In the paper, 3-D analysis method with unitive schemes is set up, which is used to resolve the uplift with multiple moving boundaries and multiple nonlinear coupling for anchored liquid storage tanks. hi it, an algori...In the paper, 3-D analysis method with unitive schemes is set up, which is used to resolve the uplift with multiple moving boundaries and multiple nonlinear coupling for anchored liquid storage tanks. hi it, an algorithm of quasi-harmonious finite elements for arbitrary quadrilateral of thin plates and shells is built up to analyze the multiple coupling problems of general thin plates and shells structures with three dimensions, the complementary equations for analyzing uplifting moving boundary problems are deduced. The axial symmetry and presumption of beam type mode are not used. In it, an algorithm is put forward for analyzing the Navier-Stokes problems of unsteady, three-dimensional, and viscous liquid with sloshing of moving boundary surfaces in large amplitude under ALE frame by scheme of time-split-steps to which linear potential theory is not applied. The algorithms can be used to analyze the solid-liquid multiple nonlinear coupling problems with 3-D moving boundary with friction in multiple places.展开更多
In this paper,we describe how to construct a finite-difference shockcapturing method for the numerical solution of the Euler equation of gas dynamics on arbitrary two-dimensional domainΩ,possibly with moving boundary...In this paper,we describe how to construct a finite-difference shockcapturing method for the numerical solution of the Euler equation of gas dynamics on arbitrary two-dimensional domainΩ,possibly with moving boundary.The boundaries of the domain are assumed to be changing due to the movement of solid objects/obstacles/walls.Although the motion of the boundary could be coupled with the fluid,all of the numerical tests are performed assuming that such a motion is prescribed and independent of the fluid flow.The method is based on discretizing the equation on a regular Cartesian grid in a rectangular domainΩ_(R)⊃Ω.Ωe identify inner and ghost points.The inner points are the grid points located insideΩ,while the ghost points are the grid points that are outsideΩbut have at least one neighbor insideΩ.The evolution equations for inner points data are obtained from the discretization of the governing equation,while the data at the ghost points are obtained by a suitable extrapolation of the primitive variables(density,velocities and pressure).Particular care is devoted to a proper description of the boundary conditions for both fixed and time dependent domains.Several numerical experiments are conducted to illustrate the validity of themethod.Ωe demonstrate that the second order of accuracy is numerically assessed on genuinely two-dimensional problems.展开更多
In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method (CSPM) for simulation of shock wave propagation and reflection from fixed and moving solid bounda...In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method (CSPM) for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.展开更多
In the present paper we study the well-posedness using the Galerkin method and the stabilization considering multiplier techniques for a fourth-order nonlinear Schrödinger equation in domains with moving boundari...In the present paper we study the well-posedness using the Galerkin method and the stabilization considering multiplier techniques for a fourth-order nonlinear Schrödinger equation in domains with moving boundaries.We consider two situations for the stabilization:the conservative case and the dissipative case.展开更多
The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive comp...The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive computational costs.To overcome this limitation,a message passing interface(MPI)parallel DEM-IMB-LBM framework is proposed aimed at enhancing computation efficiency.This framework utilises a static domain decomposition scheme,with the entire computation domain being decomposed into multiple subdomains according to predefined processors.A detailed parallel strategy is employed for both contact detection and hydrodynamic force calculation.In particular,a particle ID re-numbering scheme is proposed to handle particle transitions across sub-domain interfaces.Two benchmarks are conducted to validate the accuracy and overall performance of the proposed framework.Subsequently,the framework is applied to simulate scenarios involving multi-particle sedimentation and submarine landslides.The numerical examples effectively demonstrate the robustness and applicability of the MPI parallel DEM-IMB-LBM framework.展开更多
Considering three-dimensional model ECOMSED can not simulate wetting-drying of shoal with its fixed boundary, an approach to represent moving boundary in the model is introduced here. This approach smoothly joints the...Considering three-dimensional model ECOMSED can not simulate wetting-drying of shoal with its fixed boundary, an approach to represent moving boundary in the model is introduced here. This approach smoothly joints the internal and external mode by making use of wetting and drying technique and is verified by a numerical test which presents a good agreement with the previous test results obtained by other researchers. A three dimensional numerical model is established to simulate the hydrodynamics in spring tide in the Changjiang (Yangtze) River estuary by this modified ECOMSED model which is also validated through the observed field data, the simulation presents a good periodic tidal change. It also successfully simulates the tidal current of computational areas and reproduces the tidal flat intermittent appearance.展开更多
