Data Driven Identification of Solute Transport Processes

Solute transport may consists of several processes, such as advection, dispersion, and reaction. Lots of work existed about the modeling of these processes. Different empirical models may be proposed for modeling a process by considering different conditions. For a site with solute transport, it may be not clear about which processes occurred (or dominated). And, which is the proper model for a specific process among the existing choices? Also, what are the values for the model parameters of the empirical model? In order to answer these questions, usually we may resort to lab experiments or numerical simulations, but these may be time consuming. On the other hand, if spatial and temporal measurements are available, data driven method may provide a different option for discovering the solute transport processes with high efficiency. In this work, we propose a data driven method that combines the sparse regression and data assimilation method for identification of solute transport processes. Using available data, sparse regression can identify the occurred (or dominated) processes and select the proper empirical models among the candidate choices. By introducing a prediction error of the identified model, data assimilation method is utilized to estimate the model parameter of the selected empirical model. In order to prove the concept, several case studies are implemented. We consider solute transport with advection, dispersion, and sorption. Two sorption models, Langmuir model and Freundlich model, are considered. The results show that the proposed method can efficiently identify the occurred (or dominated) processes. When sorption process is identified, the proper sorption model can be correctly selected and the model parameter can be well estimated. We further extend the method for data driven discovery of subsurface flow equations with uncertain model parameters, and satisfactory results are obtained.