An accurate and realistic model for transient diffusion and adsorption in a biporous pellet is typically represented by two coupled second-order partial differential equations. The model, however, has been rarely used in practice because of its mathematical complexity and bulky numerical computation, and approximations of the model have been used instead. But the accuracy of the available approximations has been limited and not enough for detailed analysis and simulation of the mass transfer process. Therefore, in this study, we develop for the first time high-order approximations, of up to third order, for noncyclic and cyclic adsorption in a biporous pellet respectively. The approximations are in the form of a state equation which consists of first-order differential equations ; the number of the equations is the same as the approximation order. The approximations are easy to use and their accuracy dramatically increases with increasing approximation order, so that the second- or the third-order approximations can effectively substitute the complex biporous diffusion model.