In this work, the logistic, hyperbolic tangent and double exponential models were proposed to describe the breakthrough behaviors in the fixed-bed column. Introduction of the parameter n into the above three models resulted in the corresponding modified breakthrough models. The physical meanings of the parameters in these models were explicated. The maximum specific growth rate mu(max) lag time lambda, inflection point t(i) and half-operating time t(50), were defined to better reflect symmetry and curvature of the breakthrough curve. The breakthrough models established using mu(max) and lambda. mainly focused on the adsorption rate instead of adsorption capacity. Many attempts were made to reveal the mathematical relationships between the logistic, hyperbolic tangent and double exponential models. The obtained results indicated that the new breakthrough models could describe the two different adsorption systems very well. These empirical models provided an alternative method for the description of the breakthrough curve.