Tigranocerta/Cholimma/Chlomaron

In my opinion Tigranocerta lay on the river Garzen, about 37 kilometers east of the town of Silvan.
Here we can see the remains of the walled city, the citadel and the ruins of the theater ( According to Wikipedia :The magnificent theater that was established by the Emperor, of which he was an avid devotee, conducted dramas and comedies mostly played by Greek as well as Armenian actors) .

The ruins now called Arzen (Arzan ).
I read the description of the battle of Tigranocerta (https://en.wikipedia.org/wiki/Battle_of_Tigranocerta). It said: "Tigranocerta was still an unfinished city when Lucullus laid siege to it in the late summer of 69. The city was heavily fortified and according to the Greek historian Appian, had thick and towering walls that stood 25 meters high... The two armies converged toward the Batman-Su river slightly to the southwest is Tigranocerta.Tigranes' army was positioned on the east bank of the river while Lucullus, who had left a rear guard to continue the siege of the city, met the Armenian army on the river's west bank."
Meanwhile, Batman river flows to the east of the town of Silvan.
If we assume that the description of the battle contained in Wikipedia is true, then we must recognize that the city Silvan is not ancient Tigranocerta. Otherwise, it should be considered that the battle of Tigranocerta took place in the south-west of Silvan.
This version is not acceptable, because on the west of the town of Silvan no other river named Batman ( ancien Garzen ).