This paper describes a fully implicit four-phase (oil, water, gas, solid fuel) numerical reservoir model for simulating hot water injection, steam injection, dry combustion, and wet combustion in one, two, or three dimensions and in either a Cartesian, radial, or curvilinear geometry. The simulator rigorously models fluid flow, heat transfer (convective and conductive), heat loss to formation, fluid vaporization/condensation, and chemical reactions. Any number of oil or gas phase components may be specified, along with any number of solid phase components (fuel and catalysts).The simulator employs either D4 Gaussian elimination or powerful incomplete factorization methods to solve the often poorly conditioned matrix problems. An implicit well model is coupled to the simulator, where reservoir unknowns and well block pressures are primary variables.This paper includes (1) comparisons of the numerical model's results with previously reported laboratory physical models' results for steam and combustion and (2) analytical solutions to a hot waterflood problem. In addition, an actual field-scale history match is presented for a single-well steam stimulation problem.