[FEATURE] Condenser and LiqLiq HX leaks, and conductivity sensors

[benr-met]

What is your precise need ?

According to my research, condenser tube leaks occur frequently enough that plants often have procedures and guidelines for handling them, and they are often detected by tracking ionic conductivity of the feedwater. Also, drain coolers can experience tube rupture and partition plate leaks, though they are not overwhelmingly common. I propose adding a tube rupture leak to the condenser or LiqLiq HX components, and a partition plate leak to the LiqLiq HX. Though they might not have the largest MW impact, they would be useful to detect if they occur - especially the condenser tube rupture leaks, as it increases the ionic concentration of the feedwater which may harm equipment, and modeling a leak could help with detecting them even before the conductivity rises noticeably and to a harmful level.

Also, I propose creating a conductivity sensor, as well as a "corrosion rate" parameter for each component which increases the outlet conductivity. In the NPPs I'm working with, there are conductivity measurements before the feedwater heaters and on the feedwater line after the high pressure heaters, as well as a couple in the RWCU and in the recirculation loops. The best way to do this would be to have a quantity representing the ionic concentration and then relate that to the conductivity via a simple equation. This way, the conductivity of streams will change as expected according to mass balances (ex. the change in feedwater conductivity from a condenser tube rupture leak is automatically accounted for by the magnitude of the leak and river water ionic concentration)

What solution do you see ?

Model tube rupture leaks in the Condenser and LiqLiq HX, and partition plate leaks in the LiqLiq HX. Also, create a conductivity sensor that sets the ionic concentration of a stream. Make it in such a way that the conductivity of streams changes in accordance mass balances.

Variables (using common plant units):

lambda = limiting molar conductivity = [S*cm^2/mol]
kappa = ionic conductivity = [uS/cm]
c = ionic concentration = [mol/L]
delta_c_corr = change in ionic concentration across a component due to corrosion = [mol/L] (would likely be set equal for each feedwater heater, if we only have conductivity measurements before and after the FWH)

Modeling equations:

--> lambda(25C) = 130 Scm^2/mol = lamda at 25 C
--> lambda(T) = lambda(25C)[1 + 0.018*[T(C) - 25] + 1.210^-4 * (T(C) - 25)^2] where T(C) is T at 25 C
(The increase in ionic conductivity per increase in temperature is greater for higher temperatures - this function captures that, hitting a ~1.8% increase at 25 C and a ~3.5% increase at 200 C, which is physically realistic)
--> kappa = 1000lambda(T)*c
--> c_in_1 [mol/L] * [1000 L/ 1 m^3] * Qv_in_1 [m^3/s] + c_in_2 [mol/L] * [1000 L/ 1 m^3] * Qv_in_2 [m^3/s] + corr_rate [mol/s] = c_out [mol/L] * [1000 L/ 1 m^3] * Qv_out [m^3/s]
(general balance equation for a component with two streams entering, one exiting, and a corrosion rate which could be set to 0 by default)

Do you see any other alternative ?

For condenser tube rupture leak, resulting conductivity increase can be modeled simply by increasing the value of the conductivity variable in the streams following the condenser - we could do this if we conclude that the condenser tube rupture leak has so low an impact on other symptoms that it's not worth modeling. However, for thoroughness I think it would be good to model completely, as long as it's not too difficult

Rather than having a conductivity sensor, manually create a variable for each stream you're interested in that represents the ionic concentration and conductivity, and manually write the balance equations where relevant (say for a tube rupture leak). However conductivity sensor is useful because you can specify exactly where the measurement is