Hydrogen storage systems performance and design parameters using response surface methods and sensitivity analysis

Abstract

Design

Design of metal hydride-based hydrogen storage reactors is often performed using numerical/experimental modelling which is computationally/economically difficult. This paper investigates the applicability of Response Surface Methodology (RSM) coupled Local/Global Sensitivity Analysis (L/GSA) to investigate – i) the applicability of advanced RSMs in predicting the responses for storage systems efficiently, ii) the applicability of advanced RSMs to perform L/GSA to identify the sensitive input design parameters based on their effect on the Outputs of Interests (OIs), i.e., reaction fraction (i.e., $C$) and bed temperature (i.e., $T$), and iii) the dependence of importance ranking of design parameters on the employed L/GSA methodology. The study is conducted in two stages. In the first stage, the most accurate RSM was identified among fourteen traditional and advanced RSMs, i.e., radial basis, kriging, quadratic, moving least square, support vector machine etc., employing a measure of precision, i.e., Nash–Sutcliffe Efficiency (NSE). RSMs were constructed based on the values of OIs estimated using finite element simulation using COMSOL software for random realizations of inputs generated via Latin Hypercube Sampling (LHS). In the second stage, the importance ranking of design parameters was estimated for both OIs using six different L/GSAs based on the input-output relationships estimated in stage one. All the codes of RSMs and L/GSAs were written and validated in MATLAB. Finite element simulations of the random realizations were performed using COMSOL software. For the present study, NSEs of the considered RSMs were ranging between 0.6262-0.8544 and 0.4652–0.8081 for $C$ and $T$ respectively, indicating the importance of selection of appropriate RSM. RBF-augmented Compact-I and kriging were the most accurate RSMs with NSEs approximately 10%–20 % higher to those of frequently used polynomial RSM. Time ($t$) and mass of hydrogen to be stored ($M_H$) were the most; and external temperature ($T_{ext}$) and porosity ($E$) were the least sensitive inputs corresponding to $C$ and $T$, with differences of 80–90 % in the sensitivity indices respectively. The ranking prediction was highly dependent upon the employed L/GSA methodology, with Morris's screening observed to be the least accurate. The RSM methods described in this study help to design and investigate the metal hydride reactors for various applications (space heating, hydrogen storage, storage for vehicular application, metal hydride compressor) without undergoing detailed mathematical modelling of the system. The proposed methodology may significantly assist the designers to focus (or vary) on the sensitive inputs only during the physical modelling of systems to improve their performance. This sensitivity analysis is helpful to find out the most advance sensitivity analysis method which can be used to find out the most sensitivity parameter which can be varied according to their rankings to achieve the required performance of metal hydride reactor for the particular application. The advanced RSMs assist to identify these sensitive inputs quickly by reducing the mathematical efforts in the L/GSA by providing the accurate input-OIs relationships based on the limited numerical simulations. This will significantly save the resources and time of industries required in physical modelling/numerical simulations significantly, which otherwise would have been invested on investigating the non-sensitive inputs.