A Reduced-Dimension Solution for Spatial Modeling of Tracer Transport in Single-Well Tracer Tests

Summary Modeling tracer transport in petroleum reservoirs is an important technique for accurately estimating residual oil saturation, characterizing high-conductivity pathways, and determining well connectivity. Single-well tracer tests (SWTTs) are essential for evaluating the sweep efficiency of conventional and enhanced oil recovery (EOR) methods, as they allow for the rapid quantification of oil displacement near the injector well, thereby assessing both technical and economic aspects before implementing a field-scale recovery plan. However, current methods for examining SWTTs rely on time-consuming numerical simulations that require significant expertise. In this work, we introduce a novel 2D solution for modeling the flow of chemical tracers in SWTTs during the tracer push stage, representing the first mathematical approach that enables real-time, field-scale tracer transport modeling. Our model is derived through the analysis of tracer flow in porous media, utilizing a key transformation variable to convert the classic 2D differential equation into a reduced-order expression equivalent to solute transport in single-phase flow. This mathematical approach incorporates an approximated full hydrodynamic dispersivity term to account for mechanical and molecular dispersion mechanisms, resulting in an accurate estimation of tracer advance in the x- and y-directions as a function of the steady-state velocity field. We validated our 2D solution by comparing it against multiple numerical SWTT simulations under conditions of residual oil saturation, demonstrating that the model achieves a difference of less than 3 ft in estimating the location of tracer slugs. Our approach provides a practical, real-time tool for approximating tracer flow and location in the reservoir, significantly reducing the number of initial simulations required to evaluate tracer properties before building robust reservoir models for heterogeneous systems. We believe that this model is a valuable tool for rapid tracer transport analysis and enhances the efficiency of field-scale recovery planning.