How to model a deaereator on Simscape 2phase domain

I'm trying to model a deaereator on Simscape thorugh a Receiver Accumulator 2p. Basically I have the saturated steam at 22 bar (modelled as a reservoir), make-up water (4 bar, 80°C) and condense (4 bar, 100°C) that enter the receiver accumulator (water and condense are mixed before in a node since the inlet ports are only 2). At the outlet, there are the vented steam towards the ambient and the water towards the boiler (modelled as a reservoir). The mass flow rate of the condense (2.1 t/h )and the water-to-the-boiler (10.1 t/h) are fixed and modelled with a mass flow rate source. The steam mass flow rate is determined through a PID control based on the pressure at the water outlet (p_set=2.4 bar) applied on a local restriction, while the make-up water mass flow rate is determined by a PID control on the liquid fraction on the receiver accumulator (set point at 0.5) applied on controlled mass flow rate source. After some attempts I set the following the gains value of the PID:

Pressure pid: proportional= 0.1 integral=0.001

Liquid fraction pid: proportional= 0.05 integral=0.001

The main porblem is that the amout of steam that enters the receiver is equal to the amount that exits as vented steam, so no condensation occurs. Even if I change the time constant of the receiver accumulator, nothing changes. There's an ineffective heat transfer in the receiver between the water+condense and steam

In fact, after the simulation, the water oscillates at 85°C and remains stable at 2.4 bar. The pressure reaches (immediately!) the target pressure set at 2.4 bar, while the liquid fraction oscillates at 0.5.

I don't know if this component is the most suitable one, but I did not find an other better tank. The idea was to use a heat exchange, but this would complicate things.

Answer 1

[Satyam]

Hi Edoardo,

To model a deaerator behavior in the Simscape Two-Phase domain, the issue you observe mainly comes from the lack of thermal interaction inside the Receiver Accumulator (2P). This block primarily enforces mass storage and phase equilibrium, but it does not inherently guarantee effective condensation unless proper energy exchange and inlet conditions are established. You can consider the following adjustments:

• Ensure the energy balance is properly defined in the tank. Condensation occurs only if the steam temperature is higher than the liquid mixture temperature, enabling heat transfer. If both phases rapidly reach saturation at the tank pressure (2.4 bar), the model will simply pass steam through without condensation. You can review how the Receiver Accumulator (2P) handles phase equilibrium here: https://www.mathworks.com/help/hydro/ref/receiveraccumulator2p.html
• Instead of mixing condensate and make-up water using a simple node, consider introducing a thermal mass or controlled volume upstream so that the entering liquid temperature is realistically represented before entering the accumulator. This prevents the system from immediately reaching equilibrium conditions.
• The Receiver Accumulator (2P) assumes instantaneous thermodynamic equilibrium, which is why the pressure reaches the setpoint almost immediately and the steam entering equals the vented steam. If condensation dynamics are important, you may need to explicitly model heat transfer using a Heat Exchanger (2P) or Controlled Thermal Path between steam and liquid regions. Example guidance is available in Simscape thermal-fluid modeling documentation:https://www.mathworks.com/help/simscape/ug/modeling-two-phase-fluid-systems.html
• Check the initial conditions (pressure, liquid fraction, temperature) of the accumulator. If they start near the operating pressure and saturation state, the controller will quickly stabilize without producing significant phase change.
• You may also want to tune the control loop more gradually (smaller proportional gains or adding derivative action) because the very fast pressure stabilization from the PID can prevent the transient heat exchange needed for condensation.

I hope it resolves your query.

Answer 2

[Edoardo]

Hi Satyam,

thanks for your reply.

Actually, in the description of the Receiver Accumulator 2P, I found that condensation occurs only if hv<hv_sat(p_rec) and therefore "When the vapor specific enthalpy is higher than the saturated vapor specific enthalpy, no condensation occurs". It means that, if I want that steam condensates, it must enter the receiver at a enthalpy lower than the saturated vapor enthalpy at a pressure of the receiver.

I tried to disconnect the 2 PID controllers to better see the tank's behaviour. I set the steam's reservoir at a vapour quality 0.8 and at a pressure 22 bar, in this way its enthalpy is equal to 2400 kJ/kg. The restriction is fixed, and with this simulation the inlet steam mass flow rate is equal to 1.69 t/h.

The idea is to let the steam enters the receiver at an enthalpy lower than the saturated enthalpy.

The make-up water mass flow rate is fixed to 6.8 t/h while the condense mass flow rate is equal to 2.1 t/h. They mix in a node and than enter the receiver. The water at the outlet is fixed at 10.1 t/h, while the vented steam passes thorugh a restriction and in this simulation its mass flow rate is equal to 0.49 t/h. (In this way the mass balance is correct). The receiver is set with the following parameters:

• Total tank volume 20m3
• Tank cross-sectional area 5 m2
• Vapor heat transfer coefficient 500 W/m2K
• Liquid heat transfer coefficient 800 W/m2K
• Initial pressure: 1.5 bar
• Initial liquid volume fraction 0.5
• Time constant: 0.001
• Volume fraction threshold for trnasition to pure vapour or liquid: 0.03
• Liquid and vapour start at saturated condition

After the transient, the pressure stabilizes at 1.28 bar, outlet water temperature at 106.7°C (subcooled! Tsat=124°C) but the receiver is empty (liquid fraction 0.041). With this pressure, the saturated vapour enthalpy is 2189 kJ/kg, so it's lower than the enthalpy of the steam at the inlet and therefore, according to the matlab description the vapour does not condensate.

If I connect the pressure PID controller, the pressure reaches the target value 2.4 bar, the water outlet temepreature reaches 126 °C (subcooled, Tsat=137°C) and the inlet steam mass flow rate is equal to 2.7 t/h, while vented steam is equal to 1.5 t/h. In theory, in this condition, the condensation should occur (hv sat= 2730 kJ/kg), but again the liquid fraction is almost zero.

Now, I connect also the liquid fraction PID controller with target value at 0.5. It oscillates, but than it reaches the target value and the make-up water mass flow rate stabilizes at 7.38 t/h. The inlet vapur is equal to 2 t/h and the vnetd steam 1.5 t/h.

However the outlet water temperature decreases at 102 °C.

Probably, this component, as you told, does not model properly the heat transfer. However, in the description of the component, in the energy balance equation the terms related to heat transfer are present and seem to model it a good way. Probably, it is not satisfied the constraint on hv<hv_sat to enable condensation.