Stochastic evolution of regulation errors in a boundary-actuated desalination plant

Abstract

A desalination plant – considered in two configurations (once-through and brine recirculation) – is modelled and controlled using a system of coupled PDEs that describe the desalination processes. The analysis is conducted in two separate parts. First, the operating point of the plant is obtained based on the deterministic process models of the plant. The steady-state distillate production is optimized with respect to a reference pressure head (operating point) that is achieved by applying relatively simple boundary controls. Both deterministic plant configurations are compared in term of characteristic numbers that evaluates the energy-efficient operation of the plant. In particular, those are the thermal ratio and the specific flow rate, where gains of roughly 5.5% and 21.5% are obtained in favour of the brine recirculation plant. The pressure head is subject to turbulence phenomena that disturb its surface so that a deterministic model is an insufficient representation of the real-case scenario. Concerning the second part of the paper, the effects of turbulence are incorporated through stochastic elements given as generalized and cylindrical Wiener processes located on the boundaries and throughout the plant (subdomain), respectively. The pressure head residual is defined as the difference between the deterministic and stochastic system. As both systems are actuated by the same type of boundary controls, the residual field is interpreted as a measure of a regulation error. It is statistical characterization is done spatially by means of the first four statistical moments (sampled) and temporarily with the autocorrelation function. It is found that the applied boundary controls are robust enough to keep the regulation error within tight bounds throughout the whole subdomain of the plant. Throughout the plant, the spatial standard deviation (std) is less than 0.3.