AbstractWe consider a computational model for the evolution of methane hydrates in subsurface. Methane hydrates, an ice-like compound abundant in subsea sediments and unstable in standard conditions, are an environmental hazard and simultaneously an energy source. Our multiphysics model includes multiphase multicomponent mass conservation equations and several variants of energy balance equation with or without latent heat. We present the technique of model adaptivity which helps to assess and control the two sources of the computational error: the discretization error and the modeling error. The nature and magnitude of the modeling error is strongly dependent on the application and smoothness of solutions.