Hammerstein–Wiener Model Identification for Oil-in-Water Separation Dynamics in a De-Oiling Hydrocyclone System

To reduce the environmental impact of offshore oil and gas, the hydrocarbon discharge regulations tend to become more stringent. One way to reduce the oil discharge is to improve the control systems by introducing new oil-in-water (OiW) sensing technologies and advanced control. De-oiling hydrocyclones are commonly used in offshore facilities for produced water treatment (PWT), but obtaining valid control-oriented models of hydrocyclones has proven challenging. Existing control-oriented models are often based on droplet trajectory analysis. While it has been demonstrated that these models can fit steady-state separation efficiency data, the dynamics of these models have either not been validated experimentally or only describe part of the dynamics. In addition to the inlet OiW concentration, they require the droplet size distribution to be measured, which complicates model validation as well as implementation. This work presents an approach to obtain validated nonlinear models of the discharge concentration, separation efficiency, and discharge rate, which do not require the droplet size distribution to be measured. An exhaustive search approach is used to identify control-oriented polynomial-type Hammerstein–Wiener (HW) models of de-oiling hydrocyclones based on concentration measurements from online OiW monitors. To demonstrate the effectiveness of this modeling approach, a PI controller is designed using the Skogestad internal model control (SIMC) tuning rules to control the discharge OiW concentration directly. The identification experiment emulates an offshore PWT system with installed OiW monitors, which is realistic with the legislative incentive to include online OiW discharge measurements. The proposed approach could enable the application of OiW-based control on existing offshore PWT facilities, resulting in improved de-oiling performance and reduced oil discharge.