People have devised a number of ways to organize their prayers. All of them are valid, probably, as long as they submit to Scripture and fulfill the commands of God. And as long as they are not imposed upon others as divinely given structures.
It has been suggested, somewhat in jest, that the apostle Paul must have had some sort of prayer list, considering the many people he mentions in prayer. Maybe he just had a good memory. However he organized his prayers, he got the job done.
Some follow the ACTS acrostic: Adoration, confession, thanksgiving, supplication. One supposes that intercession is subsumed under the last item. It might be best, however, to bring prayer for others to the fore.
What’s important is that we pray, that we obey the Lord to pray as we ought, that we deepen our relationship with him, that we advance the Kingdom among the world that lies in darkness.