# Pressure increase due to the reaction of CaO and HNO3

Currently I'm facing difficulties in determining the pressure increase due to the reaction between $\ce{CaO}$ and $\ce{HNO3}$. To be more specific, we first fill a vessel with $\ce{H2O}$ and $\ce{CaO}$ which leads to the reaction between $\ce{CaO}$ and $\ce{H2O}$ forming $\ce{Ca(OH)2}$. Resulting in a very viscous solution which eventually stops reacting.

At a certain point diluted $\ce{HNO3}$ is added. (It is possible to fill the vessel with extraordinary amounts of $\ce{HNO3}$) This leads to reaction between $\ce{HNO3}$ with Ca(OH)2 which forms $\ce{Ca(NO3)2}$ and $\ce{H2O}$. Because the $\ce{HNO3}$ is diluted (38 mass%) it is likely that more $\ce{Ca(OH)2}$ will be formed with the $\ce{H2O}$ and the remaining $\ce{CaO}$.

We know that both reactions are exothermal and the most heat will be lost by heating up the mixture and evaporating the water. Since the $\ce{HNO3}$ is filled through the bottom of the vessel it is expected that the steam will be formed at the bottom of the vessel where the reaction takes place. This will result in the formation of a big bubble until either the viscous mixture cannot withstand the pressure and the bubble "explodes" upwards, which isn't a huge problem since it is an open vessel. Or the bottom of the vessel cannot hold the pressure and the bottom of the vessel will "explode".

Now is my question, does anyone know how to encouter such a problem theoretically? I want to calculate how much pressure will be build up if $\ce{HNO3}$ is added through the bottom. (because of the high viscosity I cannot assume a well-stirred mixture) Secondly, I want to know how much pressure it takes until the viscous mixture above the "bubble" will make it's place (through channels or slugging) for the steam to go through.

Addition to my question: Thanks for the bernoulli equation, I completely forgot that one! Till this point I got an idea how to approach this:

• Reaction mechanism determines the amounts of moles that will react/are produced.
• Enthalpy of reaction determines the amount of energy produced.
• Specific heat of water, $\ce{CaO}$ and produced $\ce{Ca(OH)2}$ and the vaporation enthalpy of water determines how much heat is leaving by heating up and evaporating water.
• The viscosity then determines how "well-stirred" the vessel is, which is then a function of temperature and concentration. (I have no idea how to describe this in a formula)
• The four things above are a model which has to be set up to determine the amount of moles that are used in the reaction. In my case the amount of water is limiting so almost all water is gone. (Not all the water, since the viscosity is causing the mixture to stop flowing which results in stopping the reaction)

When this is somehow set up it starts with the next problem, namely diluted $\ce{HNO3}$ is added from the bottom.

• Reaction mechanism determines the amount of moles that will react/are produced for the reaction of $\ce{HNO3}$ with $\ce{Ca(OH)2}$. The amount of water released with this reaction is reacting further with the remaining $\ce{CaO}$ producing more $\ce{Ca(OH)2}$.
• The water that comes with the $\ce{HNO3}$ causes the surrounding solids to dissolve, but then again $\ce{H2O}$ starts to react with the remaining $\ce{CaO}$ into $\ce{Ca(OH)2}$, this has to be in the model as well.
• The enthalpies of both reactions determine the amount of energy produced.
• The specific heat of water and all other components determines the temperature rise (probably up to 100 degree Celsius). Therefore the enthalpy of vaporation of water has to be used as well.
• Then the viscosity is a function of temperature and concentration.
• The produced steam cannot go through to viscous fluid. (this is expected by me) So the pressure will rise, causing the evaporation temperature of water to rise, causing the overall temperature to rise until the pressure exceeds either the critical pressure of the vessel or the critical pressure to create a bubble through the viscous mixture.
• And then again, this has to be in a model which includes all functions mentioned above.

I don't know if this is even possible to model since it encouters so much variables which are a function of each other. But this pretty much sums up the problem I have. Including the fact that I don't know which formula I can use to find a correlation between the viscosity of this multicomponent mixture, the concentrations of these components and the temperature.

• Looks like Bernoulli's equation can help. Perhaps, I'm simplifying your question. – Berry Holmes May 17 '17 at 10:23
• What kind of vessel is this? I don't think you will stop steam from escaping the solution because you are constantly reducing the viscosity of the solution as more heat energy from the reaction goes into raising the solution temperature. If you want to model this, it is a complex problem that will require CFD, some thermodynamics modeling (i'm thinking some expression for the effect of surface tension), and some particular mass transfer equations. It might be easier to do experiments and build correlations than to go from first principles if a system behavior description is what you want. – J. Ari May 17 '17 at 14:42
• Thank you for your comment. It's just a standard stainless steel vessel of approximately 35 m3. It is designed to be sealed, but due to practical reasons the lid isn't secured, causing the lid to open when the pressure exceeds 2 mbar. So it is considered as an open (atmospheric) vessel. If the steam indeed will escape than there is no need to model this, because the steam will leave the vessel through the lid. If it doesn't then I have to model this to know what's happening. So do you know where to find any proof about your argument which states that the steam will leave the solution? Thanks! – D. Nijland May 17 '17 at 15:01