It is difficult to advance an hypothesis without knowing details of what you are doing, but if your environment is water, copper corrosion can be at the origin of your observation:

2Cu + H2O ----> Cu2O +  2H+

Thanks for your answer, X. Ramón Nóvoa 

Do you mean that Copper oxide (Cu2O) can act as acidic sites ? so it increased the acidity of the catalyst

Thanks

Ahmed 

yes, that is the hypothesis. CuO can also be envisaged.

I am satisfied with Mr. X. Ramon Novoa,

It has been proved that support for the metal or metal oxide should be acidic in

nature. For more details kindly follow the link below...

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.463.6890&rep=rep1&type=pdf

Dear Colleague Varun

Thanks for your answer. Do you think alumina oxide and copper oxide have relatively similar acidity, because from the results I have it showed similar acidity

Thanks

Ahmed

Dear Mr. Ahmed,

Ideally it should not be the same as the charge distribution is different over both the metal ions, but again it depends on the physical environment present around. And this may be a reason you are getting the similar acidity for both

.