbation theory, and the equation of the liquid layer radii and the process of thermal hydrodynamics in the liquid layer are solved for a temperature distribution on the solid fiber.

Mechanical and thermal structure of a cylindrical plume in the earth's mantle

A mantle plume is understood as a hot, narrow, upwelling flow in the earth's mantle and accompanied by an efficient transfer of mass and energy from deep to upper layer of the earth. The cylindrical plume in earth's mantle plays an important role in explaining the origin of the surface hot spots and linear island chains. From the basic hydrodynamical equations, the detailed mechanical and thermal structure of a cylindrical plume of Newtouian fluids with temperature and pressure-dependent viscosity are given in the present paper. For two sets of rheological parameters the radial profiles of upward velocity, temperature and viscosity in the plume and radiuses of the plume at various depths have been calculated.

Modeling of Ammonothermal Growth of Gallium Nitride Single Crystals

Ammonothermal growth of GaN crystals with a retrograde solubility has been modeled and simulated here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the flow in the porous charge is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. For the case of retrograde solubility, the charge is put above the baffle. The temperature difference between the dissolving zone and growth zone is found smaller than that applied on the sidewall of autoclave. The baffle opening has a strong effect on the nutrient transport and supersaturation of GaN species in the growth zone.

Two-Phase Flow In Anode Flow Field Of A Small Direct Methanol Fuel Cell In Different Gravities

An in-situ visualization of two-phase flow inside anode flow bed of a small liquid fed direct methanol fuel cells in normal and reduced gravity has been conducted in a drop tower. The anode flow bed consists of 11 parallel straight channels. The length, width and depth of single channel, which had rectangular cross section, are 48.0, 2.5 and 2.0 mm, respectively. The rib width was 2.0 mm. The experimental results indicated that when the fuel cell orientation is vertical, two-phase flow pattern in anode channels can evolve from bubbly flow in normal gravity into slug flow in microgravity. The size of bubbles in the reduced gravity is also bigger. In microgravity, the bubbles rising speed in vertical channels is obviously slower than that in normal gravity. When the fuel cell orientation is horizontal, the slug flow in the reduced gravity has almost the same characteristic with that in normal gravity. It implies that the effect of gravity on two-phase flow is small and the bubbles removal is governed by viscous drag. When the gas slugs or gas columns occupy channels, the performance of liquid fed direct methanol fuel cells is failing rapidly. It infers that in long-term microgravity, flow bed and operating condition should be optimized to avoid concentration polarization of fuel cells.