Influence of Fracture Heterogeneity Using Linear Congruential Generator (LCG) on the Thermal Front Propagation in a Single Geothermal Fracture-Rock Matrix System

Abstract

An implicit finite difference numerical model has been developed to investigate the influence of fracture heterogeneity on the propagation of thermal front in a single horizontal fracture-matrix system. Instead of depending on a complex and data-demanding geostatistical method for a precise representation of fracture aperture, a statistical linear congruential generator (LCG) method was applied in the present study to replicate the unpredictable nature of fracture aperture morphology. The results have been compared with the parallel plate model and simple sinusoidal model. Finally, sensitivity analysis of fracture aperture size and fluid flow rate has been carried out to identify the conditions at which fracture heterogeneity is critical. The results indicate that LCG-aperture enhances the heat transfer between fracture and hot rock matrix compared to the parallel and sinusoidal fractures. Further, the temperature profiles in hot rock indicate that there was a greater loss of heat for the case of LCG-aperture (25% loss) compared to sinusoidal (16%) and parallel plate (8%) apertures. It was found that heterogeneity does not play a major role at small fracture aperture size (≤50 μm) and at low flow rates. However, as fracture aperture size increases, the heterogeneity plays a vital part even at low flow rates.

Keywords

• geothermal system
• fracture heterogeneity
• mathematical modelling
• linear congruential generator
• porous media