Estimation of water and heat transfer parameters of saturated silica sand by using different types of data

The hydraulic and thermal parameters of soil and aquifer are very important for quantitative description of soil water, groundwater migration and its accompanying heat and salt transport. In order to investigate the influence of different types of data on the hydraulic and thermal parameter estimation, three heat tracing experiments packed with saturated homogeneous silicon sand of three different particle size (coarse, medium and fine sands) were conducted under steady state. Twenty T-thermocouple probes were installed uniformly in the sandbox to record the temperature of the silicon sand. Two additional T-thermocouple probes were installed in the inflow and outflow chambers to record the water temperature. And then, the measured temperatures of silicon sand and water were applied for the inverses model of HYDRUS-2D software to estimate the saturated hydraulic conductivity, the thermal conductivity and the longitudinal and transverse thermal dispersivity of three saturated silicon sands. In this study, three scenarios based on different types of data were designed to estimate these parameters, i.e. R1 (including the measured temperature at the observation point alone), R2 (including the measured temperature at the observation point and the cumulated outflow) and R3 (including the measured temperature at the observation point, the cumulated outflow and the heat loss). In the addition, three more scenarios under scenario R1 consisted of different numbers of parameters were set, i.e. S1 (the thermal dispersivities were known and the empirical parameters of thermal conductivity and the saturated hydraulic conductivity were estimated); S2 (the thermal conductivities were known and the thermal dispersivity and the saturated hydraulic conductivity were estimated); S3 (the empirical parameters of thermal conductivity, thermal dispersivities and saturated hydraulic conductivity were estimated). The results showed that the thermal conductivity, the longitudinal and transverse thermal dispersivities and the saturated hydraulic conductivity of silicon sand estimated at the same time could significantly improve the accuracy of parameter estimation, and the accuracy of the saturated hydraulic conductivity was improved when the thermal conductivity was reasonable under scenario R1. The saturated hydraulic conductivity was the parameter with the highest sensitivity in parameter estimation, followed by the thermal conductivity and the longitudinal thermal dispersivity. When the simulated temperatures were consistent with the measured temperatures at observation points, there was still 10%-15% estimated error of cumulated outflow. When considering heat loss, wall flow may be the main reason for the estimated error of cumulated outflow. The additional information of water flow and heat loss was helpful to reduce the estimated error of saturated hydraulic conductivity, and then the relative error of cumulated outflow was significantly decreased for coarse, medium and fine sands. The estimated value of saturated hydraulic conductivity increased with the increasing of particle size of silicon sands while the longitudinal thermal dispersivity showed the opposite trend. And the value of transverse thermal dispersivity was same for all the sands. The additional information of water flow and heat loss improved the estimation of thermal conductivity of medium sand as well. The estimated value of thermal conductivity decreased with increasing particle size of silicon sands. This study can help for parameter estimation of homogeneous porous media based on different type of data.