Field evidence indicates that proppant distribution and threshold pressure gradient have great impacts on well productivity.Aiming at the development of unconventional oil reservoirs in Triassic Chang-7 Unit,Ordos Bas...Field evidence indicates that proppant distribution and threshold pressure gradient have great impacts on well productivity.Aiming at the development of unconventional oil reservoirs in Triassic Chang-7 Unit,Ordos Basin of China,we presented an integrated workflow to investigate how(1)proppant placement in induced fracture and(2)non-linear flow in reservoir matrix would affect well productivity and fluid flow in the reservoir.Compared with our research before(Yue et al.,2020),here we extended this study into the development of multi-stage fractured horizontal wells(MFHWs)with large-scale complicated fracture geometry.The integrated workflow is based on the finite element method and consists of simulation models for proppant-laden fluid flow,fracture flow,and non-linear seepage flow,respectively.Simulation results indicate that the distribution of proppant inside the induced cracks significantly affects the productivity of the MFHW.When we assign an idealized proppant distribution instead of the real distribution,there will be an overestimation of 44.98%in daily oil rate and 30.63%in cumulative oil production after continuous development of 1000 days.Besides,threshold pressure gradient(TPG)also significantly affects the well performance in tight oil reservoirs.If we simply apply linear Darcy’s law to the reservoir matrix,the overall cumulative oil production can be overrated by 77%after 1000 days of development.In general,this research provides new insights into the development of tight oil reservoirs with TPG and meanwhile reveals the significance of proppant distribution and non-linear fluid flow in the production scenario design.展开更多
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 neglecti...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.展开更多
Based on Huang's accurate tri-sectional nonlin- ear kinematic equation (1997), a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeabili...Based on Huang's accurate tri-sectional nonlin- ear kinematic equation (1997), a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction: The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation (PDE) sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient (TPG) has a great effect on the external moving boundary but has little effect on the internal moving boundary.展开更多
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 e...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.展开更多
The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and ex...The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of 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.A kind of characteristic finite difference schemes is put forward,from which optimal order estimates in l~2 norm are derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,the model numerical method and software development.展开更多
In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary unde...In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.展开更多
In this paper, the linear complementary method for moving boundary problems with phase transformation is presented, in which a pair of unknown vectors of heat source with phase transforming and the temperature field c...In this paper, the linear complementary method for moving boundary problems with phase transformation is presented, in which a pair of unknown vectors of heat source with phase transforming and the temperature field can be solved exactly, and a large amount of iterative calculations can be avoided.展开更多
A novel method is developed for electro-focusing and moving neutralization reaction boundary (MNRB) created with HCl and NaOH. The optimized conditions are screened out. By using this method, the experiments are perfo...A novel method is developed for electro-focusing and moving neutralization reaction boundary (MNRB) created with HCl and NaOH. The optimized conditions are screened out. By using this method, the experiments are performed on MNRB formed with HCl and NaOH in agarose gel. The experiments are quantitatively in coincidence with the predictions with the theory of moving chemical reaction boundary (MCRB).展开更多
Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploi...Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of 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.The upwind finite difference schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set.Some techniques,such as change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.展开更多
A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium w...A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.展开更多
An approximate analytical solution of moving boundary problem for diffusion release of drug from a cylinder polymeric matrix was obtained by use of refined integral method. The release kinetics has been analyzed for n...An approximate analytical solution of moving boundary problem for diffusion release of drug from a cylinder polymeric matrix was obtained by use of refined integral method. The release kinetics has been analyzed for non-erodible matrices with perfect sink condition. The formulas of the moving boundary and the fractional drug release were given. The moving boundary and the fractional drug release have been calculated at various drug loading levels, mid the calculated results were in good agreement with those of experiments. The comparison of the moving boundary in spherical, cylinder, planar matrices has been completed. An approximate formula for estimating the available release time was presented. These results are useful for the clinic experiments. This investigation provides a new theoretical tool for studying the diffusion release of drug from a cylinder polymeric matrix and designing the controlled released drug.展开更多
