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.

An Overview on Extension and Limitations of Macroscopic Darcy’s Law for a Single and Multi-Phase Fluid Flow through a Porous Medium

“…This Darcy flux is proportional to the hydraulic gradient as given in eqn. (2). The parameter C represents the coefficient of proportionality as given in eqn.…”

“…, geothermal reservoirs (Suresh Kumar and Ghassemi, 2005; Suresh Kumar and Ghassemi, 2006;Ghassemi and Suresh Kumar, 2007;Rakesh and Suresh Kumar, 2016;Bagalkot et al, 2018), shale gas reservoirs (Patwardhan et al, 2014;Samarth et al, 2015;Samarth et al, 2016), coal bed methane reservoirs and deep saline aquifers (Vivek and Suresh Kumar, 2016;Vivek et al, 2017). Since, flow through a classical homogeneous porous medium in itself has huge complexities, there are still a number of unresolved fundamental queries.…”

Colloid Transport in a Single Fracture–Matrix System: Gravity Effects, Influence of Colloid Size and Density

“…One such measuring tool can be "Rock Saturation Factor" (RSF) developed in the present study. RSF effectively measures the extent of penetration/diffusion of suspended particles/colloids within the porous rock matrix (developed based on Bagalkot et al [21]). RSF gives the information on the extent of the diffusion for various size and density of colloids or any suspended particle or solute within the rock matrix from the fracture.…”

Numerical Investigation of Techno-Economic Multiobjective Optimization of Geothermal Water Reservoir Development: A Case Study of China

“…Pandey et al found that thermochemical and thermomechanical effects were the most important consequences of heterogeneity [23]. Nikhil et al simplified the crack model by a statistical linear congruent generator method, and carried out sensitivity analysis of fracture aperture size and fluid flow [24].…”