Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for on...Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for one dimensional zero-pressure gas dynamics system.Here the first equation is the Burgers equation and the second one is the continuity equation.We consider the solution with initial data in the space of bounded Borel measures.First we prove a general existence result in the algebra of generalized functions of Colombeau.Then we study in detail special solutions withδ-measures as initial data.We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves.This gives an understanding of plane-wave interactions in the multidimensional case.We use the vanishing viscosity method in our analysis as this gives the physical solution.展开更多
In this paper, we study the vanishing viscosity limit for non-isentropic gas dy- namics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of sh...In this paper, we study the vanishing viscosity limit for non-isentropic gas dy- namics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of shocks interacting at some positive time, we show that such solution is the vanishing viscosity limit of a family of smooth global solutions for a viscous system of conservation law. We remark that, after the interacting time, not only shocks but also contact discontinuity are generated.展开更多
A compactness frame of the Lax-Friedrichs scheme for the equations of gas dynamics is obtained by using some embedding theorems and an analysis of the difference scheme and the weak entropy.
We investigate the vacuum in nonisentropic gas dynamics in one space vari- able, with the most general equation of states allowed by thermodynamics. We recall physical constraints on the equations of state and give ex...We investigate the vacuum in nonisentropic gas dynamics in one space vari- able, with the most general equation of states allowed by thermodynamics. We recall physical constraints on the equations of state and give explicit and easily checkable conditions under which vacuums occur in the solution of the Riemann problem. We then present a class of models for which the Riemann problem admits unique global solutions without vacuums.展开更多
In nonisentropic gas dynamics, with general equations of state, strong cornpressive shocks satisfying the Liu E-condition may violate the Second Law of thermodynamics.
Existence of globally bounded classical solution for nonisentropic gas dynamics system has long been studied, especially in the case of polytropic gas. In [4], Liu claimed that sufficient condition has been establishe...Existence of globally bounded classical solution for nonisentropic gas dynamics system has long been studied, especially in the case of polytropic gas. In [4], Liu claimed that sufficient condition has been established. However, the authors find that the argument he used is not true in general. In this article, the authors give a counter example of his argument. Hence, his claim is not valid. The authors believe that it is difficult to impose general conditions on the initial data to obtain globally bounded classical solution.展开更多
The 3-dimensional zero-pressure gas dynamics system appears in the modeling for the large scale structure formation in the universe. The aim of this paper is to construct spherically symmetric solutions to the system....The 3-dimensional zero-pressure gas dynamics system appears in the modeling for the large scale structure formation in the universe. The aim of this paper is to construct spherically symmetric solutions to the system. The radial component of the velocity and density satisfy a simpler one dimensional problem. First we construct explicit solutions of this one dimensional case with initial and boundary conditions. Then we get special radial solutions with different behaviours at the origin.展开更多
In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entrop...In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.展开更多
This paper gives four pairs of entropies (η_i, q_i) (i=1, 2, 3, 4) to the isentropic gas dynamics equations ρ_t+(ρu)_x=0 (ρu)_t+(ρu^2+p(ρ))_x=0 p(ρ)=k^2ρ~γ,1<γ<3。 when all the function equations are s...This paper gives four pairs of entropies (η_i, q_i) (i=1, 2, 3, 4) to the isentropic gas dynamics equations ρ_t+(ρu)_x=0 (ρu)_t+(ρu^2+p(ρ))_x=0 p(ρ)=k^2ρ~γ,1<γ<3。 when all the function equations are satisfied展开更多
The present article is concerned with the implementation of a recent semi-analytical method referred to as fractional reduced differential transform method （FRDTM） for computation of approximate solution of time-fra...The present article is concerned with the implementation of a recent semi-analytical method referred to as fractional reduced differential transform method （FRDTM） for computation of approximate solution of time-fractional gas dynamics equation （TFGDE） arising in shock fronts. In this approach, the fractional derivative is described in the Caputo sense. Four numeric experiments have been carried out to confirm the validity and the efficiency of the method. It is found that the exact or a closed approximate analytical solution of a fractional nonlinear differential equations arising in allied science and engineering can be obtained easily. Moreover, due to its small size of calculation contrary to the other analytical approaches while dealing with a complex and tedious physical problems arising in various branches of natural sciences and engineering, it is very easy to implement.展开更多
Consider an initial-boundary problem vt - ux=0,u, + （）x + f（u） = （）x,θt+ux=（）ux=（）x+ （E） v（x,0） = v0（x）,u（x,0） = u0（x）,θ（0,x） = θ0（x）, （I） u（t,0） = u（t,1） = θx（t,0） = θx（t,1） （J...Consider an initial-boundary problem vt - ux=0,u, + （）x + f（u） = （）x,θt+ux=（）ux=（）x+ （E） v（x,0） = v0（x）,u（x,0） = u0（x）,θ（0,x） = θ0（x）, （I） u（t,0） = u（t,1） = θx（t,0） = θx（t,1） （J） Sufficient and necessary conditions for （E）, （I） and （J） to have asymptotic stability of the gobal smooth solution are given by means of the elemental L2 energy method.展开更多
