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Advection-Diffusion-Reaction (ADR) Partial Differential Equations (PDEs)appear in a wide spectrum of applications such as chemical reactors,concentration flows, and biological systems. A large number of theseapplications require the solution of ADR equations involving time-varyingcoefficients, where analytical solutions are usually intractable. Numericalsolutions on the other hand require fine discretization and are computationallyvery demanding. Consequently, the models are normally not suitable forreal-time monitoring and control purposes. In this contribution, a reducedorder modeling method for a general ADR system with time-varying coefficientsis proposed. Optimality of the reduced order model regarding the reductioninduced error is achieved by using an H2-norm reduction method. The efficacy ofthe method is demonstrated using two test cases. Namely, a case for an ADR witharbitrary dynamics varying coefficients and a second case including themodeling of an exemplary water quality distribution path with randomlygenerated demand. The reduced order models are evaluated against high fidelitysimulations using MATLAB's finite element method PDE toolbox. It is shown thatthe reduction can achieve a significant computational speedup allowing for theusage of the model for real-time applications with sampling times inmilliseconds range. Moreover, the constructed ROM is shown to achieve highprediction accuracy with the normalized mean square error below 2.3 % for areal-world water quality simulation test case.

Model Order Reduction of The Time-Dependent Advection-Diffusion-Reaction  Equation with Time-Varying Coefficients: Application to Real-Time Water  Quality Monitoring