By assuming a simple relation between the minimum agitation power input for a solid suspension with aeration and the aeration power input, a new correlation was derived with which to estimate the minimum agitation power input for solid Suspension in gas-liquid-solid stirred vessels. The equation obtained is a function of aeration power input, minimum agitation power input for a solid suspension without aeration, and agitator blade angle. The minimum agitation power input for solid Suspensions estimated in this work agreed with measured data in the literature. In a stirred aerated slurry reactor, a higher agitation power input than the minimum power input estimated for a solid suspension was necessary to obtain complete reaction.