Monte Carlo and Sensitivity Analysis Methods for Kinetic Parameters Optimization: Application to Heavy Oil Slurry-Phase Hydrocracking

Abstract

A methodology to estimate kinetic parameters using the Monte Carlo algorithm and sensitivity analysis is described. The approach is applied to the experimental data reported in the literature for slurry-phase hydrocracking of heavy oil with ionic liquids. All experiments were carried out in a batch reactor at a reaction temperature of 430 °C, H 2 pressure of 12.3 MPa, and reaction times of 0.5−6 h. It is demonstrated that the reported values of kinetic parameters can be optimized so that the average absolute error is substantially reduced from 21.73 to 7.93%. Simulations with the Monte Carlo algorithm with various initial values of parameters help find the best initial guess for further optimization of parameters. The prediction of product yields was improved using the average absolute error as objective function since it was distributed equally for all products, being coke the lump with greater error reduction (from 57.39 to 7.60%). The sensitivity and statistical analyses performed on the optimized reaction rate coefficients confirmed that the obtained results are the optimal values that minimize the error between calculated and experimental data. The lowest value of average absolute error (7.93%) determined by sensitivity analysis was found for the optimized values; moreover, the slope and intercept of the parity plot are almost 1 and 0, respectively.

Comparison of Traditional and Sequential Approaches for Estimation of Kinetic Parameters of Heavy Oil Upgrading

“…The objective function was the average absolute error (AAE) because it has shown better results by distributing the error equally to all the fractions involved. 7,14 To compare with the results obtained by Tang et al, 23 the sum of square error (SSE) and the determination coefficient (R…”

“…The methodology for the estimation of the reaction rate coefficients involves the following steps: 7,14,21,24 the initial values for the optimization step are obtained using the reported literature values and the Monte Carlo algorithm, which is based on the use of random numbers (in a range of 1 × 10 1 to 1 × 10 −8 ) for each kinetic parameter. It has been previously demonstrated that using initial values determined with the Monte Carlo algorithm, better results are achieved than using other initial values (Figure S5).…”

“…1,2,4,9,10 One manner to solve this problem is by sequential parameter estimation, which reduces the number of parameters to be estimated simultaneously by dividing the complex reaction scheme into several subnetworks. 14,15 Ancheyta-Juaŕez et al 16 first proposed an approach to reduce the number of reaction rate coefficients to be estimated simultaneously for the fluid catalytic cracking process (FCC) of vacuum gas oil (VGO). A five-lump kinetic model was separated into three-and four-lump models to decrease the estimation of kinetic parameters from 9 to 3.…”

Kinetic Models of Deep Hydrotreating Reactions to Produce Ultralow Sulfur Diesel

“…Since the manner to represent the kinetic modeling and estimate the kinetic parameters of reactions is through ordinary/partial differential equations that are solved by numerical methods and linear/nonlinear optimization techniques, it is crucial to discuss some of the most popular and useful methods used worldwide to carry out parameter estimations, as well as their advantages and disadvantages. , …”

“…Since the manner to represent the kinetic modeling and estimate the kinetic parameters of reactions is through ordinary/partial differential equations that are solved by numerical methods and linear/nonlinear optimization techniques, it is crucial to discuss some of the most popular and useful methods used worldwide to carry out parameter estimations, as well as their advantages and disadvantages. 96,97 Alcaźar and Ancheyta 98 proposed a methodology based on sensitivity analysis to estimate the kinetic parameters of heterogeneous kinetic models. This methodology consists of three main steps: initialization of parameters (with the Monte Carlo method), nonlinear optimization (using the Levenberg− Marquardt algorithm), and sensitivity analysis.…”