Predict time to reaction (chemical engineering)?
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:
$A + B  -&gt; C$
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/