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 eval...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.展开更多
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 ...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.展开更多
A hybrid Cartesian structured grid method is proposed for solving moving boundary unsteady problems.The near body region is discretized by using the body-fitted structured grids,while the remaining computational domai...A hybrid Cartesian structured grid method is proposed for solving moving boundary unsteady problems.The near body region is discretized by using the body-fitted structured grids,while the remaining computational domain is tessellated with the generated Cartesian grids.As the body moves,the structured grids move with the body and the outer boundaries of inside grids are used to generate new holes in the outside adaptive Cartesian grid to facilitate data communication.By using the alternating digital tree(ADT)algorithm,the computational time of hole-cutting and identification of donor cells can be reduced significantly.A compressible solver for unsteady flow problems is developed.A cell-centered,second-order accurate finite volume method is employed in spatial discretization and an implicit dual-time stepping low-upper symmetric Gauss-Seidel(LU-SGS)approach is employed in temporal discretization.Geometrybased adaptation is used during unsteady simulation time steps when boundary moves and the flow solution is interpolated from the old Cartesian grids to the new one with inverse distance weighting interpolation formula.Both laminar and turbulent unsteady cases are tested to demonstrate the accuracy and efficiency of the proposed method.Then,a 2-D store separation problem is simulated.The result shows that the hybrid Cartesian grid method can handle the unsteady flow problems involving large-scale moving boundaries.展开更多
文摘In the paper, 3-D analysis method with unitive schemes is set up, which is used to resolve the uplift with multiple moving boundaries and multiple nonlinear coupling for anchored liquid storage tanks. hi it, an algorithm of quasi-harmonious finite elements for arbitrary quadrilateral of thin plates and shells is built up to analyze the multiple coupling problems of general thin plates and shells structures with three dimensions, the complementary equations for analyzing uplifting moving boundary problems are deduced. The axial symmetry and presumption of beam type mode are not used. In it, an algorithm is put forward for analyzing the Navier-Stokes problems of unsteady, three-dimensional, and viscous liquid with sloshing of moving boundary surfaces in large amplitude under ALE frame by scheme of time-split-steps to which linear potential theory is not applied. The algorithms can be used to analyze the solid-liquid multiple nonlinear coupling problems with 3-D moving boundary with friction in multiple places.
基金The work of A.Chertock was supported in part by the NSF Grants DMS-1216974 and DMS-1521051The work of A.Kurganov was supported in part by the NSF Grants DMS-1216957 and DMS-1521009The work of G.Russo was supported partially by the University of Catania,Project F.I.R.Charge Transport in Graphene and Low Dimensional Systems,and partially by ITN-ETN Horizon 2020 Project Mod Comp Shock,Modeling and Computation on Shocks and Interfaces,Project Reference 642768.
文摘In this paper,we describe how to construct a finite-difference shockcapturing method for the numerical solution of the Euler equation of gas dynamics on arbitrary two-dimensional domainΩ,possibly with moving boundary.The boundaries of the domain are assumed to be changing due to the movement of solid objects/obstacles/walls.Although the motion of the boundary could be coupled with the fluid,all of the numerical tests are performed assuming that such a motion is prescribed and independent of the fluid flow.The method is based on discretizing the equation on a regular Cartesian grid in a rectangular domainΩ_(R)⊃Ω.Ωe identify inner and ghost points.The inner points are the grid points located insideΩ,while the ghost points are the grid points that are outsideΩbut have at least one neighbor insideΩ.The evolution equations for inner points data are obtained from the discretization of the governing equation,while the data at the ghost points are obtained by a suitable extrapolation of the primitive variables(density,velocities and pressure).Particular care is devoted to a proper description of the boundary conditions for both fixed and time dependent domains.Several numerical experiments are conducted to illustrate the validity of themethod.Ωe demonstrate that the second order of accuracy is numerically assessed on genuinely two-dimensional problems.
文摘In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method (CSPM) for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.
基金partially financed by regular project Fondecyt 1191137.ANID.Chile.
文摘In the present paper we study the well-posedness using the Galerkin method and the stabilization considering multiplier techniques for a fourth-order nonlinear Schrödinger equation in domains with moving boundaries.We consider two situations for the stabilization:the conservative case and the dissipative case.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.12072217 and 42077254)the Natural Science Foundation of Hunan Province,China(Grant No.2022JJ30567).
