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EFFECT OF A moving boundary ON THE FLUID TRANSIENT FLOW IN LOW PERMEABILITY RESERVOIRS

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Journal of Hydrodynamics 2012年第3期24卷 391-398页

作者： LUO Wan-Jing WANG Xiao-dong School of Energy Resources China University of Geosciences Beijing 100083 China

In a low permeability reservoir, the existence of a moving boundary is considered in the study of the transient porous flow with threshold pressure gradient. The transmission of the moving boundary directly indicates the size of the drainage area as well as the apparent influences on the pressure behavior. The nonlinear transient flow mathematical model in which the threshold pressure gradient and the moving boundary are incorporated is solved by advanced mathematical methods. This paper presents some new analytical solutions describing the pressure distribution at a constant rate and the production decline in a constant pressure production with the boundary propagation. It is shown that the greater the threshold pressure gradient, the slower the transmission of the moving boundary, the larger the pressure loss will be, and there is no radial flow in the middle and later phases of the wellface pressure for a well at a constant rate. We have the the maximum moving boundary at a specific drawdown pressure for a low permeability reservoir The greater the threshold pressure gradient, the smaller the maximum moving boundary distance, the quicker the production decline for a well in a constant pressure production will be. The type curve charts for the modern well test analysis and the rate transient analysis with a moving boundary are obtained and the field test and the production data are interpreted as examples to illustrate how to use our new results.

关键词： threshold pressure gradient moving boundary well test analysis low permeability reservoir rate transient analysis

Adaptive thermo-fluid moving boundary computations for interfacial dynamics

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Acta Mechanica Sinica 2012年第4期28卷 999-1021页

作者： Chih-Kuang Kuan Jaeheon Sim Wei Shyy University of Michigan Ann ArborMIUSA Hong Kong University of Science and Technology

In this study, we present adaptive moving boundary computation technique with parallel implementation on a distributed memory multi-processor system for large scale thermo-fluid and interfacial flow computations. The solver utilizes Eulerian-Lagrangian method to track moving （Lagrangian） interfaces explicitly on the stationary （Eulerian） Cartesian grid where the flow fields are computed. We address the domain decomposition strategies of Eulerian- Lagrangian method by illustrating its intricate complexity of the computation involved on two different spaces inter- actively and consequently, and then propose a trade-off ap- proach aiming for parallel scalability. Spatial domain decomposition is adopted for both Eulerian and Lagrangian do- main due to easy load balancing and data locality for mini- mum communication between processors. In addition, parallel cell-based unstructured adaptive mesh refinement （AMR） technique is implemented for the flexible local refinement and even-distributed computational workload among processors. Selected cases are presented to highlight the computa- tional capabilities, including Faraday type interfacial waves with capillary and gravitational forcing, flows around varied geometric configurations and induced by boundary conditions and/or body forces, and thermo-fluid dynamics with phase change. With the aid of the present techniques, large scale challenging moving boundary problems can be effectively addressed.

关键词： moving boundary Eulerian-Lagrangian method Parallel adaptive mesh refinement

Effect of quadratic pressure gradient term on a one-dimensional moving boundary problem based on modified Darcy's law

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Acta Mechanica Sinica 2016年第1期32卷 38-53页

作者： Wenchao Liu Jun Yao Zhangxin Chen Yuewu Liu Institute of Mechanics Chinese Academy of Sciences School of Petroleum Engineering China University of Petroleum (Huadong) Department of Chemical and Petroleum Engineering Schulich School of Engineering University of Calgary

A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equa- tions with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be sta- bly numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy＇s flow problem, the exact analytical solution for the case of Darcy＇s flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclu- sion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equa- tions; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pres- sure gradient increasing for the one-dimensional problem.

关键词： Quadratic pressure gradient term Thresholdpressure gradient Porous media Numerical solution moving boundary

Upwind finite difference method for miscible oil and water displacement problem with moving boundary values

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Applied Mathematics and Mechanics(English Edition) 2009年第11期30卷 1365-1378页

作者：袁益让李长峰杨成顺韩玉笈 Institute of Mathematics Shandong University Physical Exploration Institute Shengli Petroleum Administration

The research of the miscible oil and water displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the twodimensional bounded region, the upwind finite difference schemes are proposed. Some techniques, such as the calculus of variations, the change of variables, and the theory of a priori estimates, are used. The optimal orderl2-norm estimates are derived for the errors in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method, and the software development.

关键词： compressible displacement moving boundary upwind finite difference frac-tional steps l2 error estimate

Geometrically nonlinear dynamic response of stiffened plates with moving boundary conditions

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Science China(Physics,Mechanics & Astronomy) 2014年第8期57卷 1536-1546页

作者： MA NiuJing WANG RongHui HAN Qiang LU YiGang School of Civil Engineering and Transportation South China University of Technology State Key Laboratory of Subtropical Building Science School of Sciences South China University of Technology

An approach is presented to investigate the nonlinear vibration of stiffened plates.A stiffened plate is divided into one plate and some stiffeners,with the plate considered to be geometrically nonlinear,and the stiffeners taken as Euler *** equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the ***,the effect caused by boundary movement is transformed into equivalent *** first approximation solution of the non-resonance is obtained by means of the method of multiple *** primary parametric resonance and primary resonance of the stiffened plate are studied by using the same *** accuracy of the method is validated by comparing the results with those of finite element analysis via *** examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary *** addition,the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried *** nonlinear vibration characteristics of stiffened plates are obtained,which are useful for engineering design.

