Libowski: A Numerical Framework for Solving Depletion and Mass Transport in Molten Salt Reactors

Molten salt reactors (MSRs) are a class of next-generation liquid fueled nuclear reactor which show great promise and industrial interest. With this type of reactor comes great difficulty in many modeling and simulation aspects which are required for design, operational efficiency and regulatory licensing. Solving the set of coupled depletion and mass transport equations required for modeling and simulations of these reactors is of great interest. This manuscript discusses the formulation of a numerical framework for solving the complex set of depletion and mass transport problems in MSRs. This is accomplished by first defining the set of equations that must be solved and then generating a framework to do so. The workhorse of this framework is the computation of the exponential of a matrix. Five different matrix exponential algorithms are presented, each showing great promise in solving the set of MSR depletion equations. Three of such methods are based on Cauchy's integral formula. Two are based on the Pad\'e approximation and one is based on a Taylor series expansion. A series of eight progression problems and five case studies are conducted to assess the accuracy and speed of the algorithms. Results indicate that all of the methods perform quite well. Cauchy solvers show high accuracy and low run times but must be coupled with sub-stepping to reduce the numerical error. The series solvers also show high accuracy but show poor scaling toward larger problems. For the MSR transport problems shown here, the Pad-method 1 solver showed the lowest overall run time along with the lowest over all error.