ABSTRACT
This paper discusses the application of preconditioned generalized conjugate gradient acceleration to fully implicit thermal simulation. The preconditioning step utilizes incomplete Gaussian elimination (IGE) to form an approximate factorization of the Jacobian matrix.
The implementation allows
any finite difference approximation
any grid block ordering
associated well constraint equations
any level of incomplete factorization
reduced system preconditioning
constrained residual preconditioning
Acceleration procedures include
ORTHOMIN
ORTHORES
IGE preconditioning and its implementation is discussed with respect to five, seven, nine or eleven-point finite difference approximations and optional well constraint equations. Numerical results were obtained using a thermal model allowing any number Nc of components. The model's implicit formulation requires the solution of a linear system of equations in which each grid block has Nc + 1 unknowns. Test problems involved combustion, steam drive and cyclic steam stimulation processes, some of which exhibited ill-conditioning, negative transmissabilities and high transmissability ratios. Numerical results indicate how different grid block orderings, different levels of incomplete factorization and different acceleration procedures affect convergence, storage and work requirements.