·Conjugate-gradient-like (CGL) methods were used to solve the matrix equations for several large-field and fine-grid models. The methods used incomplete LU (lLU) or modified incomplete LU (MILU) preconditioning coupled with orthomin acceleration. The CGL methods were applied to the original matrix or to a reduced system from red/black ordering. Test results from a black-oil model with fault throws, a fractured reservoir model, and three steamflood models are given. It was found that the CGL methods are effective for solving the matrix equations. A more powerful preconditioner improves reliability but may require more work. Guidelines for selecting the most effective method are provided.
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