Simulation of heat and fluid flow in porous medium and fractures by material point method

Abstract

Purpose

The material point method (MPM)is a particle-based numerical method suitable for solid–liquid simulation and large deformation problems. However, MPM is generally used in solid deformation at present, to develop a multi-physics coupling MPM; the purpose of this study is to extend the MPM to simulate the heat and fluid flow and address the thermal-hydrological (TH) coupling problems.

Design/methodology/approach

The porous medium was discretized into two sets of Lagrangian points, and the motion of fluid points follows the Darcy’s law. Two sets of heat transport equations were established for the heat conduction and heat exchange in the pore fluid and solid skeleton. Fractures were considered by adding the porosity gradient term in the governing equations; also a transition function was introduced to smoothen the fracture boundary.

Findings

Four cases of heat and fluid flow in porous medium and fractures were presented to verify the feasibility of the proposed method. And the effects of fractures on heat and fluid flow were investigated. Additionally, a case of geothermal extraction was solved and the importance of the interstitial convective heat transfer coefficient was analyzed.

Originality/value

The proposed method extends the conventional MPM, using two sets of material points and two sets of heat transport equations to simulate the heat and fluid flow and address the TH coupling problems, which can be applied in both porous medium and fractures.

Citation

Wang, G., Sun, F., Wang, R., Zhang, L., Cao, T. and Li, B. (2022), "Simulation of heat and fluid flow in porous medium and fractures by material point method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 10, pp. 3328-3359. https://doi.org/10.1108/HFF-12-2021-0797