关键词： stiffened plates moving boundary nonlinear vibration primary parametric resonance and primary resonance the method of multiple scales

A New Wetting and Drying Method for moving boundary in Shallow Water Flow Models

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China Ocean Engineering 2010年第1期24卷 79-92页

作者：孙健陶建华 School of Mechanical Engineering Tianjin University

To deal with the moving boundary hydrodynamic problems of the tidal flats in shallow water flow models, a new wetting and drying （WD） method is proposed. In the new method, a ＂predicted water depth＂ is evaluated explicitly based on the simplified shallow water equations and used to determine the status （wet or dry） together with the direction of flow. Compared with previous WD method, besides the water elevation, more factors, such as the flow velocity and the surface shear stress, are taken into account in the new method to determine the moving boundary. In addition, a formula is deduced to determine the threshold, as critical water depth, which needs to be preset before simulations. The new WD method is tested with five cases including three 1D ones and two 2D ones. The results show that the new WD method can simulate the wetting and drying process, in beth typical and practical cases, with smooth manner and achieves effective estimation of the retention volume at shallow water body.

关键词： moving boundary wetting anddrying tidal flat numerical simulation shallow water flow

Simulation of moving boundary of the reaction shaft in a flash smelting furnace

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Journal of Central South University 2001年第3期13卷 213-218页

作者： CHEN Zhuo 1,MEI Chi 1,CHEN Hong-rong 1,MO Jiao 2 (1 Institute on Simulation and Optimization of Pyro-installation, Central Sout h University, Changsha 410083, China 2 Science School, Beijing University of Posts and Telecommunications, Beijing 1 1. Institute on Simulation and Optimization of Pyro-installation Central South University 410083 Changsha China 2. Science School Beijing University of Posts and Telecommunications 100876 Beijing China

As to solve the online monitoring of the inner temperatur e and freezing profile of the reaction shaft of flash smelting furnace, simulation of the wall in the reaction shaft in a flash smelting furnace was made through numerical computation. The computational results are very near the data got in s ite. The error of the moving boundary is approximately 3%, and that of the tempe rature is less than 5%. It is proved that the simulation software is applicable for practice to monitor the temperature and moving boundary inside the hearth on line. Based on a large number of the data computed, the relation between the cha nge of the moving boundary and inner temperature is summarized, and the great in fluence of the cooling system on the forming and stability of the moving boundar y inside the hearth is emphasized, which provide the theoretical bases for optim izing the flash smelting operation.

关键词： flash smelting furnace moving boundary numerical computation simulation

A moving boundary problem derived from heat and water transfer processes in frozen and thawed soils and its numerical simulation

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Science China Mathematics 2008年第8期51卷 1510-1521页

作者： XIE ZhengHui SONG LiYe FENG XiaoBing Institute of Atmospheric Physics Chinese Academy of SciencesBeijing 100029China Graduate School of the Chinese Academy of Sciences Beijing 100049China Department of Mathematics the University of TennesseeKnoxvilleTN 37996USA

The seasonal change in depths of the frozen and thawed soils within their active layer is reduced to a moving boundary problem, which describes the dynamics of the total ice content using an independent mass balance equation and treats the soil frost/thaw depths as moving (sharp) interfaces governed by some Stefan-type moving boundary conditions, and hence simultaneously describes the liquid water and solid ice states as well as the positions of the frost/thaw depths in soil. An adaptive mesh method for the moving boundary problem is adopted to solve the relevant equations and to determine frost/thaw depths, water content and temperature distribution. A series of sensitivity experiments by the numerical model under the periodic sinusoidal upper boundary condition for temperature are conducted to validate the model, and to investigate the effects of the model soil thickness, ground surface temperature, annual amplitude of ground surface temperature and thermal conductivity on frost/thaw depths and soil temperature. The simulated frost/thaw depths by the model with a periodical change of the upper boundary condition have the same period as that of the upper boundary condition, which shows that it can simulate the frost/thaw depths reasonably for a periodical forcing.

关键词： frost and thaw depth moving boundary Stefan problem heat and water transfer numerical solution 80A22

Mobile observation for distributed parameter system with moving boundary over mobile sensor networks

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Journal of Control and Decision 2021年第2期8卷 124-134页

作者： Jianzhong Zhang Baotong Cui Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education) Jiangnan UniversityWuxiPeople’s Republic of China School of Internet of Things Engineering Jiangnan UniversityWuxi 214122People’s Republic of China School of Mathematics and Statistics Taishan UniversityTaian 271000People’s Republic of China

This paper considers the state observation for a class of distributed parameter systems(DPSs)with moving boundaries modelled by parabolic partial differential equations(PDEs).The method of mobile observation is presented to improve the observation performance of the systems and to eliminate the influence of moving boundaries on system observation with the aids of mobile sensor networks(MSNs).The MSNs which can move throughout the time-dependent spatial domain are used to provide the spatially averaged observations of the *** using the abstract evolution equation theory of parabolic PDEs and the Lyapunov stability arguments,a centralised observer is designed and a mobile control scheme for each of the mobile sensors is presented while taking account of the dynamics of the MSNs.A numerical example is finally presented to illustrate the effectiveness and the advantages of the proposed approach.

关键词： Distributed parameter system moving boundary abstract evolution equation state observation mobile sensor network