FINITE ELEMENT METHOD AND ANALYSIS FOR CHEMICAL-FLOODING SIMULATION

1.IntroductionThisarticlediscussestheenhanced0ilrecoverynumericalsimulationofthechemicalflood-ing(suchassurfactats,alcohol,polymers)c0mposed0f3-dimensional,multicomponent,muLtiphaseandincompressiblemixedfluids.Aftertheoilfieldiswaterfi0oded,thereisstillalargeamountofcrudeoilleftintheoildeposit.Thisamountofoil,boundedbycapillarypressure,cannotflow;or)asaresultofthedisadvantageousrateofflowbetweenthedisplacinganddisplacedphases,thevolumethattheinjectionfiowaffectsistoosmalltodrivethecrudeoil.By…     

THE UPWIND FINITE DIFFERENCE FRACTIONAL STEPS METHOD FOR NONLINEAR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

For nonlinear coupled system of multilayer dynamics of fluids in porous media,the secondorder and first order upwind finite difference fractional steps schemes applicable to parallel arithmeticare put forward,and two-dimensional and three-dimensional schemes are used to form a completeset.Some techniques,such as calculus of variations,multiplicative commutation rule of differenceoperators,decomposition of high order difference operators and prior estimates,are adopted.Optimalorder estimates in L~2 norm are derived to determine the error in the second order approximate solution.This method has already been applied to the numerical simulation of migration-accumulation of oilresources.     

Characteristic finite difference fractional step methods for three-dimensional semiconductor device of heat conduction

The mathematical model of the semiconductor device of heat conduction has been described by a system of four equations. The optimal order estimates in L² norm are derived for the error in the approximates solution, putting forward a kind of characteristic finite difference fractional step methods.     

The modified method of upwind with finite difference fractional steps procedure for the numerical simulation and analysis of seawater intrusion

Numerical simulation and analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations with initial-boundary problems. For a generic case of a three-dimensional bounded region, the modified method of upwind with finite difference fractional steps procedure is put forward. Optimal order estimates in L² norm are derived for the error in the approximation solution. The present method has been successfully used in predicting the consequences of seawater intrusion and protection projects.     

GALERKIN ALTERNATING-DIRECTION METHODS FOR NONRECTANGULAR REGIONS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

For the transient behavior of a semiconductor device, the modified method of characteristics with alternating-direction finite element procedures for nonrectangular region is put forward. Some techniques, such as calculus of variations, isoparametric transformation, patch approximation, operator-splitting, characteristic method, symmetrical reflection, energy method, negative norm estimate and a prior estimates and techniques, are employed. In the nonrectangular region case, optimal order estimates in L2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved.     

THE MODIFIED METHOD OF CHARACTERISTICS WITH FINITE ELEMENT OPERATOR—SPLITTING PROCEDURES FOR COMPRESSIBLE MULTICOMPONENT DISPLACEMENT PROBLEM

For the three-dimensional compressible multicomponent displacement problem we put forward the modified method of characteristics with finite element operator-splitting procedures and make use of operator-splitting,characteristic method,calculus of variations,energy method,negative norm estimate,two kinds of test functions and the theory of prior estimates and techniques.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.These methods have been successfully used in oil-gas resources estimation,enhanced oil recovery simulation and seawater intrusion numerical simulation.     

CHARACTERISTIC FINITE DIFFERENCE METHODS FOR POSITIVE SEMIDEFINITE PROBLEM OF TWO-PHASE(OIL AND WATER)MISCIBLE FLOW IN POROUS MEDIA

Numericalsimulationoftwo-phase(oilandwater)miscibleflowinporousmediaisthe'mathematicalfoundationinenergyproblems.Forapositivedefiniteproblem,thefamousmathematicianandinitiatorofnumericalsimulationofoildeposit,J.Douglas,Jr.putforwardthefamouscharacteristicfinitedifferencemethodll'2].However,fornumericalanalysistherearoseseriousdifficulties.Heonlystudiedtheperiodiccasesandcoercivelysupposedthedictionmatrixoftheconcentrationequationispositivedefinite.Butinmanypracticalsituationsthediffusionmatr…     

CHARACTERISTIC ALTERNATING-DIRECTION FINITE ELEMENT METHODS FOR NONRECTANGULAR REGIONS FOR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA AND ITS ANALYSIS

For coupled system of multilayer dynamics of fluids in porous media, the characteristic alternating-direction finite element methods for nourectangular regions 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 calculus of variations, isoparametric transformation, patch approximation, operator-splitting, characteristic method, negative norm estimate, energy method, the theory of prior estimates and techniques are used. For the nourectangular regions case, optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved. These methods have been successfully used in multilayer oil resources migration-accumulation numerical simulation.