(53ab) Can Kriging Replace ODE-Based Kinetic Modeling ? a Hydrocracking Case Study

Valentin Dallerit¹, Benoit Celse^1*, Victor Costa¹

1. IFP Energies Nouvelles, Rond-Point de l’Echangeur de Solaize, 69360 Solaize, France

*E-mail: benoit.celse@ifpen.fr

HIGHLIGHTS

• Comparison between kinetic model and Kriging model.

• Good predictions in both cases.

• Kinetic model can enforce constraints and trends making them more robust

• Kriging models are more accurate but less robust. They are also built with uncertainties

INTRODUCTION

Catalytic hydrocracking is used to convert heavy Vacuum Gas Oil (VGO) residue to more valuable middle distillate and/or naphtha cuts. Hydrocracking of VGO residue is performed in a two-step process:

1) a hydrotreatment step in the first reactor (R1), which serves mainly to remove nitrogen and sulfur compounds from the feedstock (Becker et al. 2015);

2) a hydrocracking step in the second reactor (R2), which performs the main hydrocracking reactions on a zeolite catalyst (Per Julian Becker et al. 2016).

Models are developed to optimize process design and operating conditions in order to maximize desired cuts and product characteristics.

Historically, kinetic model (based on ODE) were used to predict the nitrogen content on the output of the first reactor. The aim of this paper is to present a new kind of model based of Kriging (also called Gaussian process regression (Kleijnen, Jack P. C. 2009)) and compare the results with the original kinetic model.

MATERIALS & METHODS

A kinetic model of the hydrodenitrogenation (HDN) is developed containing 11 parameters. The model parameters are fitted using 115 experimental runs in a pilot plant, with 15 feedstocks. The feedstocks have different geological origins (Arabian, Ural, Forcados…) or are produced in different conversion processes (coker, deasphalting…). Feedstock characteristics (SIMDIS, sulfur/nitrogen content, aromatic carbon content etc.) are known. The reactor temperature varies from 360 to 420°C, and the liquid hourly space velocity (LHSV) varies from 1.0 to 3.5 h^-1. Experiments were performed at 90, 110 and 140 bar with a hydrogen-to-oil ratio of 600 to 1400 l/l. An additional set of experimental runs was used to validate the model.

The same data are used in order to fit a model based on Kriging. Kriging is originally an exact interpolation method. However, some improvements to the method are used to allow the use of noisy data and avoid the model to pass exactly through the experimental data.

Kriging is mainly used on data using spatial coordinates (geophysics). The use of this method to predict physicochemical properties is a real innovation. This work shows the adaptability of kriging to nonlinear regressions.

Another advantage of Kriging is that it provides a measurement of predicted values uncertainties unlike other interpolation methods. Each predicted value is associated to a confident interval, the width of which depends on the related experimental conditions. The uncertainty is equal to the noise on data used to fit the model and increase with the distance to the calibration database. This distance, defined by the Kriging, give more weight to sensible inputs and can be used as a standalone distance to compute the distance between a new data and the calibration database. This can be used as a tool in order to detect extrapolation.

RESULTS & DISCUSSIONS

The comparison with the interpolation model for the experimental validation database on the nitrogen content was carried out. It shows that the interpolation model is more accurate but less robust than the kinetic model when the distance between the point and the calibration database increase. In this case, the kinetic model provides better simulation results.

However, the kriging model provides an uncertainty estimation. This kind of method is very easy to use and parameters tuning is very fast. It can be very useful for processes where the chemical behavior is not well known. It can also be used as a tool for design of experiments. New points are added where the uncertainty is maximal.

Bibliography

Becker, Per Julian; Celse, Benoit; Guillaume, Denis; Dulot, Hugues; Costa, Victor (2015) Hydrotreatment modeling for a variety of VGO feedstocks: A continuous lumping approach. In : Fuel, vol. 139, p. 133–143. DOI: 10.1016/j.fuel.2014.08.032.

Kleijnen, Jack P. C. (2009) Kriging metamodeling in simulation: A review. In : European Journal of Operational Research, vol. 192, n° 3, p. 707–716. DOI: 10.1016/j.ejor.2007.10.013.

Per Julian Becker; B. Celse; D. Guillaume; V. Costa; E. Guillon; G. Pirngruber (2016) A continuous lumping model for hydrocracking on a zeolite catalysts: model development and parameter identification. In : Fuel, vol. 164, p. 73–82.