Heat production from Hot Dry Rocks (HDRs) using closed-loop horizontal wells is currently being tested at full-scale in Alberta, Canada. Here, a Finite Element Method (FEM) program is developed to evaluate the outlet fluid temperature from an impermeable HDR geothermal system for a single well. The analysis includes heat conduction only in the rock, convective transfer between the rock and fluid, and advection and conduction in the fluid flow along the well. In typical results, the outlet fluid temperature is constant for some time until the first change in temperature is observed, the cooling "break through"; thereafter, the outlet temperature drops rapidly because of the small contact surface (well wall area) between the rock and fluid and the slowing rate of conductive heat transfer as the temperature gradients near the well wall flatten. Different well lengths, diameters and injection flow rates are examined to demonstrate the impact of geometric parameters on the outlet fluid temperature. Change in diameter has a negligible impact on the outlet fluid temperature, indicating drilling wells with bigger diameters only increases the cost. A lower injection flow rate results in a higher outlet temperature over time; however, the short-term electricity generation capability will be decreased. Increasing the well length keeps the outlet fluid temperature at a higher level over time. Combined effects of a lower injection rate and a longer well provide longer times for fluid output at higher temperatures.
Unlike other renewable sources that are irregular and variable and thus not suitable for base-load power provision without massive storage capacity, geothermal sources provide a clean, carbon-free, reliable, and sustainable source of energy. The amount of heat in the earth has been estimated using different methodologies; although the predicted amount varies based on the definitions and the methods used, all agree that it is a huge number (Roberts 1978, Tester et al., 2012, Dickson and Fanelli 2003). Although not strictly a renewable resource in the engineering time scale for a given project, geothermal energy can be viewed as a renewable energy source at a scale of about a thousand years considering the slow replenishing of heat due to radioactive specie decay and conductive heat transfer from the mantle (roughly thousand-year scale). Hence, geothermal resources are "infinite and renewable" from a theoretical view, though not for single projects because of heat depletion.