It is proposed to review and update the role of the digital twin concept in the process of building systems for monitoring, on-line diagnostics, smart control of industrial equipment in oil processing and treatment units of oil and gas fields. The approach involving the synthesis of a hybrid analytical and experimental model, where the interrelation between the input and output variables of a controlled object is determined by developing a mathematical description of the processes based on the fundamental material laws—hydrodynamics, heat and mass transfer, kinetics, etc.—is proposed as the basic method for creating a digital twin for control purposes. The key parameters of the equations of the mentioned laws are evaluated and calculated using experimental and reference data provided in technical regulations, reports on researches based on real equipment, other scientific sources, reference books, catalogs of equipment manufacturers, etc. The methodology of creation and identification of parameters of static and dynamic models of thermal equipment using the mathematical principle of cell modeling has been described. Using an industrial crude oil emulsion line heater as an example, the method of developing the model, identifying its parameters, and creating an advanced control system for this equipment using pulse-width modulation of the control signal is described.