Tortilis is a warm grower which can dry out between waterings. Hennisiana is middle of the road on temps but does fine in cool conditions, and suavis the same. Suavis also like to be a little dryer, especially in the winter, and they all prefer lower light and very robust air movement.
My suavis bloomed at a much smaller size than I expected. Maybe in a 3 inch pot with a few pseudobulbs. I gave it Cattleya light, high humidity, and temps under 80 typically, and it was kept fairly moist consistently.
Tortilis should be ok growing intermediate. The others need cooler temps, should be in lower light and kept moist but allowed to almost dry between waterings, and given less water in the winter, esp. suavis, which enjoys a bit odf a dry rest in the winter, though not to sit dry for long periods. Mix should be well aerated and drained. Straight sphagnum hasn't been a good longterm mix for them in my experience.