The present process integration work employs two modified versions of the Bergius three-phase hydrogenation technology including the application of sieve cascade reactors. The first process operates at medium pressures (7-20 MPa and 470 degreesC) for hydroprocessing of oil refinery vacuum and or atmospheric residue to lighter products, and the second for synthetic fuel production by the direct thermal and catalytic coal liquefaction at higher operating pressures (30 MPa and 470 degreesC). Technical problems for the design of large-scale multistage reactors are analyzed including the simplified demonstration for complete integration with existing petroleum refineries. Fluid dynamics. in one-stage bubble columns, are presented including the theoretical prediction of Newtonian non-settling slurry circulatory flow. and the liquid slurry and gas dispersion mixing efficiency of the sieve cascade reactor. Scale-up methodologies are proposed for columns up to 4 m in diameter, and up to 50 m in height, based on measurements and operating experience with larger three-phase petrochemical reactors, and the existing cold flow mathematical models in slurry bubble columns. The basic geometrical parameters of the oil residue or coal hydrogenation multistage reactor are discussed, and the influence analyzed of the sieve tray geometry and stage number at high pressures and temperatures on the fluid dynamics, mixing, gas hold up and interfacial area. Evidence is established that the installation of suitably designed sieve trays, operated above the minimum required liquid and gas superficial velocity, can eliminate deficiencies in the existing gas distribution designs, and therefore once again emphasize the cost effectiveness and increased process safety in the application of sieve cascade reactors.