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I'm not sure if this is the correct SE in order to ask this, if that is true just said me that in comments and I will delete my question, there is no need of downvote or ban.

I was answering a question of World Building SE about how to make an atmosphere and I found that nitrous oxide can be used to make one. But then, I started reading how can I produce nitrous oxide (to post that information also) and I found with this on Wikipedia.

It talks about an industrial method and a laboratory method. Which is the difference?

I have the theory that a laboratory method can't be used at big scale. Is that true? But, How much is "big"? Maybe for a fabric it's too little the laboratory production (a few kilograms per minute per square meter of laboratoy???) but for me that is a lot, 1kg per minute is arround a cubic meter of air per minute (60 minutes per hour, 24 hours per day...)

P.S: Sorry for the bad tag. I don't have no idea of what to write.

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    $\begingroup$ Long story short, laboratory methods are too expensive for industry, and industrial methods are too hardcore for a lab. $\endgroup$ – Ivan Neretin Jun 19 '18 at 20:05
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This answer will be separate in few parts. In the first one I will just make a review of the scope between lab an industrial scale. In the other parts, you’ll find some things more deeply explained and exemplified. In any case, if something isn’t clear or the English grammar is wrong, please ask me a question and point it (the English mistake) out.


Part I - Short Overview

A laboratory method can perfectly be adapted at industrial scale however there are many things to take in consideration.

Let say you are working in a lab to perform the synthesis of a molecule. In the basics we will assume you will need a reactor (round-bottom flask), and a distillation column to separate your compound from the others (solvent, remaining reactants, possible side products).

If you do all that stuff at a laboratory scale, even if your reaction is super exothermic even involving very hazardous chemicals, you'll always have the possibility to do it safely or at least having the possibility to stop the reaction by cooling it down rapidly.

I would mention at this point that the ratio between the volume and the surface of an object isn't constant. For example, if you multiply by 10 the length of the sides of a cube, its volume rises by a factor 1000 whereas its surface by a factor 100. You can find more interesting information here.

So, if you make your reaction at laboratory scale, let say under few litre, even if it might be dangerous, you’ll control easily and readily the temperature inside your flask or small reactor. So, at industrial scale, let say over 1 cube meter (in general I would say 5 to 50 cube meters is the average, but some reactors are bigger than 1000 cube meter), you must take in consideration safety and security details as well as the sizing of your operation. I recommend you to read here a really nice overview about most of the kinds of the reactors used in chemical plants with many details related to them.

Now I bet you start to understand the big difference. But let me go a bit deeper on that part. If you want to size a chemical operation, you must first take in consideration the hazards of all of your chemicals as well as their fundamental properties (ebullition temperature, state at a given temperature (gas, liquid, solid, supercritical fluid , …), the possible interactions between to compounds or more.

After that you’ll need to know about the kinetics of your reaction, is it fast or slow?, you’ll also need to know about the thermodynamics of all the chemicals to make a prediction for safety (see the next part) and to complete you’ll have to take in consideration if you have a system with only liquids, with gas and liquids or even harder with gas, liquid and solid (hydrogenation (using hydrogen gas) of a liquid organic molecule (let say an oil) catalysed by a given catalysor (a solid) (see the third part).

For years now engineers and researchers, developed methods to compute thermodynamic and kinetic properties as well as many different methods for sizing many different basic or very complex operation (distillation, crystallization, multiphase reactors, drying, precipitation, …) (and I’ll give when I’ll have time as many details as I can in a fourth part about that point). So now it exits a lot of extrapolations and models made from the experiments because of the too complex existing situations to make nice calculus involving mathematics and physics learned at school. This article gives you an idea of all the possibilities of having nightmare while sizing an operation at industrial scale.


