Lattice Boltzmann method (LBM) is employed to investigate natural convection inside porous medium enclosures at high Rayleigh numbers. Volume averaged porous medium model is coupled with the lattice Boltzmann formulation of the momentum and energy equations for fluid flow. A parallel implementation of the single relaxation time LBM is used, which allows the porous medium modified Rayleigh number $Ram$ to be as high as $108$. Heat transfer results in the form of the enclosure averaged Nusselt number Nu are obtained for higher modified Rayleigh numbers $104\u2264Ram\u2264108$. The Nu values are compared with values in the absence of the form drag term. The form drag due to the porous medium is found to influence Nu considerably. The effect of the form drag on Nu is studied by using a form drag modified Rayleigh number $RaC$ (extended from $Ram$). Utilizing the results for Nu in the high $Ram$ range, a correlation is proposed between Nu and $RaC$ for Darcy numbers $10\u22126\u2264Da\u226410\u22122$, encompassing the non-Darcy flow regime.