A method of operating a hydrocarbon extraction field with the aid of a computer includes programming the computer with a virtual flow meter model. The model may be written with a notation that represents at least one of mass flow, temperature and pressure at extremities of a plurality of pressure loss elements (PLEs). The PLEs may include a plurality of wells located in the hydrocarbon extraction field. The method may further include the computer estimating, with use of the model, respective mass flow rates from a plurality of the wells. The method may further include controlling elements of the hydrocarbon extraction field based at least in part on the estimated mass flow rates.