# Predict time to reaction (chemical engineering)?

I need a hint on the problem below. This is related to predictive analysis and chemical engineering. I don't background in chemical engineering, and that's why I am looking for some hints. I want to know if there's a technical term for the variable/problem I am working on. This would help better fine my search.

Imagine I have a fluid streamline (a production line with chemicals). On the input of that line, we pour some chemicals and change some parameters (temperature, pressure, ...etc) and we want to predict the time necessary to see change at the end of that line.

We can only control the input parameters, and we want to know how long would it take to see changes at the end of the pipeline (that delay time is the target var).

I know some parts of this will depend on the velocity and length of the production line, but also there will some reactions happening on the road. Anything rings the bill here? I am trying to read some literature review about this, if you have some useful information and know some helpful keys words, please let me know.

Is the term you're looking for simply the rate law of the reaction?

Every chemical reaction has an associated kinetic rate law, consisting of its rate constant, and its reaction orders. Consider the reaction:

$$A + B -> C$$

Due to the conservation of mass, we can effectively model the rate of formation of the product C, as the rate of consumption of either reactants A or B:

$$d[C]/dt = -d[A]/dt = -d[B]/dt$$

The brackets in this equation represents the concentration of each respective chemical in the solution. That is, the how much of each molecule of chemical is in a particular volume of solution. This rate of formation is effectively the rate of the reaction itself:

$$v = d[C]/dt$$

with v being the reaction velocity. As we can see, the reaction velocity is itself a function of the rate of product formation, which is itself directly related to reactant consumption. This, in turn, also means that an instantaneous reaction velocity is also a function of the concentrations of reactant in that instant. Typically, to determine the rate law, the initial rate is measured from initial concentrations, as they are the easiest to measure.

But how do we know HOW they are related?

In short: if we don't do an experiment, we don't.

Without doing an experiment, we can only very generally describe the rate law of a reaction. One of the most common forms of rate laws is the following:

$$v = k[A]^x[B]^y$$

where k is our rate constant, and x and y are our reaction orders. The mystery lies with these variables, and they are determined experimentally as they vary with every reaction.

I am far from an expert in kinetics, but your problem must consider the kinetics of the particular reaction being done. Another quirk of your problem is that the rate constant k itself depends on temperature by a rather involved equation for someone who doesn't know of, or particularly care for the intricacies of chemical kinetics.

Additionally, if I'm understanding your model correctly, you'll also need to consider how the flow of the system itself may or may not impact the concentration of each chemical species. As far as I understand, the initial addition of reactants will generate a gradient of concentration that, as a result, will impact the kinetics of the reaction as a function of its rate of diffusion through the volume of the reaction. One can reasonably conceive that the flow you're describing can affect this rate of diffusion. This is something that is far beyond my realm of expertise, and is more in the realm of fluid mechanics. Of course, for the purpose of this problem, you can intelligently cheese these things, especially with the reaction rate issues by looking up relevant values from well-documented processes.

If you want to do some further reading on rudimentary kinetics, consider the following: https://www.chemguide.co.uk/physical/basicratesmenu.html#top https://opentextbc.ca/chemistry/chapter/12-3-rate-laws/

This is a supervised learning problem, specifically regression.

Supervised learning refers to using measured values to model and predict output values. The regression part means that you have numbers as your response variable, as opposed to categories. (Something called ordinal regression blurts the distinction between, but I don’t think you’re in an ordinal situation.)

Your inputs are the parameters of the chemical reaction, and your outputs are the reaction times. You then use these values to figure out a plausible transformation from input to output. A few popular methods are linear regression, neural networks, random forest, and additive models.

(I assume you know or can measure some reaction times for various combinations of input values. If you don’t, then your way of guessing how long the reactions will take is up to your knowledge of the chemistry and physics, not some kind of data science or machine learning.)

• Hey Dave, thank you for your answer. I know what is supervised learning. I think I wasn't clear about my question. My problem is, as you mentioned, in the last paragraph. I have no way to guess how long the reaction will take. It's not possible to compute it directly with a mathematical formula. That's what I am looking for. If this has a technical term, it will be easier to search for it. As I said, my problem, I guess, is more about chemical engineering. The last paragraph is where I am stuck. – Soufiane Chami Jun 18 at 3:51
• @SoufianeChami Then to me this doesn’t seem like a data science question. What leads you to see it as a data science question? – Dave Jun 19 at 2:58