In this paper, we provide exact analytical solutions for a new method of constant molar flow of pure gas into a reservoir containing solid adsorbents having a bidispersed structure, such as zeolite, activated carbon and alumina. Depending on the diffusion mechanism, two models are proposed under the isothermal conditions and linear isotherm. One is applicable to zeolite, and the other for alumina and activated carbon. The solutions of these two models are in the form of an infinite series, and its eigenvalues are determined from a transcendental equation. This transcendental equation is such that the eigenvalues are lumped into infinite but countable groups, and in each group there are infinite but countable eigenvalues. The dominant eigenvalues are generally the first ten to thirty eigenvalues (depending on the value of time at which the series is evaluated) in each group. The pressure response of the reservoir is a function of time as the result of the introduction of adsorbate into the reservoir, and as time is sufficiently large it asymptotes to a straight line, of which the slope is a function of the equilibrium parameters only and the intercept is found to be an explicit function of the equilibrium parameters as well as the diffusivities in the macropore and micropore.