Development of a control optimization algorithm with uncertain parameter inversion for stochastic, nonlinear systems: A proof-of-concept applied to managed aquifer recharge and recovery

Aquifers around the world show troubling signs of irreversible depletion and seawater intrusion as climate change, population growth, and urbanization lead to reduced natural recharge rates and overuse. Scientists and engineers have begun to re-investigate the technology of managed aquifer recharge and recovery (MARR) as a means to increase the reliability of the diminishing and increasingly variable groundwater supply. Unfortunately, MARR systems remain wrought with operational challenges related to the quality and quantity of recharged and recovered water stemming from a lack of data-driven, real-time control.;From a control system perspective, MARR facilities represent a difficult class of problems because they are governed by a coupled set of nonlinear, partial differential equations (e.g., unsaturated and multiphase flow) whose parameters are often uncertain and possibly time-varying. To date, engineers have developed several stochastic simulation-based control optimization methods to control similar systems; however, these methods have only been implemented in hypothetical simulations, and they often required direct access to the complex set of governing equations.;This project seeks to develop and validate a more general simulation-based control optimization algorithm that can be used to ease the operational challenges of MARR facilities as a proof-of-concept. The algorithm was designed to treat the numeric model of the physical system as a black box so that various existing simulation packages for different physical systems could be used interchangeably. The SCOA-DUPI (Simulation-based Control O ptimization Algorithm with Dynamic Uncertain Parameter Inversion) compensates for uncertainty in the modeling parameters by continually collecting data from a sensor network embedded within the physical system. At regular intervals the data is fed into an inversion algorithm, which calibrates the uncertain parameters and generates the initial conditions of a predictive model. The specific SCOA-DUPI prototype for MARR applications improved upon uncertain estimates of the hydraulic conductivity field using observed hydraulic head data. The calibrated model is then passed to a genetic algorithm to execute simulations and determine the best course of action, e.g., the optimal pumping policy for current aquifer management goals. The optimal controls are then autonomously applied to the system, and after a set amount of time, the process repeats.;Experiments to calibrate and validate the SCOA-DUPI were conducted at the laboratory-scale in a small (18"H x 46"L) two-dimensional synthetic aquifer under both homogeneous and heterogeneous packing configurations. The synthetic aquifer used uniform, well characterized technical sands and the electrical conductivity signal of an inorganic conservative tracer as a surrogate measure for water quality. The synthetic aquifer was also outfitted with an array of various sensors and an autonomous pumping system.;The results from the initial experiments validated the feasibility of the design and suggested that our system can significantly improve the operation of MARR facilities. The dynamic parameter inversion reduced the average error between the simulated and observed pressures by 12.5% and 71.4% for the homogeneous and heterogeneous configurations, respectively. The control optimization algorithm ran smoothly and generated optimal control decisions 50% of the time. The non-optimal decisions were attributed to insurmountable discrepancies between the SCOA-DUPI model and the physical system. Overall, the results from the proof-of-concept demonstration suggest that with some improvements to the inversion and interpolation algorithms the SCOA-DUPI can successfully improve the operation of MARR facilities.