文摘The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive computational costs.To overcome this limitation,a message passing interface(MPI)parallel DEM-IMB-LBM framework is proposed aimed at enhancing computation efficiency.This framework utilises a static domain decomposition scheme,with the entire computation domain being decomposed into multiple subdomains according to predefined processors.A detailed parallel strategy is employed for both contact detection and hydrodynamic force calculation.In particular,a particle ID re-numbering scheme is proposed to handle particle transitions across sub-domain interfaces.Two benchmarks are conducted to validate the accuracy and overall performance of the proposed framework.Subsequently,the framework is applied to simulate scenarios involving multi-particle sedimentation and submarine landslides.The numerical examples effectively demonstrate the robustness and applicability of the MPI parallel DEM-IMB-LBM framework.
基金The Foundation of Shanghai 908 (PJ4)the key project of the national eleventh five-year science and technology planning supported by The Ministry of Science and Technology under contract No 2008BAJ08B14the key project for the funda-mental science and technology research supported by The Ministry of Science and Technology under contract No 2007FY110300-03
文摘Considering three-dimensional model ECOMSED can not simulate wetting-drying of shoal with its fixed boundary, an approach to represent moving boundary in the model is introduced here. This approach smoothly joints the internal and external mode by making use of wetting and drying technique and is verified by a numerical test which presents a good agreement with the previous test results obtained by other researchers. A three dimensional numerical model is established to simulate the hydrodynamics in spring tide in the Changjiang (Yangtze) River estuary by this modified ECOMSED model which is also validated through the observed field data, the simulation presents a good periodic tidal change. It also successfully simulates the tidal current of computational areas and reproduces the tidal flat intermittent appearance.
基金The authors gratefully acknowledge the financial supports from the National Science Foundation of China under Grant 52274027 as well as the High-end Foreign Experts Recruitment Plan of the Ministry of Science and Technology China under Grant G2022105027L.
文摘Field evidence indicates that proppant distribution and threshold pressure gradient have great impacts on well productivity.Aiming at the development of unconventional oil reservoirs in Triassic Chang-7 Unit,Ordos Basin of China,we presented an integrated workflow to investigate how(1)proppant placement in induced fracture and(2)non-linear flow in reservoir matrix would affect well productivity and fluid flow in the reservoir.Compared with our research before(Yue et al.,2020),here we extended this study into the development of multi-stage fractured horizontal wells(MFHWs)with large-scale complicated fracture geometry.The integrated workflow is based on the finite element method and consists of simulation models for proppant-laden fluid flow,fracture flow,and non-linear seepage flow,respectively.Simulation results indicate that the distribution of proppant inside the induced cracks significantly affects the productivity of the MFHW.When we assign an idealized proppant distribution instead of the real distribution,there will be an overestimation of 44.98%in daily oil rate and 30.63%in cumulative oil production after continuous development of 1000 days.Besides,threshold pressure gradient(TPG)also significantly affects the well performance in tight oil reservoirs.If we simply apply linear Darcy’s law to the reservoir matrix,the overall cumulative oil production can be overrated by 77%after 1000 days of development.In general,this research provides new insights into the development of tight oil reservoirs with TPG and meanwhile reveals the significance of proppant distribution and non-linear fluid flow in the production scenario design.
基金funding by the project (Grant 51404232) sponsored by the National Natural Science Foundation of Chinathe National Science and Technology Major Project (Grant 2011ZX05038003)+1 种基金the China Postdoctoral Science Foundation project (Grant 2014M561074)the China Scholarship Council for its generous financial support of the research
文摘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.
基金supported by the National Natural Science Foundation of China(11102237)Program for Changjiang Scholars and Innovative Research Team in University(IRT1294)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(20110133120012)China Scholarship Council(CSC)
文摘Based on Huang's accurate tri-sectional nonlin- ear kinematic equation (1997), a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction: The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation (PDE) sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient (TPG) has a great effect on the external moving boundary but has little effect on the internal moving boundary.
基金supported by the National Natural Science Foundation of China (Grant No.10872144)the Support Plan of Science and Technology of Tianjin (Grant No.07ZCGYSH01700)
文摘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.
基金the Major State Basic Research Program of China(No.G19990328)the National Tackling Key Problem Program(No.20050200069)+1 种基金the National Natural Science Foundation of China(Nos.10771124,10372052)the Ph.D.Programs Foundation of Ministry of Education of China(No.20030422047)
文摘The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of 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.A kind of characteristic finite difference schemes is put forward,from which optimal order estimates in l~2 norm are derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,the model numerical method and software development.
