Steam is used to sanitize a vessel, and the vessel is having the following safety equipments , Pressure vacuum vent valve , Vacuum vent valve . Pressure vaccum vent valve set @100 mbar and the vacuum vent valve set@120 mbar . The VVV is interlocked to the control panel and opening of VVV disturbs the entire system. The Utility flow rate has to be designed in a such a manner that the Vacuum vent valve is never opened while cooling.

It seems to me that, if the vessel is initially filled with hot steam, as the vessel cools and the steam condenses a vacuum will unavoidably form unless the steam is replaced with another gas. If you do not want the vacuum relief valve to open, then perhaps the question should be "at what rate does the steam condense (volume reduce)?" so that you can calculate at what rate to provide a gas stream to take up the empty volume left by the steam.
In principle, the answer to your question is not hard. Work out the rate of cooling using the appropriate correlations for your vessel (you have not provided the geometry or any other information in your post), calculate the rate at which steam condenses and work out rate of change of volume. This, then, is the rate at which gas must be admitted to the vessel to avoid forming a vacuum. You can try to limit the cooling rate to match the available gas but I think it more likely that you will have to find a way to increase the gas supply rate from a source other than your vacuum relief valve.

Richard
Thanks for the reply.
Here in my vessel, I can only let a condensation rate, which ll create vaccum below my Vvv rated value. Atmosphere air can inflow to the tank through vent with filter. I have done calculations to find the temperature at a pressure rating equal to Vvv rating. And found the Steam condensation rate at that condition and designed my flow rate accordingly. Is this approach correct?. I have used clasius clapeyron equation for finding the temperature at vvv rating pressure . Kindly give your valuable opinion.

Richard,
I have got the Heat transfer coefficent and worked out the heat transfer rate, but my doubt is whether my approach towards this problem is correct or not?. I am mainly concerened with my usage of clasius clayperon equation, in the problem. I need a guidance on the right approach to this problem.
As mentioned in the above problem, my vessel is having a PVVV as well as VVV ,And Pressure vaccum vent is set at low value than the VVV, Hence in any case of vaccum PVVV opens first and the vessel is provided with a vent with air filter.
As you said, I will check the adequacy of my vent. I am briefing below, the approach I was adapted to solve this problem.
1.I have calculated the equilibrium temperature at a vaccum equal to the set pressure of PVVV, using clasius clayepron relation.
2. For the particular temperature drop , I have found out the steam condensed and the energy required for the same
3. And I have found out the utility required for taking away this heat,Using UAdT. U value obtained from the vendor.
4. Designed my utility flow rate as 50% of the value obtained from the step 3.

KIndly mention your thoughts on the same and please provide your valuable suggestion.
Thanking you in advance
Kishore RAvindran

Dear Kishore,

In fact, the condensing vapour inside the sanitized vessel will create a huge vacuum as the water to steam change of volume is approximately 1600 times. The problem would be straight forward is the system is operating at steady state, which is not the case. The approach to calculate the time that the mass of steam inside the vessel condenses is academically valid however the practical error can be high as some other factor can influence the rate of condensation such as the initial instant flow rate of cooling utility, the ambient temperature and/ or whether it is raining or not. I rather consult the manufacturers of steam vacuum breakers because they have practical data and they can advise you the conservative diameter of the PVVV (... I have no working links with them). By the way I think that the set pressure of the PVVV should be 120 mBar and the VVV 100 mBar ( in terms of absolute pressure)as you said that the PVVV open first and the VVV should never open.

Dear Kishore,

Have you thought about modeling your reactor? This would allow you to get accurate profiles vs time of the flowrates, temperature, pressure, vapor and liquid compositions, heat exchange coefficient...
Should you want to know more about this possibilty, please feel free to get in touch with me.

Joelle

Kishore,

Calculations are OK but water pressures and flow rates vary as does ambient temperature etc etc. Ideally it is better that the electromechanical control design and operational procedures do not allow a vacuum to be drawn. Suggest 2 solutions 1) Blow sterile air in as you cool and to aid cooling of the vessel before turning on the cooling water this will help displace water vapour out your vent. More tricky is ensuring your cooling rate is controlled by the vessel pressure so as to maintain the positive pressure. 2) Use a sterile filter on your vaccum vent line in case you do pull a negative pressure. I would also question the need to interlock the 2 valves. I am assuming the valves are not purely mechanical i.e. spring loaded but triggered by a pressure sensor. There is often a problem in process control where the operating accuracy band of the sensors sensing the same parameter (pressure) and feeding two separate and "antagonistic" control valves/devices overlap and you end up with the system "hunting" between the two loops. Worth ensuring there is no overlap in the sensor accuracy.

Joelle,
Hi thanks for the response ,
I am limited here by some factors like, my end user doesn't want to use a process modelling for this in any software. THey want the calculation to be simple and in MS excel.
For modelling too, Am here restricted with the choice of correct equations. I have calculated the HT and the utility rate using the concept described by Richard . And one another method by calculating the steam condensation rate using clasius clayperon equation and further finding the utility rate based on the same.
It will be really appreciable, if you can suggest the correct equations for solving the problem.
Thanks & Regards
Kishore

Dear Kishore,
Thanks for your answer.
Equations we are using to solve such unsteady-state problems are numerous and it seems to be difficult to implement them in a MS Excel sheet, and impossible to do it in a "simple" way: you would have to re-develop what is available in commercial software such as our BatchReactor that now exists, evolves and has been validated for more than 20 years.
I wish that you'll find an appropriate way of solving the problem while respecting the constraints imposed by your end user.
Thanks and best wishes,
Joelle

Joelle,
Thanks for the wishes!!
if we consider an unsteady state , the equations becomes very non linear for this particular problem. Simulataneous solution of non-linear equations in excel is beyond my knowledge. I have assumed steady state condition for the problem to make it simple and solved it as mentioned before. I am waiting to validate my results experimentally.

Regards
Kishore

Kishore,
I hope that experiments will validate your model.
Should you need transcient representation of your process in the future, please get in touch!
Regards,
Joelle