Part II - Predicting the safety of a reaction

The Semenov diagrams

So, to give some concrete applications of what I said before, I will show you a very basic thing that safety engineers will do to know more about the danger of the reaction. They will use a Semenov-diagram (or plot). The first idea is to consider your reaction having a zero-order kinetics, i.e. the kinetics doesn’t involve the concentration of the reactants. It’s a big assumption but it gives you really a good idea of how dangerous it can be. The second idea is, as your reactor will be quite big, to consider it as adiabatic. It’s not true at all of course because you wouldn’t be able to heat or cool it, but it allows you to know what could happen in the worst case. Doing an energy balance on your system you’ll get: $$Q_{acc} = k_0 \cdot C_0 \cdot \exp\left(\frac{-E_a}{RT}\right)\cdot \left(-\Delta_r H\right)-UA\cdot (T_r-T_c)$$ Where $Q$ represent the amount of heat generated by the reaction, $k_0$ is the pre-exponential factor of the Arrhenius’s law, $C$ is the concentration, $E_a$ is the activation energy, $R$ is the constant of ideal gases, $U$ is the global exchange coefficient of your reactor and $A$ the area of heat exchange. Now if you plot this equation which tells you the amount of energy liberate by the whole process at a given temperature with the plot only $UA\cdot (T_r-T_c)$, you’ll get something like that,

semenov plot

reference

If you consider the blue dotted line crossing the red plot, the blue curve tells you about how much heat you can evacuate and the red one tells you about what the whole process liberates. The point A is the stable point as even if you go under in temperature your reaction will still stay in control, however the B point is the point from which you have instability. It’s clear to understand than between these two points you can control the temperature of your reactor.

Keep in mind the heat you can evacuate is a linear function of the temperature $UA\cdot (T_r-T_c)$ and the heat produced by the whole operation is exponential with the temperature as shown by Arrhenius.

Predict the dangerous nature of a reaction

Another thing you can do easily is to predict the kind of danger of your reaction (not dangerous, a little dangerous, dangerous, extremely dangerous) using the worst case (adiabatic reactor).

Then you have rises of the temperature equal to the amount of heat produced by the reaction. Then you have, $$C_p \cdot \Delta T_{adiab} = [reactants]_0 \cdot V \cdot (- \Delta_r H)$$ Where $C_p$ is the heat capacity of your mixture, $[A]_0$ means the concentration of A at the beginning (you want to know what happens if all of it reacts), and V is the volume of the mixture.

You can then predict the variation of temperature knowing all the needed parameters. I would say if the rising of temperature is below 50 °C your reaction is quite safe; if you find something more than 100 °C you’ll have to find either another solution (a different reactor, …) or add a lot of security systems (emergency open valves, a possibility to almost instantly flush your reactor content in a inhibitor mixture under the reactor, …).


Part III - What if I have a multiphase system?

Well this is the case most of the time. It’s not common to have a system in which you only have soluble fluids (except for gases). If you are performing a treatment of your affluents or your effluents (because you can’t use row compounds and you can’t throw away your potential toxic, corrosive, … mixture in the nature) you will often have an exchange between a gas and a liquid. If you are doing a reaction involving a catalysor then you will probably have three phases if it’s a hydrogenation or a fluidized-bed reactor for a cracking operation or something else. You’ll have only one phase for vapocracking, polymerization (not in emulsion and relatives) and urea production for example.

Now in these cases you have to take in consideration of possibility of having an exchange of chemicals (the ones you want at least) between the two phases or three phases. If you have a liquid/gas system, the situation is common and even if a bit hard sometime you can get good approximation and correlation using the two films theory see that I wasn’t really confident with it some time ago.

If you use a catalysor, you have to predict the possibility of the species to go inside it so that they can react otherwise nothing will happen. Then you have to understand how your catalyst works and how to avoid the possibility of blocking it or poisoning it [ref] as in most of the cases catalysors are like sponge solids. I found two articles pdf1 and pdf2 if you want to got deeper on how complex it is.


So I hope this very long answer help you more than you need. I will also use it as a reference for some more questions in the future. You may say that all these parameters can also be taken in consideration even at a lab scale. I will anwser yes in the sense that you will never have all the data you want and you'll have to do experiment to extrapolate back to the industrial scale. But I will moderate that if you are only doing stuff in a lab scale it doesn't cost the same as when you are involving tons of chemicals and it's way more secure so even if you are wrong in something you can afford it much more easily.


I will point out that in most of the cases the chemical plants are sized as the lab plants a company may have meaning that the lab plants are made by extrapolating down the data (size of the reactors, ratios of length especially, ...) so that when you do your experiment in the lab you can then extrapolate back using your own models and then be more close to the reality with really tiny variations.

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