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Innovative interpolation methods to enhance experimental performance

September 2018

The original and promising introduction of kriging models for the prediction of the physicochemical properties of distillates makes it possible to take full advantage of the benefits provided by high-throughput experimentation targeting the accelerated development of new hydrocracking catalysts.

The oil industry is having to address a growing demand for middle distillatesand hydrocracking is one of the conversion processes used to obtain them from the heavy fraction of the crude oil. During the process, impurities are removed (the hydrotreatment step, HDT) and long molecular chains are broken in the presence of hydrogen (the hydrocracking step, HCK), making it possible to obtain the desired middle distillates and oil (Figure 1). 

Hydrocracking is a catalytic process and experiments (processes and analyses) to develop new catalysts are long and costly. To overcome this drawback, IFPEN wants to use high-throughput experimentation (HTE) units. These systems, which are equipped with parallel mini-reactors, enable researchers to test up to sixteen catalysts simultaneously.

However, the quantity of effluent discharged from each reactor is extremely low (a few milliliters) and cannot subsequently be used for distillation to obtain the cuts of interest (gasoline, diesel, oil, etc.), and then the determination of physicochemical properties. 

Consequently, using these HTE facilities to optimize catalysts as a function of the properties of the output products was a challenge IFPEN addressed within the framework of a thesis2.

                                                 Click on image to expand

An innovative methodology for predicting properties was developed from results obtained using powerful analytical techniques - two-dimensional gas chromatography (GCxGC) and carbon-13 nuclear magnetic resonance (C13 NMR) - combined with data analysis methods.
The approach, based on correlations between the desired properties and molecular descriptors, comprises two stages:

1/ Determination of relevant descriptors (Features Selection)
From the GCxGC and C13 NMR multivariate data, the impact of the various hydrocarbons (n-paraffins, isoparaffins, aromatics, etc.) and their molecular structure (chain length, degree of branching, etc.) on the properties was determined via parsimonious multivariate regression (s-PLS)3. With this understanding, descriptors of the total effluent from the HCK reactor (density d, weighted average temperature AT, aromatic carbon Ca, etc.), which are easily analyzed, were identified.

2/ Prediction of usage properties via data analysis using regression and interpolation methods [1]
Several methods were tested. The kriging method 4, generally used in geostatistics and sensitivity analysis, was selected and introduced for the first time in the oil industry[2]. An example is shown in Figure 2 for a property y measured for 10 different observations in two-dimensional space (x1x2). Kriging is used to predict property y at a new given point, by computing a weighted average of the observations in the neighborhood of the point using the generalized equation [1]:

Figure 3 presents a comparison between the results obtained using linear methods (MLR) and kriging: a significant improvement in predictions can be observed using Kriging. Moreover, one of the strengths of the new method is access to a local prediction uncertainty, unlike RLM, which gives constant uncertainty for all predicted points. This means that the user can be warned if the prediction is questionable.
Kriging was also successfully used for the prediction of the cloud point of diesels[2]. It is now possible, when screening catalysts, to directly access these properties as they exit HTE units, from the analysis of the total effluent from the reactor (giving access to the descriptors). Hence it is no longer necessary to perform a distillation step or to measure a property using a standardized method.
This innovative approach, combining analysis, molecular understanding and data analyses, has led to a significant improvement in experimental performance (analysis and processes). It raises hopes for some interesting perspectives concerning the other properties of refined products since it could be applied to other types of processes, the output products of which do not currently have property descriptors. Another potential approach is to combine kriging with multivariate analysis techniques in order to extend its use to other spectroscopic or chromatographic data.

Scientific contacts :   -   -

  1. Kerosene and diesel.
  2. Thesis by Jean-Jérôme Da Costa Soares, in partnership with the LASIR laboratory (University of Lille).
  3. Variant of the partial least squares (PLS) regression method, making it possible to reduce the number of factors while focusing on those most closely correlated with a property of given interest.
  4. Linear estimation method ensuring minimal variance.


[1] Da Costa JJ, Chainet F, Celse B, Lacoue-Nègre M, Ruckebusch C, Caillol N et al. Kriging Modeling to Predict Viscosity Index of Base Oils. Energy Fuels 2018;32(2):2588–97
>> DOI: 10.1021/acs.energyfuels.7b03266
[2] Da Costa JJ, Chainet F, Celse B, Lacoue-Nègre M, Ruckebusch C, Espinat D. Comparing Kriging, Spline, and MLR in Product Properties Modelization: Application to Cloud Point Prediction. Energy Fuels 2018;32(4):5623–34
>> DOI: 10.1021/acs.energyfuels.7b04067

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