The original model for the solar hydrogen energy system created by Veziroglu and Basar in the 70's was adapted to the State of Ceara - Brazil. The State of Ceara has one of the greatest wind potentials in Brazil and it is estimated to be around 35 GW. At the present year, there are 494 MW wind farms in operation. The aforementioned State also has a natural gas grid of pipelines serving a great number of consumers. There are studies in literature considering the injection of hydrogen into the natural gas pipeline up to 20% in volume without substantial modifications in the natural gas infrastructure. The main objective of this article is to use that model in order to evaluate long term scenarios in which the off peak wind generated hydrogen gradually replaces natural gas in such important State of Brazil. The system is supposed to start in the year 2015 and the economical revenue when it is fully implemented can reach respectively US$ 730 million or US$ 1 billion in the slow or fast scenario of hydrogen introduction into the energy matrix of that important State of Brazil. Copyright (C) 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.