This paper addresses the estimation of the specific production rate of intracellular products and the modeling of the bioreactor volume dynamics in high cell density fed-batch reactors. In particular, a new model for the bioreactor volume is proposed, suitable to be used in high cell density cultures where large amounts of intracellular products are stored. Based on the proposed volume model, two forms of a high-order sliding mode observer are proposed. Each form corresponds to the cases with residual biomass concentration or volume measurement, respectively. The observers achieve finite time convergence and robustness to process uncertainties as the kinetic model is not required. Stability proofs for the proposed observer are given. The observer algorithm is assessed numerically and experimentally.