A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced(chemical)oil production with capillary force in the porous media.Some techniques,e.g.,the calculus of variations,the energy analysis method,the commutativity of the products of difference operators,the decomposition of high-order difference operators,and the theory of a priori estimate,are introduced.An optimal order error estimate in the l~2 norm is derived.The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields.The simulation results are satisfactory and interesting. A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced (chemical) oil production with capillary force in the porous media. Home techniques, eg, the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l ~ 2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.