In the Czech part of the Upper Silesian Coal Basin (Moravian-Silesian region, Czech Republic), there are many deposits of endogenous combustion (e.g., localized burning soil bodies, landfills containing industrial waste, or slag rocks caused by mining processes). The Hedwig mining dump represents such an example of these sites where, besides the temperature and the concentrations of toxic gases, electric and non-electric quantities are also monitored within the frame of experimentally proposed and patented technology for heat collection (the so-called "Pershing" system). Based on these quantities, this paper deals with the determination and evaluation of negative heat sources and the optimization of the positive heat source dependent on measured temperatures within evaluation points or on a thermal profile. The optimization problem is defined based on a balance of the heat sources in the steady state while searching for a local minimum of the objective function for the heat source. From an implementation point of view, it is the interconnection of the numerical model of the heat collector in COMSOL with a user optimization algorithm in MATLAB using the LiveLink for MATLAB. The results are elaborated in five case studies based on the susceptibility testing of the numerical model by input data from the evaluation points. The tests were focused on the model behavior in terms of preprocessing for measurement data from each chamber of the heat collector and for the estimated value of temperature differences at 90% and 110% of the nominal value. It turned out that the numerical model is more sensitive to the estimates in comparison with the measured data of the chambers, and this finding does not depend on the type optimization algorithm. The validation of the model by the use of the mean-square error led to the finding of optimal value, also valid with respect to the other evaluation.
Keywords: COMSOL multiphysics; MATLAB; borehole heat exchanger (BHE); liveLink for MATLAB; optimization; partial differential equation.