A PROCESS FOR THE DESULFURIZATION OF HEAVY GAS OILS OR RESIDUUM BY THE EBULLATED BED CATALYTIC SYSTEM WHERIN THE FACTORS OF FEED CHARACTERIZATION, PERCENT DESULFURIZATION, TEMPERATURE, PRESSURE, AND SPACE VELOCITY, IN CONSIDERATION OF CATALYST AGE AND ACTIVITY, ARE CRITICALLY ADJUSTED AND COORDINATED BY THE FORMULA;

WHERE: WF=AVERAGE WEIGHT PERCENT SULFUR IN FEED WP=AVERAGE WEIGHT PERCENT SULFUR IN THE BUTANE AND HEAVIER LIQUID PRODUCT P=PARTIAL PRESSURE OF HYDROGEN IN REACTOR (P.S.I.A) CT=EFFECT OF TEMPERATURE ON THE RATE OF REACTION CS=EFFECT OF EXTENT TO WHICH THE OIL IS DESULFURIZED ON THE RATE OF REACTION A=THE ACTIVITY OF A PARTICULAR CATALYST WITH A PARTICULAR AGE FOR A PARTICULAR FEEDSTOCK UT=BARRELS PER DAY OF FRESH FEED OIL PASSED THROUGH THE REACTOR PER POUND OF CATLAYST PRESENT INSIDE THE REACTOR.