A new probe for groundwater flow measurement using a single borehole has been developed, which provides a simple and economical way to estimate the flowing velocity and its direction simultaneously. The principle of the measurement is based on mixed convection temperature field around a vertical heated cylinder subject to a uniform lateral flow. It is found by numerical analysis that the magnitude of temperature deviation from the concentric field has a proportionality to the strength of lateral velocity. A simple probe consisting of an electric heater and thermistors has been built and its performance is examined by a calibration system, consisting of a two-meter long water tank filled with sand. According to the calibration, a good correlation has been obtained between the temperature deviation and the lateral water velocity. In order to simulate a more practical situation, we have also examined a case, where the flow meter is placed in a casing pipe. The space between the flow meter and the perforated casing pipe is filled with rectification material, and an equally good correlation has been confirmed.
A simulator for the geothermal heat pump system considering the groundwater flow has been developed. It is known that the groundwater flow affects the ability of heat extraction such as transient response and recovery of temperature. Therefore, it is necessary to simulate the dynamic behavior of the underground heat extraction system in order to evaluate the heat extraction rate. In this paper, the heat flow in the borehole, U-tube and subsurface layers with groundwater flow have been modeled by using the advective-diffusive equation, and the temporal change of temperature has been calculated based on Finite-Element Method (FEM). We analyzed a thermal response test (TRT) data and have clarified that the tool in this paper can simulate the heat flow in the layers associated with the groundwater flow and also represents the heat exchange between U-tube and layers. It has also been demonstrated that the simulator can examine the relationship between groundwater flow and apparent thermal conductivity, groundwater flow and temperature change of layers with time during heat extraction.
The author developed and applied a simple numerical scheme for simulating a two-phase hydrothermal system by using the finite volume method. This scheme consists of two simple procedures. In the first procedure, two governing equations representing the conservation of mass and energy are integrated explicitly with time, yielding the total fluid mass M and total enthalpy H in the next time step. In the second procedure, pressure P, temperature T, and liquid saturation S in the next time step are calculated by solving two nonlinear equations with the total fluid mass M and total enthalpy H obtained in the first procedure. These two nonlinear equations define M and H under the assumptions of thermal equilibrium among water, steam, and rock and phase equilibrium between water and steam. Numerical simulations for one- and two-dimensional problems were performed. The results of these simulations were consistent with those obtained using the HYDROTHERM numerical simulator. For speeding up the simulations, parallel computing was carried out using a PC cluster containing eight CPU cores. If the two-phase region, for which a larger calculation load than that for the single-phase region was required, was evenly distributed, the efficiency of parallelization increased with a smaller overhead. Otherwise, the efficiency of parallelization tended to decrease by the use of a domain decomposition method under a distributed memory environment. Shared memory computers are useful because not only they are advantageous in that they can be easily programmed but also they can achieve higher efficiency of parallelization. The upper limit of the length of the time step for maintaining numerical stability was experimentally investigated. The result of the numerical experiment showed that numerical stability was maintained if the dimensionless parameter PckΔt/μcφΔx2 , where Pc is the critical pressure; k, the permeability; Δt, the length of the time step; μc, the critical viscosity; φ, the porosity; and Δx, the length of the spatial step, was equal to or less than 10-2. The important difference between the scheme developed in this study and a conventional scheme using implicit time integration is the most costly process involved from programming to calculations. In the developed scheme, calculations are the most costly process because they require a long time. In the conventional scheme, on the other hand, programming is the most costly process because of the complicated algorithm. Researchers intending to perform numerical simulation should decide which scheme to adopt for achieving the desired cost-benefit balance.
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