基金Project supported by the National Natural Science Foundation of China (Nos. 11901555, 11901213,11871448, and 11732016)the National Numerical Windtunnel Project (No. NNW2019ZT4-B10)。
文摘In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.
文摘In this paper, the linear complementary method for moving boundary problems with phase transformation is presented, in which a pair of unknown vectors of heat source with phase transforming and the temperature field can be solved exactly, and a large amount of iterative calculations can be avoided.
基金the NSFC (No. 29775014) and Chinese Health Committee (98-2-334).
文摘A novel method is developed for electro-focusing and moving neutralization reaction boundary (MNRB) created with HCl and NaOH. The optimized conditions are screened out. By using this method, the experiments are performed on MNRB formed with HCl and NaOH in agarose gel. The experiments are quantitatively in coincidence with the predictions with the theory of moving chemical reaction boundary (MCRB).
基金supported by the Major State BasicResearch Program of China(19990328)the National Tackling Key Problem Programs(20050200069)+4 种基金the National Natural Science Foundation of China(1077112410372052)the Doctorate Foundation of the Ministryof Education of China(20030422047)Shandong Provance Natural Science Foundation(2R2009AQ12)the Independent Innovation Foundation of Shandong University(2010TS031)
文摘Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of 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.The upwind finite difference schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set.Some techniques,such as change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.
基金Project supported by the Major State Basic Research Program of China (No. 19990328)the National Tackling Key Problems Program (No. 20050200069)+4 种基金the National Natural Science Foundation of China (Nos. 10771124, 10372052, 11101244, and 11271231)the Doctorate Foundation of the Ministry of Education of China (No. 20030422047)the Shandong Province Natural Science Foundation (No. ZR2009AQ012)the Independent Innovation Foundation of Shandong University(No. 2010TS031)the Scientific Research Award Fund for Excellent Middle-Aged and Young Scientists of Shandong Province (No. BS2009NJ003)
文摘A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.
文摘An approximate analytical solution of moving boundary problem for diffusion release of drug from a cylinder polymeric matrix was obtained by use of refined integral method. The release kinetics has been analyzed for non-erodible matrices with perfect sink condition. The formulas of the moving boundary and the fractional drug release were given. The moving boundary and the fractional drug release have been calculated at various drug loading levels, mid the calculated results were in good agreement with those of experiments. The comparison of the moving boundary in spherical, cylinder, planar matrices has been completed. An approximate formula for estimating the available release time was presented. These results are useful for the clinic experiments. This investigation provides a new theoretical tool for studying the diffusion release of drug from a cylinder polymeric matrix and designing the controlled released drug.
基金supported by the Major State Basic Research Development Program of China(No.G19990328)the National Key Technologies R&D Program of China (No.20050200069)+1 种基金the National Natural Science Foundation of China (Nos.10771124 and 10372052)the Ph. D. Pro-grams Foundation of Ministry of Education of China (No.20030422047)
文摘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.
基金supported by NASA Constellation University Institutes Program (CUIP), Claudia Meyer program manager
文摘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.
基金supported partly by the National Basic Research Program of China(″973″Program)(No.2014CB046200)
文摘A hybrid Cartesian structured grid method is proposed for solving moving boundary unsteady problems.The near body region is discretized by using the body-fitted structured grids,while the remaining computational domain is tessellated with the generated Cartesian grids.As the body moves,the structured grids move with the body and the outer boundaries of inside grids are used to generate new holes in the outside adaptive Cartesian grid to facilitate data communication.By using the alternating digital tree(ADT)algorithm,the computational time of hole-cutting and identification of donor cells can be reduced significantly.A compressible solver for unsteady flow problems is developed.A cell-centered,second-order accurate finite volume method is employed in spatial discretization and an implicit dual-time stepping low-upper symmetric Gauss-Seidel(LU-SGS)approach is employed in temporal discretization.Geometrybased adaptation is used during unsteady simulation time steps when boundary moves and the flow solution is interpolated from the old Cartesian grids to the new one with inverse distance weighting interpolation formula.Both laminar and turbulent unsteady cases are tested to demonstrate the accuracy and efficiency of the proposed method.Then,a 2-D store separation problem is simulated.The result shows that the hybrid Cartesian grid method can handle the unsteady flow problems involving large-scale moving boundaries.