Robust modeling, analysis and optimization of entrained flow co-gasification of petcoke with coal using combined array design

https://doi.org/10.1016/j.ijhydene.2019.10.153Get rights and content

Highlights

  • Robust model for entrained flow co-gasification of petcoke and coal was built.

  • Combined array design was used to build the robust model.

  • Some controllable operating parameters were robust assessed systematically.

  • The entrained flow co-gasification of petcoke and coal was robust optimized.

Abstract

This study is focused on robust modeling, analysis and optimization of entrained flow co-gasification of petcoke with coal, which is very important to the stable operation of this process as well as downstream processes. Unlike general robust modeling method that traditional Taguchi's crossed array design is applied, combined array design was used in this study. Then based on the exiting general experiments and the constructed robust models, a systematic investigation was conducted into the effects exerted by oxygen and steam concentrations (OC and SC) not only on the mean but also on the variance of H2, CO and (H2 + CO) production. Finally, the co-gasification process was robustly optimized. The result reveals that the average production of H2, as well as that of (H2 + CO), rises with OC increasing but declines with SC increasing. Moreover, higher OC inhibits the fluctuations in H2 and (H2 + CO) production, while higher SC makes their fluctuations more notable. The robust optimization solutions of OC and SC are observed to be 1.56% and 50%, respectively.

Introduction

Petcoke is known as a significant by-product derived from the oil refining process. However, the high level of sulfur contents have imposed some environmental restrictions on their utilizations as combustion fuels [[1], [2], [3]]. Gasification is regarded as a promising and eco-friendly method to convert them into syngas (H2 + CO) for production of some valuable chemicals or generation of electricity [4]. On the other hand, coal gasification is a well-established technology. As compared to petcoke, coal contains higher ash content, and the metallic elements in the ash are capable of promoting the gasification process [3,5,6]. Therefore, co-gasification of petcoke with coal is widely recognized as an effective method of petcoke utilization [2,4,5,7]. Generally, the blended coke-coal feedstock can be co-gasified in fixed-bed [8,9], fluidized-bed [10,11] and entrained-bed gasifiers [[12], [13], [14], [15]]. However, entrained-flow gasifier is regarded as the best-suited choice because this type of gasifier operates at a higher temperature, for which it can enhance the reactivates of petcoke for gasification significantly [1].

In order to better understand the co-gasification process and provide valuable and practical guidance for operation, various lab-scale and pilot–scale experimental researches on co-gasification of petcoke-coal have been performed over the most recent years. For instance, Vejahati et al. [12] performed some lab-scale co-gasification experiments on oil sand coke with sub-bituminous coal in an entrained-flow gasifier to make assessment of the combined effects of the operating variables (i.e., temperature and oxygen and steam concentrations, T and OC and SC) on the gasification performance. In the work of Ren et al. [6], experimental study on co-gasification reactivity of petcoke with coal was investigated in a lab-scale reactor in the temperature range of 1200–1400 °C, and the effect of blending ratio on carbon conversion ratio was investigated. Shen et al. [13] conducted an experimental study on the co-gasification performance of coal and petroleum coke (petcoke) blends in a pilot-scale entrained-flow gasifier. They focused on the effects of O2/C ratio on the syngas concentration and ascertained the better operational conditions of O2/C. Also in the work of Lee et al. [14], the effect of O2/fuel on the gasification characteristics, such as syngas flow rate, compositions, of mixture of petroleum coke and lignite were experimentally investigated in a pilot (1 T/d) entrained-flow gasifier. Cousins et al. [15] reported their pilot-scale experimental study on the oil sand coke with sub-bituminous and lignite coal. They investigated the influence of steam on CO and H2 concentrations in the syngas. Other similar experimental studies can be seen the literatures reported by Hernández et al. [16], Sofia et al. [17], Fermoso, et al. [18], and Zhan et al. [19]. In a large majority of these experimental studies, a classical experiment method with “one-factor-at-a-time” philosophy, known as factorial design (FD), had been most commonly used. Besides, a statistical design of experiment (DOE) based on response surface methodology (RSM) has been also conducted in a few studies. For example, Azargohar et al. [10], as well as Vejahati et al. [12], used RSM methodology for the design of their experiments and applied quadratic regression model to make careful evaluation of the combined effects of the operating variables and coke blending ratio (CBR) on the petcoke-coal co-gasification process.

