derivative generator 506 the modeling engine 304 provides the open form of model equations to the solution engine 310 the solution engine 310 in turn solves the equations in an alternative embodiment a closed form of the model equations may be provided by the modeling engine 304 the model generator 502 creates a math model of the flowsheet for input to the solution engine 310 in the exemplary embodiment the math model is a large set of equations and variables that comprehensively models all or part of the process 101 the math model will typically be in the form of a matrix which represents the equations contained in the flowsheet model in the form f x 0 standard equations and variables associated with a corresponding unit model or stream model are provided in a previously compiled standard library 508 the equations may comprise mass material equilibrium thermodynamic and physical property related equations applicable to all or part of the process 101 equation based simulators such as the simulation module 340 typically effect a desired simulation by operating on multiple levels in particular unit processes are characterized by a u201c top u201d level of a simulator used in simulation of a process model during operation of the simulator calls are made from this top level to mass and energy balance equations embedded in a lower.