As Salam u Alaikum
الجواب وبالله التوفيق
When it comes to ending the Nikah through Talaq, the words used as per the description of your question are considered sarīh(explicit) which do not need an accompanying intention for the divorce to take effect. Even without an accompanying intention, just by uttering the word “Talaq” will be effective, it is not necessary to say the words like “I divorced” or “I issue two divorces”.
Since your issuance of two divorces and your wife’s listening to it (i.e. both the divorces) is definite, the two divorces have taken effect, however, there is possibility of ruju(reconciliation). If the husband performs rujuthe Nikah will become restored. However, if the husband does not performrujuby either verbal statement, marital relations or any other physical acts of affection and the wife’s three menstrual cycles passed, then the husband and wife will become separated. If they decide to live together after that, a new Nikah will have to be performed.
واللہ اعلم بالصواب