Abstract: A numerical simulation at last comes down to calculation of a number of large linear equation groups, and an excellent simulator should be provided with advantages of wide application and rapid convergence.As implicit pressure and explicit saturation (IMPES) method is selected to calculate black oil model and the bottom-hole pressure is introduced, the coefficient matrix of pressure equation becomes bordered seven-symmetrical matrix.The modified incomplete factorization (MILU) -orthogonal minimization (ORTHOMIN) method can be used to calculate large asymmetric sparse matrix as one of the pretreatment conjugate gradient methods.MILU method keeps the sparse character of sparse matrix and saves the storage space, while ORTHOMIN method accelerates the rate of iteration convergence obviously.According to the MILU-ORTHOMIN method, the horizontal single well simulator is programmed.The IMPES and the implicit wellbore pressure method are employed in this paper.As the same iteration accuracy rate is selected to solve the same problem, it is found that the MILU-ORTHOMIN method makes the convergence speed increased by 100 times compared to that of normal Gauss-Seidel method (asynchronous iteration).

Key words: numerical simulation, black-oil model, method, horizontal well