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert’s and Enskog’s methods are discussed. The equations system of multicomponent non- equilibrium gas dynam...In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert’s and Enskog’s methods are discussed. The equations system of multicomponent non- equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asym- ptotic) method for solution of the system of kinetic Boltzmann equations.展开更多
In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discreti...In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.展开更多
Industry and energy continue to require piston engines(PICE)at a high level worldwide.Therefore,science and technology must urgently work on improving the PICE working cycle.Improving the quality of the intake process...Industry and energy continue to require piston engines(PICE)at a high level worldwide.Therefore,science and technology must urgently work on improving the PICE working cycle.Improving the quality of the intake process of theworking fluid into the cylinder is one of the most effective ways to improve the operational performance of PICE.The purpose of the study was to assess the impact of various cylinder head(CylH)designs on the gas-dynamic and heat-exchange qualities of air flows within an engine model’s intake system.Three different CylH designs were studied:the basic configuration and upgraded cylinder heads with a square valve and a square valve port.These designs are innovative.Laboratory conditions were used to conduct the studies for stationary air flow.The experiments covered the range of Reynolds numbers from 8500 to 96,000.The intake system’s gas dynamics and heat transfer were determined using the thermal anemometry method,which was based on constant-temperature hot-wire anemometers.It has been established that the use of upgraded CylHs causes an increase in the turbulence number of flow by an average of 13.5%.Additionally,itwas found that the increase in the turbulence number of flowin the cylinder is about 19%when installing new CylH designs.It was shown that therewas an increase in the heat transfer coefficient in the intake pipe by 10%–40%when installing modernized CylH designs in the intake system.The article focused on the problems of increasing the turbulence level and intensifying the heat transfer of stationary air flow in the intake system,specifically in PICEs.The study’s findings are novel in the areas of applied gas dynamics and PICEs.展开更多
The semiconductor bridge(SCB)ignites through bridge film discharge,offering advantages such as low ignition energy,high safety,and compatibility with digital logic circuits.The study uses laser interferometry to inves...The semiconductor bridge(SCB)ignites through bridge film discharge,offering advantages such as low ignition energy,high safety,and compatibility with digital logic circuits.The study uses laser interferometry to investigate the gas dynamics of the bridge film after SCB plasma extinction.Interferometric images of the SCB film gas were obtained through a laser interferometry optical path.After the degradation model of digital image processing,clearer images were produced to facilitate analysis and calculation.The results show that the gas temperature at the center of the SCB film reaches a maximum of 1000 K,and the temperature rapidly decreases along the axial direction of the bridge surface to room temperature at 300 K.The maximum diffusion velocity of the plasma is 1.8 km/s.These findings provide critical insights for SCB design and ignition control.展开更多
The precision of dynamic reserve calculations in gas reservoirs is crucial for the rational and efficient development of oil and gas fields and the formulation of gas well production plans.The Shaximiao gas reservoir ...The precision of dynamic reserve calculations in gas reservoirs is crucial for the rational and efficient development of oil and gas fields and the formulation of gas well production plans.The Shaximiao gas reservoir in the ZT block of northwestern Sichuan is densely packed and highly heterogeneous,featuring complex gas-water distribution,substantial variations in test production among gas wells,and a rapid decline rate.To precisely determine the dynamic reserves of these tight water-bearing gas wells,this study focuses on the water-tight gas reservoirs in the ZT block of northwestern Sichuan,conducting core X-ray diffraction,constant-rate mercury injection,and reservoir rock stress sensitivity experiments.Utilizing the experimental findings,the porosity and permeability of the rock samples under effective stress conditions are adjusted via binary linear regression.These adjusted parameters are then incorporated into the water-sealed gas material balance method,thereby establishing a novel approach for calculating dynamic reserves in water-tight gas reservoirs under stress sensitivity conditions.The results show that:(1)the rock porosity ranges from 6.08%to 10.22%,permeability ranges from 0.035 mD to 0.547 mD,clay mineral content ranges from 6.58%to 19.14%,pore radius distribution ranges from 90μm to 180μm,throat radius distribution ranges from 0.61μm to 3.41μm,with significant differences in throat distribution,indicating poor reservoir fluid flow capacity and strong tightness;(2)after aging experiments,rock samples exhibit plastic deformation,with porosity and permeability unable to fully recover after pressure relief.The stress sensitivity curve of rock samples shows a two-stage characteristic,with moderate to strong stress sensitivity;(3)porosity stress sensitivity is mainly influenced by pore radius and mineral