Not to spilt hairs here but most of the A/C are leased and BP used to run most of them and why they have BP as the tail number and not CP
Actually, the first two B737-700s have the following "N" numbers: N959BP and N660CP. And a third 73G has now joined the small "shared services" fleet with the "N" number N668CP.
This shuttle service is currently operated by the ConocoPhillips corporate flight dept. Of course, both CP and BP personnel are transported to and from the North Slope and BP pays ConocoPhillips for the service. In the spirit of cooperation, one of the 73Gs does indeed have "BP" in the "N" number.
My source is a senior manager with CP's corporate flight dept. They proudly display a B737-700 "shared services" model at their headquarters office. And BTW, CP also operates a scheduled corporate shuttle service with an Embraer ERJ-135 between southeast Texas and Oklahoma. In addition, CP actually owns an airport in Oklahoma as well.