Spectral method based on POD are an effective approach for model reduction but variable boundary conditions are often a problem, since basis functions must satisfy boundary conditions at all times. In this work we introduce weak imposition of boundary conditions by means of a penalty method and apply the method to develop reduced order models of two different chemical reactors. A quantitative analysis shows that, by changing the values of the penalty parameters, arbitrary accuracy can be achieved at the expense of increasing CPU time. Computations can be reduced by a factor 50 at least, by maintaining still acceptable accuracy. Performance parameters of the approach appear to be model dependent. (c) 2011 Elsevier Ltd. All rights reserved.