composition-larger pore radius and higher clay content lead to stronger stress sensitivity,with porosity loss rates ranging from 8.26%to 23.69%.Permeability stress sensitivity is mainly influenced by throat radius and mineral composition-smaller throat radius and higher clay content result in stronger stress sensitivity,with permeability loss rates ranging from 47.91%to 62.03%;(4)a comparative analysis between the traditional dynamic reserve calculation method for gas wells and the new method considering stress sensitivity shows a relative error between 0.90%and 2.41%,with the new method demonstrating better accuracy.This study combines physical experimental results with an effective stress model of reservoir rocks to develop a new method for calculating dynamic reserves of water-bearing tight gas reservoirs under effective stress conditions,providing experimental data and example calculation results to support subsequent dynamic evaluation of gas reservoirs and the establishment of rational well allocation plans.展开更多
In this paper,firstly,by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation,we construct parameterized delta-shock and constant density solutions,then we show that,as the f...In this paper,firstly,by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation,we construct parameterized delta-shock and constant density solutions,then we show that,as the flux perturbation vanishes,they converge to the delta-shock and vacuum state solutions of the zero-pressure flow,respectively.Secondly,we solve the Riemann problem of the Euler equations of isentropic gas dynamics with a double parameter flux approximation including pressure.Furthermore,we rigorously prove that,as the two-parameter flux perturbation vanishes,any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow;any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum intermediate state in between tends to a vacuum state.Finally,numerical results are given to present the formation processes of delta shock waves and vacuum states.展开更多
In this paper, the Riemann problem with delta initial data for the onedimensional system of conservation laws of mass, momentum and energy in zero-pressure gas dynamics is considered. Under the generalized Rankine-Hug...In this paper, the Riemann problem with delta initial data for the onedimensional system of conservation laws of mass, momentum and energy in zero-pressure gas dynamics is considered. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtained the global existence of generalized solutions which contains delta-shock. Moreover, the author obtains the stability of generalized solutions by making use of the perturbation of the initial data.展开更多
We propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations.By all regime,we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolve...We propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations.By all regime,we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M,i.e.such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1.The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M.This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy.A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism.A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed.Then a simple and efficient semi implicit scheme is also proposed.The resulting scheme is stable under a CFL condition driven by the(slow)material waves and not by the(fast)acoustic waves and so verifies the all regime property.Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.展开更多
基金supported by the TIFR-CAM Doctoral Fellowshipthe NISER Postdoctoral Fellowship (through the project “Basic research in physics and multidisciplinary sciences” with identification # RIN4001) during the preparation of this papersupported by the Raja Ramanna Fellowship
文摘Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for one dimensional zero-pressure gas dynamics system.Here the first equation is the Burgers equation and the second one is the continuity equation.We consider the solution with initial data in the space of bounded Borel measures.First we prove a general existence result in the algebra of generalized functions of Colombeau.Then we study in detail special solutions withδ-measures as initial data.We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves.This gives an understanding of plane-wave interactions in the multidimensional case.We use the vanishing viscosity method in our analysis as this gives the physical solution.
基金Xiaoding Shi was supported by National Natural Sciences Foundation of China(11471321)Yan Yong was supported by National Natural Sciences Foundation of China(11201301)
文摘In this paper, we study the vanishing viscosity limit for non-isentropic gas dy- namics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of shocks interacting at some positive time, we show that such solution is the vanishing viscosity limit of a family of smooth global solutions for a viscous system of conservation law. We remark that, after the interacting time, not only shocks but also contact discontinuity are generated.
文摘A compactness frame of the Lax-Friedrichs scheme for the equations of gas dynamics is obtained by using some embedding theorems and an analysis of the difference scheme and the weak entropy.
基金supported in part by NSF Applied Mathematics Grant Number DMS-0908190
文摘We investigate the vacuum in nonisentropic gas dynamics in one space vari- able, with the most general equation of states allowed by thermodynamics. We recall physical constraints on the equations of state and give explicit and easily checkable conditions under which vacuums occur in the solution of the Riemann problem. We then present a class of models for which the Riemann problem admits unique global solutions without vacuums.
