The asymptotic behavior of the solutions of some nonlinear variational inequalities with highly oscillating coefficients modeling chemical reactive flows through the exterior of a domain containing periodically distributed reactive solid obstacles, with period \varepsilon , is analyzed. In this kind of boundary-value problems there are involved two distinct sources of oscillations, one coming from the geometrical structure of the domain and the other from the fact that the medium is heterogeneous. We focus on the only case in which a real interaction between both these sources appears, i.e. the case in which the obstacles are of the so-called critical size and we prove that the solution of such a boundary-value problem converges to the solution of a new problem, associated to an operator which is the sum of a standard homogenized one and extra zero order terms coming from the geometry and the nonlinearity of the problem.

PACS numbers: 02.60.Lj, 82.39.--k