Is the word naturalmente the same in Brazilian and European Portuguese?

Yes

The only difference between "naturalmente" in Brazilian Portuguese and Continental Portuguese is pronunciation. The spelling, grammar, and fundamental meaning (both as an adverb describing a natural process and as a synonym for "of course" or "obviously") are identical in both dialects.

In Brazilian Portuguese, the pronunciation is more "open" and melodic. The vowels are clearly articulated, and the final "e" is typically pronounced as a short, light [i] sound. The rhythm is more syllable-timed, making the word sound more fluid.

In Continental Portuguese, the pronunciation is more "closed" and stress-timed. The unstressed vowels are heavily reduced or "swallowed," making the final "e" nearly silent. This gives the word a more truncated, sharper sound.

Brazilian Portuguese Example Sentences

1. Naturalmente, eu vou à sua festa. (Of course, I am going to your party.)
2. Isso acontece naturalmente com a idade. (This happens naturally with age.)
3. Naturalmente, precisamos de mais tempo para o projeto. (Naturally, we need more time for the project.)
4. Naturalmente, ele não sabia de nada. (Of course, he didn't know anything.)
5. Naturalmente, você é o melhor candidato. (Naturally, you are the best candidate.)

Continental Portuguese Example Sentences

1. Claro que vou à tua festa. (Of course I am going to your party.)
2. Isto acontece naturalmente com a idade. (This happens naturally with age.)
3. Com certeza, precisamos de mais tempo para o projeto. (For sure, we need more time for the project.)
4. É óbvio que ele não sabia de nada. (It's obvious that he didn't know anything.)
5. Naturalmente, tu és o melhor candidato. (Naturally, you are the best candidate.)