Master's thesis and Internship : Development of a dynamic tool for a molten salt electrical heater

Abstract

The strategic transition towards global carbon neutrality requires the implementation of high-temperature thermal storage solutions for industrial decarbonisation. In this context, John Cockerill uses a mixture of molten salts (60% NaNO₃ / 40% KNO₃) as a heat transfer fluid and storage medium, heated from 290°C to 565°C by a molten salt electrical heater (MSEH). While steady-state sizing tools already exist within the company, the study of the MSEH’s dynamic behaviour during transient conditions (start-ups, shutdowns, load variations) still needs to be carried out to ensure the integrity of the equipment.

This work presents the development of a robust physical dynamic model of the MSEH, structured around three fundamental pillars: a thermal model, a hydraulic model and an advanced control strategy. The thermal model is based on a concentrated capacitance approach (RC network) that incorporates the variation of thermophysical properties with temperature. A major contribution of this work is that the massive metal components (the inlet tube sheet and the shell) have been integrated as dedicated thermal nodes. Failing to account for these structures leads to an underestimation of the system’s overall thermal response time. Indeed, these masses act as a buffer as they absorb part of the energy stored in the salt. Furthermore, in order to capture transport phenomena and better capture the real thermal profile of the equipment, spatial discretisation was carried out. To this end, a spatial convergence study based on the ASME V&V 20 standard was carried out. A discretisation into n = 32 sub-elements per MSEH was selected, offering an optimal compromise between execution speed and accuracy, with the residual error during power transients limited to 2.4%. In parallel, the hydraulic model accurately reproduces the fluid inertia and the flow rate evolution governed by the dynamic equilibrium between motive and resistive pressures during valve actuation. These models were created using MATLAB Simulink, which consists of a block-based architecture.

To maintain a stable outlet temperature of 565°C in load variation despite the high thermal inertia and non-linearities of the process, a cascade control strategy was implemented, coupling the fast actuator loop from the slow thermal process. Initially tuned using the IMC method and then manually optimised (Kₚ = -0.01 [(kg/s)/°C], Tᵢ = 200 s, T_d = 50 s), the PID controller was enhanced with gain scheduling on Kₚ and Tᵢ to provide required performance in all the working range. Finally, the implementation of a feed-forward control strategy based on the energy balance enables near-perfect compensation for electrical power disturbances.

The full model was used to analyse various accident and operational scenarios within strict limits (maximum temperatures of 580°C for the salt, 600°C for the sheath, 700°C for the wire, and a temperature gradient limited to ± 25°C/min). During a shutdown, maintaining the nominal flow rate when power is cut off causes a severe thermal shock (gradient of -43.6°C/min). Alternatively, an optimised shutdown with a flow rate proportional to the power limits the gradient to -9°C/min, while keeping the system warm to facilitate a subsequent restart. For cold starts, a full-flow strategy combined with a power ramp of 10 minutes and 42 seconds was identified as the optimal solution to meet the 25°C/min constraint. Warm start strategies were also analysed to achieve a faster start-up while complying with strict limits. This showed that with a flow rate proportional to power, given the excessive gradient, the system is unable to start up more quickly. The model shows, however, that by operating at full flow rate, the MSEH is capable of absorbing 100% of the power in approximately 3 minutes.

This dynamic model therefore serves as a powerful engineering tool for John Cockerill to define safe operating windows and optimise the control systems for industrial heaters. Indeed, this model will form the basis for determining the optimal start-up scenario and for implementing the control loop on the physical MSEH.