TECHNOLOGY FOCUS - POLYMERS - Preferred Components: The polyimidazole polymer comprises repeating units (IIb). The polyimide polymer comprises repeating units of formula (Ia), or (Ib). The polyimide polymer comprises repeating unit 1,3-di-yl-2-methyl-benzene (i) (10-25%, preferably 16%), repeating unit 2,4-di-yl-1-methyl-benzene (ii) (55-75%, preferably 64%), and repeating unit bis(4-yl-phenyl)methane (iii) (20-40%, preferably 20%). The repeating units of (Ib) constitute of 1-99 (preferably 30-50, especially 40)% of a total of the repeating units of (Ia) and (Ib); 1-99 (preferably 10-30, especially 20)% of the R6 in the (Ia) is (i) and 99-1 (preferably 90-70, especially 80)% of the R6 in the (Ia) is (ii) such that the total of R6 that are the (i) or (ii) is 100%; and 1-99 (preferably 10-30, especially 20)% of the R7 in the (Ib) is (i) and 99-1 (preferably 90-70, especially 80)% of the R7 in the (Ib) is (ii) such that the total of R7 that are (i) or (ii) is 100%. The mass ratio of the polyimide polymer to the polyimidazole is at least about 1 (preferably at least 2). The membrane comprises the polyimide polymer 20-95 mass%. The polyimide polymer is the polycondensation reaction product of an aromatic diisocyanate and a dianhydride, the aromatic diisocyanate being selected from 2,4-toluenediisocyanate, 2,6-toluenediisocyanate, and 4,4'-methylene-bis(phenylisocyanate); the dianhydride being selected from pyromellitic dianhydride, benzophenonetetracarboxylic dianhydride, 3,3',4,4'-diphenylsulfone tetracarboxylic dianhydride, and/or 3,3',4,4'-biphenyl tetracarboxylic dianhydride. The membrane has a configuration selected from asymmetric membrane, uniformly dense membrane, hollow fiber membrane, and composite membrane. The membrane is configured as several composite hollow fibers, each of the fibers having a supporting core layer surrounded by fluid-separating sheath layer, the fluid-separating sheath layer comprises the material made of the blend of the polyimide and polyimidazole. The polyimidazole polymer is 2,2'-(m-phenylene)-5,5'-bibenzimadazole.R6=R2;R7=groups (i), or (ii).Preferred Method: In the method, where a pressure gradient across the membrane is of 20-2000 psi, the membrane operating temperature is greater than 50 degrees C. Preferred Definitions:    R4=biphenyl group;    R5=phenyl group.    EXAMPLE - No suitable example given.