Modeling Heat Transfer in Saturated Soil
Open Access
- Author:
- Wang, Chu
- Graduate Program:
- Civil Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 14, 2022
- Committee Members:
- Yuan Xuan, Outside Unit & Field Member
Patrick Fox, Chair & Dissertation Advisor
Tong Qiu, Major Field Member
Ming Xiao, Major Field Member
Patrick Fox, Program Head/Chair
Pinlei Chen, Minor Field Member - Keywords:
- Heat transfer
Thermal conductivity
Thermal dispersion
Effective porosity
Thermal nonequilibrium
Numerical modeling
Layered soil
Local thermal equilibrium - Abstract:
- Heat transfer through porous media occurs for a variety of important engineering applications, including geothermal energy extraction, packed beds, waste disposal, and buried high voltage power cables. Associated models have been developed with various capabilities, and often assume a condition of local thermal equilibrium (LTE), in which adjacent solid and fluid temperatures are equal. This considerably simplifies the modeling process (i.e., one energy equation) and allows for the development of analytical solutions that otherwise would be intractable. However, the LTE assumption represents a significant compromise for certain conditions, including soils with large particles, high fluid flow velocity, and small thermal conductivities for solid and fluid. Such conditions can invalidate the LTE assumption, giving rise to local thermal non-equilibrium (LTNE) in which adjacent solid and fluid phases have different temperatures. For LTNE conditions, the heat transfer process for each phase must be analyzed separately and heat transfer occurs between the phases based on the local temperature difference. Closed-form analytical solutions are first derived for one-dimensional heat transfer saturated soil with steady fluid flow and effective porosity (i.e., the fraction of total porosity that contributes to fluid flow). The solutions yield distributions of temperature and total heat flux for both transient and steady-state conditions within an incompressible soil layer having constant temperature boundaries. A numerical model, called HT1, is then developed for LTE heat transfer in saturated incompressible layered soil with steady fluid flow and effective porosity. The key to HT1 is the definition of separate columns for the solid matrix and mobile pore fluid. The solid matrix column includes the solid phase and immobile pore fluid and consists of fixed elements. The mobile pore fluid column uses Lagrangian element-tracking to follow the fluid motion, which reduces numerical dispersion and simplifies heat transfer to that of dispersive flux between contiguous elements. The HT2 numerical model is further developed using HT1 as a point of departure. Following HT1, HT2 uses a series-parallel approach for heat transfer and accounts for advection, conduction, thermal mechanical dispersion, and interstitial heat transfer mechanisms. The key to HT2 is the definition of separate columns within the soil that represent immobile and mobile components under fluid flow conditions. This approach is well suited for LTNE analysis because heat transfer in each column is treated separately, and local temperature differences allow for the calculation of kinetic heat transfer between the columns. Finally, this study numerically assesses the conditions under which the conventional LTE model is inapplicable and the LTNE condition must be considered, with solution charts presented for the threshold between LTE and LTNE conditions. Validation of the developed models has been performed with existing analytical solutions, numerical solutions, and experimental data. Comprehensive parametric studies are also presented.