Paul could complete only 26 laps of the Barcelona track as a delay on some parts arriving gave only limited running.
However, the Scot could still set the sixth quickest time.
The programme focussed on putting more miles on the car to gather more information on performance and balance, plus conducting aero and tyre testing in the latter stage of the day yesterday.
Paul will remain in the car for another day before Adrian Sutil takes over for the remaining two days.
"We did some productive running to get a good baseline set-up for next day when we'll have a much more extensive test programme to carry out," said Paul.
"I definitely feel there is more to come from the car and I'm looking forward to getting back out there to help the team get as much out of this test as possible," he added.
The circuit engineering director, Dominic Harlow, meanwhile defended the delay in start for the testing.
"We didn't run in the morning as we were waiting for some parts to arrive at the track until early in the day, and the knock on effect of the turnaround from Jerez meant there was a lot to do to complete the car build. The track conditions weren't good anyway, with wet, cold and slippery conditions so we felt we did not miss too much.
"The afternoon's session was much better and we started our testing with some aerodynamic tests and tyre comparison looking at the new soft," he said.
Second VJM04 test starts in Barcelona
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