文摘In nonisentropic gas dynamics, with general equations of state, strong cornpressive shocks satisfying the Liu E-condition may violate the Second Law of thermodynamics.
文摘Existence of globally bounded classical solution for nonisentropic gas dynamics system has long been studied, especially in the case of polytropic gas. In [4], Liu claimed that sufficient condition has been established. However, the authors find that the argument he used is not true in general. In this article, the authors give a counter example of his argument. Hence, his claim is not valid. The authors believe that it is difficult to impose general conditions on the initial data to obtain globally bounded classical solution.
文摘The 3-dimensional zero-pressure gas dynamics system appears in the modeling for the large scale structure formation in the universe. The aim of this paper is to construct spherically symmetric solutions to the system. The radial component of the velocity and density satisfy a simpler one dimensional problem. First we construct explicit solutions of this one dimensional case with initial and boundary conditions. Then we get special radial solutions with different behaviours at the origin.
基金Supported in part by the National Natural Science of China, NSF Grant No. DMS-8657319.
文摘In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.
文摘This paper gives four pairs of entropies (η_i, q_i) (i=1, 2, 3, 4) to the isentropic gas dynamics equations ρ_t+(ρu)_x=0 (ρu)_t+(ρu^2+p(ρ))_x=0 p(ρ)=k^2ρ~γ,1<γ<3。 when all the function equations are satisfied
文摘The present article is concerned with the implementation of a recent semi-analytical method referred to as fractional reduced differential transform method （FRDTM） for computation of approximate solution of time-fractional gas dynamics equation （TFGDE） arising in shock fronts. In this approach, the fractional derivative is described in the Caputo sense. Four numeric experiments have been carried out to confirm the validity and the efficiency of the method. It is found that the exact or a closed approximate analytical solution of a fractional nonlinear differential equations arising in allied science and engineering can be obtained easily. Moreover, due to its small size of calculation contrary to the other analytical approaches while dealing with a complex and tedious physical problems arising in various branches of natural sciences and engineering, it is very easy to implement.
文摘Consider an initial-boundary problem vt - ux=0,u, + （）x + f（u） = （）x,θt+ux=（）ux=（）x+ （E） v（x,0） = v0（x）,u（x,0） = u0（x）,θ（0,x） = θ0（x）, （I） u（t,0） = u（t,1） = θx（t,0） = θx（t,1） （J） Sufficient and necessary conditions for （E）, （I） and （J） to have asymptotic stability of the gobal smooth solution are given by means of the elemental L2 energy method.
文摘In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert’s and Enskog’s methods are discussed. The equations system of multicomponent non- equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asym- ptotic) method for solution of the system of kinetic Boltzmann equations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035,11171038,and 10771019)the Science Reaearch Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No. 2012MS0102)
文摘In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
文摘Industry and energy continue to require piston engines(PICE)at a high level worldwide.Therefore,science and technology must urgently work on improving the PICE working cycle.Improving the quality of the intake process of theworking fluid into the cylinder is one of the most effective ways to improve the operational performance of PICE.The purpose of the study was to assess the impact of various cylinder head(CylH)designs on the gas-dynamic and heat-exchange qualities of air flows within an engine model’s intake system.Three different CylH designs were studied:the basic configuration and upgraded cylinder heads with a square valve and a square valve port.These designs are innovative.Laboratory conditions were used to conduct the studies for stationary air flow.The experiments covered the range of Reynolds numbers from 8500 to 96,000.The intake system’s gas dynamics and heat transfer were determined using the thermal anemometry method,which was based on constant-temperature hot-wire anemometers.It has been established that the use of upgraded CylHs causes an increase in the turbulence number of flow by an average of 13.5%.Additionally,itwas found that the increase in the turbulence number of flowin the cylinder is about 19%when installing new CylH designs.It was shown that therewas an increase in the heat transfer coefficient in the intake pipe by 10%–40%when installing modernized CylH designs in the intake system.The article focused on the problems of increasing the turbulence level and intensifying the heat transfer of stationary air flow in the intake system,specifically in PICEs.The study’s findings are novel in the areas of applied gas dynamics and PICEs.
基金supported by the Anhui Zhongchuang Energy New Energy Technology Co.,Ltd.,Entrusted Project.
