A simplified model for geochemical reactions in a geothermal reservoir

Hot water pumped out of the ground for purposes of geothermal energy extraction cools down after it is used in a heat exchanger. The now cold water contains minerals that undergo a shift in chemical equilibrium. This may cause the minerals to come out of solution and become sediments. When pumping the cold water back into the porous ground, these sediments can cause cloggings that eventually lead to a net energy loss using this source. It will requiremore mechanical energy to pump up the water, than we gain in geothermal energy. In this reportwe aimto create a simple computer programthat models the creation of these sediments. The goal is to knowwhat minerals cause cloggings, and which do not. The program approximates the underground as a 0-dimensional tank with inflow and outflow called a Continuously Stirred Tank Reactor (CSTR).We derive a set of differential equations for both the inflow and outflow and the chemical reactions that take place. The chemistry used in this model uses data from individual reactions, which gives us differential equations for the concentrations of the minerals. These chemical reactions are very dependent on the temperature in the tank. Because the inflow water may have a different temperature than the tank, we will alsomake a differential equation for the temperature. Using a fourth order Runge-Kutta scheme we can numerically integrate these equations in time. To test the program we use 6 of the most common dissolution reactions in ground water. When using the program we can see that some concentrations change a very insignificant amount and therefore do not contribute to the cloggings. These minerals were Mg 2+ from the dissolution of dolomite and Fe2+ from the dissolution of magnetite. The programworks as desired, but does lack some elements, first and foremost the reactions between acids and bases, such as HCO− 3 and H+.Applied Mathematics | Applied Physic