Industrialization of bioreactors has been achieved by integrating knowledge from several applying core concepts of chemical engineering, cellular and molecular biology, and biochemistry. Mathematical modeling has provided insight into biological and physical phenomena in bioreactors. Currently, cell culture models focus on the relevant portions of the cellular activities that control the production of protein of interest. Application of existing models for improvement of bioreactor operation is first investigated. Particular attention is paid to large scale mammalian cultures for their key role in production of complex therapeutic proteins and financial success of biotechnology industry. The attributes of such culture demand enhancement in modeling as their performance is sensitive to local gradients of chemical and physical stimuli. A framework for development of dynamic and computationally feasible models that take into account the interactions of hydrodynamics and cellular activities is presented. The system is modeled as a network of zones to capture spatial heterogeneity. For computational tractability the biophase evolves dynamically over continuous time while hydrodynamics is defined over a discrete space. The discrete space consists of steady states of flow under predetermined operating conditions. Definition of states for operation through discretization of process parameters converts the problem into a dynamic transition problem. The decomposition of time and space provides the necessary formulation and modeling environment for coupling the model with nonlinear solvers and optimization of operation policy. Sensitivity of the cell culture model to operating conditions is a novel feature which allows studying the effects of hydrodynamics on growth, viability and productivity of organisms. Finally, the application of surrogate modeling for replacing the discrete space of hydrodynamics with a semi-continuous space is investigated.