文摘The semiconductor bridge(SCB)ignites through bridge film discharge,offering advantages such as low ignition energy,high safety,and compatibility with digital logic circuits.The study uses laser interferometry to investigate the gas dynamics of the bridge film after SCB plasma extinction.Interferometric images of the SCB film gas were obtained through a laser interferometry optical path.After the degradation model of digital image processing,clearer images were produced to facilitate analysis and calculation.The results show that the gas temperature at the center of the SCB film reaches a maximum of 1000 K,and the temperature rapidly decreases along the axial direction of the bridge surface to room temperature at 300 K.The maximum diffusion velocity of the plasma is 1.8 km/s.These findings provide critical insights for SCB design and ignition control.
基金supported by CNPC Southwest Oil and Gas Field Branch's 2023 Scientific Research Program Project(20230303-14).
文摘The precision of dynamic reserve calculations in gas reservoirs is crucial for the rational and efficient development of oil and gas fields and the formulation of gas well production plans.The Shaximiao gas reservoir in the ZT block of northwestern Sichuan is densely packed and highly heterogeneous,featuring complex gas-water distribution,substantial variations in test production among gas wells,and a rapid decline rate.To precisely determine the dynamic reserves of these tight water-bearing gas wells,this study focuses on the water-tight gas reservoirs in the ZT block of northwestern Sichuan,conducting core X-ray diffraction,constant-rate mercury injection,and reservoir rock stress sensitivity experiments.Utilizing the experimental findings,the porosity and permeability of the rock samples under effective stress conditions are adjusted via binary linear regression.These adjusted parameters are then incorporated into the water-sealed gas material balance method,thereby establishing a novel approach for calculating dynamic reserves in water-tight gas reservoirs under stress sensitivity conditions.The results show that:(1)the rock porosity ranges from 6.08%to 10.22%,permeability ranges from 0.035 mD to 0.547 mD,clay mineral content ranges from 6.58%to 19.14%,pore radius distribution ranges from 90μm to 180μm,throat radius distribution ranges from 0.61μm to 3.41μm,with significant differences in throat distribution,indicating poor reservoir fluid flow capacity and strong tightness;(2)after aging experiments,rock samples exhibit plastic deformation,with porosity and permeability unable to fully recover after pressure relief.The stress sensitivity curve of rock samples shows a two-stage characteristic,with moderate to strong stress sensitivity;(3)porosity stress sensitivity is mainly influenced by pore radius and mineral composition-larger pore radius and higher clay content lead to stronger stress sensitivity,with porosity loss rates ranging from 8.26%to 23.69%.Permeability stress sensitivity is mainly influenced by throat radius and mineral composition-smaller throat radius and higher clay content result in stronger stress sensitivity,with permeability loss rates ranging from 47.91%to 62.03%;(4)a comparative analysis between the traditional dynamic reserve calculation method for gas wells and the new method considering stress sensitivity shows a relative error between 0.90%and 2.41%,with the new method demonstrating better accuracy.This study combines physical experimental results with an effective stress model of reservoir rocks to develop a new method for calculating dynamic reserves of water-bearing tight gas reservoirs under effective stress conditions,providing experimental data and example calculation results to support subsequent dynamic evaluation of gas reservoirs and the establishment of rational well allocation plans.
基金supported by National Natural Science Foundation of China(Grant No.11361073)
文摘In this paper,firstly,by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation,we construct parameterized delta-shock and constant density solutions,then we show that,as the flux perturbation vanishes,they converge to the delta-shock and vacuum state solutions of the zero-pressure flow,respectively.Secondly,we solve the Riemann problem of the Euler equations of isentropic gas dynamics with a double parameter flux approximation including pressure.Furthermore,we rigorously prove that,as the two-parameter flux perturbation vanishes,any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow;any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum intermediate state in between tends to a vacuum state.Finally,numerical results are given to present the formation processes of delta shock waves and vacuum states.
基金supported by the TianY uan Special Funds of the National Natural Science Foundation of China(No.11226171)the Research Award Fund for Young Teachers in Shanghai Higher Education Institutions(No.shdj008)the Discipline Construction of Equipment Manufacturing System Optimization Calculation(No.13XKJC01)
文摘In this paper, the Riemann problem with delta initial data for the onedimensional system of conservation laws of mass, momentum and energy in zero-pressure gas dynamics is considered. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtained the global existence of generalized solutions which contains delta-shock. Moreover, the author obtains the stability of generalized solutions by making use of the perturbation of the initial data.
文摘We propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations.By all regime,we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M,i.e.such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1.The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M.This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy.A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism.A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed.Then a simple and efficient semi implicit scheme is also proposed.The resulting scheme is stable under a CFL condition driven by the(slow)material waves and not by the(fast)acoustic waves and so verifies the all regime property.Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.
