The formulation of an axial solid concentration profile in the upper dilute region of circulating fluidized beds is analyzed based on the lateral solid transfer model which includes mass transfer of particles between the core and the annulus, analogous to the countercurrent absorption process. The operating region is mapped on a phase plane of solid concentration in the core region versus that in the annulus region. It is demonstrated that if the core diameter is assumed constant, the model faces a serious paradox of having either a negative decay factor/positive solid fraction epsilon(pC,infinity) or a positive decay factor/negative solid fraction epsilon(pC,infinity). This paradox was found to be solved by the introduction of a variable core diameter assumption. The calculated results of solid concentration along the riser with Werther correlation for core diameter distribution showed a fair agreement with previous experimental results.