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 μ_max, lag time λ, inflection point t_i and half-operating time t₅₀ were defined to better reflect symmetry and curvature of the breakthrough curve. The breakthrough models established using μ_max and λ 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.

在这项工作中，提出了逻辑，双曲正切和双指数模型来描述固定床色谱柱中的突破行为。将参数n引入上述三个模型中，产生了相应的修改后的突破模型。阐明了这些模型中参数的物理含义。的最大比生长速率μ_最大，滞后时间λ，拐点吨_我和半操作时间吨₅₀更好被定义以反映穿透曲线的对称性和曲率。这项突破性的车型使用μ建立_最大和 λ 主要侧重于吸附速率而不是吸附容量。进行了许多尝试来揭示逻辑，双曲正切和双指数模型之间的数学关系。所得结果表明，新的突破模型可以很好地描述两种不同的吸附系统。这些经验模型为描述突破曲线提供了一种替代方法。