A mathematical model is the representation of the phenomena occurring in a process, enabling the simulation of its physical behavior. Once validated against real experimental data, it allows predictions of a system’s outputs as operating conditions vary, without having to test them physically each time. It is also possible to work in the reverse direction: determining the operating conditions required to achieve a predefined output.
Conducting Research and Development without modeling means that every process variation (temperature, flow rate, geometry, feed composition) requires a new experimental cycle. With a validated model, that variation becomes a simulation, enabling a structural saving in terms of time and laboratory costs.
Modeling also accounts for the interaction between phenomena: with trial-and-error approaches, it is not always possible to predict the consequences of modifying a parameter when phenomena are strongly interconnected. This interaction, however, is clearly represented in mathematical models.
At K-INN Tech, simulation models are developed and validated on internal experimental data or on industrial data provided directly by clients. They are mainly applied to the study of chemical reactivity and integrate kinetic analyses with mass and energy transport phenomena, variables that, in industrial plants, cannot be isolated from one another.
Some practical examples
Multiphysics CFD simulations
CFD (Computational Fluid Dynamics) simulations make it possible to numerically solve flow, heat transfer, and chemical reaction equations on real or virtual geometries. K-INN Tech has experience in developing multiphysics CFD simulations, also in the presence of chemical reactions. This includes both heterogeneous-phase reactions (with the use of catalysts) and homogeneous-phase reactions, including combustion processes. In some cases, non-thermofluid dynamic phenomena have also been integrated (microwave heating, which requires electric field distribution, and photocatalysis, which requires the local distribution of light intensity on the catalytic surface).
In one case study, for example, we developed a CFD model to describe the mixing of a hot air stream containing molten salts with a cold air stream: the objective was to verify that the mixing ensured temperature and mixing targets before reaching a wall, thus avoiding salt solidification on it, and to implement the geometric corrections to the mixing system needed to achieve this goal.
The operational advantage is direct: geometric or operational modifications are tested in simulation before any intervention on the plant.
Stand-alone models tailored to the client
Not all problems require a finite element (CFD) approach. In some cases, the most effective solution is a parametric model capable of answering specific client questions quickly and repeatedly.
A concrete case concerns the sizing of filters for the removal of arsenic from drinking water. Adsorption is relatively easy to model under ideal conditions, but in industrial practice these conditions are never met: flow rate, pH, temperature, and feed composition vary over time, the filter material has a non-uniform particle size distribution, and the presence of other substances (phosphorus, vanadium, silica, etc.) interferes with the adsorption of the target compound.
The developed model overcomes these limitations: it handles operating conditions that vary over time, accounts for interference between contaminants, and models non-uniform particle size distributions. Each use automatically generates an Excel report. The client receives a stand-alone tool, fully customizable to their operating conditions.
The role of experimental validation
An unvalidated model is a formalized hypothesis. Validation on real data, either internal laboratory data or data provided by the client, is the step that transforms it into a reliable decision-making tool. Once validated on the client’s experimental data, the model allows prediction of system behavior following changes in operating conditions and geometries.
The models we develop account for reaction kinetics, mass and energy transfer, and material properties. Most importantly, they account for the interconnection among these factors. Once validated, they are used to size new process units or optimize existing ones.
This is the point at which applied research generates measurable economic value: the client does not buy laboratory hours, but the ability to make process decisions backed by reliable data.
What we offer in modeling
We have experience in the mathematical representation of a wide range of phenomena, not only those strictly related to the chemical industry. Model development enables the design of new equipment (such as multiphase reactors and combustors), the optimization of existing ones, and also the identification and resolution of issues, including those not initially known to the client and identified through a modeling approach.
The on-demand approach allows the development of experimental campaigns and simulation models tailored to the client. There is no standard package: each project starts from the analysis of real operating conditions and builds a model calibrated on those data.
For any request for information, write to us at: info@k-inntech.it