The experimental studies are undoubtedly beneficial for guiding gasification practices. However, the founded models in the current experimental studies were just conventional “deterministic models” as the factors involved in these models were usually assumed to be equally controllable and treated as deterministic variables. This may be not the case in the actual process of gasification. In practice, oxygen and stream are relatively stable and easy to control as they are spouted into the gasifier in gaseous phase. While other operational parameters may be difficult to control. For instance, temperature is not an independent variable and normally has an uneven distribution in the gasifier. In addition, the inhomogeneous characteristics of feedstock as well as non-uniformity of particle size make CBR a parameter that is unstable and difficult to control. As a result, the gasification performance usually exhibits inconsistency due to these hard-to-control factors. In view of the uncontrollability of these factors and the fluctuations in gasification performance resulting from them, a “robust model” rather than “deterministic model” should be constructed. Robust modeling, known as robust parameter design (RPD) problem, first proposed by Taguchi [20], aims to reduce the sensitivity of processes to the action of noise or uncertainty variables by adjusting the controllable factors to a particular value [21,22]. Robust modeling for petcoke-coal co-gasification is particularly important for keeping the co-gasification process stabilized, because not only the gasification performance indexs themselves but also their fluctuations could be investigated in a systematic way in robust model.

In reviewing the current studies, there are still few reports focusing on the robustness of petcoke-coal co-gasification. Differing from the general certainty studies, this study is to present the robust modeling and assessment for the petcoke-coal co-gasification process. Studying this problem is of significance because it would help to gain a steady co-gasification process as well as downstream processes.

Traditional solution to RPD problems is Taguchi's crossed array design (a combination of an inner array formed by control variables and an outer orthogonal array consisting of noise factors). The subsequent dual response surface approach is common in applying crossed array to design the experiments [[23], [24], [25]]. Taguchi's crossed array design has two defects: one is that it usually results in an exorbitant number of runs; another is that it is incapable of measuring the interaction between control and noise variables [20]. An alternatively experimental design and mathematical modeling strategy overcoming these shortcomings is combined array design [26]. Combined array design, in which the control and noise factors are combined in a single array, displays great flexibility in the estimation of effects as well as savings in the run size. Also, this methodology provides convenience in using the existing experiments designed by general FD or RSM design. This is exceptionally beneficial for robust modeling and analysis considering uncertainties, which is true even based on the general experiments where all the factors are well controlled.

In brief, to our best knowledge, there are still few reports focusing on the robustness of petcoke-coal gasification, let alone the application of combined array design to robust assessment and optimization of this type of co-gasification process. This paper presents a study conducted on robust modeling, analysis and optimization of an entrained flow petcoke-coal co-gasification process based on the general experiment carried out by Vejahati et al. [12]. In their work, all experiment factors were assumed to be equally well controllable, and the deterministic RSM models were founded to assess the effects of operating variables. While in this paper, we assumed T and CBR as hard-to-control variables with uncertainty forms, and we build some robust RSM models to analysis the robust effects of some vital operating conditions on the gasification performance. The realization of robust analysis for petcoke-coal co-gasification based on general experiment using combined array design is the remarkable feature of this paper.

Section snippets

Methodology

For plenty of process optimization problems, the variables involved in modeling are deterministic with no uncertainties taken into account, and the dependent variable itself is usually optimized via RSM approach [26,27]. However, a common scenario arising for a process is that not all input variables are controllable and deterministic. Some uncontrollable or hard-to-control factors have a potential to spread their own uncertainties to the process output. Therefore, taking the actions of the

Experiment

Although co-gasification of petcoke with coal have been operated for many years, little literature has been reported on industrial-scale experiments with detailed information about this process. Current researches on this co-gasification process are mostly various lab-scale experimental ones. Although there are differences between lab-scale experiments and industrial-scale experiments, the mathematical analysis and optimization of lab-scale experiments still play a guiding role in industrial

Model development

Modeling for gasification process could usually be divided into mechanism modeling (kinetic or equilibrium models) that is most based on overall mass and heat balance and empirical modeling that use non-physical modeling approach such as RSM regression or artificial neural network. Unlike the mechanism model, its validity depends on the reaction equation and reaction parameters, the validity of empirical model are usually assessed by some statistics such as analysis of variance (ANOVA), R2, and

Conclusions

Robust modeling analysis and optimization of entrained flow co-gasification of petcoke with coal, is very important to the stable operation of this process as well as the downstream processes. Using combined array design methodology, some robust models for this co-gasification process were constructed. After a systematic investigation conducted into the effects of OC and SC on the robustness of the co-gasification performance, the co-gasification process were robust optimized. Some conclusions

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant number 51774113, 51674102), and Science and Technology Department of Henan Province, China (Grant number 172102210288). The authors also wish to thank reviewers for kindly giving revising.

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