Use of the Distance Transform for Integration of Local Measurements: Principle and Application in Chemical Engineering

Abstract

We propose an original methodology to integrate local measurement for nontrivial object shape. The method employs the distance transform of the object and least-square fitting of numerically computed weighting functions extracted from it. The method is exemplified in the field of chemical engineering by calculating the global metal concentration in catalyst grains from uneven metal distribution profiles. Applying the methodology on synthetic profiles with the help of a very simple deposition model allows us to evaluate the accuracy of the method. For high symmetry objects such as an infinite cylinder, relative errors on global concentration are lower than 1% for well-resolved profiles. For a less symmetrical object, a tetralobe, the best estimator gives a relative error below 5% at the cost of increased measurement time. Applicability on a real case is demonstrated on an aged hydrodemetallation catalyst. Sampling of catalyst grains at the inlet and outlet of the reactor allowed conclusions concerning different reactivity for the trapped metals.

Bifunctional Intimacy and its Interplay with Metal‐Acid Balance in Shaped Hydroisomerization Catalysts

“…For every profile, 25 points were measured resulting in a constant step of about 56 μm. Local measured concentrations were then processed using the method of the distance transform [33] to obtain the overall concentration of each element in the extrudate.…”

From powder to extrudate zeolite-based bifunctional hydroisomerization catalysts: on preserving zeolite integrity and optimizing Pt location

“…The metal dispersion was calculated by means of a 0.75 O 2 :Pt stoichiometric coefficient [44,45]. Local measured concentrations were then processed using the method of the distance transform [49] to obtain the overall concentration of each element in the extrudate.…”