A regional spatial nonlocal continuous time random walk model for tracer transport in fluids

Geological formations exhibit complex and diverse structures, which affect the transport behavior of tracers such as contaminants and sediments in fluids through various complex processes. Traditional models like the advection–diffusion equation and continuous time random walk (CTRW) have limitations in characterizing regional spatial nonlocal tracer transport processes, leading to unpredictable results. This study proposes a novel regional spatial–temporal (ST) nonlocal CTRW (ST-CTRW) model that employs the peridynamic differential operator and memory kernel to incorporate spatial–temporal nonlocalities. The ST-CTRW model can effectively capture both spatial and temporal nonlocal transport behaviors by utilizing varying weight function, interaction domain, and tracer resting time distribution. This model is capable of characterizing both normal and anomalous tracer transport behaviors and converges to the space fractional CTRW model with a power-law weight function coupled with a global interaction domain. As a generalized tool, the ST-CTRW model bridges the gap between spatial nonlocal tracer transport processes at regional scales, extending from local to global levels.