A coupled age–viscosity–flow finite-element framework for ageing-gel injection and sealing in underground void networks

Abstract

Age-dependent viscosity strongly influences gel migration and sealing in underground void networks. However, conventional models commonly update viscosity using global elapsed time and cannot represent spatially non-uniform transport histories. This study develops a finite-element framework in which a gel-occupancy-weighted fluid-age field is transported as an Eulerian internal state variable and two-way coupled with viscosity and flow. The concentration-weighted source recovers unit-rate accumulation in pure gel, suppresses accumulation in pure air and varies continuously with local gel occupancy in mixed cells. The weighted fluid-age field therefore represents an occupancy-weighted transport history rather than the conditional material age of an individual gel parcel. The numerical implementation of the transport equation was verified against a one-dimensional analytical benchmark, with a maximum relative error below 0.08 %. Comparisons among the Bulk Ageing, Frozen-Flow Age and Coupled Age formulations show that only the fully coupled treatment captures feedback-driven flow redistribution. Ageing increases viscosity and resistance in gel-filled preferential pathways, suppressing their flux and redirecting flow towards lower-resistance routes. In a representative void network, concentration weighting further suppresses non-target history accumulation in air-filled and weakly swept regions. At comparable gel filling, in-situ ageing increased hydraulic resistance by approximately 69-fold relative to the no-ageing control, while cumulative gel retention reached 98.8 %. These model-based results clarify how gel filling and in-situ ageing jointly govern simulated sealing evolution, although quantitative application requires physical validation and site-specific calibration.