Methodology to evaluate the uncertainty on the design length calculation of vertical ground heat exchangers
In the first part of this study, various calculation methods to determine the design length of vertical ground heat exchangers are reviewed and compared to each other using five test cases. This comparison indicates that one can expect a ±10% accuracy on calculation methods. Then, two calculation methods (L2 and L4) are used to quantify the uncertainty in the design length ????????. The L2 method is based on the ASHRAE three-pulse equation while the L4 method uses hourly simulations. The uncertainty is quantified using two methods. The first one evaluates a local uncertainty using an uncertainty propagation technique. The second gives a global uncertainty and is based on Monte-Carlo-type simulation where significant parameters are varied according to a statistical distribution. In the evaluation of the local uncertainty, the impact of individual uncertainties on 7 parameters (ground thermal conductivity and diffusivity, three ground loads (peak, monthly, annual) undisturbed ground temperature and borehole thermal resistance) are examined for five test cases using a L2 method. When a ±1? uncertainty is assigned to the undisturbed ground temperature and a ±10% uncertainty on the six other parameters, the resulting local uncertainty varies from ±11.5% to ±14.2% for the five test cases. A total of 1024 simulations using a Sobol sequence are performed on L2 and L4 methods to obtain the global uncertainty on ???????? for all test cases. Results obtained with the L2 methods range from ±11.4% to ±14.4% for all five test cases and are thus very similar to the results obtained with local uncertainty calculations. The potential impact of uncertainties on the outlet fluid temperature from the borehole field is also examined. It is shown that the uncertainty on the outlet fluid temperature at peak conditions is of the order of ±2?.