Virtual Flow Metering using B-spline Surrogate Models

Abstract

Existing optimization-based virtual flow metering solutions use advanced, blackbox process models directly in the optimization problem. This approach has many potential disadvantages, for example: non-smooth models and lack of derivative information may hamper the optimization solver. In this paper a new approach to optimization-based virtual flow metering using B-spline surrogate models is presented. In this approach the black-box process models are replaced with smooth B-spline approximations, with gradients readily available to the solver. We show that the approximation can be done without any significant loss of accuracy. By using surrogate models the optimization solver can be decoupled from the process simulator, saving I/O-operations and evaluations of the process model, resulting in reduced solution times. Another beneficial feature of the problem formulation is that poorly calibrated models may be identified and weighed less in the optimization problem. Some insight on how to select measurement noise and model error weights is shared with the reader.