Dua is supplication to Allah and performing dua can be done anywhere and anytime correspond to our circumstances and what we are doing.
The obligation of performing dua is writen in Al Quran and Al Hadith. The way of performing dua is also guided in Quran and Hadith.
Allah decree and Rasulullah SAW spoke about the compulsory of dua confirmed in Quran and Hadith:
Al Quran Surah Al Ghafir verse 60
وَ قَالَ رَبُّكُمْ ادْعُونِي أَسْتَجِبْ لَكُمْ إِنَّ الَّذِينَ يَسْتَكْبِرُونَ عَنْ عِبَادَتِي سَيَدْخُلُونَ جَهَنَّمَ دَاخِرِينَ ~ القرعن سورة الغافر ٦٠
Allah decree,"Pray to me(Allah) I'm going to have to answer you all (your prayer), verily whom is boast (reject) to worship to Me I will take them into the hell disgracefully".حَدَّثَناَ اَحْمَدُ بْنُ مَنِعٍ حَدَثَناَ مَرْواَنُ بْنُ مُعَاوِيَاةَ عَنِ الَأ عْمَشِ عَنْ ذَرٍ عَنْ يُسَيْعٍ عَنِ النُّعْمَانِ بْنِ بَشِيرٍ عَنِ النَّبِيِّ صَلَّى اللَّهُ عَلَيْهِ وَ سَلَّمَ قالَ الدُّعَاءُ هُوَ العِبَادَةِ ثُمَّ قَرَاَء وَ قَالَ رَبُكُمُ ادْعُونِى أَسْتَجِبْ لَكُمْ إِنَّ الَّذِيْنَ يَسْتَكبِرُونَ عَنْ عِبَادَتِى سَيَدْخُلُونَ جَهَنَّمَ دَاخِرِيْنَ ~ رواه الترمذى ج ١٢ ص٢٦٧
Rasulullah spoke,"Prayer is worship", then The Apostle recited Allah decree,"Pray to me(Allah) I'm going to have to answer you all, verily whom is boast (reject) to worship to Me I will take them into the hell disgracefully". حَدَّثَناَ عَبَا بْنُ عَبْدِالعَظِيِمِ العَنْبَرِيِّ وَ غَيْرُ وَاحِدٍ قَالُوا حَدَثَنا أَبُودَاوُدَ الطَّيَا لِيِسِىُّ حَدَّثَناَ عِمْرَانُ القَطَّانُ عَنْ قَتَادَةَ عَنْ سَعِيْدِبْنِ أَبىِ الحَسَنِ عَنْ أَبِى هُرَيْرةَ رضاللَّه عنه عَنِ النَّبِىِّ صَلَّى اللَّه عليه و سلم قَالَ لَيْسَ شَيْءٌ أَكْرَمَ عَلَى اللَّه تَعَالَى مِنَ الدُّعَاءِ ~ رواه الترمزى ج ١٢ ابواب الدعاء
From Abi Hurairah from The Apostle SAW, The Apostle spoke,"Nothing more gracious according to Allah The High but prayer".