  Smooth surfaces have finitely generated canonical rings and projective
canonical models. For normal surfaces, however, the graded ring of
multicanonical sections is possibly nonnoetherian, such that the corresponding
homogeneous spectrum is noncompact. I construct a canonical compactification by
adding finitely many non-Q-Gorenstein points at infinity, provided that each
Weil divisor is numerically equivalent to a Q-Cartier divisor. Similar results
hold for arbitrary Weil divisors instead of the canonical class.
