Acta mathematica scientia, Series B >
THEORY AND APPLICATION OF FRACTIONAL STEP CHARACTERISTIC FINITE DIFFERENCE METHOD IN NUMERICAL SIMULATION OF SECOND ORDER ENHANCED OIL PRODUCTION
Received date: 2015-02-02
Revised date: 2014-05-08
Online published: 2015-11-01
Supported by
This work is supported by the Major State Basic Research Development Program of China (G19990328), National Tackling Key Program (2011ZX05011-004, 2011ZX05052, 20050200069), National Natural Science Foundation of China (11101244, 11271231, 10771124, 10372052) and Doctorate Foundation of the Ministry of Education of China (20030422047).
A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced (chemical) oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l2 norm is derived. This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields, and the simulation results are quite interesting and satisfactory.
Yirang YUAN , Aijie CHENG , Danping YANG , Changfeng LI . THEORY AND APPLICATION OF FRACTIONAL STEP CHARACTERISTIC FINITE DIFFERENCE METHOD IN NUMERICAL SIMULATION OF SECOND ORDER ENHANCED OIL PRODUCTION[J]. Acta mathematica scientia, Series B, 2015 , 35(6) : 1547 -1565 . DOI: 10.1016/S0252-9602(15)30073-4
[1] Ewing R E, Yuan Y R, Li G. Finite element for ehemical-flooding simulation//Proceeding of the 7th Inter- national Conference Finite Element Method in Flow Problems. The University of Alabama in Huntsville, Huntsville, Alabama: UAHDRESS, 1989: 1264-1271
[2] Yuan Y R. Theory and application of numerical simulation of energy sources, basis of numerical simulation of chemical production (tertiary oil recovery), Chapter 3. Beijing: Science Press, 2013: 257-304
[3] Yuan Y R, Yang D P, Qi L Q, et al. Research on algorithms of applied software of the polymer//Gang Qinlin. Proceedings on Chemical Flooding. Beijing: Petroleum Industry Press, 1998: 246-253
[4] Douglas Jr J, Russell T F. Numerical method for convection-dominated diffusion problems based on com- bining the method of characteristics with finite element or finite difference procedures. SIAM J Numer Anal, 1982, 19(5): 871-885
[5] Douglas Jr J. Simulation of miscible displacement in porous media by a modified method of characteristic procedure//Lecture Notes in Mathematics 912. Numerical Analysis, Proceedings, Dundee, 1981. Springer, 1982: 64-70
[6] Douglas Jr J. Finite difference methods for two-phase incompressible flow in porous media. SIAM J Numer Anal, 1983, 20(4): 681-696
[7] Ewing R E, Russell T F, Wheeler M F. Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics. Comp Meth Appl Mech Eng, 1984, 47(1/2): 73-92
[8] Douglas Jr J, Roberts J E. Numerical method for a model for compressible miscible displacement in porous media. Math Comp, 1983, 4(164): 441-459
[9] Yuan Y R. Time stepping along characteristics for the finite element approximation of compressible miscible displacement in porous media. Math Numer Sinica, 1992, 14(4): 385-400
[10] Yuan Y R. Finite difference methods for a compressible miscible displacement problem in porous media. Math Numer Sinica, 1993, 15(1): 16-28
[11] Ewing R E. The Mathematics of Reservior Simulation. Philadelphia: SIAM, 1983
[12] Yuan Y R. Characteristic finite difference methods for moving boundary value problem of numerical simu- lation of oil deposit. Science in China, 1994, 37A(12): 1442-1453
[13] Yuan Yi-rang, The characteristic mixed-finite element method and analysis for three-dimensional moving boundary value problem. Sci China Math, 1996, 39(3): 276-288
[14] Yuan Y R. Finite difference method and analysis for three-dimensional semiconductor device of heat con- duction. Sci China Math, 1996, 39(11): 1140-1151
[15] Axelsson O, Gustafasson I. A modified upwind scheme for convective transport equations and the use of a conjugate gradient method for the solution of non-symmetric systems of equations. J Inst Maths Applics, 1979, 23: 321-337
[16] Ewing R E, Lazarov R D, Vassilevski A T. Finite difference shceme for parabolic problems on composite grids with refinement in time and space. SIAM J Numer Anal, 1994, 31(6): 1605-1622
[17] Lazarov R D, Mishev I D, Vassilevski P S. Finite volume method for convection-diffusion problems. SIAM J Numer Anal, 1996, 33(1): 31-55
[18] Peaceman D W. Fundamantal of Numerical Reservoir Simulation. Amsterdam: Elsevier, 1980
[19] Douglas Jr J, Gunn J E. Two order correct difference analogues for the equation of multidimensional heat flow. Math Comp, 1963, 17(81): 71-80
[20] Douglas Jr J, Gunn J E. A general formulation of alternating direction methods, Part 1. Parabolic and hyperbolic problems. Numer Math, 1964, 6(5): 428-453
[21] Marchuk G I. Splitting and alternating direction method//Ciarlet P G, Lions J L, eds. Handbook of Numerical Analysis. Paris: Elsevior Science Publishers BV, 1990. 197-460
[22] Yuan Y R. Theory and application of upwind finite difference method for moving boundary value problem of three-dimensional percolation coupled system. Sci China Math, 2010, 40(2): 103-126
[23] Yuan Y R. The second-order upwind finite difference fractional step method for moving boundary value problem of nonlinear percolation coupled system. Sci China Math, 2012, 42(8): 84-864
[24] Shen P P, Liu M X, Tang L. Mathematical problems of petroleum exploration and development: Mathe- matical problems of oil-gas fields development, Part III. Beijing: Science Press, 2002: 197-264
/
| 〈 |
|
〉 |