Modeling tracer dispersion in a coupled system composed of a proppant-packed hydraulic fracture and a tight porous medium

Abstract

Tracer tests are widely performed for the characterization of reservoir properties during the hydraulic fracturing operation. The dispersion of the tracer depends on the interaction of the proppant-packed hydraulic fracture and the tight porous medium through the naturally porous walls. However, the effects of the interaction of the porous walls and dynamics of flow in the proppant-packed hydraulic fracture on the tracer dispersion and reservoir dynamic mass/heat storage capacity have not yet been reported in the literature. In this work, the tracer dispersion in a proppant-packed hydraulic fracture surrounded by a tight porous medium is theoretically modeled and the dynamic storage capacity is evaluated. The Darcy-Brinkman equation is used to describe the fully developed laminar Stokes fluid flow in the proppant-packed hydraulic fracture. We used the Taylor dispersion theory and Reynolds decomposition approach to derive the exact equivalent transport parameters, including dispersion and advection coefficients, as well as the storage capacity of the tight porous medium. It is found that the tracer dispersion is controlled by the Darcy and the Peclet numbers in the proppant-packed hydraulic fracture. The results indicate that the ratio of tracer dispersion in the proppant-packed hydraulic fracture with porous walls to that with nonporous walls ranges from zero for very small Darcy numbers to 0.3 for large Darcy numbers. The ratio of the advection velocity in the proppant-packed hydraulic fracture with porous walls to that with nonporous walls ranges from unity for very small Darcy numbers to 7/5 for large Darcy numbers. The results also indicate that tracer mass storage capacity in the tight porous medium increases as the Peclet number for fluid flow in the proppant-packed hydraulic fracture increases. Conversely, storage decreases as the Darcy number in the proppant-packed hydraulic fracture rises. A comparison reveals that a flow transport model based on proppant-free hydraulic fracture may lead to the overestimation of the tracer mass/heat storage capacity. The findings of this study pave the way to advance our understanding of tracer tests for evaluating reservoir characteristics during fracturing operations in enhanced geothermal systems.