A novel inverse model insensitive to initial guesses for estimating parameters of continuous time random walk-truncated power law model

Abstract

This study introduces a new, user-friendly inverse model based on the teaching learning-based optimization (TLBO) algorithm for estimating the parameters of the continuous time random walk-truncated power law (CTRW-TPL) model, including normalized transport velocity ($v_{\phi }$), normalized dispersion coefficient ($D_{\phi }$), power law exponent (β), and time scale of $t_2$. A sensitivity analysis revealed that the β has the most effect on the results of the CTRW-TPL model, followed by the $v_{\phi }$, $D_{\phi }$, and $t_2$, respectively. The sensitivity of the proposed inverse model (CTT) to initial parameter guesses was significantly lower compared to the CTRW MATLAB toolbox (CMT). Performance comparisons of the CTT using synthetic, experimental, and direct numerical simulation (DNS) breakthrough curves (BTCs) demonstrated that it provides more accurate estimates for the parameters β, $v_{\phi }$, and $D_{\phi }$ compared to the CMT. In a nutshell, the CTT is an efficient and robust tool for estimating the CTRW-TPL parameters in both porous and fractured media.