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

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 analysisis 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 respectto a reference pressure head (operating point) that is achieved by applying relatively simple boundarycontrols. Both deterministic plant configurations are compared in term of characteristic numbers thatevaluates the energy-efficient operation of the plant. In particular, those are the thermal ratio and thespecific flow rate, where gains of roughly 5.5% and 21.5% are obtained in favour of the brine recirculationplant. 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 thepaper, the effects of turbulence are incorporated through stochastic elements given as generalized andcylindrical 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 stochasticsystem. As both systems are actuated by the same type of boundary controls, the residual field is inter-preted as a measure of a regulation error. It is statistical characterization is done spatially by means of thefirst four statistical moments (sampled) and temporarily with the autocorrelation function. It is foundthat the applied boundary controls are robust enough to keep the regulation error within tight boundsthroughout the whole subdomain of the plant. Throughout the plant, the spatial standard deviation (std)is less than 0.3.