Electric Submersible Pump Lifted Oil Field: Basic Model for Control, and Comparison of Simulation Tools

Optimal operation of petroleum production is important in a transition from energy systems based on fossil fuel to sustainable systems. One sub-process in petroleum production deals with transport from the (subsea) well-bore to a topside separator. Good control design for such operation requires a dynamic model of the petroleum flow from the well-bore to the separator. Here, such a dynamic model is considered for liquid production (oil/water) using an electric submersible pump (ESP) to aid in counteracting gravity and friction forces. Based on an existing model used for industrial control design, one goal is to report a complete dynamic model in a single paper. Emphasis is put on dimensionless equipment models for the simple change of units, and the model is developed from physical laws for easy replacement of sub-models, if needed. All the necessary information (equations, parameters) for model implementation is provided, and two candidate equation-based modeling languages are selected and compared: Modelica and ModelingToolkit [MTK] for Julia. The simulation results are virtually identical for the two languages and make sense from physics; however, there is a minor discrepancy in one plot—likely caused by slight differences in accuracy in handling initialization in the implicit algebraic equations. The implementation structures of the model in Modelica and MTK are similar. Modelica is a mature and excellent modeling tool, handles large-scale models, and has tools for producing C code and integration with other tools. MTK is still in rapid development, supports more model types than Modelica, and is integrated in an eco-system with excellent support for control design, optimization, model fitting, and more. To illustrate the suitability of using the developed model for control design, a simple PI controller is designed within the eco-system of MTK/Julia.