In Biggles and the Plot That Failed, El Arig was a small uninhabited oasis which Biggles used as an advanced base in his mission to search for Adrian Mander in the Great Sand Sea in the Western Desert of Egypt.
The location of El Arig is not stated precisely in the text. At one point, Biggles stated that, going west from Khargah oasis, there was nothing for five hundred miles except for El Arig. The tomb of Ras Tenazza was, according to Hassan Sekunder, some two to three hundred miles south of Siwa. Later, Biggles would find that the tomb was about 150 miles south of El Arig, which would suggest that the oasis was between 50 and 150 miles south of Siwa.
El Arig is a fictional location. There is an oasis named El-Areg but this is about 30 miles or so east of Siwa, and not a useful place to serve as an advance base for a search to the south.